Hi, this is George Cao, and I'm here walking my little dog buddy, and in this short video I want to talk with you about how we can more purposefully and productively relate to our time. And I've noticed that there are three conscious modes of living on a day-to-day basis. And by the way, I'm in such a beautiful park, so I'll just kind of pan around slowly as I talk through the three modes of conscious living. The first mode is flow. You may have heard of this idea of the flow state. The flow state is when you are feeling engaged in a productive activity, a productive or contributive activity. It usually involves the sense of almost losing track of time or losing yourself in the thing that you're doing. So you may achieve a flow state at work with some of your activities there, or even at home. So when you might be doing some of the chores that are important for you to do, and you feel productive and contributive, and you can be in a mindset of just noticing that activity and doing it as well as you can, and hopefully also bringing some gratitude that you can be doing that. So that's the flow state. And high performers, whether it's athletes or musicians or successful business people, they try to achieve the flow state as often as possible. And I invite you to consider what activities in your work and in your life help you get into that flow state, and to do more of that. So that's the first mode of conscious living. And I'm going to give you some tools towards the end of this video about how to actually apply this. So flow is the first state. The second state is recovery. And I should really say quality recovery activities.  Now, there are recovery activities that are not good for you, like maybe going out drinking with friends, maybe you overdo it, or maybe binging on Netflix and overdoing that. But so there are recovery or eating junk food, right? So the recovery activities are not good for you, but I really invite you to think about what are the quality recovery activities. So one example is when I come out and walk in nature and take my dog Buddy out, that's a quality recovery activity. Another quality recovery activity for me is, and this one is really short, is doing an energy reboot. I did a video specifically about how I do that, so I'll link to that in the notes of this video. Okay, now the third state, which is maybe the most important of all, is mindful transitions between flow and recovery, and recovery back to flow. Because if you don't, if you aren't aware of your transitions between those two states, it can get easily into doing unhealthy recovery activities, or from recovery you may stay too long there and given to inertia, and therefore you're not being conscious of the transition back to, and I was trying to show my dog Buddy running back, but anyway, not a great cameraman holding with one hand here. If you're not conscious between flow and recovery, you'll go into unhealthy recovery. If you're not conscious between the transition between recovery and flow, you'll tend to stay too long in recovery and waste time and let inertia stop you from getting back into flow in a timely way. So this is why mindful transitions is probably the most important, to be aware of when you're in a transition mode, going from, okay, I need to stop my flow right now because I've done enough, go into healthy recovery, and okay, I've been in recovery long enough, get back into healthy flow, okay? So let me give you two tools to end this video to help you do this and apply this knowledge. The first tool is to write down what are your activities in flow, what are your activities for healthy and high quality recovery, or self-care, some people call that, and third is what is a good or what are your best activities for mindful transitions? What are you going to do when you transition? So for example, I do my energy reboot. You might just simply close your eyes and take a few deep breaths and envision what's coming up next. What are, what, how are you going to do recovery or how are you going to go back and flow? So, so write down what are your activities for flow, for recovery, and for transition, okay? That's the first tool in the homework assignment that I want to give you. And feel free to comment below if you want to share some of those things that you've written down. The second tool I want to give you is time awareness. Time awareness is to be aware that you are what mode you're in basically. So there's two little tools you can use for time awareness. One is a timer and one is a stopwatch, okay? A timer counts down so you set a time for example 15 minutes. The next 15 minutes I'm going to be in recovery mode and I'm going to do this. And then when you do that, you're more conscious that, okay, I'm in recovery mode right now, I still have 10 minutes left, so I'm not going to overdo it.  And the second and same thing with flow, you could let's say set a timer for 25 minutes. So I'm going to go into flow in the next 25 minutes or try to work on this productive activity, okay? So the timer is counting down. A stopwatch is counting up and that helps you to kind of log your time. I use an app on the iPhone and it's also on the Android called a time logger. It helps me to log my time. What am I doing right now? I don't use it all year long, but I do use it several times a year for like a week or two at a time to recalibrate my time awareness. So I'm aware of what I'm doing. So for example, I have a time log running right now. I'm walking my dog and doing some thinking, okay? So that's my recovery mode right now. So I hope that this is helpful and I invite you any kind of comments or questions you have. I always welcome them. And until the next video, I wish you flow states, I wish you healthy recovery and mindful transitions.


Thank y'all so much, what an amazing turnout. This is what neighborhoods are about and I'm honored to be able to represent you all as the council six or district six council member. My name is Dr. Jared Williams and I'll just kind of give the welcome and kind of a rundown of what we're gonna do today and then I'll hand it off. So first of all, I like to thank, first of all, I like to thank the Westminster Presbyterian Church for their hospitality and opening their doors for us. So let's give the team here a warm hand clap for hosting us. So today it's no surprise we're here to give an update on egrets. Of course they are in their migratory season here in Fort Worth, they're nesting. And so our goal really is to bring a couple of our city departments, co-compliance and animal control for them to give an update about where we are in this season in terms of some of the activities that we're doing to respond to the real impacts that egrets nesting are having in our neighborhoods. And then once our city representatives give you an update on kind of what we're doing in this season, I'll come back up and I'll talk about what me and my office are doing to create a long-term plan to ensure that we're proactive with addressing egrets and it's gonna take all of us, all hands on deck with this plan. And so I'll give you an update on what we're proposing to my colleagues on council and working alongside our city departments like co-compliance and animal control to ensure that we're addressing this issue more proactively and thinking about the long-term future of the impacts that egrets have on our homes and most importantly on our pocketbooks and our budget. I know that egrets nesting generates unexpected bills for our families and it is my sincerest priority to ensure that our office does everything that we can to ensure long-term that we're reducing those impacts on you, your family and our neighbors. So without further ado, I'm gonna invite Barry Alexander. He's gonna give you all an update on what we're doing to address the immediate impact of egrets. And again, we'll come back and give more updates. I'm at the conclusion, we'll open the floor and my district director, Kendall Locke, will open the floor up to hear questions and me and the team will be able to fill your questions and also any issues that you're having. We'll be able to connect with you directly and make sure that we're helping you find the answers and solutions to your specific issues as well. So without any further ado, Barry, folks. Thank you, Barry. Good afternoon, everyone. Some of you I know, I've met in the fight with egrets and then some of you I've not, for those of you that have not met, I'm Barry Alexander. I'm one of the field supervisors under the Code Compliance Department in Animal Control. We got involved in this a few years ago with a fight with egrets because they got in and nested and we weren't aware of it and then we got notified. So we've been fighting these things and so we did some things in preparation for Candle Ridge because we knew they were coming back and we've all got very well schooled as some of the neighbors have in egrets. So we got, did some things. We got a permit to help us with the egrets and it wasn't what we'd hoped for, but it helped a lot and along with everybody in the Candle Ridge neighborhood we fought them and all respectively we won, but they got, the problem is once they nest, you run them off, they fly very fast and very low and they're really hard to keep up with. So if someone doesn't actually see them in their trees and it's too late, they build a nest and once they build that nest, we've still got a little leeway but once they lay those eggs, we're in trouble. Then it becomes an issue. So the permit kind of helps us through some of that and we're gonna definitely be applying that, applying for another permit and sending our report into the state and doing some things like that and then of course preparing and trying to get the word out what to look for. Over on Winchester, they're already nested, they've already got eggs and on top of that, now the birds are being kicked out of the nest so the fledglings are being kicked out of the nest.  That's their survival thing. They have three or four young, the nests aren't big enough for them so they end up kicking some of the babies out. So it's just a normal thing. So we're seeing birds on the ground, we're seeing baby birds down and we're also seeing young birds in feathers which we know now we've got a waiting period. So it gets really nasty, we're trying to do what we can but we're picking up the dead birds and we're picking up the injured ones and then we're thinking that unfortunately, the way they got nested in there is probably gonna be to the end of August before somewhere around there when they get, when they'll finally be old enough to fly off. So we're hoping it's earlier than that. But I don't suspect it will be. So. Oh, hello everyone. My name is Neil Johnson. I'm with Code Compliance also, but a different area. I'm with Code Compliance Solid Waste Division. I'm actually a superintendent over Solid Waste. I'm on a different end. First of all, I sympathize or empathize with you guys on what's going on. We're learning as we're going along as of the past year and trying to do our best to educate and make things a lot better in the future. So my job is to make things once the egress have nested to make things a little bit easier or bearable with street sweeping and also litter pickup throughout your neighborhoods. I don't know if you've seen the street sweepers come through on Winchester and even on the other end last year, they're coming through approximately three times a week and sweeping those effective areas along the curb side. So we try not to let the accumulation, you know, get too far before we get the street sweepers out to clean those areas. The one thing that I ask that you do, we try to stay away from Fridays, which is your, I think, your trash pickup days because obviously it impairs the street sweepers from actually having access to the curbs. So if you are in one of the impacted homes or please keep the curbs clear of any cars or, you know, whenever your trash pickup, you know, just bring it in immediately so the guys would have access to the curbs. So we work diligently with Barry and the crew with the pickup of the caucuses. So if you incline to put it to the curb and we'll pick it up. But we're trying to make things a lot bearable. This is my job to speak with the residents. If you do see them out there and if you have another area that you see as impacted or you feel like some other areas within your neighborhood is not being addressed with the street sweepers or cleaning, please contact us immediately. I think we have the, my fault worth that, that is set up in which you can actually report that. So please feel free to, you know, to report it if there's another area. If we don't report it, if you don't report it, we don't know. We, Barry and Chris have done a great job with the officers of, you know, going through the neighborhood and tracking everything and letting us know where we can kind of fit in and make things a lot bearable for you. So please, you know, just know that we're working hard to work with you and make sure that next year we don't have this problem again. So we appreciate your help and your patience. And again, feel free to let us know if there's anything else we can do to make things more bearable, okay? All right, thank you so much. Hello, my name is Chris Loret. I am the superintendent over Animal Control. I'm Barry's boss and I'm also the Animal Control officers that are out in the neighborhood every week, helping y'all with the egress and all that. I'm just gonna touch base on a little bit that you might wanna look at once we get the birds out, okay? Once the birds leave is whenever the hard work really starts, okay, it's the cleanup. That's when we need to get everything out of the trees, birds and nests, everything that they could come back and reuse, all right? Cause we don't want them back. We definitely don't want them to use what's left in the trees. There's limitations to what the city can do on private property, on getting these out, okay? We try to do the best we can from the road, what we can reach with, what tools we have, but as your property, you have to do it, unfortunately. That means getting arbiters. They go up there, it's money and it hurts, I know. Y'all gotta pay for that. But like I said, it's limitations of what we can do and what everybody, we got to get these nests out once the birds leave, once the birds are gone, there's preparations for next year, okay? Trimming trees, getting that already. My people getting stuff to help y'all next year when the birds start coming in. I brought flyers, all these flyers that I brought, there is stuff online for the city website. It's all on the egress. I have PowerPoints that I will be addressing, we'll look at doing another meeting before next year comes, probably about three or four, just to make sure we keep everybody updated. And when January comes, on the sheet it says February. It says February to March and I was addressed about that. So you wanna start looking out January, okay? February to March is what the state says, that's when they come in, okay? January, end of January is when we look at ground zero, okay? That's when they start flying in. You're looking for the night herrings. Night herrings, they're dark colored, they got the little yellow in the hair. Those are the first guys to come in.  You don't want them, okay?  That's the first bird that's there. They blend in to the tree that has the nice pretty cover, okay? And I was talking to one citizen coming in here, I'm driving down the road and Winchester was ground zero, okay? But there's a lot of ground zeros that I seen coming in here. That could have been that house, could have been that house. You don't wanna be that house, okay? So it's gonna take not just the neighborhood, okay? It takes the whole city. Me and Barry's been working on this since I started with the city back in 2008, okay? Since 2008, okay? Sorry. It's tough. Every year we see something different. We learn something different. I've talked to wildlife biologists. I almost feel like I have the degree now. I've been talking to them for so long. They've given me a lot of good information. I research it, I look at it, I try to pass that information on. I talk to our PIO who puts the information out. There's every year I change something, okay? I change something on our information that I put out because something new happened. COVID hit. That changed a lot. Because the birds just flew in, nobody knew. Everybody was in their house hiding from COVID and ground zero was candle ridge. John Stone, a couple other neighborhoods, about three or four blocks. We had one up north. Lady was in the hospital, didn't even know her house. You had about 50, 60 birds. This year they had about 130 that tried to come in. So the city, my employees that I work with, we were in two different areas. Not just one, and we was working around the clock, okay? So it's not like we're not doing anything. We're trying to do the best we can for all of y'all because we got the whole city to help, but we need your help too. So January to March, but it goes through all the way to September, October, okay? October is sometimes when they leave. I'm gonna be honest with you, Barry said late August. I mean, worst case scenario, it could be late September. But we gotta be vigilant, because I definitely do not want to have to deal with it in another neighborhood next year. So if you know people, pass it along, let them know what we're going through this year. John Stone, a lot of them told, they told the people last year, hey, look out, we had a lot of people running around with pots and pans, clapping them. That's what it takes if that's all you can do. We got incineraries that we bought the city. We have permits for that. So a lot of people can't use that. You gotta be careful, because I don't want y'all getting in trouble with PD and all that PD knows what we do. They know what we're doing all year. We're gonna get ready for next year. Once these birds get out, we'll be out every day doing what we do. And then next year, we'll be out again. Y'all gonna see us around all year round because we're not going nowhere. Hopefully the birds do though. I'll give you back to Mr. Williams. So before I talk about the council plan that we're working on, I just wanna give a huge shout out and thanks to Code Compliance, Animal Control, to 4th PD. They've been working around the clock, just really trying to make this situation as lighter of an impact on y'all as possible. I also wanna thank each of you for calling our office. You all help us to address issues, day-to-day issues that you experience every day. And so thank y'all for emailing us and calling us. I also wanna give a huge shout out to my district director, Mr. Kendall Locke. He's been filled in a lot of your calls while I'm working on the long-term plan from a policy perspective. He's coordinating with the department's day-to-day. So thank y'all, thank y'all, thank y'all. We'll share with y'all all of our contact information. Egrets is an important issue right now, but each of you will have additional issues coming up and just know that our office is open and it works for you all. And so please continue that. We really appreciate that. From my perspective as your representative on council, one of the things that I'm really focused on, and I work with Kendall a lot on this, is thinking about how do we address this issue, not just for the here and now, but how do we ensure that we're addressing migratory birds of all sorts, whether they're egrets or any other species? How do we ensure that we're working with our city departments to create a plan that we can continue to implement with fidelity long after I'm gone and long after the next representative is gone as well? And so what we've been working on is a three-step approach in partnership with the departments that I've named. The first piece is really about education. The plan that we're putting forward is really designed to get the word out faster and more efficient in ways that you all like to be communicated with, right? Like the website is an important first step, but we have to go deeper and deeper in neighborhoods with our education. And so the plan will authorize the city department to go above and beyond on an education basis. I think education piece is so important, especially in that late September to January period before the egrets are back for the next season. I guess it's important for all of us as residents to know how we all can do our part to ensure that we're deterring egrets from nesting during the season. I think that the second part is that deterrence piece. We need your help in deterring them, but also the city staff, once council authorizes the city staff to do more, we can come out and help deter. And so there will be a deterrence piece in this plan to make sure that egrets are not nesting in our neighborhoods. The third piece is a conservation perspective. With me having a doctorate in environmental science, I really understand how important conservation is. And right now with the egrets being federally protected, we really have to be a strategic with how we relocate birds to more suitable habitat. And so one of the things we're working with in partnership with a program that was relatively new in the city of Fort, the open space conservation program is a fund that allows us to find suitable open space areas and purchase that as conservation areas for long term. And so this plan will authorize the city staff to relocate birds that haven't laid eggs in their nest yet and relocate them to suitable habitats. If you've ever been to Fort Worth Nature Center, that's a classic example of what we're talking about when we talk about open space conservation areas. And I think that long term, that's a comprehensive plan that of course requires all of us doing our part, but that ultimately helps us to reduce the impact that egrets have. I'm also really sensitive to the financial impacts that this has on our neighborhoods. And so we'll also be having conversations about how to help address some of the impacts that are especially in our common areas, but even in our neighborhoods as well where law permits. So I just wanted to present that to you to let you know that that's the plan that I'm working with the departments. And after your questions and the stories that you all shared this evening, that'll help me go back and inform the work that we're planning with your experiences as well. So thank you in advance. We're gonna open up the floor for Q and A and I'm gonna ask my friends from the city of Fort to come stand up here with me. We'll have an extra microphone for you if you have questions or if you wanna share just a real quick sound bite of how you've been impacted by egrets. That way we'll make sure that we have as many perspectives as possible as we continue to advocate for y'all from a city council perspective. So with that being said, I'm gonna invite Kendall Lockup. He's gonna help me facilitate this and we'll bring around the mic to you if you have any questions about what you can do to prepare for the next season or if you wanna share some issues about how you've been impacted with egrets. I'll just say from a protocol perspective, if you can talk in sound bites, that'll be great because I know there's a lot of folks here and we wanna make sure that we have time for all those who are wanting to express a question or express how they've been impacted in particular so that we all have a chance to lift up our perspective. So thank y'all in advance and I'll come around with the mic for you, okay? Well, good evening everybody. Like council member Williams said, my name is Kendall Lock and I'm the district director for district six and I know I've talked with many of you guys already and had conversations come to some of you guys' houses. We've rolled around the neighborhood. But like council member Williams said, today is just literally having a conversation and listening from you guys about the egrets. We are in the process of scheduling a few additional meetings in September and in the following months to touch on a few other things that are important and that are happening across the city that's having an effect on us as neighbors. So we will get started with questions and just kind of raise your hand and council member Williams will. And so just raise your hand, council member Williams will bring over a mic. And so like I said, just questions that are about egrets in particular about preventative measures. Maybe you need to pick our brain about what's something that you can do, what kind of noise maker do you need to purchase, what kind of tree trim do you need to get, those different kind of questions. So we will get started. Yes, ma'am. I'm secretary of Wedgwood South neighborhood and two years ago we had an infestation of two or three houses and it was just awful. The stench a block away, I walk with the neighbor, we wouldn't even go near that street.  He installed bright lights, he installed scare eye balloons and he had sound that came on automatically. But what we did this past January, our neighborhood association was proactive. We mailed via postal service educational mailing with information about the scouts that come in February and pictures and what they could do to deter it and we included the Fort Worth website and we had signs posted, we had 20 signs placed strategically throughout our neighborhood at intersections where people would see it. We had an army of people who fought the egress and luckily they did not come in our neighborhood but we directly mailed, not emailed but via postal service every registered, every homeowner's address between Woodway and Kingswood and Alta Mesa and French Lake. So we educated first and we had good compliance. Thank you so much and for those of y'all who couldn't hear just to summarize that my friend and neighbors down in Wedgwood, they basically implemented a really robust education program from mailing information about what folks can do to prevent egress from roosting on their property to posting signs all across the neighborhood about how folks can prepare for the upcoming migratory season and they saw success there. So thank you for the work that y'all did in the neighborhood. I know that it required some elbow grease and I appreciate that and that's really, we wanna replicate that all across the city, right? Us as neighbors and neighborhoods have some best practices out there and from a council perspective, we're gonna be really focused on how do we do that type of education city-wide and how can the city help with some of that education and the costs with that, so thank you for that. And I'll also mention that we've been in contact, our council office has been in contact with the communications and public engagement department and in our conversations, literally within the past two weeks that has been something that the director of that department has brought up is piecing together some of those different programs such as mailers, the signs, of course still doing things digitally and we'll do a more robust digital program next year with videos and different things that'll be disseminated not only through the city channels but through the homeowners associations and neighborhood associations but printed material is definitely kinda at the forefront going into next year because we know a lot of people, I mean, if you're being honest, you don't have the time to check the website or you're not looking at the website or you're not on Facebook, so we're trying to meet you guys where you are and so that's definitely at the forefront and I've been getting that from a lot of you guys in our conversations and just email so we're keeping that definitely at the forefront. Next question. Here's my question. Because a lot of times people, they left our last meeting and everybody heard something different. What I wanna know is this. Have they quit nesting and are the brownbirds that we're seeing walking in yards that are egrets? I don't know if they have the yellow thing on their head or not and the brown ones are flying into neighbor's trees over there on court side. Are they still nesting or is nesting over? From all indications that we've seen thus far, they are not nesting anymore.  So as a result of them nesting where they did on Winchester, we were getting calls just like every day, multiple, multiple calls. I've got birds in my trees. So we would go out there and even we had help from Candle Ridge, Dibert Association going out there. Maxwell helped us and we would look every time because we were worried that maybe they were trying to nest and they were just late, late. But everything from up to this point we believe that they're completely nested where they're gonna be nested. So and as far as we know, the only place that they've nested is a couple of houses on Winchester. Thank you. Not a problem. Thank you again for that question and from a council perspective in the future with our plan, we wanna be able to track egrets as well, their migratory patterns here in the season so that we can start finding hotspots so that we can do preventative measures where we've seen egrets nest in the past. So we'll come, yes ma'am. And if there were eggs in there and you took them but the parents still stayed here, how did the parents know where you took them and they're still gonna build new nests? Because they're fairly protected, we're not allowed to touch the nest, both the city and also residents. We're not allowed to disturb the nest once there are eggs in the nest. So yeah, but. Let me touch, so okay. So in reference to some nests whenever we first started dealing with the nests and the egrets was coming in, I have a permit that would allow me to get into the nest, take the birds, the bird eggs and scare off the rest of them, okay. I also have, that permit also allows me to take a bird which is basically kill it, okay. So we didn't do any killing of any large egrets. We took the eggs, we destroyed the nests, and we scared off the birds to go fly somewhere else, okay. My director said do not take any birds because you can only take it with a shotgun. That's the permit. There's specifications and limitations on the permit, okay. We filled that permit up. My permit was done whenever they got to Winchester, okay. That's the permit that everybody is talking about. I, because I'm with the city, I submitted for the permit for the city, for all over the city. The airports also have a permit, but that's only for the airports. There's no, it's a limitation for how many you can take. The federal government gives you a limit on each breed. So I can only take that limit for that breed. How do we avoid the birds coming back? And I think you guys addressed that through, once you did the take of the nests and the eggs, there were a number of us that helped out and tried to make sure they did not come back to that area. And so both that tree behind the church as well as the one that was behind on the other side of the fence, I think that's how we've maintained or the city's maintained not having birds come back in those areas. I think the timing was unfortunate by the time the three weeks that it took to get them cleaned out, they had started migrating to other trees, Barry and the city ran out of permits. And so they were sort of at a loss with being able to do any more to help that part of the community. So that is correct. And that's why we said early on that it is very important in their next year's coming to make sure that you're vigilant for watching for the scout birds.  They're the ones that come in hundreds at a time. The gray herrings or donut scout birds, night herrings, they're different. There's a lot of different breeds, but they're the ones that they'll come in about two or three. You won't even know they're in the net, in your tree. They don't make a lot of noise. They fly at night a lot. They come in late in the evenings.  And once they get in, then you're in big trouble. I know houses in all the neighborhoods around here that have had a couple of night herrings in them. They've nested. And fortunately, they nested, they grew up and they left. And you didn't have a big impact of a lot of white eagles coming in. But then we have the total opposite of that effect. Where a couple of birds get in, the homeowner does not have any idea they were in there. And then all of a sudden they walk out one day and there's 50 birds. Then a week later, they walk out, there's 100 birds. So during this time, or last year in Cantaloupe Ridge, when we were fighting them, three officers from Animal Control picked up a little under, around a thousand birds. So you can imagine the scope of that. So that's what this is all about. And we believe they're nested. We don't believe they're nested anywhere else. We haven't had any reports.  And so we haven't had any other reports. We don't believe they're nested. We just need to be vigilant when these birds leave and getting the nest out of the trees. Next year, trimming the trees back. We're not saying you gotta cut your tree down. We're saying you need to have like 80% cover in there and get 20% of it out. Because, and these particular birds are attracted to post oak. That's just the tree they like. And there's a limitation too, when an arborist will wanna trim those trees because of disease. So be diligent about thinking about an arborist and get online, look at some different ones and study it and then get online and look at, there's a lot of information out there on egress that we're telling you tonight. But there's a lot still out there. Thank you for that, Barry. I think we had a few over here, Kendall and then Anita will come to you as well, okay. Hi, her and I were wondering, are the blue herons, are they protected as well as a species? Anything that's a migrating bird, blue herrings, snowy egress, night herrings, they're all protected. They're all migratory birds. There are ducks, they're migratory birds. There's a whole bunch of, there's probably about 30,000 birds that are protected and it's online. You can look at all, it's a long list. A lot of houses down from the bird tree, so the smell and seeing the poor little baby birds dead and dying is not my thing, but I'm wondering what is or up to the limit that we're allowed to, as they're trying to nest, what is our limitation as a homeowner to protect our house, our roof, our trees, besides just truing back the trees and scaring them off? What is our limitation? Cause y'all come out with the flashbangs. I don't think we can do that, can we? Well, Barry was out there. We did have PD come out there. We did have wildlife and fishery come out there. They didn't know we had a permit.  All right. Your limitation is basically as long as the birds are trying to nest. Just nesting, collecting.  If they're trying to make nests in your trees, get a stick, try to get up there and get the nest out. Don't let them do anything in your tree. Well, what I'm wondering is between the time that I realized animal control actually let me know that I had a blue herring in my tree, then like literally a week or two later, a hundred of the friends of the white herrings came and all of a sudden the blue herrings were, I mean the blue egrets, the blue birds were gone and all the white birds were in. Yeah, the white birds scared out the blue. The blue, the white, they're all noisy, they're all nasty. Do we have any kind of idea if they're gonna get rid of this federal protection? Cause it sure doesn't seem like they need too much protecting. So the migratory bird tree act of 18, 1918, 1918. I'm thinking it's a little outdated. 1918, yeah. Well, it's between like 36 countries and they have tried to get 36 countries together to do something with it. They've been trying to do that for years, so. Well, they haven't had them live in their tree, so.  They got $40,000 worth of fines. Oh, okay. That's why I'm asking, like, what is our limitation as a homeowner besides seeing them do the sticks and running them off, at what point do you realize that they're there and they've nested and they have eggs, sometimes you just don't know. They blend into the sky and the leaves, you can't see them. I get that, you know, I drive down through neighborhoods and I catch myself looking up and I don't wanna run into nobody. So it's tough, it is very tough. Me and Barry, we run all over the place. Right. Barry doesn't have great eyes, my eyes are not great either. We miss things, but if you get a neighborhood together or a city together, you'll be surprised whatever everybody can do. Right, right. So it's just being vigilant, talk to your neighbor, let them know, let us know, we'll come out with the vangers in there, okay, now another part of the question is, what do we do once they're gone? Because I have a neighbor where his one tree is affected next to the one that looks like a big cotton ball exploded. So once those birds are gone, you say it's up to the person that owns a house or whatever, I mean, are we gonna get any kind of help money-wise in combination of what we do to clean it up? So a great question from my perspective on the council, that's why I'm working so hard on this plan. I mean, is there gonna be some joint thing where the homeowners and y'all can kind of where we can pull money together to help those who can't clean it up? So that is well received and we will bring that in discussions in the plans. Thank you for that. I know that the financial impact is huge. That's why this plan is so important. That's why the education piece, where if we're all aware and the city's leveraging the resources that we have to make sure that we get the word out to residents, we can all be looking so that it's not a one neighbor, to have to spot that burden. So this plan is gonna be comprehensive. That has come up in our conversations and I wanna keep continuing to bring that up as well to see what type of fun we can create long term. So for those of y'all didn't hear, she asked, will there be a fund for the end of this season? I'm currently, there are not funds available for this, which as a representative, that's something that I'm very sensitive to. I'm in the term of how do we really address this systemically? I know that some of the work that we do from a policy perspective doesn't happen like tomorrow, but I wanna make sure that we're addressing this like once and for all. So we're not gonna be forgotten in the loop anywhere. No, you won't be forgotten. Yes, sir. Thank you for that. So we'll have a time, I wanna honor the time in the church. They have us here from six to seven. So we'll take about two to three more questions and Kendall will come around before round enough. Also at the end of this event, if y'all like to continue the conversation with us, and we'll hang around for maybe five to 10 extra minutes, we can share with you our contact information if you'd also like to call our office. That way we're making sure we're getting all of your feedback and perspective, okay? Okay, my question was going to be about the law that was passed where it's made these little darlings to where you can't do anything to them. Well, you're saying that there's other countries that have signed a treaty, an agreement, whatever it might be. Why can we not pull out of that agreement? So the question was in regards to the federal treaty and whether or not we could pull out of that, that is definitely a congressional conversation and the discussion that the Congress would have to act on. We have congressional representatives that we also wanna build a working relationship with as well, but that's definitely gonna be an act of Congress to amend that treaty or to make other provisions that allow cities to address migratory birds in a different way. So we need to get after Congress is what you're saying. Everybody hear that, Congress? Okay, thank you. Thank you. Can't you guys like use hawks, owls? You know, where I live, we have a hawk. We have actually two or three of them. They fly around between about two or three houses. I live on Winchester. Okay, so even in Candle Ridge, there is a lot of hawks flying around and if they go to a nest and take a bird or if they knock one out, that's totally legal. I mean, that's nature. But as a protected bird, we can't use hawks or anything now. As I said before, we had a permit and we got that permit. This was the first year. But it's natural if a hawk attacks another bird, isn't it? Exactly, but that's what I'm saying. So they can do that. But we can't physically set that up. It would be just like us being able to shoot them with a 12 gauge, but here's the good news. Here's what we're trying to do. So Chris spent a lot of time doing the paperwork. With the fishing game, we contacted them. We talked to them and we have established kind of hopefully a working relationship with them. So all over the United States, they deal with this as well. So we're hoping all the birds and the eggs that we removed this year with our permit, we have to keep track of that. Then we have to submit that to the state or to the federal government and we're hoping next year we get a better permit. We get more. We get the ability to deal with them more strongly. Now, this year we took hundreds of eggs to steal. So like Chris said, we didn't kill any bird and we took them to a rehabber. So we're proud of that fact, but we're hoping that we have a better permit. We have better communication. We're working even on trying to get a drone that is infrared, state-of-the-art, so that when we do have to run these eggs off, we can track them better, we can see them better, where they go, we can push them out. Because once we get them nested somewhere else, if they're out in the country, then they're not an issue. And they'll come back there every year. All right, well, what about using speakers to make loud noises, you know, put a speaker in there, it could play on a loop, find some fake hawks, some fake owls. But fake hawks, fake owls will work. That costs money, but it's cheaper to have, and you guys come by every so often. That works, and people were putting balloons up with faces on them, in the trees, they were doing, and a lot of it was helping and working. What we worry about at Code, and with the police department is that you can go online and you can get fireworks, you can get all kinds of stuff. People were firing fireworks and stuff at birds that were just flying over. So if you get an entire neighborhood, riled up and they're firing just every time they see a bird, we had people firing at ducks.  We found that out firsthand in Galleridge. So what we ask you to do is use pots and pans, and it works, and use boards, and it works. Well what's gonna end up happening is somebody's gonna fall out the tree and get hurt really bad. Well they don't, you don't have to climb in the tree. Yeah, I mean, yeah, you don't need to climb your trees. Yeah, don't get in your trees. Have an arborist train professionals do that. So, because you're right, you will fall out. So, but anyway, I want to touch base on that because I didn't want people getting all worked up, and then, because there's a city ordinance, if you're firing, we had people that we pretty sure were firing guns at them. First of all, they're federally protected. Second of all, you're committing a crime, and it was just not good for anybody. It is not good for the neighborhood. So, that's it. Thank you for that, Barry. Kendall, if we can go over to Anita for the last question, and remember we're short on time, but please come talk to us after the event, and we'll make sure that we engage in that conversation after, so we'll still hang around. Thank you. My question was about the permitting, and are we guaranteed to get it next year, this year? That's what concerns me. The number of birds and eggs. Peggy is here. She had, I don't know how many birds in her trees, but what if we use up a permit and there's still nests there? How does all that work? I'm concerned about going forward how we can be guaranteed of getting that permit and removing everything that needs to be removed if other areas in the city also have egrets. Okay, so no, the permit is not guaranteed, right? That's why I had to build a relationship with the federal government, along with several wildlife biologists to get them to help me fill out part of the permits because I have to get paperwork from the USDA, wildlife people, also wildlife and fishery, and me filling out several forms and giving them a guideline of what they're expecting me to do before I even take anything. So it's a long process. I submitted it probably in November, and I finally got it like April 1st. So the birds were already coming to us. So it's, there's no guarantees anything with wildlife. I'm gonna be honest with you, it's tough, but I think I worked out a good relationship with them and I filled out the forms correctly, thank God. Yeah, so, and they gave it to us. The only thing is, is they do, they have to look at the impact on everything.  I had to show them the whole lay of the land, saving as many birds, even though I did take eggs and all that and break nests and all, I was still bringing the eggs to a wildlife rehabber that is licensed with the federal birds. So with all of that, we have guidelines and limitations, even with that, but nothing is guaranteed. And I'm hoping that I know the whole process now. So it should be a little bit easier. And I've made that relationship with the USDA and Wildlife and Fishery, which I've been knowing them for 14 years. So it should be a good relationship. So, but yeah. And I just wanna say, you know, special thanks again to our team and specifically to you, Chris. I know it's not easy to get federal permits and from, you know, a council representative, we wanna work with y'all moving forward. For those of y'all don't know, we have a lobby team that has a federal program each year. We go to Washington DC with a list of agenda items that are important to us and we talk to our, not only our Tarrant County delegation, we talk with representatives from all over the country on issues that are important to us. And this will be something that I'm presenting to our lobby team because part of this, part of our issue is with working with our federal, you know, representatives and with our departments to make sure that we're working together to really address this issue in a way that's meaningful to you all as neighbors and also that puts forth some best practices and conservation. So like Chris said, we are conserving as many of these e-grids as possible and moving them to, you know, more a suitable habitat. So with that being said, thank you all for engaging in tonight's conversation. Thank you for, you know, your feedback. I know this is, you know, a really tough issue that's impacting all of us in many different ways. And as your representative, I know that I'm deeply, you know, concerned and also, you know, my sleeves stay rolled up constantly because, you know, I'm really willing to work on all of the issues that are important to our district. And so just know that this issue is a priority for our office. Please, please, please continue to engage with us. If you all see new issues that come up, feel free to reach out to our office. We'll be passing out our cards with all of our information for our folks watching. You can find our information online on the District 6 webpage that has our office phone number and our emails. Please feel free to contact us with the issues that you're facing with e-grids and other issues that you face from day to day. Like I said, our team will be hanging out for about five to 10 minutes to exchange contact information and to hear a little bit about how each of you have been impacted by e-grids during this migratory season. So thank you all again. Again, thank you to our friends at the Westminster Presbyterian Church. We really, really appreciate you all opening up your space for us. And we look forward to doing many more of these listening circles on a number of topics. In fact, Kendall's gonna talk to you about some of the exciting events we have from our council office, including a back to school backpack giveaway event that's gonna happen right down the street at Trademark Church. So, Kendall, if you would give them a rundown of upcoming events. So yeah, so we have a back to school event that is coming up on August the 7th. That's the first Saturday in August at Trademark Church. And so that will be from 11 a.m. to 1 p.m. We're giving upwards of 500 backpacks with school supplies geared towards middle school students. So if you know anyone, if you have, you know, those individuals in your home or in your families, definitely invite them to come out. It's a drop through event, so they just pull up. We give them the backpack and then they continue on with their day. So that's one event that we have coming up on September the 2nd, Thursday, September the 2nd at six o'clock we have an event where we'll take a deeper dive into bond projects for the district. So bond projects looking at some things and budget priorities across the district and getting some feedback from you guys. Looking at redistricting. Of course, we're redrawing a few maps or all of the council maps and adding two additional seats. So we'll be touching on redistricting. Also touching on the my for worth app and things that are available to you through that app. In addition to that, we are currently planning two other town halls that will come at letter days. One that will be geared towards the new my H2O program that's through the water department. So of course, many of you guys probably know there has been new meters that has been installed. So we'll be touching base about that and talking to you guys about some exciting things on how you can actually view the breakdown of your water bill, view your water usage and just all of the great things with that department. And then also to a town hall that's gonna be geared towards just traffic, infrastructure, speeding, things as stop signs. We've been working hard with transportation and public works and have some great things that are coming to the district as far as new stop signs, new signals and just things that's all about traffic infrastructure.  Of course, everything will be disseminated through all of the city channels, our channels. You can always reach out to the office. I'll give you guys our office number if you wanna write it down. And of course I have cards that you can get as well. But it's<PHONE_NUMBER>. And so that's the office number. You can feel free to reach me if you text, if you call on my cell, it's<PHONE_NUMBER>.<PHONE_NUMBER>. And like Council Member Williams said, our office is open, feel free to call, email. And we're here for you guys. So thank you for being here.


when it comes to integration the religion of Islam encourages it as long as any other identity whether it's american arab any other form does not clash with the principles and the values of these three things servitude submission and as long as these are kept as the governing identity islam says you can integrate indeed what islam encourages is what it mandates exemplary citizenship the quran states that by wearing this identity with pride and honor you are able to come forward wherever living in the world and present a good picture of the religion and yourself you can be indeed a beacon of light an example for people to look at when it comes to the principles that human beings all share peace coexistence love tolerance islam says when you adopt this particular identity you are able to indeed move forward in your journey present yourself in the best possible way yet at the same time it discourages this at the idea of assimilation meaning what there is a difference between integration and assimilation we should not sacrifice our own values in order to reach the satisfaction of others what do you mean i come to the mosque i come to the jamia to the center i am a muslim i am praying i'd say salam to others a sister wears hijab i go to school i go to my office the i muslim identity unfortunately sometimes is left is left at home is left at the jamia so for instance sisters may take their hijab lightly brothers when it comes to come in speaking to others they're afraid of expressing their islamic ness their islamic background their muslim identity and we see this present in many shapes or forms yet today we are told there are some inspirational stories out there which highlight to us how we should be proud of our identity and Allah would bless us and would give us strength and success if we stand there and wear the badge of the religion of islam with pride and honor how you've heard of the story of the lady by the name of naima in belgium 2005 she wears hijab and she works in a factory packaging food what happened was that the manager of the factory in belgium in europe receives a letter the letter says that we will attack this particular factory and later on the letter اگر برج لیسم ہے اگر you do not stop employing ladies wearing hijab then your death is soon he was threatened with death this lady hears about it she's struggling with the notion what does she do does she come and say to her manager you know what i'm gonna take my hijab off for you it's okay you know i have to fit in no she doesn't She stands by her principles. اللہ سبحانہ وتعالیٰ says من کانا مع اللہ کان اللہ معا If you support the cause of Allah, Allah will be with you. It might be an examination. It might be a difficult position that you may go through. But rest assured you will attain success at the end. Look at this story as an example. Her boss says to her don't worry. She says what do you mean? Her boss says to her keep wearing the hijab. Notice that sometimes non-muslims adhere to these principles. She keeps wearing the hijab. He collects 20,000 signatures from the city itself and from the company to demonstrate what support for this lady when it comes to wearing the hijab and to stand against the extremists who are threatening this particular institution. Later on the king because this particular new episode gets publicity. The king of Belgium is traveling in the area. Here's about this visits the same factory and stands next to this نعیمہ and the boss and addresses the people of Belgium and says we are against discrimination. People are free to wear this particular dress code and to express their religion. Can you imagine that اللہ تبارک وتعالیٰ indeed احدی برائی پاسیک والا لیٰ آرین باہت اٹھا سکتا ہے. پہنچ مطالوعا ہی دبارتی ہوتا ہے اور یہ بورت ہے کہ کبھی آپ و میں لگتا ہے۔ ایک ع حافت ہی وقت کے عاربت پیٹکیلہ کند ، بہت ہی جب لگتا ہے کہ ہم کونا کو سلالا ваш جب جب صلاح پر فرمی پر بھی تے جب ایشان بھی رہ رہتا ہے۔ ایک مدن دی۔ اسے موجودہ شک خوالی ہیں۔ہاں گئی کہ ان میں صلاح پر پرمی کرو گیا۔ انہوں نے کہتا ہے کہ آپ یہاں نہیں should not do so here i don't like religious expressions in the office you must do it outside he said i can't do it outside the weather doesn't help i don't there's no mosque or place of worship close by he said take it or leave it you are not allowed to perform any religious form or worship here in the office what did this man do he said thank you very much i resign he said what you will resign he said yes my religion is important to me if you do not allow me to practice it then i cannot work here anymore he himself tells me what did he say he said i placed my resignation on friday he said the manager said fine you can go he says wallahi by monday i received an offer from a company and the salary was much much bigger and the job was much better these are demonstrations and examples that we are presented with when it comes to feeling a sense of pride and at the same time confidence in our belief in our muslim identity in coming forward with this notion because sometimes we assess ourselves with regards to where we come from with regards to our families there is no problem when it comes to cultural tendencies sometimes culture has a lot of value has a lot of meaning islam is not against culture many of us should adhere to the culture provided it doesn't clash with the islamic principles


Hello, welcome back. In today's class, we will be looking at hypothesis testing in linear regression. So, what is the motivation for doing this test? When we develop a linear regression model, we want to see which of the variables we had taken or considered in the experiment are really important. At the beginning, when we are not having prior knowledge or experience, we really do not know which variables are important, which variables are not important. So, we would like to include as many variables as possible in our experimental program and we perform the experiment and we get the data. Now, we want to analyze the data and identify which of the variables are really significant and influence the experiment strongly. So, how do we go about it? That is what we are going to see in today's lecture. So, as a slide indicates, the test is meant to check whether there is a linear relationship between the response y and the subset of the regressor variables x1, x2 so on to xk. So, these regressor variables are actually the variables we are investigating in the experiment. So, we carry out the hypothesis testing in multiple linear regression. Our null hypothesis is beta 1 equals beta 2 so on to beta k is equal to 0 and make a small correction here. So, we have beta 1 equals beta 2 so on to beta k is equal to 0 that is a null hypothesis. So, what it really means is that none of the regression coefficients are having numbers that are significantly different from 0. Look, the beta 1, beta 2 so on to beta k may take either negative values or positive values. If they take positive values, it means that they are positively affecting the response. For example, the yield of a chemical reaction may increase with increasing temperature. On the other hand, if you have a negative value for beta j, then it means that when the variable increases, it actually has a negative effect on the response. For example, when pressure increases, the volume may decrease. So, it depends upon the experiment we are looking at. When the beta j that is one of the regression coefficients becomes 0, then beta j x j will be 0. This means that whatever may be the value taken by x j, the effect of that particular variable on the experiment is insignificant. So, this is what we are trying to test. The null hypothesis says that all the regression coefficients are 0. That means none of the variables are really affecting the process. This is the most skeptical point of view a person may take at the beginning of the experiment. But as experimenters, we should be really skeptical and not have some preconceived notions. See, the alternate hypothesis says that beta j is not equal to 0 for at least 1 j. This means that among all the regression coefficients, at least one of them is non-zero. In other words, there is at least one variable in the experiment which is actually affecting the process response. So, when we accept the null hypothesis, we agree that none of the regression coefficients are taking a value other than 0. So, we say that H0, the null hypothesis is beta 1 equals beta 2 so on to beta k is equal to 0. If we agree with this, then none of the variables are really affecting the response. The alternate hypothesis is for at least 1 j beta 1 or beta 2 or so on to beta k, at least one of them is non-zero. It may be negative or it may be positive. So, the rejection of H0 implies that at least one of the regressor variables x1, x2 so on to xk contributes significantly to the linear regression model. So, here we are having k variables, k independent variables x1, x2 so on to xk and these are the regression coefficients which are attached to these regressor variables. And when let us say that beta j takes a value 0, beta j xj will be equal to 0 and there would not be any effect of that particular regressor variable xj on the process response. So, how to carry out this hypothesis testing? So, we have the experimental data with us and we first find the total sum of squares and then we split it into regression sum of squares and residual sum of squares. So, I have indicated this briefly here, sum of squares total equals sum of squares regression plus sum of squares residual. So, whenever we compute the squares, we also have to find the degrees of freedom. Whenever we want to compute the variance not only we find the deviation from the mean but we also divided by n-1 where n is the total number of observations. So, the sum of squares is actually divided by a certain value which is related to the data size. In our present analysis also whenever we are considering linear regression, we have the total sum of squares and we have to scale it by the appropriate or associated degrees of freedom. So, the total sum of squares has n-1 degrees of freedom where n is the total number of observations. The sum of squares of regression has k degrees of freedom where k is related to the total number of regression coefficients in the following manner. So, we have p equals k plus 1. I think we have already come across this earlier to re-itrate p is the total number of parameters and that includes the parameter beta not the so called intercept of the regression model. The residual sum of squares will then have n-p degrees of freedom where n is the total number of responses. So, now we can go to the analysis of variance table. We have in the ANOVA table the usual entities, the source of variation, the sum of squares associated with the source of variation, the degrees of freedom and we divide the sum of squares with the associated degrees of freedom to get the mean square. So, k is equal to p-1 that means the total number of parameters minus 1. Here we are not considering the intercept, we are only considering the regression coefficients beta 1, beta 2 so on to beta k. And when we divide the sum of squares of regression with the k degrees of freedom, we get the mean square regression. And then we also have the residual sum of squares. This is a very important aspect in regression analysis because only by looking at the residuals and the pattern of the residuals, we can really judge about the quality of the fit. So, we have the residual sum of squares as sum of squares of E. Again instead of rather writing residuals, I have used the subscript E. Residuals may also be associated with the error because it is the difference between the experimental value and the model prediction. So the residual is defined as the difference between the experimental value and the model prediction and so we have the error with respect to the model prediction and the sum of squares associated with the residuals is given by SSE. And the degrees of freedom associated with that is n-p. So the mean square would be sum of squares of the residuals divided by n-p that will give you mean square residuals. So we take the ratio of mean square regression to the mean square residual to get the f0 value. So we also have the total sum of squares SST which is having n-1 degrees of freedom.  So n-p plus p-1 will give us n-1 degrees of freedom. So when you add up these two, you get the total degrees of freedom as n-1. So that is what this slide also tells. Repeating n is the total number of observations and p is the total number of parameters including the intercept parameter beta0 and so we have k is equal to n-1-n-p and we get k is equal to p-1. What I am doing is we saw that k and n-p add up to give n-1. This is telling the same thing in a different way. We just subtract n-p from n-1 and we get p-1, k is equal to p-1. So we can take whatever root we want. The regression mean square scaled by error variance sigma squared follows a chi square distribution with k degrees of freedom. We have to make proper judgment regarding the observed mean squares. So we have mean square regression, we have mean square error or mean square residuals. So the ratio of the two we consider and we have to test it against a suitable distribution. What is that suitable distribution? We also know that the mean square regression and the mean square residual are independent and we divide both of them by sigma squared and we then have the mean square regression divided by sigma squared to form the chi square distribution with k degrees of freedom. So when we divide msr by sigma squared it leads to a chi square distribution with k degrees of freedom and when you divide msr by sigma squared you have to divide msc also by sigma squared and you get another chi square distribution with n-p degrees of freedom and the ratio of the two chi square distributions is the f distribution. So the regression and residual mean squares are independent and the ratio follows an f distribution with k numerator and n-p denominator degrees of freedom. So you can see that we have f0 here and that is sum of squares of regression divided by k and this is the sum of squares of the residuals or the sum of square of the error divided by n-p. The k degrees of freedom are in the numerator and n-p degrees of freedom are in the denominator. What I am trying to say here is the k degrees of freedom are associated with the sum of squares in the numerator and the n-p degrees of freedom are associated with the sum of squares of the residuals which is in the denominator. So we have f0 is equal to mean square regression by mean square error. The sigma squared actually cancels out. So we can simply take f0 as msr by mse and we do the usual f test. By now you should be familiar with the implementation of the f test. We have also done some practice problems or example sets earlier. So I request you to go through those problems and refresh your memory. So we also know that we reject the null hypothesis H0 if the test statistic computed above is greater than f alpha kn-p. Alpha is the significance level usually taken as 0.05. So if it lies in the critical region or in the rejection region then we reject the null hypothesis. So continuing with our discussion on the resolution of the total sum of squares, the total sum of squares is given by sigma i is equal to 1 to n yi-y bar whole squared where yi is the actual ith experimental data recorded by the experimenter and y bar is the average of all the n experimental observations. So you have this relationship given here. This may be expanded and simplified. The derivation is fairly straightforward and you get sigma i equals 1 to n yi squared-sigma i equals 1 to n yi whole squared divided by n. This indicates the sum of the square of all the responses and this is the sum of the observations is squared. So please do not confuse this with this term. Here the individual observation is squared. Similarly all the other observations are also squared. Then the sum is taken. Here first the sum is taken and then it is squared. So this may be represented by y prime y. Sigma i equals 1 to n yi squared is nothing but y prime y. So you have the column vector of the responses and a transpose is taken for the column vector and then it is multiplied with the actual response column vector and when you do that you will get the sum of the square of all the observations. And then you also have the sum of the observations squared divided by n. Here n is the total number of responses. So this is the total sum of squares and as you can see we are gradually moving on to the representation of the various sum of squares using matrix notation. The matrix method is quite convenient and it helps us to do the calculations which are otherwise tedious in a very efficient manner. So we have the sum of squares of the residuals as y prime y minus beta hat prime x prime y. So the sum of squares of the residuals may be written as y prime y minus sigma equals 1 to n yi whole squared by n minus beta hat prime x prime y minus sigma equals 1 to n yi whole squared divided by n. What I am doing here is I am subtracting and adding this term sigma equals 1 to n yi whole squared by n and that leads to by definition the sum of squares of the total here and we also have this term as the sum of squares of regression. We started off by saying that sum of squares total is equal to sum of squares regression plus sum of squares residual. So we have the expression for the sum of squares of the residuals and we also have the expression for the sum of squares total and so when we subtract the sum of squares of the residuals from the total sum of squares we get the regression sum of squares. So this blue term here represents the sum of squares of regression. So when you have the regression linear regression parameters estimated and you have the x matrix and you have the y column vector you can get the regression sum of squares by considering beta hat prime x prime y minus sigma equals 1 to n yi whole squared by n. Beta hat is nothing but the vector of the estimated regression parameters including the intercept beta hat naught and then x is the matrix x matrix so x prime would be the transpose of the x matrix. We have already seen how to set up the x matrix in one of the earlier lectures and then y is the vector of observations. So we have sum of squares of residual sum of squares of total minus sum of squares of regression and we have the sum of squares of error given by this relation and then the sum of squares of regression is given by this relation. So now coming back to the hypothesis tests on individual regression coefficients okay. So we have to see whether a particular regression coefficient beta j is actually taking up a particular value beta j naught or it is not taking that particular value. So now we are concentrating on the individual regression coefficients and whether they take up a value or not okay. So you can put 0 here and see that that pretty much the regression coefficient is insignificant and does not affect the model or it does not affect the response in fact. And then the alternate hypothesis is the value is not equal to 0 but it may be less than 0 or greater than 0. So to be more general instead of fixing the value to be 0 all the time instead of fixing beta j naught to be 0 all the time we can fix it to some other value 100 for example. So it need not be always 0. You can also hypothesize on a particular value taken by the regression parameter. Instead of looking at the whole bunch of regression parameters now we are concentrating on a single regression parameter. It may be a good idea for you to not proceed with the lecture as of now just pause a bit and then think yourself how you will carry out the test okay for this particular case. We have already come across this earlier and I would like you to think about it and then write down on a notebook you must be carrying with you as to how you would proceed. So I hope you have at least made an attempt and let us see how to do it. So we have the tests on individual regression coefficients. So the H naught is beta j is equal to beta j naught and H 1 is beta j is not equal to beta j naught. And then as you can see here we carry out a t test okay. So you must recollect the t test now if you are unable to remember I request you to just go back and refresh your memory. So t naught is equal to beta j hat minus beta j naught by square root of sigma squared cjj that is beta j hat minus beta j naught by standard error of beta hat j. Now we know that the t test is associated with a certain degrees of freedom and what degrees of freedom we should use in the t test. Very interesting result is use the degrees of freedom which you had used for the residual sum of squares in the t test also. And you should also by now be familiar with what is meant by the standard error of beta j hat and you should recollect that it is sigma squared cjj where cjj is the diagonal jjth element of the variance covariance matrix and sigma squared is the error variance. Unfortunately we do not know the error variance the true value of the error variance. So what we do is we use the standard error instead. So as I said earlier just now cjj is the diagonal element of the variance covariance matrix and the variance covariance matrix is given by x prime x inverse corresponding to beta hat j. Now let us see the regression sum of squares due to the intercept beta hat naught. This is a very interesting thing and in some places it may be skipped and that may lead to some loss of clarity in understanding the concept of linear regression. In some ANOVA tables you would find the sum of squares corrected for beta hat naught or in some tables of ANOVA you will find uncorrected total sum of squares. So what is really the correction all about? So it depends on whether we consider the intercept or not. So we know the total sum of squares is y prime y minus sigma is equal to 1 to n yi whole squared by n. The actual total sum of squares based on the responses is y prime y. You simply square each response and then total it up and that gives you the actual total sum of squares. So you are deducting some portion from the actual total sum of squares that is you are deducting i is equal to 1 to n sigma yi whole squared by n okay. So this is the correction you are doing to the total sum of squares and the regression sum of squares does not include the intercept beta hat naught contribution and has contributions only from beta hat 1, beta hat 2, beta hat 3 so on to beta hat k. So that is the reason why since you are having these 1 to k which is k independent regression parameters you have k degrees of freedom. So what actually happens is the contribution to the sum of squares due to beta hat naught is sigma is equal to 1 to n yi whole squared by n okay. So we are removing the contribution to the total sum of squares that is y prime y with the subtraction by n y bar squared okay. Sigma is equal to 1 to n yi whole squared by n is n y bar squared and what we are doing is we are subtracting from the total sum of squares n y bar squared. We call that as the contribution by the intercept parameter beta hat naught okay. Why should it be n y bar squared okay. This is a very simple explanation to this it is quite nice actually. So when you consider no other parameter except beta hat naught okay in your regression model then the regression parameter beta hat naught would be simply the average of the experimental data points okay. What does it mean? Suppose we are very lazy to fit a regression model considering the variables. We say that y predicted is equal to beta hat naught only okay. So then what will happen is if we carry out the regression analysis we will find that the estimated beta naught parameter would be only y bar okay. The average of all the responses. So when you have scattered data then let us say that we are having only one regressor variable x1. So we are having y1 as a function of x1 and when you plot the data on the graph sheet you will find that you will have scattered data and when you are fitting only a simple model then the model will be nothing but y hat is equal to y bar where y bar is the average of the responses and you will have one horizontal line passing through the data points. Let me illustrate this on the board. So what we have here is the experimental data we are plotting y as a function of x1. Obviously there is a effect of x1 on the response that is why you are finding that when x1 increases the data also increases. But if we take up a regression model saying that y hat is equal to beta naught okay this is our very simple regression model then all we are doing is fitting a straight line which is nothing but the average of all the responses and so we get a horizontal or a straight line parallel to the x axis and that straight line is nothing but the average value y bar. So since beta hat naught is equal to y bar the sum of squares contribution from beta hat naught will be y bar squared plus y bar squared for the n experimental data points and you will get n y bar squared. So this is the contribution to the sum of squares by the parameter beta hat naught. So if you want to correct your sum of squares and the regression sum of squares with the contribution from beta hat naught then you subtract it with n y bar squared and that is what we are doing. Now it is go back to the resolution of the residual sum of squares and even before that we looked at the resolution of total sum of squares you can see that the sum of squares of total we have subtracted the contribution by the parameter beta hat naught and that is y prime y minus n y bar squared. So the n y bar squared represents the contribution from the intercept beta hat naught. So when you are subtracting n y bar squared from the total sum of squares you should also subtract n y bar squared on the other side of the equality so that you maintain the balance okay. So we see that this is the total sum of squares and this is the regression sum of squares y prime y is the actual total sum of squares beta hat prime x prime y is the regression sum of squares including all the regression coefficients and we are subtracting here n y bar squared and then we are also subtracting n y bar squared. So this is the total sum of squares corrected for beta hat naught and this is the regression sum of squares excluding the parameter beta hat naught. So I hope now you have understood why we subtract n y bar squared from the total sum of squares and from the regression sum of squares. Then we looked at the contribution from beta hat naught and the regression sum of squares when it is subtracted by n y bar squared does not include the contribution from beta hat naught. So the number of degrees of freedom is reduced by 1 because we are removing beta hat naught from the list of parameters from the list of p parameters so p-1 will be equal to k. Now let us look at the extra sum of squares method. This is a very interesting issue okay. What we saw earlier was looking at individual regression coefficients. So we can keep doing it for all the regression variables or regression coefficients. We can start with beta 1 hat then we can look at beta 2 hat and so on to beta k hat okay. So that is somewhat tedious process and sometimes you may also have an existing model and when you report the existing model to your supervisor, he may say that you have considered only a model with 2 variables. Why do not you consider or build a model with 5 variables? So what I am trying to say is we can use the matrix or linear algebra concepts to do this pretty efficiently rather than do one variable or one regression variable at a time which is a somewhat tedious process. We can first analyze a model with a certain bunch of variables and that would be an existing model and then we can also see the impact of adding another bunch of variables to the already existing model and we can then decide whether adding the additional bunch of variables also has any impact or value addition to the regression model okay. So normally the simpler the model, the less number of variables a model has, it is elegant and it is convenient to use and it is also efficient okay. So you have done lot of work and then reduced complicated process by describing its dependence with only a few selected variables and when you present this model to let us say to the management, the people there may be a bit disappointed okay. We thought this is such a complicated process, why do you have only few variables describing the response? It looks like other parameters or other regressor variables also might influence the experiment. So why do not you go back and check your model? So what we can do is instead of adding one regressor variable by considering the effect of one regression coefficient at a time, we can take a whole bunch of regressor variables with their associated regression coefficients and use a method called as the extra sum of squares approach to see the impact on the process response. So what we are doing is we are going to conduct a hypothesis test to see whether the new bunch of regression coefficients are indeed valuable and if the test says that none of the new added regression coefficients are significant, all of them may be pretty much taken to be 0, then you may go to the management and say look my original model was in fact adequate, there was absolutely a very negligible impact of considering the effect of additional variables. So what we do here is something which may be a bit difficult for people who are not familiar with linear algebra but actually it is very simple, okay. So let us look at the beta column vector which is comprised of 2 sub vectors if you can call it like that beta 1 and beta 2, so beta 2 is column vector and beta 1 is also another column vector when you put them one below another it leads to the complete column vector beta. So beta 2 is an pre-existing or model which is already existing and beta 1 is the set of regression coefficients which you want to add to an already existing model. So let us say that beta 1 comprises of r regression coefficients and beta 2 is comprising of p minus r regression coefficients. So we say that H naught beta 1 is equal to 0 and H 1 beta 1 is not equal to 0, there is a small difference here from what we have done earlier, earlier we were looking at scalars or just single values beta 1 but now I am putting beta 1 in bold that means it is a vector comprising of r regression coefficients beta 1 hat beta 2 hat so on to beta r hat, okay. So we are saying that the entire bunch of entities in that beta 1 column vector is equal to 0 and the alternate hypothesis says that beta 1 is not equal to 0, okay and so you are having the new model represented by beta 1 and already existing model by beta 2. So the regression coefficient vector beta is split into what was already present in the model equation beta 2 and what is currently being added to it which is beta 1, okay. So we want to see what is the impact of adding the new terms in beta 1 vector to an already existing model. So what we do here is we first look at the full model so that is what we have to do. First we know the sum of squares of regression including the parameter beta hat not as beta hat prime x prime y. Let me sort of revise when you include in the intercept also we have beta prime beta hat prime x prime y but if you want to exclude the parameter intercept beta hat not then you have to subtract n y bar square but you are not doing it here, okay you are considering all the parameters including the intercept beta hat not that is why you have sum of squares of regression as beta hat prime x prime y and then you have the mean square error as y prime y minus beta hat prime x prime y and that you scale it by the n minus p degrees of freedom, okay. But also another thing you have to notice whether you consider beta hat not or not consider beta hat not the mean square error does not really care because the n y bar square you subtract it from y prime y you are also subtracting from beta hat prime x prime y so that n y bar square actually cancels out. So whether you consider n y bar square or not consider n y bar square it does not really matter to mean square error because you are subtracting consistently n y bar square from y prime y and also from beta hat prime x prime y so that thing actually cancels out and so this mean square error does not really bother about it, okay. In other words it does not really care whether you are considering the model with the intercept or without the intercept, okay. So we have the mean square residual or the mean square error here and let me sort of make a correction here to be consistent with what I had written earlier I will change this mean square error to mean square residual since both of them have the same starting alphabet r we use MSE, okay but we use mean square residual when we use the full form. So I would like to conclude by saying that the mean square residual does not really depend upon whether you have considered the actual total sum of squares or the corrected sum of squares be it total sum of squares or regression sum of squares. If you are considering the corrected sum of squares the n y bar square will consistently cancel out here and here, okay but if you are not using it well and good no problem you are considering the parameter beta hat naught and the mean square residual value will be unchanged, okay. So the sum of squares of regression beta hat naught is the regression sum of squares due to beta hat naught corresponding to the full model including all the partial regression coefficients beta hat naught beta hat 1 so on to beta hat k, okay. So as beta hat naught is included the term n y bar square is not subtracted, okay. So the full model this is what we have been considering until now is now split into a model already existing with the subset of the coefficients and a new model with the additional set of regression coefficients, okay. So let us look at the full model this is the vector of responses this is the x matrix this is the beta column vector which is the full set of regression coefficients and then you also have the error column vector. You might not probably for whatever reason you might not have considered beta naught and beta 1. You might have started your model with the beta 2, beta 3 so on to beta k only that is your existing model but then your boss would say what happened to the intercept what happened to the variable 1 they also look important to me from an intuitive point of view why do not you include it so then a new model would be adding beta naught and beta 1, okay. So what we do is this is the full model we split this into x1 beta 1 plus x2 beta 2 plus epsilon actually this is not simple algebraic addition this is involving matrices this is the overall response vector y and then you have the x1 beta 1 plus x2 beta 2 beta 1 is the new model it is a new vector comprising of the new regression coefficients and beta 2 is the column vector comprising of the old regression coefficients and x1 is again a sub matrix of x which are dealing with the regressor variables corresponding to beta 1. So x1 is the columns of x associated with the beta 1 and x2 is the columns of x matrix associated with beta 2. So just let us go back for example I told you that the new model was based on beta naught and beta 1 based on the bosses recommendation, okay. So then the x1 matrix will be the sub matrix obtained by taking the first two columns, okay that is what we are looking at the intercept will be associated with just one and then the beta 1 would be associated with the x11 x21 so on to xn1. For example you will have beta naught plus beta 1 x11 and then you will have beta naught plus beta 1 x21. So you are considering the effect of the intercept and you are also considering the effect of the first regressor variable x1, okay. So this is how we do it. The old model already had these regressor variables starting from x2, x3 so on to xk. So x2 would be associated with beta 2, x3 would be associated with beta 3 and xk would be associated with beta k. So we have to consider a hypothesis test to check if beta 1 is really significant. The reduced model if the null hypothesis is true becomes y is equal to x2 beta 2 plus epsilon. Null hypothesis means that there is no value addition on adding the elements in beta 1 so you are okay with this model y is equal to beta 2 x2 beta 2 plus epsilon. So the coefficients of the reduced model can be found in the usual way by x2 prime, x2 inverse, x2 prime y. So we have the extra sum of squares method. This is the full model. This is the model split into contributions from beta 1 and then beta 2 or in fact let me come again. It is the contributions from beta 2 and then from beta 1 and the sum of squares of regression due to beta 2 hat alone is pretty straightforward. It is beta hat 2 prime x2 prime and so the sum of squares of regression due to beta hat 1 given beta 2 hat already present in the model is the beta hat prime x prime y minus beta hat 2 prime x2 prime y okay. In order to find the regression contribution by the new model we take the full model first the regression sum of squares from the full model and then from that we subtract the regression sum of squares from the already existing model so that the difference will give you the contribution to the regression sum of squares from the new model. And the degrees of freedom for the original or the full regression sum of squares is p. It includes all the parameters while the degrees of freedom for the sum of squares of regression beta hat 1 given beta hat 2 is r because if you recollect we split the beta column vector into 2 parts into 2 column vectors. The first column vector was of size r and the second column vector was of size p minus r. So the full model is having degrees of freedom of p and the new model is having the degrees of freedom of r okay. And so the sum of squares of regression beta hat 1 given beta hat 2 is also termed as the extra sum of squares due to beta hat 1. So what is the extra regression sum of squares brought in by the new set of regression coefficients. So it is the increase in the regression sum of squares due to including the variables x1, x2 so on to xr in the model and it is also independent of mean square error. So this concludes our lecture on the hypothesis testing in linear regression. It is quite elegant and you can see that whatever we did in our earlier phase or the first phase of the design of experiments namely the hypothesis testing is also playing a very valuable role here. Thanks for your attention.


Hey, hello friends. So welcome again to another session on Serds and today We are going to discuss a very critical and very very important topic. That's called rationalization Now many students we have observed they struggle a lot when this particular concept is applied into Serds So let's try and understand these concepts in the best possible way and further to this you'll have to solve obviously Some amount of problems to get it affected. So let's begin So as the name suggests rationalization, that means you are converting something which is not rational into Something which is rational. That's why the name rationalization Now usually it is used for you know in context of Serds. So let us say If I have a Serd, let's say root 3. Okay, and I want to rationalize it So there exists another Serd which when multiplied with root 3 will render it a rational number So for example, if I multiply root 3 by another root 3 if you see what will you get you will get 3 Isn't it? Now 3 is a rational number. So what do we conclude? What do we conclude that this process of converting an irrational number Into a rational number by multiplication with another Serd is called the process of Rationalization you understood rationalization rationalization So I converted some irrational into Rational hence rationalization, right? So what do we understand or what do we conclude for any Serd? Whether it is a pure Serd or a compound Serd there exists another Serd Which when multiplied with the original Serd? Will give you a rational result? So let us take another example. Let us say I have root 2. I want to convert into a rational number So if I multiply either by root 2 or any multiples of root 2, I will get 2 So root 2 into let's say 2 root 2 will fetch 4 so everywhere you see whether you multiplied by root 2 or By 2 root 2 the result is always a rational number Rational number isn't it? So that's this process is called rationalization to convert a Ugly looking Serd into a beautiful looking rational number. So let us take an example of a compound Serd So let us say root 2 Plus root 3 is a compound Serd. I want to rationalize it What do I do? I multiply this with another Serd Let us say root 2 minus root 3 and why do I do this? You'll get to know in a short time.  So this one is called the conjugate Serd What is it called? conjugate Serd Conjugate Serd, right? This is conjugate Serd or the another name is Complementary Serd Complementary Serd so these are the two names given to let us say Something which is be being multiplied with a compound. So this is the this is the compound Serd original compound Serd And you wanted to find out what should be it what should the other Serd be? Which will multiplied with this compound Serd will fetch you a rational number. So hence This is the Serd which is being multiplied is called the conjugate Serd, right? So every compound Serd will have a conjugate Serd. So what how do I define conjugate Serd? So we say so let us define this as well so that you get an understanding so to quadratic or to binomial binomial quadratic Now, you know make sure that the order is to so hence it is to binomial quadratic Serds Serds which differ Which differ? Which differ only? Which differ only in the sign only in the sign Which connects them? which connects them Right are called conjugate Serds, right? So example of conjugate Serds are Examples are for example example of root 2 plus root 7 What is the connecting sign connecting sign is this plus isn't it so root 2 plus root 7 conjugate will be nothing but root 2 Minus root 7 you can also say that root 2 plus root 7 conjugate could be minus root 2 Plus root 7 why because this could have been written as root 7 Plus root 2 so this is the conjugate of this and this is the conjugate of this, right? So these are called conjugate Serds. Obviously, you have to see that they are quadratic Quadratic order 2 so hence you can't say root through 3 Sorry third root of 4 Minus third root of 7 the conjugate is not third root of 4 Plus third root of 7. This is not going to yield you any rational number when you multiply these two So hence always remember this has to be for quadratic what Quadratic Serds, right? So that is how we define conjugate. So now, I hope you understood rationalization So what to do if there is a pure Serds, so you know this let us say if it is a pure Serd then Then what do you need to do? Multiply be multiply multiply it with itself and You will get rational Result, right? If it is a conjugate Serd, sorry if it is a compound Serd compound Serd Then multiply with its Conjugate, isn't it or complementary? Sir Example of one, let us say let us say example of one. So if it is root 3, I will multiply it by root 3 to get 3 If it was let's say root of 19, what do you need to do? Multiply by root of 19. You will get 19 right and examples of 2 examples of 2 if it is root 3 plus root 7 Then you multiply this with root 3 minus root 7 If it is 2 root 2 minus 3 root 5 Then you multiply this with 2 root 2 plus 3 root 5 if it is minus 2 root 7 plus 4 root 3 you multiply this with minus 2 root 7 minus 4 root 3 like that So these are all examples of you see everywhere. I'm just changing the sign. This is plus it becomes minus here This is minus this becomes plus here. So connecting sign Change, right? This is what we learned about conjugate Oh, sorry rationalization of Serds. Let us take an example. So example is rationalize the denominator rationalize rationalize the denominator Okay, so let us say first example is 1 upon root 2. I have to rationalize its denominator What do I know if it is a pure shirt multiply it with pure shirt? Same number, but then when you are rationalizing the denominator, you are changing the denominator basically So you have to multiply the numerator also with the same quantity to compensate the change So hence it is nothing but root 2 upon 2 now if you see the denominator has been rationalized Another example rationalizing 1 minus root 3 1 by root 3, sorry So hence it is nothing but minus 1. So you have to multiply with the same Sir same sir So hence it is minus root 3 by 3 rationalized now if it is a Let's say compound sir or a rational plus irrational sir. Let's say 2 plus root 3 So what do you do? You simply do 1 by 2 plus root 3 times 2 minus root 3 I change the connecting sign But I have to compensate also by multiplying the numerator so that the value doesn't change So what do I get I get 2 minus root 3 upon? 2 square minus root 3 squared now This is simply this one if you observe this is a plus b times a minus b form Which is nothing but a square minus b square so hence what do we get I get 2 minus root 3 upon 4 minus 3 hence it is 2 minus root 3 upon 1 that is 2 minus root 3 Let us take another Example so you have to let's say you have to rationalize 3 by 4 minus root 3 Yep, or let us say 2 root 3 right 4 minus 2 root 3 So how do I rationalize the denominator that is so it is 4 minus 2 root 3 multiplied by 4 plus 2 root 3 I multiplied with the conjugate and On top also it will be 4 plus 2 root 3 right so what should be the value now the value is 12 Plus 6 root 3 so I multiplied the numerator now and in the denominator you'll get 4 square minus 2 root 3 square again a plus b a minus b form so it is 12 plus 6 root 3 and Divided by 16 minus 12 right so you'll get 4 come sorry not 4 is not common so hence you'll get what 12 plus 6 root 3 divided by 4 and So you cancel can cancel 1 2 so it is 6 plus 3 root 2 3 root 3 sorry divided by 2 Okay, or you can further simplify it as 3 plus 3 by 2 Rule 3 so this is what? We get if we rationalize the denominator So likewise now you understand if it is a pure sword then you simply multiply by its No same number right but then since since we multiplied something in the denominator which will effectively change The value of the You know given you know sir, so hence what do I do? I multiply the numerator also to constant compensate that change and eventually I get this right so and if it is a Conjugate sir, then you know what to do Multi the sorry if it is a compound sir, then you know what to do multiplied by its conjugate top and bottom both to get The rationalized Combinator I hope you understood this and for more such you know you need to do some more Practice solve the worksheet which is attached and you will be able to perfect it