Last night, Dr. Brown responded to my presentation, still unanswered with a video presentation of his own. And again, I will thank him for engaging, allowing the conversation to proceed. Dr. Brown seems to be worried that this conversation will go on and on for years. I have a feeling that that's not going to happen. You see, it's not about me, it's not about Dr. Brown. It's about you and God's truth. Dr. Brown says, read the Bible. And that is exactly the same thing that I say. Read the Bible. But go back to the world before Jesus. How would a Jew have read the Bible before Jesus came on the scene? What would have been his worldview? Read the Jewish Bible, draw out a worldview on the basis of the Jewish Bible alone. Put Jesus and Christian theology aside and draw a worldview from the Bible itself. Don't listen to what the rabbis say. Don't listen to what the missionaries say. In this presentation, I don't find it necessary to respond in detail to what Dr. Brown added to the conversation in his last presentation. I will just be asking you a few questions, because again, it's not about me, it's not about Dr. Brown. It's about you and God's Word. Turn to Zachariah chapter 6, verses 9 through 15, and ask yourself a simple question. If this verse is messianic, if this passage is messianic, and if the author is trying to highlight this passage, what message is he trying to tell you? Is he trying to tell you that the Messiah will be someone who builds a temple? He will be a temple builder? Or is the author trying to tell you that the Messiah will be someone who dies for your sins? Read the Bible. Come to your own conclusions. Question number two. Genesis 18, Exodus 24-10, Numbers 12-8. Why is it that the author didn't do anything to tell you that these are teachings on the subject of directing your worship? Why did the author leave that for the Christian theologians? Why did he ask wait for the Christian theologians to come and tell you that these verses are teachings on those subjects? Question number three. Where does the Bible say that the blood sacrifices of Leviticus point to something, point to anything, point to something better or bigger? Why did the author not say that? Another question. Why is it that the day of atonement, which is introduced in Leviticus chapter 16, the opening verses of the chapter don't open with listen people. If you need to repair your relationship with God, just follow these instructions. That's not what it says. If you look in the Bible, it says this is the correct way for the High Priest to enter the Holy of Holies. Why? Why isn't this passage introduced as a teaching on the subject of how to repair your relationship with God? Why is it another question? Why is it that the author of Scripture never, never came out and said there is no remission for sin without the shedding of blood? The author knows how to say things. He knows how to get points across. He knows how to make things clear. Why is it that that concept is nowhere to be found in the Bible? Why not? Why did the author not say that? I want to draw your attention to two verses in the book of Proverbs chapter 15 verse 8 and chapter 21 verse 27. In both of those passages, the Bible tells us the offerings of the wicked are an abomination. Okay, you know what that means?  How are you going to do that?  So, again, let's remind you my first question in my previous presentations was simply, which one of us is a Christianity or Judaism that is imposing its theology on the Bible? Only one of us is reading the Bible with the authorial intent, looking to the author to tell us what is the message, and the other one is trying to impose theology on the Bible. And again, I encourage you, read the Bible, try to read the Bible as a Jew would have read it before Jesus came on the scene. And I trust that you will concur, you will agree with a former Christian, a man who risks his life for Christianity. And he told me the Bible, the Jewish Bible is the most powerful counter-missionary book ever published. Let me move on to the second question that I spoke about in the previous presentations. I spoke about the question of directing our devotion, the love that the Jewish people have for God. I just want to clarify one detail. When the missionary is knocking on your door, he is not trying to tell you to love the God that you already love more powerfully, more strongly, put batteries into that love. He's trying to introduce a new love, a love that your heart never knew, a magnetism, an attraction that didn't draw your heart beforehand. So again, it's not a matter of taking that same attraction, that same magnetism, and infusing it with more power. It's introducing a new magnetism, a new attraction to your heart. That is idolatry. Now as it related to my third question, my third question was about Dr. Brown's contradiction as it relates to the Messianic prophecies. So Dr. Brown gave us a slew of quotations from Scripture, and he said that my quotations, the ones that I presented, are not relevant to the subject, or at least three out of the four are not relevant to the subject. You decide. I'll read the numbers, the chapter and verses slowly to you so you can come to your own conclusions. The verses that I quoted as they relate to the Restoration of the Sacrifices are Isaiah chapter 56 verse 7, chapter 60 verse 7, Ezekiel chapter 20 verses 40 and 41, and Malachi chapter 3 verses 3 and 4. Dr. Brown quoted Isaiah chapter 30 verse 26, chapter 33 verse 24, chapter 53 verses 4 and 5, chapter 57 verses 18 and 19. In the book of Jeremiah, Dr. Brown quoted chapter 30 verse 17, chapter 33 verse 6, and Malachi chapter 4 verse 2. Now again, you do your homework. You read the Bible because again it's not about me, it's not about Dr. Brown. Ask yourself, what was the author, look at all the verses, put them all on the table before you. What was the author trying to tell you with all of these verses? Was he trying to tell you that the way you're going to identify the Messiah is by when you see someone healing a blind man that will help you identify the Messiah? Or is the author perhaps telling you that when the Messiah comes and when the messianic age will be here, we will see the sacrifices restored to the temple in Jerusalem? It's not about me, it's not about Dr. Brown. You read the verses, come to your own conclusions. Dr. Brown spends a lot of time arguing why don't I debate him in a live format. I wrote at length about this many times. The first time I met him 15 years ago, I told him I will not debate him. My responsibility is not to entertain, my responsibility is to educate. I try to keep my personality out of this as much as possible. I encourage you to read what I wrote. The purpose of all of this is I didn't even want to make these videos. The only reason I wrote a comprehensive refutation to every argument that Dr. Brown raised. There's not one argument that I did not respond to in writing. You could take that yourself quietly when no one's distracting, read it, decide for yourself if my arguments hold water, if they make sense, if they talk to your heart. You don't have to get back to me. It's not my business. It's your business between you and God. The purpose of these videos is simply because Dr. Brown has dismissed my writings for all these years. For the past 10 years, he didn't share any of his answers about my writings with the public. So, he has a choice. He could say, my writings are meaningless. My writings are meaningless. Ignore them. But to tell the public that my writings are meaningful and my questions are real and that they deserve answers. But he won't share those answers with the public unless I agree to a formal debate. It's cheating the public. If these questions are real, the public deserves answers. You could choose whatever format you choose to publicize your answers. That's your business, Dr. Brown. But if the questions are real, then the truth seeker deserves answers.


Hey everyone, welcome back. I don't normally like to start out episodes with food eating, but it's just kinda on the go pace right now. I swear this channel was not sponsored by Chick-fil-A, although I wish it was. I'm really not planning on going too far this week, but I am planning on doing a lot of fishing this week. A lot of filming really. The last couple of years of my life, I've filmed a lot of stuff for companies in the outdoor industry, and then I've gone fishing and done stuff for my channel and sometimes I get caught up in doing both things in the same day. This week is just a perfect example of that. It's gonna be outside this channel filming. So the rest of this week we're gonna be doing filming for this channel. I'm gonna show you guys some, there's bugs. I'm sitting under a tree. Bugs falling out of it. Good bluegill tree. Today is all about simply trying to figure out a lake that has been giving me fits here lately. I don't even know if we'll catch a fish, but I'm gonna try something bit my neck. I don't know. Something jumped up and bit me. So it's real busy week, but I'm gonna take you guys along for a ride. See what's going on. You know, hop in the back seat, ride shotgun if you don't too. Right now though, I gotta do this. I gotta finish this Chick-fil-A. I got burger juice, Chick-fil-A juice on my brand new boat that I waxed. I waxed this thing up just for you guys. Although there's probably been like 2% of the episodes on this channel that actually show my boat from the outside. Most of the time, it's always on the inside. You guys are on the inside. You're the LFG insiders. So if you guys were wondering why I changed shirts, it's not because I want you to think it's a different day. It's because something I couldn't see was stinging my back. And I think it was the thing that was on my neck. Those welps on my back. And it was like in my shirt, I had a freak out moment. I basically ripped the shirt off. I was scared to wear it again. Be quite honest with you. Have you ever had something like that happen? Oh, okay, we've made landfall. It's basically summer now. It's getting hot. It's in the 90s pretty much every day. These fish have gotta be starting to move off the bank a little bit, at least to some nearby cover. Last time I was here, I tried flipping for like five hours and couldn't get a bite. Today, I'm gonna try that again. May sound stupid, but that was weeks ago. Things can change. The Shadspawn is the weird deal that keeps those fish up shallow for longer. But as soon as the Shads move off the bank and they get out deep in their normal situation, those bass just move right with them. It's such a great thing because you can catch them concentrated in one area. I mean, who doesn't like catching them like that? I certainly do. But this lake is not known for its deep structure fish. We've got marinas over here. Those are always a good summer area. The turtles are out. So, you know, they like sun. That's given. Oh, and the white bass are out. Woo-wee! Y'all know what happens when the white bass are out. I don't ever turn my back on white bass. Let me know in the comments.  Who can turn their back on some white bass? Some of my best friends turn their backs on white bass. It's like being Democrat or Republican. Two different ways of doing it. Let's go see what we can get into y'all. I'll be honest with you, I'm really surprised I tried about staying there the whole time. Where are you gonna be? What you gonna be doing, fish? What are we dealing with here today? The main thing is though, I wanna find out, are these fish up shallow?  I just don't know. We got a nice steady 10 to 15 mile an hour wind here. Gonna make it a little tough to flip my jigs in the right little corner area, but it also might make a bite a little better. It's about midday, like literally lunchtime. It's the Chick-fil-A. And I'm already hung on my second flip, so looks like we're heading down that path today. No, we're not. Get that negativity out of our heads right now. I might need to go to a straight, like brushed flipping bait. Here's a fish. Got it. Yes, yes. Oh, that's a good sign, because he ate it like a champion, black and blue jig in the brush. That's the bite I was looking for weeks ago. Got another little patch of brush right here.  Oh, there's one. Got it. Oh, it came off. Oh, that's a good sign though. They might be in the brush now. There's another patch right here. Little color change in the water. Right there, switched up to the spinner bait. Fat, fat, fat, fat. That right there is a good example, a little bait switch. So I flipped in there multiple times with that jig, didn't get bit. That fish ate old trusty and didn't even need the trailer hook. He ate the whole thing. Reeling it through the edges. You know what he's been feeding on. Shad, Shad or Bluegill right now. See, it's a post spawn fish. He's got that little notch in his tail but he's recovering nicely. He's fattening it up. Good fish. We have a pattern going. That's three little brush isolated bush areas on this windy bank that have had fish. When you make contact, just like on a spinner bait or a crankbait. Hello. Hey, oh, fighting a fish. Yeah, I'm fighting a fish right now. I got, I'm getting them in. Here he is. I just saw Shad get sprayed right here. Jumping out of the water. Something, something's eating him. Now, this is what I like to do on these windy days like this. If you're doing some flipping, you know, fishing is, it's not overcast or not exactly munching on the moving baits. I'll still throw them if it's windy. Just in between these little areas. If I'm going in between docks or trees or brush like I've got today. Like I've got brush out in front of me but I'm just throwing a little moving bait in between just to see if I can pick up a few extra fish. Sometimes it works out. At least fish might even be just holding on this color change with that mud coming off the bank. There's one. Got him. Well, it's a big one too. And that's a big one. Oh, it's a good one anyway. Come here. Got you on that old trusty baby. Oh, what are you doing? Are you up there hiding in that mud line? Definitely post spawn skinny. Y'all are revealing yourselves today. Love it. Quality 12 inch or noted. Well, it's been a couple more hours out here and we've got some overcast conditions that are starting to roll in. And the wind is shifting a little bit. I've tried some other things besides the brush just to see what's going on. I haven't had much luck. Seems like the bluegill and the shad are up in that brush in particular that area I was in there was a lot going on. I could see bass actually busting up shallow which is always good. I really need to go back home and do some stuff but the traffic's gonna be really bad right now. So I think I'm gonna hold off. I'm gonna fish a little bit more until the traffic dies down and I've gotta get the kayaks rigged up. That's right. I think it's gonna be the first time I'm getting out the kayaks of the year.   And I certainly don't wanna go sit in that right now. I'm on the lake. I might as well fish. See if we can pull out a couple more till we head back. No fish in the calm areas. All right, I'm gonna pick up old trusty. Come on old trusty. Let's get us through the rest of the day. I know there's probably not a way that you're gonna believe me.  On the spinner bait, I looked down at my GoPro and I had to release it. I'm like, that's how I like to end the day. It's not, it's not on, not rolling. It's terrible. Sarah, I didn't even take a photo. So I have no evidence. You're just gonna have to go on faith right there. But I caught it on this little point as I was coming down the bank. This little point right here with the wind blowing on it. And it wasn't even really that close to the bank. It was kind of off the bank a little bit. So that would have been a great one to end on but I'm gonna try to get another one. You got a big one. Come on over. You got a fishing freak right here. He's got a giant. Biggin dude, nice. I don't even need to catch one more fish. You guys are so good. You're just gonna close this video out for me. And one of the fishing freaks just came up, showed us a six and a half pounder. Said the fishing was tough. He caught that one deep though. And that fish I just had was probably suspended in about six feet of water but there's 20 feet really close by. So it kind of got me thinking as I'm sitting here, just kind of chunking around on this point area, seeing fish kind of come through on this bait and everything, that there might be some fish moving out deep. There's always gonna be those ones that stay up shallow and feed on bluegill and everything like that. But if they're shat out deep, he said he caught it around some hybrids. So I like that kind of fishing. Unfortunately, we didn't catch any big ones like that today but at least one of you guys did. Got some balance right there. I think you can wait, Melan. There's more fishing freaks at the ramp.  I saw these guys. Out on the lake, Mason came up here to the ramp. You guys caught a limit of crappie today. You were slaying it. Good job, man. Another fishing freak out on the water.  He caught it out deep. So you guys were slaying crappie. I caught a few bass. Obviously didn't have as good a day as these guys but you got anything else you wanna say to the fishing freaks at home? No. Make every cast count, maybe? Yup. Woo, man. All right, time to head home. Oh, I saw Mason out there on those bridge pilings over there where I caught that four pounder that you guys missed. So cool. So cool to see Mason excited. Catching fish, catching a limit of crappie. You fishing freaks made my day because I was having a tough one and it was kind of a short outing out there but just seeing y'all out there always makes my day. So thanks. If you ever see me on the water, come by and say hi. Don't be shy. Ready to go for tomorrow. This silver bullet is gonna stay here. This is an LFD. He's checking things. That's right, we're gonna get this kayaks on board. So your truck is rigged to do double kayaks which I think is pretty cool. I don't know, man. That thing looks a little shifty. It'll be okay. It'll be all right. They're just dusty. Okay. They haven't been used since our Canada trip. That's true. So, no rocket launchers. We got a lot of work to do here. We got this big old kayak which this is a 14 footer. It's basically a boat. And this is a 12 right here. We're gonna use it too. And we gotta get it down. It's currently hanging in the air.  Correct? Correct. And then the yellow one's gonna go on the top and then we'll put our rods in the cab. We got the whole family joining out here tonight. Leaving. Oh, my mom's leaving. Like four pounds leaving. It's all of us. Oh, she's not scared though. It is all of us. It is. We're trying to figure out if she can get somewhere. How was on the water day? It was a little better. A little better? Not quite a barn burner. I was just having a vision though of Stephanie with our little baby out here while I'm doing tackle. Hopefully won't be at the parent's house.  Are you a rascal? Rascal. Rascal. She was humiliated that night. It was a duck noise. These bass don't stand a chance. We're double loaded. Yeah, one more. Is that the street legal? She's legal now. All right, y'all. This is the portion of the video where I gotta sign off. We gotta finish strapping this stuff down. I gotta eat. I gotta edit this. And we gotta get up and go in the morning. We're meeting up at five. Hopefully we're gonna bring out some good action. There's definitely no lack of effort here. If y'all are digging what's going on here on this channel, make sure to subscribe out here and hit the ding dongs for more. It's gonna be a crazy week coming along for the adventure. See you guys on the next video.


What's up everybody once again is Bram and Sean and this video is brought to you by Bram Man Network.com because I signed myself. Now I got to talk to you all about something that's you know low-key one of the big reasons for Old Town Rolls success that people don't really talk about and it's really a big opportunity for anybody who has that entrepreneurial savvy, that entrepreneurial inkling when it comes to the music industry and that is the kids man the kids. Now what do I mean by that exactly well alright every kid in my family loves Old Town Rolls and it's not just the kids in my family but I'm talking about like three to seven years old when I'm talking about the kids. Be clear when I say the kids I really do mean kids and the big part about this to really keep in mind is a lot of people say yo like who's even still playing that song why is it still on the charts and this isn't the only reason a song like that will stay on the charts that long but you have to consider a lot of times there are people who are outside of your demographic playing the music in this case a lot of kids do account for some of those people and it might be indirect because of course it might be parents playing it for the kids but the point is the reason this is a huge opportunity is because like no error before like people are able to account for the amount of times kids like to play music in the same way beforehand before streaming when it came out the hip hop was the most powerful and listen to genre it wasn't really that big of a surprise for the you know younger generations who are in the know but it was a huge surprise for those other folks right the industry a lot of people in the corporate sphere and the reason is because so much of hip hop was pirated right people were getting it for free so it wasn't being accounted for in official records in the same way but the kids have that similar effect it's not that they were stealing music necessarily however it's just the fact that children stream things so much they listen to things so so often right or they can assume so often so it's not even necessarily specific to stream but they can assume so many times because for one kids have way more time than anybody else way more time on their hands so they have more time to consume even teenagers right most likely a huge portion of the time that you spend on just consumption is going to be in your teenage years right and that's that more impactful period where you're really intentionally thinking certain things out but when you're a kid children are listening to things over and over and over again I mean the same thing over and over again once again this isn't just music right my daughter she would literally watch Toy Story again and again and again with no sound right just addicted to watching the same thing over and over again until they move on to the next thing but then they do it again and again and again and again until they move on to the next thing so their extreme consumer behavior is something that's extremely beneficial for the industry and anybody who can tap into that market I know a lot of teachers who have music that they started to like create their own rap songs and now they've kind of blown up in that niche where so many kids are playing their music over and over again and I mean several teachers I know multiple teachers who have done this because as a marketplace once you're in there the kids will sing it over and over again to the point that is getting on the parents nerves it's a common thing so once again just to bring it full circle a huge entrepreneurial opportunity for people who haven't really identified this yet especially in the streaming era is tapping into the kids market because not only was it always beneficial because people buy stuff for their kids right people are looking for things to entertain their kids or teach their kids but even more so the market is even bigger than before because so many of those streams that would have actually been lost when they came to just buying a CD back in the day are being accounted for in streams and actually being multiplied so if you feel like hacking a niche just for a quick little check that's something might want to check out but in all seriousness is a real thing and you will see more and more people looking to strategically jump into that I know as an artist it might not necessarily sue you and what you're trying to do but it is one of the reasons you will find a lot of people who have some incredibly simple songs that they like to keep that way because it makes it easy for the kids to remember and obviously not being super explicit makes it easier to listen around the kids and once they get caught on to something and they have a song they will listen to that same song in a short period of time far more times than an adult ever would trust me like all opportunities is not an opportunity for everybody but it is an opportunity man I would love to know what you guys think about this but other than that if you liked this video go ahead and like button if you like it might as well share it and if you're not subscribed you know what to do hit that subscribe


Hi, I am Munni from localization team Khan Academy. You remember we met last time and I launched a talent search for localization in Khan Academy? Well thank you so much everybody who applied and really supported us for our mission to provide world-class education. But if you couldn't apply or didn't get the chance to apply, we have a good news for you. We are extending the deadline to now third of March so you've got few more days to apply for this golden opportunity and we have immediate project openings for Assamese, Bengali, Marathi and Hindi. So if you know someone who knows these languages and math, please ask them to apply. But if you are from any other language, well don't get sad, you can also apply and probably we'll have projects soon on these languages as well. So really hoping to see you here very very soon. The application form I can hear a lot of you asking how we can apply, well the application form is down in the description box. Please go and apply now.


The narcissist doesn't really consider whether you like them or not, whether or not you are interested in them. It doesn't matter because they feel entitled to you. They feel entitled to your time, energy, space, mind, body and soul. They have this arrogance where despite having nothing to offer you, they believe that they are deserving of you. They really believe that they should have you just because they want you. Even if they have spent the last few months or years abusing and manipulating you. They still expect you to find them irresistible as though they are God's gift to you. Deep down they know they do not deserve you. They know that they are not good enough for you. They know that they have nothing to bring to the table but they are in denial. They have to deny any responsibility or accountability for all of the abuse and manipulation. They have to pretend that they are these amazing, interesting people who have everything to offer you. To compensate for their low self-worth, low self-esteem, low self-belief, insecurities and inferiority complex. The narcissist likes to play different roles. In one moment they are the sadistic abuser, bringing pain and misery to you. Then in another moment they want to be this charming, irresistible character.  To suddenly be in this charming, irresistible person who has apparently everything you have ever been looking for.   It's going to make you avoid them and want nothing to do with them. Making it difficult for them to obtain narcissistic supply. So now they have to switch roles, try to obtain positive supply from you. They try to get a positive reaction by being the charming, irresistible character they believe you desire. But once you begin to show a positive reaction to this character, they have obtained their supply. The illusion falls apart and then they go back to who they really are. The abuser manipulation starts all over again. This is because they are slaves to their obsession of seeking constant validation and attention. They will throw away loving relationships, even their children if it means that they can obtain a fresh source of validation. Another role they like to play is the hero. I think that most narcissists want to be a hero at times as it satisfies their ego. It also provides them with positive attention, validation and approval. They are not heroes really though. They just pretend to be in that moment to obtain narcissistic supply. How can you be a hero when you abuse and manipulate someone every day? You cannot have a narcissist who is also a hero because they do so much damage to your life. It greatly outweighs anything good that they do. They are destroyers itching to abuse someone or manipulate something at every moment of their lives. The narcissist may feel entitled to you but it doesn't matter because they do not deserve you. You have value, you have depth, you have self-worth, self-esteem, self-respect and self-belief. You experience genuine love, happiness, empathy and consideration. They do not possess these valuable qualities. So what makes them think that they deserve you? What gives them the sense of entitlement? It's their arrogance and denial. They do not deserve you because they never began to work on themselves. They don't self-reflect or look within. They don't take responsibility or accountability for their abuse or manipulation. They never even began to work on healing their childhood traumas. They never even acknowledged them. Instead they pretend as though they are fine and don't need to work on anything. And maybe that's why they feel so entitled to you. They believe that they are already complete. Well that couldn't be further from the truth and it's clearly obvious by their behaviors. Emotionally healthy people do not do what they do. They do not abuse or manipulate. They do not project their insecurities onto you. They do not need to create illusions. But narcissists do all of that. Yet they have this delusional belief that they are entitled to you and deserve you. Why they have such low self-esteem, low self-worth, low self-belief. They are insecure and have an inferiority complex. They do not respect you or your boundaries. And while I can respect someone who is working on these issues. The narcissists have never even begun to work on any of that. They pretend as though they have no issues. They are in denial. Which is why they feel so entitled to you. They have to exaggerate their worth and self-importance to compensate for how small, boring and lifeless they really are. They see you and want to be like you. So much that it becomes an endless competition. They create illusions and play different roles. Because they don't want you to see them for what they really are. They don't want you to have a mind of your own. Because they see you as an extension of them. They expect you to think exactly the way that they think. They expect you to believe what they believe and see everything the way that they do. If you do not, they will gaslight you until you do. So that they can regain control over your mind. They will under exaggerate if you have done something good or if they have done something bad. They will over exaggerate if you have done something wrong or if they have done something right. They make you believe that you do not deserve them. The truth is, you do not deserve them. Because you deserve better. And this is why they never fully give themselves to you. Because they know you will be disappointed. They know that they do not meet your standards. So if they fully gave themselves to you, you would realise that straight away. You would know that you deserve so much better. And they don't want you to realise this. So they hold back. They also like to have control at all times. If they give themselves to you, they believe that they are losing control. So yes, the narcissist feels entitled to you. Their arrogance and denial make some believe that they do deserve you. And this could trick you into believing that they are on the same frequency as you. But they're not. Remember they haven't even begun to work on healing their childhood traumas. They have low self-worth, low self-esteem and low self-belief. They are insecure and have an inferiority complex. They do not respect you or your boundaries. This is how you know that they are not on your frequency. They are not of like kind. So leave them to think they are entitled to you. Move on with your life and find someone who is on your frequency. Someone who does practice self-love.


Box 13. With the star of Paramount Pictures, Alan Ladd has Dan Holliday. Box 13. Box 13. Box 13. Copy boy. Copy boy. Hiya, Mr. Holliday. What do you say? Where's that society page lead? Hiya, Holliday. Hiya. Jerk the first paragraph in that Simmons story. Hiya, Dan. How are you? Hiya, Susie. Hiya, Mr. Holliday. What's in Box 13? You are listening to Box 13 starring Alan Ladd as Dan Holliday. Now for Box 13 starring Alan Ladd as Dan Holliday. Here I am again standing at the wanted counter of the star times looking for what? An idea for a story. I could have stayed here as a reporter. I could have been searching for facts instead I'm fumbling for fiction. Instead of a blonde, I'm meeting a deadline. Instead of Chanel number five, I'm heading for a sniff of printer's ink.  Hi. What's that, Susie? I said there's a letter in Box 13 for you. It's special. Special? Special delivery. It was mailed only a couple of hours ago. Something like that could be important. Could be. Could be adventure. Could be. Could be a girl. Could be. By the way, Susie, how come you're working so late this evening? Oh, my boss asked me to. He's paying me overtime. Time and three quarters. Time and three quarters? I held out for double time when he offered me time and a half. What happened? Oh, we affected a compromise. Goodbye, Susie. Special delivery. This could be very important, also it couldn't. Come on, open it up Holliday. Haven't got all night. I'm in terrible trouble. Please come to room 718 at the Bradford Hotel. Hurry. Signed Agatha Marsh. That sounds urgent. Who are you, young man? What do you want? I'm the man from box 13. I'm looking for Agatha Marsh. I'm Agatha Marsh. Come in, come in. You're Agatha Marsh?  Never can tell who might be snooping around the hall.  Now, what's your name? Dan Holliday. Well, Mr. Holliday. I don't believe in drinking or I'd offer you one, but I have got some sauerkraut juice in my thermos bottle. Oh, no, thanks. Just the same.  I liked your ad in the paper. Adventure wanted. We'll go any place, do anything. It was just what I needed. Well, thanks again. Now then, what's your charge? Charge? For helping me, your fee. Oh, that. No charge, Miss Marsh. Are you trying to be chivalrous? No, you see, I'm a writer. I'm looking for ideas. If I get a good idea, I consider I've been well paid. Well, that seems a little silly. Might I ask just what your trouble is? Oh, you don't think a girl my age could get into trouble, do you? Well, you look like a very charming old... Oh, I'm sorry.  Now, no doubt you want to know a few things about me. Well, that would be very interesting. Yes, well, I live in Muncie, Indiana, alone. I've got a big house and an independent income. Every year I go someplace for a vacation, and this year I came here. Is that all? Isn't that enough? But the letter you wrote me, you said you were in terrible trouble. Well, I am. If anyone ever finds out about this, I don't know what'll happen. Finds out about what?  I want to show you something. Look. On the floor. Well, that's a dead man lying there. Well, this would make a good opening chapter for a story. Young man goes to help charming old lady who is in terrible trouble.  Corpse? Hey, wake up, holiday. This is the real thing. Now. Now do you believe me, young man? When did you find him? Just before I wrote you that letter. Before you wrote the letter? Well, that's hours ago. I know, but what could I do? What could you do? Miss Marsh, you could call the police. And get my name in the papers. Back in Muncie, no, there was a dead man in my room. Oh, no. Miss Marsh, listen to me please. There's a dead man in that closet. There's a law about dead men. We have to notify the police immediately. You can go to jail for hiding a body. A fiddle sticks. But Miss Marsh, look at this man. He's been shot at close range. There are powder burns on his coat. I know. I examined him before I wrote you. You see, I read all the current detective stories. Detective stories? This isn't a story. This is the real thing. I know. Why don't you try to prove that I did it? With what? A cap pistol?  But this is going to be tough. Well, don't get so excited. A girl my age could kill a man if she wanted to. Rub him out, as they say in the murder mysteries. Please, Miss Marsh, be sensible.  Now pick up that phone and call the police right away. Mr. Halliday, in all seriousness, I can't do it. Think of what my lifelong friends would say. Yes, yes, I know it doesn't look good. I can see the headlines now. Prominent, munchy pioneer woman found with dead body in hotel. Oh, please, Mr. Halliday, help me. Well, I don't know. There's a little out of my department. Just this once, Mr. Halliday. I've never asked for help before. I'm an old woman. Well, all right. What do you want me to do? I want you to help me get rid of the body. Get rid of the body? Now, look, Miss Marsh, you're not serious. You didn't mean that. Oh, you don't know me. I fully intend to get rid of that body. OK, go right ahead. It's your course. And you're going to help me. No, no, I'm sorry. Try a bell. And have him snitch to the desk clerk. Besides, you advertised for adventure. But this isn't adventure. It's a nightmare. Come on, Miss Marsh. Let me notify the police. Now, there's a broom closet down the hall. That's very interesting. I just remember I'm eating someone in the lobby. I take the body there myself, but I'm not strong enough. Goodbye, Miss Marsh. I'll scream. Go right ahead. The hotel detective will show up. Just a man I'd love to see. And I'll tell him you killed that man. Oh. Now, would you help me? Suppose we get caught. Then you'll help me. Now, wait a minute. You said we. Now, I'll open the door and watch the hall. Case the joint, as they say, in the mysteries.  You're strong. You can do it. Oh, sure. I'm strong all right. But not in the head. Oh, this can't be happening to you, Holiday. You can't be dragging your body down the hall of the Bradford hotel. You're no better. And as soon as you can get away from this charming, but cracked old gal, you're going to talk to the police. Harry. Harry. I'll open the closet door. Put him in the middle right there. Stick him in good. I must be crazy. Now, back into my room before anybody sees us. There. Wasn't that easy? Easy, she says. Well, I must say you carry out your part very well. What's next in this little scheme of yours, Miss Marsh? Why don't you know? We have to find out who killed that Michael O'Brien. You know who he is? What I do know? I went through his pockets. Frisked him, as they say, in the stories. Well, it cuts it. You stay here. I'm going downstairs. Who's that? Just keep cool. I'll handle everything. Oh, I can't believe this. It just can't happen. My name is Kling, Lieutenant, homicide bureau. Oh, come in. Come in, won't you? I intend to. Holiday. What are you doing here? Hello, Lieutenant. Oh, do you two know each other? Never mind the social chatter. I thought this was some kind of a gag. Now I'm sure of it. How are they just what are you trying to dream up? If I told you, Kling, you'd never believe me. Sit down, Lieutenant.  Well, I don't mind if I do. Some what? Sauerkraut juice. Oh, no thanks. Now listen, somebody, some crackpot, phoned in the tip that there was a dead man in this room. Well, Lieutenant, how can you say such things? Lieutenant, now listen. You'll be quiet. Miss Marsh, mind if I have a look around? Not at all. Not at all. Here's the closet. Kevin, you can see for yourself, Lieutenant. There's nobody there. I got your name from the desk clerk, Miss Marsh. Maybe you better tell me about yourself. I can tell you all about it. I was talking to Miss Marsh. Are you Miss Marsh? Right now I think I'm dead. You will be if you keep interrupting.  Tell me about yourself. Certainly. I live in Muncie, Indiana. I arrived this morning for a two-week vacation. I'm well known back there, and you can find out everything about me if you care to wire. How did you happen to meet Mr. Holliday here? Look, Lieutenant, if you'll permit me to tie on this... I'm asking the lady. I went to school with his mother. That's what I did. Huh? See. Well, I guess it was the work of some would-be comic. But I had to investigate it just the same. Well, of course you do. I'll be clean, listen. Goodbye, Miss Marsh. It's a long holiday. But clean, wait. I want to go with you. Why don't you two have a fast game of hearts? Holiday wasn't that thrilling, just like in the Maxine's. Miss Marsh, you're going to stay in this room until I get Clang back here. Oh, no, no, no. I want to solve this case myself. I wonder how Clang found out that... Miss Marsh... Yes?  Of course I know. It was I. What in the world are you doing? I made the call from the corner drug store a little while ago. I wanted to throw the lieutenant off the trail, like they say. You know what I say. Know what? You're going down to police headquarters and tell the truth. Oh, just a second. Excuse me, please. Yes? Yes, this is Miss Marsh. Oh, you did it. I thought so. It should have had 817 instead of this room. Oh, no, don't bother. I like it here. I knew it. I knew it all the time. What did you know? That was the room clerk. He got my reservation mixed up. I was supposed to get 817, and I got 718 instead. You mean the person who killed Michael O'Brien wanted to get back in here to remove the body? No, no, no. It doesn't sound reasonable. No, it doesn't. Well, guess who was supposed to get this room? Never mind. We're going to police headquarters. It was Tony Bascari. He's the biggest racketeer in town. He's dynamite. Miss Marsh is deadly. I know Mr. Holliday, and I love it. Oh, no, no. You are listening to Box 13, starring Alan Ladd as Dan Holliday. Now back to Box 13, starring Alan Ladd as Dan Holliday. Two o'clock in the morning, and I can't go to sleep. That little old girl has me worried to death. She wouldn't go to the police headquarters, and when I went down and talked to her, clingy actors, though, were a big joke, and sent me on my way. Hello. This is Agatha Marsh. Now what? Where are you? At the hotel. I went up to see Tony Bascari. You what? Miss Marsh, don't you know that's the place you could have done? I had to talk with him. I put the heat on him, as they say in the murder mysteries. And you're still alive? I accused him of killing that O'Brien man. I came right up with it. But, of course, he wouldn't admit a thing. What are you expecting to do? Break down and confess? Well, I think I've got him on the run, but I'm worried. Oh, if I had Tony Bascari on the run, I'd be worried too. Because when I came back, I discovered someone had searched my room. Well, you call a police. You should have. Oh, no, no, no. I couldn't. I want you to come over right away. At two in the morning? Mr. Holliday, someone's trying my door. Hang up quick. Call the room clerk. But, Mr. Holliday, I'd... Hurry, I said.  End your close, Holliday, because here we go again. And don't forget your boy, Scott Badge. You'll make the beaver patrol tonight. Oh, no, no, no. I can't. I can't. I can't. I can't. I can't. I can't. All right. Back to your seat. Dad! we left my acknowledgement. Yes. Not now. I know. but I know there's a cost to you. It's all that l road. There's a cost. No, no, no, no. No. No, no, no, no, no. It's so awesome. It's the best place. Yes, yes, yes. I think it's so awesome. Yes, yes, yes. It doesn't go any Например otherwise. I can't over umm, You gonna do the thing? But why should she be making paper airplanes airplanes the airport? That's where they took her Keep that motor running. I'll be right back how many people around this hour the night Well, there she is The man with her has his hand in his pocket, and I don't think it's there because it's cold What I need now is a little fast talk and a little faster action Okay, I'll take over from here Who are you? What are you talking about the old doll best carry wants a bag best carry told me to put her on a plane I'm doing it. Yeah changes mind. He wants a back. I don't think so besides I never saw you before I told you if you don't turn her over best carry might get sore when he called me It's only a half hour ago. I was still at the hotel. He could have called and spilled everything over a phone Yeah nuts This don't sound right. Yeah, I forget it. Take any old doll back with me. Wait a minute.    Show me something. It'll prove Tony sent you Got a match stop stalling. This is a gun in my pocket. Let's talk to Tony. I've got some matches here. Thanks Yeah I'm not as young as I used to be you should have remembered that before you got mixed up in this. Come on get in Driver get out of here fast What did you do to that guy anyway? I Stuck him with my head pain. I might have guessed Now Miss Mars what happened at the hotel? Well, I hung up when I heard him trying the door But I was too late the door was unlocked So it was Tony best carry He wanted you out of town fast, but they were very nice to me you can thank your lucky stars for that Usually best carries enemies wind up in some ditch I didn't see him again that man the one you knocked out at the airport He was the one who came in my room. Well, you must have their goods on best carry You must have killed this man or had him killed But why didn't he take him out of the hotel right away? But there was a convention there last night the whole place was literally crawling with people. Oh That's the reason all that paper airplane that was fast-thinking this March. Oh, thank you Now we can go back to bascari. We've got the goods on it We can crack the cakes like they say in the murder mysteries this March. I've got news for you We're not going to see bascari. We're not well. Where are we going? You'll hate me? I know, but it's the police station Well holiday what happens now?  I've got a man telling her okay Okay, but what happened in that office? What does he tell you plenty my friend.  There really was a body in the hotel. You know Look holiday it. Do you know what you're saying sure? I know what I'm saying there really was a body in that hotel Holiday why didn't you tell me I tried to twice once in the room in the last time when I came in here I'll think holiday carefully Where is the body in a broom closet down the hall? I put it there you put it there. Yes. I put it there holiday Get out of here Well holiday now you're fixed even cling looked at you like those things in your belfry weren't bats And more like eagles But you're in it now, so you've got to follow through and that indicates a fast ride over to the Bradford hotel Oh clerk hey clerk Yes, I'd like to find out who occupied Agatha Marsh's room the day before she did that question is highly irregular Oh Then here's a $10 bill. That's highly regular. Oh Let me think as she has 718. She checked in day before yesterday. Yes The man who had the room before that was a traveling salesman in lady suits. I believe you must have cut quite a figure She must be in this hotel someplace her room's empty, but she must be around but where What are you worrying about holiday? You couldn't wait to get rid of her now.  Oh Hello, Mr. Holiday Miss Marsh, what happened? How'd you get in that closet isn't this thrilling? No, it isn't there was a detective training me But he was knocked unconscious Saft as they say in the murder mysteries and you were brought up here by the same man who tried to put me on the plane He hit the detective put me in the car and brought me here Well you two what are we playing now? But where is the man I put on you miss Marsh? He was hit over the head lieutenant, but I'm sure he's all right now This the closet where you said the body was was is right lieutenant. Let me take a look You know what I think holiday What I think both of you crackpots are making this all up I don't believe there ever was a body Kling you have my word for it Your word doesn't mean as much as a Chinese dollar Kling listen. They brought her back here locked her up They took the body away didn't they miss Marsh probably going to sink it in cement as they say in the murder mysteries Bascaries in his room. I'll bet go up and talk to him surely put the heat on him just once more I'll play with you kiddies Come along where Miss Marsh's room I'm locking you pixies in till I get to the bottom of this Things been gone 15 minutes. I wonder what's happening up there not much. I haven't heard any shooting. No, that's Haven't heard any in that case. How could a man be shot here? And that shot not be heard. What's very easy. Mr. Holiday the killer would use this Miss Marsh now, where'd you get that gun? Just took it out of the drawer. It was here all the time Well, put it down until Kling returns, but I just want to show you why the shot wouldn't be heard What do you mean? Would you excuse me, please?  You know miss March you found out a lot since you came here Oh, yes, I've done all right since early this morning Early this morning, but the clerk said I thought that's only mascara and he said Miss Mike me that thing you shouldn't have moved mr. Holiday. I was really shooting at you Ask this all about holiday. What was she doing with that gun in her hand?  Dragged it back to the closet in this room.  It was easy I got him to turn around and hit him over the head with my purse Why did you kill Michael O'Brien? Did you have something against him? No, no, I never saw him before and why kill a perfect stranger. I Saw play one. I like those ladies in that play. They killed lots of people. I wanted to also Only I should have done it like the ladies You don't mean our snick and old lace. Yes, and I should have worn the lace and given you the arsenic Oh Holiday you're back in your apartment again The Sun is shining through the window a Sun you might never seen again You know, I've got an idea for you holiday Give up this business and go into something quiet like night watchman in a cemetery holiday Well, what's that clean they examined the old girl down at the psychopathic ward of the city hospital She's baddie is alone. You're telling me I saw that in her eyes when she wrapped the towel around that gun But what happened to best carry any stooge when she heard he was the room above. She tried to pin the body on him Oh, so he tried to get her out of town in self-defense Holiday you're a very lucky lucky guy. You can say that again and again and again Oh just a minute Hello, Mr. Holiday Susie What are you doing up here at my apartment? Why aren't you done at the start times? Well, my boss and I have been talking about another compromise Another one he wants to fire me and I want to quit. Oh, but Susie if you left the paper What would I do for my mail? I was thinking maybe you'd like to hire a good combination Stenographer and secretary, huh? That's you. That's me Well, I don't know Susie, but as they say in murder mysteries. I'll have to think it over You better think fast. Good help is hard to find Goodbye Susie Next week same time Alan Ladd stars as Dan holiday in box 13 Alan Ladd appears through the courtesy of Paramount Pictures and may currently be seen in Wild Harvest Box 13 is written and directed by Ted Hediger Original music was composed and conducted by Rodie Schrager. This is a Mayfair production


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Statistics and Excel correlation simple with few data points example got data let's get stuck into it with statistics and Excel you're not first a word from our sponsor yeah actually we're sponsoring ourselves on this one because apparently the merchandisers they don't want to be seen with us but but that's okay whatever because our merchandise is is better than their stupid stuff anyways like our accounting rocks product line if you're not crunching cords using Excel you're doing it wrong a must-have product because the fact as everyone knows of accounting being one of the highest forms of artistic expression means accountants have a requirement the obligation a duty to share the tools necessary to properly channel the creative muse and the muse she rarely speaks more clearly than through the beautiful symmetry of spreadsheets so get the shirt because the creative muse she could use a new pair of shoes if you would like a commercial free experience consider subscribing to our website at accounting instruction.com or accounting instruction.thinkific.com require to but if you have access to one note we're in the icon left hand side one note presentation 1725 correlation simple few data points example tab also uploading transcripts to one note so that you can go into the view tab immersive reader tool change the language if you so choose be able to either read or listen to the transcript in multiple different languages using the time stamp to tie in to the video presentations one note desktop version here thinking about correlation having different data sets to see whether there's a mathematical relation or correlation between the different data sets in other words are the dots and the different data sets roughly moving together in some way shape or form if there is a mathematical relation or correlation between the two different data sets the next logical question would be is there a cause and effect relationship that is causing the correlation or mathematical relation between the two different data sets and if there is a causal relationship the next logical question would be what is the causal factor which is causing the causal relationship which is causing the correlation or mathematical relation between the different data sets and prior presentations we thought about a perfect positive correlation and a perfect negative correlation things that are useful to think about in theory but aren't usually exactly what we have in practice because normally we don't have a perfect correlation we have somewhat of an imperfect correlation or trend that we are observing so this time we'll look at a data set that has less information in it but is not perfectly correlated so our example we're going to imagine that X is now going to be the number of hens so we're talking about hens and why is going to be the number of eggs now note that if you're looking at two different data sets you might have some pre assumption some hypotheses that you are going to make from the data so for example if you're talking about hens and eggs you might be thinking that the hens are going to be the causal factor that's going to be producing the eggs but you do have a chicken and eggs problem I mean if you were the farmer you could buy eggs that would produce hens that would then make the eggs but you know you might usually generally think that the farmer is going to buy the hens first which are going to be you know producing the eggs or something like that so that's a question of the cause and effect kind of relationship remember that when we're thinking about the mathematical correlation we don't necessarily know if there's a causal factor or not and what that causal factor is we're just looking at the relationship with the mathematics so we're going to imagine that if we had three hens we've got the number of eggs 105 five hens we got the eggs at 185 and six hens the eggs at 201 is going to be eggs per year given the number of hens and then seven hens 345 now the the idea here would generally be well if I had more hens then I would you know produce more eggs you would think so you would think that there would be you know a causal relationship between them if we plotted these out if I just plot these four points noting that now that it's an easier thing to plot because we're looking at few data points and we can see kind of just from the type of data that we have that you would think that there would be a causal relationship between the number of hens and the number of eggs so now we're going to say if we were to plot this then and if I plot this in Excel I can just select the X and the Y the X will automatically plot as a default on the X axis here which is which is good for us we're using a scatter plot and then we can basically label this thing so you can see our four points so with three hens we have 105 eggs we had the five hens here with five hens we had 185 eggs and then with six hens we had the 200 eggs and with the seven hens we had the 350 now as you would expect we have a positive kind of correlation type of relationship we can draw a line a trend line in there and that is a useful thing to do because if we were trying to think about in the future whether or not we need to buy more hens if we want to have more eggs and we're trying to think how many more hens do we need in order to achieve so many more eggs I can't really look at these these different dots and try to figure that out I can kind of like say okay I'm going to put a dot up here somewhere but if I have a line then of course we can use the formula of a line to give an idea of what the approximate number of hens would be to produce the the next number of eggs now also again remember that usually we put the hens or we put the independent variable in this case the hens on the x generally and we put the dependent variable on the y so again I would imagine as a farmer you're thinking about how many eggs you're gonna make that you would go buy hens and then say how many hens do I need in order to possibly produce enough eggs however again you could think of it as well what if they were to buy eggs and then the eggs would make the hens but some roosters maybe roosters that you have to eat or something before they start roostering and then you but you so you could think about it that way too but but so that so but there it is so you now if I was to flip them what would happen what if I put the eggs eggs on the x and the hens on the y would I get a negative correlation no you're still gonna get a positive correlation mathematically you still have the the positive correlation showing here so now you've got the number of eggs so if I had this number of of eggs then you've got three hens right if I had so you can think of it in this fashion if I had around 100 and whatever that is eggs 180 I think it was then you can predict that you had you know five hens or in that fashion as well so you still have the positive our relationship you can still draw the trend line whether you put you switch is you switch out the x's or the y's okay so now let's do the mathematical kind of relationship we can say what's the mean of this so the mean calculation like normal is the average so if I take the average number of x's we can actually calculate this in the calculator because we don't have many x's 3 plus 5 plus 6 plus 7 divided by 4 is going to be the 5.25 and on the y's 105 plus 185 plus 201 plus 345 divided by 4 is going to be the 209 and then we're going to take the sample and the sample is going to be the formula in excel equals the stand I'm sorry the standard deviation not the sample of standard deviation of the sample standard Eve dot s of these two data sets we get the 1.71 that's the major of the spread and the 99.92 so once we have that we can do our calculation which is going to be here's our formula for the calculation which we're going to take each x minus the mean divided by the standard deviation so we'll do this in a step-by-step format so we're going to take each of the x's here are the x's and then do the same with the y's subtract minus the mean over the standard deviation which is basically the z score then we'll sum all of them up and divide by n minus one let's do that one by one we're going to say first we have the x's so let's do it each of the data points minus the x so we're going to say 3 3 5 and 7 minus x so we have also look at that over here the 3 here minus minus the 5.25 which is the mean we get to the negative 2.25 and then I take the 5 minus the 5.25 and I get to the point 2 5 I take the 6 minus the 5.25 and I get to the point 7 5 and I take the 7 minus the 5.25 and I get to the 1.75 so that's what we have here there's those three numbers and then to get to the z score we take those numbers and divide them by the standard deviation so all we're doing now is the next step we would say okay what do we do again we took the 3 minus the 5.25 divided by the standard D divided by 1.71 and then the next one would be 5 minus the 5.25 divided by the standard D 1.71 and so on and so forth so we we have those here's the second one approximately 1.15 and then we do the same with the y's here's all the y's minus the mean of the y so so we'd say okay the y's over here would be for example 1.05 minus the 2.09 boom and then we would take the next one 1.85 minus the 2.09 and so on and so forth so if I go over here we're going to say there we have it negative 24 negative 8 and then we take each of those and divided by the standard D so we're just would do then same thing if I took this first one 105 minus the 2.09 divided by the standard D 99.92 about 1.04 on the negative so there we have that and then we just multiply the z's together so these two together and that will give us then if I take this first one 1.32 times the 1.04 we get the 1.37 and so on so if I sum up this last column I get the numerator so I can then use my little table here and sum that up I'm going to put it in a table format here's the sum of this column I can actually do it in the calculator why not because there's only four numbers 1.34 plus 0.04 minus 0.04 plus 1.39 gives us about 2.77 rounding is involved then the denominator is just n minus one n is the number of items there's rows one row two row three row four row n minus one is going to give us three and then we have the numerator and denominator in the outer columns 2.77 divided by three is going to give us the 0.92 notice again the format that I have here of this formula kind of useful to put it in a table when you're working like an excel spreadsheets or something like that it's useful to see it this way you can build your worksheets this Wednesday this is the numerator which is this bit and then the denominator I'm going to do a sub calculation and I'm going to break that out as many sub calculations as I need and pull them into the inner column indicating it's a sub calculation with the colon with the indentation n minus one the result then bouncing back out into the outer column which I can call n minus one or simply in this case the denominator and then I'm dividing out just the outer columns 2.77 divided by 3.92 now I can see this and excel and use excel to do this with the analysis tool which isn't in excel by it's in excel but it's not turned on by default you can find that in the options we do that in the excel problem if you want to look at that in more detail but then in there I can do the correlation and just pick up this data set you have to have the data set next to each other so I just highlight that data set in excel and excel will then give me this prompt and I'll have to populate here's where the data set goes I'd have to check off the range or that I had the labels involved if I clicked on the labels and then tell me where I want to put it if I was to put it in excel and it'll give me something like this and I'm focused in on the x and the y which are intersecting here there's the point nine two one nine and so on that we got to here although we rounded it so this isn't dynamic however so if I change the data set this isn't going to change with it so it's not a great tool for your worksheet if you're making a dynamic worksheet but it's a great tool to analyze the data up front or to check your data kind of as we are doing here you can also use the the same data analysis tool and look at this descriptive data and I just want to point that out even though it's not our main point of focus here to give you this kind of descriptive information for the x and the y this is our general kind of statistics info you've got the mean you got the standard error the median the mode the standard deviation the sample variance the minimum the maximum the sum the count and so on I and this again is not dynamic it doesn't change as your data changes so it's a good tool to use as a preliminary analysis it might be the first thing you do before you build something out of your data set to get a feeling or an idea of what's going on with them and you can highlight multiple data sets and have it spit out or you can use it as a check figure for your data sets so just a quick recap here we're now looked at a at a perfect positive correlation a perfect negative correlation now we're looking at more of a realistic example where it's not perfectly correlated but you have a general trend this one being one where in advance you would expect to see some kind of general trend and by plotting out that trend you can get more understanding about the data sets and possibly giving you predictive power into the future such as how many hens would I would I need to buy by you know using the mathematical formula obviously that you know these hens we're doing we're doing great and then these purchases of hens were kind of slacker hens and they weren't up to you know the production line that that we were expecting from them but again laying eggs is I'm not laying eggs is difficult I would I would assume so I'm not complaint I'm not like you know it's tough work but you would think like the other hens were doing you know did a little bit better some you know then these hens but then this one is outside but then you have the trend line and the trend line can help you to predict to predict of course and and then of course we can see what the exact correlation is with our calculation here mathematically which will give you an understanding of how good that relationship is how reliable you can kind of be on using that you know basically the trend line possibly to make predictions you can do that with a formula calculation which is useful sometimes because as we'll see in future examples breaking this information out like this looking at the z-scores will often give you more information or could quite likely give you more information then simply using excel to spit out the z the correlation so but either method would be good and then of course graphing it when you graph it out you give that pictorial representation so we can look at the correlation conceptually we can might have an idea about what the correlation might be and then of course we can plot out it on a graph and see it pictorially and pick up the formula of the trend line which could be useful and then we can do a mathematical calculation of the correlation in this case having of course a positive correlation but not perfectly positive


We might be able to separate a graph by removing one edge, and any graph can be separated by removing all its edges. A key concept in mathematics and in life, if you can do it at all, there's a first time. And so we define the edge connectivity of a connected graph G, denoted lambda G, is the minimum number of edges whose removal produces a disconnected graph. More generally, if we're not starting with a connected graph, it's the number of edges whose removal breaks off one more component. Note that we may have to remove lambda G-specific edges. For example, suppose our graph is a tree, let's find lambda G. Since every edge of a tree is a bridge, removing any single edge disconnects the graph. So the number of edges we need to disconnect the graph is 1. What if we have a cycle? If we remove a single edge from a cycle, the vertices are still connected. But if we remove a second edge, they are not. So lambda Cn is 2. How about a complete graph? So a useful idea in math and in life, set your boundaries first. Let's find some bounds on our edge connectivity. Now remember, definitions are the whole of mathematics. All else is commentary. The graph we're talking about, Kn, is the graph with n vertices, each of which is connected to every other vertex. Since each vertex in Kn is connected to the other vertices, it must have n-1 edges instant on it. So we can definitely detach the vertex and disconnect the graph by removing these n-1 edges. So lambda Kn is less than or equal to n-1. Could it be less? Well, suppose we want to detach a pair of vertices. We need to have at least three vertices. And we need to remove n-2 edges from each vertex. So we could disconnect the graph by removing 2 times n-2 edges. Now, in order for 2n-4 to be less than n-1, we'd need, but we assume that we had at least three vertices, so in these cases n-1 is always smaller. And so it appears that lambda Kn is n-1. But it's conceivable we might be able to remove fewer edges, so let's prove it. Now, proof is not such a terrible thing. Remember, the purpose of proof is to review concepts, reveal consequences, and raise new questions. And if that's not enough, remember, if you don't find the flaws in your work, someone else will. So let's think about this. Suppose we separate Kn into two parts, g-1 and g-2, by removing our minimum number of edges. Since this is the fewest number of edges we can remove, then our subgraphs should have the maximum number of edges. This suggests they're complete graphs, but are they? Suppose at least one is not a complete graph. It doesn't matter which, so we'll say it's g-1. Since g-1 is not a complete graph, then at some point we've removed an edge in g-1. But since there's something joining vertices in g-1, it can't connect g-1 and g-2. Restoring the edge is the same as removing one viewer edge. So we have a disconnected graph that resulted from removing lambda Kn minus one edges from Kn, but this is impossible. So if we remove the minimum number of edges from Kn, we'll end with two complete graphs, kp and kq. Since we've started with Kn, every point in kp would have originally been connected to every point in kq. So to separate the two graphs, we need to remove q edges from each of p points. Alternatively, we could remove p edges from each of q points, but in either case we need to remove pq edges where p plus q is equal to n. So what's the least value of pq where p plus q equals n? We find the least value occurs when p is n minus one, which separates Kn into Kn minus one at an isolated point. So lambda Kn is n minus one. And again it's worth pointing out proof has value beyond verification. In fact verification should be considered the least important part of proof. In this case, it reveals new consequences. So if we wanted to separate Kn into kp and kq, we need to remove pq edges. And if we didn't separate it this way, we could have separated it more efficiently by removing fewer edges. Perhaps the most important aspect of proof is that proof also raises new questions. And in mathematics and in life, asking questions is important. In this case, suppose g isn't a complete graph but could be separated into kp, kq as disjoint subgraphs. Do we know anything about our original graph? And can we say anything about lambda g? We'll take a look at that later.