I hope you guys have gone through the assessment on your own and now we're just going to confirm if what you have done is it correct or not. So we're going to just go into it, welcome, without wasting any time because we only have one hour 30 minutes today. So we're going to do question by question and all that, the five assessments, they follow the same format. So if you know how to answer one, you should be able to answer the rest of them. So I'm only going to show you how to answer assessment A, but with your help as well. So we will have the discussions and then you should be able to go on your own and answer assessment B, C, D, and E on your own. Okay, so the first question is consider the following table with two variables X and Y and use the following information to answer question number one to question number four. So it means the same table, we will use it for question number one, two and three and four. Now with linear regression, you can save a lot of time, instead of calculating manually, you can use your calculator and put your calculator to the table and remember that the function for the straight line is Y is equals to or Y hat is equals to be zero plus B1X.  It depends on what kind of a calculator you are using, so it might be A or B or Y hat is equals to be A plus BX. So we know that for A it's the same as your B zero, for B will be the same as B1 and we know this is your, this is your intercept and this is your slope, that's what we know. So now the question is asking you to calculate the slope, which is this first question. What we do, we can put our calculator to state mode, depending on the kind of a calculator you are using, remember different people use different calculators, you need to know your steps. So I'm going to use case for my calculations for today. So if you have a sharp financial calculator or a sharp scientific right view calculator, you can use that, it's also followed the same concept. So the first step we do is to put our calculator to state mode. On this one my state mode is on button number three, then I press three and I can see there is number two, which looks like A, Y is equals to AX plus BX, so I'm going to press number two and I get this table. I'm going to start first by putting the value of X, which is easy by saying one equal, then I say two equal, three equal, four equal, six equal, eight equal, nine equal, eleven equal, and I should have one, two, three, four, five, six, seven, eight, eight values, there are eight. And now I'm ready to capture the value of Y. So I go to, sorry, I'll be on the calculator using the arrow from my PC. So then I go to the right, with the right arrow, and then I press the up arrow up until I get to number one. When I get to one, I can start capturing and remember, you need to make sure that you align the values. One needs to go with seven, so it will be seven equal, then you say, eleven equal, fifteen equal, eighteen equal, twenty equal, eighteen equal, twenty-five equal, twenty-one equal, and you should align. So I have all the values on my calculator, then you can press the AC button. Now I'm ready to do any calculations that needs to follow. So now I know I need to calculate B1, and I know that my B1 is my slope, so therefore it means I will have on my calculator, I will need to calculate it by placing the value of B, so that will be the capital letter B that I will see, the value of B. So to get to the value of B on your calculator, if you are using the sharp, the case, it will have the state function on button number one or button number two, depending on the type of calculator you are using. Those who are using the scientific calculator, once your calculator is on a state mode, depending on those who are using the sharp calculator, you will press the line, you will select where it says state mode, and you will press the line because you're going to be doing the regression line. And then you will capture the data by following the steps, we did the steps previous weeks when we were doing the linear regression. And once we are ready, calculate the slope, you're going to press shift, and then press the S-T-A-T button, and it takes you to reg, which is on button number five, and then you press five, and there are my values, A, B is on A is on button number one, and B is on button number two, so I'm going to press two for B because that's what I am looking for, and then I press equal side, and the answer I get is 1,376, which is that answer. That's how easy it is, easy, simple to do. Going to question number two, remember it says one till four, so we're done with one, go to two, two says calculate B zero, remember now Y is equals to A plus BX, which is Y is equals to B zero plus B one, we calculated B one, so now we need to calculate B zero, so it means we need to calculate one, so you can clear your calculator and go back again, shift, set five for reg, and we're going to press one for the intercept, which when I press equal and the answer I get is 9,333, because it's two decimals, so therefore it means the answer is option number one as well, A is our answer, going down to the next exercise, which is exercise three, it says calculate the coefficient of determination, now the other thing you must remember on your calculator you only have coefficient of correlation, once you have your R on your calculator then you need to press the X squared button so that you can get R squared, so now I go AC on my calculator, since I'm using the same data which is thought into the calculator, makes my life easy, shift and then we press one and go back to reg which is five and number three relates to R and when I press three and I press equal and that is my coefficient of correlation and with coefficient of correlation which is 0,86, I'm not looking for coefficient of correlation, I'm looking for coefficient of determination, I need to press the X squared button and when I press the X squared button and I press equal sign, the answer I get is 0,734 and that is the answer we are looking for, that is question number three, to answer question number four you go and you need to make a correction on question number four, this is for relation, it was just a mistake on this A, what is the value of your coefficient of correlation and we've calculated it before so since I can just press the square root to get back and that will get me back to my coefficient of correlation or I can go back and do the same steps, set one and I press five for reg and I press three and I press equal and 0,857 is the correct answer, that's how easy it is to answer the question but I just want to see if I can use the sharp calculator but it might take longer and now you're going to be seeing what is happening on my PC since I have so many things happening here, opened one of them, let's hope it will open, it does open, okay let's do this way, let's use the sharp calculator, so we'll use the sharp calculator but this calculator looks different to the rest of the other calculators that you have, so those who have the financial calculators, the values are on the patterns, you will notice that all your values that you are looking for, they will be visible for you on the pattern in green and you will just press the shift button, so now we need to take this to stat mode, you press mode and you press one for stat and then you will press one a plus bx, the other calculators on your one it will say line, instead of saying a plus bx it will say line and for my one I want that and it gives me the table which looks almost exactly the same as what you have, so I press one and I press equal and two so the steps on this calculator are almost the same as the the case your calculator, three equal, four equal, six equal, eight equal, nine equal, eleven equal, then I must go to the top again on the y, so right at the top so five seven equal, eleven equal, fifteen equal, eighteen equal, twenty equal, eighteen equal, twenty five equal, twenty one equal and I have kept all the values and then I can go on and off my calculator and my this calculator shows that I am in stat mode, now I'm ready to calculate any of the values, so since I am on the coefficient of correlation I can start with that but on this calculator it will give me all the values that I want by just pressing alpha and you press the step button and it will tell you whether you want to see the statistic or the regression and I want the regression which is button number one and all the values are here and if you can see here I have my r which is zero comma eight eight five seven which is the same and if I go back to the others this was coefficient of determination and you won't find on this one you will be able to see your coefficient of determination and there it is zero comma seven three four and that's what we select when you go up and I should be able to see my b one I went up too too much my b one which is my b it's one comma three seven and my b zero which is my a it's nine comma three three three as you can see some calculators are easy to to do the calculations from using them those who are using the math and you can ask me how do you do it all those who are using the financial time you can see if I can remember all the steps so to answer all the questions that we have done I guess one thing is late somewhere where I can write the steps for you so you're going to press the mode so this is for the sharp financial calculator or those who are using the d.a.l calculator so you first need to press the mode button then once you press the mode button you will press one for state and then you will press one for line and your calculator will be in state one mode now you need to capture your data so different calculator captures data differently so those with a d.a.l calculator you will use when you capture your calculator the st.o and the m plus button you will use both of those button those who are using your financial calculator which is a shop business financial calculator el 738 you will use the bracket x y and the n t button so when when we put in these values you will say one and then you will press I will start with the financial calculator then you will press the x and y button and then you will press seven and then you will press the e n t button so those are the buttons you press so you say one and then you press the x and y and then you press the e n t those who are using the gl you will say one and then you will say st.o button and then you will press seven and then you will press the m plus next to each other there are next to one another then you press the m plus and then you continue like that so you will say two and then you press that button and then say eleven and then press that then you go three x and y and you say fifteen and then you say that you do the same with the st.o until you captured all the values on your calculator now once you have captured your values on your calculator you must remember as well so every time you capture your value it will say data set one or data set two data set three until you get to data set eight once you are done then you can press the on and off button or the ac button which appears on your calculator once you have captured all your values you can just press the on on and c button now you are ready to capture the to uh to to answer the question you must also remember to write for yourself y is equals to b zero plus b one x it's very important that you write that so that you don't mix match the values and you must also write what your calculator looks like so on on both the calculator you will have an a small a plus small b x and since you are using different calculators as well you have to classify so those with the financial calculator you will you will press for a on the division side for b it's on the delete sign so this a is on the division sign and b is on the delete and this is for the shop for the case you're not the case you're the shop d a l so you will also do the same so you will have a plus b x which corresponds to b zero plus b one x remember that you will also have the same so on your one your a is on the it's on the open bracket and your b is on the closed bracket so when you press a for b zero for example to answer that question that we have now in front of us which is b one so you will press the alpha so yours you will press press alpha and then press either the closed bracket or the open bracket the same will press alpha either the division or the closed bracket to calculate the regression which is your r for both calculators r on on the g a l it is on the division side so you will press alpha division it will give you r and to get r squared you just need to press the x squared pattern for those who are using the financial calculator to press r it is on the closed on the open bracket and to uh to get to r squared you will need to press the x squared button and remember where your expert button it's on the dot so yours you will press second function not shift second function to get to the x squared it is second function and dot it will get you to the x squared button so you just need to know your calculator and you need to know how to use your calculator so that will help you to answer the questions like the ones we just did so I just summarized question number one number two number three number four for all the four calculators that I can help with if you're using any other calculator which is not the ones that I gave hints to like an HP page I don't know how to help you I don't also own a manual but I can find the manual and mail it to you you just need to let me know if you're using any of the calculator that I didn't explain today okay so that that is question number one two three and four now let's look at how we answer some of the questions in the exam so sometimes in the exam you might not get all like a table way you are given x and y values but they will give you formulas like this so when they give you formulas like this it becomes a little bit tricky because you cannot use any of the functions I just showed you need formula so we need to go and get the formula sheet from your exam your tutorial letter can open the tutorial letter and oh no your tutorial letter doesn't come with formulas I will need to open the past exam paper just give me a sec I must go to my download probably I should get one exam paper there there we go can open this one okay go to the end of the exam paper and I must look for the values that they are saying we must use so here is b1 let's go to the question ask calculate b1 that's what they're saying and based on this it says b1 is your sum sum x and y so I need to go find the sum sum x and y which is that formula the sum of x and y minus the sum of x times the sum of y divided by n that's what I need to write at the top so this is the sum x and y minus the sum of x times the sum of y divide by n divide by because I need to go back to do the bottom part which is the sum of x the sum of x is given by there which is the sum of x squared minus the sum of x squared divide by n this is the sum of x squared minus the sum of x everything squared divided by n so now is the matter of substituting the values so they've given you the sum of x the sum of y the sum sum sum of x squared and the sum of y squared we don't need to use the sum of x squared because this formula doesn't require yet so substituting into the formula we need sum of sum sum sum of x and y which is 1778 minus the sum of x is 75 I just want to go back to the formula I need to check okay I wrote them right 75 times the sum of y 225 divide by n how many they are the sample size of 10 so that is our n they tell us 10 is our sample size everything divide by in here I need to say everything divide by the sums x squared which is 610 645 minus the sum of x which is 75 squared divide by 10 now when it comes to this kind of complex calculation I rely on my case here because it has the fraction capability so but I need to get out of the state mode and go back to a normal calculator I know that I need to do my fraction since I'm and then at the top it's 1778 minus and I must do my top times 75 times 225 those but I can't go down to the denominator which is 10 then I must go down to the bottom one and say 645 minus so you will have to do this step by step so that you get the answer correct unless if you have a case you then you must also make sure that you you do it correctly so this is 75 squared oh before I do 75 squared I need to apply the fraction and this is 75 squared and I must go down to the denominator and find 10 and go to the end and then press equal and since my calculator is case you it gives me as a fraction because I was working with fraction I just need to press the sd which says change from one unit to a decimal or something like that and when I press that this means there are many other values following but since I'm only interested in the two decimals so I can see there if I round it off to two decimals the answer here will be equals to one comma one oh and that will be the answer any question let's see are you posting any questions or comments or queries or anything are you saying anything okay any question both are so good okay great no question yet ma'am just happy that you showed us how to calculate the fractions yeah so this is if you have a case your calculator with this fraction this fraction button if you don't have that then you will have to calculate this manually like if for example you are using the other calculator like the like the shop the shop calculator like this it doesn't come with the what you call the fractions so you will have to do the steps one by one manually so if I go back to the table so you will say you you will probably start this site before you even do the minus so you will say 75 times 225 equals and then divide by 10 and get the answer for the question and once you have the answer you write it down so this will be 1778 minus 16875 that's what you will write and then you go to the bottom you do the same you will go to the bottom and say 645 minus and then you say 75 and then you press the x-square button and say equal and then divide that by 10 and say equal and it will give you the answer and this is 562.5 uh 62.5 so if you have this kind of a calculator also you can use the change it changes from a fraction to a depends on the type of a calculator as well so now I have it as a decimal now I can just calculate this so you go to the top and say 1778 minus 16875 equal and you will get your answer is I think my calculator didn't calculate right let me just double check why am I getting a negative value 725 times 225 equals 16 oh it didn't divide by 10 so it should be 16.6 1687.5 sorry not not what I have I'm sorry I see that now it was 0.5 so this will be uh 1778 minus 1687.5 equals okay it will be equals 90.5 divide by and we divide by 645 minus 562.5 equals 82.5 and then we can take 90.5 and divide that by 82.5 and we get the same yes so it might take you longer if you have those kind of other calculators okay moving on to question number six if this was five oh six it says calculate b0 so we've calculated b1 if we go to the formulas if you look at the formula it says for b0 we need to use the mean of y minus b1 times the mean of x so we write the formula down it's sorry for b0 it's the mean of y minus b1 times the mean of x we've calculated b1 remember that that is the answer we got so we're going to use that and we know what the mean of y is because we are given the mean of we're given x and y so we can calculate the mean of y will be the sum of x the sum of y it will be the sum of y divide by n and the mean of x will be the sum of x divide by n that's all what we need to do so we know this is 75 divide by 10 because they are 10 and this will be why am i using the wrong means this is y is 225 and this is x divide by 10 so to calculate that i can just put it to the calculate times 75 divide by 10 which just gives me 7.5 so this will be 7.5 minus 1.10 times the mean of x which is oh gosh again using wrong values add the wrong place so this will be 7.5 that will be 20 22.5 so now you just need to solve the equation so this will be 22.5 minus open bracket 1 1.10 times 7.5 close bracket equals and change the values 14.25 i think it's because i used 1.1 let's use the whole value that we got for which was 1.09 because i dropped off some of the some of the decimals that's why i'm not matching it 100% so if i would use i then write the whole value that i saw e to us we can calculate it quickly because we have the answer was 90.5 divide by 82.90.5 divide by 82.5 equal okay this one keeps only four decimals let's see if we use the four decimals the three decimals sorry so this will be 1.096 so if we do it that way then we'll have it's basically recurring on 9 6 9 6 9 6 yeah yes 22.5 minus into bracket 1.0 9 6 you're saying it's 9 6 9 6 9 6 correct okay i can leave it at 5 decimals it's fine multiply that with 7.5 close bracket and there we go so if you if you cut short the decimals you might not get the right answer because you are dropping off some of the important decimals or chopping off some of the important decimals so you need to keep all of them or you need to keep at least maximum of five it makes it easier oh that is question six going to question seven which also still uses the sums sums some measures so question seven they are asking us to calculate the coefficient of determination so now we need to go and find r squared an r squared that is the formula which is the sum of the sum sum square regression divided by the total variation and the sum square regression that is the formula which is very long i won't remember it even if i want to so let me write it down then i will go write it on the other side it is b0 b0 sum of y plus b1 sum xy minus sum y squared divided by n okay go write it all up and i must also find the sum square the total variation the sum square total she's total variation which is given by your sum y squared minus the sum y squared divided by n okay go back there you need to write this formula down which is r squared is equals to and it was b0 times sum of y plus b1 sum xy minus sum y squared divided by n everything divided by your sum y squared minus your sum y squared divided by n substituting b0 we need to go back to our formulas now b0 as or b0 is right here in front of us it's 14 yeah 14.2728 i'm going to four of them that i see in front of me sum of y which is times 225 plus b1 we said it was 1 comma 09696 times our sum sum xy which is 1778 minus the sum y which is 225 225 divide by 10 everything divide by take it back up a little bit sum y squared sum y squared five seven seven three you must pay attention to the formula don't get confused with sum y squared and sum y into bracket square two different measures minus sum y is 225 divide by n 10 oh we need to square this it's 225 squared okay so now I will do this one step by step I prefer to use the this one because this can keep all the decimals oh so 14.2728 times 225 equals 3211.38 right okay then one point zero nine six nine six times 11 is my delete okay next place one seven seven eight equals one nine five zero point three nine four eight eight minus 225 squared equals divide by 10 equal 5062.5 I think if they give you the table it might make it easier in the exam than when they give you all the sums sums to calculate it takes longer unless if you have the case you'll calculate or keep on going to the mode button okay so at the bottom we have five seven seven three minus we calculated this I'm not going to repeat it again is the same as what we did which is 5062.5 which is the same as what we calculated there so I'm not going to repeat it so the top part three two three two one one point three eight plus remember botmas addition and subtraction name the same priority we can work from left to right so I can just add all of them and subtract whatever it's on the other side one nine five zero point three nine four eight eight minus five zero six two point five equals the entire gate here is nine point two seven four eight eight divide by five seven seven three minus five zero six two point five equals seven one zero point five now we need to apply the division 99.27488 divide by seven one zero point five equals since we are rounding off to two to four decimals let's see that will be let's try to be rounding off to three decimals that is the three decimal the number to the right is bigger than six so bigger than five so we add one so that will be zero that will be four and that will be one so therefore it means the answer is option number E okay so we did we did the coefficient of determination now we need to do coefficient of correlation also coefficient of correlation I will say in my own view if I have coefficient of determination which is r squared I can find coefficient of correlation which is r I can take the square root of r squared and this will be the square root of zero comma one four zero that I have there or I just take the answer as I have the answer here and press the square root and press equal because it will give me the square root of the answer and I will have my answer as option number eight that's the easiest way of doing it instead of going and using the formula and this is my lazy what do you call that my lazy head at this point because I feel like I've been doing so many calculations my head is spinning but if you want to use the formula this is the formula so this is the formula to calculate the coefficient of correlation which takes the covariance of your x and y values divided by the standard deviation of your x value and the standard deviation of multiplied by the standard deviation of your y so these are the formulas you will need to use in order to substitute into the also very very huge formula to use so I'll have to write them down even though I've shown you the shortcut I still in case in the exam they don't ask you to calculate the coefficient of determination but they ask you to calculate coefficient of correlation and I haven't shown you it will be my fault so let me show you how to calculate it one over n minus one times the sum of x y minus the sum of x the sum of y divided by n and because we're multiplying so it will be one over n minus one sum of x square minus the sum of x square divided by n and I can repeat the same for the y I don't have to write the formula again so how do we then do it okay let me remove this and use the formula so now we need to calculate our r which is one over n minus one times the sum of your x and y minus sum of x times sum of y divided by n close bracket everything else divide by the standard deviation which is one over n times the sum of x square minus the sum of x square divided by n times let me use a multiplication because then I'm going to use the multiplication because I need to repeat the n minus one times the sum of y square minus sum of y everything squared divided by n so that is the formula now substituting into this formula will be one over 10 minus one times the sum of x y it's one seven seven eight minus the sum of x and y sum of x and sum of y which is 75 times 225 divided by n everything else one over 10 minus one times the sum of x square is 645 minus the sum of x 75 squared divided by 10 multiply by one over n over one over 10 minus one times the sum of x y square it's five seven seven three minus 225 over square over 10 some of these values we've calculated them before you have them in front of you so that I don't have to repeat them again and again and again so this will be one over nine times and I feel like we did this one one seven seven minus didn't we do it somewhere we did it here one seven seven eight minus 75 times 25 minus da da da we did it here and we found that it was 90.5 so we're just going to take 90.5 I'm not going to recalculate everything so whatever it's oh sorry this is divided by 10 this we did calculate we found that it was 90.5 not divided by sorry it's because I'm running out of space I'm gonna save time so this I can multiply by one which is 90.5 divide by 10 divide by 10 minus one it's nine so I can have it like that divide by and I can do the bottom the only thing that I we didn't calculate is this the x one for the y I'm also going to just go grab the y then we did calculate it it is this one at the bottom which is 5773 minus 22 square divide by 10 we did calculate it and we found that was equals to 710.5 so times 710.5 divide by 9 because I'm just going to divide by 9 on this so this is divide by and we just need to calculate the x for x let's do that we'll be I'm going to revet back to k show because it makes my life easy what happened to my k show now got it back so this is 645 minus 75 square divide by 10 82.5 so this will be 82.5 divide by 9 oh I'm going to use k show so I'll start with the first bigger bracket fraction then at the top I must also do a fraction which is 90.5 divide by 9 divide by 9 then I go to the bottom I must do a fraction and it must be 82.5 divide by 9 and I must go to the end then multiply this by another fraction which will be 710.5 divide by 9 as you can see this is the same as what I have here I could have included all this the first step into the calculator and then press equal and I would get the answer so I need to go to right to the outside and I press equal change the value and the answer I get is not the answer that is there it says it's 0 comma 013 there is no answer like that somewhere somewhere we got it wrong so easy to calculate all of them so let's let's use the calculator for its papers okay so I'm going to only do the top part and then I will do the the second part and then do the third part and get the answers I'm not going to do all of them at once in one shot so let's see I'm going to do one by one so let's start with the top part the top part which is sum sum x y and I substitute right x and y is 170 and sum x 75 times 225 we substitute it right this is 645 minus 75 squared divided by 10 we substitute it right 5773 it's y squared sum of y squared 225 squared 10 okay so let's do the top part fraction one over 10 times not there go out multiply by actually I don't even have to put the multiply can use the bracket which is 1778 minus fraction open bracket 75 times 225 close bracket go down 10 and then go out and close my bracket sorry ma'am one over 10 is minus one minus oh yes yes yes right to the end to close the bracket close the bracket and then press equal do the change okay so this is way different to what I had previously which is equals to the top part is equals to 10.055 I don't know how many 5s 1 2 3 4 5 6 7 2 3 4 5 I'm going to stop it right there divide by and then I will do the the other one one divide by 10 minus one go out open bracket 645 minus 75 squared fraction 75 squared divided by 10 close bracket equal 9.16666 I'm going to stop it today with seven there are enough multiply by and then we do the same one divide by 10 minus one open bracket 5773 minus fraction 225 squared divide by 10 close bracket equal times 7894444 78.4444 okay so now we can use fraction 10.0 5555 divide by 9.166667 times 78.98444444 which is the same as what I had previously which is not on the answer sheet and which is not what we got when we were multiply when we convert remember if I use this I get that is the answer if you take the square root of 0.140 equal 0 comma 37 so it means the formula that we are using for the coefficient of correlation I don't think the formula works well I don't think that is the right formula let me just sample check where did we go wrong oh sorry yes my bad this is the variance we need to take the square root of the answers sorry my bad now I know where we going wrong when we get to sorry we need to fix the our formula this we need to take the square root and that should be the square root so they both have to be the square root so when we get here we need to take the square root of this answers all of them is to be the square root you just need to fix that part the bottom part so let's do that you just need to fix the bottom part only the bottom part and say the square root of 9.166667 then go out with the multiplication then do the square root again of 78.9 to go out and press equal yay there we go answer is number one all we just need you miss one thing you get everything wrong so we needed to put the square root because the question was that this is the variance and the formula uses the standard deviation the formula we used was for the variance apologies for that and I think we can call it the quick for today and then tomorrow we will continue and do the last one which is the interpretation oh let's see we can actually do that and then tomorrow we do as assessment two we have eight minutes left so we can still do the last bit so with question number nine it says consider the regression equation they gave you the regression equation which is y is equals to be one x so this is y is equals to be one x plus b zero and they also give you the coefficient of determination which is r squared all you need to remember is the coefficient of determination tells you whether the total variation is of x explain what happens to y that's one you need to remember then the other thing you also need to remember is with the coefficient of determination you can find the coefficient of correlation which tells you the strength so both r squared and also the value of your b1 will tell you what's happening with your data so since it's positive it says with one unit increases it will increase by that much so if if we increase by one unit so it means if we replace x by one what will be the increase in the value of your y v that's all what you need to also know so if we go through each statement remember the statement says choose which one is correct number one i said the variation or the coefficient of determination tells you what total variation in the value of y explains what happens to the value of your y that's y sorry the total variation in value of y can be explained by what is happening in the values of your x something like that so if you remember that so how we interpret the coefficient of determination we say if it 50 percent will say 50 percent of the variation in y in the values of y are explained by the values of x that's how we explain it so now let's read each statement and make sure that we understand which one might be the right one so i'll actually start at the top so number one it says 13 percent 13.97 percent of total variation in x can be explained by y we are not predicting x we predicting y so we cannot explain what happens in x by it is in the value of y so it needs to be vice versa this needs to be there that needs to be there so the total variation in y can be explained by the variation of x or the values of x so then it means number one is not correct number two the value of y when x is equals to one is equals to that and that is what i explained so if we substitute y is equals to 1.1 if we substitute by value of one what will be your value of y 14.27 we can take your calculator and calculate that and see how much it will be so let's do that it is 1.1 times one is one times one it will be one plus because that is an addition plus 14.27 equal and change the value change the value 15.37 so when the value the value of y is when x is equals to one is equals to that that is correct because we just calculated it when x is equals to one the value of y will be equals to 15.37 and you can stop right there you don't even have to continue but just for interesting a unit increase in the values of x in a decrease in the values of y since the slope is positive it can never be a decrease it can only be an increase so it means if a unit increase happens in the values of x there will also be a positive increase in the values of y and we just saw that because if x is zero y will be 14 so if i increase by one it will increase to 15.37 if i increase by two if i increase the value of x by two it will also increase it will not decrease the value of y when x is equals to one is equals to 14.7 we just did this so this is not correct remember some of them we just did them now now so we know that that is not correct that is not correct that is not correct because this we calculated it we knew that it was 15.7 when the values of x is one it should be 15.7 it will be 14.27 only if x is equals to zero a unit increase in x is an increase in y by 14.27 it cannot be by 14.27 because it's positive and the slope is 1.1 so the unit increase will also have to include the value of your slope so this also is incorrect and that's how you will answer the question we have one minute and that one minute i can just use it to answer the last press the last question the last question is about coefficient of correlation and coefficient of determination now if you look at each statement it just says if coefficient of correlation is zero what will be coefficient of determination so we know that coefficient of correlation is r coefficient of determination is r squared so it means if this is one therefore if i take x squared of one this will be equals to one if i take if my r squared is zero this will also be zero but if my x my r is 0.36 what will be my r it will be the x squared of 0 0.36 that's all what they want you to do so you just take the value and take the square the square of it so 0.36 i'm just making an example and you press the x squared and say equal and that will give you zero comma one two let's say one comma three and that's all what they want you to find to check so yeah it says when a coefficient of correlation is equals to zero then the coefficient of determination will be equals to zero and the question says which one will be incorrect we've dealt with this one and i did it i said when it this is zero this will be zero so that is this is correct actually in terms of what we're looking for we're looking for the incorrect one but we know that this is correct when the coefficient of correlation is one we dealt with this one as one as an example if it's one so if i r is one therefore x squared not 11 if r is one then x squared will be equals to one so this will be correct when the coefficient of correlation is minus one so let's say is minus one then the coefficient of determination is one so let's take the x squared of minus one no man sometimes the calculator doesn't recognize that that is a one sum so you need to put it in bracket when you do the x squared so minus one squared minus one equals to one so that is also correct number two it says when the coefficient of correlation is 0.5 the coefficient of determination is 0.5 so you can test that 0.5 squared equal to 0.25 0.25 so that is the incorrect one the coefficient of correlation is the square root of your coefficient of the coefficient of correlation is the square root of the coefficient of determination yes because no yes because if i have coefficient of determination and i want to find r i will have to put the square the root of proficient of determination so that I can calculate my R. That means that is correct. The only one that is not correct is D. And that is chapter 11 in a nutshell. Tomorrow we will do self-assessment B together. Now, since today I was the only one mostly talking. So tomorrow you will be the one doing the exercises. Because now I've shown you how to do it. Then tomorrow you can do assessment B. All the assessments have the same question, like they are almost the same. So for example, question number one, question two, question three and four, you will be getting a table. We'll be asking you to calculate B1, B0 coefficient of termination, coefficient of correlation. They are all the same. Question five, six, seven, they will be asking you to use the sum square measures to calculate. And then the last two questions, they will just be theoretical questions on coefficient of determination and coefficient of correlation. So for two hours, you should be able to do the exercise. I will see you tomorrow when you assessment B. Then once you are done with assessment B, you can do assessment C, D and E on your own because it follows the same. You have all the skills now, it follows the same. So take a chance, do all of them when you have time. Then I will see you tomorrow. Thank you guys for coming through. If you have any question, you can ask. If not, then we can call it a quiz. Thank you so much, good night. Thank you, bye. Good night all. Thank you for everything, good night.


is an under provision in England, so have you lobbied the UK Government? How have you got on with that? We have been in close contact with our sister officers in England and Wales and with legal and human rights organisations in both jurisdictions. In fact, and I should have said it at the start, the position that we have taken in relation to these regulations was informed very, very strongly by a round table that we conducted shortly after the regulations were published, and that involved children's commissioners' offices, advocates, solicitors from both jurisdictions and human rights organisations. The view reflected in that round table was absolutely unanimous about what needs to change around the regulations and how strong they are. Really, it is the Scottish Government that has the contact with UK Government ministers that needs to make that argument for additional provision. It is out with the mandate of the Children's Commissioner in Scotland to be telling the UK Government how to set up its own care system. Our sister office in England has been very strong on this over the last few years. They have conducted a lot of research. The previous Children's Commissioner was very vocal about it. The courts in England have been very vocal about it, both in terms of the High Court and the Supreme Court. Lady Black, again in the retake case, referred to matters having been brought repeatedly to the attention of those whose job it is to do something about it. This is not an issue that the UK Government is unaware of, but what we have in front of us now are Scottish regulations, which are very much within the mandate of the Scottish Children's Commissioner to comment on and to effect. We have the Education Committee here, and you are here in front of us. Is that a route to the Education Select Committee at Westminster? Obviously, it is ministers that are going to make that decision, so it is to get to them. We are very happy to provide evidence to the Education Committee at Westminster about that. It is an issue that has come before the Parliament down there. As I said, this is not a new issue. This is something that the courts and the Children's Commissioner in England have been lobbying on and advocating for for some years now. I am sure that my good friend Robert Halfon will be very pleased to hear from you and others. Does any other member of the committee wish to say anything at this point? Well, thank you to Nick Hobbs and Maria Galley for being with us in person to give this very important evidence to the committee. I wish you very pleasant rest of the day. The public parts of today's meeting is now in end. We will now consider a private, a final agenda item in private, and so can I ask members attending virtually to reconvene on Microsoft Teams. Thank you and good morning to everyone.


All right, you just brought up Sam Laporta. He's been a revelation for these Lions, of course. We typically don't see like rookie tight ends super lighting it up. I know we have some footage for you. What makes him so special to you? Yes, just his instinct for the game, the instinct to be able to catch the ball. He can catch the ball and the run very, very well. Like I said a little bit earlier that he's definitely the steal of the draft. He's got speed and he's just savvy out there. He's a savvy guy and what's impressive is he's only a rookie. I think he has beaten the, if I'm correct, he has beaten the record, the tight end record for most amount catches in the first three games of a season for a rookie. And I think he has 18 catches already.  He's gonna be one of the best tight ends in the upcoming years in the NFL. And he's just super, super savvy. He just has that football instinct. How do you, like, what is it about him that you see? Like, how can you make that call right now? Just the way that he runs his routes, you know? He's just very instinctive. That's what you gotta be. That's what makes him a good football player. It's like he goes out in the field and he doesn't think, he just reacts, you know?  So he's a good player. He was a second rounder, 34th pick overall. I think he should have probably been the first tight end taken in the draft. And Jared Goff is just gonna keep feeding him. He loves him.


Hi, I'm Zor. Welcome to Unisor Education. I would like to start a new chapter in this energy section of this course. This chapter will be dedicated to light, light and energy which it carries. Well, first of all, this lecture is part of the course called Physics for a Team presented in Unisor.com. I do suggest you to watch this lecture from this website. You just have to go to Physics for a Team course, then energy, and that's one of the topics which is presented on the next screen. The reason for this is that, again, as a course, it has certain logical sequence, so there are prerequisites for this particular lecture. And also there is another course called Maths for Teens on the same website. And math is very important for physics. I mean, especially calculus and vector algebra, they are used everywhere in physics, so you definitely have to be proficient. And if you are not, take the Maths for Teens course on this website. The courses are completely free. There are no ads, so your attention will not be distracted at all. Okay, now back to light. You see, the problem with light is it's really a very difficult subject from the physics perspective, primarily because people did not really understand clearly what light actually is. You see, the Newtonian mechanics was primarily dedicated to like plain objects, which we can observe, and we can measure them, etc., etc. And it's all related to matter, something which we can feel, we can look at, etc. Now, the first problem with light, for instance, the light of the sun, is that there is no medium between sun and earth. How this light actually travels in the vacuum. And on the top of this, we are talking about energy which it carries. How can it carry energy if it doesn't seem to be any material substance in between sun and earth? Well, some time ago, people were thinking that there is something in between called ether. But then they basically completely negated this particular theory. There were other theories. So that's what we are talking about right now. These evolutions of different views onto light. So let me just start talking about light as carrier of energy. Well, first of all, I would like to state that light carries energy. Now, why is it obvious? Well, primarily because when you are leaving something under the direct sunlight, it will warm up. Now, warm means kinetic energy of the molecules inside the object. So, who provides this kinetic energy if it's just lying under the sun's light? Well, the light. So, light carries energy. Now, there is a very interesting experiment. There is a device called radiometer. And here is how it's arranged. So you have some kind of a axis and you have four perpendicular, small, very light rods or whatever. And you have a little plate on each rod. Now, this plate has two sides. One side is silverish, like mirror kind of thing. And another is black. So black absorbs light, as we know. And the silver surface reflects the light. Now, if you will, now, and it's supposed to basically rotate in this point. So, and also it should be in the vacuum. So, this is called radiometer. And I have a picture in one of the notes for this particular lecture. And on YouTube, which I have a reference to, by the way, in the notes, you even have a video, what happens. So, if you will put this device under light, these plates will start rotating. And if you will put it back in the darkness, for instance, it will start rotating, not under direct sun. Now, why? Well, obviously, if we put it under the light, it starts rotating. It means light has energy, obviously. So, why is it rotating? Well, primarily because the silver side of each plate is reflecting light. The black side is absorbing light, which means it absorbs the energy, which means the molecules on the surface of the black side start moving faster. So, if you have, this is your plate. This is a silver and this is black. So, the molecules here on this left side becomes agitated more because the sunlight energy is absorbed. And they're heating more from this side than from that side. And since these plates are arranged that the faces which are silver, they're all on the same side of the plate. So, the rotation starts as a main motion of this construction. Now, another proof that the light has energy is that we see it, we see the light. Now, what does it mean that we see the light? Well, obviously, light comes into the eye. It somehow affects certain receptacles over there, certain cells. And they are, again, being somehow agitated and they're sending electric signal to the brain and that's how we see the light. So, again, without energy, it would be impossible. So, I think I have convinced you that light carries energy. The question is why, how much? That's a very big question, actually. And people were suffering with this issue for a very, very long time. Well, and still suffer. Okay. So, let's just go back to the previous lectures related to gravitation. Now, we were introducing the concept of gravitational field. It has certain force, it pulls and it has, therefore, certain energy. But if you're just putting into an object into the gravitational field, if it doesn't move, it still has a potential energy. If you let it go, it will go towards the source of gravity, converting potential energy into kinetic energy. Now, so the concept of field is very important. What is gravitational field? It's a special kind of a state of a space. It doesn't have any material substance which actually carries the gravitational field. This is certain domain of the space which has certain forces and it has certain energy in it. Exactly the same thing we were talking, we can talk about the light. There is a concept of electromagnetic field. We will talk about electromagnetic field in details when we will talk about magnetism and electricity. However, as of right now, you just probably have to accept my word electromagnetic. This is a field and the light is going through this electromagnetic field in the same way as gravity goes through the gravitational field. I mean, they're completely different fields, obviously. But the concept of non-material substance, some kind of a special kind of a space which actually is a carrier of the energy and the forces, that's what the field actually is. This is just a separate kind of a field, electromagnetic field. Now, it was actually very difficult for people to come up with this particular idea and to prove that this is really electromagnetic field. And there is a lot of very interesting historical books and articles about this, how the whole theory of light was developing. So, from the very simple kind of a concept that there is substance, material substance called ether and light is just the waves inside of that ether in as much as you have the water waves on the surface of the water. Well, that was an idea. But then again, it was kind of disproved differently and certain other ideas were introduced. And electromagnetic field as a carrier of the light is the idea which is considered to be right now the most important kind of a thing and true to the moment, let's put it this way. And the light is basically the waves in this electromagnetic field. We are replacing the term ether which is kind of a material substance with the word electromagnetic field, but we are still retaining the term waves. So, the light is basically the waves of electromagnetic field. Now, the wave has certain parameters. What's the most important parameters of the wave? Well, there are basically two. If we imagine the wave as just a sinusoidal kind of oscillations, let's say waves on the surface of water, right? So, what's the most important characteristics? Well, one is called amplitude. Well, that's basically the deviation from the neutral state. So, on this, this is basically amplitude from this point to this point. This is amplitude. Now, the greater the amplitude, well, the more energy this wave actually carries, right? Another very important characteristic of the wave is frequency. So, you can have these waves with this amplitude or you can have this wave with the same amplitude. So, there is a frequency. Now, what is frequency? Number of oscillations per unit of time. It's measured, by the way, in the units called Hertz. Hertz is one Hertz is one oscillation per second. So, if we observe the waves on the surface of the water, we can always check how many of these waves are moving per second. So, that's what basically our frequency actually is. Now, here is a very important thing, energy. We are talking about energy, right? So, it's kind of obvious that the amplitude of the waves is directly related to the energy. Well, it's less obvious what is the relationship between frequency and the waves and the energy. Well, let me put it this way. If you know something about photo labs, which were developing the old-fashioned film, not the contemporary digital one, but the old one, with chemicals, etc., etc. So, you probably know that usually these labs were lit with a red light. So, why red light? Why not white? Well, for obvious reason, we don't want to overexpose our film, right? So, it means that the red light doesn't really expose our film. So, what does it mean? It means that the red light carries less energy than, let's say, white light, right? Less energy because, obviously, again, the film developing the whole procedure was based on the properties of the light to somehow affect the chemical composition of the film. And then, using certain chemicals, we can make it stable and the image actually is retained on the film. But the red light doesn't do this. So, red light, the only explanation you can have is that the red light doesn't have as much energy to change the chemical composition of the film. Okay. So, what's the difference between red light and white light? Well, we all know what is the rainbow, for instance, and we all know that white light is actually a combination of many different monochromatic, as we are saying, lights. Red is a color, as well as green and blue and violet, etc. So, it looks like the light has certain characteristics which we, the people, view as color. Again, why do we have different kind of understanding, different view and different lights? Well, again, because certain lights are affecting our receptacles in our eye, our cells, which are responsible for accepting this light, they affect it differently. And what's the difference? Again, energy. So, certain lights are affecting more, certain less. And it appears that something like the red light, it affects less than, let's say, green light. Or white light, which is a combination of red, blue, green, etc. So, what exactly is the source of this difference? What's the difference between red and green? Well, yes, the energy which they carry. But from this perspective, from perspective of amplitude and frequency, amplitude is basically the brightness of the light, right? So, if the brightness is exactly the same, what's the difference between red and green? The frequency. And it was actually determined through many different very sophisticated experiments that, yes, every different color of light which we observe has different frequencies. And red has the lower and the violet has the higher frequency. Actually, right now we know that red is something around 0.4 times 10 to the 15 hertz. And violet is something like 0.7 times 10 to the 15 hertz. So, 10 to the 15 is more or less where these lights which we can observe are concentrating. Now, but we also know, well, at least you remember, like ultraviolet lights or infrared lights, right? Infrared, for instance, is something which our remote controls are using to control the TV. UV ultraviolet lights is something which we're trying to protect our eyes using special sunglasses. Now, why do we have to protect our eyes? Well, again, violet has the highest frequency and therefore the highest energy. Ultraviolet has even more. So, my point right now is that not only the visible light is basically a manifestation of the waves of electromagnetic field. There are some other electromagnetic field waves which are not really perceived by our eyes as visible light, but nevertheless they exist and we can use them. Well, again, significant number of important experiments and technical developments basically have established that we have the whole set of different phenomena related to electromagnetic waves, waves of electromagnetic field rather. Now, the most energetic with the highest frequency, electromagnetic waves, are related to so-called gamma rays which we're actually getting, we're bombarded from space and our atmosphere is, well, partially shields us from these rays. Now, then there was a discovery of X-rays, if you remember, by the person called Rand-Gen. X-rays are also electromagnetic waves of the frequency less than gamma rays. Now, this is on the level of 10 to the 24 hertz. So, X-rays is less frequency. Then we have ultraviolet lights. Still, we are not seeing these, but gamma rays actually, or X-rays actually, you know, it can actually damage because they're very energetic. That's why when we are getting an X-ray in the dental office, for instance, they usually cover with some kind of a protective piece, all the body, right? Now, ultraviolet light, it's not really adversely affect our body, but it can affect our eyes and that's why we're trying to protect against it. Well, then we have the visible spectrum. The visible spectrum is from violet down to the red and then even less frequent oscillations have infrared. Then we have microwave. Yeah, the regular kitchen microwave, it's also using electromagnetic fields. Magnetron is something which is inside, which is a source of electromagnetic field of this particular frequency. And then we have radio waves. Now, radio waves are also different. We have AM, FM, we have long, short, medium range waves and the longest waves, the longer, obviously, the less frequent these waves are. They have actually about like three or four hertz, three or four per second. So you see from the range of different wave frequencies of electromagnetic field are from something like this, three, four hertz to 10 to the 24 hertz. It's an extremely wide range and obviously extremely wide energy which they carry. And again, we will talk about how to measure it, etc. Right now, this lecture is only kind of introduce you to a concept of light. And everything, whatever people have learned about light, which I was just trying to convey right now, turned upside down with development of the quantum theory. Well, I am not the person who can explain what is quantum theory is right now, at least not at the moment. But believe me, it was a revolution. I mean, the light also, electromagnetic theory, electromagnetic field theory of the light still is the one which we are using as the theory right now. However, quantum mechanics and quantum theory of light brought a little bit more to this. Apparently, according to the quantum theory, light is not really like this plain sinusoidal wave, like we have on the, let's say, on the surface of the water. It actually comes in packets. And it's difficult for me to explain right now what packet is, but maybe you can imagine it as high frequency and then low frequency and high frequency again and low, maybe.  So you can view the packet, for instance, like this one. And only these guys are actually carrying the real energy, nothing in between. Now, this packet is called photon. So there is a concept called photons. And this is the most elementary, so to speak, part of light which still is the light. Remember what molecule is? The molecule is the smallest piece of matter which still carries the chemical characteristics of this particular matter, like molecule of water or molecule of nitrogen or something. Again, the photon is actually the smallest unit. We can measure the energy which is carried by the light. Well, anyway, it seems to be representing certain other view to the light, the view to the light as the number of certain particles which are flying.  Let's put it this way, because if you have something like this pulsation or, I don't know, maybe it's a pulse or whatever. Anyway, packets. Each packet, while being still a wave, might be viewed as a particle. And this is the contemporary view towards light. The energy can be measured for one particular photon, of particular frequency, obviously, etc. So this is the smallest part of the light. There is no smaller part. Let's put it this way, because, again, if you kind of try to think about the waves in the water, you can basically divide it as much as possible. It will still be a wave. But here, we have this smallest part, like in matter, we have a molecule. Now, in light, we have this photon, which is the smallest part, a smallest particle. You can say it's like, it behaves like a particle. Let's put it this way.  And basically, the number of photons is the characteristic of the brightness of the light. Now, the frequency each photon is oscillating is the frequency of light. So these two characteristics are expressed in a slightly different way through the photons. Now, again, I will not go into any details of the quantum mechanics, but I will still employ a regular wave-like properties of the light, which is amplitude and frequency. And they basically define the light. Maybe sometimes I will do something related to characteristics of the photons, but that's not right now part of this particular lecture. So, again, this lecture, I wanted to introduce you to a concept of light. And I don't know if I succeeded, but I wanted to impress you with how difficult it is to really go into the very root of what actual light is. It was a very painful kind of process of development of this physics of light. And certain mathematical calculations, which are related very important and very involved mathematical calculations like Maxwell's equations. So anyway, and then theory of relativity actually also related to light, which says the speed of light is the maximum speed possible to achieve. So all these are components of contemporary view on what is actually light. And again, my purpose was to basically convince you that light as a source of energy as a carrier of the energy is a very sophisticated object of research and development and science. But there is something which we call contemporary level. So that's it. I would suggest you to read the notes for this lecture because they might contain something which I have missed. And if you're interested, actually, there is a video in the notes for this lecture. There is a video of how radiometer is working. So you put it in light and it starts spinning and you put it back into the darkness, it stops. So that's a very interesting experiment just to show you how energy is carried by light. All right, that's it for today. Thank you very much and good luck.