00:01
Hello students, a random sample of 11 students produce following data where x is the hours to spend per month playing video games and y is the first semester grade out of 80 points.
00:13
So data presented below in the table of values and we need to find the equation of regression line, right? so how can we find it? so according to the formula of regression line equation, so if i write regression equation equation of y on x is y minus y var this is basically mean equals to r sigma y divided by sigma x x x minus x war right and this r sigma y divided by sigma x can be written at summation of x y divided by summation of x squared now let us calculate all the values to solve this equation right so here if i calculate x bar is summission of x values from i equals to 1 say n and this is x divided by n.
01:10
So total values are 1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 9, 10 and 11, right? and if i sum up all the values, what will be my final value if i write? this is 23, 23 plus 21, if i add here.
01:31
So 23 plus 21 is 44 right and 44 plus 23 again is 67 again 23 is 90 again 24 is 114 again 25 is 139 again 29 is 168 and 168 plus 32 is 200 right and if i talk about this is 200 and plus 33 plus 34 plus 33 plus 34 right so submission is 267 if i write submission is 267 so i will write here summation 267 divided by so if i write here this will come out as 1 2 345 6 7 8 9 10 and 11 right so i will write here 11 so what is my x bar value 267 divided by 267 divided by 11 which is basically 24 .27.
02:43
Now let us talk about y bar.
02:45
Y bar is again summation of y values and divided by n.
02:48
So 76 plus 80.
02:50
First we calculated 76 plus 80, 156 and this is 69 -225 and this is 64.
02:57
Again 289, this is 50.
03:00
This is 339, this is 56, 395 plus 61.
03:05
Is 456 plus 62 is 518 plus 7 3 if i write 591.
03:13
Next values will be added which are 49 plus 45.
03:19
So answer is 685 685 divided by 11 again so 685 divided by 11 is 62 .27 right now we need to calculate these values too.
03:35
So if i write submission of x y that that can be written as summation of x y we need to to write so if i write here then 10 multiply by 76 we need to do 10 multiply by 76 right and this can be written as if i write whole terms 10 multiply by 76 plus 13 multiply by 80 and so on to up to 34 multiply by 45 right these values are getters so we'll calculate them directly right roughly so as a rough calculation i can write this is 76 plus this is 760 plus 13 multiply by 80 plus if i write 21 multiply by 69 plus 23 multiplied by 64 right plus 23 multiplied by 50 plus this is 24 plus this is 24 multiplied by 56 plus if i write 24 multiply by 56 plus 25 multiplied by 61 plus 29 multiplied by 62 plus 32 32 multiplied by 73 right now next value will be added and this is 33 multiplied by 49 plus 34 multiplied by 45 so final value will be 16 ,000 if i calculate roughly so this is and we need to calculate summation of x square so summation of x square will be we have to calculate again so this is basically 10 multiply by 10 plus 13 multiply by 13 plus if i write here this is 21 multiply by 21 plus 23 multiply by 23 right plus 24 multiply by 24 plus 25 multiply by 25 plus 29 multiply by 29 plus 32 right and next terms are 32 multiply by 34 and plus 33 multiply by 33 and plus 34 24 multiply by 34 right so final answer is 6 55 5 5 5 so if i write we need to calculate something like this 10 square plus 13 square and dot dot dot 34 square.
06:13
So final value roughly is 6550.
06:16
Now what is what is summation of xx by summation of xx by summation of x squared? so this is 16 .01 divided by 6550...