00:01
Okay, so for a, we want to calculate the value of the product moment correlation coefficient, and this is given by r equals sum over xi minus x bar yi minus y bar over square root of sum over xi minus x bar squared times sum over yi minus y bar squared.
00:30
Now, the numerator, i'm gonna call this rn, and denominator as rd.
00:42
The numerator can be expanded to xi yi minus xi y bar minus x bar yi plus x bar y bar.
01:02
So that we have a sum x i y i minus y bar x i minus x bar sum y i plus n x bar y bar, which could be simplified to xi yi minus 1 over n yi xi minus 1 over n xi yi plus n times x bar y bar so that we have xi yi minus 2 over n n x i y i plus n x bar y bar.
02:08
So this is equal to 12515 minus 2 over 6 times 200 times 436 plus 6 times.
02:34
Times.
02:36
So the average of x is just 200 over 6, average of y is just 436 over 6, which gives negative 2018 .33.
02:56
Now, as for the denominator, this expression, first i'm going to expand the square root of xi sum of xi minus x bar squared which gives sum of xi squared minus 2 xi x bar plus x bar squared so that we have square root of sum of xi squared minus 2 times xi x bar sum xi plus n times x bar squared which is equal to sum xi squared minus 2 over n and sum of xi squared plus n x bar now we're gonna plug in the given values, which is 7250 -2 over 6 and 200 squared plus 6 times 200 over 6 squared, which brings to 24 .152.
04:37
Now, as for the expression, sum yi minus y bar squared, this can be similarly calculated as before for the case of x, and we get 86 .898.
05:14
So the denominator is 24 .152 times 86 .898.
05:24
And so we're just gonna divide the numerator by the denominator, which gives negative 0 .9617...