00:01
So for this problem, i first need to note that as uploaded on numerate, this problem is missing the original data.
00:07
I was able to find the same question uploaded to another site, so i'll be working off of the data set that was available elsewhere.
00:16
Hopefully, even if the data itself is different, the process, the formulas used, and everything will be the same.
00:23
So for part a, we want to find the correlation coefficient, rxy, which we can calculate as the sum, the difference between, each x value and the mean x value times each y value and the mean y value divided by the square root of the sum of the squared deviations for x times the sum of the squared deviations for y so we're taking the square root of everything in the denominator there and i find that using the data or using the data set that i have available we find that the correlation coefficient is going to be 0 .98.
01:11
Then, additionally, one moment here, i'll note that using formula y hat is equal to alpha plus, or, yeah, alpha plus beta x, where beta is equal to the sum of x i minus x bar times y i minus y bar over the sum of x i minus x bar squared we'll get that beta the slope of our equation is going to be equal to 0 .97 alpha is equal to y bar minus beta x bar and for that we'll find a value of 16 .19.
02:06
So the regression equation given is y hat equals 16 .19 plus 0 .97 x.
02:16
Then applying the, or for part b, applying the same sort of linear regression, but changing what we're considering to be x and y, we'll still find that the correlation coefficient, rxy, is going to still be 0 .98...