Suppose a regression analysis estimating the relationship be

Suppose a regression analysis estimating the relationship between variable x and variable y resulted in SSE=375 and SST=500. If we know that x and y are positively correlated, what would be the correlation coefficient between x and y relationship. (Pleaseinclude work)

Solution

R-square = 1 - SSE/SST = 1 - 375/500 = 0.25

r = sqrt(R-square) = sqrt(0.25) = 0.5

We took positive sign after square root because it is given that correlation is positive.