In simple linear regression, the i-th prediction is denoted as yi = 0 + 1xi , let b0 = 0 = b0, b1 = 1, we also have: b1 = r sy sx , b0 = y b1x where r is the correlation between x and y, and sy and sx are the standard deviation for x and y, respectively.

(a) [5 pts] Sum of Residuals: The i-th residual from ordinaary least squares is defined as the difference between the observed data and the predicition, i.e. ei = yi yi . What is Pn i=1 ei? (Show details about how to get this value)

(b) [5 pts] Sum of Fitted Values: show the sum of the observed value yi equals the sum of the fitted values yi . That is, Pn i=1 yi = Pn i=1 yi .