Consider a multiple linear regression with n observations and p predictors. Y=X8+e, where Y = (Y1,.Y) is the nx 1 vector of responses: X is the nx(p+1) matrix of predictors, including a column of l's for the intercept: unde = (...) is the n x 1 vector of statistical errors. Let Y =( ...) denote the fitted values and e= ( ) denote the residuals. (Note: show all the derivation steps for the following questions)

Show that Couple, Y) = 0.

 Show that the sample covariance of è and Ý is 0.

What is the slope of the simple regression of è on Ý (that is, e Y)? [intercept term is included in the model

 What is the slope of the simple regression of è on Y (that is, é Y)? [intercept term is included in the model