Problem 1 Suppose that ()1 ,X]), ()2,X2),....., ()'n > >" ) is a data set to which we fit a simple regression model. Let , be the least square estimate of the model slop and 7 be the simple correlation coefficient between 1, - - -. ), and X1 --., X ,. (a) Show that B, = -r, where s, and s are the sample standard deviations of S x V1>- -.,)'n and X ],-.,x, respectively. (b) Show that , is an unbiased estimate of P, . (c) Show that Bi run -2 SE( B, ) 2 (d) In the estimated model, prove that the sum of the residuals equal zero and estimated line pass through the point (X , Y )