Consider the simple linear regression model Xk D 0 C 1 tk C p

v k, k D 1; : : : ; n, and assume that the variance v > 0 is known. Show the following.

(a) If the error vector has a multivariate standard normal distribution, then the least squares estimator O D .O0; O1/ is also a maximum likelihood estimator of D .0; 1/.

(b) Defining the residual and regression variances by

one obtains the partitioning of variation

(c) The statistic T D O1 p nV.t/=V
resid, which can be used to test the null hypothesis H0 W 1 D 0, can be written in the form T 2 D V
regr=V
resid.

V Resid =V= n-2 11 (Xk-o-k) and V k=1 n = regr o+k-M), k=1