90. Consider the model y  b0  b1x1  e for the data x1 .5 .5 .5 .5 .5 .5 .5 .5 y 1 2 2 3 8 9 7 8

a. Determine the X and y matrices and express the normal equations in terms of matrices.

b. Determine the vector, which contains the estimates for the two coef cients in the model.

c. Determine , the predictions for the eight observations, and also obtain the eight residuals.

d. Find SSE by summing the eight squared residuals.

Use this to get the estimated variance MSE.

e. Use the MSE and c11 to get a 95% con dence interval for b1.

f. Carry out a t test for the hypothesis H0: b1  0 against a two-tailed alternative.

g. Carry out the F test for the hypothesis H0: b10.

How is this related to part (f)?