Consider fitting the multiple linear regression model y = B0 + fax\ + 32x2 to the data set in DS 13.3.2.
a. What is the 8 × 1 vector of observed values of the response variable Y?
b. What is the 8 × 3 design matrix X?
c. What is the 3 × 3 matrix X'X?
d. What is the 3 × 3 matrix (X'Xr1?
e.What is the 3 × 1 vector X'Y?
f. Calculate the parameter estimates β
g. What is the 8 x 1 vector of predicted values of the response variable Y?
h What is the 8 x I vector of residuals e?
i Show that SSE = 20.0.
j What is the estimate of the error variance σ^2 ?
k What is the standard error of β^1 Of β^2? Should either of the input variables be dropped from the model?
(1) What is the fitted value of the response variable when x1 = x2 = 1? What is the standard error of this fitted value? Construct a 95% confidence interval for the expected value of the response variable when x1 = x2 = 1.
m. Construct a 95% prediction interval lor a future value of the response variable when . x1 = x2 = I.