Consider fitting the multiple linear regression model
y = β0 + β1x1, + β2x2
to the data set in DS 13.3.1.
(a) What is the 10 × 1 vector of observed values of the response variable Y?
(b) What is the 10 × 3 design matrix X?
(c) What is the 3 × 3 matrix X'X?
(d) What is the 3 × 3 matrix (X'X)"1?
(e) What is the 3 × 1 vector X'Y?
(f) Show that the parameter estimates are

(g) What is the 10 × 1 vector of predicted values of the response variable Y?
(h) What is the 10 × 1 vector of residuals e?
(i) What is the sum of squares for error?
(J) Show that the estimate of the error variance is σ^2 = 17/15.
(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 = 1 and x2 = 2? What is the standard error of this fitted value? Construct a 95% confidence interval for the expected value of the response variable when x1 = 1 and x2 = 2. (m) Construct a 95'7

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