Use hand calculations to t the multiple linear regression

Chapter 13, Problem 13.7.2

(choose chapter or problem)

Use hand calculations to t the multiple linear regression model y = 0 +1x1 +2x2 to the data set in DS 13.7.2. (a) Write down the vector of observed values of the response variable Y and the design matrix X. (b) Calculate XX. (c) Verify that (XX)1 = 73/680 1/136 0 1/136 1/136 0 0 0 1 /116 (d) Verify that 0 =4, 1 =3, and 2 =1. (e) Calculate the vector of predicted values of the response variable Y and the vector of residuals e. (f) What is the sum of squares for error? (g) Show that the estimate of the error variance is 2 =54/7. (h) What is the standard error of 1? Of 2? Should either of the input variables be dropped from the model? (i) What is the tted value of the response variable when x1 =2 and x2 =2? What is the standard error of this tted value? (j) Construct a 95% prediction interval for a future value of the response variable obtained with x1 =2 and x2 =2.