Consider a regression model: Y ¼ Xb þ e, where Y is n 1 vector of observations, X is n p matrix, b..

Consider a regression model: Y ¼ Xb þ e, where Y is n  1 vector of observations, X is n  p matrix, b is a p  1 vector of regression coefficients and e is an n  1 vector of random errors. (a) Write the expression for residual sum of squares. (b) Write the expression for mean square residual. (c) Construct the ANOVA table for n = 40 and k = 3: (d) From the ANOVA table in (c), show the test for H0: b1 ¼ b2 ¼ b3 ¼ 0. (e) How can you comment from (d)? (f) Construct the 95% confidence interval for bj; j ¼ 1; 2; 3. (g) What is the extra sum of squares principle? Comment on the

Consider a regression model: Y ¼ Xb þ e, where Y is n  1 vector of observations, X is n  p matrix, b is a p  1 vector of regression coefficients and e is an n  1 vector of random errors. (a) Write the expression for residual sum of squares. (b) Write the expression for mean square residual. (c) Construct the ANOVA table for n = 40 and k = 3: (d) From the ANOVA table in (c), show the test for H0: b1 ¼ b2 ¼ b3 ¼ 0. (e) How can you comment from (d)? (f) Construct the 95% confidence interval for bj; j ¼ 1; 2; 3. (g) What is the extra sum of squares principle? Comment on the hypothesis H0: b3 ¼ 0 using the extra sum of squares principle.