Conisder the simple linear linear regression model, Y = Ba+BX+ei, i = 1, 2, ..., n;...

 

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Conisder the simple linear linear regression model, Y = Ba+BX+ei, i = 1, 2, ..., n; where, are independent normally distributed random errors each with expectation zero and vari- ance 2 (a) Given that SSE/a2, where SSE denotes the sum of squares of the error terms, has a chi squared squared (x2) distribution with -2 degrees of freedom and is independent of and B deduce the sampling distribution of (B- B)/se(B), where se) denotes the standard error of . (6) (b) Give an expression for the regression sum of squares, SSR in terms of , and (x,-). (2) (c) Show that the F and test statistics for testing the hypothesis Ho: B = 0 against Ha: B #0 are related as F (1). (d) Show that E[MSR] =+(x), where MSR = SSR/1. (3) (5) Conisder the simple linear linear regression model, Y = Ba+BX+ei, i = 1, 2, ..., n; where, are independent normally distributed random errors each with expectation zero and vari- ance 2 (a) Given that SSE/a2, where SSE denotes the sum of squares of the error terms, has a chi squared squared (x2) distribution with -2 degrees of freedom and is independent of and B deduce the sampling distribution of (B- B)/se(B), where se) denotes the standard error of . (6) (b) Give an expression for the regression sum of squares, SSR in terms of , and (x,-). (2) (c) Show that the F and test statistics for testing the hypothesis Ho: B = 0 against Ha: B #0 are related as F (1). (d) Show that E[MSR] =+(x), where MSR = SSR/1. (3) (5)