Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained. = 17.6 +3.821 -2.3x2 + 7.603 + 2.724 For this estimated regression equation SST = 1805 and SSR = 1,756. a. At a = 0.05, test the significance of the relashionship among the variables. SSE (to 1 decimal, if necessary) MSR (to 1 decimal, if necessary) MSE (to 2 decimals, if necessary) What is the value of the F test statistic (to 1 decimal)? Use Table 4 in Appendix B. What is the p-value? - Select your answer - Using a = .05, what is your conclusion? - Select your answer - b. Suppose variables i and 34 are dropped from the model and the following estimated regression equation is obtained. y = 11.1 -3.6x2 + 8.123 For this model SST = 1805 and SSR = 1,705. Compute SSE(21, 12, 13, 24). (to 1 decimal, if necessary) Compute SSE22, 23). (to 1 decimal, if necessary) c. Use an F test and a = .05 to determine whether & and 24 contribute significantly to the model. What is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. What is the p-value? - Select your answer - What is your conclusion about the two variables 2 and 24? - Select your answer -

Answer 1

k=independent variables =	4
n=sample size =		30
SST=	1805	SSR =	1756

a)

SSE =SST-SSR=	49
MSR=SSR/k=	439
MSE=SSE/(n-k-1)=	1.96
F =MSR/MSE =	223.98
p value <0.01

Conclude the relationship is significant

b)

SSE(x1,x2,x,3,x4) =	49
SSE(x2x3) =	100
F =	((100-53)/2)/(53/25)=	13.01
p value <0.01
x1 and x4 are jointly significant