Question

a. In a regression analysis involving 30 observations, the following estimated regression equation was obtained: y=17.6+3.8x₁-2.3x₂+7.6x₃+2.7x₄

For this estimated regression equation SST=1805, and SSR=1760. At α=0.05, test the significance of the relationship among the variables.

Answer 1

We have here k=4 independent variables

SST=SSR+SSE

Substitute here given /known values and solve for SSE

1805=1760+SSE

=>SSE=1805-1760=45

Degree of freedom for SSR=k=4

Degree of freedom for SSE=n-(k+1) = 30-(4+1) = 25

MSR=SSR/df = 1760/ 4 = 440

MSE=SSE/df= 45/25=1.8

F=MSR/MSE = 440/1.8 = 244.44

P value is approximately 0...........................by using Excel command =FDIST(244.44,4,25)

P value is 0 < 0.05

We have sufficient evidence to say that, there is significant relationship.