Question

6. In a regression model involving 46 observations, the following estimated regression equation was obtained. û = 17+4X1 - 3X2 + 8X3 +5X4 + 8Xs For this model, SST = 3410 and SSE = 510. a. Compute the coefficient of determination. b. Perform an F test and determine whether or not the regression model is significant

Answer 1

From provide information

N = 46

P= number of parameters estimated = 6

SST = 3410

SSE = 510

SSReg = SST- SSE = 3410 - 510

SSReg = 2900

DF ( SSReg) = P-1 = 5

DF( SSE) = N - P = 46-6 = 40

DF( SST) = N-1 = 45

a. Coefficient of determination (R² )

R² = SSReg / SST = 2900/3410

R² = 0.8504

b.

F - test = ( SSReg/ Df(SSReg)) /(SSE/Df(SSE))

F- test = (2900/5) /(510/40)

F - test = 45.490

Fcri = F_5,40,0.05 = 2.449

Decision : Rejected null hypothesis.because F- test > Fcri.

Conclusion : The regression model is significant.

Thank You !

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