In a regression model involving 46 observations, the following estimated regress

Question

In a regression model involving 46 observations, the following estimated regression equation was obtained. y = 17 + 4x_1 - 3x_2 + 8x_3 + 5x_4 + 8x_5 For this model, SST = 3410 and SSE = 510. Compute the coefficient of determination. a. (Notice that R-square = SSR/SST) Perform an F test and determine whether or not the regression model is significant. b (F critical from the F table is 2.45). Notice that F-stat = MSR/MSE and MSR=SSR/(p-l) and MSE = SSE/(n-p) where n is the sample size and p is the number of independent variables a. 0.89 b. F = 48.49 > 2.45; model is significant b.F = 48.49 > 2.45; model is significant a.0.85 b.F = 45.49 > 2.45; model is significant a.0.85 b. F = 48.49 > 2.45; model is significant a.0.85 b. F = 47.49 > 2.45; model is significant

Explanation / Answer

Given n=46

    Variables P=5

SST =3410

SSE =510

SST = SSR+SSE

Hence SSR =SST – SSE

            = 3410 – 510

SSR = 2900

SSE – d.f (n – P- 1) = 46 – 5 – 1 =40

SSR - d.f (P) = 5

SST – d.f (n-1) =46-1 =45

a) Coefficient of determination R-square

R-square = SSR /SST

                                        =2900/3410 = 0.850439

                                    = 0.85

b) F-Stat =MSR/MSE ~ FP, (n-P-1)

MSR =SSR/P = 2900/5 =580

MSE = SSE/n-P-1 =510 / 40 = 12.75

Hence F-Stat =580 / 12.75

                                                                        =45.49

At =0.05 level (5,40) d.f is from F-table =2.45

45.49 >2.15

Fcal >F-Table

Hence regression model is significant

a. 0.85

b. F. =45.49> 2.45 ; model is significant

Second option was correct

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