Question

5. Summary of regression between a dependent variable y and two independent variables X, and x2 is as follows. Please complete the table: SUMMARY OUTPUT Regression Statistics Multiple R 0.9620 R Square R2E? Adjusted R Square 0.9043 Standard Error 12.7096 Observations 10 ANOVA F Significance F F=? Overall p-value=? Regression Residual Total 2 df of SSE MS MSR=? MSE? 14052.1550 1130.7450 SSTE? MSE? 9 Coefficients -18.3683 Standard Error 17.9715 t Stat -1.0221 Intercept ty=? 2.0102 4.7378 0.2471 0.9484 P-value 0.3408 p-value for B,=? p-value for B-2 Lower 95% -60.8641 Lower limit of CI for B.=? Lower limit of CI for B=? Upper 95% 24.1276 Upper limit of Ci for B,=? Upper limit of Cl for B =? ?

Answer 1

Answers :

i) R-square = $^{(MultpleR)^{2}}$ = $^{(0.9620)^{2}}$ = 0.8575

ii) df of SSE = df(Total) - df(Regression) = 9-2 = 7

iii) SST = SS(Regression)+SS(Residual) = 14052.1550+1130.7450 = 15182.90

iv) MSR = SS(Regression) / df(Regresssion) =  14052.1550/2 = 7026.078

v) MSE = SS(Residual) / df(Residual) = 1130.7450/7 = 161.535

vi) F = MSR / MSE = 7026.078/161.535 = 43.4957

vii) overall p-value (Significance F ) = 0.000113 ( using Excel function "=1-F.DIST(43.4957,2,7,TRUE)" )

viii) t1 ( t Stat ) = Coefficient (x1) / Standard Error (x1) = 2.0102/0.2471 = 8.1352

ix) t2 ( t Stat ) = Coefficient (x2) / Standard Error (x2) = 4.7378/0.9484 = 4.9956

## End of Answer

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