SUMMARY OUTPUT Statistics Regression Multiple R R Square Adjusted R Square Stand

Question

SUMMARY OUTPUT Statistics Regression Multiple R R Square Adjusted R Square Standard Error Observations 0.981102 0.962562 0.958242 0.262008 30 ANOVA Significanc MS 15.2965 222.824 Regression 3 45.88961 6 1.17E-18 0.06864 Residual 26 1.784857 29 47.67447 Coefficient Standard Upper 95% Error tStat P-value Lower 95% Intercept 9.13298 0.504927 -18.0877 3E-16 -10.1709 -8.09508 17.5802 0.046270.002632 3 5.95E-16 0.04086 0.05168 studying hours 0.098135 0.009586 10.2374 1.3E-10 0.078431 0.11784 0.08198 High school 15.8709 score 0.072586 0.004574 7 6.83E-15 0.063185 (i) Please comment on whether the multiple regression model [from c)] is a good model based on the histogram of residuals (2 marks) Residuals histogram 20 15 10 0 0.75 0.5 -0.25 00.25 0.5 More Residuals

Explanation / Answer

The histogram of the residuals represents an almost symmetric normally distributed residuals. Hence the residuals are approximately normally distributed. The residuks are very small. The magnitude of almost all residuals is less than 0.5 and mostly it is less than 0.5 Thus we observe a very small value of residuals from the fitted multiple regression model and hence the multiple regression model is good.

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