A statistics professor investigated some of the factors that affect an individual student's final grade in his course. He proposed the multiple regression model Y=B + B X + B X + X + Where Y final mark out of 100 X = # of lectures skipped; X = # of late assignments; X = mid-term test mark (out of 100) The professor recorded the data for 44 randomly selected students. Results were obtained from EXCEL as follows: Summary Output Regression Statistics Multiple R R Square Standard Error No. observations ANOVA Source Regression Residual Total b. .5477 .3000 14.74 44 Constant X, No. skipped lectures X, No. late assignments X, Mid-term test mark df 3 determination? 40 43 SS 3716 8688 12404 e. Coefficients 41.6 - 3.18 -1.17 0.63 MS 1238.667 217.20 Std Error 17.8 1.66 1.13 0.13 What is the standard error of the estimate? F 5.70 a. What is the regression equation? Please interpret the meaning of the partial regression coefficients-bo, b, b, and b. t-Stat 2.337 -1.916 -1.035 4.846 P-value .012 P-value .008 .056 .302 .0033 What is the coefficient of C. At the 5% level of significance, is the mid-term mark a statistically useful predictor of a student's final grade? Explain what steps you used to draw your conclusion (hypotheses, test statistic (use t-test or p-value), decision rule, and conclusion). d. At the 5% level of significance, is the number of late assignments a statistically useful predictor of a student's final grade? Explain what steps you used to draw your conclusion (hypotheses, test statistic (use t-test or p-value), decision rule, and conclusion). Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final mark? (State your hypotheses, test statistic; decision rule and conclusion) f. Calculate the 95 percent confidence interval for the conditional mean of the final grade for students who missed 6 lectures, handed in 3 late assignments, and scored an 80 on the midterm exam.