Question

A multiple regression model is to be constructed to predict the final exam score of a university student doing a particular course based upon their mid-term exam score, the average number of hours spent studying per week and the average number of hours spent watching television per week. Data has been collected on 30 randomly selected individuals: show data a) Find the multiple regression equation using all three explanatory variables. Assume that xi is mid-term score, x2 is hours studying per week and x is hours watching television per week. Give your answers to 3 decimal places. ^-□ □ + mid-term score +[ hours studying-L hours watching television b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis rejected. c) The explanatory variable that is most correlated with final score is: O mid-term score 0 hours studying per week O hours watching television per week d) The explanatory variable that is least correlated with final score is: O mid-term score O hours studying per week O hours watching television per week e)The value of R2 for this model, to 3 decimal places, is equal to匚 f) The value of s for this model, to 3 decimal places, is equal to g) Construct a new multiple regression model by removing the variable average hours spent watching television per week. Give your answers to 3 decimal places. The new regression model equation is: d-term score + studying h) In the new model compared to the previous one, the value of R (to 3 decimal laces) : O increased O decreased O unchanged i) In the new model compared to the previous one, the value of s (to 3 decimal places) is: O increased O decreased unchanged the average number of hours spent studying per week and the average number of hours spent wato Data has been collected on 30 randomly selected individuals: hide data Hours studying Hours watching TV Final score 48 52 68 75 83 Mid-term Score per week per week 48 12 73 19 85 23 10 37 92 75 80 13 21 15 26 50 13 12 17 61 75 47 76 49 76 76 94 48 65 26 49 15 34 82 65 85 19 13 12 15 16 17 26 35 18 12 47 63 50 61 15 15 15 18 52 56 85 21 83 24 40 49 21 40 24 18 17 10 18 19 18 30 20 68 73 34 a) Find the multiple regression equation using all three explanatory variables. Assume that x, is mid-term television per week. Give your answers to 3 decimal places. d-term scorehours studying hours watching televisi score + Q Type here to search

Answer 1

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SPSS Output of regession

hrs_stdyina hrs_watching 6.00 22.00 19.00 23.00 var ore TV 48.00 52.00 68.00 75.00 83.00 33.00 80.00 64.00 50.00 88.00 61.00 49.00 66.00 34.00 82.00 65.00 85.00 54.00 47.00 63.00 50.00 61.00 55.00 83.00 48.00 66.00 77.00 85.00 99.00 37.00 92.00 75.00 57.00 99.00 75.00 47.00 76.00 49.00 76.00 76.00 94.00 48.00 65.00 66.00 52.00 56.00 85.00 88.00 7.00 12.00 11.00 8.00 10.00 4.00 13.00 12.00 7.00 13.00 12.00 17.00 2.00 30.00 21.00 26.00 11.00 6.00 26.00 15.00 9.00 6.00 17.00 26.00 35.00 18.00 12.00 9.00 18.00 21.00 29.00 12 13 19.00 13.00 12.00 15.00 8.00 15.00 15.00 15.00 2.00 .00 20 21 23 24 ata ViewVariable View

Font Paragraph Styles 26 Coefficients Standardized Unstandardized Coefficients Coefficients Correlations Model Std. Error Beta Sig Zero-order Partial Part (Constant) 654 14.846 5.075 -.964 912 .312 -.059 722 .22 242 705 -.124 12 -.061 135 -.186 a. Dependent Variable finalscore Regression Equation- Y-2.030+0.722* mid-term score+ 1.137% hours stdying-0.124 * hrs watching TV Model Summary Change Statistics Adjusted R Std. Error of R Square Model R R Square Square the Estimate Change F Change df1 df2 Sig. F Chang 5.712 79.583 ictors: (Constant),bics.watchine.b..per.weak Here from the F value We Can Reject the Hypothesis Because the P - value is 0.0000 which is Less Than 0.05 The Value of R squared is 0.902 English India) 申

Correlations Finalscore mid term scorel brs stdying 242 .071 .897 Pearson Correlation Finalscore 165 132 1.000 239 191 244 242 .071 165 132 .099 Sig. (1-tailed) Fnalscore 191 244 30 brs watching The Explanatory Variable which is most correlated is Mid-Term Score i.e. 0.897 The Explanatory Variable which is Least correlated is hrs-watching TV i.e. 0.135

.11, 1-12, 1 .13-1314- ו15' .ו 16. .ו 17. -ו 18' ו-19' . I '20. I '21. 1 .22, 1 .23. .24. .25. ו26 The Modedl With only TWO Exlny Variable Coefficients Standardized Unstandardized Coefficients Coefficients Correlations Model Std. Erron Beta Sig Zero-order Partial Part (Constant) 048 91 916 1.106 221 4.995 24 69 307 a. Dependent Variable Finalscore 0.589+0.7132 *mid term score+1.106* hrs stdying Model Summary Adjusted R Square Std. Error of the Estimate Model R Square 898 891 5.70411 a. Predictors. (Constant), br. wing, mid-term-score The New Model Compare with previous model R squared Value Is Decreased lish ndia)