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hw_04_sol

hw_04_sol - Homework 4 Covers Chapters 7 Use the Project...

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Homework 4 Covers Chapters 7 Use the Project Talent data set. 1. Perform a multiple regression by regressing Math on Gender, SES, Sociability, Reading, and Mechanical Reasoning entering the predictors in this order. a. What is the interpretation of the t-tests for SES and Sociability? Be sure to include the null and alternative hypothesis being tested, the degrees of freedom, the p- value, and your conclusion and decision about Ho at a 10% level of significance. SES Ho: B 2 = 0 Ha: B 2 ≠ 0 t-stat: 1.63 DF: 19 p-value: 0.119 Decision/Conclusion: Since p-value is greater than 0.10 we would not reject Ho. Plausible that the addition of SES makes no significant linear contribution to prediction of Math Achievement when Gender, Sociability, Reading, and Mechanical Reasoning are in the model. Sociability Ho: B 3 = 0 Ha: B 3 ≠ 0 t-stat: - 0.11 DF: 19 p-value: 0.912 Decision/Conclusion: Since p-value is greater than 0.10 we would not reject Ho. Plausible that the addition of Sociability makes no significant linear contribution to prediction of Math Achievement when Gender, SES, Reading, and Mechanical Reasoning are in the model. Regression Analysis: Math versus Gender, SES, Social, Reading, Mech The regression equation is Math = - 19.4 - 0.63 Gender + 0.231 SES - 0.050 Social + 0.237 Reading + 1.28 Mech Predictor Coef SE Coef T P Constant -19.36 14.14 -1.37 0.187 Gender -0.635 3.101 -0.20 0.840 1

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SES 0.2312 0.1415 1.63 0.119 Social -0.0501 0.4476 -0.11 0.912 Reading 0.2370 0.1826 1.30 0.210 Mech 1.2820 0.4641 2.76 0.012 b. State the null and alternative hypotheses being tested by the ANOVA table in output. Include the F-statistic, p-value, and your decision and conclusion about Ho. Ho: All slopes equal 0 Ha: Not all slopes equal 0 F-stat: 8.83 p-value: 0.000 Decision/Conclusion: Reject Ho and conclude at least one slope does not equal 0. Analysis of Variance Source DF SS MS F P Regression 5 1769.93 353.99 8.83 0.000 Residual Error 19 761.91 40.10 Total 24 2531.84 Source DF Seq SS Gender 1 401.28 SES 1 582.95 Social 1 48.57 Reading 1 431.08 Mech 1 306.04 c. Create an ANOVA table that shows the contributions of each of these predictors using the Sequential Sum of Squares from output. The addition of these sum of squares should equal the SSR (Sum of Squares Regression) found in the ANOVA table of your output.
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