Exercise 3

1. Refer to the grade point average (GPA) problem (problem 1 Exercise 1). The results are in file GPA and a brief description of the variables is in the file GPAd.

  • Set up the ANOVA table.

  • What is estimated by MSR in your ANOVA table? What is estimated by MSE in your ANOVA table? Under what conditions do MSR and MSE estimate the same quantity?

  • Conduct an F-test of whether or not b1 = 0. Control the risk at 0.01. State the alternatives, decision rule and conclusion.

  • What is the absolute magnitude of the reduction of the variance of Y when X is introduced in the regression model? What is the relative reduction? What is the name of the later measure?

  • Obtain r and attach the appropriate sign.

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    2. Refer now to the Muscle Mass problem (problem 2 Exercise 1). The results are in file MUSCLE and a brief description of the variables is in the file MUSCLEd. X is the age and Y is a measure of muscle mass.

    1. Plot the deviations {Yi-Yhati} against Xi on one graph. Plot the deviations {Yhati-Ybar} against Xi on another graph. From your graphs, does SSE or SSR appear to be the larger component of SSTO?

    2. Set up the ANOVA table.

    3. Conduct an F-test of whether or not b1 = 0. Control the risk at 0.10. State the alternatives, decision rule and conclusion.

    4. What proportion of the total variation of mass muscle remains "unexplained" when age is introduced into the analysis? Is this proportion relatively small or large?

    5. Obtain r and r2.

     

    3. Refer again to the grade point average (GPA) problem (problem 1 Exercise 1).

    1. Would it be more reasonable to consider the Xi on as known constants or as random variables here? Explain.

    2. If the Xi were considered as random variables, would this have any effect on prediction intervals for new applicants? Explain.