11.36 Predicting GPA of seventh-graders. Refer to the educational data for 78 seventh-grade students given in Table 1.3 (page 26). We view GPA as the response variable. IQ, gender, and self-concept are the explanatory variables.

  1. (a) Find the correlation between GPA and each of the explanatory variables. What percent of the total variation in student GPAs can be explained by the straight-line relationship with each of the explanatory variables?

  2. (b) The importance of IQ in explaining GPA is not surprising. The purpose of the study is to assess the influence of self-concept on GPA. So we will include IQ in the regression model and ask, “How much does self-concept contribute to explaining GPA after the effect of IQ on GPA is taken into account?’’ Give a model that can be used to answer this question.

  3. (c) Run the model and report the fitted regression equation. What percent of the variation in GPA is explained by the explanatory variables in your model?

  4. (d) Translate the question of interest into appropriate null and alternative hypotheses about the model parameters. Give the value of the test statistic and its P-value. Write a short summary of your analysis with an emphasis on your conclusion.