Question: In Exercise 10 of Section 16.1, a model was estimated that explained a student's grade point average as a function of entrance scores on a math test \((X)\) and on an English test \((Z)\). (R ² = 0.781971, n = 9, p = 2).

1. Calculate \(R^{2}\) and \(\bar{R}^{2}\) for the estimated multiple regression equation.
2. Omit the variable \(Z\) from the equation and reestimate the model.
3. Calculate \(R^{2}\) and \(\bar{R}^{2}\) for the reestimated model, and compare the results with the results obtained before? Do the changes in \(R^{2}\) agree with the conclusions from Exercise 5?

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