Question: The following pairs arc the pre- and post-test scores for students enrolled in a foreign language class.

A scatter plot, a least squares regression line, and a residual plot is shown below.

(a) Compute the estimated post-test score for a person who scores 13 on the pre-test. Show your work.

(b) Is the proposed linear model reasonable? Explain.

(c) A linear regression t-test was performed on the hypothesis \({{H}_{0}}:\beta =0\) vs. \({{H}_{A}}:\beta \ne 0\) where \(\beta \) is the slope of the theoretical regression line. The value of the t-statistic is 3.88 with 7 degrees of freedom. Is this strong evidence to reject the null hypothesis? Explain.

(d) The coefficient of determination is 0.68. Explain what this means in the context of the problem