It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizes, etc.) with high GPA would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. The data for her class are provided below. GPA Achievement 3.6 98 2.7 96 3.1 94 4.0 88 3.2 91 3.0 77 3.8 86 2.6 71 3.0 69 2.2 63 1.7 84 3.1 79 2.6 75 2.9 72 2.4 86 3.4 85 2.8 71 3.7 93 3.2 90 1.6 62 1. Determine which one is the response and which one is the explanatory variable? 2. Fit a linear regression model to the data and interpret the slope coefficient. 3. What percent of the total variability in achievement score can be explained by fitting a linear regression line? 4. Test the significance of the slope at α=0.05 level. Clearly state your regression model and hypotheses. 5. Construct a 95% confidence interval for the slope parameter. 6. Plot the residuals versus the X variable. From the plot, does it appear to have any issues with a linear fit?
