Problem 4. (13 points) Do sports help academics? ~ In a 2003 article in the Journal of Higher Education, a group of authors set out to investigate the impact of intercollegiate athletics on graduation rates among major NCAA Division | Universities. They were specifically interested in the relationship between a successful sports program and the graduation rate of university students. In this problem you will look at a sample of 57 universities from the data set used by the authors and the two variables: Graduation Rate: The average 6-year graduation rate for 1996, 1997, and 1998 BB Index: Composite of basketball ranking (a normalized value between 0 and 5) A scatterplot of your sample data is given below. NCAA Division I Universities 100 80 60 Graduation rate 40 2 3 BB Index - Composite basketball ranking If you fit a linear model to the data using the statistical software R, you see the following summary of the model: Coefficients Estimate Std Error t value |Pr( > t) (Intercept) 59.5 4.957 12.003 5.43e-17 BB Index 0.2773 2.18 0.127 0.899 Residual standard error: 16.239 on 55 degrees of freedom Multiple R-squared: 0.0003, Adjusted R-squared: -0.0179 Round all calculated answers to 4 decimal places. 1. Use the computer output to write the estimated linear regression equation for predicting Graduation Rate from BB Index. 1 = 2. Which of the following is the correlation coefficient for the linear relationship between BB Index and Graduation Rate? O A. -0.0171 O B. 0.0003 O C. 0.0171 O D. -0.0003 3. Each additional 1 unit of BB Index is associated with a(n) |??? of percent in Graduation Rate. 4. Shaquille checks the data and sees that the BB Index of their university is 1.39699. Calculate the estimated value for the Graduation Rate for Shaquille's university that is predicted by the linear model. Estimated value =5. Shaquille's university's Graduation Rate is reported as 58. Use this information and your result from part 4 to calculate the residual for this university. Residual = 6. What are the null and alternative hypotheses to test if there is a linear relationship between BB Index and Graduation Rate? O A. Ho: B1 = 0 vs. HA: B1 >0 O B. Ho: B1 = bj vs. HA: B1 # by O C. Ho: B1 = 0 vs. HA: B1 #0 O D. Ho: b1 = 0 vs. HA: b, # 0 7. Based on the computer output, what is the test statistic for the test in part 6? Test statistic: 8. Based on the computer output, the results of the hypothesis test tell us that we have ? V evidence that there ??? a linear relationship between BB Index and Graduation Rate. 9. Use information from the computer output to calculate a 90% confidence interval for the slope, 81, of the regression line predicting Graduation Rate from BB Index. IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places
