Chapter 14.3, Problem 41E

Data from a random sample of 107 students taking a managerial accounting course were used to obtain the estimated regression function 2.178 + 0.469x₁ + 3.369x₂ + 3.054x₃ where y = Student’s exam score, x₁ = Student’s expected score on the exam, x₂ = time spent studying (hr/week), and x₃ = Student’s grade point average or GPA (“Effort, Expectation and Academic Performance in Managerial Cost Accounting,” Journal of Accounting Education [1989]: 57–68). The value of R² was 0.686, and the estimated standard deviations of the statistics b₁ b₂, and b₃ were 0.090, 0.456, and 1.457, respectively.

1. a. How would you interpret the estimated coefficient 0.469?
2. b. Does there appear to be a useful linear relationship between exam score and at least one of the three predictors?
3. c. Calculate a 95% confidence interval for the mean change in exam score associated with a 1-hour increase in study time when expected score and GPA remain fixed.
4. d. Obtain a point prediction of the exam score for a student who expects a 75, has studied 8 hours per week, and has a GPA of 2.8.
5. e. If the standard deviation of the statistic on which the prediction of Part (d) is based is 1.2 and SSTo = 10,200, calculate a 95% prediction interval for the score of the student described in Part (d).