Data from a random sample of 107 students taking a managerial accounting course were used to obtain the estimated regression equation 2.178 + .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 .686, and the estimated standard deviations of the statistics b1, b2, and b3 were .090, .456, and 1.457, respectively.
a. How would you interpret the estimated coefficient .469?
b. Does there appear to be a useful linear relationship between exam score and at least one of the three predictors?
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.
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.
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).
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