A large proportion of US. teenagers work while attending high school. These heavy workloads often result in underachievement in the classroom and lower grades. A study of high school students in California and Wisconsin showed that those who worked only a few hours per week had the highest grade point averages (Newsweek, Nov. 16, 1992). The following table shows grade point averages (GPAs) and number of hours worked per week for a sample of five students. Consider a simple linear regression relating GPA (y) to hours worked (x).
a. Find the equation of the least squares line.
b. Plot the data and graph the least squares line.
c. Test whether the model is useful for predicting grade point average. Use a = .10.
d. Predict the grade point average of a high school student who works 10 hours per week using a 90% prediction interval. Interpret the result.