A random sample of 100 college students was asked to rate their courses on a scale of 1 to 10 (10 being best) and state their grade in the course on a scale of 1 to 12 (A = 12, A− = 11, and so on). The average rating was 5.53 and the average grade 9.69. A least squares regression of rating (Y) on grade (X) gave these results:

The standard errors are in parentheses.

a. What does a least squares regression tell us that a comparison of the average values, 5.53 versus 9.69, does not?

b. How do you interpret the estimate −2.14?

c. How do you interpret the estimate 0.79?

d. Is the estimated relationship between X and Y statistically significant at the 1 percent level?

e. Do you think that grades influence ratings or that ratings influence grades?

f. If so, what difference does it make to a regression equation?

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Y = -2.14+0.79X (2.91) (0.296)