The following regression equation was estimated using data on college applicants who were admitted both to Pomona College and another college ranked among the top 20 small liberal arts colleges by U.S. News & World Report:

where ( ) = standard deviation.
Y = fraction of students who were admitted to both this college and Pomona College who enrolled at Pomona, average value = 0.602.
X = U.S. News & World Report ranking of this college.

a. Redraw Figure 8.16 and add the estimated regression line.

b. Use your graph to explain how the estimates 0.2935 and 0.0293 were obtained.

(Do not show the formulas; explain in words the basis for the formulas.)

c. Explain why you are not surprised that the R² for this equation is not 1.0.

Transcribed Image Text:

Y=0.2935+0.0293X, R2 = 0.562 (0.0781) (0.0065)