Suppose that you work in the admissions office of a

Suppose that you work in the admissions office of a college that doesn€™t allow prospective students to apply by using the Common Application.9 How might you go about estimating the number of extra applications that your college would receive if it allowed the use of the Common Application? An econometric approach to this question would be to build the best possible model of the number of college applications and then to examine the estimated coefficient of a dummy variable that equaled one if the college in question allowed the use of the €œcommon app€ (and zero otherwise).

For example, if we estimate an equation using the data in Table 2.3 for high-quality coed national liberal arts colleges, we get:

N = 49 R² = .724 R̅² = .705

Where:

APPLICATION_i = the number of applications received by the ith college in 2007

SIZE_i = the total number of undergraduate students at the ith college in 2006

RANK_i = the U.S. News¹⁰ rank of the ith college (1 = best) in 2006

COMMONAPP_i = a dummy variable equal to 1 if the ith college allowed the use of the Common Application in 2007 and 0 otherwise.

Table 2.3 Data for the College Application Example

a. Take a look at the signs of each of the three estimated regression coefficients. Are they what you would have expected? Explain.

b. Carefully state the real-world meaning of the coefficients of SIZE and RANK. Does the fact that the coefficient of RANK is 15 times bigger (in absolute value) than the coefficient of SIZE mean that the ranking of a college is 15 times more important than the size of that college in terms of explaining the number of applications to that college? Why or why not?

c. Now carefully state the real-world meaning of the coefficient of COMMONAPP. Does this prove that 1,222 more students would apply if your college decided to allow the Common Application? Explain.

d. Now use the same data and estimate Equation 2.18 again without the COMMONAPP variable. What is the new R̅²? Does R̅² go up or down when you drop the variable? What, if anything, does this change tell you about whether COMMONAPP belongs in the equation?

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