. Exercise 2: The Cost of College. You want to understand the effect of reputati

Question

. Exercise 2: The Cost of College. You want to understand the effect of reputation on the cost of attending college. To investi- gate this, you collect data randomly for 200 national universities from the 2016- 2017 U.S. News and World Report annual rankings. Your perform the following regression: where cost is tuition, fees, room and board in dollars, reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 ("marginal") to 5 ("distinguished"), size is the number of undergraduate students, and private is a binary variable indicating whether the institution is private. The numbers in parenthesis are White heteroskedasticity-robust standard errors. 1. Interpret the results in column (1) and indicate whether or not the coefficients are significantly different from zero. Do the coefficients have the expected sign? 2. What is the forecasted cost for a private university, with a size of 2,000 students anda reputation level of 4? 3. To save money, you are willing to switch from a private university to a public university, which has a ranking of 0.5 less and 10,000 more students. What is the effect on your cost? Is it substantial:?

Explanation / Answer

1.
For a unit increase in reputation, the cost of attending college will increase by 3985.21.
Let n be number of observations, k is number of coefficients including intercept.
Degree of freedom = n-k = 200 - 4 = 196
Critical value of t for 0.05 significance level and df 196 is 1.97

t = 3985.21 / 650.28 = 6.13
As t value is greater than the critical value, the coefficient of reputation is significantly different from 0.

For a unit increase in size, the cost of attending college will decrease by 0.20.
t = -0.20 / 0.14 = -1.43
As absolute t value is less than the critical value, the coefficient of size is not significantly different from 0.

For private institution, the cost of attending college will increase by 8653.33.
t = 8653.33 / 2154.68 = 4.02
As absolute t value is greater than the critical value, the coefficient of private is significantly different from 0.

All the coefficients have expected signs as the cost will increase with reputation and for private institutions (thus have positive signs) and decrease with size of students (have negative sign).

2.
The regression equation is,
Cost = 7412.71 + 3985.21 reputation - 0.20 size + 8653.33 private

For size = 2000, private = 1, reputation = 4
Cost = 7412.71 + 3985.21 * 4 - 0.20 * 2000 + 8653.33 * 1 = 31606.88

3.
If private becomes from 1 to 0 (decrease by 1)
reputation decreases by 0.05,
size increases by 10,000
The effect on cost will be
3985.21 * (-0.5) - 0.20 * 10000 + 8653.33 * (-1)
= 12645.93

Thus, the cost of attending college will decrease by 12645.93

4.
For variable size,
t = -0.20 / 0.14 = -1.43
Degree of freedom = n-k = 200 - 4 = 196
P(t < -1.43, DF = 196) = 0.07715457
P-value = 2 * 0.07715457 = 0.1543

As, the p-value is greater than the significance level of 0.05, the variable size is not significant for the model and we should eliminate the variable from the regression.

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