Question

1. In order to investigate the hypothesis that greater prestige leads to higher costs of attendance at higher educational institutions, a researcher randomly sampled national universities and liberal arts colleges from the U.S. News and World Reportrankings. Based on the data collected, they estimated a model that sought to explain costs as a function of a number of institutional characteristics, with the following results (standard errors in parentheses):

   Cost= 7,502 + 3,818Reputation– 0.21Size+ 8,391Dpriv

                          (1,277)                 (0.13)      (2,386)

   R^2= .72 N = 92

whereCostis tuition and fees in dollars, Reputation is the index used in U.S. News and WorldReport(based on a survey of university presidents and chief academic officers), which ranges from 1 (“marginal”) to 5 (“distinguished”), Sizei s the number of undergraduate students, and Dprivis a dummy variable for being a private institution.

Provide a clear interpretation of the estimated coefficient on Dpriv; your answer should clearly reflect the fact that Dprivis a dummy variable.

Answer 1

Given: Fitted model,

Cost= 7502 + 3818 Reputation - 0.21 Size + 8391 Dpriv

Hypothesis: Greater prestige leads to higher costs of attendance at higher educational institutions

Dpriv is a dummy variable for being a private institution

So, let us suppose Dpriv takes value 1 if the institution is private and 0 if the institution is non-private in the data set.

Estimated coefficients other than the intercept term indicates the rate of change in the average value of Cost when there is a unit change in the value regressors.

Interpretation of the estimated coefficient on Dpriv

Estimated Coefficient is 8391 for Dpriv which indicates that Cost for the private institutions is very high compared to the non-private institutions.

Standard error for Dpriv is 2386 indicates the measure of precision for regression coefficient. Precision is indirectly proportional to Standard error. If the coefficient value is larger than the standard error then it significantly differs from 0.

Further, we can calculate t - statistics and p-value for the Dpriv coefficient to know significance of it.

t-statistics for Dpriv is

t= 3.5167.

Note that if t-statistics or p-value comes out to be insignificant then it indicates that Dpriv does not impact Cost.