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ECON 584

Fall 2022

Homework #7

1. Skim the Dubin-Noll Caltech admissions report.

2. Would you conclude that only the total SAT scores determines admissions as compared to the composition? 

Hint: Based on Table 3-11 for instance, would a student with combined SAT score of 1500 (800 M 700V) be more or less likely to gain admission to Caltech as a student with a combined score of 1500 (700 M 800 V)? Are there positive or negative effects of having a relatively higher SATV score, and a lower SATM score with the combined SAT score not changed? Show your work!

3. Using the results in Table 3-11 (see PDF of same name on blackboard), how many math SAT points was it worth to be a female applicant to Caltech) relative to a male applicant (circa 1981)?  (Hint: Assuming all other variables are constant except gender and SATM, how would the coefficient of male change in the Logit model if male were replaced by female under the usual condition that male+female=1).

4. Using the same table, how many verbal SAT points was it worth to be a black male applicant to Caltech? Hint: assume that white males are the omitted category in this model. Would you conclude that Hispanic students received a significant admission bump according to this model?    

5. How could you determine the significance of the estimate you made in Question 3? Hint: See e.g. http://www.stat.cmu.edu/~hseltman/files/ratio.pdf. What information would you need to know to answer this question?

6. How could a discrete choice model be used to analyze the time of day that individuals pick to go to movies? How might a movie theatre use this information to maximize revenues?