1. Write down the population regression equation for the model in column (4) 2.
ID: 3311772 • Letter: 1
Question
1. Write down the population regression equation for the model in column (4)
2. What is the dependent variable? What are the regressors? List all the regressors.
3. Write down the estimated regression equation for the model in column (4).
4. Do you agree with the negative coefficient estimate on Student/faculty ratio? Explain!
5. Find out how Sports dummy is measured.
TABLE1 SAT SCORES AND BIGTIME ATHLETICS (Dependent Variable: Average SAT Scores of Entering Freshmen) COEFFICIENT INDEPENDENT (9.49)10.08 (10.86 2.19) 216 0.5 13.74) Sports dummy 12.83) (2.56) Volumes in library × Salary of full professors x 10* Age of the university Private school dummy Student faculty ratio Total enrollment × 103 Endowment per student x 109 Number of Ph.D.'s awarded per Male proportion of under- 4.04) graduate enrollment 96.70 81.44 67.50 60.63 74.95 66.88 86.84 7308 8031 139 7311 7511 8057 8015 Number of observations 156 156 156 139 SoURGE-Americen Un nd Coliges (1971) NOTE--ratios are in parenthesesExplanation / Answer
Q1.
The population regression equation for the model in column (4) is:
Average SAT scores of entering freshmen = A + B * sports dummy + C * tution + D * volumes in library (in 106) + E * salary of full professors (in 102) + F * age of the university + G * private school dummy + H student/faculty ratio
We cannot write the population regression equation for the model in column (4) based on the given information (data) of a sample of size 156 since the coefficients can be obtained only if we have the data for the entire population. Rather, we specify the estimated regression equation, answered in Q3.
Q2.
Average SAT scores of entering freshmen is the dependent variable.
Q3.
The estimated regression equation for the model in column (4) is:
Average SAT scores of entering freshmen = 596.25 + 28.0 * sports dummy + 0.11 * tution - 2.42 * volumes in library (in 106) +1.65 * salary of full professors (in 102) + 0.33 * age of the university - 22.67 * private school dummy - 3.23 student/faculty ratio
Q4.
I agree with the negative effect of student/faculty ratio on the average scores as the lower student/faculty ratio leads to a less attention being provided by a faculty to each individual student, which is an important factor in the understanding of the student and may lead to a negative effcet on his/her scores.
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