SCENARIO 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.)The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below:
-Referring to Scenario 14-18, which of the following is the correct interpretation for the Toefl90 slope coefficient?
A)Holding constant the effect of SAT, the estimated mean value of school type is 0.1928 higher when the school has a TOEFL criterion that is at least 90.
B)Holding constant the effect of SAT, the estimated school type increases by 0.1928 when the school has a TOEFL criterion that is at least 90.
C)Holding constant the effect of SAT, the estimated natural logarithm of the odds ratio of the school being a private school is 0.1928 higher for a school that has a TOEFL Criterion that is at least 90 than one that does not.
D)Holding constant the effect of SAT, the estimated probability of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not.

Question

SCENARIO 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.)The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below: 
-Referring to Scenario 14-18, which of the following is the correct interpretation for the Toefl90 slope coefficient?
A)Holding constant the effect of SAT, the estimated mean value of school type is 0.1928 higher when the school has a TOEFL criterion that is at least 90. 
B)Holding constant the effect of SAT, the estimated school type increases by 0.1928 when the school has a TOEFL criterion that is at least 90. 
C)Holding constant the effect of SAT, the estimated natural logarithm of the odds ratio of the school being a private school is 0.1928 higher for a school that has a TOEFL Criterion that is at least 90 than one that does not. 
D)Holding constant the effect of SAT, the estimated probability of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not.

Quizplus · Accepted Answer

The Toefl90 slope coefficient is associated with the predictor variable Toefl90, which is the TOEFL criterion for a university or college. The coefficient of 0.1928 indicates that holding the effect of SAT constant, the estimated natural logarithm of the odds ratio of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not. In other words, there is a positive relationship between being a private school and having a TOEFL criterion of at least 90, controlling for mean total SAT score.

SCENARIO 14-18 a Logistic Regression Model Was Estimated in Order