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 ,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 ,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 ,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 ,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 ,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 ,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 ,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 ,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 the coefficient for the variable Toefl90. According to the output, the estimate for this coefficient is 1.6346. Since we have a binary logistic regression model, we need to interpret the coefficient in terms of odds. The odds ratio for Toefl90 is exp(1.6346) = 5.129, which means that the odds of a school being private is 5.129 times higher for a school that has a TOEFL criterion that is at least 90 than one that does not, holding constant the effect of the mean total SAT score. Taking the natural logarithm of this odds ratio, we get 0.1928, which is the interpretation of the Toefl90 Slope coefficient. Therefore, choice C is correct.

SCENARIO 14-18 A Logistic Regression Model Was Estimated in Order to Predict