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 SAT slope coefficient?
A) Holding constant the effect of Toefl90, the estimated mean value of school type increases by 0.0028 for each increase of one point in average SAT score.
B) Holding constant the effect of Toefl90, the estimated school type increases by 0.0028 for each increase of one point in average SAT score.
C) Holding constant the effect of Toefl90, the estimated probability of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score.
D) Holding constant the effect of Toefl90, the estimated natural logarithm of the odds ratio of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score.

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 SAT slope coefficient?
A) Holding constant the effect of Toefl90, the estimated mean value of school type increases by 0.0028 for each increase of one point in average SAT score. 
B) Holding constant the effect of Toefl90, the estimated school type increases by 0.0028 for each increase of one point in average SAT score. 
C) Holding constant the effect of Toefl90, the estimated probability of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score. 
D) Holding constant the effect of Toefl90, the estimated natural logarithm of the odds ratio of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score.

Quizplus · Accepted Answer

The correct interpretation of the SAT slope coefficient in a logistic regression model (which is implied by the context of estimating the probability of a school being a private school) is that, holding other variables constant (in this case, Toefl90), the estimated natural logarithm of the odds ratio of the dependent variable (here, being a private school) changes by the coefficient value (0.0028) for each one-unit increase in the independent variable (SAT score). This interpretation is specific to logistic regression models, which deal with odds ratios rather than direct probabilities or mean values.

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