SCENARIO 18-11 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, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.)The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below:
-Referring to Scenario 18-11, which of the following is the correct interpretation for the Tofel500 slope coefficient?
A)Holding constant the effect of the other variables, the estimated mean value of school type is 0.39 lower when the school has a TOEFL criterion that is at least 550.
B)Holding constant the effect of the other variables, the estimated school type decreases by 0.39 when the school has a TOEFL criterion that is at least 550.
C)Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.
D)Holding constant the effect of the other variables, the estimated probability of the school being a private school is 0.39 lower for a school that has a TOEFL criterion That is at least 550 than one that does not.

Question

SCENARIO 18-11 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, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.)The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: 
-Referring to Scenario 18-11, which of the following is the correct interpretation for the Tofel500 slope coefficient?
A)Holding constant the effect of the other variables, the estimated mean value of school type is 0.39 lower when the school has a TOEFL criterion that is at least 550. 
B)Holding constant the effect of the other variables, the estimated school type decreases by 0.39 when the school has a TOEFL criterion that is at least 550. 
C)Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not. 
D)Holding constant the effect of the other variables, the estimated probability of the school being a private school is 0.39 lower for a school that has a TOEFL criterion That is at least 550 than one that does not.

Quizplus · Accepted Answer

The correct interpretation of a slope coefficient in a logistic regression (which is implied by the context of odds ratio) is that it represents the change in the log odds of the dependent variable for a one-unit increase in the independent variable, holding other variables constant. Choice C correctly describes this as a change in the estimated natural logarithm of the odds ratio, which is consistent with logistic regression interpretation.

SCENARIO 18-11 a Logistic Regression Model Was Estimated in Order