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

question 30

Multiple Choice

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) .
The PHStat output is given below:
Binary Logistic Regression $$\begin{array}{l}\begin{array} { l r r r r } \hline { \text { Predictor } } & \text { Coefficients } & \text { SE Coef } & { Z } & p \text {-Value } \\\hline \text { Intercept } & - 3.9594 & 1.6741 & - 2.3650 & 0.0180 \\\text { SAT } & 0.0028 & 0.0011 & 2.5459 & 0.0109 \\\text { Toefl90:1 } & 0.1928 & 0.5827 & 0.3309 & 0.7407\end{array}\\\\\begin{array} { l l } \text { Deviance } & 101.9826\end{array}\end{array}$$
-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.

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