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

question 148

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 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.

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Definitions:

Acetylcholine

A chemical messenger that plays a significant role in muscle activity and memory retention.

Dopamine

A neurotransmitter in the brain that plays a key role in regulating mood, motivation, pleasure, and reward.

Endorphins

These are neurotransmitters produced in the brain that act as natural painkillers and are also associated with feelings of pleasure and well-being.

Serotonin

A neurotransmitter that contributes to feelings of well-being and happiness, also involved in regulating mood, appetite, and sleep.