SCENARIO 13-18
a Logistic Regression Model Was Estimated in Order

question 139

Multiple Choice

SCENARIO 13-18
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:
Binary Logistic Regression $$\begin{array}{l}\begin{array} { l r r r r } \hline { \text { Predictor } } & \text { Coefficients } & \text { SE Coef } &{ Z } & p \text {-Value } \\\hline \text { Intercept } & - 3.9594 & 1.6741 & - 2.3650 & 0.0180 \\\text { SAT } & 0.0028 & 0.0011 & 2.5459 & 0.0109 \\\text { Toefl90:1 } & 0.1928 & 0.5827 & 0.3309 & 0.7407\\\text { Deviance } & 101.9826\\\end{array}\\\end{array}$$
-Referring to SCENARIO 13-18, which of the following is the correct interpretation for theToefl90 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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The ratio or relation of the benefits received by different groups or individuals, often used in contexts like taxation or public spending.

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