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

question 223

Short Answer

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, what is the estimated probability that a school is a private one with a mean SAT score of 1250 and a TOEFL criterion that is at least 90?

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Definitions:

Degrees of Freedom

Refers to the number of independent values or quantities which can be assigned to a statistical distribution.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis, representing a threshold chosen to determine the significance of the test statistic.

Independent Variables

Factors that are manipulated or changed in an experiment to determine their effect on dependent variables.

Multiple Coefficient

Often refers to the coefficient of determination (R^2) in multiple regression analysis, indicating the proportion of variance in the dependent variable predictable from the independent variables.