TABLE 14-11
a Logistic Regression Model Was Estimated

question 98

Short Answer

TABLE 14-11
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 average 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:
Logistic Regression Table
$\begin{array}{lrrrrrrr} & & & && \text { Odds } & \text { 95: CI } \\\text { Predictor } & {\text { Coef }} & \text { SE Coef } & Z &{\text { P }} & \text { Ratio } & \text { Lower } & \text { Upper } \\\text { Constant } &-27.118&6 .696& -4.05 & 0.000 & & & \\\text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\\text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\\text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60\end{array}$

Log-Likelihood = -21.883
Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000
Goodness-of-Fit Tests

$\begin{array}{lrcr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046\end{array}$

-Referring to Table 14-11, what is the estimated odds ratio for a school with an average SAT score of 1250, a TOEFL criterion that is at least 550, and the room and board expense of 5 thousand dollars?

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Definitions:

Psychological Interpretation

The process of analyzing behavior, symbols, or events to gain insight into the underlying psychological processes and motives.

Internal Reaction

The psychological and emotional response of an individual to external stimuli or events.

External Force

Influences originating outside an individual or system that can affect behaviors, decisions, or change trajectories.

Conscientious

A personality trait characterized by being diligent, careful, meticulous, and responsible.