TABLE 14-11
a Logistic Regression Model Was Estimated in Order

question 206

Multiple Choice

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, which of the following is the correct expression for the estimated model?

• A) ln (estimated odds ratio) = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• B) Y = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• C) Y^{^} = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• D) ln (odds ratio) = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd

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Definitions:

Conjunction

A word used to connect clauses or sentences or to coordinate words in the same clause.

Counterfactual Thinking

The mental process of imagining alternative outcomes to events that have already occurred, often focusing on "what could have been."

Meta-Cognition

Self-awareness and understanding of one’s own thought processes, or thinking about one's own thinking.

Collectivist Cultures

Societies that prioritize the needs and goals of the group over individual desires or achievements.