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

question 276

Multiple Choice

TABLE 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, 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
$\begin{array}{lrrrcrrrr} & & & & &{\text { Odds }} &{95 \% \mathrm{CI}} \\\text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm{Z} & \mathrm{P} & \text { Ratio } & \text { Lower } & \text { Upper } \\\text { Constant } & -27.118 & 6.696 & -4.05 & 0.000 & & & \\\text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\\text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\\text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60\end{array}$
Log-Likelihood $= - 21.883$
Test that all slopes are zero: $\mathrm { G } = 62.083 , \mathrm { DF } = 3 , p$ -value $= 0.000$
Goodness-of-Fit Tests
$\begin{array} { l r r c } \text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046 \end{array}$
-Referring to Table 14-18, which of the following is the correct expression for the estimated model?

• A) Y = -27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• B) \(\hat{Y}\) = -27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• C) 1n(odds ratio) = -27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
• D) 1n(estimated odds ratio) = -27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd

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Definitions:

Parasympathetic Nervous System

A division of the autonomic nervous system responsible for conserving energy and lowering the stress response by slowing the heart rate and increasing intestinal activity.

Respiration Rate

The number of breaths an individual takes per minute, considered an essential vital sign in assessing physical health.

Sympathetic

Pertaining to or arising from the sympathetic nervous system, often described as promoting arousal and energy expenditure.

Parasympathetic

A component of the autonomic nervous system responsible for energy conservation, it decelerates the heart rate, enhances the activity of intestines and glands, and loosens the sphincter muscles.