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:

Discount Rates

The rate of interest applied to calculate the current value of future cash flows.

Market Proxy

A singular asset or portfolio that represents the characteristics of an entire market segment or the market as a whole.

CAPM

The Capital Asset Pricing Model, which describes the relationship between systematic risk and expected return for assets, particularly stocks, suggesting that investors need to be compensated in two ways: time value of money and risk.

Fama and French

Scholars who developed a three-factor model for explaining the risk and return of stocks and other investments.