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

question 132

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

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



TABLE 14-10

Regression Analysis
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline\text { Multiple R} & 0.63 \\\text {R Square }& 0.40 \\\text {Adjusted R Square} & 0.23 \\\text {Standard Error }& 50.00 \\\text {Observations} & 15.00 \\\hline\end{array}$

ANOVA
$\begin{array}{lccccc}\hline & \text { d f} & \text {SS} & \text {MS} & \text {F } & \text {Significance F } \\\hline \text {Regression} & 3 & & 5994.24 & 2.40 & 0.12 \\\text {Residual }& 11 & 27496.82 & & & \\\text {Total }& 45479.54 & & & \\\hline\end{array}$

$\begin{array}{lccrrrr}\hline & \text {oefficients}&\text { Standard Error }& \text { t Stat} &\text { p-value }& \text {Lower 99.0\% }& \text {Upper 99.0 \% } \\\hline\text { Intercept} & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\\text {AGE }& -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\\text {TICKETS}& 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\\text {DENSITY} & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\\hline\end{array}$

-Referring to Table 14-11, what is the estimated probability that 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 will be a private school?

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