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

question 240

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 should be the decision ('reject' or 'do not reject') on the null hypothesis when testing whether Toefl500 makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

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Definitions:

Marginal Analysis

An examination of the benefits and costs of increasing or decreasing a unit of production or consumption.

Hungry

The physical sensation of needing or wanting to eat; a condition resulting from not consuming enough food.

Slice of Pizza

A single triangular piece cut from a round pizza, typically topped with cheese, tomato sauce, and various toppings.

Economic Thinking

Economic thinking involves analyzing the production, distribution, and consumption of goods and services by applying principles such as scarcity, choice, and cost-benefit analysis.