Answered: Table 4.18 shows estimated effects for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y. Smoking status (S) equals 1 for at least one pack per day and 0 other- wise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. A. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fitted YS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable. B. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P -values refer to for these variables? C. Suppose the model also contained an A × R interaction term, with coefficient 0.04. In the prediction equation, show that this represents the difference between the effect of A for blacks and for whites.