Question 17.21

17.21 Interpret the results.

Refer to the previous exercise. The researchers also reported odds ratios with 95% confidence intervals for this logistic regression model. Here is a summary:

Explanatory variable		95% confidence limits
Explanatory variable	Odds ratio	Lower	Upper
Reader age	1.65	1.27	2.16
Model sex	3.70	2.74	5.01
Men's magazines	0.96	0.67	1.37
Women's magazines	1.57	1.11	2.23

Explain the relationship between the confidence intervals reported here and the results of the significance tests that you found in the previous exercise.
Interpret the results in terms of the odds ratios.
Write a short summary explaining the results. Include comments regarding the usefulness of the fitted coefficients versus the odds ratios in making a summary.

17.21

(a) If the confidence interval for the odds ratio includes the value 1, the variable is not significant in a logistic regression. (b) Because the Reader age, Model sex, and Women's magazines intervals all do not contain 1, they are all significant. The Men's magazine interval contains 1 and is not significant. (c) Interpreting only significant effects: When the reader age is mature adults, the model clothing is 1.27 to 2.16 times more likely to be not sexual. When the model sex is male, the model clothing is 2.74 to 5.01 times more likely to be not sexual. When the intended readership is women, the model clothing is 1.11 to 2.23 times more likely to be not sexual. The odds ratios are often much easier to interpret than the fitted coefficients.