A health clinic sent fliers to its clients to encourage everyone to get a flu shot. In a follow-up study, 159 elderly clients were randomly selected and asked if they received a flu shot. A client who received a flu shot was coded y = 1, and a client who did not receive a flu shot was coded y= 0. Data were also collected on their age, X1, health awareness rating on a 0-100 scale (higher values indicate greater awareness), X2, and gender, 23, where males were coded x3 = 1 and females were coded X3 = 0. A first order logistic regression model was fitted and the output is displayed below. Coefficients: Estimate Std. Error z value Pr(>121) (Intercept) -1.17716 2.98242 -0.395 0.69307 age 0.07279 0.03038 2.396 0.01658 * aware -0.09899 0.03348 -2.957 0.00311 ** gender 0.43397 0.52179 Null deviance: 134.94 Residual deviance: 105.09 on 158 degrees of freedom on 155 degrees of freedom (a) Interpret the estimated coefficient for 23, gender, in context.
(b) Conduct the Wald test for B3. State the null and alternative hypotheses, calculate the test statistic, and make a conclusion in context.
(c) Calculate a 95% confidence interval for B3, and interpret the interval in context.
(d) Comment on whether your conclusions from parts 2b and 2c are consistent.
(e) Suppose you want to drop the coefficients for age and gender, B1 and 33. A logistic regression model for just awareness was fitted, and the output is shown below. Coefficients: Estimate Std. Error z value Pr(>[z]) (Intercept) 4.91133 1.62651 3.02 0.00253 ** aware -0.11931 0.03013 -3.96 7.5e-05 *** Null deviance: 134.94 Residual deviance: 113.20 on 158 degrees of freedom on 157 degrees of freedom Carry out the appropriate hypothesis test to see if the coefficients for age and gender can be dropped.
(f) Based on your conclusion in question 2e, what are the estimated odds of a client receiving the flu shot if the client is 70 years old, has a health awareness rating of 65, and is male? What is the estimated probability of this client receiving the flu shot?
(g) Based on your conclusion in question 2e, interpret the estimated coefficient for age, in context. What does this interpretation tell us about the estimated probability of a client receiving the flu shot if the client is 71 years old, has a health awareness rating of 65, and is male, compared to the estimated probability found for a similar client who is a year younger?