11.-/4 points The following table contains statistics from a logistic regression
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Question
11.-/4 points The following table contains statistics from a logistic regression analysis for a study on intravenous drug use among high school students in United States. Drug use is characterized as a dichotomous variable, where 1 indicates that an individual has injected drugs within the past year and O that he or she has not. Factors that might be related to drug use are instruction about the HIV in school (1 represents "had HIV education" and O represents "did not have HIV education"), age of the student (in years), and gender (1 represents male and O represents female). Statistics in the table are estimated coefficients of the logistic regression model and p-values for testing the significance of the coefficients Variable Intercept (Constant) HIV instruction Coefficient p-value 0.164 0.078 0.019 0.928 0.064 0.036 1.032 0.014 Age Gender What is odds ratio of having used intravenous drugs in the past year for a male student versus a female student? The odds ratio is (Use all the predictor variables to build the regression model, and round your answer to the second decimal place. That is, 23.421 - 23.42 and 15.8673 = 15.87) [Write the answer in the following text box.]Explanation / Answer
The logistic regression is,
log(odds) = -0.164 + 0.019 HIV + 0.064 Age + 1.032 Gender
For male, Gender = 1
log(odds_male) = -0.164 + 0.019 HIV + 0.064 Age + 1.032 * 1
log(odds_male) = 0.868 + 0.019 HIV + 0.064 Age
odds_male = exp[0.868 + 0.019 HIV + 0.064 Age]
For female, Gender = 0
log(odds_female) = -0.164 + 0.019 HIV + 0.064 Age + 1.032 * 0
log(odds_female) = -0.164 + 0.019 HIV + 0.064 Age
odds_female = exp[-0.164 + 0.019 HIV + 0.064 Age]
Odds ratio = odds_male / odds_female = exp[0.868 + 0.019 HIV + 0.064 Age] / exp[-0.164 + 0.019 HIV + 0.064 Age]
= exp[0.868 + 0.164] = 2.81
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