Suppose that you are interested in studying intravenous drug use among high school students in the...

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Suppose that you are interested in studying intravenous drug use among high school students in the United States. Drug use is characterized as a dichotomous random variable, where 1 indicates that an individual has injected drugs within the past year and 0 that he or she has not. Factors that might be related to drug use are instruction about the human immunodeficiency virus (HIV) in school, age of the student, gender, and general knowledge about HIV, including the various modes of transmission and ways to reduce risk. The estimated coefficients and standard errors from a logistic regression model containing each of these explanatory vari- ables as well as the interaction between instruction and gender are displayed below [5]. Variable Intercept HIV Instruction Age Gender HIV Knowledge HIV Instruction/Gender Coefficient -1.183 0.039 -0.164 1.212 -0.187 -0.663 Standard Error 0.859 0.421 0.092 0.423 0.048 0.512 (a) Conduct tests of the null hypotheses that each of the coefficients in the popu- lation regression equation is equal to 0. At the 0.05 level of significance, which of the explanatory variables influence the probability of intravenous drug use in the past year? (b) As a student becomes older, does the probability that he or she has used intra- venous drugs in the past year increase or decrease? (c) The dichotomous random variable gender is coded so that 1 represents a male and 0 a female. What are the estimated odds of injecting drugs for males rela- tive to females? (d) Does HIV instruction have a different relationship with the probability of in- travenous drug use for males as opposed to females? Suppose that you are interested in studying intravenous drug use among high school students in the United States. Drug use is characterized as a dichotomous random variable, where 1 indicates that an individual has injected drugs within the past year and 0 that he or she has not. Factors that might be related to drug use are instruction about the human immunodeficiency virus (HIV) in school, age of the student, gender, and general knowledge about HIV, including the various modes of transmission and ways to reduce risk. The estimated coefficients and standard errors from a logistic regression model containing each of these explanatory vari- ables as well as the interaction between instruction and gender are displayed below [5]. Variable Intercept HIV Instruction Age Gender HIV Knowledge HIV Instruction/Gender Coefficient -1.183 0.039 -0.164 1.212 -0.187 -0.663 Standard Error 0.859 0.421 0.092 0.423 0.048 0.512 (a) Conduct tests of the null hypotheses that each of the coefficients in the popu- lation regression equation is equal to 0. At the 0.05 level of significance, which of the explanatory variables influence the probability of intravenous drug use in the past year? (b) As a student becomes older, does the probability that he or she has used intra- venous drugs in the past year increase or decrease? (c) The dichotomous random variable gender is coded so that 1 represents a male and 0 a female. What are the estimated odds of injecting drugs for males rela- tive to females? (d) Does HIV instruction have a different relationship with the probability of in- travenous drug use for males as opposed to females?

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a The null hypothesis that each of the coefficients in the population regres sion equation is equal ... View the full answer