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A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set µ = P(Y = 1) and the following model is fit: logit(µ) = Bo + B1I(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Во -4.565 0.128 0.380 0.087 -0.198 0.042 0.163 B3 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence interval for the odds ratio in part a. Does this interval give evidence that there is an effect of being female on the odds of case being unsolved. c. Interpret the coefficient estimate (or a function of) B3 = 1.128 within context of the problem. Remember that the base age group is younger than 14 years old.

A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set µ = P(Y = 1) and the following model is fit: logit(µ) = Bo + B1I(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Во -4.565 0.128 0.380 0.087 -0.198 0.042 0.163 B3 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence interval for the odds ratio in part a. Does this interval give evidence that there is an effect of being female on the odds of case being unsolved. c. Interpret the coefficient estimate (or a function of) B3 = 1.128 within context of the problem. Remember that the base age group is younger than 14 years old.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set u = P(Y = 1) and the following model is fit: logit(u) = Bo + BịI(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Bo -4.565 0.128 0.380 0.087 B2 Вз -0.198 0.042 0.163 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence interval for the odds ratio in part a. Does this interval give evidence that there is an effect of being female on the odds of case being unsolved. c. Interpret the coefficient estimate (or a function of) B3 = 1.128 within context of the problem. Remember that the base age group is younger than 14 years old. d. Say you want to see if age group can be dropped from the model. What is the null and alternative hypothesis of this test? How would you go about obtaining a test statistic for this test? e. Now say the response can be one of three categories: Unsolved, solved, and still pending. Using the same covariates, extend the logistic regression stated earlier to a multi category model (use solved as base group) . Be clear and define your notation.
Transcribed Image Text:A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set u = P(Y = 1) and the following model is fit: logit(u) = Bo + BịI(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Bo -4.565 0.128 0.380 0.087 B2 Вз -0.198 0.042 0.163 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence interval for the odds ratio in part a. Does this interval give evidence that there is an effect of being female on the odds of case being unsolved. c. Interpret the coefficient estimate (or a function of) B3 = 1.128 within context of the problem. Remember that the base age group is younger than 14 years old. d. Say you want to see if age group can be dropped from the model. What is the null and alternative hypothesis of this test? How would you go about obtaining a test statistic for this test? e. Now say the response can be one of three categories: Unsolved, solved, and still pending. Using the same covariates, extend the logistic regression stated earlier to a multi category model (use solved as base group) . Be clear and define your notation.
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