Section-3.4-Q3-Template

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Jan 9, 2024

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Exam PA – Section 3.4 Question 3 Business Problem You are a consultant for a regional hospital outside of a major metropolitan area. Due to growing concerns of the hospital nearing full capacity, the hospital has come to your consulting firm to determine the number of visits a patient is likely to make in the upcoming 2 weeks given the medical information they are allowed to provide, which is heavily restricted due to the Health Insurance Portability and Accountability Act. Note that the hospital is strongly concerned with interpretation. Doctors feel that they should be able to communicate the results to hospital administrators. Specific Task You decide that the best course of action is to model the data using GLM. To kick things off, you investigate the quality of the provided dataset. However, the time sensitive nature of this project means you are not able to spend time fixing or cleaning any errors or issues that might be present in the data. In carrying out due diligence, you choose to at least note any concerns you find. (a) Comment on your findings. ANSWER: Your supervisor recommends the gaussian family with identity link to model the number of hospital visits. However, you decide to proceed with the Poisson family and log link. (b) Critique your supervisor’s recommendation in light of your modeling choices. ANSWER:

You decide to run a stepwise selection procedure to determine what features should belong in your GLM. (c) (i) Recommend a specific stepwise procedure. Justify your recommendation. (ii) Provide details on the coefficients of both the full GLM and the resulting stepwise model. ANSWER: Code is provided to obtain log-likelihoods in order to assess the two models that have been created. You consider it as part of your analysis in choosing a final model. (d) Recommend your model of choice. Justify your recommendation. ANSWER: Code is provided to aid with interpreting your chosen model from (d) by exponentiating its coefficient estimates. (e) (i) Explain the reason for exponentiating the estimates. (ii) List several of the most impactful predictors. (iii) Describe the impact of each predictor mentioned in (ii) in terms of model predictors. ANSWER:

Given that you are modeling with GLM, you consider the issue of overdispersion. (f) (i) Describe how overdispersion can be addressed for the models you considered. (ii) State whether your solution in (i) would affect the model predictions. (iii) Describe whether your chosen model has concerns with overdispersion. ANSWER:

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Data Dictionary Variable Description Values visits Number of doctor visits in past 2 weeks integer gender Individual’s gender female male age Individual’s age years income Annual income $ illness Number of illnesses in past 2 weeks integer reduced Number of days of reduced activity in past 2 weeks due to illness or injury integer health General health questionnaire score using Goldberg’s method integer private Does the individual have private health insurance? no yes freerepat Does the individual have free government health insurance due to old age, disability, low income, or veteran status? no yes_age yes_disability yes_income yes_veteran chronic Is there a chronic condition which limits activity? no_condition yes_always_limiting yes_but_not_limiting yes_sometimes_limiting

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