--- title: | | STAT 491: Final Exam | Due: May ? | Name: output: pdf_document --- ```{r setup, include=FALSE} library(knitr) knitr::opts_chunk$set(echo = TRUE) ``` Please turn in the exam to D2L and include the R Markdown code, SAS code *and either* a Word or PDF file with output. While the exam is open book, meaning you are free to use any resources from class, this is strictly an individual endeavor and **you should not discuss the problems with anyone outside the course instructor including class members.** The instructor will answer questions related to the data, expectations, and understanding of the exam, but will not fix or troubleshoot broken code. # (60 points Indeed.com Data Analysis) This exam will focus on small dataset containing information from Indeed.com, which can be accessed using [http://www.math.montana.edu/ahoegh/teaching/stat491/data/bzn_jobs.csv](http://www.math.montana.edu/ahoegh/teaching/stat491/data/bzn_jobs.csv). ```{r} bzn.jobs <- read.csv('http://www.math.montana.edu/ahoegh/teaching/stat491/data/bzn_jobs.csv') head(bzn.jobs) ``` This dataset contains the following variables: - jobAgeDays: number of days the job has been posted on Indeed.com - normTitle: name of job position - estimatedSalary: estimated annual salary - localClicks: number of people clicking on job posting ## Question 1. (36 points) - Bayesian Linear Models For this question we will fit a regression analysis to model estimated Salary. For full credit you need to consider all other variables as predictors. #### a. (4 points) Explain the purpose of this model - you can assume you talking to a freshman in high school. #### b. (4 points) Select and Justify a Sampling Model #### c. (4 points) Write out the Linear Combination of Predictors for your model and justify this selection #### d. (4 points) State and Justify Priors Used for this Model #### e. (4 points) Use JAGS to fit the Posterior Distribution for this Model and Summarize the Results #### f. (4 points) Use your model to construct a posterior predictive distribution for the estimatedSalary of a new job with: jobAgeDays = 1, normTitle = registered nurse, and localClicks = 11. #### g. (4 points) Explain the results of this model - you can assume you talking to a freshman in high school. #### h. (4 points) Discuss the differences between using normTitle as a nominal value and fitting a hierarchical regression model with normTitle as the group. You don't need to fit these models, but be specific in your discussion. #### i. (4 points) Discuss the differences between using a t-distribution and a normal distribution on the sampling model. How would you decide which was more appropriate? ## Question 2. (24 points) - Bayesian Poisson Regression Now assume the goal is to model the number of localClicks for each job using Poisson regression. #### a. (4 points) Explain the purpose of this model - you can assume you talking to an executive considering whether to post a job on Indeed.com. (Note: companies posting featured jobs pay Indeed based on the number of clicks on the job posting) #### b. (4 points) Use a Poisson distribution as the sampling model and write out the linear combination of predictors for your model and justify this selection #### c. (4 points) State and justify priors used for this model #### d. (4 points) Use JAGS to fit the Posterior Distribution for this Model and Summarize the Results #### e. (4 points) Use your model to construct a posterior predictive distribution for the localClicks of a new job with: jobAgeDays = 1, normTitle = registered nurse, and estimatedSalary = 70000. #### f. (4 points) Explain the results of this model - you can assume you talking to an executive considering whether to post a job on Indeed.com.