---
title: "Lab 6"
author: "Name here"
output: html_document
---

Please use D2L to turn in both the PDF or Word output and your R Markdown file in. 

For this lab we will again use the Seattle Housing dataset [http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/SeattleHousing.csv](http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/SeattleHousing.csv). Assume your goal is to model housing prices in Seattle using a normal distribution.

### Q1.
#### a. (4 pts)
Write out the sampling model for this dataset, define all variables.

#### b. (4 pts)
State and justify prior distributions for $\mu$ and $\sigma^2$. Plot both of these prior distributions.

#### c. (4 pts)
Using the priors above fit the model in JAGS. Include trace plots and summaries of your output.

#### d.  (4 pts)
Print and interpret an HDI for $\mu$.

#### e. (2 pts)
Calculate the $Pr[\mu > 650,000]$.

#### f. (2 pts)
Calculate the probability of an individual house, say $y^{*}$ costing more than $\$650,000.$

#### g. (4 pts)
Summarize the results from part d so that your aunt who is a realtor in Billings can understand.