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. 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.