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.