Please note that the dataset you are given is a fabricated dataset by using real data after a number of other analyses for the population distributions of the variables included in the dataset. This is done to comply with the rules around the use and distribution of the real data.
Assignment2PropertyPrices.csv Download Assignment2PropertyPrices.csvincludes the following variables:
SalePrice: Sale price in AUD
Area: Land size in m2 of the sold property
Bedrooms: The number of bedrooms
Bathrooms: The number of bathrooms
CarParks: The number of car parks
PropertyType: The type of the property (0: House, 1: Unit)
You will model the sale prices in Melbourne using the other predictors given in the dataset and expert knowledge from a real estate agent. For each predictor, expert information and the degree of belief in the prior information is given as follows:
Area: Every m2 increase in land size increases the sales price by 90 AUD. This is a very strong expert knowledge.
Bedrooms: Every additional bedroom increases the sales price by 100,000AUD. This is a weak expert knowledge.
Bathrooms: There is no expert knowledge on the number of bathrooms.
CarParks: Every additional car space increases the sales price by 120,000AUD. This is a strong expert knowledge.
PropertyType: If the property is a unit, the sale price will be 150,000 AUD less than that of a house on the average. This is a very strong expert knowledge.
The following steps are given to help you to complete the tasks. Please follow the steps given below to build a Bayesian regression model to predict sale prices using the past sales information and expert knowledge:
Create a JAGS model diagram showing the multiple linear regression setting in this problem.
Specify the prior distributions reflecting the expert information for each predictor.
Create JAGS data and model blocks based on the model diagram and prior distributions at the previous steps.
Compile your model and create Markov chains using the compiled model.
Assess the appropriateness of the chains for each parameter using the MCMC diagnostics.
Display the posterior distribution of each parameter and draw inferences on Bayesian point and interval estimates.
Use the Bayesian point estimates of the model parameters to write the predictions model.
Find the predictions of sale prices for the properties given below:
Property No
Area
Bedrooms
Bathrooms
CarParks
PropertyType
1
600
2
2
1
Unit
2
800
3
1
2
House
3
1500
2
1
1
House
4
2500
5
4
4
House
5
250
3
2
1
Unit