Bayesian Homework 2 Solved

Data

The data in ‘ElectricCarData_Clean.csv’ (from Kaggle) represent quantitative characteristics of a sample of n = 103 electric vehicles available in Europe. For this homework assignment, we seek to construct a Bayesian regression model to pre- dict vehicle price (PriceEuro; in Euros) based on range (Range_Km; in kilometers) and number of seats (Seats).

Questions

Prepare a written response to the following, using Overleaf. The assignment shouldn’t be longer than 10 (double-spaced, excluding title page, references, and appendices). Due Thurs., Feb. 17, at the beginning of the class period. Please submit the assign- ment as a PDF through CANVAS.

1. Develop a MCMC algorithm to fit a Bayesian regression model using a normal likelihood, multivariate normal prior for the coefficients β, and normal prior for log(σ). Use a random walk proposal for log(σ) in the Metropolis-Hastings updates for log(σ).
2. Conduct a Bayesian regression analysis based on the data set using vehicle price as the response variable and the three sets of covariates below. Compare the 3 models using DIC.

   (a) Range_Km and Seats (b) Range_Km

   (c) Seats

3. ForthebestperformingmodelbasedonDIC,makeinferenceaboutyourfindings using the associated MCMC sample.

4. For a new EV that is not in the data set but has Range_Km = 500 and Seats = 4, predict the vehicle price using the best performing model you identified above.

References

• https://www.kaggle.com/kkhandekar/cheapest-electric-cars