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Introduction to Multiple Regression: How Much Is Your Car Worth?

Shonda Kuiper 

Grinnell College

Journal of Statistics Education Volume 16, Number 3 (2008), www.amstat.org/publications/jse/v16n3/datasets.kuiper.html

Copyright © 2008 by Shonda Kuiper all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.

Key Words: Multiple Regression; Dummy Variables; Heteroskedasticity; Data Transformation; Residuals.

Abstract

Data collected from Kelly Blue Book for several hundred 2005 used General Motors (GM) cars allows students to develop a multivariate regression model to determine car values based on a variety of characteristics such as mileage, make, model, engine size, interior style, and cruise control. Students learn to look at residual plots to check for heteroskedasticity, normality, autocorrelation, and multicollinearity as well as explore techniques for variable selection and develop specially constructed variables.

1. Introduction

This paper discusses the development of a multivariate regression model to predict the retail price of 2005 General Motor (GM) cars. Statistical textbooks typically offer many small data sets chosen to illustrate a variety of issues and techniques that a user of regression should know. Although small data sets can offer the advantage of sharp focus on particular issues, their narrow focus carries disadvantages as well. Working with a large, richly structured data set can give students a kind of experience not possible with a succession of smaller data sets. Accordingly, many courses use projects to ensure that students experience the challenge of model building and the opportunity to synthesize the elements of regression learned one at a time from smaller data sets. However, students can often have difficulty adjusting from traditional homework to a true research project that...