Probability, Statistics, and Forecasting OPRE 433 Fall 2013

Regression Report

Xie Gehui
(gxx24@case.edu)

Dec 2, 2013

I.

Introduction

The data set given contains more than one independent variable, so the target of our regression analysis is to build an appropriate multiple regression model. To realize this target, we have to build a multiple linear regression model to test the regression assumptions: model appropriateness, constant variance, independence, and normality. Certainly we need to modify the data set or the model itself to satisfy these assumptions, and at last get the model acceptable. In the original data set that we are going to deal with in this report, there are 20,640 observations of 8 explanatory variables labeled X1, X2, X3, X4, X5, X6, X7, X8 and 1 dependent variable labeled Y. All of the 9 variables are continuous.

II.

Method of analysis

To check the model appropriateness assumption, we need to make sure the functional form is correct. The residual plot will show the pattern suggesting the form of an appropriate model. To check the validity of the constant variance assumption, we need to examine residual plots. A residual plot with a horizontal band appearance suggests that the spread of the error terms around 0 is not changing much as the horizontal plot value increases. Such a plot tells us that the constant variance assumption approximately holds. To check the independence assumption, we need to detect if any positive autocorrelation or negative autocorrelation exist. If a plot of the time-ordered residuals has a random pattern, the error terms have little or no autocorrelation. In such a case it is reasonable to conclude that the independence assumption holds. To check the normality assumption, we need to construct a normal plot of the residuals. If the normality assumption holds, the normal plot should have a