Applied Regression Modeling: A Business Approach

Problem on multiple linear regression model building I

The following problem provides a challenging dataset that students can use to try to find their best multiple linear regression model.

You've been asked to find out how restaurant profits are affected by certain characteristics of the restaurants. You have data on 39 restaurants, and would like to build a regression model for predicting Y = annual profits (in thousands of dollars) from 5 potential predictor variables:

X1 = number of meals (in thousands)
X2 = food costs (in thousands of dollars)
X3 = overhead costs (in thousands of dollars)
X4 = labor costs (in thousands of dollars)
region = geographical location (Mountain, Southwest, or Northwest)

Note that region is a qualitative (categorical) variable with three levels; the following data files (in SPSS, text, and Excel format, respectively): RESTAURANT.SAV, RESTAURANT.TXT, RESTAURANT.XLS contain two dummy indicator variables to code the information in region: "D5" = 1 for Southwest, 0 otherwise, and "D6" = 1 for Northwest, 0 otherwise. (So, the Mountain region is the reference level with zero for both "D5" and "D6.")

Build a suitable regression model. You may want to consider the following topics in doing so:

models with both quantitative and qualitative variables
polynomial transformations
interactions
comparing nested models

You may use the following for terms in your model:

X1, X2, X3, X4, D5, D6 (do not use region however!)
interactions between each of the quantitative predictors and the dummy variables, such as D5X1, D6X1, etc.
quadratic terms, such as X1² (do not use terms like D1² however!)
use Y as the response variable (i.e., do not use the natural logarithm of Y or any other transformation)

[Hint: a "good" model should have R² around 0.93 and a regression standard error, s, around 10.6.]

Last updated: June, 2008

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