Alternative Approaches to Demonstrate Regression Diagnostics in an Introductory Regression Class

• Activity Number: 699
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Robert Pavur*+ and Kellie Keeling
• Companies: Univ of North Texas and University of Denver
• Keywords: Leverage ; diagnostics ; spreadsheets ; L1 regression

Abstract

All regression diagnostic measures are composed of two quantities: leverage and residual. This topic is difficult to present in business statistics class. Although Microsoft Excel does not provide leverage values as an option in its multiple regression procedure, a novel approach using Excel is demonstrated. The notion of leverage is introduced as the predicted value of a dependent variable having a value of one while the remaining observations have values of zero for the dependent variable. The next step is to introduce influence measures such as Cook's D, DFFITS, and DFBETAS by illustrating their relationship with leverages and residuals. This introduction is kept at a level that is not mathematically complex with spreadsheet calculations illustrating the functional relationships. The notion of leverage values for L1 regression, commonly referred to as least absolute deviation (LAD) regression, does not have a precise meaning. Leverage for L1 regression can be generalized. Since leverage can be interpreted as the predicted value of an observation when the dependent variable is a unit vector, this straightforward interpretation has appeal in defining leverage for LAD models.