Special Topics in Multiple Regression Analysis Chapter 11 – Appendix 11-A Learning Objectives: • Explain the use of dummy variables in regression analysis. • Examine residuals and outliers as they relate to multiple regression analysis.
Dummy Variable . . . . an independent variable that has two (or more) distinct levels, which are coded 0 and 1.
Dummy Variable Coding Category X1 X2 Physician 0 0 Attorney 1 0 Professor 0 1
Exhibit A-1 Selected Variables from Employee Survey Independent Variables (Job Satisfaction & Gender) 2. I am doing the kind of work I want. Strongly Strongly Disagree Agree 1 2 3 4 5 6 7 5. My job allows me to learn new skills. Strongly Strongly Disagree Agree 1 2 3 4 5 6 7 7. My work give me a sense of accomplishment. Strongly Strongly Disagree Agree 1 2 3 4 5 6 7 19. Gender 0 = Male 1 = Female Dependent Variable 15. I am proud to tell others that I work for Samouel’s restaurant. Strongly Strongly Disagree Agree 1 2 3 4 5 6 7
Exhibit A-2 Regression Model of Job Satisfaction and Commitment for Samouel’s Employees Model Summary *Predictors: (Constant), X19 – Gender, X7 – Accomplishment, X5 – Learn New Skills, X2 – Work I Want Dependent Variable: X15 – Proud
Exhibit A-3 Beta Coefficients for Job Satisfaction and Commitment Regression Coefficients *Dependent Variable: X15 – Proud
Exhibit A-4 Comparison of Male and Female Employee Perceptions Residual Statistics
Exhibit A-4 Comparison of Male and Female Employee Perceptions Continued ANOVA Table
Regression Analysis Terms • Explained variance = R2. • Unexplained variance or error = residuals.
Regression Assumptions • The error variance is constant over all values of the independent variables; • The errors are uncorrelated with each of the independent variables; and • The errors are normally distributed.
Residuals Plots • Plot of standardized residuals – enables you to determine if the errors are normally distributed (see Exhibit A-5). • Normal probability plot – enables you to determine if the errors are normally distributed. It compares the observed standardized residuals against the expected standardized residuals from a normal distribution (see Exhibit A-6). • Plot of standardized residuals – can be used to identify outliers. It compares the standardized predicted values of the dependent variable against the standardized residuals from the regression equation (see Exhibit A-7).
Exhibit A-5 Histogram of Employee Survey Dependent Variable X15 – Proud
Exhibit A-6 Normal Probability Plot of Regression Standardized Residuals
Exhibit A-7 Scatterplot of Employee Survey Dependent Variable X15 – Proud
Exhibit A-8 Residual Statistics for Employee Survey Residual Statistics* *Dependent Variable: X15 – Proud
Exhibit A-8 Casewise Diagnostics for Employee Survey Casewise Diagnostics* Dependent Variable: X15 – Proud