1. 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.
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

2. Dummy Variable
an independent variable that has two (or more) distinct levels, which are coded 0 and 1.
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

3. Dummy Variable Coding Category X1 X2 Physician 0 0 Attorney 1 0
Professor
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

4. 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
5. My job allows me to learn
new skills Strongly Strongly
7. My work give me a sense of
accomplishment Strongly Strongly
19. Gender 0 = Male
1 = Female
Dependent Variable
15. I am proud to tell others that I
work for Samouel’s restaurant. Strongly Strongly
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

5. Exhibit A-2 Regression Model of Job Satisfaction and Commitment for Samouel’s Employees
Model Summary
Model R
R Square
Adjusted R Square 1
.627*
.393
.351
Model
Sum of Squares
Mean Square F
Sig. 1
Regression
21.138
5.284
9.399
.000*
Residual
32.608
.562
Total
53.746
*Predictors: (Constant), X19 – Gender, X7 – Accomplishment, X5 – Learn New Skills, X2 – Work I Want
Dependent Variable: X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

6. Standardized Coefficients
Exhibit A-3 Beta Coefficients for Job Satisfaction and Commitment Regression
Coefficients
Model
Unstandardized
Coefficients
Standardized Coefficients t
Sig. B
Std.
Error
Beta 1
(Constant)
2.716
.702
3.871
.000
X2 – Work I Want
.348
.148
.325
2.344
.023
X5 – Learn New Skills
9.943E-.02
.109
.100
.911
.366
X7 – Accomplishment
5.017E-02
.122
.055
.410
.683
X19 – Gender
.853
.210
.445
4.056
*Dependent Variable: X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

7. Exhibit A-4 Comparison of Male and Female Employee Perceptions
Residual Statistics
X19 –
Gender
X2 – Work
I Want
X5 – Learn
New Skills
X7 –
Accomplishment
X15 –
Proud
Males
Mean
4.83
5.10
4.95
5.15 N 40
Females
5.17
4.61
6.09 23
Total
4.92
5.03
5.49 63
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

8. Exhibit A-4 Comparison of Male and Female Employee Perceptions Continued
ANOVA Table
Sum of
Squares
Mean
Square F
Sig.
X2 – Work I Want*
X19 – Gender
Between Groups Combined
Within Groups
Total
1.778
45.079
45.857
.739
2.406
.126
X5 – Learn New Skills*
3.525
51.078
54.603
.837
4.210
.044
X7 – Accomplishment*
.732
63.204
63.937
1.036
.707
.404
X15 – Proud*
12.820
40.926
53.746
.671
19.108
.000
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

9. Regression Analysis Terms
Explained variance = R2.
Unexplained variance or error = residuals.
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

10. 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.
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

11. 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).
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

12. Exhibit A-5 Histogram of Employee Survey Dependent Variable X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

13. Exhibit A-6 Normal Probability Plot of Regression Standardized Residuals
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

14. Exhibit A-7 Scatterplot of Employee Survey Dependent Variable X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

15. Exhibit A-8 Residual Statistics for Employee Survey
Minimum
Maximum
Mean
Std.
Deviation N
Predicted Value
4.41
6.95
5.49
.58 63
Residual
– 1.35
1.70
– 8.18E-16
.73
Std. Predicted
Value
– 1.858
2.500
.000
1.000
Std. Residual
– 1.805
2.263
.967
*Dependent Variable: X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.

16. Exhibit A-8 Casewise Diagnostics for Employee Survey
Number
Std.
Residual
X15 – Proud
Predicted
Value 14
2.263 7
5.30
1.70 51 53
2.130
5.40
1.60
Dependent Variable: X15 – Proud
Hair, Babin, Money & Samouel, Essentials of Business Research, Wiley, 2003.