1. Business Statistics, 4e by Ken Black
Chapter 13
Simple Regression
Analysis
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

2. Learning Objectives
Compute the equation of a simple regression line from a sample of data, and interpret the slope and intercept of the equation.
Understand the usefulness of residual analysis in testing the assumptions underlying regression analysis and in examining the fit of the regression line to the data.
Compute a standard error of the estimate and interpret its meaning.
Compute a coefficient of determination and interpret it.
Test hypotheses about the slope of the regression model and interpret the results.
Estimate values of Y using the regression model.
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 2

3. Regression and Correlation
Regression analysis is the process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable.
Correlation is a measure of the degree of relatedness of two variables.
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

4. Simple Regression Analysis
bivariate (two variables) linear regression -- the most elementary regression model
dependent variable, the variable to be predicted, usually called Y
independent variable, the predictor or explanatory variable, usually called X
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 5

5. Airline Cost Data Number of Passengers X Cost ($1,000) Y 61 4.280 63
4.080 67
4.420 69
4.170 70
4.480 74
4.300 76
4.820 81
4.700 86
5.110 91
5.130 95
5.640 97
5.560
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 6

6. Scatter Plot of Airline Cost Data
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 7

7. Regression Models Deterministic Regression Model Y = 0 + 1X
Probabilistic Regression Model Y = 0 + 1X + 
0 and 1 are population parameters
0 and 1 are estimated by sample statistics b0 and b1
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8. Equation of the Simple Regression Line
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 9

9. Least Squares Analysis
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10. Least Squares Analysis
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

11. Solving for b1 and b0 of the Regression Line: Airline Cost Example (Part 1)
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12. Solving for b1 and b0 of the Regression Line: Airline Cost Example (Part 2)
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13. Graph of Regression Line for the Airline Cost Example
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 14

14. Airline Cost: Excel Summary Output
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 12
ANOVA df SS MS F
Significance F
Regression 1
2.7E-06
Residual 10
Total 11
Coefficients
t Stat
P-value
Intercept
Number of Passengers
2.692E-06
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

15. Residual Analysis: Airline Cost Example
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16. Excel Graph of Residuals for the Airline Cost Example
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 16

17. Nonlinear Residual PlotX
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18. Nonconstant Error VarianceX X
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19. Graphs of Nonindependent Error TermsX
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20. Healthy Residual Plot X 21X
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21. Standard Error of the Estimate
Sum of Squares Error
Standard Error
of the
Estimate
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22. Determining SSE for the Airline Cost Example
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 23

23. Standard Error of the Estimate for the Airline Cost Example
Sum of Squares Error
Standard Error
of the
Estimate
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 24

24. Coefficient of Determination
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 25

25. Coefficient of Determination for the Airline Cost Example
89.9% of the variability
of the cost of flying a
Boeing 737 is accounted for
by the number of passengers.
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26. Hypothesis Tests for the Slope of the Regression Model
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27. Hypothesis Test: Airline Cost Example (Part 1)
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28. Hypothesis Test: Airline Cost Example (Part 2)
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29. Testing the Overall Model (Part 1)
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

30. Testing the Overall Model (Part 2)
ANOVA df SS MS F
Significance F
Regression 1
2.7E-06
Residual 10
Total 11
F = > 4.96, reject H0
Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

31. Point Estimation for the Airline Cost Example
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32. Confidence Interval to Estimate Y : Airline Cost Example
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33. Confidence Interval to Estimate the Average Value of Y for some Values of X: Airline Cost Example
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34. Prediction Interval to Estimate Y for a given value of X
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35. Confidence Intervals for Estimation6 7 8 9 1 4 5 N u m b e r o f P a s n g C t R i % I l
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36. MINITAB Regression Analysis of the Airline Cost Example
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37. Pearson Product-Moment Correlation Coefficient
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38. Three Degrees of Correlation
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