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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 1

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Presentation on theme: "PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 1"— Presentation transcript:

1 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 1

2 Regression Analysis Scatter Diagram
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 2

3 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 3

4 Regression Analysis Regression Line: Line of Best Fit
Regression Line: Minimizes the sum of the squared vertical deviations (et) of each point from the regression line. Ordinary Least Squares (OLS) Method PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 4

5 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 5

6 Ordinary Least Squares (OLS)
Model: PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 6

7 Ordinary Least Squares (OLS)
Objective: Determine the slope and intercept that minimize the sum of the squared errors. PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 7

8 Ordinary Least Squares (OLS)
Estimation Procedure PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 8

9 Ordinary Least Squares (OLS)
Estimation Example PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 9

10 Ordinary Least Squares (OLS)
Estimation Example PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 10

11 Standard Error of the Slope Estimate
Tests of Significance Standard Error of the Slope Estimate PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 11

12 Tests of Significance Example Calculation
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 12

13 Tests of Significance Example Calculation
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 13

14 Tests of Significance Calculation of the t Statistic
Degrees of Freedom = (n-k) = (10-2) = 8 Critical Value at 5% level =2.306 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 14

15 Tests of Significance Decomposition of Sum of Squares
Total Variation = Explained Variation + Unexplained Variation PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 15

16 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 16

17 Coefficient of Determination
Tests of Significance Coefficient of Determination PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 17

18 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 18

19 Coefficient of Correlation
Tests of Significance Coefficient of Correlation PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 19

20 Multiple Regression Analysis
Model: PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 20

21 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 21

22 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 22

23 Multiple Regression Analysis
Adjusted Coefficient of Determination PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 23

24 Multiple Regression Analysis
Analysis of Variance and F Statistic PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 24

25 Problems in Regression Analysis
Multicollinearity: Two or more explanatory variables are highly correlated. Heteroskedasticity: Variance of error term is not independent of the Y variable. Autocorrelation: Consecutive error terms are correlated. PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 25

26 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 26

27 Durbin-Watson Statistic
Test for Autocorrelation If d = 2, autocorrelation is absent. PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 27

28 Chapter 4 Appendix PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 28

29 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 29

30 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 30

31 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 31

32 Getting Started Install the Analysis ToolPak add-in from the Excel installation media if it has not already been installed Attach the Analysis ToolPak add-in From the menu, select Tools and then Add-Ins... When the Add-Ins dialog appears, select Analysis ToolPak and then click OK. PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 32

33 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 33

34 Entering Data Data on each variable must be entered in a separate column Label the top of each column with a symbol or brief description to identify the variable Multiple regression analysis requires that all data on independent variables be in adjacent columns PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 34

35 Example Data PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 35

36 Running the Regression
Select the Regression tool from the Analysis ToolPak dialog From the menu, select Tools and then Data Analysis... On the Data Analysis dialog, scroll down the list of Analysis Tools, select Regression, and then click OK The Regression tool dialog will then be displayed PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 36

37 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 37

38 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 38

39 Select the Data Ranges Type in the data range for the Y variable or select the range on the worksheet Type in the data range for the X variable(s) or select the range on the worksheet If your ranges include the data labels (recommended) then check the labels option PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 39

40 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 40

41 Select an Output Option
Output to a selected range Selection is the upper left corner of the output range Output to a new worksheet Optionally enter a name for the worksheet Output to a new workbook And then click OK PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 41

42 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 42

43 Regression Output PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 43

44 Multiple Regression Data
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 44

45 PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 45

46 Regression Output PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 46

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