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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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