Managerial Economics in a Global Economy

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Marketing Research Approaches to Demand EstimationConsumer Surveysdata from survey questionsObservational Researchdata from observed behaviorConsumer Clinicsdata from laboratory experimentsMarket Experimentsdata from real market tests

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Scatter DiagramRegression Analysis

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Regression AnalysisRegression 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

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Ordinary Least Squares (OLS)Model:

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Ordinary Least Squares (OLS)Objective: Determine the slope and intercept that minimize the sum of the squared errors.

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Ordinary Least Squares (OLS)Estimation Procedure

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Ordinary Least Squares (OLS)Estimation Example

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Ordinary Least Squares (OLS)Estimation Example

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Tests of SignificanceStandard Error of the Slope Estimate

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Tests of SignificanceExample Calculation

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Tests of SignificanceExample Calculation

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Tests of SignificanceCalculation of the t Statistic

Degrees of Freedom = (n-k) = (10-2) = 8Critical Value at 5% level =2.306

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Tests of SignificanceDecomposition of Sum of Squares

Total Variation = Explained Variation + Unexplained Variation

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Tests of SignificanceCoefficient of Determination

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Tests of SignificanceCoefficient of Correlation

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Multiple Regression AnalysisModel:

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Multiple Regression AnalysisAdjusted Coefficient of Determination

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Multiple Regression AnalysisAnalysis of Variance and F Statistic

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Problems in Regression AnalysisMulticollinearity: 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.

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Durbin-Watson StatisticTest for Autocorrelation

If d = 2, autocorrelation is absent.

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Steps in Demand EstimationModel Specification: Identify VariablesCollect DataSpecify Functional FormEstimate FunctionTest the Results

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Functional Form SpecificationsLinear Function:Power Function:

Estimation Format:

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Chapter 4 Appendix

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Getting StartedInstall the Analysis ToolPak add-in from the Excel installation media if it has not already been installedAttach the Analysis ToolPak add-inFrom the menu, select Tools and then Add-Ins...When the Add-Ins dialog appears, select Analysis ToolPak and then click OK.

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Entering DataData on each variable must be entered in a separate columnLabel the top of each column with a symbol or brief description to identify the variableMultiple regression analysis requires that all data on independent variables be in adjacent columns

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Example Data

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Running the RegressionSelect the Regression tool from the Analysis ToolPak dialogFrom 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 OKThe Regression tool dialog will then be displayed

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Select the Data RangesType in the data range for the Y variable or select the range on the worksheetType in the data range for the X variable(s) or select the range on the worksheetIf your ranges include the data labels (recommended) then check the labels option

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Select an Output OptionOutput to a selected rangeSelection is the upper left corner of the output rangeOutput to a new worksheetOptionally enter a name for the worksheetOutput to a new workbookAnd then click OK

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Regression Output

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Multiple Regression Data

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Regression Output

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