Illustration of Regression AnalysisStage 1: Definition Of The Research ProblemStage 2: Develop The Analysis Plan: Sample Size IssuesStage 2: Develop The Analysis Plan: Measurement IssuesStage 3: Evaluate Underlying AssumptionsNormality of metric variablesRun the 'NormalityAssumptionAndTransformations' ScriptComplete the 'Test for Assumption of Normality' Dialog BoxOutput for a Variable that Passes the Test of NormalityOutput for a Variable that Fails the Test of NormalitySlide 11Linearity between metric independent variables and dependent variableRun the 'LinearityAssumptionAndTransformations' ScriptComplete the 'Check for Linear Relationships' Dialog BoxThe Scatterplot MatrixThe Correlation MatrixOutput Demonstrating NonlinearitySlide 18Constant variance across categories of nonmetric independent variablesRun the 'HomoscedasticityAssumptionAndTransformations' ScriptComplete the Dialog BoxOutput for the Test of Homogeneity of VariancesOutput Failing to Pass the Homogeneity of Variance TestStage 4: Compute the Statistics And Test Model Fit: ComputationsSlide 25Request the Regression AnalysisSpecify the Dependent and Independent Variables and the Variable Selection MethodSpecify the Statistics OptionsSpecify the Plots to Include in the OutputSpecify Diagnostic Statistics to Save to the Data SetComplete the Regression Analysis RequestStage 4: Compute the Statistics And Test Model Fit: Model FitSignificance Test of the Coefficient of Determination R SquareSlide 34Significance Test of Individual Regression CoefficientsStage 4: Compute the Statistics And Test Model Fit: Meeting AssumptionsLinearity and Constant Variance for the Dependent Variable: Residual PlotNormal Distribution of Residuals: Normality Plot of ResidualsLinearity of Independent Variables: Partial PlotsSlide 40Independence of Residuals: Durbin-Watson StatisticIdentifying Dependent Variable Outliers: Casewise Plot of Standardized ResidualsIdentifying Independent Variable Outliers - Mahalanobis DistanceIdentifying Independent Variable Outliers: Mahalanobis DistanceIdentifying Statistically Significant Mahalanobis Distance ScoresIdentifying Potential OutliersIdentifying Influential Cases - Cook's DistanceSorting Cook's Distance Scores in Descending OrderCases with Large Cook's DistancesStage 5: Interpret The Findings - Regression CoefficientsDirection of relationship and contribution to dependent variableImportance of PredictorsStage 5: Interpret The Findings - Impact of MulticollinearityTolerance or VIF statisticsStage 6: Validate The ModelInterpreting Adjusted R SquareSplit-Sample ValidationSet the Starting Point for Random Number GenerationCompute the Variable to Randomly Split the Sample into Two HalvesSpecify the Cases to Include in the First Screening SampleDefine the Case Selection RuleComplete the Regression Analysis Request for the First Screening SampleSpecify the Cases to Include in the Second Screening SampleComplete the Regression Analysis Request for the Second Screening SampleSummary Table for Validation AnalysisSlide 66Slide 1 Illustration of Regression AnalysisThis problem is the major problem for Chapter 4, "Multiple Regression Analysis," from the textbook.Illustration of Regression AnalysisSlide 2 Stage 1: Definition Of The Research ProblemIn the first stage, we state the research problem, specify the variables to be used in the analysis, and specify the method for conducting the analysis: standard multiple regression, hierarchical regression, or stepwise regression.Illustration of Regression AnalysisRelationship to be AnalyzedHATCO management has long been interested in more accurately predicting the level of business obtained from its customers in the attempt to provide a better basis for production controls and marketing efforts. To this end, analysts at HATCO proposed that a multiple regression analysis should be attempted to predict the product usage levels of customers based on their perceptions of HATCO's performance. In addition to finding a way to accurately predict usage levels, the researchers were also interested in identifying the factors that led to increased product usage for application in differentiated marketing campaigns. (page 196)Specifying the Dependent and Independent VariablesThe dependent variable is Product Usage (x9). The independent variables are Delivery Speed (x1), Price Level (x2), Price Flexibility (x3), Manufacturer's Image (x4), Service (x5), Sales force Image (x6), and Product Quality (x7). (page 196)Method for including independent variables: standard, hierarchical, stepwiseSince this is an exploratory analysis and we are interested in identifying the best subset of predictors, we will employ a stepwise regression.Slide 3 Stage 2: Develop The Analysis Plan: Sample Size IssuesIn stage 2, we examine sample size and measurement issues.Illustration of Regression AnalysisPower to Detect Relationships: Page 165 of TextIf the significance level is set to 0.05, then with a sample size of 100, we can identify relationships that explain about 13% of the variance. (text, page 196), referencing the power table on page 165 of the text.Missing data analysisIf the significance level is set to 0.05, then with a sample size of 100, we can identify relationships that explain about 13% of the variance. (text, page 196), referencing the power table on page 165 of the text.Minimum Sample Size Requirement: 15-20 Cases Per Independent VariableWith 100 cases in the sample and 7 independent variables, we are very close to satisfying the 15 case per independent variable requirement.Slide 4 Stage 2: Develop The Analysis Plan: Measurement IssuesIn stage 2, we examine sample size and measurement issues.Illustration of Regression AnalysisIncorporating Nonmetric Data with Dummy Variables All of the variables are metric, so no dummy coding is required.Representing Curvilinear Effects with Polynomials We do not have any evidence of curvilinear effects at this point in the analysis.Representing Interaction or Moderator Effects We do not have any evidence at this point in the analysis that we should add interaction or moderator variables.Slide 5 Stage 3: Evaluate Underlying AssumptionsIn this stage, we verify that all of the independent variables are metric or dummy-coded, and test for normality of the metric variables, linearity of the relationships between the dependent and the independent variables, and test for homogeneity of variance for the nonmetric independent variables.Illustration of