Hierarchical Multiple RegressionDifferences between standard and hierarchical multiple regressionDifferences in statistical resultsVariations in hierarchical regressionConfusion in Terminology over the Meaning of the Designation of a Control VariableResearch Questions for which Hierarchical Regression is UsefulThe Problem in BlackboardThe Statement about Level of MeasurementMarking the Statement about Level of MeasurementSatisfying the Assumptions of Multiple RegressionUsing the Script to Evaluate AssumptionsOpening the ScriptSelect the VariablesSelect the Reference Category for SexSelect the Reference Category for RaceRequest the Tests of Assumptions for Multiple RegressionThe Variables Included in the AnalysisEvaluating the Assumption of Independence of VariablesEvaluating the Assumption of LinearityEvaluating the Assumption of HomoscedasticityEvaluating the Assumption of NormalityEvaluating the Assumption of Independence of ErrorsExcluding Extreme Outliers to Try to Achieve NormalityFeedback on Extreme OutliersOutliers and Extreme Outliers in SPSS OutputTesting Normality for Variables Treated as Metric: empathy7Test of Normality in SPSS OutputAdding the Transformation of Empathy7 to Data SetTesting Normality for Variables Treated as Metric: polviewsSlide 30Testing Normality for Variables Treated as Metric: fundSlide 32The Hierarchical Regression with Transformed VariablesSlide 34Slide 35Evaluating the Assumption of HomoscedasticitySlide 37Slide 38Excluding Extreme OutliersFeedback on Extreme Outliers in the ScriptSlide 41Marking the Check Boxes for Regression AssumptionsRemoving the Transformed VariableRetaining the Dummy-coded Variables for the Hierarchical RegressionThe Dummy-coded Variables in the Data EditorRunning the Hierarchical Regression Model in SPSSIncluding the Dependent and Control Variables in the AnalysisAdding the Predictor Independent Variables to the AnalysisRequesting Additional Statistical OutputAdditional Statistical OutputCompleting the Request for the Hierarchical RegressionThe Statement for Sample SizeSatisfying the Sample Size RequirementMarking the Check Box for Sample Size RequirementStatement about Predictors and Controls as Independent VariablesSignificance of the Predictor VariablesStrength of the Relationship of the Predictor VariablesMarking the Statement for Predictors and Controls as Independent VariablesStatements about Individual RelationshipsSlide 60Output Before and After Predictors are Included.Religious Fundamentalism and Empathy - 1Religious Fundamentalism and Empathy - 2Marking the Statement on Religious Fundamentalism and EmpathyStatement on Political Conservatism and EmpathyPolitical Conservatism and EmpathyMarking the Check Box for Political Conservatism and EmpathyStatement on the Relationship between Sex and EmpathySex and Empathy - 1Sex and Empathy - 2Marking the Statement on the Relationship between Sex and Empathy7Statements on the Relationship between Race and EmpathyRace and Empathy - 1Race and Empathy - 2Marking Statements on the Relationship between Race and EmpathyThe Problem Graded in BlackBoardRemoving the Variables Created by the ScriptLogic Diagram for Solving Homework Problems: Level of MeasurementRegression Assumptions for Model 1: Original Variables, All CasesRegression Assumptions for Model 2: Original Variables, Excluding Extreme OutliersRegression Assumptions for Model 3: Transformed Variables, All CasesRegression Assumptions for Model 4: Transformed Variables, Excluding Extreme OutliersSample Size RequirementOverall Relationship – Change in R2Relationships with Individual Controls and PredictorsSlide 1Hierarchical Multiple RegressionSlide 2Differences between standard and hierarchical multiple regressionStandard multiple regression is used to evaluate the relationship between a set of independent variables and a dependent variable.Hierarchical regression is used to evaluate the relationship between a set of independent variables (predictors) and the dependent variable, controlling for or taking into account the impact of a different set of independent variables (control variables) on the dependent variable.For example, a research hypothesis might state that there are differences in the average salary between male employees and female employees, even after we take into account differences in education levels and prior work experience.In hierarchical regression, the independent variables are entered into the analysis in a sequence of blocks, or groups that may contain one or more variables. In the example above, education and work experience would be entered in the first block and sex would be entered in the second block.Generally, our interest is in R² change, i.e. the increase when the predictors variables are added to the analysis rather than the overall R² for the model that includes both controls and predictors.Moreover, the interpretation of individual relationships may focus on the relationship between the predictors and the dependent variables, and ignore the significance and interpretation of control variables. However, in our problems, we will interpret both controls and predictors.Slide 3Differences in statistical resultsSPSS shows the statistical results (Model Summary, ANOVA, Coefficients, etc.) as each block of variables is entered into the analysis.In addition (if requested), SPSS prints and tests the key statistic used in evaluating the hierarchical hypothesis: change in R² for each additional block of variables.The null hypothesis for the addition of each block of variables to the analysis is that the change in R² (contribution to the explanation of the variance in the dependent variable) is zero.If the null hypothesis is rejected, then our interpretation indicates that the variables in block 2 had a relationship to the dependent variable, after controlling for the relationship of the block 1 variables to the dependent variable, i.e. the variables in block 2 explain something about the dependent variables that was not explained in block 1.The key statistic in hierarchical regression is R² change (the increase in R² when the predictors variables are added to the model that included only the control variables). If R² change is significant, the R² for the overall model that includes both controls and predictors will usually be significant as well since R² change is part of overall R².Slide 4Variations in hierarchical regressionA hierarchical