Assumptions of multiple regressionAssumptions of Normality, Linearity, and HomoscedasticityAssumption of NormalityAssumption of Normality: Evaluating NormalityAssumption of Normality: Histograms and Normality PlotsAssumption of Normality: Hypothesis test of normalityAssumption of Normality: Skewness, kurtosis, and normalityAssumption of Normality: TransformationsAssumption of Normality: Computing TransformationsAssumption of Normality: When transformations do not workAssumption of Normality: Computing “Explore” descriptive statisticsAssumption of Normality: Adding the variable to be evaluatedAssumption of Normality: Selecting statistics to be computedAssumption of Normality: Including descriptive statisticsAssumption of Normality: Selecting charts for the outputAssumption of Normality: Including diagnostic plots and statisticsAssumption of Normality: Completing the specifications for the analysisAssumption of Normality: The histogramAssumption of Normality: The normality plotAssumption of Normality: The test of normalityAssumption of Normality: The rule of thumb for skewness and kurtosisAssumption of LinearityAssumption of Linearity: Evaluating linearityAssumption of Linearity: Interpreting scatterplotsSlide 25Assumption of Linearity: Scatterplots that are difficult to interpretAssumption of Linearity: Using correlation matricesAssumption of Linearity: The pattern of correlations for no relationshipAssumption of Linearity: Correlation pattern suggesting transformationAssumption of Linearity: Correlation pattern suggesting substitutionAssumption of Linearity: TransformationsAssumption of Linearity: When transformations do not workAssumption of Linearity: Creating the scatterplotAssumption of Linearity: Selecting the type of scatterplotAssumption of Linearity: Selecting the variablesAssumption of Linearity: The scatterplotAssumption of Linearity: Adding a trendlineAssumption of Linearity: The scatterplot in the SPSS Chart EditorAssumption of Linearity: Requesting the fit lineAssumption of Linearity: Requesting r²Assumption of Linearity: Completing the request for the fit lineAssumption of Linearity: The fit line and r²Assumption of Linearity: Computing the transformationsAssumption of Linearity: Creating the scatterplot matrixAssumption of Linearity: Selecting type of scatterplotAssumption of Linearity: Specifications for scatterplot matrixAssumption of Linearity: The scatterplot matrixAssumption of Linearity: Creating the correlation matrixAssumption of Linearity: Specifications for correlation matrixAssumption of Linearity: The correlation matrixAssumption of HomoscedasticityAssumption of Homoscedasticity : Evaluating homoscedasticityAssumption of Homoscedasticity : The boxplotAssumption of Homoscedasticity : Levene test of the homogeneity of varianceAssumption of Homoscedasticity : TransformationsAssumption of Homoscedasticity : When transformations do not workAssumption of Homoscedasticity : Request a boxplotAssumption of Homoscedasticity : Specify the type of boxplotAssumption of Homoscedasticity : Specify the dependent variableAssumption of Homoscedasticity : Specify the independent variableAssumption of Homoscedasticity : Complete the request for the boxplotSlide 62Assumption of Homoscedasticity : Request the test for homogeneity of varianceSlide 64Slide 65Assumption of Homoscedasticity : The homogeneity of variance test is an optionAssumption of Homoscedasticity : Specify the homogeneity of variance testAssumption of Homoscedasticity : Complete the request for outputAssumption of Homoscedasticity : Interpreting the homogeneity of variance testUsing scriptsUsing a script for evaluating assumptionsOpen the data set in SPSSInvoke the script in SPSSSelect the scriptThe script dialogComplete the specifications - 1Complete the specifications - 2The script finishesOutput from the script - 1Closing the script dialog boxProblem 1Level of measurementRun the script to test normality - 1Run the script to test normality - 2Run the script to test normality - 3Normality of the dependent variableNormality of transformed dependent variableNormality of the independent variables - 1Normality of the independent variables - 2Run the script to test linearity - 1Run the script to test linearity - 2Linearity test with age of respondentLinearity test with respondent’s incomeRun the script to test homogeneity of variance - 1Run the script to test homogeneity of variance - 2Levene test of homogeneity of varianceAnswer 1Problem 2Slide 99Slide 100Slide 101Slide 102Slide 103Normality of the first independent variablesNormality of transformed independent variableNormality of the second independent variablesSlide 107Normality of the third independent variablesSlide 109Slide 110Linearity test with population growth rateLinearity test with population literacyLinearity test with per capita GDPSlide 114Answer 2Steps in evaluating assumptions: level of measurementSteps in evaluating assumptions: assumption of normality for metric variableSteps in evaluating assumptions: assumption of linearity for metric variablesSteps in evaluating assumptions: homogeneity of variance for nonmetric variablesSW388R7Data Analysis & Computers IISlide 1Assumptions of multiple regressionAssumption of normalityAssumption of linearityAssumption of homoscedasticityScript for testing assumptionsPractice problemsSW388R7Data Analysis & Computers IISlide 2Assumptions of Normality, Linearity, and HomoscedasticityMultiple regression assumes that the variables in the analysis satisfy the assumptions of normality, linearity, and homoscedasticity. (There is also an assumption of independence of errors but that cannot be evaluated until the regression is run.)There are two general strategies for checking conformity to assumptions: pre-analysis and post-analysis. In pre-analysis, the variables are checked prior to running the regression. In post-analysis, the assumptions are evaluated by looking at the pattern of residuals (errors or variability) that the regression was unable to predict accurately.The text recommends pre-analysis, the strategy we will follow.SW388R7Data Analysis & Computers IISlide 3Assumption of NormalityThe assumption of normality prescribes that the distribution of cases fit the pattern of a normal curve. It is evaluated for all metric variables included in the analysis, independent variables as well as the dependent variable.With multivariate statistics, the assumption is that the combination of