Satisfying Assumptions of Linear RegressionConsequences of failing to satisfy assumptionsCorrecting violations of assumptions - 1Correcting violations of assumptions - 2OutliersDifferent types of outliersDetecting outliersRemoving outliersDetecting an removing outliers in SPSSTransformationsTransformations change the measurement scaleTransformations: Computing transformations in SPSSTransformations: Two forms for computing transformationsTransformations: Functions and formulas for transformationsTransformations: Transformation of positively skewed variablesTransformations: Example of positively skewed variableTransformations: Transformation of negatively skewed variablesSlide 18Transformations: Example of negatively skewed variableTransformations: The Square Transformation for LinearityTransformations: Example of the square transformationWhich transformation to useComputing transformations in SPSS: Transformations for normalityComputing transformations in SPSS: Determine whether reflection is requiredComputing transformations in SPSS: Compute the adjustment to the argumentComputing transformations in SPSS: Computing the logarithmic transformationComputing transformations in SPSS: Specifying the transform variable name and functionComputing transformations in SPSS: Adding the variable name to the functionComputing transformations in SPSS: Adding the constant to the functionComputing transformations in SPSS: The transformed variableComputing transformations in SPSS: Computing the square root transformationSlide 32Computing transformations in SPSS: Adding the variable name to the functionSlide 34Slide 35Computing transformations in SPSS: Computing the inverse transformationComputing transformations in SPSS: Specifying the transform variable name and formulaSlide 38Computing transformations in SPSS: Adjustment to the argument for the square transformationComputing transformations in SPSS: Computing the square transformationSlide 41Slide 42Sample homework problemRun the script - 1Run the script - 2Assumption of linearity - 1Slide 47Initial test of conformity to assumptions - 1Initial test of conformity to assumptions - 2Initial test of conformity to assumptions - 3Initial test of conformity to assumptions - 4Initial test of conformity to assumptions - 5Initial test of conformity to assumptions - 6Initial test of conformity to assumptions - 7Initial test of conformity to assumptions - 8Model: original variables, excluding outliersEvaluating assumptions for original variables, excluding outliers - 1Evaluating assumptions for original variables, excluding outliers - 2Evaluating assumptions for original variables, excluding outliers - 3Evaluating assumptions for original variables, excluding outliers - 4Selecting transformationsTest the normality of the dependent variable - 1Test the normality of the dependent variable - 2Test the normality of the independent variable - 1Test the normality of the independent variable - 2Substituting the transformed variables - 1Substituting the transformed variables - 2Substituting the transformed variables - 3Substituting the transformed variables - 4Substituting the transformed variables - 5Slide 71Evaluating assumptions for transformed variables - 1Evaluating assumptions for transformed variables - 2Evaluating assumptions for transformed variables - 3Evaluating assumptions for transformed variables - 4Evaluating assumptions for transformed variables - 5Slide 77Slide 78Substituting the transformed variables and excluding extreme outliers - 1Substituting the transformed variables and excluding extreme outliers - 2Substituting the transformed variables and excluding extreme outliers - 3Substituting the transformed variables and excluding extreme outliers - 4Testing for a quadratic relationship - 1Slide 84Testing for a quadratic relationship - 3Slide 86Slide 87Other features of the script - 1Other features of the script - 2Other features of the script - 3Logic for satisfying the assumptions of simple linear regression - 1Logic for satisfying the assumptions of simple linear regression - 2Logic for satisfying the assumptions of simple linear regression - 3Logic for satisfying the assumptions of simple linear regression - 4Logic for satisfying the assumptions of simple linear regression - 5Logic for satisfying the assumptions of simple linear regression - 6SW388R6Data Analysis and Computers ISlide 1Satisfying Assumptions of Linear RegressionCorrecting violations of assumptionsDetecting outliersTransforming variablesSample problemSolving problems with the scriptOther features of the scriptLogic for homework problemsSW388R6Data Analysis and Computers ISlide 2Consequences of failing to satisfy assumptionsWhen a regression fails to meet the assumptions, the probabilities that we base our findings on lose their accuracy. Generally, we fail to detect relationships for which we might otherwise have found support, increasing our chances of making a type II error.If we are using the regression to model expected values for the dependent variable, our predictions may be biased in that we are systematically making non-random errors for subsets of our population.SW388R6Data Analysis and Computers ISlide 3Correcting violations of assumptions - 1There are three strategies available to us to correct our violations of assumptions:1. we can exclude outliers from our analysis2. we can transform our variables3. we can add a polynomial term (square, cube, etc.) for an independent variable. Employing one strategy generally has an impact on other the other strategies. For example, transforming a variable may change a case’s status as an outlier. Excluding an outlier reduces the skew of the distribution, thereby improving normality.SW388R6Data Analysis and Computers ISlide 4Correcting violations of assumptions - 2The availability of multiple strategies creates the opportunity to report our findings for a relationship in different ways, requiring us to choose to report one that we can defend.Unless we test all possible combinations, we cannot be certain that we are reporting the optimal relationship.When we utilize these remedies, we are required to report them with our findings.SW388R6Data Analysis and Computers ISlide 5OutliersOutliers are cases that have data values that are very different from the data values for the majority of cases in the data set.Outliers are important because they can change the results of our data analysis.Whether