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PSCH 443 Multiple Regression 3 Evaluating Assumptions Part 2

Assumptions in Regression Analysis

  • Normality

    • Refers to the assumption that predictor and outcome variables are normally distributed.

    • Essential to check for normal distribution before conducting regression analyses.

  • Multivariate Normality

    • Involves combining individual variables in the regression equation.

    • Errors in prediction should also be normally distributed (centered around zero).

    • If errors are normal, we can assess the multivariate normality assumption effectively.

    • Use SPSS to plot residuals against a normal curve for evaluation.

Evaluating Normality

  • Residual Analysis

    • Showcases whether predicted values closely align with observed values.

    • Examine plots; deviations indicate flaws in the data.

  • Example of Normal PP Plot

    • Data points should ideally follow a straight line. Deviations signal potential issues.

Consequences of Violating Assumptions

  • Impact of Non-Normality

    • Affects parameter estimates and may complicate interpretation.

    • Increased error can diminish statistical significance in results.

    • Results may still be interpretable if one predictor is statistically significant, even amidst assumption violations.

Linear Relationships

  • Linearity Assumption

    • Assumes a straight-line relationship between predictors and outcomes.

    • Consider potential curvilinear relationships at the conceptual level before analysis.

Homoscedasticity

  • Refers to the uniformity of residual variation across predicted values.

  • Plot residuals against predicted values; expect a random scatter of dots.

  • Detecting Violations

    • Heteroskedasticity: Identified by a triangular pattern; variability increases in one direction.

    • Non-Linearity: Curvilinear relationships invalidate linear regression assumptions.

Independence of Errors

  • Errors of prediction need to be independent, especially in repeated measures or longitudinal designs.

  • Durbin-Watson Statistic

    • Helps assess autocorrelation among prediction errors. A result near 2 indicates independence.

Suppressor Effect

  • Occurs when predictors correlate in a way that influences each other's predictive power

  • Notable features include:

    • Absolute value of a beta weight exceeds its univariate correlation.

    • Changes in beta weights may indicate suppression when variables are added or removed.

Avoiding Errors

  • Conduct bivariate correlation analyses to prepare for regression.

  • Keep an eye on correlation size and direction to identify potential issues early.

  • Basic checks ensure proper interpretation and prevent misleading results in reporting.