Bivariate Regression Notes

  • Bivariate Regression Concepts

    • Relationship between two continuous variables: Y predicted from X.

    • Assumptions include normality, linearity, and homoscedasticity, aiming for p > .05$ in tests of assumptions.

  • Regression Equation

    • Model: Y = b0 + b1X + ext{error}

    • b0 (intercept) indicates the value of Y when X = 0.

    • b1 (slope) represents the change in Y with a one-unit change in X.

  • Example

    • Victimization as a predictor for depression:

    • Sample of 125 youths, outcomes measured on a scale.

    • Predicted equation: Y = 1.00 + 2X resulting in depression scores.

  • Model Estimation

    • Utilize the Method of Least Squares to minimize residuals, represented by the difference between predicted and observed values.

  • Model Testing with ANOVA

    • Compares model fit vs mean; tests if SSM significantly exceeds SSR, judging model validity.

  • Interpreting Outputs

    • R² indicates variance explained; larger values signify better model fit.

    • Individual slope values b: change in outcome per unit change in predictor.

  • APA Formatting Reminders

    • Correct reporting of statistics essential, including decimals and p-values details.

  • Key Takeaways

    • Master bivariate regression concepts, regression equation interpretation, and ANOVA applications in predicting outcomes.