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Understanding Multiple Regression Analysis in Statistics

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Learn how multiple regression helps predict outcomes using several variables and control for confounding factors, examining causal relationships and interactions in statistical modeling.

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Understanding Multiple Regression Analysis in Statistics

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  1. Multiple Regression

  2. So we know what linear regression is for • Predicting one variable with another variable • Yes, predicting • For example: Does gender (X1) significantly predict years of life (Y)? • What does significantly depend on?

  3. Multiple Regression • While we are predicting things…what happens when you want to predict with more than one variable? • For example: does gender and familial history of heart disease predict blood cholesterol?

  4. “Controlling For” • What is the effect of walking on BMI after controlling for age? • What is the effect of physical activity on depression after controlling for

  5. Causal Inference • Relatedness: X is Correlated With Y • Temporal Precedence: X precedes Y in time • Non-Spuriousness: X and Y are still related after accounting for other relationships. (Bollen, 1989; Kenny, 1979; In Aitken, Aitken and West)

  6. Statistical Questions Just like in linear regression • Is the whole model predicting a significant amount of variance in the dependent variable? • R-squared- ANOVA table • Are each of the Betas different than zero • T-tests

  7. The Interaction • Does the effect of one variable depend on the level of another? • Does the effect of familial history of heart disease depend on the gender of the individual? • For example…maybe a family history of heart disease confers a risk of shorter lifespan for males but not females.

  8. The Interaction • The fundamental equation: • What is going on here?

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