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Trivariate Regression

This comprehensive guide details the process of conducting trivariate regression analysis by hand, covering essential calculations such as mean, standard deviation, intercept, and R squared values for predictors. It explains how to derive unstandardized beta weights and assess the significance of the regression model using F-tests. Additionally, we explore semipartial and partial correlations to interpret the unique contribution of each predictor. Ideal for students and researchers, this resource includes practical examples and is compatible with SAS for deeper analysis and visual representation.

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Trivariate Regression

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  1. Trivariate Regression By Hand

  2. Variable N Mean Std Dev   ar54 2.37969 0.53501 ideal 154 3.65024 0.53278 misanth154 2.32078 0.67346 arideal misanth ar1.00000 0.053120.22064r 0.5129 0.0060 p ideal 0.05312 1.00000 -0.13975r 0.5129 0.0839 p

  3. Beta Weights

  4. Unstandardize the Weights

  5. Obtain the Intercept

  6. Obtain R2

  7. R2 For 2 or More Predictors

  8. Test the R2 • SSy = (N-1)s2 = 153(.53501)2 = 43.794 • SSregr = R2SSY =.0559(43.794) = 2.447;df = p = 2; MSregr = 2.447/2 = 1.2235 • SSerror = SSY – SSregr= 43.794 - 2.447 = 41.347; df= n-p-1 = 151;MSerror = 41.347/151 = 0.2738 • F(2, 151) = 1.2235/0.2738 = 4.468, p = .013

  9. Obtain the Semipartial Corrs2

  10. Obtain the Partial Corrs2

  11. Test the Partials df = N - p– 1 = 151

  12. Also See • Obtaining Exact Significance Levels with SAS • Correlation and Regression Analysis: SAS - bivariate and trivariate, with plots • Annotated output

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