Trivariate Regression By Hand

Variable N Mean Std Dev   ar 154 2.37969 0.53501 ideal 154 3.65024 0.53278 misanth 154 2.32078 0.67346 ar ideal misanth   ar 1.00000 0.05312 0.22064 r 0.5129 0.0060 p ideal 0.05312 1.00000 -0.13975 r 0.5129 0.0839 p

Beta Weights

Unstandardize the Weights

Obtain the Intercept

Obtain R2

R2 For 2 or More Predictors

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

Obtain the Semipartial Corrs2

Obtain the Partial Corrs2

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

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