Solved – How to split r-squared between predictor variables in multiple regression

importancemultiple regressionrr-squaredvariance-decomposition

I have just read a paper in which the authors carried out a multiple regression with two predictors. The overall r-squared value was 0.65. They provided a table which split the r-squared between the two predictors. The table looked like this:

            rsquared beta    df pvalue
whole model     0.65   NA  2, 9  0.008
predictor 1     0.38 1.01 1, 10  0.002
predictor 2     0.27 0.65 1, 10  0.030

In this model, ran in R using the mtcars dataset, the overall r-squared value is 0.76.

summary(lm(mpg ~ drat + wt, mtcars))

Call:
lm(formula = mpg ~ drat + wt, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.4159 -2.0452  0.0136  1.7704  6.7466 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   30.290      7.318   4.139 0.000274 ***
drat           1.442      1.459   0.989 0.330854    
wt            -4.783      0.797  -6.001 1.59e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.047 on 29 degrees of freedom
Multiple R-squared:  0.7609,    Adjusted R-squared:  0.7444 
F-statistic: 46.14 on 2 and 29 DF,  p-value: 9.761e-10

How can I split the r-squared value between the two predictor variables?

Best Answer

You can just get the two separate correlations and square them or run two separate models and get the R^2. They will only sum up if the predictors are orthogonal.

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