I understand total variance and R squared in linear regression outputs, but I have difficulty to understand the percent of variation explained by each covariates in a multiple regression analysis. I have two question. 1. How could I explaine the %var explained by one covariates in multiple regression?. 2. Above all how could implement this in Stata or R?. A paper on Table 4, page 7 of the link below has provided such output. Could anyone explain the 1.3% output of Gas stove? The adjusted R squared for the whole regression is 0.79 and the % variance explained by the covariates is 56.8. What does explain the rest?



  • $\begingroup$ The use of 3D barcharts in that paper invites skepticism. $\endgroup$ – Matthew Drury Aug 19 '15 at 22:29

This is my guess as to how one could calculate the individual covariate contribution

You can calculate the total sums of squares (TSS) even without running regression


  1. Now you run the regression with one variable, then calculate the regression sums of squares (RSS)

RSS1= Formula

The contribution from variable 1 towards the explained variance is:

  1. Then add the second variable and calculate the regression sums of squares (RSS2) Contribution from variable 2 towards the explained variance is:

    = (RSS2-RSS1)/TSS

and so on....

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    $\begingroup$ (+1) Although this is a reasonable guess concerning what these authors might have done, please note that the procedure is well-defined only when the regressors are orthogonal. The results depend on the order in which the regressors are chosen. See, for instance, Montgomery, Vining, & Peck, Introduction to Linear Regression Analysis (5th Ed.), section 3.2.2. Ordinarily that ambiguity would lead me to guess that the authors must have done something different, but since they made other huge blunders in their statistical analysis, perhaps this really is what they did... . $\endgroup$ – whuber Aug 20 '15 at 20:53

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