I am working in R on linear regressions with covariates, looking like : lm(x ~ y + a + b + c)
With the summary() function, I can get the p value corresponding to each of the variables of the model. However, I only have the R^2 corresponding to the whole model, which isn't informative of the contribution of my variable of interest (y).
How do I get the R^2 corresponding to the part of the variance explained by y alone ?
I tried :
sapply(model,function(x) summary(x)$r.squared)
as advised here : Print R-squared for all of the models fit with lmList but it returns `
Error in summary(x)$r.squared : $ operator is invalid for atomic vectors"`
I was also advised to calculate the difference between the R^2 of my model and the R^2 of a linear model without my variable of interest. Is that a valid method ? Anyway I would still like to know if there is an easier way to do it, for example included in some package.
It doesn't make much sense to talk about the R-squared of individual variables in a multivariate model. Delta R-squared, as Zephryl mentions, or partial R-squared are two measures that will do something like what you want.
Discussion on delta R-squared and partial R-squared: https://stats.stackexchange.com/questions/64010/importance-of-predictors-in-multiple-regression-partial-r2-vs-standardized
Partial R-squared can be calculate like this:
fm1 <- lm(rating ~ ., data=attitude)
# summary(fm1 <- lm(sr ~ ., data=LifeCycleSavings))
# summary(fm1 <- lm(Employed ~ ., data=longley))
# summary(fm1 <- lm(stack.loss ~ stack.x))
reduced <- lapply(seq_len(ncol(fm1$model)-1), function(x) update(fm1, terms(fm1)[-x]))
reduced.sse <- sapply(reduced, function(x) deviance(x))
fm1.sse <- deviance(fm1)
partial.r2 <- c(0, (reduced.sse - fm1.sse)/reduced.sse)
(fm1.coefs <- cbind(summary(fm1)$coefficients, partial.r2))
# Estimate Std. Error t value Pr(>|t|) partial.r2
# (Intercept) 10.787076386 11.58925724 0.93078238 0.36163372105 0.0000000000
# complaints 0.613187608 0.16098311 3.80901816 0.00090286788 0.3868076082
# privileges -0.073050143 0.13572469 -0.53822295 0.59559392051 0.0124382943
# learning 0.320332116 0.16852032 1.90085160 0.06992534595 0.1357684079
# raises 0.081732134 0.22147768 0.36903102 0.71548008844 0.0058861866
# critical 0.038381447 0.14699544 0.26110638 0.79633426421 0.0029554369
# advance -0.217056682 0.17820947 -1.21798623 0.23557704863 0.0605914609