Estimating R square for each of the predictors in the multiple linear regression model

[Atulya212]

How can I determine the relative contribution(R- Square) of predictors in multiple regression models?

Dear all,

do you have any suggestions about how to estimate the relative contribution of different predictors in a multiple regression model of the type:

y = b0 + b1x1 + b2x2 + ... + bnxn I have already finalized the model now I want to see the what is the R square of each of the predictors so I have an idea about the relative contribution of each of the predictors in the overall model?

[PaigeMiller]

R-squared is defined for the entire model. R-squared is not defined for an individual predictor variable in a model.

[Atulya212]

Yeah, you are correct but I need to find a way to estimate the individual contribution of each of the independent variables in the overall model R square. 

Being able to report such a decomposition of R square will be very useful to assess the explanatory power of individual regressors or groups of regressors. 

[PaigeMiller]

Unless you are modeling data collected in an orthogonal experiment, there is no unique decomposition of the contribution of each x-variable in a regression-like model. This is because your x-variables are correlated with one another, and it is impossible both logically and mathematically to determine what the contribution to R-squared of each x-variable is.

Perhaps you mean (but didn't say) you want to find out which variables are the strongest predictors (in other words which variables have the steepest slopes)?

[StatDave]

See this note which discusses statistics for assessing variable importance, including the RsquareV macro to estimate the partial R-square for each effect in the model.