# Is there an equivalent measure of explanatory power in Support Vector Regression (SVR) like in Least Squares?

In Least Squares regression, we have statistics like $R^2$ to measure the strength of the explanatory variables. Are there similar measures when we are dealing with Support Vector Regression (SVR)? They question I want to answer is: how much does explanatory variable $X$ contribute to the accuracy of the results?

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$R^2$ is really just the reduction in deviance from a null model that predicts the mean response for everyone. You can do the same calculation for an SVM model. I'd recommend using a validation set separate from your training data (or full bootstrap / k-fold cross validation if you prefer.) I would also recommend training your OLS on the same training data (and also calculating the OLS $R^2$ on the validation set).
You also ask about how much a specific feature (explanatory variable) contributes to the fit. That isn't exactly computed in basic OLS summary statistics. If you have your nice validation set environment, you can just try leaving that feature out and see how it affects your $R^2$. You can use the very same framework for the SVM.