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Resampling is usually used to find the best tuning parameters for a model. However, for some models, such as linear regression model, there is no tuning parameters. In this case, what can we get from resampling on them?

In particular, in R caret package, you can train a linear regression model by using cross validation control function. In this case, how is the coefficient estimated? On the whole training sample? If so, what extra information can we get from applying CV on linear regression models?

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Resampling isn't the same as tuning. It gives you an estimated performance metric. When you tune over a hyperparameter subspace you actually perform your resampling strategy over each evaluation point of that subspace.

So, in caret, when you resample a linear regression without tuning you get an estimate of the performance metric of your choice, and the regression coefficients are estimated over the training data of each resampling instance.

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Yes, the coefficient is estimated based on the whole training sample. Resampling, in this case, gives you an estimated performance metric, such as RMSE.

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