If I compare two models, linear regression and ridge regression, with their RSS

Question

If I compare two models, linear regression and ridge regression, with their RSS value. If I take RSS for ridge / RSS for linear regression, and the answer is less than 1, does that mean that Ridge is better and if it is bigger than 1 that linear is better? If I compare two models, linear regression and ridge regression, with their RSS value. If I take RSS for ridge / RSS for linear regression, and the answer is less than 1, does that mean that Ridge is better and if it is bigger than 1 that linear is better?

Explanation / Answer

To look at the Residual Sum of Squares (RSS) is one way of judging how good a proposed statistical model fits. A model having minimum RSS among a collection of models is considered best (in the sense of having "least squared error") among that class of models.

So the answer to your question is 'YES'. If model-A uses ridge regression technique and model-B uses linear regression, and you find that (RSSA)/(RSSB) < 1, then it implies that the ridge-regression model fits better to the data than any other from the class {model-A, model-B } (in the "least squared error" sense!).

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