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Interesting question. I'd say it is correct not to divide, due to the following reasoning... For linear regression there is no difference. The optimum of the cost function stays the same, regardless how it is scaled. When doing Ridge or Lasso, the division affects the relative importance between the least-squares and the regularization parts of the cost ...


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The lambda parameter in ridge regression penalizes larger coefficients and pushes the model to balance the trade-off between fitting the data the best it can while taking into account the size of the coefficient. As a result coefficients are generally pushed closer to zero, which a larger amount of shrinkage for larger values of lambda.


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