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Why by increasing value of λ in Ridge estimator the slope of the line is decreasing? How exactly λ affects to the y = kx + b?

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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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  • $\begingroup$ Yes, I understand this, but how this push of coefficients to zero is performed mathematically ? $\endgroup$
    – Dablup
    Sep 21, 2021 at 9:01
  • $\begingroup$ I am not exactly sure what it is you are looking for, but the lambda parameter is multiplied by the sum of the squared coefficients, which is then added as an extra term to the cost. This cost is then minimized by whichever optimization method you are using, whether that is using the closed form solution or something like gradient descent. $\endgroup$
    – Oxbowerce
    Sep 21, 2021 at 10:34

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