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Sorry if this is a bad use of answer to add comment but since my reputation is not high enough this is only way to leave a comment to OP's question. I think some of the answers misunderstood the OP's intention. Over fitting is used as a means to test the complexity of the model - if a model cannot overfit a small dataset then it's likely not able to ...

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The answer is largely the same whether we consider $\ell_1$ or $\ell_2$ regularisation, so I will just speak generally about regularisation. Mean square error for training data Given some training data $\{(x_i, y_i)\}_{i = 1}^n$, a linear regression line $Y = aX + b$ fit using the least squares method looks for coefficients that minimise the sum of squares, ...

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