# Questions tagged [ridge-regression]

A regularization method for regression models that shrinks coefficients towards zero.

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### If there any benefit to using ridge regression in a simple linear regression problem where the aim is prediction?

Consider the following situation: We have a simple linear regression model (as opposed to a multiple regression model or a polynomial regression model). We are interested in prediction rather than ...
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### What does it mean for ridge regression solution to not be “equivariant” under scaling of inputs?

For Ridge Regression, I've seen the statement that the solutions aren't equivariant to scaling of the inputs so we typically preprocess the response and regressors by standardizing. What does "...
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### Does Ridge Regression generally improve the condition number?

While learning about Ridge regression and its applications I found a test question about impact of Ridge regression on the condition number. As far as I understand, Ridge regression can decrease the ...
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### Linear regression overfitting and regulization

When creating a linear model with many variables, there can be overfitting. Let's say that the training error is 10, and the testing error is 12. So one can use Ridge or Lasso regression to used the ...
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### Do residuals sum to zero for ridge regression?

In OLS, residuals are guaranteed to sum to zero because that's how OLS is essentially defined/derived since the residual vector is orthogonal to the column space spanned by by the $p$ independent ...
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### What does it mean to have a “gaussian prior?”

When reading up on ridge regression, I saw it stated that it has a "gaussian prior." I realized that I don't know what the word prior means in this context and what it is applied to? I ...
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### Penalizing non-OLS models

Letās consider some common linear time series models for which OLS does not usually yield unbiased coefficient estimates. These include ARIMA and ARIMAX models, regression models with ARIMA errors, ...
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### Bayesian interpretation of logistic ridge regression

Most textbooks (also this blog) cover the fact that ridge regression,  \hat y = \hat \beta X; \\ \hat \beta = \underset{\beta}{\text{argmin}}\ \ \frac{(y-\beta X)^T(y-\beta X)}{\sigma^2} + \lambda \...
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### How to implement the closed form solution of Ridge Regression in Python when intercept is not 0 (fit_intercept=True) without using sklearn?

The well-known closed-form solution of Ridge regression is: I am trying to implement the closed-form using NumPy and then compare it with sklearn. I can get the same result when there is no ...