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- Ridge regression is a term used to refer to a linear regression model whose coefficients are estimated not by ordinary least squares (OLS), but by an estimator, called ridge estimator, that, albeit biased, has lower variance than the OLS estimator.
www.statlect.com/fundamentals-of-statistics/ridge-regression
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Ridge regression is a term used to refer to a linear regression model whose coefficients are estimated not by ordinary least squares (OLS), but by an estimator, called ridge estimator, that, albeit biased, has lower variance than the OLS estimator.
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Ridge regression modifies OLS by calculating coefficients that account for potentially correlated predictors. Specifically, ridge regression corrects for high-value coefficients by introducing a regularization term (often called the penalty term) into the RSS function.
Oct 12, 2014 · In an unpenalized regression, you can often get a ridge* in parameter space, where many different values along the ridge all do as well or nearly as well on the least squares criterion.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences ...
Both Ridge and Lasso have a tunning parameter λ(or t) • The Ridge estimates βˆj,λ,Ridge’s and Lasso estimates βˆj,λ,Lasso depend on the value of λ(or t) λ(or t) is the shrinkage parameter that controls the size of the coefficients • As λ↓0 or t ↑∞, the Ridge and Lasso estimates become the OLS estimates
Ridge regression was developed as a possible solution to the imprecision of least square estimators when linear regression models have some multicollinear (highly correlated) independent variables—by creating a ridge regression estimator (RR).
The basic requirement to perform ordinary least squares regression (OLS) is that the inverse of the matrix X’X exists. X’X is typically scaled so that it represents a correlation matrix of all predictors. However, in certain situations (X’X)-1 may not be calculable.
