Will we use ridge in linear regression if there is no multicolinearity I know that adding L2 regularization (ridge) can reduce multicolinearity in linear regression. I originally understand as multicolinearity will increase the estimation variance and L2 regularization can reduce the estimation variance. So ridge can be used to reduce multicolinearity.  Namely  I understand as ridge is primary used for reducing variance and reducing multicolinearity is an addition product. However when I search wiki:
https://en.wikipedia.org/wiki/Ridge_regression
I found that the original intention of developing ridge is primary used for reducing multicolinearity but not for reducing variance. Namely in a interview, someone asked me what's the usage of ridge, I should answer reducing multicolinearity rather than  reducing variance to avoid overfitting?
And does it mean if the sample matrix is far way from the degenerate (multicolinearity ), we will never use ridge to avoid overfitting?

The original paper by Hoel-Kennard showed that as you increase $k$ from zero, bias will monotonically increase and variance decrease in such a way that there is always a value of $k$ giving smaller MSE than ordinary least squares (OLS). Hence, theoretically, ridge always dominates OLS for a "good" choice of $k$.
However, you have to guess a good $k$ so, in practice, ridge is mostly used in cases of heavy collinearity. In these cases, the reduction in variance is very large and likely to compensate (in terms of MSE) the increase of bias, even if you don't guess very well a "good"  $k$.
