# Ridge regression is similar to Linear regression [duplicate]

I can not see any difference between Ridge Regression and Linear Regression

MY understanding, The point of ridge Regression is based on the training data we find the best line that fits training data.

Best line means minimum RMSE

then try to play with the line sloop to get better results through n-fold cross validatin!.

isn't easier and simpler to use all dataset (both training and test) to build this line and find sloop through

$$y\ =\ \beta_0+{\beta_1x}_1$$

$$\beta_1\ =\ \rho\frac{\sigma_y}{\sigma_x}$$

$$\beta_0\ =\ \mu_y\ -\ \mu_x\beta_1\$$

$$\rho\ =\ [(x-μx)(y-μy)] [(x-μx)2][(y-μy)2]$$

$$\sigma_x=\ \sqrt{\frac{{\sum{(x-\mu_x)}}^2}{n}}$$

$$\sigma_y=\ \sqrt{\frac{{\sum{(y-\mu_y)}}^2}{n}}$$

the linear regression will give us the best fit.

if i misunderstood.

please tell me what is the difference between these models before down rating my question.

Thanks

## marked as duplicate by Martijn Weterings, whuber♦ regression StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 27 at 14:22

• Ridge regression is not just similar to linear regression... instead, it is exactly like linear regression. It is a specific type of linear regression, where the 'linear' refers to the model $y = \beta X$. How ridge regression differs from the most common type of linear regression, ordinary least squares regressions, is in the added penalty that makes one favor solutions with small effect sizes (this is advantageous when you have lots of regressors for which you can reasonably expect that most of the associated effects should be equal to zero or close to it). – Martijn Weterings Jun 27 at 12:18