Effect of regularisation error Following is the formula to estimate parameters
w =(λI+ΦTΦ)−1* ΦTt

lambda is the regularization coefficient and w are the parameters of our model. fi are the features. And in order to compute the error
E= SSE + (λ/2)*wTw

SSE is the usual sum of squared errors but here the additional term is regulariser error.It is said in theory that as we increase lambda, the effect of wTw is reduced. But considering it, if lambda=0 then wTw will have no effect. Is it not a bit contradictory?
Moreover, addition of regulariser should decrease the overall error but it is actually increasing it by small numbers and it is increased.
 A: What regularization does is to bias your parameter estimates to a certain regularization target. We select this target based on some prior knowledge or beliefs that we have about the parameters we're trying to estimate. For example, a common regularization target is 0, because in many situations we can assume that most of our parameters have relatively small values (i.e. are close to 0). 
When the assumptions behind our choice of regularization target are correct (e.g. when the true parameters really do tend to be close to 0), this leads to more accurate parameter estimates. We have used our prior knowledge to decrease our uncertainty about the parameter estimates, and these estimates therefore follow a more narrow distribution around their mean. This decreases the amount of random error in your parameter estimates.
The decreased random error comes at a cost however, and that cost is a larger systematic error (or bias). The prior assumptions we have imposed on our parameter estimates are "pulling" them towards the regularization target. As we increase the regularization strength $\lambda$, this pull will become stronger and so we see a larger bias.
So we have a trade-off between random and systematic errors; also known as "variance" and "bias". In your formula, these correspond to the SSE and the $\frac{\lambda}{2}w^Tw$ terms, respectively. And you are right that the bias term will increase with the value of $\lambda$. However, your formula is hiding the fact that the SSE (or random error) term will actually decrease with increasing values of $\lambda$. 
The trick with regularization is to find the right value of $\lambda$, with the optimal trade-off between systematic and random error, such that the overall error is minimized. 
