DDE-1/Regression.md

@@ -7,9 +7,20 @@ In regression tasks, we use the data to predict,the correct real-valued labels o
 The simplest algorithm for regression known as linear regression. Here the proposed solution assumes that the label can be generated as a linear combination of the input variables:
 
 ```math 
-y(x, w) = w0 + w_1x_1 + . . . + w_ix_i
+y_p(x, w) = w_0 + w_1x_1 + . . . + w_ix_i
 ```
 
+Relative importance of the features x is described by the corresponding weights. Here $`w_0`$ is the bias, a trick learned to adjust the magnitude of the output. 
+
+This formulation however, has strong limitations and is prone to over-fitting and suffers from the presence of outliers. As a remedy,  we add a regularization term to the error function in order to control over-fitting:
+
+```math 
+E_data = y_true - y_p(x, w)
+E_total = E_data + $lambda$ E_regularization
+```
+
+
+
 ## Additional Sources
 
 - [Seeing theory: linear regression](https://seeing-theory.brown.edu/#secondPage/chapter6)