# Why adding Gaussian noise increased MSE on the test set?

I have a multi-variable linear model. More precisely, a set of variables to explain a target variable. After adding Gaussian noise ($\sim N(0,1))$, the MSE increased from roughly $21$ to roughly $22$.

How can it be explained? Is that what's called overfitting?

• To what do you add the noise? To the dependent variables in the training set? Or in the test set? Or to independent variables? If so, in which set? – Stephan Kolassa Jun 23 '17 at 9:53
• I added the noise to the test set's y. I'm using the well-known data-set: cs.toronto.edu/~delve/data/boston/bostonDetail.html – Covvar Jun 23 '17 at 9:55
• the dependent variable is medv – Covvar Jun 23 '17 at 9:58