title: how to properly use sklearn to predict the error of a fit
body: <p>I'm using <code>sklearn</code> to fit a linear regression model to some data. In particular, my response variable is stored in an array <code>y</code> and my features in a matrix <code>X</code>.</p>
  
  <p>I train a linear regression model with the following piece of code</p>
  
  <pre><code>    from sklearn.linear_model import LinearRegression
      model = LinearRegression()
      model.fit(X,y)
  </code></pre>
  
  <p>and everything seems to be fine.</p>
  
  <p>Then let's say I have some new data <code>X_new</code> and I want to predict the response variable for them. This can easily done by doing</p>
  
  <pre><code>    predictions = model.predict(X_new)
  </code></pre>
  
  <p>My question is, what is this the error associated to this prediction?
  From my understanding I should compute the mean squared error of the model:</p>
  
  <pre><code>    from sklearn.metrics import mean_squared_error
      model_mse = mean_squared_error(model.predict(X),y)
  </code></pre>
  
  <p>And basically my real predictions for the new data should be a random number computed from a gaussian distribution with mean <code>predictions</code> and sigma^2 = <code>model_mse</code>. Do you agree with this and do you know if there's a faster way to do this in <code>sklearn</code>?</p>