title: Predict different values from same inputs in a linear regressor model?
body: <p>Let's suppose I have a noisy 2d data set where one person watching the data could easily draw a straight line in the data so that the mean squared error is minimized.</p>
  
  <p>The model of the line has the form <code>y = mx + b</code>, where <code>x</code> is the input value, <code>y</code> is the predicted value of the model and <code>m</code> and <code>b</code> are trained variables to minimize the cost.</p>
  
  <p>My question is that if we plug some input <code>x1</code> to the model, it will always output the same number, not taking into account how sparse the data is. How can a model like this predict different values from same inputs?</p>
  
  <p>Maybe this could be done taking all the errors from the model line to the points, making a distribution of them, taking an expected value of such distribution and then adding that value to <code>y</code>?</p>