title: How do you go about estimating parameters for a known polynomial regression model using training data?
body: <p>So rather than trying to find models, there is already a nonlinear polynomial regression model, for which I need to find the theta parameters.</p>
  <p>= 1<em>2 + 2</em>(1)^3 +3*(2)^4 +  + </p>
  <p>How would you go about estimating the  parameters using least squares on a training dataset with four features x1-x4? I'm thinking forward subset selection, but I'm not sure how to implement this in Python.</p>
  <p><strong>Edit</strong>:
  If you already have the form of the model as shown above, do you still need to carry out subset selection in order to estimate model parameters? or can you just go ahead and use your training data in:</p>
  <p>theta = (X<sup>T</sup>X)<sup>-1</sup>X<sup>T</sup>y</p>
  <p>I gather forward subset is a model selection technique for when you don't already have a candidate model.</p>
  <p>Thanks in advance.</p>