title: Excel Polynomial Regression with multiple variables
body: <p>I saw a lot of tutorials online on how to use polynomial regression on Excel and multi-regression but none which explain how to deal with multiple variable AND multiple regression.</p>
  
  <p>In  <a href="https://i.stack.imgur.com/MnG1s.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/MnG1s.png" alt="this image"></a>, the left columns contain all my variables X1,X2,X3,X4 (say they are features of a car), and Y1 is the price of the car I am looking for.</p>
  
  <p>I got about 5000 lines of data that I got from running a model with various values of X1,X2,X3,X4 and I am looking to make a regression so that I can get a best estimate of my model without having to run it (saving me valuable computing time).</p>
  
  <p>So far I've managed to do multiple linear regression using the Data Analysis pack in Excel, just by using the X1,X2,X3,X4. I noticed however that the regression looks very messy and inaccurate in places, which is due to the fact that my variables X1,X2,X3,X4, affect my output Y1 non-linearly.</p>
  
  <p>I had a look online and to add polynomials to the mix, tutorial suggest adding a X^2 column. But when I do that (see right part of the chart) my regression is much much worse than when I use linear fits.</p>
  
  <p>I know that polynomials, can over-fit the data, but I though that using a quadratic form was safe since the regression would only have to return a coefficient of 0 to ignore any excess polynomial orders.</p>
  
  <p>Any help would be very welcome,</p>
  
  <p>For info I get an adujsted-R^2 of 0.91 for linear fits and 0.66 when I add a few X^2 columns.</p>
  
  <p>So far this is the best regression I can get (black line is 1:1):</p>
  
  <p><a href="https://i.stack.imgur.com/SmNDL.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/SmNDL.png" alt="enter image description here"></a></p>
  
  <p>As you can see I would like to increase the fit for the bottom left part and top right parts of the curve.</p>