Regression analysis with 1 independant variable (error) and multiple dependant variable

So I took a lot of data (~10000) on a machine (3D printer). For each reading, I got the error and a lot of different parameter (speed, voltage, angle, temperature etc.).

My first analysis showed me that none of the parameter clearly explain my error, but a correlation is clearly visible (Coefficient of determination around 50% with Polynomial regression or Savitzky–Golay filter) with many of those parameter.

But even if each of those individuals parameters doesn't explain my error perfectly, I highly confident a combination of 2-3-4 parameter would have a really high r2.

My question is, how can I fit a Regression analysis with multiples dependant variable on matlab. What are your suggesting?

Thanks.