How to select regression algorithm for noisy (scattered) data?
The model I would use is the one that minimizes the accumulated quadratic error. Both models you are using, linear and quadratic, looks good. You can compute which one has the lowest error.

If you want to use an advanced method you can use RANSAC. It is an iterative method for regression that assumes that there are outliers and remove them from the optimization. So your model should be more accurate that just using the first approach I told you.