In order to avoid overfitting in regression due to too many feature while at the same time have enough features to minimize the sum of squared errors in order to get a more accurate fit on the test data, you need to regularize the regression.

This can be done with a Lasso regression where you want to minimize the sim of squared errors + plus a penalty parameters times the coefficient of the regression (which indicates the amount of features)

minimize SSE + λ|β|