# Do P values really matter for Regression in Machine Learning?

When doing statistics with linear regression, p-values and statistical significance are fundamental aspects for building a linear regression model.

But unlike in statistics, machine learning is all about making correct predictions. The more variables we add to a linear regression model, the higher we expect the machine learning accuracy to be.

Would you agree that p values and an analysis of statistical significance are not important during machine learning model evaluation when building a linear regression?

I ask because my professor during my masters degree made that point but I have seen data scientists spend a lot of time discussing p values.

I'm afraid, you are wrong. Suppose $$Y = \alpha + \beta_1 X_1 + \beta_2 X_2 + \varepsilon,$$ $$\varepsilon\sim N(0,\sigma^2).$$ Suppose further that $$Z_1$$, ..., $$Z_k$$ are "nuisance" candidate predictors, uncorrelated with $$Y$$. Gauss-Markov theorem proves that the best estimate of the model will be the regular OLS (ordinary least squares) estimate of coefficients $$(\alpha, \beta_1, \beta_1)$$ based on predictors $$X_1$$ and $$X_2$$. Any machine learning algorithm will achieve this result at best.
If the sample size is substantial, examination of p-values will be instrumental in identification of informative predictors $$X_1$$ and $$X_2$$ in the candidate set $$\{X_1, X_2, Z_1, ..., Z_k\}$$ and then following the Gauss-Markov approach.