# Why are correlation matrices used versus a matrix of R^2 values?

I'm relatively new to DS, so forgive me if this is a dumb question or in the wrong forum

When evaluating features it seems that almost everywhere a correlation matrix is used [df.corr(), cor(df, method="pearson")].

The way I understand it is that a correlation matrix describes the stregnth and directionality of the linear relationship (strong negative through strong positive) between each feature/predictor and all others.

HOWEVER

If $$R^2$$ indicates the amount of variability explained by the linear relationship, between each feature/predictor (as a proportion), wouldn't that provide more information for model selection or feature engineering?

THEREFORE

1. Would it make sense to always square a correlation matrix to get the $$R^2$$ values without reviewing the correlation matrix?

2. How relevant to model selection or feature engineering is understanding if there's an postive or negative correlation among features?

• You get no additional information by doing this, but you do lose the information about the sign of the correlation. Any rule you use in terms of $R^2$ can be phrased in terms of the correlation, but no rule involving the sign of $R$ can be phrased in terms of $R^2$ (except for something silly like $sign(R) \times R^2$. // "Squaring" a matrix $S$ typically means $S \times S$, not squaring every element of $S$. This might coincide (e.g., identity matrix, zero matrix), depending on the matrix elements, but they do not have to.
– Dave
Jun 29 at 17:20
• Thanks for the feedback!! Jun 30 at 1:06