# Why is pearson correlation popular if it detects only linear correlation?

Pearson's correlation coefficient is widely used to check for relationship between predictors in a dataset. However, since it measures only linear relationships between variables, wouldn't it be better to make some other correlation measure the conventional measure, say distance correlation that can measure both linear and non-linear relationships?

• linear correlation is very frequent, so Pearson correlation is very valuable. Furthermore it is well-defined mathematically, whereas other approaches are mostly heuristics, or highly complex Commented Nov 14, 2021 at 14:41
• Who said that it’s the conventional measure?
– Dave
Commented Nov 15, 2021 at 2:00

Linear correlation is useful because it is the simplest possible one. Consider an independent variable $$x$$ and dependent variable $$y$$, and some model that relates them:
$$y=f\left(x\right)$$
In many cases $$f$$ is sufficiently well behaved for derivatives of it to be defined. Therefore if you have prior training data to estimate those derivatives you can predict $$y$$ close to your nearest known training point $$\left(x_0,\,y_0\right)$$:
$$y=f\left(x\right)\approx y_0 + f'\left(x_0\right)\left(x-x_0\right)+...$$