Q:

Why is Pearson correlation is not an effective metric?

I found this statement in some documentation but I could not make sense of it.
"Correlation is not a good metric for regression because it is scale and offset invariant".
I understand that correlation between height and weight remains the same whether we measure in kg or pound, but what does offset mean and how does this impact regression performance?

A:

Correlation Coefficient can be used to measure goodness-of-fit of a model to data. This means, that we compare prediction created by model with the real values. It would be generally good, if our predicted values highly correlated with real values. The higher correlation, the better fit of model to data.
Nevertheless, correlation as a measure of goodness-of-fit may lead to some pitfalls:

Imagine that a model, for some unknown reason, adds a huge constant to every predicted value. Correlation being invariant to a constant may suggest great result, when model somehow is very bad.
Imagine that a model, for other unknown reason, multiplies every predicted value by some huge constant. Prediction also might be very bad, while correlation is great, because it is invariant to scale.

