a measure of the strength and direction of the association/relation between two variables.
Might be none (r≈0).
Correlation might mean one variable causes the other but by itself is insufficient to establish causation.
Pearson's product moment correlation coefficient r.

-1 ≤ r ≤ 1

x,y both go up together and both go down together: positive r.
One goes up, the other goes down: negative r.

Strength: the closer r is to |1|, the stronger the relationship/association.

X values:
Y values:

n=    Σ x=    Σ y=    Σ x2=    Σ y2=    Σ xy=
x̄=     ȳ=     sx=     sy=    

r=     r2= % of variation in y explainable by [variation in] x

    Linear regression line: y=βx+α     β=r(sy/sx)=    α=ȳ-βx̄=    

X min: X max: Y min: Y max:

mean distance from (x̄,ȳ) =    s.d. distance=