Tuesday, 8 May 2012

Affine Transformation Does not Alter Correlation Coefficient

if $X$ and $Y$ are Two Random Variables with Correlation Coefficient $\rho$, Then the Correlation Coefficient of Random Variables
$$ a_1X+b_1\;\text{and}\; a_2Y+b_2$$, Where $a_1$ and $a_2$ are Non Zero Real Numbers with Same Sign is also $\rho$. if They have Opposite Signs, The Correlation Coefficient is $-\rho$.

1 comment:

  1. Ya that's right, I like your way to describe it, an affine transformation is any transformation that preserves col-linearity and ratios of distances. In this sense, affine indicates a special class of projective transformations that do not move any objects from the affine space to the plane at infinity or conversely. An affine transformation is also called an affinity.
    Affine Transformation