correlation coefficient

**sagarmte** · December 1st 2012, 06:06 AM

The correlation coefficient between x and y is 0.85

Statement 1-then the correlation coefficient between x/2 and y/2 is 0.85/2
Statement 2-then the correlation coefficient between - X and Y is - 0.85

how are above two statements true?

**Scopur** · December 1st 2012, 07:47 PM

Use the definition of the correlation coefficient

$\frac{E[XY]-E[X]E[Y]}{\sigma(x) \sigma(y)}$ and these properties
$E[aX] = aE[X]$ and $Var(aX) = a^2Var(X)$ .

Also i believe the first statement is not true. I get that $Cov(X/2,Y/2) = 1/4Cov(X,Y)$ and that
$\sigma_{X/2} = \sqrt{Var(X/2)} = \sqrt{1/4Var(X)} = 1/2\sigma_X$
You can find the variance of $Y/2$ the same way. Giving us that statement 1 is 0.85.

Thread: correlation coefficient

LinkBack

Thread Tools

Display

correlation coefficient

Re: correlation coefficient

Similar Math Help Forum Discussions

Coefficient of correlation

correlation coefficient, determination coefficient, coeficient of variables

Correlation Coefficient, Covariance, Least Squares Method Line, and Coefficient of De

correlation coefficient

correlation coefficient help

Search Tags