Question

Whats the numerator mean

When you calc Pearson correlation 2 data - x and y,

i. not any of these. ii. sum of the variances of x and y. iii. The product of the standard deviations of x and y. iv covariance of x and y

Answer 1

Ans. The correct option is (iv), i.e., The numerator term in the correlation coefficient formula is Covariance of x and y.

The formula for pearson correlation coefficient(r) :

$r=\frac{\Sigma{(x-\bar{x})(y-\bar{y})}}{\sqrt{\Sigma{(x-\bar{x})^{2}}}\sqrt{\Sigma{(y-\bar{y})^{2}}}}=\frac{\frac{1}{N}\Sigma{(x-\bar{x})(y-\bar{y})}}{\sqrt{\frac{1}{N}\Sigma{(x-\bar{x})^{2}}}\sqrt{\frac{1}{N}\Sigma{(y-\bar{y})^{2}}}}$

where,

Cou(a, y

standard deviation of x.         $\sigma_{x}=\sqrt{\frac{1}{N}\Sigma{(x-\bar{x})^{2}}}$

standard deviation of y,           $\sigma_{y}=\sqrt{\frac{1}{N}\Sigma{(y-\bar{y})^{2}}}$

Then pearson correlation coefficient(r) is written as:     

Cov(r, y)