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Correlation and Covariance

Correlation

  • Positive correlation exists when larger values of
    xx
    correspond to larger values of
    yy
    and vice versa.
  • Negative correlation exists when larger values of
    xx
    correspond to smaller values of
    yy
    and vice versa.
  • Weak or no correlation exists if there is no such apparent relationship.

Covariance

It is a measure that quantifies the strength and direction of a relationship between a pair of variables.
cov(x,y)=1nin(xix)(yiy)cov(x,y)=\frac{1}{n}\sum_i^n(x_i-\overline{x})(y_i-\overline{y})

Correlation Coefficient

The correlation coefficient, or Pearson product-moment correlation coefficient is another measure of the correlation between data. You can think of it as a standardized covariance.
rxy=cov(x,y)σ(x)σ(y)=in(xix)(yiy)in(xix)2in(yiy)2r_{xy}=\frac{cov(x,y)}{\sigma(x)\sigma(y)}=\frac{\sum_i^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum_i^n(x_i-\overline{x})^2\sum_i^n(y_i-\overline{y})^2}}
Make a Scatter Plot, and look at it! You may see a correlation that the calculation does not.
Correlation Is Not Causation which says that a correlation does not mean that one thing causes the other.