Correlation and Covariance

Correlation
Positive correlation exists when larger values of xxx
 correspond to larger values of yyy
 and vice versa.
Negative correlation exists when larger values of xxx
 correspond to smaller values of yyy
 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)=1n∑in(xi−x‾)(yi−y‾)cov(x,y)=\frac{1}{n}\sum_i^n(x_i-\overline{x})(y_i-\overline{y})cov(x,y)=n1​i∑n​(xi​−x)(yi​−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(xi−x‾)(yi−y‾)∑in(xi−x‾)2∑in(yi−y‾)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}}rxy​=σ(x)σ(y)cov(x,y)​=∑in​(xi​−x)2∑in​(yi​−y​)2​∑in​(xi​−x)(yi​−y​)​
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.

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Hypothesis Test

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Outline

Correlation

Covariance

Correlation Coefficient