Answer
Section 1:
Correlation coefficient.
Pearson correlation coefficient quantifies how strong two variables share a linear relationship.
There can be two kinds of correlation coefficients, namely, population and sample correlation coefficient. The population correlation coefficient is denoted by p and the sample is denoted by r.
The formula for sample correlation coefficient is
\[r=\frac{n\,(\sum{xy)-}(\sum{x)(\sum{y)}}}{\sqrt{[n\sum{{{x}^{2}}-}(\sum{x{{)}^{2}}}][n\sum{{{y}^{2}}-}(\sum{y{{)}^{2}}}]}}\]
Where
\[\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftharpoonup}$}}{x}\]is the sample mean for variable x.
\[\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftharpoonup}$}}{y}\]is the sample mean for variable y.
n is the total number of people.
Section 2:
If the value of \[({{x}_{i}}-\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftharpoonup}$}}{x})\]and \[({{y}_{i}}-\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftharpoonup}$}}{y})\]are positive, so will be their product. This will indicate that the two variables have a positive linear correlation. If the product is negative, then they will share a negative linear correlation.
Work Step by Step
Given above.
