The #pearson-correlation-coefficient or Pearson product-moment correlation coefficient quantifies the linear relationship between two variables. It measure how well a straight line can describe their relationship, ranging from -1 (perfect negative relationship) to +1 (perfect positive relationship). Other Names: - Pearson correlation - Correlation coefficient **The Pearson Correlation Coefficient** $ \begin{align*} r = \frac{\sum (x_i - \overline x)(y_i - \overline y)}{\sqrt \sum (x_i - \overline x)^2 \sum (y_i - \overline y)^2} \\ \\ r = \text{correlation coefficient} \\ x_i= \text{values of the x-variable in the sample} \\ \overline x = \text{mean of the values of the x-variable} \\ y_i= \text{values of the y-variable in the sample} \\ \overline y = \text{mean of the values of the y-variable} \end{align*} $ ![[correlation-coefficient.png]]