Bivariate Data

Bivariate data consist of paired measurements $(x, y)$ on each individual, and the goal is to describe and quantify the relationship between the two variables. The starting point is always a scatter diagram, in which each pair is plotted as a point. From a scatter plot you judge three things: the direction of any relationship (positive if $y$ tends to rise with $x$, negative if it falls), the form (linear or curved), and the strength (how tightly the points cluster around a trend).

Pearson's correlation coefficient

To measure linear association numerically we use Pearson's product-moment correlation coefficient, $r$. It always satisfies $-1 \le r \le 1$. A value of $r = 1$ indicates a perfect positive linear relationship, $r = -1$ a perfect negative one, and $r = 0$ no linear relationship.