Bivariate Data — Correlation and Regression

Relationships between two variables

Much of applied statistics concerns whether two quantities move together. Bivariate data consist of paired measurements $(x, y)$. An ice-cream vendor might record daily maximum temperature $x$ (°C) and sales $y$ (units):

Temp $x$	18	20	22	25	27	30	32
Sales $y$	44	52	58	70	78	92	101

Scatter plots

The first step is always a scatter plot, plotting each pair as a point. We look for the direction (positive, negative, or none), form (linear or curved), and strength of any association. The ice-cream data rise steadily from lower-left to upper-right, suggesting a strong positive linear relationship: warmer days bring more sales.

Pearson's correlation coefficient

The strength and direction of a linear relationship are quantified by Pearson's product-mom