IB Maths AA 4.4 Notes

Scatter diagrams & correlation

Linear statistics studies the relationship between two numerical variables. The main tools are scatter diagrams, Pearson's product-moment correlation coefficient $r$, and regression lines. These are used to describe, model and predict linear relationships in bivariate data.

Bivariate data consists of paired values, usually written as $(x,y)$. For example, $x$ might represent hours studied and $y$ might represent test score. Each student gives one pair of values.

A scatter diagram is a plot of paired data values on a coordinate grid. Each point represents one observation. Scatter diagrams help us see whether there is a relationship between the variables.

A line of best fit drawn by eye should pass through the mean point $(\overline{x},\overline{y})$.

There are three main types of correlation seen in a scatter diagram:

• If the points tend to rise from left to right, there is positive correlation.
• If the points tend to fall from left to right, there is negative correlation.
• If there is no clear pattern, there is no correlation.

The correlation may also be described as strong or weak depending on how closely the points follow a straight-line pattern. It is important to remember that correlation does not imply causation.