Correlation

Lesson

Part 1 — how two variables move together, and how a scatter diagram shows it.

In this lesson you will

Define correlation and distinguish positive, negative, linear and non-linear relations
Draw and read a scatter diagram for perfect, high, low and no correlation
Explain why correlation does not prove causation, using a third variable and spurious correlation
State the properties of the coefficient and show that it is unaffected by a change of origin and scale

Part 1 at a glance

Concept

What is correlation?

Correlation is the degree and direction of the linear relationship between two variables.

Table of kinds of correlation, positive, negative, linear, non-linear and none, each with its meaning and an imagined example
Kind	Meaning	Imagined example
Positive	The variables rise and fall together	Temperature and cold drink sales at a juice corner
Negative	One rises while the other falls	Temperature and hot soup sales at a hill stall
Linear	The dots lie around a straight line	Hours of study and marks of a class
Non-linear	The dots follow a curve	Temperature and electricity use in a hill town
None	The dots show no pattern	Shoe size and marks of students

Diagram

Imagined pairs of values: positive, negative and no correlation