- A-Level Maths

# Correlation & Regression

**Bivariate** data is data with two variables, and can be represented in a scatter diagram. We can describe the correlation between the two variables based on how much of a straight line the points on the diagram form.

Correlation describes the nature of the linear relationship between two variables.

A

**negative correlation**occurs when one variable increases as the other decreases.A

**positive correlation**occurs when both variables increase together.

### Causation

The relationship can be described as **causal** if a change in one variable induces a change in the other. It is vital to remember that just because there may be a correlation, no matter how strong, between two variables, it does not mean the relationship is causal.

Correlation does not imply causation

You need to consider the **context **of the variables and **use common sense** to decide whether or not there is causation as well as correlation.

Measuring Correlation

The **product moment coefficient, r**, is a measure of strength for linear correlation between two variables. It takes values from -1 to 1, where

If

the correlation is perfect and positive*r = 1*If

there is no correlation at all*r = 0*If

the correlation is perfect and negative*r = -1*

You calculate the product moment coefficient using a stats-equipped scientific calculator.

On a ** CASIO ClassWiz fx-991EX**, to calculate the product moment coefficient,

*r*:

Click

**MENU**Click

**6**: statisticsClick

**2**: y=a+bxInput your data in the table

Click

**AC**Click

**OPTN**Click

**3**: Regression Calcr is the product moment coefficient