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• 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 r = 1 the correlation is perfect and positive

• If r = 0 there is no correlation at all

• If r = -1 the correlation is perfect and negative

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:

2. Click 6: statistics

3. Click 2: y=a+bx

4. Input your data in the table

5. Click AC

6. Click OPTN

7. Click 3: Regression Calc

8. r is the product moment coefficient