Correlation

Grade 4

What correlation tells you

When you plot two variables on a scatter graph, the pattern of points tells you whether there is a correlation — a relationship between the two variables.

There are three types: positive (as one increases, so does the other), negative (as one increases, the other decreases), and no correlation (the points are scattered with no pattern).

Strength of correlation

As well as the direction, you need to describe how strong the correlation is. If the points lie close to a straight line, it's strong. If they're more loosely spread around a line, it's weak.

Use both words together in your answer: "strong positive correlation" or "weak negative correlation". Just saying "positive correlation" without a strength will usually lose you a mark.

Worked example — describing correlation

EXAMPLE

A scatter graph shows revision hours on the x-axis and test scores on the y-axis. The points roughly follow a line going from bottom-left to top-right, fairly closely bunched. Describe the correlation.

Points go from bottom-left to top-right → positive direction. Points are fairly closely bunched around a line → strong. As revision hours increase, test scores increase. Strong positive correlation.

Correlation is not causation

Correlation means two things change together — it does not mean one causes the other. Ice cream sales and sunburn both increase in summer, but ice cream doesn't cause sunburn. Always be careful about what you conclude from a correlation on an exam.

Try this one

A sports scientist records the daily temperature (in °C) and the number of cold drinks sold at a leisure centre. The scatter graph is shown below.

(a) Write down the word that best describes the correlation. [1]

Positive Negative No correlation

(b) On a day when the temperature is 22°C, estimate the number of cold drinks sold. [1]

(c) Give one reason why it would not be reliable to use this graph to predict the number of drinks sold on a day when the temperature is 50°C. [1]

Nova's hint:

This question covers scatter graphs, correlation and the reliability of predictions.

For part (b), trace up from 22°C to the trend of the points and read across.

For part (c), ask yourself: 'what would have to be true about the data for a prediction at 50°C to be trustworthy?'

Try to Solve it with Nova?