Correlation Vocabulary

A scatter diagram displays these pairs. One variable is shown on the horizontal axis and the other on the vertical axis. Each point represents one pair of measurements; the points are not joined together. The overall pattern helps us describe the correlation: how the two numerical variables tend to vary together.

Positive, negative and zero correlation

Positive correlation means that as one variable increases, the other tends to increase too. Temperature and cold-drink sales provide an example: warmer days tend to have higher sales. On a scatter diagram, the points form an overall pattern rising from bottom left to top right.

Negative correlation means that as one variable increases, the other tends to decrease. For example, as a car gets older, its value tends to fall. The pattern slopes downwards from top left to bottom right.

Zero correlation, also called no correlation, means there is no apparent upward or downward trend. Knowing the value of one variable does not suggest a consistently higher or lower value of the other. The points look like a scattered cloud rather than following a rising or falling pattern.

Read each panel from left to right, so that the horizontal variable is increasing. Ask whether the vertical values generally rise, generally fall, or do neither. Describe the overall pattern rather than expecting every point to follow it exactly.

Association is not the same as causation

An association is a relationship between variables. When two variables show positive or negative correlation, they are associated. This describes a pattern in the data, but does not by itself explain why the pattern exists.

Causation means that a change in one factor produces a change in another. Establishing a cause-and-effect relationship requires more than observing that two quantities change together. This is the meaning of ‘correlation does not imply causation’.

Imagine recording the height of a growing sunflower and the mass of a growing puppy each day. Both may increase, producing positive correlation. However, making the sunflower taller would not make the puppy heavier. Their growth occurs as time passes: time helps explain why both measurements increase together.

A correlation may therefore reflect a causal relationship, another factor affecting both variables, or a coincidental pattern. The correlation alone cannot tell us which explanation is correct.

Interpolation: estimating within the data range

When a scatter diagram shows a useful trend, a line of best fit can represent its general direction. We can use this line to estimate one variable from the other. The estimate follows the overall trend rather than any single data point.

Interpolation means estimating within the range of the observed data. For example, suppose computers with prices from £220 to £900 have been tested to record how long they take to complete the same task. Estimating the completion time for a £500 computer is interpolation because £500 lies within that price range. The dataset need not contain a computer costing exactly £500.

To make this estimate on a graph with price on the horizontal axis, start at £500, move vertically to the line of best fit, then horizontally to the time axis. Read the estimated time with its unit.

Extrapolation: estimating beyond the data range

Extrapolation means estimating outside the range of the observed data. Using the same computer data to estimate the completion time for a £1500 computer would be extrapolation because £1500 is above the highest observed price of £900. Estimating for a price below £220 would also be extrapolation.

Extrapolation assumes that the observed trend continues beyond the data. This makes it generally less reliable than interpolation: more expensive computers might not keep completing the task faster in the same way.

Interpolation is not guaranteed to be accurate either. A sample may be unrepresentative, and individual values may differ from the line of best fit. Both methods produce estimates, not certain outcomes.