Scatter diagrams

• Plot each pair of values as a small cross (×) on a scatter diagram.
• Positive correlation: as one goes up, so does the other. Negative: as one goes up, the other goes down. Zero: no relationship.
• A line of best fit is a single ruled line drawn by eye, across the full data set, with points roughly evenly on both sides.
• Use the line to estimate values inside the range of the data; estimates outside it are unreliable.
• Correlation does not prove that one thing causes the other.

Pairs of values as crosses

Each item gives a pair of values, such as hours revised and test score. Put one variable on each axis, with an even scale on both, and plot each pair as a small, clear cross (×). Do not join the points.

These ten points rise from bottom left to top right: more revision goes with higher scores.

Describing the pattern

The closer the points lie to a straight line, the stronger the correlation. When asked to interpret, describe the relationship in words: “the more hours a student revised, the higher their score tended to be”.

One ruled line, drawn by eye

The syllabus is specific about what a line of best fit must be:

• a single ruled straight line, drawn by inspection (not joining the points dot to dot);
• it should extend across the full data set, from the first point to the last;
• it need not pass through any of the points, but there should be a roughly even spread of points on either side along its whole length.

Only draw a line if there is correlation. A useful check, though not required: the line should pass close to the point (mean of x, mean of y).

Interpolation and extrapolation

Estimating within the range of the data (here 1 to 8 hours) is reliable when the correlation is strong. Going beyond the data assumes the pattern carries on, which it may not.