Plotting scatter graphs, describing correlation, drawing a line of best fit, using it to estimate values, and recognising the limits of extrapolation.

What this dot point is asking

AQA wants you to plot a scatter graph, describe the correlation, draw a line of best fit by eye, use it to estimate values, and understand the limits of prediction (extrapolation) and the difference between correlation and causation. This topic links statistics to straight-line graphs, and the interpretation marks reward precise language about strength, direction and the dangers of predicting beyond the data.

Plotting and describing correlation

A scatter graph plots two variables, one on each axis, with a point for each paired observation. The pattern of points reveals the relationship. Read three features:

• Direction: positive (points rise from lower left to upper right), negative (points fall from upper left to lower right), or no correlation (no clear trend).
• Strength: strong if the points lie close to a straight line, weak if they are scattered loosely around it.
• Outliers: single points well away from the main cluster, which may be data errors.

So "strong positive correlation" means the points rise together and sit close to a line, while "weak negative correlation" means a loose downward trend.

The line of best fit

A line of best fit is a single straight line drawn through the data to summarise the trend. Draw it so that roughly equal numbers of points sit above and below, balancing the scatter; it should pass through the mean point (the average of the $x$ values and the average of the $y$ values). It is not a "join the dots" line and need not pass through any particular data point.

Interpolation, extrapolation and causation

Estimating a value inside the range of the data is interpolation, which is usually reliable because the trend is supported by data there. Estimating outside the range is extrapolation, which is unreliable because the linear pattern may not continue (it could level off, reverse, or hit a natural limit). Always flag an extrapolated prediction as uncertain.

A strong correlation shows that two variables move together, but it does not prove that one causes the other. There may be a third (lurking) variable, the causation could run the other way, or the link could be coincidence. "Correlation does not imply causation" is a standard exam response.

Outliers and the line of best fit

A single outlier can distort the line of best fit, pulling it toward itself and changing both its gradient and position. Before drawing the line, scan for any point well away from the main cluster; it may be a recording error worth ignoring, or a genuine but unusual case. When an exam shows an outlier, you are often asked to identify it and to comment on its effect: removing a clear error before fitting the line gives a more representative trend. The line should follow the bulk of the points, not be dragged off course by one stray.

Linking correlation to the gradient

The gradient of the line of best fit has a real meaning: it is the predicted change in the $y$ variable for each unit increase in the $x$ variable. If hours of training against fitness score has a line of gradient $8$, then each extra hour of training is associated with about $8$ more score points, on average and within the data range. This connects scatter graphs to straight-line graphs and to rates of change, and it lets you interpret the relationship quantitatively rather than only describing it as "positive" or "strong".