Scatter graphs

A scatter graph plots pairs of data to see if they're linked. The link is called correlation:

• positive: as one goes up, the other goes up
• negative: as one goes up, the other goes down
• no correlation: no pattern.

Correlation can be strong (points close to a line) or weak (more spread out).

Example: describe the correlation between hours revised and test score.

1. As hours revised goes up, the score goes up
2. The points are close to a straight line
3. Strong positive correlation

A line of best fit is a straight line through the middle of the points, with about as many above it as below. Draw it with a ruler, ignoring any outliers.

• Interpolation is estimating inside the range of the data: reliable.
• Extrapolation is estimating outside it: unreliable, because the pattern may not continue.

Example: use line L to estimate the score for 4.5 hours of revision. Would it be sensible to estimate for 12 hours?

1. Up from 4.5 to the line, then across
2. About 55%
3. 12 hours is outside the data (1 to 8 hours), so it's extrapolation
4. No: the line would give about 98%, but scores can't keep rising forever

An outlier is a point that doesn't fit the pattern, such as P at (6, 30) on the scatter graph. It may be a mistake, or a real but unusual result. Leave outliers out when drawing the line of best fit.

Correlation doesn't mean causation: two things being linked doesn't prove that one causes the other. Both might be caused by something else.

Example: ice cream sales and sunburn cases show positive correlation. Does eating ice cream cause sunburn?

1. Both go up in hot, sunny weather
2. No: the weather causes both