Scatter Graphs

Each pair of values gives one point: the explanatory variable on the $x$-axis, the response on the $y$-axis.

An $\textbf{outlier}$ is a point that does not fit the pattern of the rest. It might be a recording error or a genuine unusual case, and is usually ignored when drawing a line of best fit.

$\textbf{Positive correlation}$: as one variable increases, the other tends to increase — height and shoe size.

$\textbf{Negative correlation}$: as one increases, the other tends to decrease — a car’s age and its value.

$\textbf{No correlation}$: no clear relationship — height and exam score.

Strength describes how close the points are to a straight line: strong, moderate or weak.

A line of best fit is a single straight line that follows the trend, with roughly equal numbers of points on each side. It does not have to pass through the origin or through any particular point.

Ignore outliers when drawing it.

To estimate a value, read up from the known value to the line, then across.

$\textbf{Interpolation}$ — estimating within the range of the data — is fairly reliable when the correlation is strong.

$\textbf{Extrapolation}$ — estimating outside the range — is unreliable, because the trend may not continue. The revision line above would predict 130 marks for 20 hours, which may be impossible.

$\textbf{Correlation does not mean causation}$. Ice-cream sales and sunburn are positively correlated, but ice cream does not cause sunburn — hot weather affects both.