A scatter diagram plots paired data $(x,y)$ as points, to investigate whether a relationship exists between two variables.

Zero correlation means the points are scattered with no consistent upward or downward trend at all — this is different from the points forming a tight cluster or a curve; a scatter diagram can show a clear pattern that still isn't a straight-line trend, in which case describing it simply as "no correlation" would understate what the diagram actually shows.

A line of best fit is a single straight line, drawn by eye with a ruler, that follows the overall trend, extends across the full range of the data, and has a roughly even scatter of points above and below it along its whole length.

Reading off the line lets you estimate a value within the data range (interpolation).

Worked example. A scatter diagram compares hours of sunshine and ice cream sales, rising from bottom-left to top-right. (a) State the correlation. (b) Using the line of best fit through $(2, 20)$ and $(8, 80)$, estimate sales at $5$ hours of sunshine.

(a) Points rising left to right $\implies$ positive correlation.

(b) $5$ hours is exactly halfway between $2$ and $8$: $\dfrac{20+80}{2} = 50$.

Once two points on the line of best fit are identified (they don't need to be actual data points — any two points the line passes through will do), the equation can be found the same way as for any straight line, using $y=mx+c$.

Worked example. Using the same line of best fit through $(2,20)$ and $(8,80)$, find its equation, and use it to estimate sales at $10$ hours of sunshine.

At $x=10$: $y=10(10)=100$. Since $10$ hours lies just beyond the original data's range (up to $8$ hours), this estimate is an extrapolation and should be treated with more caution than the earlier estimate at $5$ hours.