Scatter diagrams and correlation
Scatter diagrams, correlation and lines of best fit
A scatter diagram shows paired bivariate data, one variable on each axis. Put the explanatory (independent) variable on the x-axis and the response (dependent) variable on the y-axis. Describe correlation in two parts: direction (positive - both increase together; negative - one increases as the other decreases) and strength (strong, moderate, weak, or no correlation).
Correlation measures linear association only, so a strong curved relationship can have a correlation coefficient near zero. The line of best fit is drawn by eye through the mean point (x̄, ȳ), with roughly equal numbers of points above and below it and following the general trend. Predictions inside the data range are interpolation and are reasonably reliable; predictions outside it are extrapolation and may be unreliable because the relationship can change.
Trap: correlation does not imply causation - a third variable may drive both. An outlier can pull the line of best fit and distort the apparent correlation, so identify it first. Spearman's rank correlation coefficient, r_s = 1 − 6Σd² ÷ (n(n² − 1)), compares two rankings and is used when data are ranked or the relationship is monotonic rather than linear; values near +1 or −1 indicate strong agreement.
Worked example. Data have mean point (10, 25) and the line of best fit has gradient 2. Then y − 25 = 2(x − 10), so y = 2x + 5: the line must pass through (10, 25).