Example 1 — computing r
For and , find the product-moment correlation coefficient.
- 1, , , , Lay the sums out in a table before substituting.
- 2
- 3
- 4
- 5
- 6Between and 1 ✓ A fairly strong positive linear relationship.
Correlation and Linear Regression
Try each one on paper first, then check a single step. That is worth far more than reading a finished solution.
Example 2 — the regression line
Using the same data, find the regression line of on and predict when .
- 1The gradient.
- 2 and
- 3
- 4Check: at , ✓ The line always passes through the means.
- 5At :
- 6Reliable, since 2.5 lies inside the data range 1 to 5.Interpolation, not extrapolation.
Example 3 — Spearman's rank correlation
Two judges rank five entries, giving rank differences . Find .
- 1Only ranks matter, not the raw values.
- 2Squaring removes the signs.
- 3
- 4
- 5Strong agreement between the judges.