Descriptive statistics, correlation and regression
Descriptive statistics, correlation and regression
This domain tests summarising data, comparing distributions, measuring linear association and fitting a least-squares regression line. Interpretation matters as much as calculation.
Core rules
- Mean, median and mode describe centre; range, interquartile range and standard deviation describe spread. The IQR is resistant to outliers.
- For grouped data, use class midpoints and frequencies; for coded data, reverse the coding when reporting mean and standard deviation.
- Pearson's product-moment correlation r measures the strength and direction of linear association, with −1 ≤ r ≤ 1. Spearman's rank correlation is used for ordinal data or monotonic non-linear association.
- Least-squares regression of y on x: b = Sxy/Sxx, a = ȳ − bx̄, so the line passes through (x̄, ȳ). r² is the proportion of variation in y explained by the linear regression.
- Predict only within the observed range; extrapolation is unreliable.
Worked example
For x = 1, 2, 3, 4 and y = 2, 4, 5, 7, x̄ = 2.5 and ȳ = 4.5. Sxx = 5 and Sxy = 8, so b = 8/5 = 1.6 and a = 4.5 − 1.6(2.5) = 0.5. The regression line is y = 0.5 + 1.6x; at x = 5 it predicts 8.5, but this is an extrapolation.
Common traps
Claiming correlation proves causation; confusing regression of y on x with x on y; using the wrong quartile method; forgetting that coding changes regression coefficients; and treating an outlier as representative.