Investigation station
Independent observations, approximately normal residuals and constant spread.
Given observations
Concept figure
Intervals represent uncertainty in a population mean, not the range of individual observations.
Live regression and residuals
Analysis controls
Analyse the data, then check your decision.
The maths
Least-squares line: y = a + bx. The slope uncertainty is SE(b) = √[RSS / ((n − 2)Sxx)].
One-sample t: t = (sample mean − hypothesised mean) / (sample SD / √n), with df = n − 1.
Confidence interval: sample mean ± t critical × sample SD / √n.
Pooled two-sample t assumes equal population variances. Welch does not; Welch's degrees of freedom need not be an integer.
Chi-square goodness of fit: χ² = Σ(observed − expected)² / expected; df = category count − 1 when no parameters are estimated.
Student t p-values here are two-sided; chi-square p-values use the upper tail.