Sattumaosuus

Sattumaosuus is a Finnish statistical term describing the portion of a variable’s variation that arises from chance or random factors, as opposed to variation explained by systematic or known factors. It corresponds to the stochastic component or error term in a model. In a typical regression Y = β0 + β1X + ε, the sattumaosuus is the error term ε, with expected value often zero and variance σ². The relative size of the sattumaosuus to the explained variation affects the model’s predictive power.

Measurement and estimation of sattumaosuus occur through residuals and variance components. In regression analysis, the sattumaosuus is estimated by the residual sum of squares and the mean square error. In analysis of variance and mixed models, it is described by variance components and random-effects terms. Distinctions may be made between variability due to random sampling and variability due to measurement error, both contributing to the sattumaosuus.

Applications and interpretation: Understanding sattumaosuus helps quantify uncertainty in predictions, inform sample size decisions, and indicate when a model misses important factors. Practically, a large sattumaosuus suggests that much of the outcome’s variation remains unexplained by the model, signaling potential model improvement or the influence of unobserved variables.

Example: Forecasting daily sales with price and promotion variables leaves a sattumaosuus representing unobserved influences such as weather or consumer mood. If the model explains a portion of the variance, the remaining portion is the sattumaosuus.