Akaike information criterion

The Akaike information criterion (AIC) scores competing regression models by rewarding a better fit and penalising extra explanatory variables, so the model with the lowest AIC is preferred over the one with the highest raw R-squared.

ByHoang TruongUpdated July 5, 2026

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Fitted to the same 40 observations, Model A (2 predictors, 3 parameters) has SSE = 500 and AIC = 107.03. Model B adds five more predictors (8 parameters) and reaches a lower SSE of 470, yet its AIC rises to 114.56. The extra parameters cost more than the small fit improvement is worth, so Model A is preferred.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicMultiple Regression & InterpretationAdvanced

The formula

LaTeX

AIC = n \ln\!\left(\dfrac{SSE}{n}\right) + 2k

Variables

$n$: Number of observations
$S S E$: Error sum of squares (squared units of y)
$k$: Number of estimated parameters, including the intercept

Scores a regression model by trading off fit (lower SSE) against complexity (more parameters); the model with the lowest AIC is preferred.