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For a normal linear model with $n$ fixed observations and $p$ mean coefficients, maximizing over the error variance gives ${\hat{\sigma }}^2=\mathrm{RSS}/n$. The maximized negative twice log-likelihood is $n\log (\mathrm{RSS}/n)$ plus a constant common to the candidate models. Counting the variance as another parameter adds the same penalty two to every model, so the stated criterion is equivalent for comparing them:The Akaike information criterion balances fit against parameter count; smaller values are preferred. It does not compare models using different response scales or different sets of observations without further adjustment.

Stepwise selection by the Akaike information criterion compares allowed one-term additions and deletions, takes a change lowering the criterion, and repeats until no allowed change improves it. The search direction, initial fit and lower/upper scopes matter. A displayed no-change row represents the current model. The term degrees of freedom show how many coefficients a change removes, the residual sum reflects its fit, and the AIC column determines the selected move. The search is greedy, not a guarantee of the best subset over the entire model space. The software's scope and direction conventions are documented in stat.ethz.ch/R-manual/R-devel/library/MASS/html/stepAIC.html .

Deleting $q$ coefficients changes the criterion byThus the AIC deletion threshold in a normal linear model isFor a single coefficient, its partial F-test statistic must be below $(n-p)(e^{2/n}-1)$ for AIC to favor deletion. At the full 47-observation, 16-coefficient fit this is approximately $1.348$, corresponding to $|t|<1.161$. Therefore AIC selection is not equivalent to retaining only coefficients with a conventional five-percent p-value.

The final model should be described by its retained terms, signs, conditional effect sizes, uncertainty, residual diagnostics and prediction behavior. A coefficient that survives selection need not identify a causal mechanism, and its ordinary final-model p-value ignores the preceding search. Stability under bootstrap resampling and predictive cross-validation are useful. The absent search trace and final model prevent identifying the actual deletion sequence, final predictors, coefficients, RSS or AIC. The given starting name does not specify any of those facts.