= Solution
For a <normal linear model> with $n$ fixed observations and $p$ mean coefficients, maximizing over the error variance gives $\widehat\sigma^2=\operatorname{RSS}/n$. The maximized negative twice log-likelihood is $n\log(\operatorname{RSS}/n)$ 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:
$$
\operatorname{AIC}=n\log(\operatorname{RSS}/n)+2p.
$$
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 https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/stepAIC.html .
Deleting $q$ coefficients changes the criterion by
$$
\Delta\operatorname{AIC}=n\log\frac{\operatorname{RSS}_{\mathrm{reduced}}}{\operatorname{RSS}_{\mathrm{full}}}-2q.
$$
Thus the <AIC deletion threshold in a normal linear model> is
$$
\boxed{\operatorname{RSS}_{\mathrm{reduced}}/\operatorname{RSS}_{\mathrm{full}}<e^{2q/n}.}
$$
For 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. \b[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.
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