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paper/src/chapters/04-results.tex
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@@ -40,12 +40,26 @@ We report two preliminary stages before the full factorial interpretation. First
\subsubsection{The Impact of Contamination on Revenue}
The contamination--revenue slope is estimated on a controlled cohort (single sweep, baseline policy, $n_{\text{products}}=100$, $n=95$). In this setting, contamination $\alpha$ is set exogenously by the experiment, so the slope identifies the within-sweep causal effect of contamination on revenue under fixed policy and environment settings. The fitted linear model is
The contamination--revenue slope is estimated on a controlled cohort (single sweep, baseline policy, $n_{\text{products}}=100$, $n=95$). In this setting, contamination $\alpha$ is set exogenously by the experiment, so the slope identifies the within-sweep causal effect of contamination on revenue under fixed policy and environment settings.
\[
\widehat{y}=348{,}823.41-90{,}140.53\,\alpha,
\]
with $t(93)=-61.45$, $p=4.27\times10^{-77}$, $R^2=0.976$, and a 95\% confidence interval for the slope of $[-93{,}053.38,\,-87{,}227.68]$. Interpreted on the contamination grid, a $+0.1$ increase in $\alpha$ corresponds to an average revenue decrease of about $9{,}014$ units. A heteroskedasticity-robust check (HC1) preserves the same direction and significance ($t=-41.25$, $p=1.42\times10^{-61}$), supporting a large and statistically stable impact in this controlled regime.
\begin{table}[ht]
\centering
\caption{Slope verification table for contamination versus revenue (OLS-style report).}
\label{tab:contamination_slope_table}
\begin{tabular}{@{}lrrrrr@{}}
\toprule
Term & Coef. & Std. Err. & $t$ & $p>|t|$ & 95\% CI \\
\midrule
Intercept & 348,823.41 & 784.29 & 444.77 & $<10^{-99}$ & $[347,264.96,\,350,381.86]$ \\
$\alpha$ & $-90,140.53$ & 1,466.90 & $-61.45$ & $4.27\times10^{-77}$ & $[-93,053.38,\,-87,227.68]$ \\
\midrule
HC1 robust check ($\alpha$) & $-90,140.53$ & 2,185.22 & $-41.25$ & $1.42\times10^{-61}$ & -- \\
\bottomrule
\end{tabular}
\end{table}
Interpreted on the contamination grid, a $+0.1$ increase in $\alpha$ corresponds to an average revenue decrease of about $9{,}014$ units, and the robust check preserves both direction and significance.
% TODO: add a compact proposal note for re-running tests with statsmodels in the appendix methodology notes.
\subsubsection{Large Scale Factorial Training}