This study examines the relationship between public expenditure and infrastructural development in Nigeria, addressing a persistent methodological gap in the literature: the tendency to specify functional expenditure categories based on theoretical assumptions rather than formal statistical testing of their independent explanatory power. Since Nigeria's four functional expenditure categories administration (ADEX), economic services (ECEX), social and community services (SOEX), and transfers (TREX) are drawn from the same constrained budget envelope and tend to move together in response to common macro-fiscal shocks, models that retain all categories simultaneously risk multicollinearity, unstable coefficients, and inflated standard errors. To address this, the study applies a stepwise regression approach forward selection, backward elimination, and bidirectional stepwise procedures to 35 annual observations (1991–2025) obtained from the CBN, NBS, Budget Office of the Federation, and World Bank WDI, in order to identify which categories are genuinely significant, non-redundant predictors of the Infrastructure Development Index (IFDI). Forward selection and backward elimination independently converge on an identical three-variable model retaining ADEX, ECEX, and TREX, while excluding SOEX as statistically redundant, explaining approximately 97% of the variation in IFDI (Adjusted R² = 0.9684; F = 348.238, p = 0.0000). All three null hypotheses are rejected. While TREX's significant negative coefficient is consistent with a crowding-out mechanism, the positive ADEX and negative ECEX coefficients diverge from a priori expectations and prior Nigerian evidence, plausibly reflecting collinearity-induced suppression. The study concludes that expenditure composition, not merely volume, matters for infrastructural outcomes, and recommends further diagnostic testing before treating these provisional findings as policy-actionable.