Polynomial Regression Analysis: Testing for Curvilinear Effects of Internal Supervision Practices and Teachers' Effectiveness on Teaching Quality
DOI:
https://doi.org/10.64348/zije.2026420Abstract
All prior regression analyses of this dataset assumed linear relationships between predictors and outcomes. The present study extended this framework by testing polynomial (curvilinear) models to determine whether the effects of Internal Supervision Practices (ISPS) and Teachers' Effectiveness (TES) on Teaching Quality (TQS) depart significantly from linearity in a sample of N = 386 teachers from private secondary schools in Gusau, Zamfara State, Nigeria. Using hierarchical polynomial regression, quadratic terms (ISPS² and TES²) were entered in Block 2 following the linear main effects in Block 1. For ISPS, the quadratic increment was non-significant (ΔR² = .003, FΔ[1, 383] = 1.33, p = .249), confirming that the supervision–the linear model adequately describes the quality relationship. For TES, the quadratic term likewise produced a non-significant increment (ΔR² = .001, FΔ[1, 383] = 0.47, p = .496). A combined model incorporating both quadratic terms explained R² = .143, representing a marginal improvement of ΔR² = .003 over the linear baseline (R² = .140, FΔ[2, 382] = 0.67, p = .513). Residual diagnostic plots confirmed homoscedasticity and approximate normality of residuals for the linear model. Post-hoc power analysis revealed that N ≥ 2,500 would be required to detect the observed quadratic signal (f² = .003) with 80% power, indicating the null finding is indeterminate rather than conclusive. These results justify the linear modelling approach adopted in prior analyses and effectively rule out U-shaped or inverted-U relationships between supervision intensity and teaching quality within the empirically observed ISPS range (2.22–4.00).
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