Predictive Modelling, Statistical Validation, and Diagnostic Evaluation of Eco-Friendly Sida acuta Leaf Extract for Aluminium Corrosion Inhibition in Acidic Medium

582 Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 p ISSN: 2635-3342; e ISSN: 2635-3350 Original Research Article Predictive Modelling, Statistical Validation, and Diagnostic Evaluation of Eco-Friendly Sida acuta Leaf Extract for Aluminium Corrosion Inhibition in Acidic Medium *1Okpanachi, C.B., 1Agada, I.U., 2Onoyima, C.C., 1Egu, S.A., 1Abalaka, E., 1Ameh, E.M. and 1Ejukwa, E. 1Department of Pure and Industrial Chemistry, Prince Abubakar Audu University, Anyigba, Kogi State, Nigeria. 2Department of Chemistry, Nigeria Police Academy, Wudil, Kano State, Nigeria. *[email protected] http://doi.org/10.5281/zenodo.18062007 ARTICLE INFORMATION ABSTRACT Article history: Received 08 Nov. 2025 Revised 28 Nov. 2025 Accepted 12 Dec. 2025 Available online 30 Dec. 2025 This study investigated the corrosion inhibition performance of Sida acuta leaf extract on aluminium in an acidic medium, focusing on its phytochemical constituents, inhibition efficiency, and statistical modelling. A quadratic model developed using Response Surface Methodology (RSM) assessed the influence of immersion time, temperature, and extract concentration. Experimentally, inhibition efficiency increased with concentration, reaching values above 80% at higher extract dosages under moderate temperature conditions (20 - 40 °C). However, efficiency declined to below 60% at an elevated temperature of 60 °C, while extended immersion for 168 h resulted in a 20 - 25% reduction, demonstrating susceptibility to thermal degradation and inhibitor desorption. The model produced a coefficient of determination (R²) of 0.8039, accounting for about 80% of the variation in inhibition efficiency. The Adjusted R² (0.7317) and Predicted R² (0.5951) showed reasonable agreement, while the Adequate Precision value of 14.17 exceeded the minimum acceptable threshold of 4, indicating a strong signal-to-noise ratio. Model reliability was further supported by a coefficient of variation (CV) of 7.44%, a standard deviation of 5.04, and a PRESS value of 764.86, confirming acceptable predictive accuracy. Diagnostic evaluations affirmed model adequacy, showing normal residual distribution, absence of influential outliers (Cook’s distance <1.0), leverage values <0.80, and a Box–Cox λ ≈ 1.0 within the confidence limits. Overall, Sida acuta extract demonstrated effective (>80%) and eco-friendly inhibition under optimized conditions, supported by robust statistical indicators (R² = 0.8039; Adequate Precision = 14.1692; CV = 7.44%), validating its potential as a sustainable corrosion inhibitor. © 2025 RJEES. All rights reserved. Keywords: Acidic medium Aluminium corrosion Inhibition efficiency Quadratic Model Green corrosion inhibitor Sida acuta 1. INTRODUCTION Aluminium and its alloys are among the most versatile metallic materials, widely employed in the automotive, aerospace, packaging, and construction industries due to their low density, high strength- 583 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 to-weight ratio, good electrical and thermal conductivity, and excellent recyclability (Chopra et al., 2025). Despite these merits, aluminium remains susceptible to corrosion in aggressive environments, especially in acidic media where its naturally protective oxide film becomes unstable or dissolves. In solutions such as hydrochloric acid (HCl), nitric acid (HNO₃), and sulfuric acid (H₂SO₄), the metal undergoes active dissolution, forming soluble aluminium salts like AlCl₃, Al(NO₃)₃, and Al₂(SO₄)₃ (Mansor et al., 2024; Liu et al., 2023). Such degradation compromises structural integrity, increases maintenance costs, and may lead to environmental pollution due to the release of metal ions. To mitigate corrosion, conventional protection strategies including coatings, cathodic protection, and the application of synthetic inhibitors have been widely adopted (Mahmood et al., 2025). However, coatings tend to deteriorate over time, cathodic systems are costly to maintain, and synthetic inhibitors such as chromates and phosphates pose serious environmental and health hazards due to their toxicity and non-biodegradability (Zhang et al., 2025). Consequently, the search for safer, sustainable alternatives has intensified, in line with the principles of green chemistry, which advocate for renewable, non-toxic, and environmentally benign chemical practices (Golovin & Ilain, 2023). Plant-derived corrosion inhibitors, commonly known as green inhibitors, have attracted considerable attention as promising substitutes for conventional synthetic compounds. These natural extracts are rich in phytochemicals such as alkaloids, flavonoids, tannins, and phenolics, which contain heteroatoms (O, N, S) and π-electrons capable of adsorbing onto metal surfaces and forming protective films that hinder corrosion processes (Kuraimid et al., 2023). Among such plants, Sida acuta, a widely distributed medicinal shrub, contains abundant bioactive compounds that make it a potential candidate for ecofriendly corrosion inhibition, although its efficiency on aluminium in acidic environments remains underexplored. To enhance inhibition performance and process understanding, statistical optimization techniques such as Response Surface Methodology (RSM) provide a powerful alternative to traditional one-factor-at-atime methods. The Box–Behnken Design (BBD), a subset of RSM, allows efficient modeling of variable interactions while minimizing experimental runs (Nguyen et al., 2024; Lamidi et al., 2023). Therefore, this study investigates the corrosion inhibition efficiency of Sida acuta leaf extract on aluminium in acidic media using BBD under RSM to evaluate the effects of inhibitor concentration, acid strength, temperature, and immersion time. This approach aims to establish optimal conditions for maximum inhibition efficiency and contribute to the development of sustainable, plant-based corrosion control strategies. 2. MATERIALS AND METHODS 2.1. Materials All chemicals and reagents used were of analytical grade and employed without further purification. The experimental apparatus included beakers, volumetric flasks, measuring cylinders, spatulas, stirring rods, retort stands, a manual weighing balance, and a hot plate. The reagents utilized comprised concentrated sulfuric acid (H₂SO₄), ethanol, acetone, and distilled water. 2.2. Sample Collection Fresh leaves of Sida acuta were collected from agricultural fields in Anyigba, Kogi State, Nigeria. The leaves were washed with distilled water to remove surface impurities and air-dried under shade for five days to prevent the degradation of thermolabile and light-sensitive compounds. The dried leaves were pulverized into fine powder using a laboratory grinder and stored in airtight containers for subsequent extraction and analysis. 2.3. Preparation of Plant Extract A 40 g portion of the powdered Sida acuta leaves was subjected to Soxhlet extraction using 180 mL of ethanol for four hours. The obtained extract was concentrated to remove residual solvent and filtered to yield 584 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 a clear filtrate. The filtrate was used as a stock solution for preparing various inhibitor concentrations in sulfuric acid (corrosive medium). 2.4. Phytochemical Analysis Qualitative phytochemical screening of the ethanolic extract of Sida acuta was conducted to identify the presence of active organic compounds known to influence corrosion inhibition. Standard analytical methods were employed to detect alkaloids, tannins, flavonoids, and saponins compounds recognized for their ability to adsorb onto metal surfaces and form protective films against corrosion. 2.5. Preparation of Aluminium Coupons Aluminium sheets were cut into coupons of dimensions 2 cm × 2 cm × 0.2 cm, each drilled with a 0.2 cm central hole to facilitate suspension. The specimens were polished with emery paper to remove surface oxides, degreased with acetone, rinsed with distilled water, and air-dried. The prepared coupons were stored in a desiccator prior to use. The initial weight of each coupon was recorded before immersion in the corrosion test solution. 2.6. Preparation of Test Solution A 0.1 M sulfuric acid solution was prepared by carefully diluting 5.43 mL of concentrated H₂SO₄ (98% purity, density 1.84 g/mL, ≈18.4 M) into approximately 500 mL of distilled water with continuous stirring. After cooling, the solution was transferred to a 1 L volumetric flask and diluted to the mark with distilled water. The prepared solution was thoroughly mixed, labelled, and stored for subsequent experiments. 2.7. Experimental Design The optimization of experimental parameters influencing corrosion inhibition was performed using Response Surface Methodology (RSM) based on the Box–Behnken Design (BBD) implemented in DesignExpert software (Version 13). A total of 17 experimental runs were generated, comprising three independent variables: temperature, immersion time, and inhibitor concentration. Each factor was studied at three coded levels (−1, 0, +1). The corresponding factor levels and design matrix are presented in Tables 1 and 2, respectively. Statistical analysis of variance (ANOVA) was used to evaluate model significance, while response surface plots were generated to visualize the interactive effects of the studied parameters on corrosion rate and inhibition efficiency. Table 1: Experimental range of the independent variables Independent variable Symbols Range and Levels -1 0 +1 Time of Exposure (h) X1 24 96 168 Temperature of the solution (oC) X2 20 40 60 Inhibitor concentration in the extract (v/v) X3 1 4 7 2.8. Weight Loss Measurements and Response Surface Methodology Gravimetric (weight loss) measurements were performed under total immersion conditions using 250 mL glass beakers containing the prepared corrosive solutions. Aluminium coupons were immersed in 0.1 M H₂SO₄ solutions with and without Sida acuta extract as inhibitor. The experiments were carried out according to the Box–Behnken design matrix by incorporating the specified combinations of inhibitor concentration, immersion time, and temperature. The operational parameters were varied as follows: immersion time between 24 and 168 hours, inhibitor concentration between 1 and 7% (v/v), and temperature from 20°C to 60°C. Temperature control during immersion was maintained using a thermostatically regulated water bath to ensure uniform heating and experimental reproducibility. After each exposure period, the aluminium coupons were carefully retrieved, washed with distilled water, and scrubbed lightly with fine emery paper to remove corrosion products. The specimens were then rinsed with distilled water, degreased with acetone, dried thoroughly, and reweighed to determine the final mass. The weight loss for each sample was obtained as the difference between the initial and final weights of the aluminium coupon. The weight loss data were used to calculate the inhibition efficiency (IE) using standard gravimetric equations. The experimental data 585 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 were analyzed using Response Surface Methodology (RSM) within the Design-Expert software (Version 13) to evaluate the interactive and individual effects of temperature, inhibitor concentration, and immersion time on corrosion behavior. The resulting statistical models and response surfaces were subsequently used to predict optimal inhibition conditions and validate the experimental findings. Weight loss was calculated by finding the difference between the weight of each coupon before and after immersion; ∆W= Wb – Wa (1) Where Wb is the weight before immersion, Wa is the weight after immersion. Inhibition efficiency was calculated as: IE% = Wo−W1 𝑊𝑜 x 100 (2) Where W1 and Wo are the weight loss values in the presence and absence of the inhibitor, respectively, IE% is the inhibition efficiency. 3. Results and Discussion 3.1. Phytochemical Analysis Phytochemical screening of the Sida acuta leaf extract in Table 2 confirmed the presence of key secondary metabolites commonly associated with corrosion inhibition. The ferric chloride and Folin–Ciocalteu tests indicated the presence of tannins and total phenols, respectively, while the NH₃–H₂SO₄ and Wagner’s tests revealed moderate levels of flavonoids and high concentrations of alkaloids. A stable froth formation during the frothing test confirmed the presence of saponins in low amounts. The identified phytochemicals are known to enhance corrosion resistance through adsorption and film formation on metal surfaces. Tannins and phenols, being polyphenolic compounds, form coordination complexes with aluminium ions, thereby reducing anodic dissolution (Pant et al., 2024). Flavonoids and alkaloids contribute additional adsorption sites via π-electron interactions and lone pair donation from oxygen and nitrogen atoms, stabilizing the protective film. Although saponins were less abundant, their surfactant nature promotes uniform surface coverage and hydrophobic protection (Umoren and Obot, 2024). The combined action of these constituents produces a synergistic inhibitory effect, leading to the formation of an adherent, protective film on the aluminium surface (Ayeni et al., 2014). This film minimizes charge transfer between the metal and corrosive medium, effectively reducing the overall corrosion rate. The qualitative abundance; high in tannins and alkaloids, moderate in phenols and flavonoids, and low in saponins thus substantiates Sida acuta’s potential as an efficient green inhibitor for aluminium in acidic environments. Table 2: Determination of phytochemicals present in the ethanol extract of the Sida acuta Leaves Parameter Observation Inference Tannins Blue black colouration observed Present {+++} Total Phenol Blue black colouration observed Present {++} Flavonoid Yellow coloration observed Present {++} Alkaloid Reddish Brown colouration observed Present {+++} Saponins Stable Prothing was observed Present {+} 3.2. Fit Summary Statistics The statistical evaluation of the response surface model in Table 3 further provided insights into the reliability of the experimental data obtained for the inhibition of aluminium using Sida acuta leaf extract. The coefficient of determination (R²) was recorded as 0.8039, which implies that approximately 80% of the variation in the inhibition efficiency could be explained by the model. This level of correlation indicates that the model is sufficiently robust for predicting the effect of the extract on aluminium corrosion under the studied conditions (Okuma et al., 2024). Although it does not represent a perfect fit, the value is within the acceptable range commonly reported in corrosion inhibition studies involving plant extracts. The standard deviation was found to be 5.04, which is relatively low compared to the mean inhibition efficiency of 67.84%. This observation suggests that the experimental data points are closely distributed around the 586 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 predicted values, thereby confirming the reliability and reproducibility of the results. The coefficient of variation (C.V.) was calculated as 7.44%, which is well below the commonly accepted threshold of 10% in design experiments. A low C.V. value implies a high degree of precision and dependability in the experimental data, reinforcing that the extract consistently influenced the corrosion behavior of aluminium in the test medium (Toghan et al., 2023). Furthermore, the Adequate Precision value was obtained as 14.17, which is significantly higher than the minimum acceptable value of 4. This indicates that the signal-to-noise ratio of the model was strong enough to navigate the design space with confidence. In other words, the model not only captured the main effects of the variables but also provided a reliable platform for optimization of the extract concentration and environmental conditions (Ekeke, 2020). Table 3: Fit summary statistics for the inhibition efficiency by Sida acuta extracts Parameter Value R-squared 0.8039 Std. dev 5.04 Mean 67.84 C.V (%) 7.44 Adequate precision 14.17 3.3. Box–Behnken Response for the Inhibition Efficiency of Sida acuta Leaf Extract The inhibition efficiency (IE) of Sida acuta leaf extract on aluminium was optimized using a Box–Behnken design considering immersion time, temperature, and concentration. The extract showed high inhibition at early immersion stages, with efficiencies of 82.17% (24 h, 20 °C, 4 %) and 80.76% (24 h, 40 °C, 7 %), indicating rapid adsorption and protective film formation. Prolonged exposure led to a gradual decline, with efficiencies reducing to 56.87% (168 h, 40 °C, 1 %) and 50.56% (168 h, 40 °C, 7 %), reflecting film desorption or degradation. Temperature had a pronounced effect; performance remained high at 20 – 40 °C but decreased at 60 °C (e.g., 52.63% at 96 h, 1 %), suggesting that elevated temperatures promote desorption of active constituents. Similarly, concentration influenced efficiency higher extract levels enhanced protection initially (88.83% at 96 h, 20 °C, 7 %) but showed no consistent improvement at longer exposures. Overall, Sida acuta extract effectively inhibited aluminium corrosion under mild to moderate thermal conditions and short immersion periods, confirming an adsorption-controlled mechanism. Optimal inhibition occurred at 20 – 40 °C and within 24 – 96 h, emphasizing the importance of maintaining film stability for sustained corrosion protection. Table 4: Design matrix and response for the inhibition efficiency by the Sida acuta leaf extracts Run Time (h) Temp (oC) Conc. (v/v) Inhibition Efficiency (%) 1 96 40 4 67.74 2 168 60 1 50.56 3 24 40 7 80.76 4 24 60 4 72.39 5 96 40 4 67.74 6 96 60 1 52.63 7 24 20 4 82.17 8 24 40 1 75.48 9 96 60 7 64.31 10 168 60 4 58.35 11 96 20 7 88.83 12 96 40 4 67.72 13 96 20 1 70.35 14 168 20 4 61.87 15 96 40 4 67.74 16 168 40 1 56.87 17 96 40 4 67.72 587 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 3.4. Diagnostics 3.4.1. Perturbation plot The perturbation plot (Figure 1) was employed to evaluate the sensitivity of inhibition efficiency (IE%) to individual process variables namely, inhibitor concentration (A: 96 mg/L), temperature (B: 40 °C), and immersion time (C: 4 h), while keeping the other factors constant at their reference levels. The analysis revealed that inhibitor concentration and temperature exerted the most significant influence on corrosion inhibition. In particular, inhibitor concentration displayed a negative gradient, indicating that increasing the concentration beyond 96 mg/L led to a reduction in inhibition efficiency. This behavior was attributed to the formation of a thicker but less compact inhibitor film, which hindered effective adsorption of the active phytochemical constituents of Sida acuta extract (Ezeugo et al., 2018). Conversely, slight reductions in concentration below the reference value enhanced efficiency, likely due to improved molecular packing and more uniform surface coverage on the aluminium substrate. Temperature also exhibited a negative slope, suggesting that values above 40 °C decreased inhibition efficiency. This decline was ascribed to the desorption of phytochemicals from the aluminium surface at elevated temperatures, compromising the integrity of the protective film (Carmona-Hernandez et al., 2024). In contrast, operating at slightly lower temperatures promoted stronger adsorption interactions, resulting in more stable film formation and improved protection. Immersion time had the least impact, as indicated by its nearly flat curve. A slight positive slope suggested that longer exposure marginally improved inhibition efficiency, probably due to more complete surface coverage; however, within the studied range, time was not a major determinant compared to concentration and temperature. Figure 1: Perturbation plot on the inhibition efficiency by Sida acuta leaves extract 3.4.2. Normal probability plot The normal probability plot of residuals in Figure 2 was used to assess the adequacy of the statistical model employed to predict the corrosion inhibition efficiency of aluminium in the presence of Sida acuta leaf extract. In this plot, the externally studentized residuals were plotted against the expected normal percentage probability. Ideally, a normal distribution of residuals would result in data points closely aligning along the reference straight line, indicating that model errors are random and Gaussian. It was observed that the majority of residuals clustered tightly around the diagonal reference line, with only minor deviations at the extremes. This suggested that the experimental data reasonably conformed to the assumption of normality, which is essential for the validity of regression analysis and statistical inferences. The absence of systematic deviations or curvature indicated that the model adequately captured the relationship between the independent variables such as inhibitor concentration, temperature, and immersion time, and the dependent variable, inhibition efficiency (Khormali and Ahmadi, 2023). The close alignment of points to the reference line further implied that variations in inhibition efficiency were primarily due to inherent experimental error 588 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 rather than deficiencies in the model (Tolumoye et al., 2025). Minor departures at the tails were attributed to variability under extreme operating conditions, such as very high or low inhibitor concentrations, but these did not compromise the model’s validity. Figure 2: Normal probability plot on the inhibition efficiency 3.4.3. Predicted vs. actual values From the plot of the Predicted vs Actual values in Figure 3, it was observed the the data points were observed to cluster closely along the diagonal line, representing perfect agreement between predicted and measured responses. This alignment indicated that the quadratic regression model derived from the Box–Behnken Design (BBD) effectively captured the experimental trends. Minor deviations from the diagonal were noted in a few experimental runs; however, the overall distribution demonstrated a strong correlation between predicted and actual inhibition efficiency values (Peter et al., 2025). These small discrepancies were attributed to experimental uncertainties and the inherent variability in the adsorption behavior of phytochemical constituents on the aluminium surface (Olawale et al., 2018). The strong agreement confirmed the high predictive accuracy of the model and validated its adequacy. This finding reinforced conclusions drawn from the residual diagnostics and leverage analyses, demonstrating that the selected model terms successfully described the adsorption-controlled inhibition behavior of Sida acuta extract. Figure 3: Predicted vs actual values plot on the inhibition efficiency 3.4.4. Residuals vs run number The residuals versus run number plot (Figure 4) for inhibition efficiency of Sida acuta leaf extract on aluminium was examined to assess the presence of systematic patterns in the residuals across experimental runs. Ideally, residuals should be randomly distributed around zero, indicating that the model appropriately 589 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 accounted for variability in the response. In this study, most externally studentized residuals fell within the control limits of ±3.71733, as indicated by the threshold lines, confirming the absence of severe outliers. The majority of residuals fluctuated closely around the zero line, demonstrating that the model predictions were in good agreement with the experimental inhibition efficiency values (Jomy et al., 2025). Minor deviations were observed in runs 2 and 11, where residuals approached the control limits. These deviations were attributed to minor experimental inconsistencies or the complex adsorption behavior of phytochemicals in the Sida acuta extract. Importantly, these deviations were isolated and did not exhibit a systematic trend, indicating that the model effectively captured the experimental variations. The random scatter of residuals across the sequence of runs suggested that no time-related or lurking factors influenced inhibition efficiency. Figure 4: Residual vs run number plot on the inhibition efficiency 3.4.5. Leverage vs run number The leverage versus run number plot for inhibition efficiency of Sida acuta leaf extract on aluminium (Figure 5) was analyzed to evaluate the influence of individual experimental runs on the fitted regression model. Leverage identifies points that may disproportionately affect regression coefficients and, consequently, model predictions. In this study, all 17 experimental runs exhibited leverage values below the critical threshold of 0.470588, with most values clustered around 0.28 and a few as low as 0.06. This indicated that no run exerted excessive influence on the regression model. Runs with leverage near 0.28 corresponded to factorial and axial points in the Box–Behnken Design, contributing evenly to model estimation, whereas lower leverage values represented center points, which were included to improve precision and estimate pure error. The absence of extreme leverage values confirmed the statistical adequacy of the experimental design and indicated that the predicted inhibition efficiencies were not biased by individual runs. These results reinforced the reliability of the regression model and validated the robustness of the Box–Behnken Design for assessing the corrosion inhibition performance of Sida acuta extract on aluminium surfaces. 3.4.6. Cook’s distance Cook’s Distance was employed to assess the influence of individual experimental runs on the regression model for inhibition efficiency of aluminium in acidic medium using Sida acuta leaf extract. From the plot, (Figure 6), the red horizontal line represented the critical influence threshold of 0.884546, above which a data point would be considered disproportionately influential and potentially distort model estimates (Jayakumar and Sulthan, 2015). The analysis revealed that none of the experimental runs exceeded this threshold, indicating the absence of high-influence outliers and confirming the statistical robustness of the model. Runs 2 and 11 exhibited the highest Cook’s Distance values (~0.70), yet these remained below the critical limit. The moderately elevated influence of these runs was attributed to specific combinations of process variables, such as higher inhibitor concentrations (>500 ppm) or elevated temperatures (>50 °C), which yielded inhibition efficiencies that deviated from mid-range responses. These deviations were consistent with the adsorption behavior of key phytochemical constituents in Sida acuta, including tannins, alkaloids, and flavonoids, which form protective films on the aluminium surface and affect corrosion rates. 590 C.B. Okpanachi et al. / Nigerian Research Journal of Engineering and Environmental Sciences 10(2) 2025 pp. 582-593 Figure 5: Leverage vs run number plot on the inhibition efficiency Figure 6: Cook’s distance plot on the inhibition efficiency 3.4.7. Box-Cox plot The Box-Cox plot for power transformations was employed to determine whether a transformation of the response variable (inhibition efficiency) was necessary to stabilize variance and improve the adequacy of the quadratic response surface model. This method evaluates different values of the transformation parameter (λ) and identifies the range where model assumptions, including homoscedasticity and normality of residuals, are satisfied. In this study, (Figure 7), the plot indicated that the minimum residual sum of squares occurred at λ = 1, corresponding to the untransformed model. The vertical green line at λ = 1 fell within the 95% confidence interval (red and blue lines), confirming that no transformation of the response variable was required (Anusi et al., 2025). The recommended transformation was reported as “None,” indicating that the quadratic model adequately met the assumptions of regression analysis without the need for logarithmic, square-root, or reciprocal transformations. Furthermore, the relatively low natural logarithm of the residual sum of squares [Ln(Residual SS) ≈ 5.8] at λ = 1 further supported the statistical adequacy of the fitted model. Since no transformation was necessary, the inhibition efficiency could be interpreted directly on its natural scale, enhancing the practical relevance and interpretability of the results. 3.4.8. DFBETAS plot for intercept vs. run number The DFBETAS diagnostic plot for the regression intercept against run number was analyzed to assess the influence of individual experimental runs on the estimation of the intercept in the corrosion inhibition model for Sida acuta leaf extract. From the plot (Figure 8), the horizontal threshold lines at ±0.7276 represented