Rather than feeding raw ingredient quantities into the model, the author restructured the variables. Cement, slag, and fly ash were combined into two physically meaningful descriptors: total binder content and the slag-to-binder ratio. The final model retained the water-to-cement ratio alongside superplasticizer and aggregate contents.

This parsimonious set of predictors achieved a full-data coefficient of determination, or R2, of 0.821, meaning the model explains roughly 82 percent of the variance in measured compressive strength across the dataset. The author used nested GroupKFold cross-validation, grouping folds by unique mixture design so that mixtures from the same design never appeared in both training and test sets. Under this rigorous scheme, the model achieved a mean outer-fold R2 of 0.805 with a standard deviation of 0.018, a root-mean-square error of 7.30 megapascals, and a mean absolute error of 5.62 megapascals.

Statistical diagnostics support the model's reliability. Multicollinearity was controlled, with a maximum variance inflation factor of 6.35 and a condition number of 4.97. All predictors were statistically significant at p less than 0.001, and the maximum Cook's distance was 0.0217, indicating that no single observation unduly influenced the fitted coefficients.

To benchmark performance, the study compared the linear model against two tuned ensemble methods: Random Forest and XGBoost. Under the same nested cross-validation, Random Forest reached an R2 of 0.884 and XGBoost 0.882. The ensembles are therefore more accurate, but their predictions cannot be decomposed into transparent, physically interpretable coefficients in the way a linear model can.

That trade-off is the central argument of the paper. For preliminary screening of mixture designs, an engineer may value a model whose coefficients can be read directly, showing how a change in water-to-cement ratio or slag fraction shifts the expected strength. The author positions the linear model as a transparent screening tool for preliminary strength estimation within the range of the studied dataset, not as a replacement for high-accuracy ensembles when maximum precision is required.

By grouping cross-validation folds by mixture design, the evaluation prevents information leakage between nearly identical mixes, producing error estimates that better reflect performance on genuinely new formulations.

Subject of Research: Interpretable linear regression modeling of concrete compressive strength prediction

Article Title: Practical prediction of concrete compressive strength using an interpretable enhanced linear regression model

Article References: Sadeghi, A. (2026). Practical prediction of concrete compressive strength using an interpretable enhanced linear regression model. Scientific Reports. https://doi.org/10.1038/s41598-026-77642-y

Image Credits: AI Generated

DOI: 10.1038/s41598-026-77642-y

Keywords: concrete, compressive strength, linear regression, machine learning, cross-validation, Random Forest, XGBoost, civil engineering, interpretability, quality control, Practical, prediction