# Multivariate Analysis for Prediction of Splitting Tensile Strength in Concrete Paving Blocks
## 1 Introduction
### Related Work
In Indonesia, the study carried out by [14] uses different ratios of NaOH/Na\({}_{2}\)SiO\({}_{3}\) and fly ash as a substitute for cement to predict the performance of paving blocks; higher Na\({}_{2}\)SiO\({}_{3}\) content results in lower percentage absorption and higher endurance. Ref. [15] details that two groups were compared; the first group incorporates only sand, and the second gravel (stone). It was indicated that a high-quality paving block has a high compressive strength and low water absorption percentage. The results show that the resistance of the paving block only with sand gives greater resistance. The elaboration of different mixtures incorporating wheat straw fibers with and without treatment with sodium silicate was studied by [16], where the untreated mixtures increased the percentage of water absorption and decreased the compressive strength and tensile splitting strength. In this study, it can be seen from the graphs that the mixture with the lowest compressive strength and tensile splitting strength is the one with the highest percentage of water absorption. The authors of [17] prepared concrete mixes with different water/cement ratios in cubes, subjecting them to different curing methods. The authors indicated no clear relationship between compressive strength and water absorption. Simple linear regression is a method that is basic and easy to calculate. However, it can only be accurate if it does not violate the assumption of linearity. Multivariate methods and machine learning are revolutionizing data analysis in scientific research. These powerful tools allow us to explore complex relationships between multiple variables, discover hidden patterns in large datasets, and build superior predictive models. In the study carried out by [18], 40 types of methods for data analysis are summarized and discussed with an approach to pavement engineering for the prediction and classification of variables. They delved into the data analysis, explaining in detail the definition of each one, making the regression models understandable and easy to interpret as linear and nonlinear equations, logistic regression, survival analysis, and stochastic processes, giving the coefficients of regression a quantitative meaning. Supervised machine learning models, such as artificial neural networks, decision trees, support vector machine, and k-nearest neighbors, give the ability to predict and classify large volumes of data. The investigation carried out by [19] to predict the tensile splitting strength in concrete indicates that the compressive strength and tensile strength are essential characterization indices of the concrete, indicating that generally, the compressive strength is much lower than the tensile strength; the study proposes an alternative method to predict the tensile splitting strength by compressive strength using a novel method called GEP, which is a gene expression programming technique based on constantly adapting tree structures. Different regression methods were studied by [20], such as neural networks and gene expression programming, to predict splitting tensile strength and water absorption using predictor variables such as the amount of cement, amount of ZnO\({}_{2}\) nanoparticles, type of aggregate, content of water, amount of superplasticizer, age and cured type, and number of test attempts with various types of concrete including ZnO\({}_{2}\) nanoparticles. The training and validation data are separated to test two models with different design parameters. The determination coefficients for the relationship between predicted values and values of the validation set were above 0.9. Ref. [21] applied Random Forest, Support Vector Regression, and XGBoost to predict the resistance of high-performance concrete, finding XGBoost to be the most accurate.