Chapter 4: The power of carefully specified linear models: Steel fibre-reinforced concrete and its variability

There are two common misconceptions around multiple linear regression. One is that its applicability is limited to the modelling of linear problems. The other is that it is mostly concerned with fitting an equation to data with the objective of using it for predictive purposes. However, it is a powerful machine learning tool when sufficient attention is paid to the specification of the regression model so that it is informed by previous knowledge. This chapter demonstrates the application of multiple linear regression to the modelling of the relationship between the residual flexural strength of steel fibre-reinforced concrete (SFRC) and the variables describing the mix design. It explains the importance of the preparation of the training dataset, aspects such as parsimony, overfitting or cross-validation, and how a well-specified regression model can be simple, useful and reasonably accurate. The optimisation and trend visualisation possibilities that explicit multivariate equations offer are examined in detail in relation to the optimisation of SFRC mixes. Finally, a methodology for studying the effect of the mix design variables on the variability of residual flexural strength parameters, which can be used even in the absence of replicates, is presented.