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# Multiple Regression Analysis

## Definition of Regressors

As concluded in the previous section, two variables were retained as representative of the mechanical performance of the material: the average compressive strength at 28 days fC, in MPa), and the flexural toughness (T, in MPa).

The load ratio (IFa, in percentage) was considered to account for the sustained load applied.

The fibre material was also considered, as a binary variable (Mat): synthetic or non-synthetic, as synthetic fibres were found to be significantly different (p- value = 0.00125).

## Summary of the MLR Models Obtained

Multiple linear regression (MLR) was used to relate each of the creep parameters under consideration to the aforementioned regressors. Initially, models with different formulations including all variables, squared variables, second order interactions and some selected third order interactions were considered. Stepwise and best subsets regression procedures were applied to simplify these models by discarding those terms that were not statistically significant.

Table 3 summarises the MLR models as obtained after this sequential process. The terms that were identified as statistically significant (p-values up to 0.05) are marked with an asterisk. These models were used as a tool to obtain average

Table 3 Summary of the MLR models

 Creep coefficients Crack opening ratios 14 days 30 days 90 days 0-14 days 14-30 days 30-90 days IFa * IFa2 * fc T * * Mat * * * T x IFa * Txfc * * * * Mat x IFa * * * * * * Mat x IFa2 * * * * * * Mat x T * * * Mat x fc * * * * Mat xf * * * * * * Mat x IFa x T * * * * Mat x IFa x fc * * * * * * Mat x IFa2 x T * * * Mat x IFa2 xf * * * * * * R-squared 0.55 0.51 0.46 0.54 0.43 0.41

estimates and trends for the creep coefficients, which allowed the study of these multivariate relationships as reported in the following sections. Furthermore, it is anticipated that future post-processing of these models can increase their predictive accuracy.

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