## 2 Materials and Methods
### Regression Analysis  
Each response's Reduced Quadratic Regression Model (RQRM) is computed as follows:  
\[\gamma_{k}=a_{k}+\sum_{i=1}^{n}b_{i,k}x_{i}+\sum_{i=1}^{n}c_{i,k}x_{i}^{2}+e_{k} \tag{6}\]  
where k stands for the output quality (for example, printing time, weight, modulus of elasticity, toughness, compressive strength, SPE, SPE, EPC), a, b, c, e, and xi stand for the value that remains persistent, the coefficients of the linear terms, the quadratic terms, the error amount, and the seven control factors, respectively (layer thickness, printing speed, infill density, raster deposition angle, orientation angle, bed, and nozzle temperatures). The ANOVA for the response measures examined here is shown in tables in the Supplementary material of the work (Tables S3-S10). This investigation resulted in the formation of the related prediction equations for the response factors, which are (7)-(14). It should be noted that in the adjusted mathematical models there are non-significant  
Figure 9: Plots of the compressive strength and the energy in relation to the work’s control factors. parameters, as shown by the collection of _p_-values obtained. It would be interesting to eliminate these non-significant parameters and adjust the models again to avoid over-fitting problems. This was not performed due to the added complexity and length of the work. From the analysis of the ANOVA, the following was derived:  
* The F-value for the weight response factor is 45.20 (>4), the _p_-value is almost zero, and the calculated values for the regression parameters are higher than 79.82%. These measures show that the Equation (7) prediction model is adequate for forecasting the weight response factor. * The F-value for the printing time response factor is 96.61 (>4), the _p_-value is nearly zero, and the calculated values for the regression parameters are higher than 89.69%. These measures show that the Equation (8) prediction model is adequate for forecasting the printing time response factor. * The F-value for the compressive strength response factor is 67.08 (>4), the P-value is nearly zero, and the calculated values for the regression parameters are higher than 85.66%. These measures show that Equation (9), which serves as the prediction model, is adequate for forecasting the compressive strength response factor. * The F-value for the compression modulus of elasticity response factor is 43.86 (>4), the _p_-value is nearly zero, and the calculated values for the regression parameters are higher than 79.31%. Based on these metrics, it can be concluded that Equation (10)'s prediction model is adequate for forecasting the compression modulus of the elasticity response factor. * The F-value for the compression toughness response factor is 59.30 (>4), the _p_-value is nearly zero, and the calculated values for the regression parameters are higher than 84.02%. These measures demonstrate that Equation (11)'s prediction model is adequate for forecasting the compression toughness response factor. * The EPC response factor's F-value is 168.97 (>4). The regression factor values are computed to be greater than 93.89%, and the _p_-value is almost zero. According to these statistics, the prediction model outlined in Equation (12) is appropriate for predicting the EPC response factor. * The F-value for the SPE response factor is 233.02 (>4), the _p_-value is nearly zero, and the regression factor values were computed to be larger than 95.51%. These metrics show that Equation (13) in the prediction model is adequate for forecasting the SPE response factor. * The F-value for the SPP response factor is 34.29 (>4), the _p_-value is nearly zero, and the estimated values for the regression parameter are higher than 74.69%. These measures show that the Equation (14) prediction model is adequate for forecasting the SPP response factor. \[