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Inference
Published in Julian J. Faraway, Linear Models with Python, 2021
Now RSSΩ=(y−Xβ^)T(y−Xβ^)=ϵ^Tϵ^, the residual sum of squares for the full model, while RSSω=(y−y¯)T(y−y¯)=TSS, which is called the total sum of squares corrected for the mean. The F-statistic is: F=(TSS−RSS)/(p−1)RSS/(n−p)
Regression for Data Analytics
Published in Mohiuddin Ahmed, Al-Sakib Khan Pathan, Data Analytics, 2018
Here, RSS means residual sum of squares. This is also called Sum of squared errors (SSE). If we take the mean, it will be MSE=1NSSE
Thermal decomposition kinetics of synthesized poly(N-isopropylacrylamide) and Fe3O4 coated nanocomposite: Evaluation of calculated activation energy by RSM
Published in Petroleum Science and Technology, 2023
Ersin Pekdemir, Ercan Aydoğmuş, Hasan Arslanoğlu
Root mean square error (RMSE) is the standard deviation for the estimation errors. Predictive errors are a measure of how far the data points are from the regression line. Also, RMSE is a measure of the propagation of these errors that show how dense the data is at the optimal line. Chi-square statistic is commonly used to evaluate tests of independence when using a crosstab (bivariate table). The cross-tabulation presents the intersections of the bivariate distributions simultaneously. If the variables are independent of each other, the independence test evaluates the pattern observed in the cells, that is, whether there is a relationship between the two variables. Residual sum of squares (SSR) is a statistical technique used to measure the amount of variance in a data set that is not explained by the regression model. SSR is also known as the sum of remaining squares, essentially determines how well a regression model describes or represents the data in the model. In statistics, a total sum of squares (SST) has been defined as sum of squared errors (SSE) and residual sum of squares (SSR). Consequently, it is a measure of the discrepancy between the data and the forecast model, which can be used as an optimal criterion in parameter selection and model selection (Azari et al. 2015; Phogat et al. 2016; Azari et al. 2019; Asdagh et al. 2021; Azari et al. 2021; Demirpolat, Aydoğmuş, and Arslanoğlu 2022).
Adsorption and recovery of cadmium and copper ions in mono and bicomponent systems using peanut shells biochar as a sustainable source: model development
Published in Chemical Engineering Communications, 2022
Brígida Maria Villar da Gama, Celmy Maria Bezerra de Menezes Barbosa, Joan Manuel Rodríguez-Díaz, Deivson Cesar Silva Sales, Marta Maria Menezes Bezerra Duarte
The unknown parameters (Equations (3–10)) were determined by means of a non-linear regression analysis carried out using Origin 8.0 software (OriginLab, MA, USA). The non-linear regression (), chi-square coefficient (Equation (11)), and residual sum of squares (Equation (12)) were then determined: where (mmol·g−1) is the experimental adsorption capacity at equilibrium, (mmol·g−1) is the adsorption capacity at equilibrium estimated by the model, n is the number of the experiment and d is the numbers of data and the distribution parameter.
Effect of MIST conditioning on the air voids and permeability of hot asphalt mixes containing reclaimed asphalt pavement
Published in Road Materials and Pavement Design, 2021
Burhan Showkat, Dharamveer Singh
Exponential, power law and linear models were fitted to the observed experimental results for control and RAP mixes. The degree of fitness of a model was judged based on the magnitude of R-squared (R2). Furthermore, R2 was computed as the following: Considering dataset of n values, , and n values predicted by the model, , then the residuals are . Furthermore, the total sum of squares , and the residual sum of squares . Finally, .