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Sampling—Measurement Variables
Published in Frank R. Spellman, Fundamentals of Wastewater-Based Epidemiology, 2021
The coefficient of determination, denoted R2, is used in the context of statistical models whose main purpose is the prediction of future outcomes on the basis of other related information. Stated differently, the coefficient of determination is a ratio that measures how well a regression fits the sample data. Coefficient of determination(R2)=Reduction SSTotal SS=2.11152.7826=0.758823
Empirical shear stiffness of embankment dams
Published in Jean-Pierre Tournier, Tony Bennett, Johanne Bibeau, Sustainable and Safe Dams Around the World, 2019
D.S. Park, D.-H. Shin, S.-B. Jo
After the first stage of statistical processing described above, a second-stage regression was performed to obtain Vs profiles as a function of depth for each survey dataset. The regression model form used was Vs = a * zb, where Vs is the shear wave velocity, z is the depth, and a and b are factors that are correlated with each other. The R2 (coefficient of determination) value for the correlation between a and b was determined each regression. The coefficient of determination is an indicator of the fit of a statistical model.
Separating Signals from the Noise
Published in Perry D. Haaland, Experimental Design in Biotechnology, 2020
The R-squared value is also called the coefficient of determination. This is because the R-squared value is calculated from the following relationship: R-squared = variation explained by model / total variation Thus, the larger the R-squared, the more accurately the value of the response can be predicted by the model.
A review of response surface methodology for biogas process optimization
Published in Cogent Engineering, 2022
Solal Stephanie Djimtoingar, Nana Sarfo Agyemang Derkyi, Francis Atta Kuranchie, Joseph Kusi Yankyera
With the regression analysis, the fitness of a model is checked from its coefficient of correlation (R) and its coefficient of determination (R2). The coefficient of correlation (R) is the acceptability of the relationship between predicted and actual values obtained in a statistical experiment. The value obtained for the coefficient of correlation (R) explains the accuracy between the predicted and the actual values. The values of R lie between −1 and +1; a positive value of R translate a similar or identical relation between the two variables. A negative value, however, explains a dissimilarity. The coefficient of determination (R2) also called R square method is the fraction of the total variation of the dependent variable that is predicted from the independent variable. This method is used to predict the outcomes of a model. Since the coefficient of determination (R2) is the square of the coefficient of correlation (R), the values of R2 lie between 0 and 1. A value of coefficient of determination of 0 means that the dependent variable is not predictable from the independent variable while a value of 1 translates that the dependent variable is predictable from the independent variable without any error. Values between 0 and 1 indicate the extent of predictability of the dependent variable.
A simplified model to predict and optimize energy consumption of residential buildings in the cold climate regions of Iran
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Alireza Baheri, Mohammad Najafi, Aziz Azimi, Cyrus Aghanajafi
It should be noted that the correlation coefficient test is done to make sure that the correlation between two variables is not by chance or accidental, and there is enough proof for further correlation investigations. If the correlation coefficient is close to 1 or −1, the regression line on data is proper as an appropriate model but if it is near to zero, the fit of the regression line will be low as an inappropriate model. In this respect, the coefficient of determination is the square of correlation coefficient and represents what percentage of dependent variable changes is explained by independent variable ones. The problem of coefficient of determination is that it cannot change as much as necessary by adding a number of dependent variables, so it is better to report the adjusted coefficient of determination along with the coefficient of determination. This coefficient is accordingly adjusted based on the number of independent variables and indicates a more realistic value, achieved by Equation (3) (www.spss-tutorials.com/standard-deviation-what-is-it):
Sediment yield prediction using neural networks at a watershed in south east India
Published in ISH Journal of Hydraulic Engineering, 2018
To determine the performance of the selected network models, two different statistical parameters have been used i.e. Mean-Squared Error (MSE), and Coefficient of Determination (R2). Mean-squared Error represents the average of the square of the error or deviation. MSE can be estimated using the following equation, . Where, xactual is the actual (data used for calibration) output and xpredicted is the estimated/predicted output. N is the total number of samples used. Coefficient of determination represents the square of correlation between actual and predicted outcomes. R2 estimates the coefficient of determination interpreted by the model. Values closer to unity represent fit predictive ability of the model. Coefficient of determination is the square of correlation coefficient.