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The square of regression coefficient was obtained 0.9880.
The performance of all models is evaluated using concepts of the square of regression coefficient (R2), MSE and symmetric mean absolute percentage error (SMAPE), shown in Table 5.
The F value is defined as the ratio of the mean square of regression (MRR) to the error (MRe), representing the significance of each controlled variable on the tested model.
The square of regression was found to be 0.9840 and 0.8671 for pectin yielded and reducing sugar, respectively.
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Ridge regression uses the L2 penalty (sum of squares of regression coefficients multiplied by the penalty factor), thus shrinking regression coefficients closer to zero [ 36].
To control for this bias we also fitted a non-linear model including the variance term (whose regression parameter is the square of the regression parameter for the mean term divided by two).
In 2007, the determination coefficient (R), the adjusted-R and the root mean square error of regression analysis between measured and estimated concentrations were 0.61, 0.61, and 5.38 respectively.
For the first period, the determination coefficient (R), the adjusted-R and the root mean square error of regression analysis between measured and estimated concentrations were 0.67, 0.66, and 3.24 respectively.
They claimed that a reasonable choice of λ is given by: λ = r s 2 (m ^ ) ′ (m ^ ), where r is the number of parameters in the model not counting the intercept, s is the residual mean square obtained by linear least squares estimation, and m ^ is the vector of least squares estimates of regression coefficients.
They included the tolerance test for multicollinearity, its reciprocal variance inflation factors (VIF) [ 28, 29], presence of outliers and estimates of adjusted R square of the regression model.
They included the tolerance test for multicollinearity, its reciprocal variance inflation factors (VIF), presence of outliers and estimates of adjusted R square of the regression model.
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