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Beyond the scope of determining color removal efficiencies, one of the main outputs that can be produced from the data in Table 2 is the development of a linear equation to describe the behavior This is accomplished through the use of regression coefficients.
Therefore, the use of regression coefficients based on PM2.5 mass may underestimate associations with some PM2.5 components.
Finally, the use of regression coefficients based only on PM2.5 mass may underestimate the effects of some of its specific components.
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For ease of use, the values of regression coefficients (B) incorporated into the index were doubled and then rounded to the nearest 0.5 to provide a simplified prognostic index for clinical application, without substantially altering the prognostic utility of the tool.
Experimental data were used for evaluation of regression coefficients of polynomial equation.
P values for regression coefficients are calculated using the estimates of regression coefficients and associated standard errors.
Because many of the interaction terms were statistically significant, strata-specific effects were calculated using linear combinations of regression coefficients from the multivariate models.
However, using the product of regression coefficients for making inferences about indirect effects, involves implicit assumption that the sampling distribution of the indirect effect is normal.
Because we used a two-arm crossover design in this study, data were pooled between the two treatment phases after finding no carryover effect, and we report between-group differences at the end of study time points (week 8 and week 20) using general contrast of regression coefficients in the mixed-effects models.
In the linear regression analyses the caries indices were used as dependent variables and the t-test was used for statistical evaluation of regression coefficients.
Finally, Group Lasso regression can be used when the number of regression coefficients that must be estimated is large or even exceeds the sample size [ 43].
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