R-squared

The R-squared value, which indicates how well the three chosen parameters account for the variability in the yield, was 84.2%. The analysis of variance indicates that only temperature and pressure (both P-value = 0.026) have significant impact at 90% confidence level. The P-value of 0.37 for [NaOH] indicates that, within the parameter space examined, the concentration of NaOH does not significantly affect the cyclohexanone yield. Based on the above equation, one can predict the cyclohexanone yield at any given condition within the parameter space chosen. Since [NaOH] does not have a significant effect on the yield, one can fix its value and plot the yield of cyclohexanone as a function of temperature and pressure (Figure 1). 

Table I. Summary of R-Square Values for the Various Variance Models...

The figure shows minimum, average, median and maximum elasticity for product 1 and product 2 respectively across 12 months. The average elasticity for product 1 across all 12 months is 0.5, for product 2 0.4 but are volatile analyzed for 12 months. The number of customers for one product and one location varied each month between 10 and 36. The R-squared value for the linear regression varied monthly between 0.4 and 0.99. 

Without having conducted a full elasticity analysis across the entire portfolio, the analysis helps to prove market perceptions such as a higher elasticity exist in one market compared to another market or comparing elasticity between products being perceived to have a different elasticity. The statistical quality of the linear regression analysis in selected months is considered as good in terms of the number of customers involved and the R-squared value proving the applicability of the approach. 

Maintain the logbook for the instrument used in this experiment. Record the date, your name(s), the experiment name or number, the R square value, and the results for the control sample. Also plot the control sample results on a control chart posted in the laboratory for this experiment. 

This measure is the R-squared measure that was already mentioned in the univariate case above. Coming back to the test for all coefficients being zero, the test statistic is... 

Starting Geometries (in parentheses), Energies, H), Virial Coefficients, r. Squared Gradient Norms, II grad Ip, and Optimized Geometries for the Hydrogen Clusters"... 

Predictions of log P with regression. As would be expected, the largest values of the explained variation (r squared) and the smallest standard error of estimates found with the regression models were those that Included all 90 variables. These models... 

Data in Table 4.2 corresponds to the application of the H-point standard addition method to a mixture of a commercial madder pigment diluted with silica, using morin as a reference compound. Calculations were performed by taking m/niR = 10.246, using square-wave voltammetric currents measured for sample-modified PIGEs in contact with an acetate buffer of pH 4.90. Linear plots of ii/ip(R) (squares) and i2/ip(R) (solid squares) vs. mA/mp for additions of purpurin are shown in Fig. 4.17. 

The binding energy curves for the four-atom molecules shown in Fig. 4.1 will be sensitive to the degree of normalized hardness, och. Summing over all the bonds in eqn (4.1), the total binding energies of the tetrahedron (t), rhombus (r), square (s), and linear chain (1) are given by... 

A number of points should be noted concerning the statistics displayed In the table. First, If the researcher wishes to rank the variables In order of their Importance within the equation, absolute values of the beta values are the appropriate Indicators of rank (7, p. 284). Second, the t-values of the regression coefficients give us estimates of the statistical significance of the Independent variables used. Third, the R-square, or coefficient of determination. Is an estimate of the percent of variation In the dependent variable (the functional property) explained by the corresponding regression equation. 

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