Standard deviation of regression

Recorded kinetic curves were fitted to the five-parameter Equation (1). The parameters pj with their errors and the standard deviation of regressions are summarized in Tables 1-6. Comparison of the data confirm the previously reported (refs. 8,12) similarity in the behavior of the two isomers in the presence of strong bases in spite of the different shape of the kinetic curves. The relatively good agreement of exponents p2, P4 computed for the diastereomers at the same temperature and amine concentration demonstrates the validity of the model used. From comparison of Equations (4) and (7) it follows that both reaction must give the same exponent. 

Number of measured points (N) = 95 ASD Average standard deviation of regression... 

The standard deviations of regression between the experimental data and the values obtained from the above equations are 0.03, 0.03, and 0.12 mV for x = 10, 30, and 50 mass percent monoglyme, respectively. 

Some comments should be made in regard to the arbitrary choice of the ion-size parameter, a0, in the determination of E°. The suitability of the value of the ion-size parameter was based on the standard deviation for regression of the experimental E0/ in Equation 6 as a function of m using a° equal to 0.2,0.4, 0.6, and 0.8 nm, successively. Table VIII indicates that a0 = 0.6 nm gives the best linear fit, and consequently a0 = 0.6 nm was used at all temperatures. It should be mentioned, however, that the standard deviation of regression is not a reliable guide to the best choice of the ion-size parameter. 

The least-squares estimate of the intercept for the linear regression of pK/ vs. I from Equation 4 (using the proper value of a0) was termed the actual pKi, the values of which are presented in Tables VII, VIII, and IX, for 10, 30, and 50 mass % THF-H20, respectively. In order to obtain the best linear fit of the data, several values of a0 (from 0.1 to 0.8 nm) were inserted into this equation. The true values of pKi were those which gave the smallest standard deviation of regression. 

Sometimes the lack of significance of individual LSER descriptors is evident because the standard deviations of regression coefficients are relatively large (e.g., the standard deviation of the coefficient at 2T in eq. 3 in ref. 1102] is 0.19, whereas the regression coefficient itself has a value oif —0.12). However, in some publications there is not... 

To calculate the standard deviations of regression coefficients obtained by using the Solver, the macro uses the same approach outlined in the preceding example. The SSresiduals/ SSregression arid SE y) are calculated from the known... 

Figure 1 A QSAR equation (cf. Eq. (14) recalculated from original values) should contain 95% confidence intervals of all regression coefficients (preferable to standard deviations of regression coefficients), the number of objects ( = compounds) included in the analysis, the correlation coefficient r or a squared correlation coefficient r2, the standard deviation s, the Fisher F value (optional), the crossvalidation correlation coefficient Q 2, and the crossvalidation standard deviation press (both optional but recommended).

This quantity is also called the standard deviation of regression, sr. The Sy value can be used to obtain uncertainties for the slope, m, and intercept, b, of the least-squares line since they are related to the uncertainty in each value of y. For the slope ... 

See Chapter 16 for the spreadsheet calculation of the standard deviation of regression and the standard deviation of an unknown for this. 

In many cases standard deviations of regression coefficients are given instead of confidence intervals, suggesting that terms are significant which in reality are not significant. 

To obtain a standard deviation to express an experimental error with a confidence area, procedures to obtain standard deviations of parameters of general functions are indispensable. These are, however, quite complex. With the aid of spreadsheet software, the standard deviations can be obtained relatively easily. In this case, a convenient way to obtain the standard deviation is to apply the Solvstat macro to the spreadsheet. Doing so is easy and provides reliable results. First, a spreadsheet to obtain regression coefficients by using Solver must be prepared. Then the Solvstat add-in can be used to elucidate standard deviations of regression coefficients. ... 

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