Standard error of the estimate

The standard error of the estimate 5delds information concerning the reliability of the values predicted by the regression equation. The greater the standard error of the estimate, the less reliable the predicted values. 

---

Shear cell measurements offer several pieces of information that permit a better understanding of the material flow characteristics. Two parameters, the shear index, n, and the tensile strength, S, determined by fitting simplified shear cell data to Eq. (6), are reported in Table 2. Because of the experimental method, only a poor estimate of the tensile strength is obtained in many cases. The shear index estimate, however, is quite reliable based on the standard error of the estimate shown in parenthesis in Table 2. The shear index is a simple measure of the flowability of a material and is used here for comparison purposes because it is reasonably reliable [50] and easy to determine. The effective angle of internal... 

Sest The standard error of the estimate. It is a measure of the error to be expected in predicting a value of the dependent variable from the appropriate parameter values. 

A number of studies reported that several kinetic models can describe rate data well, when based on correlation coefficients and standard errors of the estimates [25,118,131,132]. Despite this, there often is no consistent relation between the equation which gives the best fit and the physicochemical and min-eralogical properties of the adsorbent(s) being studied. Another problem with some of the kinetic equations is that they are empirical and no meaningful rate parameters can be obtained. 

The standard error of the estimate, also called standard deviation. 

As shown in Table VII there appears to be no significant change of k with respect to temperature. These data were plotted using Equation 3 and from linear regression analysis, the heat of solution was tO.IE Kcal/mole. Since Ah should be negative, this low value is obviously caused by experintental error. Furthermore, the Ah calculated from the standard error of the estimate (t1 standard deviation units) of the linear regression line is +0.17 Kcal/mole. Since Ah is zero or is very close to zero. Equation 3 reduces to... 

Included one with log-transformed variables and the other with both log-transformations and with each variable standardized by size (Table IV). In general, the standard errors of the estimates were large relative to the mean which Indicates a relatively poor fit for the models tested here. 

Figure 1. Trend in annual and monthly means of total column ozone in Hradec Kralove determined from 1962-90 and 1962-97 series. The vertical lines demarcate the standard error of the estimated trend.

The result of the validation using the ISO/MPEG 1991 database is given in Fig. 1.9. A good correlation (R3=0.91) and a reasonable low standard error of the estimate (S3=0.48) between the objective PAQM and the subjective MOS values was found. 

The 95% confidence intervals of the MOS lie in the range of 0.1-0.4. For some items, which differ significantly from the fitted curve, the confidence intervals are given. The correlation and standard error of the estimate (R3=0.9 1 and S3=0.48) are derived from the third order regression line that is drawn using a NAG curve fitting routine. 

The correlation and standard error of the estimate (R3=0.81 and S3=0.35) are derived from the third order regression line that is drawn using a NAG curve fitting routine. 

The optimization of a freq, Ot time and y is performed using the subjective audio quality database that resulted from the ISO/MPEG 1990 audio codec test [ISO90, 1990]. The optimization used the standard error of the estimated MOS from a third order regression line fitted through the PAQM, MOS datapoints. The optimization was carried out by minimization of the standard error of the estimated MOS as a function of O.freq, (X time, Y... 

Lenth (1989) referred to this estimator 67. as the pseudo standard error of the estimators Pi. He recommended using the test statistic P, / i to test the null hypothesis Pi = 0 and recommended using the quantity (Pi — Pi)/aL to construct a confidence interval for p,. 

Figure 4. Joint effect of sustainable pollution in the south (v.spoll.s) and change in sustainable pollution in the south (v.cfsus.s) on HDI in the Wonderland model (a) estimated effect (b) pointwise standard error of the estimated effect.

Multiple Correlation Coefficient =. 994 Standard Error of the Estimate - 2.6%... 

---