Regression confidence limits

Fig. 9. The two materials, A and B, have overlapping 95% confidence limits at the LD q level. Because the slopes of the dose—mortahty regression lines for both materials are similar, there is no statistically significant difference in mortahty at the LD q and LD q levels. Both materials may be assumed to be lethahy equitoxic over a wide range of doses, under the specific conditions of the test.

Confidence limits are also drawn on Figure 2.15(a) to give boundaries of Cpi for a given q determined from the analysis, which are within 95%. The relationship between q and Cp is described by a power law after linear regression giving ... 

Calculations of the confidence intervals about the least-squares regression line, using Eq. (2-100), reveal that the confidence limits are curved, the interval being smallest at Xj = x. 

The model of simple competitive antagonism predicts that the slope of the Schild regression should be unity. However, experimental data is a sample from the complete population of infinite DR values for infinite concentrations of the antagonist. Therefore, random sample variation may produce a slope that is not unity. Under these circumstances, a statistical estimation of the 95% confidence limits of the slope (available in most... 

FIGURE 6.6 Schilcl regression for pirenzepine antagonism of rat tracheal responses to carbachol. (a) Dose-response curves to carbachol in the absence (open circles, n = 20) and presence of pirenzepine 300 nM (filled squares, n = 4), 1 jjM (open diamonds, n=4), 3j.lM (filled inverted triangles, n = 6), and 10j.iM (open triangles, n = 6). Data fit to functions of constant maximum and slope, (b) Schild plot for antagonism shown in panel A. Ordinates Log (DR-1) values. Abscissae logarithms of molar concentrations of pirenzepine. Dotted line shows best line linear plot. Slope = 1.1 + 0.2 95% confidence limits = 0.9 to 1.15. Solid line is the best fit line with linear slope. pKB = 6.92. Redrawn from [5],... 

CL is inserted in Eqs. (2.18) and (2.19), with k - oo, and using the + sign. The intercept of the horizontal with the lower confidence limit function of the regression line defines the limit of quantitation, jcloq, any value above which would be quoted as 2f(y ) t s ... 

Situation A cream that contains two active compounds was investigated over 24 months (incomplete program if today s ICH standards are applied, which require testing at 0, 3, 6, 9, 12, 18, and 24 months). The assays resulted in the data given in file CREAM.dat. Program SHELFLIFE performs a linear regression on the data and plots the (lower) 90% confidence limit for the regression line. For each full time unit, here months, it is determined whether this CL drops below levels of y = 90% resp. y = 95% of nominal. Health authorities today require adherence to the 90% standard for the end-of-shelf-life test, but it is to be expected that at least for some products the 95% standard will be introduced. 

Figure 4.26. Shelf-life calculation for active components A and B in a cream see data file CREAM.dat. The horizontals are at the j = 90 (specification limit at t = shelflife) resp. y = 95% (release limit) levels. The linear regression line is extrapolated until the lower 90%-confidence limit for Kfl = a + h x intersects the SLs the integer value of the real intersection point is used. The intercept is at 104.3%.

Calculate linear regression and display graph points, regression line, upper and lower 95% confidence limits CL for regression line... 

Purpose Calculate the intersection of two linear regression lines and estimate the 95% confidence limits on the intersection coordinate. (See Fig. 2.19.)... 

SHELFLIFE.dat The content (% of nominal) of two active components in a dosage form was assayed at various times (0-60 months) during a pharmaceutical stability trial to determine the acceptable shelf-life of the formulation the point at which the lower 90% confidence limit of the finear regression model intersects the 90%-of-nominal line gives the answer. Use with SHELFLIFE or LINREG. 

The models with insignificant overall model regression as indicated by the F -value and with meaningless parameter estimates (with confidence limits) as indicated by r-values should be rejected. If rejection of the parameter does not lead to a physically nonsensical model stmcture, repeat parameter estimation and statistical analysis. 

Comparison of Goodness of Fit Statistics for Linear Regression Part 3 - Computing Confidence Limits for the Correlation Coefficient... 

Workman, J. and Mark, H., Chemometrics in Spectroscopy Comparison of Goodness of Fit Statistics for Linear Regression - Part 3, Computing Confidence Limits for the Correlation Coefficient, Spectroscopy 19(7), 31-33 (2004). 

Confidence limits of the regression line from which predictions are made can be calculated. For example, a procedure is given in IEC 60216 [2] for an Arrhenius plot. These, however, only reflect the variability of the measured points... 

In this and later regression equations, the 95% confidence limits are given in parentheses. Eqn. 8.1 quantitates the facilitation of hydrolysis by electron-withdrawing substituents. Because such substituents decrease the electron density on the carbonyl C-atom and render it more susceptible to nucleophilic attack, Eqn. 8.1 is compatible with a base-catalyzed reaction, as indeed shown. Eqn. 8.1, thus, leads to mechanistic insights, but its predictive power is narrow since the o parameter is available for only a few substituents. 

Table IV. Regression and Correlation Coefficients (with Confidence Limits) for decrease in trifluralin content of field soil for 140 days after application, based upon the equalion log P = log (100 ) - c. t.

Figure 2. Series of plots of five cases showing linear regression model with raw data points (a-e) and the 0.975 Working-Hotelling confidence limits about the regressed line (aa-ee). The letter a and aa refers to chlorothalonil and b-e and bb-ee refer to Datasets B, C, D, and E, respectively.

An approach for analyzing data of a quantitative attribute that is expected to change with time is to determine the time at which the 95% one-sided confidence limit for the mean curve intersects the acceptance criterion. If analysis shows that the batch-to-batch variability is small, it is advantageous to combine the data into one overall estimate by applying appropriate statistical tests (e.g., p-values for level of significance of rejection of more than 0.25) to the slopes of the regression lines and zero-time intercepts for individual batches. If it is inappropriate to combine data from several batches, the overall shelf life should be based on the minimum time a batch can be expected to remain within the acceptance criteria. 

Figure 7.2. (A) The greased-gap technique for recording depolarizations of the rat isolated vagus nerve. (B) The effect of ondansetron on depolarizations of the rat isolated vagus nerve induced by 5-HT. Symbols indicate controls (9) or in the presence of ondansetron at I x 10 M (O), 3 X 70" M (M), I X 10 M (O) or 3 x 10 M (A). Results are the mean + S.E.M. of at least four determinations. Experiments were performed as described by Ireland and Tyers [21J. (C) Data from the experiments illustrated in B plotted according to Arunlakshana and Schild [22]. Each point is the result from a separate tissue. The gradient of straight line (95 Vo confidence limits) was determined using linear regression analysis.

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