Original regression

QSAR. Quantitative structure-activity relationships—the science of deriving quantitative linear or nonlinear mathematical relationships between physicochemical and topo-logical/topographical properties of chemical structures and their biological activity. Originally, regression analysis was the only tool used to derive QSAR equations. More re-... 

Recently Wohl (30) reported on extensive studies on the competitive antagonism of Ca2+-induced rat aortic vasoconstriction in vitro by a series of 36 benzothiadiazines. The Extended Huckel Theory (EHT) was used to calculate the preferred tautomer in solution, and charges, etc., on all atoms. The final equation was fairly successful in predicting the activity of several moderately potent compounds not included in the original regression. 

The additional data indicates that the rate of carbon deposition appears to follow a parabolic relationship. The original regression equation derived in... 

Before developing the studies, the 24 standardization lines thus obtained were compared statistically. For this purpose the joint confidence region of the slope and the intercept was calculated for the original regression. Here, this procedure is introduced briefly. 

Joint confidence ellipse for the ordinate and intercept of the original regression, along with the pairs (intercept, slope) obtained for each of the 24 simulated calibration lines. The triangles, squares and circles correspond to modifications in the lowest (Addi), intermediate (Add2) and highest addition (Add3), respectively. 

Using a hand calculator, find the slope of the linear regression line that passes through the origin and best satisfies the points... 

Construct an appropriate standard additions calibration curve, and use a linear regression analysis to determine the concentration of analyte in the original sample and its 95% confidence interval. 

Abstracted from the compilation by Jaffe, where original references may be found. Value of log k on the least-squares regression line where a = 0 the time unit is seeonds. 

Classical least-squares (CLS), sometimes known as K-matrix calibration, is so called because, originally, it involved the application of multiple linear regression (MLR) to the classical expression of the Beer-Lambert Law of spectroscopy ... 

It is often helpful to examine the regression errors for each data point in a calibration or validation set with respect to the leverage of each data point or its distance from the origin or from the centroid of the data set. In this context, errors can be considered as the difference between expected and predicted (concentration, or y-block) values for the regression, or, for PCA, PCR, or PLS, errors can instead be considered in terms of the magnitude of the spectral... 

However, it can be shown easily that a regression line of a given set of points does not remain the regression line after the transformation, and also that the correlation coefficient is altered. Let us denote in the original coordinates log k2 versus logki r, the correlation coefficient b2.i and l/bi.2 the slopes of... 

Both pairs of lines are identical only when r = 1 in this limiting case, all four expressions in eqs. (30) and (31) are equal, and statistics has been replaced by simple geometry. If there is no correlation at all between the original values log k2 and log ki, i.e., ri2 = 0, apparent regression lines are obtained in the E versus log A plane (Figure 10) with the slopes (when Si = S2)... 

However, it is not proper to apply the regression analysis in the coordinates AH versus AS or AS versus AG , nor to draw lines in these coordinates. The reasons are the same as in Sec. IV.B., and the problem can likewise be treated as a coordinate transformation. Let us denote rcH as the correlation coefficient in the original (statistically correct) coordinates AH versus AG , in which sq and sh are the standard deviations of the two variables from their averages. After transformation to the coordinates TAS versus AG or AH versus TAS , the new correlation coefficients ros and rsH. respectively, are given by the following equations. (The constant T is without effect on the correlation coefficient.)... 

Strong, F. C., Regression Line That Starts at the Origin, Anal. Chem. 51, 1979, 298-299. 

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