Both programs are freely available, and can be obtained by contacting the authors. The principle of least-squares in the context of regression states that the line with the best fit to the data is that for which the sum of squared residuals, RSS=∑inYi−Y^2, is the smallest (where Yi and Ŷ are the observed and expected values, respectively, of the response variable for the ith value of the dose (or explanatory) variable, and Selleckchem LDK378 i is the number of pairs of values in the data). The Excel template presented here

contains VBA macros that utilize the built-in Solver tool to perform iterations to determine the best-fit curve by minimizing RSS (cell O9 in Fig. 2). The Excel 2010 + version of Solver uses Generalized Reduced Gradient (GRG), a robust algorithm for non-linear regression programming ( Lasdon, Waren, Jain, & Ratner, 1978). The initial value for c in Eq.  (1) is the calculated midpoint of the range of the data (explanatory variable), and d is set to equal 1. Solver is adequate for this purpose and generally determines the values of c and d quite accurately. However, accuracy is achieved only when the initial values used for these parameters are close approximations of their final values. The find more formulae used in the spreadsheet

provide those approximations automatically and the VBA macro has been programmed to check the R2 value (coefficient of determination) that reflects the goodness of fit of the model to the data. For the first run, the starting value for c is the median of the X variable and for d, it is 1. If the first run yields a R2 ≥ 0.99, the regression results are accepted, as it is likely that Solver will not fit the data any better if run again. If not, Solver is run automatically again with the values of c and d determined from the initial fit, to yield better results. For this second run, the stringency is reduced, such that the results are accepted if R2 ≥ 0.95. If an R2 of 0.95 or higher is not achieved in the second run, Solver

is run one last time with the third set of starting values for c and d determined in the same manner as for the second run, and the R2 value is reported. If R2 ≤ 0.50 or the analysis with Solver does not converge (perhaps because the starting found values are too far from the final values), producing an error, the macro has been programmed to recognize this and repeat the estimation with different starting values. These starting values are determined for c by systematically selecting values from the range of the dose variable, and d by choosing among the empirically determined Hill slope values in the Call laboratory for sensitive and resistant relationships. This exercise is done in order to reach or exceed the threshold of R2 ≥ 0.95. This process has yielded excellent results with R2 values typically > 0.95 in the Call laboratory. If R2 is still short of 0.