MedCalc will substitute the symbol &Y with the dependent Y-variable we have selected in the dialog box which is Response. VMAX(variable) returns the maximum value of a variable. for d we take the maximum value of the Response variable, so we can use the formula VMAX(&Y).MedCalc provides some useful functions which can provide a general solution for establishing initial parameter values: We can enter these numbers in the corresponding input fields: b is the Hill's slope and we guess it with the slope of the line between first and last point.

c is the inflection point (the dose where you have half of the max response) and we estimate its value to be 18 which is approximately the dose whose response is nearest to the mid response.a is the lower asymptote and we guess it with the minimum value of the Response variable, which is about 0.d is the upper asymptote and we guess it with the maximum value of the Response variable, which is about 25.The scatter diagram above is useful for finding the following estimates:

We now need to enter initial values or best guesses for the different parameters. We click Get parameters from equation and MedCalc extracts the parameter names from the equation: d, a, c and b: We select the options to display a scatter diagram with fitted line and the residuals plot. We leave the default values for Convergence tolerance and for Maximum number of iterations unchanged. Nonlinear regressionįirst we enter the regression equation d+(a-d)/(1+(x/c)^b) (we don't need to enter the 'y=' part) and select Response as dependent variable Y and Dose as independent variable X: This results in the following scatter diagram:įrom this graph we will be able to estimate initial values for the parameters of the 4-parameter logistic model (see below). In the scatter diagram, we want to plot a LOESS smoothed trendline. In a bioassay where you have a standard curve, this can be thought of as the response value for infinite standard concentration.įirst we look at the scatter diagram with Response as dependent variable Y and Dose as independent variable X. The inflection point is defined as the point on the curve where the curvature changes direction or signs. The Hill's slope refers to the steepness of the curve (can be positive or negative). In a bioassay where you have a standard curve, this can be thought of as the response value at 0 standard concentration.

The equation for the 4-parameter logistic model is as follows: In this example we will fit a 4-parameter logistic model to the following data: Nonlinear regression worked example: 4-parameter logistic model Data

Non linear regression excel