How to fit standard curves

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In April 2003, GraphPad released Prism 4 and published Fitting Models to Biological Data using Linear and Nonlinear Regression. This book includes all the information that comprises curvefit.com, and much more. You can read this book as a pdf file.

How to fit standard curves

Before you can read unknown values, you first must fit a line or curve through your standard points. Prism lets you fit a standard curve with one of these methods:

Creating a standard curve with linear regression

Standard curves are often nearly linear, at least within a certain range of concentrations. If you restrict you standard curve values to a linear region, you can analyze the curve with linear regression. This will be a useful analysis, even if the overall standard curve is not quite straight, so long as you choose a reasonable range. The standard curve should start a little below your lowest unknown value and extend to a little beyond your highest unknown value. There is no benefit to continuing the standard curve far above or below the range of your unknowns.

See Linear regression.

Creating a standard curve with cubic spline (or lowess)

The easiest way to fit a curve is to create a cubic spline or lowess curve. They are easier than nonlinear regression, because you don't have to choose an equation. Spline and lowess curves tend to wiggle too much, so are not often used as standard curves.See Fitting a curve without choosing a model.

Creating a standard curve with polynomial regression

Polynomial regression is a convenient method to create a smooth curve. With Prism, you perform polynomial regression by choosing a polynomial equation from the nonlinear regression dialog. Try a second, third or fourth order polynomial equation. The higher order polynomial equations generate standard curves with more inflection points.

See Polynomial Regression .

Creating a standard curve with nonlinear regression

Nonlinear regression is often used to fit standard curves generated by radioimmunoassay (RIA) or similar assays (ELISA). These assays are based on competitive binding. The compound you are assaying competes for binding to an enzyme or antibody with a labeled compound. Therefore the standard curve is described by equations for competitive binding. Try the one-site competitive binding curve. If that doesn't fit your data well, try the sigmoid dose response curve with variable slope. When fitting sigmoid curves, enter the X values as the logarithms of concentrations, not concentrations.Ordinarily, the choice of an equation is very important when using nonlinear regression. If the equation does not describe a model that makes scientific sense, the results of nonlinear regression won't make sense either. With standard curve calculations, the choice of an equation is less important because you are not interested in the best-fit values of the variables in the equation. All you have to do is assess visually that the curve nicely fits the standard points.

See Nonlinear regression with Prism.

Determining unknown concentrations from standard curves