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 Equations: Polynomial models

## Step by step

Create an XY data table. There is one X column, and many Y columns. If you have several experimental conditions, place the first into column A, the second into column B, etc.

After entering data, click Analyze, choose nonlinear regression, choose the panel equations for polynomial equations, and choose one.

The "order" of a polynomial equation tells you how many terms are in the equation. Prism offers first to sixth order polynomial equations (and you could enter higher order equations as user-defined equations if you need them). Higher order models wiggle more than do lower order models. Since the equation rarely corresponds to a scientific model, use trial and error. If it isn't close enough to the data, pick a higher order equation. If it wiggles too much, pick a lower order equation.

## Polynomial models

 Order Equation First Y=B0 + B1*X (straight line) Second Y=B0 + B1*X + B2*X^2 (quadratic equation) Third Y=B0 + B1*X + B2*X^2 + B3*X^3 Fourth Y=B0 + B1*X + B2*X^2 + B3*X^3 + B4*X^4 Fifth Y=B0 + B1*X + B2*X^2 + B3*X^3 + B4*X^4 + B5*X^5 Sixth Y=B0 + B1*X + B2*X^2 + B3*X^3 + B4*X^4 + B5*X^5 + B6*X^6

There is no general way to interpret the coefficients B0, B1, etc. In most cases, the goal of fitting a polynomial model is to make a curve that looks good, and the parameters really don't matter.

## Centered polynomial models

The Centered polynomial models are identical to the ones listed above, with one exception. Wherever X appears above, replace it with (X - XMean), where XMean is the mean of all X values (for rows that have Y values). Using a centered model can avoid computer math problems (overflows), and we recommend that you use them routinely.