Polynomial fitting

FIT POLYNOMIAL...        4       In some cases, relationships between different variables are best expressed with a polynomial regression.  LabAnalyst lets you fit pairs of channels with polynomials of up to 9 degrees.  The model is:
        Channel Y = (polynomial expression of Channel X).
After you select the X and Y channels (as described above for linear regression), the program computes and displays a default polynomial of 3 degrees.  Regression statistics (mean and SD of X and Y, residual Y variance, and r2) as well as the polynomial coefficients are shown.   You can then select other degrees using the pop-up menu.  In this example, a 5-degree polynomial was used to predict the temperature of a small sunlit sphere from shade air temperature; the resulting equation -- shown at the right of the window -- explains about 52% of the variance in sphere temperature.

After completing the analysis, several options are available.  The 'Calculate Y' button opens a small window in which you can enter an X value and obtain the Y value derived from the computed polynimlal.   The 'New X and Y' button lets you change the X and Y variables.  The 'Make New Channel' button (only available if the number of channels is less than 40) generates a new channel by applying the current polynomial equation to the data in the X channel -- in other words, it computes and saves a new Y value for every sample in the X channel.

The 'Show All r^2' button helps you select the most appropriate degree for the polynomial equation.  The predictive value of a polynomial always increases as the degree increases.  However, the increase in accuracy usually plateaus, so it is reasonable to use the simplest equation consistent with good predictive power.  When the 'Show All r^2' button is clicked, the program computes the r2 value for all degrees between 1 and 9, and then shows a bar graph of the results.  [You can remove this plot by clicking the 'Show All r^2' button again, or click the plot's standard 'close' control at the top left.]

In the example shown at right, predictive power increased until the degree of the polynomial exceeded 4, with little additional change at higher degrees (you can select the color of bar graph plots in the Colors and lines option in the VIEW menu.)

Additional considerations:

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