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rainbowkoala
29 Posts |
 Posted - 09/16/2013 : 11:02:44 AM
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Origin Ver. and Service Release (Select Help-->About Origin): OriginPro 8.5.0 SR1
Operating System: win7
I have the following problem:
The polynomial fitting result is the red line. However, I will get much smaller value using the fitting equation. I just thought the fitting equation was wrong, then how the fitting line was drawn?
please find more details in the insert image.
Thanks for your help.
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rainbowkoala
29 Posts |
Posted - 09/16/2013 : 11:05:36 AM
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| The fitting method was just using "analysis-fitting-polynomial fit". |
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Hideo Fujii
USA
1582 Posts |
Posted - 09/16/2013 : 11:58:21 AM
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Hi rainbowkoala,
Your axis scales are log10, and the default of "Apparent Fit" option in the Polynomial Fit tool is ON.
However, NLFit doesn't have this option with various reasons.
Therefore, using Polynomial Fit tool, the fit result is usually visually satisfactory on the plot,
but NLFit usually gives numerically minimum chi-square, which means larger (X or Y) coordinate
has more significant contribution to the fit, but often results visually not intuitive.
--Hideo Fujii
OriginLab |
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rainbowkoala
29 Posts |
Posted - 09/17/2013 : 9:21:46 PM
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Hi Fujii,
Thank you for the response. I have learned more about apparent fit, however, I also have the follow problems:
1 Are the following views about the polynomial fit right?
1.1 There are two ways to apply the polynomial fit. One is using "analysis-fitting-polynomial fit" (Polynomial Fit for simplicity); The other is using "analysis-fitting-nolinear curve fit-open dialog-select polynomial in the category" (NLfit for simplicity).
1.2 The first method Polynomial Fit without selecting "Apparent Fit" is the same as the second method NLfit.
1.3 We will get the same result using Polynomial Fit with or without "Apparent Fit" when the axis scales are linear.
1.4 We will get the same result using Polynomial Fit when the axis scales are linear and Polynomial Fit without "Apparent Fit" when the axis scales are log.
1.5 Using Polynomial Fit without "Apparent Fit", we get the fitting result about y and x when the axis scales are log. E.g. The polynomial equation y=a+b*x+c*x^2+d*x^3 is used to fit the data.
1.6 Using Polynomial Fit with "Apparent Fit", we get the fitting result about logy and logx when the axis scales are log. E.g. The polynomial equation logy=a+b*logx+c*(logx)^2+d*(logx)^3 is used to fit the data.
2 How can I get good fitting result about the relation of y to x using 3 order polynomial equation y=a+b*x+c*x^2+d*x^3?
When I use Polynomial Fit with "Apparent Fit" in a log-log plot, I get the good fitting result, however, the result is about the relation of logy to logx. I want to get the fitting result about the relation of y to x. As you say, I can not get good fitting to my data using Nlfit (see the follow insert image).
Thank you!
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rainbowkoala
29 Posts |
Posted - 09/17/2013 : 10:55:32 PM
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3 What is the fitting function of the fitting red line in the first insert image?
In the first insert image, the fitting result y=6.137+0.44268*x-0.1569*x^2-0.01008*x^3 is got by using polynomial function logy=a+b*logx+c*(logx)^2+d*(logx)^3 actually, and the fitting red line does not coincide with the function y=6.137+0.44268*x-0.1569*x^2-0.01008*x^3. Then, what is the fitting function of the fitting red line? |
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polynomial fitting