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gibbons81
2 Posts |
 Posted - 09/18/2009 : 2:40:23 PM
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Origin Ver. 6.0
Operating System: XP
Hello,
Can someone please explain why the results for Allometric1 function (y=a*x^b) in Origin and the Power - Regression - Trend line function (also y=a*x^b)in Excel differ? Additionally, if one were to take the log of the data, plot and take a linear fit, or simple graph the raw data on a log-log scale, the result is different from the Allometric1 function in Origin, but the same as the Regression - Trend line function in Excel. If the plot is of log(y) = b*log(x) + log(a), shouldn't the power exponent, b, be the same as when analyzed as y=a*x^b? This seems to be the case no matter the data set. Also, the R^2 coeff of determination value is always highest when using the Allometric1 function.
Here is a generic data set:
0.021 505
0.062 182
0.202 55.3
0.523 22.2
1.008 11.3
3.320 4.17
7.290 1.75
This data results with a power exponent, b, and R^2 of of:
b=-0.95655 with the Allometric1 function in Origin, R^2=0.99992
b=-0.96342 when plotted on a log-log scale and taking a linear fit in Origin, R=-0.99971 R^2=0.99942
b=-0.96342 when using the Power - Regression - Trend line function in Excel, R^2=0.99942
b=-0.96342 after taking the log of the values and using the Linear - Regression - Trend line function in Excel, R^2=0.99942
This discrepancy seems to increase as the data sets become more complicated.
Thank you,
Gibb |
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easwar
USA
1965 Posts |
Posted - 09/21/2009 : 10:41:04 AM
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Hi Gibb,
What Excel does in the case of the power function is an "apparent fit". You can do the same in Origin by plotting the raw data, changing the x and y scales to log, and you will get the same number as in Excel.
When you fit the raw data directly to Allometric1 in Origin, you are not fitting the same data/parameter space as the apparent fit, so the result is different, the value of b is different by about 0.7%
And when i use other products that can perform the actual nonlinear fitting with the a*b^x equation, I get the same result as Origin.
So I think the bottom line is that if you have raw data and know what model is best (such as allometric1 in this case), just use that function to fit and do not perform apparent fit or change the data by converting to log first.
Easwar
OriginLab |
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easwar
USA
1965 Posts |
Posted - 09/21/2009 : 11:20:26 AM
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Hi Gibb,
Also, instead of doing the tredline on the chart in Excel, try using the Solver under Tools menu.
If you set up the Excel Solver with the raw data and try find optimal values for a and b with the equation a*b^x, the values of a and b you get in Excel will match what you get in Origin with allometric1.
Easwar
OriginLab
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gibbons81
2 Posts |
Posted - 09/22/2009 : 11:18:41 AM
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Thank you Easwar. I assumed this was the case but needed to be sure. Very concise and clear response.
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Allometric1-Origin / Power Regression-Excel Differ