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#1
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trendline equation doesn't fit data
I fit a trendline to some data I have, shown below.
809920.89 1688.50 811026.35 1685.90 812370.50 1680.80 813553.47 1673.80 814357.32 1670.65 the equation given by excel (polynomial 2nd degree fit) is y=-4e-7x^2+.6676x-267718 however, if you plug the first x point (809920) into this equation, the value given is over 10,000. where is the problem? the trendline appears to fit, but the equation given doesn't fit at all |
#2
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trendline equation doesn't fit data
How did you get the fit ?? Using Solver I get:
y=0x^2 - 0.003024729x + 4136.60627 with fitted data: 809920.89 1686.815012 811026.35 1683.471295 812370.5 1679.405605 813553.47 1675.827441 814357.32 1673.396013 -- Gary''s Student - gsnu200735 |
#3
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trendline equation doesn't fit data
i just added a trendline, using a 2nd order polynomial fit to better match the curve of the data. r^2 = .994. |
#4
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trendline equation doesn't fit data
I don't understand how your r-squared can be so good if the variation at a
single point is so large. Using the simple linear fit I posted, here are the x-values, y-values, fitted y-values and the variation-squared at each point: 809920.89 1688.5 1686.815012 2.839185485 811026.35 1685.9 1683.471295 5.898609287 812370.5 1680.8 1679.405605 1.944336986 813553.47 1673.8 1675.827441 4.110518666 814357.32 1670 1673.396013 11.53290394 -- Gary''s Student - gsnu200735 "tom r" wrote: i just added a trendline, using a 2nd order polynomial fit to better match the curve of the data. r^2 = .994. |
#5
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trendline equation doesn't fit data
well, i think that the high variation at individual points is due to an error
in excel, i don't believe that the equation it is giving me is the same one that it is plotting. It isn't set up so the trendline is too high at the beginning and too low at the end, its about 9,000 ft too high at both ends. "Gary''s Student" wrote: I don't understand how your r-squared can be so good if the variation at a single point is so large. Using the simple linear fit I posted, here are the x-values, y-values, fitted y-values and the variation-squared at each point: 809920.89 1688.5 1686.815012 2.839185485 811026.35 1685.9 1683.471295 5.898609287 812370.5 1680.8 1679.405605 1.944336986 813553.47 1673.8 1675.827441 4.110518666 814357.32 1670 1673.396013 11.53290394 -- Gary''s Student - gsnu200735 "tom r" wrote: i just added a trendline, using a 2nd order polynomial fit to better match the curve of the data. r^2 = .994. |
#6
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trendline equation doesn't fit data
On Aug 3, 9:34 am, tom r <tom wrote:
I fit a trendline to some data I have, shown below. 809920.89 1688.50 811026.35 1685.90 812370.50 1680.80 813553.47 1673.80 814357.32 1670.65 the equation given by excel (polynomial 2nd degree fit) is y=-4e-7x^2+.6676x-267718 however, if you plug the first x point (809920) into this equation, the value given is over 10,000. where is the problem? The "problem" is: if you use -4e-7 verbatim, it is rounded off too much for the magnitude of your "x" numbers, e.g. 809920.89^2. If you double-click the textbox that shows the equation in the chart, you can format all of the coefficients, say to Scientific with 14 decimal places. When I use the more exact coefficient -4.13596749594073E-07 in the equation above, I get values closer to your data (e.g. 1677.36 for 809920.89). Substituting all 3 coefficients, I get 1688.70 for 809920.89 -- a difference of only 0.20. Although that should answer your question, there is much more to say about your dubious usage of the trendline feature. I'll post again when I have more time. |
#7
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trendline equation doesn't fit data
On Aug 3, 9:34 am, tom r <tom wrote:
I fit a trendline to some data I have, shown below. 809920.89 1688.50 811026.35 1685.90 812370.50 1680.80 813553.47 1673.80 814357.32 1670.65 the equation given by excel (polynomial 2nd degree fit) is y=-4e-7x^2+.6676x-267718 however, if you plug the first x point (809920) into this equation, the value given is over 10,000. where is the problem? As I wrote previously, your problem was basically due to not formatting -4e-7 to sufficient precision for the magnitude of "x" values that you have. You would not have encountered the problem in the first place if you had used LINEST() to compute the coefficients in your worksheet formula. Refer to http://j-walk.com/ss///excel/tips/tip101.htm . However, there is a more fundamental question to ask yourself, namely: why are you using a 2nd order polynomial to fit your data? True, that might give you the illusion of the best fit. But the highest RSQ alone does not necessarily determine the best fit. For example, a 2nd order polynomial describes a parabolic curve. In your case, the vertex (maximum point on the curve) is at about 807083.88. If you were to use the characteristic formula to extrapolate beyond that point, is the trendline truly behaving the way the data would? When I look at your data, I see either a linear or logarithmic curve with a downward slope. That really depends on your interpretation of the model that produced the data. I just wanted to express some suspicious that a 2nd order polynomial is really the right answer. (But it might be.) On the other hand, if you do not intend to extrapolate beyond the "x" limits in your data, it might make sense to use the 2nd order polynomial because it presumably does provide the closest fit within those limits. |
#8
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trendline equation doesn't fit data
Hi. Here's an interesting reference:
Chart trendline formula is inaccurate in Excel http://support.microsoft.com/kb/211967 I don't have the original post, but with this data... 809920.89 1688.5 811026.35 1685.9 812370.50 1680.8 813553.47 1673.8 814357.32 1670 I get: = 5163.22295426061-0.00428863203403701*x or =-317931.918702048+0.791376677921689*x-4.8985630175318E-07*x^2 Assuming of course that these are the appropriate equations. -- Dana DeLouis "Gary''s Student" wrote in message ... I don't understand how your r-squared can be so good if the variation at a single point is so large. Using the simple linear fit I posted, here are the x-values, y-values, fitted y-values and the variation-squared at each point: 809920.89 1688.5 1686.815012 2.839185485 811026.35 1685.9 1683.471295 5.898609287 812370.5 1680.8 1679.405605 1.944336986 813553.47 1673.8 1675.827441 4.110518666 814357.32 1670 1673.396013 11.53290394 -- Gary''s Student - gsnu200735 "tom r" wrote: i just added a trendline, using a 2nd order polynomial fit to better match the curve of the data. r^2 = .994. |
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