File:Random-data-plus-trend-r2.png
Random-data-plus-trend-r2.png (601 × 447 pixels, file size: 9 KB, MIME type: image/png)
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Image of random data plus trend, with best-fit line and different smoothings
The data is 1000 points (plotted in black), with an increasing trend of 1-in-100, with random normal noise of standard deviation 10 superimposed. The red-line is the same data but averaged every 10 points. The blue line is averaged every 100 points.
For the three series, the least squares fit line is virtually the same, with a slope of 0.01, as expected.
The r2 fit for the raw data is 0.08; for the 10-pt-filtered, 0.57; for 100-pt-filtered, 0.97.
Ignoring autocorrelation, a confidence limit for the slope of the fit line is [0.0082, 0.0127] for the raw data (which include 0.01, as it should). For the 10-pt-filtered the limits are slightly narrower at [0.0084, 0.0125] and for the 100pt-filtering the limits are again slightly narrower.
So what does that all mean?
- for the raw data, the simple trend line explains almost none of the variance of the time series (only 8%).
- for the 100-pt filtering, the trend line explains almost all of the data (97%).
- nonetheless, the trend lines are almost identical as are the confidence levels.
The time series are, of course, very closely related: the same except for the filtering. This shows that a low r2 value should not be interpreted as evidence of lack of trend.
Source code
Source in IDL. pp_regress
and reg_explain
not given.
n=1000
data=10*randomn(seed,n)+indgen(n)/100.
y=indgen(n)
y1=y(indgen(n/10)*10+5)
y2=y(indgen(n/100)*100+5*10)
ret=pp_regress(y,data)
print,reg_explain(ret)
data1=reform(data,10,n/10)
data1=avg(data1,0)
ret1=pp_regress(y1,data1)
print,reg_explain(ret1)
data2=reform(data,100,n/100)
data2=avg(data2,0)
ret2=pp_regress(y2,data2)
print,reg_explain(ret2)
plot,y,data,yr=[-20,30]
pp_regress_plot,ret,th=3
oplot,y1,data1,col=2,th=3
oplot,y2,data2,col=3,th=3
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation Licence, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the licence is included in the section entitled GNU Free Documentation Licence.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported licence. | ||
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Transferred from en.wikipedia to Commons by Maksim.
date/time | username | edit summary |
---|---|---|
21:25, 20 December 2004 | en:User:Quadell | (tagged) |
22:13, 14 August 2004 | en:User:Danakil | (fmt) |
21:17, 14 August 2004 | en:User:William M. Connolley | (Add code.) |
14:05, 12 August 2004 | en:User:William M. Connolley | (I bumped up the SD to make the point obvious.) |
14:00, 12 August 2004 | en:User:William M. Connolley | (Comments) |
13:50, 12 August 2004 | en:User:William M. Connolley | (...partial before reload) |
13:32, 12 August 2004 | en:User:William M. Connolley | (Image of random data plus trend, with best-fit line and different smoothings) |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:49, 21 March 2006 | 601 × 447 (9 KB) | wikimediacommons>Maksim | La bildo estas kopiita de wikipedia:en. La originala priskribo estas: '''Image of random data plus trend, with best-fit line and different smoothings''' {{GFDL}} The data is 1000 points, with a trend of 1-in-100, with random normal noise of SD 10 super |
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