Image:Random-data-plus-trend-r2.png
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Random-data-plus-trend-r2.png (601 × 447 pixel, file size: 9 KB, MIME type: image/png)
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La bildo estas kopiita de wikipedia:en. La originala priskribo estas:
Image of random data plus trend, with best-fit line and different smoothings
The data is 1000 points, with a trend of 1-in-100, with random normal noise of SD 10 superimposed. The red-line is the same data but averaged every 10 points. The blue line is every 100 points.
The r2 fit for the raw data is 0.08; for the 10-pt-filtered, 0.57; for 100-pt-filtered, 0.97.
For all series, the least squares fit line is virtually the same, with a slope of 0.01, as expected.
Ignoring autocorrelation, a confidence limit for 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.
[edit] Source code
Source id 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
| 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) |
[edit] Historio de la dosiero
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Click on date to download the file or see the image uploaded on that date.
- (del) (cur) 13:51, 12 August 2004 . . en:User:William_M._Connolley William M. Connolley ( en:User_talk:William_M._Connolley Talk) . . 601x447 (9644 bytes)
- (del) (rev) 13:32, 12 August 2004 . . en:User:William_M._Connolley William M. Connolley ( en:User_talk:William_M._Connolley Talk) . . 592x447 (7139 bytes) (Image of random data plus trend, with best-fit line and different smoothings)
