Gambar:Random-data-plus-trend-r2.png - Wikipédia

# Gambar:Random-data-plus-trend-r2.png

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Random-data-plus-trend-r2.png‎ (10KB, 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

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, 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 license is included in the section entitled "GNU Free Documentation License".

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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

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

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)

## Tumbu gambar

Kaca nu numbu ka gambar ieu:

- Trend estimation

Disalin ti "http://su.wikipedia.org../../../r/a/n/Gambar%7ERandom-data-plus-trend-r2.png_7846.html"

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