Ignore:
Timestamp:
Jun 19, 2006, 11:56:04 AM (15 years ago)
Author:
Peter
Message:

closes #23 redesign of regression classes

File:
1 edited

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  • trunk/doc/Statistics.tex

    r494 r586  
    4949
    5050The first group is when some of the measurements are known to be more
    51 precise than others. The more precise a measuremtns is the larger
     51precise than others. The more precise a measurement is, the larger
    5252weight it is given. The simplest case is when the weight are given
    5353before the measurements and they can be treated as deterministic. It
     
    7070can be treated as independent of the observable.
    7171
    72 Since there are various origin for a weight occuring in a statistical
    73 analysis, there are various way to treat the weights and in general
     72Since there are various origins for a weight occuring in a statistical
     73analysis, there are various ways to treat the weights and in general
    7474the analysis should be tailored to treat the weights correctly. We
    7575have not chosen one situation for our implementations, so see specific
     
    8383\end{itemize}
    8484An important case is when weights are binary (either 1 or 0). Then we
    85 get same result using the weighted version as using the data with
     85get the same result using the weighted version as using the data with
    8686weight not equal to zero and the non-weighted version. Hence, using
    8787binary weights and the weighted version missing values can be treated
     
    182182the variance is estimated as $\sigma_x^2=\frac{\sum
    183183w_xw_y(x-m_x)^2}{\sum w_xw_y}$. As in the non-weighted case we define
    184 the correlation to be the ratio between the covariance and geomtrical
    185 avergae of the variances
     184the correlation to be the ratio between the covariance and geometrical
     185average of the variances
    186186
    187187$\frac{\sum w_xw_y(x-m_x)(y-m_y)}{\sqrt{\sum w_xw_y(x-m_x)^2\sum
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