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09yschen

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[求助] 50金求解：关于lack-of-fit test的意义及应用

我得到的标准曲线是用origin进行线性拟合的，但审稿人说加个lack-of-fit test，因为我的r值不太好。有位大神对我的数据用matlab进行了test,，请见http://muchong.com/bbs/viewthread.php?tid=4020335。但问题是，我看不懂……
我想请问：标准曲线是用origin进行线性拟合的还是用lack-of-fit test得到的呢，帖子里的P值能说明什么，应该如何应用，我看到直接给了个P值，但也有人用F值，真的不明白，想请教下，对下那位大神的数据，我应该如何应用。
求解……急
我特意取了一些文献的表达，请见图，我应该用哪个好。
PS:我是做分析方法的。

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1楼2012-01-06 21:20:35

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dbb627

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【答案】应助回帖

感谢参与，应助指数 +1
09yschen(金币+10): 2012-01-08 20:51:17

见帖
http://en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares
http://muchong.com/bbs/viewthread.php?tid=4020335&pid=7&page=1#pid7
LOFRTEST Lack-of-fit test for regression model with independent replicate values.
LOFRTEST(D,alpha) is a statistical test that gives information on the form
of the model under consideration. A significant lack-of-fit suggest that there
may be some systematic variation unaccounted for in the hypothesized model
(chosen model does not well describe the data). It arises when there are exact
replicate values of the independent variable in the model that provide an estimate
of pure error. Pure error is in essence the amount of error that cannot be accounted
for by any model. Then allows a test on whether there is error present aside
from pure error. For the construction of the lack-of-fit test we need to examine
three common types of linear models:
   - single mean (one parameter)
   - slope and intercept or common regression model (two parameters)
   - separate means for each x-value or one-way ANOVA (many parameters).
So, the pure error is the error of the separate means on ANOVA and the total error
in the residual resulting in the regression analysis: the lack-of-fit results
to be the difference between this two sources of error,

               SS(LOF) = SSR(Model) - SSE(ANOVA).

Syntax: lofrtest(D,alpha)

Inputs:
      D - matrix data (=[X Y]) (last column must be the Y-dependent variable).
         (X-independent variable entry can be for a simple [X], multiple [X1,X2,X3,...Xp]
         or polynomial [X,X^2,X^3,...,X^p] regression model).
alpha - significance level (default = 0.05).

Outputs:
      A complete summary (table) of analysis of variance partitioning sources of
      variation for testing lack-of-fit.

Example from the data on height and weight of 19 students in Psy 202. Assigment 3 of Psych
3030 from the Department of Psychology of the York University. Available on Internet at
the URL address http://www.psych.yorku.ca/lab/psy3030/assign/assign3.htm
We are interested to test with a significance-value = 0.05 if there is a lack-of-fit on the
regression model due to the height replicate values.

            ------------------- -------------------
               Height Weight    Height Weight
            ------------------- -------------------
               60    90          68    140
               60    100          68    135
               62    110          70    160
               62    116          70    145
               62    120          70    148
               66    140          71    143
               66    170          71    135
               68    130          74    195
               68    117          74    164
               68    155
            ------------------- -------------------

Data matrix must be:
D=[60 90;60 100;62 110;62 116;62 120;66 140;66 170;68 130;68 117;68 155;68 140;68 135;
   70 160;70 145;70 148;71 143;71 135;74 195;74 164];

Calling on Matlab the function:
            lofrtest(D)

Answer is:

Lack-of-fit test for regression model with independent replicate values.
--------------------------------------------------------------------------
SOV                   SS       df          MS       F       P
--------------------------------------------------------------------------
Model             7658.359       1    7658.359    31.720 0.0000
Residual          4104.378       17    241.434
--------------------------------------------------------------------------
Lack-of-fit       2142.011       5    428.402    2.620 0.0797
Pure error       1962.367       12    163.531
--------------------------------------------------------------------------
Total             11762.737       18
--------------------------------------------------------------------------
If the associated P-value for any F test is equal or larger than 0.05
The corresponding null hypothesis is met. Otherwise it is not met.

Created by A. Trujillo-Ortiz, R. Hernandez-Walls, A. Castro-Perez and
            F.J. Marquez-Rocha
            Facultad de Ciencias Marinas
            Universidad Autonoma de Baja California
            Apdo. Postal 453
            Ensenada, Baja California
            Mexico.
            atrujo@uabc.mx
Copyright (C) March 4, 2005.

To cite this file, this would be an appropriate format:
Trujillo-Ortiz, A., R. Hernandez-Walls, A. Castro-Perez and F.J Marquez-Rocha.
   (2005). lofrtest:Lack-of-fit test for regression model with independent replicate
   values. A MATLAB file. [WWW document]. URL http://www.mathworks.com/matlabcentral/
   fileexchange/loadFile.do?objectId=7074

References:

Department of Psychology of the York University. Available on Internet at the
         URL address http://www.psych.yorku.ca/lab/psy3030/assign/assign3.htm
Zar, J. H. (1999), Biostatistical Analysis (2nd ed.).
         NJ: Prentice-Hall, Englewood Cliffs. p. 345-350.