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[求助]
50金求解：關(guān)于lack-of-fit test的意義及應(yīng)用
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我得到的標(biāo)準(zhǔn)曲線是用origin進(jìn)行線性擬合的，但審稿人說加個lack-of-fit test，因為我的r值不太好。有位大神對我的數(shù)據(jù)用matlab進(jìn)行了test,，請見http://www.gaoyang168.com/bbs/viewthread.php?tid=4020335。但問題是，我看不懂…… 我想請問：標(biāo)準(zhǔn)曲線是用origin進(jìn)行線性擬合的還是用lack-of-fit test得到的呢，帖子里的P值能說明什么，應(yīng)該如何應(yīng)用，我看到直接給了個P值，但也有人用F值，真的不明白，想請教下，對下那位大神的數(shù)據(jù)，我應(yīng)該如何應(yīng)用。 求解……急 我特意取了一些文獻(xiàn)的表達(dá)，請見圖，我應(yīng)該用哪個好。 PS:我是做分析方法的。 |
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09yschen(金幣+10): 2012-01-08 20:51:17
09yschen(金幣+10): 2012-01-08 20:51:17
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見帖 http://en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares http://www.gaoyang168.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. |
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