polyfit doesn't fit the data
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>> mdl=fitlm(X,Y)
mdl =
Linear regression model:
y ~ 1 + x1
Estimated Coefficients:
Estimate SE tStat pValue
________ _______ _______ __________
(Intercept) 16.325 1.8303 8.9194 1.054e-16
x1 -1.1809 0.14751 -8.0059 4.5928e-14
Number of observations: 250, Error degrees of freedom: 248
Root Mean Squared Error: 1.19
R-squared: 0.205, Adjusted R-Squared 0.202
F-statistic vs. constant model: 64.1, p-value = 4.59e-14
>> plot(X,Y,'.')
hold on
plot(X,polyval(p,X),'r.')
hold on
f=16.3250-1.1809*X
plot(X,f,'.b')
Attached figure:
in blue: data
in red: polyfit regression
in green: fitlm model
polyfit does not fit the data whereas fitlm does. Is there anything I can do to fix that? I would rather not use fitlm as I have to do thousand of regressions and it seems more complex and using more memory
5 个评论
John D'Errico
2015-5-19
Usually, when someone says something like this, they did not really do what they think they did. The fact is, polyfit WILL generate the same model as does fitlm. Here for example, you don't show where you did the polyfit call. Did you use the same data? What were the coefficients produced by polyfit?
采纳的回答
Titus Edelhofer
2015-5-19
Hi,
I guess it's another problem here: note, that if you call polyfit with
[p,s,mu] = polyfit ...
you get the scaled and shifted representation of the polynomial. Therefore you would need to take mu to transform logX->\hat logX (see doc of polyfit).
If you call polyfit only with output p you get a different result that coincides with fitlm.
Titus
2 个评论
Geoff
2018-5-21
I realize this post is now three years old but as of 2018a, the help file describing polyfit is not clear.
In the help file, p is described as the coefficients of the unscaled and uncentered data. In the description of the [p,S,mu] syntax, however, there is no mention that the returned p is now of the scaled and centered data.
Perhaps Mathworks should change their description and use [phat,S,mu] rather than p, or automatically rescale polynomial coefficients back to the original space if scaling and centering are used.
更多回答(3 个)
John D'Errico
2015-5-19
编辑:John D'Errico
2015-5-19
GIVE US A BREAK!
You used polyfit on the log of the data! But you used fitlm on the unlogged data! Here are the calls you yourself showed:
mdl=fitlm(X,Y)
[p,s,mu]=polyfit(logX,logY,1);
I've just copied what you yourself typed. Don't tell us that the variables are the same, but they just have a different name. Show us what happens when you use polyfit like this:
p = polyfit(X,Y,1)
Please tell us why we should be surprised that there is a difference. If you change the data, then expect to get a different answer.
Next, READ THE HELP! From the help for polyfit, it tells us that when you call it with THREE output arguments, it performs a centered and scaled regression.
[P,S,MU] = polyfit(X,Y,N) finds the coefficients of a polynomial in
XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
centering and scaling transformation improves the numerical properties
of both the polynomial and the fitting algorithm.
So in order to predict the result, you need to use the centered and scaled variable.
XHAT = (X-MU(1))/MU(2);
where MU(1) = MEAN(X) and MU(2) = STD(X). For example...
X = rand(10,1);
X = 10 + 100*rand(10,1);
Y = rand(size(X));
p = polyfit(X,Y,1)
p =
-0.0047359 0.94733
[p,S,mu] = polyfit(X,Y,1)
p =
-0.15668 0.58731
S =
R: [2x2 double]
df: 8
normr: 0.7445
mu =
76.021
33.084
See that there IS a difference in the coefficients produced. READ THE HELP. What you actually did wrong is only for you to know, since you have not proved to us that logX and X are truly the same thing, as with logY and Y.
Ok. Since you actually gave us the results from polyfit, lets try something:
p=[-0.6039,1.6844];
mu=[12.3973;0.5114];
syms X Y
xhat = (X - mu(1))/mu(2);
yhat = p(1)*xhat + p(2);
vpa(yhat,10)
ans =
16.32407436 - 1.180876027*X
AGAIN, IF you use polyfit with THREE output arguments, it produces a DIFFERENT model. You can recover the untransformed model as I did, but if you can't bother to read the help, what do you expect?
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florence briton
2015-5-19
2 个评论
John D'Errico
2015-5-19
编辑:John D'Errico
2015-5-19
ARGH!
READ THE ANSWERS!
First, PROVE TO USE THAT X AND logX ARE THE SAME. For example:
min(X-logX)
max(X-logX)
should both be essentially zero.
Then call polyfit using a call that WILL PRODUCE the same result!
p = polyfit(X,Y,1)
READ THE HELP FOR POLYFIT! READ THE ANSWERS. Don't just keep repeating the same nonsense. (See my edit to my answer, where I show how the coefficients that you got ARE the correct coefficients but for a different model.)
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