How to find a polynomial that best fit with scatter plot?

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Andi 2023-5-12

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https://ww2.mathworks.cn/matlabcentral/answers/1961999-how-to-find-a-polynomial-that-best-fit-with-scatter-plot

评论： Andi 2023-5-14

采纳的回答： Walter Roberson

lv_vl.csv

在 MATLAB Online 中打开

Hi everyone,

I am trying to find a best-fit polynomial equation that works well for my data set (two parameters x, and y).

First, I attempt to fit a polynomial line using Excel (figure attached). The equation shows the best fit with the original scatter plot (the red line is the best fit polynomial line).

However, when I try to estimate values with the best-fit equation, it looks very different from actual data points.

A similar error is observed when I attempt to use the Matlab function polyfilt.

clear all
clc
data=readmatrix('lv_vl.csv');
x=data(:,1);
y=data(:,2);
scatter(x,y,'b')
p = polyfit(x,y,2)

May someone suggets me how i can fix this.

(data is also attached).

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采纳的回答

Walter Roberson 2023-5-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1961999-how-to-find-a-polynomial-that-best-fit-with-scatter-plot#answer_1233539

编辑：Walter Roberson 2023-5-12

在 MATLAB Online 中打开

lv_vl.csv

data=readmatrix('lv_vl.csv');

x=data(:,1);

y=data(:,2);

scatter(x,y,5,'.r')

p = polyfit(x,y,2);

eqn = poly2sym(p)

eqn =

xest = linspace(min(x), max(x), 75);

yest = polyval(p, xest);

hold on

plot(xest, yest, '-b');

title(char(vpa(eqn,5)))

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Walter Roberson 2023-5-14

The sum of squared error is still pretty high for degree 4, and there are still fairly visible artifacts.

Andi 2023-5-14

True, but if I overestimate, then I am unable to incorporate other parameters that have a time-varying influence on the time series. Therefore, I decided to go with a 4-order polynomial.

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