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

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Andi
Andi 2023-5-12
评论： Andi 2023-5-14
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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Walter Roberson
Walter Roberson 2023-5-12
编辑：Walter Roberson 2023-5-12
Ran in:
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
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
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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