I want to make curve fitting to these points

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noura 2024-7-29

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编辑： dpb 2024-7-30

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I want to make curve fitting to these points but when i made it the blue straight line appeared. What does it mean ?

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Umar 2024-7-29

Hi @noura,

If you don’t mind, can you share your code with us to help resolve your issue.

dpb 2024-7-29

You don't need his code; the answer is obvious by inspection. Put any set of symmetric points in and overall OLS will always return the mean; it's inevitable conclusion from the basis of the method to minimize the overall error sum of squares.

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dpb 2024-7-29

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编辑：dpb 2024-7-29

在 MATLAB Online 中打开

The top and bottom are identical pairs above and below the mean; hence when/if you fit the whole dataset, the single line that best fits all the data is (drum roll, please...) the mean.

You need two fits; one for the upper and one for the lower. The slope of one will be exactly the negative of the other, but the two intercepts will be different.

X=[16 17.5 20 25 32.5 37 42.5 45 48].';

Y=[0 9 17 21 27 34 41 48 55 ];

DY=Y-Y(end);

Y=[Y;Y(end)-DY].';

scatter(X,Y,'filled')

box on, grid on

ylim([-5 118])

b1=polyfit(X,Y(:,1),3)

b1 = 1x4

0.0037 -0.3546 11.9781 -113.5101

b2=polyfit(X,Y(:,2),3)

b2 = 1x4

-0.0037 0.3546 -11.9781 223.5101

y1=polyval(b1,X);

y2=polyval(b2,X);

hold on

plot(X,y1,'b-')

plot(X,y2,'r-')

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Umar 2024-7-29

@dpb, thanks for your contribution and sharing your thoughts, really appreciated. @noura, please go ahead accept @dpb answer and give him a vote. If there are still further questions or issues, please let us know, we will be more happy to help.

dpb 2024-7-30

编辑：dpb 2024-7-30

在 MATLAB Online 中打开

"...the coefficients of the two are the negative of each other for the terms in X while the intercepts are different."

Also, notice that

X=[16 17.5 20 25 32.5 37 42.5 45 48].';
Y=[0  9   17 21 27   34 41   48  55 ];
DY=Y-Y(end);
Y=[Y;Y(end)-DY].';
b1=polyfit(X,Y(:,1),3);
b2=polyfit(X,Y(:,2),3);
mean_intercept=mean([b1(end) b2(end)])
mean_intercept = 55.0000
mean_y=mean(Y,'all')
mean_y = 55

The average of the two intercepts is the mean of the overall data to within machine precision/roundoff in the fitting calculations...

That being so, it is in one sense only one polynomial, the second is completely known by only fitting the first; the issue still being there isn't any convenient way to return the double-valued function from only a f(x).

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