Polynomial graph(using plot function), Deflection Problem
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I implemented the first, second, and third regression models for the data and showed them using the plot function.
But, for the 3rd regression model, the graph was bent, such as the part in red.
How can we solve this problem?
I think a 3rd regression model is like a 3rd polynomial, so there should be no bends.
This is the code
load accidents
x = hwydata(:,6); %Population of states
y = hwydata(:,4); %Accidents per state
scatter(x,y,'filled')
X = [ones(size(x)) x];
b = regress(y,X)
hold on
YFIT = b(1) + b(2)*x;
plot(x,YFIT)
X2 = [ones(size(x)) x x.^2];
b2 = regress(y,X2);
YFIT2 = b2(1) + b2(2)*x + b2(3)*x.^2 ;
plot(x,YFIT2)
X3 = [ones(size(x)) x x.^2 x.^3];
b3 = regress(y,X3);
YFIT3 = b3(1) + b3(2)*x + b3(3)*x.^2 + b3(4)*x.^3 ;
plot(x,YFIT3)
xlabel('Registered vehicles[thousands](x)');
ylabel('Accidents per state(y)');
plot1_legend=legend('Data','1st Order','2nd Order', '3rd Order')
hold off
3 个评论
Robert Daly
2021-6-25
I think this is just what polynomials do.
Have you tried the native matlab function for fitting polynomials?
p = polyfit(x,y,n)
gives thepolynomial parametrs that fit the best for an n degree polynomial.
then
y1 = polyval(p,x1)
is used to create y vales using the parameters and the given x coordinates.
Sanghyuk Kim
2021-6-25
编辑：Sanghyuk Kim
2021-6-25
Sanghyuk Kim
2021-6-25
回答（1 个）
Sulaymon Eshkabilov
2021-6-25
You need to employ polyfit() for your anticipated fit models or just least squares method with Vandermonde matrix with \. SInce you are trying to find a fit model with a single variable x.
E.g.:
x = hwydata(:,6); %Population of states
y = hwydata(:,4); %Accidents per state
FITmodel1 = polyfit(x, y, 1); % Linear fit
FITmodel2 = polyfit(x, y, 2); % Quadratic fit
FITmodel3 = polyfit(x, y, 3); % Cubic fit
%% OR
X1 = [ones(size(x)) x ];
FITmodel1 = X1\y; % Linear fit model
FITmodel1_val = FITmodel1(1)+FITmodel1(2)*x; % Calculated vals of Lin. fit model
X2 = [ones(size(x)) x x.^2];
FITmodel1 = X2\y; % Quadratic fit model
FITmodel1_val = FITmodel1(1)+FITmodel1(2)*x+FITmodel1(2)*x.^2; % Calculated vals of Quad. fit model
...
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2021-6-25
2021-6-25
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