Polynomial graph(using plot function), Deflection Problem

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

[Robert Daly]

I think this is just what polynomials do.

Have you tried the native matlab function for fitting polynomials?

Polynomial curve fitting - MATLAB polyfit - MathWorks Australia

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]

I think

p = polyfit(x,y,n)

is using for interpolation model that includes all data. I want to implement a regression model.

i.e. it is not a model that includes all data.

thanks for your Ans.

[Sanghyuk Kim]

3rd regression model is

YFIT3 = 201.6374 + 0.0815*x + (9.7323e-6)*x.^2 - (2.6249e-10)*x.^3

My guess is that the error is probably due to the coefficient being too small.

how to fix it?

Answer 1

[Sulaymon Eshkabilov]

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
...