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
