Regression Model Graph(plot), Deflection Problem(sharp point or cusp)

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Sanghyuk Kim 2021-6-24

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编辑： Scott MacKenzie 2021-6-27

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?

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Sanghyuk Kim 2021-6-25

I think a 3rd regression model is like a 3rd polynomial, so there should be no bends.

Sanghyuk Kim 2021-6-25

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?

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回答（1 个）

Scott MacKenzie 2021-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/863910-regression-model-graph-plot-deflection-problem-sharp-point-or-cusp#answer_733260

编辑：Scott MacKenzie 2021-6-27

在 MATLAB Online 中打开

You are getting the sharp bend because you are calculating YFIT using the x sample points (which are sparce at the inflexion point). To see the curvature in the model, you need to calculate YFIT using a set of x query points (xq) that are finely spaced over the full range of interest (including about the inflexion point):

load accidents
x = hwydata(:,6); % population of states
y = hwydata(:,4); % accidents per state
scatter(x,y,'filled')
hold on;
% use xq for plotting (to expose curvature in models)  
xq = linspace(min(x), max(x));
X = [ones(size(x)) x];
b = regress(y,X)   
hold on
YFIT = b(1) + b(2)*xq; % use xq, not x
plot(xq,YFIT);
hold on;
X2 = [ones(size(x)) x x.^2];
b2 = regress(y,X2);
YFIT2 = b2(1) + b2(2)*xq + b2(3)*xq.^2 ; % use xq, not x
plot(xq,YFIT2);
X3 = [ones(size(x)) x x.^2 x.^3];
b3 = regress(y,X3);
YFIT3 =  b3(1) + b3(2)*xq + b3(3)*xq.^2 + b3(4)*xq.^3 ; % use xq, not x
plot(xq,YFIT3) ;
xlabel('Registered vehicles[thousands](x)');
ylabel('Accidents per state(y)');
legend('Data','1st Order','2nd Order', '3rd Order', 'location', 'southeast');

BTW, consider using polyfit (along with polyval) instead of regress. It's a bit easier overall:

pf1 = polyfit(x, y, 1)
yfit1 = polyval(pf1, xq)
plot (xq, yfit1)
pf2 = polyfit(x, y, 2)
yfit2 = polyval(pf2, xq)
plot (xq, yfit2)
pf3 = polyfit(x, y, 3)
yfit3 = polyval(pf3, xq)
plot (xq, yfit3)