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regression line in quadratic form

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TAEKYU EOM
TAEKYU EOM on 9 Sep 2020
Commented: J. Alex Lee on 13 Sep 2020
Hi, all
During my exercise, I'd like to draw a regression line fitted with the following quadratic equation.
The followings are the code I wrote down.
y = log(wage(index));
x = [ones(length(y), 1) experience(index) experience(index).^2];
b = (x'*x)^(-1)*x'*y;
yhat = x*b;
figure;
plot(x(:, 2), y, '.', x(:, 2), yhat);
title('exercise');
xlabel('experience');
ylabel('log(wage)');
print('-dpdf', 'excercise');
close;
And this is the result.
I firstly guess the single curve will be shown on the figure, but... why is there a bunch of lines, and how can I fix this with minimization of fixing?
Thank you in advance, guys.

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Answers (1)

J. Alex Lee
J. Alex Lee on 9 Sep 2020
Edited: J. Alex Lee on 12 Sep 2020
[edited] Alternatively, just create a new variable to hold an already sorted "model" experience
N = 200; % choose an arbitrary number of points to define model
ExperienceMdl = linspace(0,70,N)';
xMdl = [ones(N,1),ExperienceMdl,ExperienceMdl.^2]
yhat = ExperienceMdl * b;
And also, your compuation b looks inefficient, you can simply do
b = x\y

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TAEKYU EOM
TAEKYU EOM on 12 Sep 2020
I am sorry, but why did you use linspace()?
TAEKYU EOM
TAEKYU EOM on 13 Sep 2020
and could you explain why there are multiple regression lines, not a single non-linear regrssion line?
J. Alex Lee
J. Alex Lee on 13 Sep 2020
You saw multiple regression lines because you plotted the results of your model based on the data, which is not ordered in "experience" variable.
One of the previous answeres suggested you to sort your data in order of your "experience" variable. But you can realize that there is no need to plot your model based on the data points alone.
linspace(a,b,N) will generate a vector of N-values evenly spaced (and sorted) from a to b. I chose N=200 points because that should be more than enough to resolve the shape of your model over the domain 0~70, which is roughly the extent of your data.

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