regression line in quadratic form

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.

Answer 1

[J. Alex Lee]

[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

[TAEKYU EOM]

Thx for the efficient notation. However, I'm afraid creating new variable does not affect the figure.

[J. Alex Lee]

are you plotting as

plot(ExperienceMdl,yhat);

[TAEKYU EOM]

I am plotting as following,

plot(x(:,2), y, '.', x(:, 2), yhat);

since it does not work with

ExperienceMdl = linspace(0,70,200)';

[J. Alex Lee]

of course the plot will not change if you don't change the code for plotting...as for "not working", what exactly is the issue?

[TAEKYU EOM]

I did not understand why you use linspace() and elemets are 0,70,200.

index = find(female==0&race==1&education==12);

y=logwage(index)
ExperienceMdl = linspace(0,70,200)';
xMdl = [ones(size(y)),ExperienceMdl(index),ExperienceMdl(index).^2]
b = xMdl\y
yhat = ExperienceMdl * b;

number of index is 6969x1.

Index exceeds the number of array elements (200).

Error in Untitled (line 19)
xMdl = [ones(size(y)),ExperienceMdl(index),ExperienceMdl(index).^2]
 

[J. Alex Lee]

yes, sorry about that, i edited the answer, but xMdl should be defined

xMdl = [ones(size(ExperienceMdl)),ExperienceMdl,ExperienceMdl.^2]

[TAEKYU EOM]

I am sorry, but why did you use linspace()?

[TAEKYU EOM]

and could you explain why there are multiple regression lines, not a single non-linear regrssion line?

[J. Alex Lee]

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.