Dimensions of arrays being concatenated are not consistent but both arrays have the same size

Question

I'm trying to perform the least-squares regression to check whether the optimal parameters of my distribution are approximately equal to the ones used to generate the random numbers.

I generated a probability density function on a histogram obtained by taking random points from the same distribution and I am trying to perform least-squares regression but I am having problems with dimension inconsistency.

N = 10000;
mu = 5; sigma = 2;
r = randn(N,1);
x = mu+sigma*r;
bin=mu-6*sigma:0.5:mu+6*sigma;
[~,centers]=hist(x,bin);
f=hist(x,bin);
plot(bin,f,'bo'); hold on;
xlabel('bin');
ylabel('f');

y_ = f;
x_ = bin;

H = [ones(length(y_),1),x_];   % This is the problem

% Least-Squares Regression
Astar = inv(H'*H)*H'*y_;
Ytilde = H*Astar;
plot(x_,Ytilde, 'r-','LineWidth',2)

When I try to run this, I get an error stating

Dimensions of arrays being concatenated are not consistent.

But when I check y_ and x_, both have the same size. What is the problem?

Answer 1

In your code

H = [ones(length(y_),1),x_];   % This is the problem

the statement ones(length(y_),1) is creating a 49x1 column vector, while x is a 1x49 row vector. So you need to one or the other of the below to concatenate depending on whether you want a 2-row or 2-column matrix

H = [ones(length(y_),1),x_'];   % creates a 49x2
H = [ones(1,length(y_)),x_];   % creates a 2x49