% This symbol (%) indicates that the line is a comment. 
% To run this file : 
%  1- Press the "play" button in the matlab text editor OR ;
%  2- In the command line, type the name of this file (without the ".m")
%       but make sure matlab looks for the right directory.
%
% basic_examples.m 
% runs basic examples (duh)

clear %This clears everything in memory

x = 10 %Affectation (x == 10)

x = x + 10 %Now, x == 20

x = [1, 0.5; 0.5, 1] %x is now a matrix

y = 2 * x %scalar multiplication

y = x * y %(matrix multiplication)

z = x.*y %element by element multiplication

z = x.^y %element by element exponentiation

%Note that the semi-colon ";" suppress the output. 

x = x / 2; %<-- No output, though the value of x changed...

%So all this is fairly trivial. Here is a slightly more advanced example of what could be
%done...

clear %Clears all the previous stuff.

%Let y = 10 + 12*x + eps be a regression model where : 
%   x is distributed uniformly (and is independent of eps)
%   eps is normally distributed.
%   
%   What are the OLS estimators of (b_0 = 10,  b_1 = 12) ?
%
%   Lets make a sample of n = 100 : 

x = rand(100, 1); %Creates an 100x1 vector of uniform numbers.

cons = ones(100,1); %Creates a 100x1 vector of ones.

y = cons*10 + 12*x + randn(100,1);
%randn(100,1) creates a nx1 vector of normally distributed numbers...

%Now, we perform the regression : 
X = [cons, x]; %Full set of regressors. 
b = (X'*X)^(-1)*X'*y %OLS formula (see the output on display)