% Estimate the Growth Rate of U.S. GDP (1947-2015).
 clc;
 
 % Load Data.
 M = importdata('GDP.txt');
 data = M.data;
 n = size(data,1);
 
 % Let's define variables.
 year = data(:,1);
 GDP = data(:,2);
 lnGDP = log(GDP);
 p = data(:,3);
 lnP = log(p);
 xmat = [ones(n,1) year-1946 lnP];
 
 % Now, OLS
 b = inv(xmat'*xmat)*(xmat'*(lnGDP));
 disp(b);
 
 % Next, we will plot the residuals over time.
 e = lnGDP - xmat*b;
 plot(year,e);