clear all
close all
clc

load wage2.mat;

%   Obs:   935

data = wage;

%   1. wage                     monthly earnings
%   2. hours                    average weekly hours
%   3. IQ                       IQ score
%   4. KWW                      knowledge of world work score
%   5. educ                     years of education
%   6. exper                    years of work experience
%   7. tenure                   years with current employer
%   8. age                      age in years
%   9. married                  =1 if married
%  10. black                    =1 if black
%  11. south                    =1 if live in south
%  12. urban                    =1 if live in SMSA
%  13. sibs                     number of siblings
%  14. brthord                  birth order
%  15. meduc                    mother's education
%  16. feduc                    father's education
%  17. lwage                    natural log of wage

wage    = data(:,1);
hours   = data(:,2);
IQ      = data(:,3);
KWW     = data(:,4);
educ    = data(:,5);
exper   = data(:,6);
tenure  = data(:,7);
age     = data(:,8);
married = data(:,9);
black   = data(:,10);
south   = data(:,11);
urban   = data(:,12);
sibs    = data(:,13);
brthord = data(:,14);
meduc   = data(:,15);
feduc   = data(:,16);
lwage   = data(:,17);

avg_wage = mean(wage);
avg_IQ = mean(IQ);
std_wage = std(wage);
std_IQ = std(IQ);

figure
    subplot(2,1,1)
    plot(wage,'*')
    hold on
    plot(avg_wage*ones(size(wage)),'r')
    xlabel('pozorovani')
    ylabel('mzda')
    
    subplot(2,1,2)
    plot(IQ,'*')
    hold on
    plot(avg_IQ*ones(size(IQ)),'r')
    plot((avg_IQ+2*std_IQ)*ones(size(IQ)),'k:')
    plot((avg_IQ-2*std_IQ)*ones(size(IQ)),'k:')
    xlabel('pozorovani')
    ylabel('IQ')
    legend('IQ','prumer','2*std')
    

    
yy = wage;
XX = [ones(size(yy)) IQ hours];
result = ols(yy,XX);
vnames = strvcat('mzda','konstanta','IQ');
prt_reg(result,vnames);

ii = ones(935,1);
M0 = eye(935)-ii*inv(ii'*ii)*ii';

XX0 = M0*XX;
XX0(:,1)=[];

result = ols(M0*yy,XX0);
vnames = strvcat('mzda','konstanta','IQ');
prt_reg(result,vnames);

result = ols(yy,XX0);
vnames = strvcat('mzda','konstanta','IQ');
prt_reg(result,vnames);

result = ols(yy,[ones(935,1) XX0]);
vnames = strvcat('mzda','konstanta','IQ');
prt_reg(result,vnames);

result = ols(M0*yy,XX(:,2:end));
vnames = strvcat('mzda','konstanta','IQ');
prt_reg(result,vnames);