%Open pdf and cdf visualization GUI 
disttool
%Also can call pdfs and cdfs from the command line 
s=-2:.01:2;
%call exp pdf of mean 1
exp1=exppdf(s,1);
%plot exp pdf
plot(s,exp1);
%compare exp1 with exp pdf of mean 2;
exp2=exppdf(s,2);
hold on;
plot(s,exp2);


%Run simple regression on wage1 data
load('wage1.mat');
%call regressand data
y=data(:,1);
%call dependent variable data
X1=data(:,2);
%run fit of degree one 
polyfit(y,X1,1);
%run ttest against null hypothesis h: B(2)=0, obtain pvalue and conf
%interval
[h,pvalue,ci]=ttest(X1,0);
%notice that h=1, i.e we reject null.  Compare with h: B(2)=12.5;
[h, pvalue, ci]=ttest(X1,12.5);
%now notice that h=0.  
%Condcut analysis of variance to determine if two samples come from same
%population 
X2=[data(1:525,1) data(1:525,2)];
p=anova1(X2);
%We obtain p value very close to zero and so we conclude samples do not
%come from same population
%run a multiple linear regression with wage1 data 
%include column of ones to compute intercept
X3=[ones(size(data,1),1) data(:,2:4)];
[b, bint,r,rint,stats] = regress(y,X3);
%show regression stats, i.e Rsquared,F-stat,pvalue, error variance
stats;