% load data
load ('smoke.txt')
smoking = smoke(:,1);
mort = smoke(:,2);

%  make a scatterplot
figure
plot(smoking,mort,'bo');
title('Relationship between smoking and lungcancer');
ylabel('Mortality Index');
xlabel('Smoking Index');


n = length(smoking);
% create the design matrix
X = [ones(n,1),smoking];

% find the least square estimate of beta
betahat = inv(X'*X)*(X'*mort);

% find  the fitted values and the residuals

fitted = X*betahat;
res = mort - X*betahat;

% plot the regression line
figure
plot(smoking,mort,'k.',smoking,fitted,'c');
title('Smoking and Lung Cancer');
ylabel('Mortality Index');
xlabel('Smoking Index');
legend('Data','Fitted Model',0);

% look at the residual plots to see if any model assumptions
% are violated

figure
plot(res,'bo');
  xlabel('Observation Number');
ylabel ('Residual');
title('Residual Plot');


figure
plot(fitted,res,'bo');
  xlabel('Fitted Values');
ylabel ('Residual');
title('Residual Plot');


% see how good our model fits the data
figure
plot(smoking,mort,'k.',smoking,fitted,'c',smoking,fitted,'r*');
title('Smoking and Lung Cancer');
ylabel('Mortality Index');
xlabel('Smoking Index');
legend('Data','Fitted Model',0);