%Lab 22 Solutions
%MatLab - Using M-files, 
%loading files and plotting
%Patrick D. Schmid

clear;

%load the text file
%note that the current directory in MatLab has to be set to the directory
%containing this m file and the data file
load data.txt;

%extract the x and y columns from the data
%note that MatLab uses 1 as smallest array index (in contrast to C++!)
xdata = data(:,2);
ydata = data(:,3);

%%display the read data and then the extracted column vectors
data
xdata
ydata

%run a linear regression over our data
%note that the 1 at the end means that we are looking for a polynominal of
%the sort: c * x^1 + b * x^0
coeff=polyfit(xdata, ydata, 1);

%based on the equation above, m is stored in the first array index, b in
%the second. Hence with y = m * x + b, we get
yline=coeff(1)*xdata+coeff(2);

%Plot our data
%Contrary to the assignment, this solution plots all charts asked for with
%the same m-file, but in different figures. It also adds labels and a
%legend

%first plot objective: a plot of the x and y data using red x's and the best fit
%line using a blue line
figure(1);
plot(xdata, ydata, 'ro', xdata, yline, 'b-'),
title('1) ydata and yline in same figure'), xlabel('xdata'), ylabel('y')
legend('original data', 'linear regression');

%second plot objective: red x data points are on one Figure and the blue line is on
%another Figure
figure(2);
plot(xdata, ydata, 'ro'),
title('2) ydata '), xlabel('xdata'), ylabel('ydata')
legend('original data');

figure(3);
plot(xdata, yline, 'b-'),
title('2) yline'), xlabel('xdata'), ylabel('yline')
legend('linear regression');

%third chart: red x data points are on one subplot of a Figure and the blue
%line is on another subplot of the same Figure.
figure(4);

subplot(2,1,1),
plot(xdata, ydata, 'ro'),
title('3) ydata '), xlabel('xdata'), ylabel('ydata'),
legend('original data');

subplot(2,1,2),
plot(xdata, ydata, 'b-'),
title('3) yline'), xlabel('xdata'), ylabel('yline'),
legend('linear regression');