%Lesson 3c - Math 151 
%Objective is to illustrate ability to do 
%a linear regression on a semilog plot.
%This is for equations like 
%      y = a (b^x) for constants a,b.
% This is the same as 
%     N(t) = N(0) exp(k t) for a constant k.
% k>0 gives exponential growth 
% k<0 gives exponential decay.
%First read in data from a file
%   load b:semilog.dat
%then read in a command file that is
%this file of commands for MATLAB
%by first telling MATLAB to use the b: drive
%   !b:
%then telling it to run lesson3b
%   lesson3c
%where lesson3c.m is a file on your 
%floppy in the b: drive
who,pause
!c:
% First plot the raw data
plot(x,y,'+w')
title('x versus y'),pause
% Now plot the data on semilog scale
semilogy(x,y,'+')
title('x versus y semilog scale'),pause
% Can see that the above plot is the same
% as plotting x versus log(y) from the below
% we let ly = vector of log(y) values base 10
ly=log10(y),pause
plot(x,ly,'+')
title('x versus log(y)'),pause
% Now do a linear regression of the
% x versus log(y) plot
c=polyfit(x,ly,1),pause
% here c(1) is the slope of the regression
% which for the above equation is log10(b)
% and c(2) is the intercept of the regression
% which for the above is log10(a)
% Now plot the regression line on plot
% of x versus log(y)
m=[min(x) max(x)],pause
ym=polyval(c,m),pause
plot(x,ly,'+',m,ym)
title('x versus log(y)'),pause
% Now to show original data and the fitted
% regression model, first set up the fitted
% model y values (called yfit)
len=length(x)
a=10^c(2),pause
b=10^c(1),pause
for i=1:len
   yfit(i)=a*b^x(i);
end
plot(x,y,'+w',x,yfit)
title('x versus y and fit'),pause