% Simple pseudocode for calculating the first-order least-square fit of y vs x,
% including the Slope and Intercept and the predicted standard deviation of
% the slope (SDslope) and intercept (SDintercept).
% Uses only the length function and sqrt (square root) functions
%
% Assumptions: The data are in the arrays x and y;
% length(x) returns the nunber of points; 
% x(i) is the ith element of array x, where i is integer;
% x^2 is the square of x, etc.
% The for loops (for i=1:n....end) increment i in unit steps.

n=length(x)
sumx=0
sumy=0
sumxy=0
sumx2=0
for i=1:n
   sumx=sumx+x(i)
   sumy=sumy+y(i)
   sumxy=sumxy+x(i)*y(i)
   sumx2=sumx2+x(i)*x(i)
end
meanx=sumx/n
meany=sumy/n
slope=(n*sumxy-sumx*sumy)/(n*sumx2-sumx*sumx)
intercept=meany-(slope*meanx)
ssy=0
ssr=0
ssx=0
for i=1:n
   ssy=ssy+(y(i)-meany)^2
   ssr=ssr+(y(i)-intercept-slope*x(i))^2
   ssx=ssx+(x-meanx).^2
end
R2 = 1-(ssr/ssy)
SDslope = sumy/sqrt(sxx)
SDintercept = sumy*sqrt(1/(n-(sumx^2)/sumx2))