% JAPPROX file japprox.m Basic quantities for ac pair {X,Y}
% Version of 5/7/96
% Assumes tuappr has set X, Y, PX, PY, t, u, P
EX  = total(t.*P)          % E[X]
EY  = total(u.*P)          % E[Y]
EX2 = total(t.^2.*P)       % E[X^2]
EY2 = total(u.^2.*P)       % E[Y^2]
EXY = total(t.*u.*P)       % E[XY]
VX  = EX2 - EX^2           % Var[X]
VY  = EY2 - EY^2           % Var[Y]
cv = EXY - EX*EY;          % Cov[X,Y] = E[XY] - E[X]E[Y]
if abs(cv) > 1e-9  % to prevent roundoff error masking zero
   CV = cv
 else
   CV = 0
end
a = CV/VX                  % regression line of Y on X is
b = EY - a*EX              % u = at + b
R = CV/sqrt(VX*VY);
disp(['The regression line of Y on X is:  u = ',num2str(a),'t + ',num2str(b),])
disp(['The correlation coefficient is:  rho = ',num2str(R),])
disp(' ')
eY = sum(u.*P)./sum(P);    % eY(t) = E[Y|X = t]
RL = a*X + b;
plot(X,RL,X,eY,'-.')
grid
title('Regression line and Regression curve')
xlabel('X values')
ylabel('Y values')
legend('Regression line','Regression curve')
clear eY                   % To conserve memory
clear RL
disp('Calculate with X, Y, t, u, P, as in joint simple case')