%% Quiz 11 (Matlab)
%

%% Section 6.6, 8(a, b)

x=[4;6;8;10;12;14;16;18];
y=[1.58;2.08;2.5;2.8;3.1;3.4;3.8;4.32];

% We'll label the "design matrix" X:
X=[x, x.^2, x.^3];
B=inv(X'*X)*X'*y;

B

xx=linspace(min(x),max(x),200);
yy=B(1)*xx+B(2)*xx.^2+B(3)*xx.^3;

plot(x,y,'r^',xx,yy);

%% Section 6.6, 11

theta=[0.88;1.10;1.42;1.77;2.14];
r=[3;2.3;1.65;1.25;1.01];

% Model equation is r = beta + eccent * (r * cos(theta))
%  which is linear in beta and eccent:

X=[ones(length(theta),1),r.*cos(theta)];
B=inv(X'*X)*X'*r;

B

beta=B(1);
eccent=B(2);

%Solve for r if theta=4.6: 
theta=4.6;
R=beta/(1-eccent*cos(theta))