X = [2 4 6 7 10 11 14 17 20];
Y = [4 5 6 5 8 8 6 9 12];
a1_1 = X(:)\Y(:) % Using ‘mldivide,\’
You may want to check your calculations and derivation, since I get a different result from taking the first (partial) derivative of:
S = sum((Y - a1*X)^2)
with respect to ‘a1’, then setting it to zero and solving for ‘a1’:
a1_2 = sum(X.*Y)/sum(X.^2) % Using Computed Least Squares
My derivation result agrees with the mldivide result.
Plotting:
figure(1)
plot(X, Y, 'pg')
hold on
plot(X, a1_1*X, '-r')
hold off
grid
text(7, 11, sprintf('Y = %.3f\\cdotX', a1_1))
text(7, 13, sprintf('Y = %.3f\\cdotX', a1_2))
