Exercise 2

Suppose we would like to find the best quadratic function $$\beta_0 + \beta_1x + \beta_2x^2=y$$ fitting the points $$(0,1), (1,0), (2,1.5), (3,4), (4,8).$$

1. Set up a linear system $A\xvec = \bvec$ describing the coefficients $\xvec = \threevec{\beta_0}{\beta_1}{\beta_2}$.

2. Find the singular value decomposition of $A$.

3. Use the singular value decomposition to find the least-squares approximate solution $\xhat$.