Exercise 3

Consider the four points in this table.

1. Set up a linear system $A\xvec = \bvec$ that describes a quadratic function $$\beta_0+\beta_1x+\beta_2x^2 = y$$ passing through the points.

2. Use a $QR$ factorization to find the least-squares approximate solution $\xhat$ and plot the data and the graph of the resulting quadratic function.

3. What is your predicted $y$-value when $x=3.5$?

4. Find the coefficient of determination $R^2$.