Suppose that we have a single input variable X and an output variable Y. To predict Y, consider a piecewise polynomial model with quadratic order. Also, suppose that this model has two knots = 5 and ₂ = 10.
(1) How many free parameters does this model require? Justify your answer.
(2) Specify the model for a region 5 < X < 10. You should represent it as a quadratic equation (i.e., find a, b, c in Ya+bx+cX²).
(3) Suppose that we have 3 observations of X. ( 12. 22, 36). Construct
the input matrix X.