2. (40 pts.) Regression. The following function f is proposed to describe the given data. f(x) = a0*go(x) + a1*g1(x) + az*g2(x) + ... + an*gn(x) Given data i X y 0.9 1 0.1 2 0.7 3 0.4 n Xn In interpolation and regression, the basis function go(x) generates a column vector X50, g1(x) generates a column vector X , and so on. Given that the basis vectors are orthonormal, answer the following questions. Unless specified (as in Part h)), the basis functions g;(x) used to generate basis vectors X ] are arbitrary. If it helps you, you may think of sine functions or Bessel functions. a. (5 pts.) What are the coefficients aj for interpolation? What are the coefficients a; for regression? interpolation: y = ag*x + a,*X + . + *x n=10 - aj=? regression : y = ag*X*0> + a1*X + e m) = (ZiXi, j)/(n+1) = ? (a mathematical formula involving a;) c. (5 pts.) What is the variance of y in terms of the coefficient(s) a;? variance(y) = E;(y; ) = ? (a mathematical formula involving a;)<><>