You estimate the polynomial regression model: b mK (x) b0 b1x b2x2 bp xp. You are interested in the

You estimate the polynomial regression model:

b mK (x) Æ b¯0 Å b¯1x Å b¯2x2 Å¢ ¢ ¢Å b¯p xp.

You are interested in the regression derivativem0(x) at x.

(a) Write out the estimator b m0 K (x) of m0(x).

(b) Is b m0 K (x) is a linear function of the coefficient estimates?

(c) Use Theorem 20.8 to obtain the asymptotic distribution of b m0 K (x).

(d) Show how to construct standard errors and confidence intervals for b m0 K (x).