Coding: Causality Generate a vector x = (1, 2, . .., 100). Suppose y and z are affected by a in the following way: y = 0.5 + 1.5 . x te, e~ N(0, 1) z = 0.2 + 0.4 . x +7, n ~ N(0, 0.5) Here N(u, o) means normal distribution with mean u and standard deviation o. (1) Simulate y and z. (2) Regress y with z. Is the coefficient significant? (3) Regress y with z and x. Are the coefficients significant? (4) Compare your results for (2) and (3), and explain shortly. (Provide code and display your results)