EECS 2031 Midterm: EECS 2031 solution-to-midterm-sample

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 2031
• Professor: All

Document Summary

Solution:v ar(yi) = v ar( i) = 2 for i = 1, , n. b. (4 marks) suppose we have n = 2 observations in the observation vector y = (y1, y2) . Compute the variances of y and ay, where a = 1 0. 0 1 ! (2points), v ar(ay) = 2aa = 2 1 1. 1 2 !. (2points) c. (4 marks) given x = xnew, when the parameters 0, 1 and 2 are known, compute. Solution: e(ynew) = 0 + 1xnew (1point), ynew e(ynew) So 1 prediction interval would be e(ynew) z(1 /2) . (2points) N (0, 1). (1point) d. (4 marks) given x = xnew, when the parameters 0, 1 and 2 are unknown, compute. Solution: let 0 and 1 be least squares estimates of 0 and 1, respectively. The 1 prediction interval would be ynew t(1 /2; n 2)rm se(1 + 1 n + (xnew x)2.