ECON 257D2 Lecture Notes - Lecture 6: Regression Analysis, Round-Off Error, Analysis Of Variance

• School: McGill University
• Department: Economics
• Course: ECON 257D2
• Professor: Victoria Zinde- Walsh

Document Summary

Part 2: inference in the simple linear regression model. Properties and the distribution of the ols estimators. ^(cid:12)0 = (cid:22)y (cid:0) ^(cid:12)1 (cid:6)yixi (cid:0) n (cid:22)y (cid:22)x. ^(cid:12)1 = i (cid:0) n (cid:22)x 2 (cid:6)x 2 and write (cid:6)yi(xi (cid:0) (cid:22)x) (cid:6)(xi (cid:0) (cid:22)x)2. = (cid:6)wiyi with wi = xi(cid:0) (cid:22)x (cid:6)(xi(cid:0) (cid:22)x)2 : coe cients. (show for ^(cid:12)0; too). The estimators are linear functions of the random yi with non-random. Properties of the weights: a. (cid:6)wi = 0; b. (cid:6)wixi = 1: (cid:6)w2. Proof. (cid:6)(xi(cid:0) (cid:22)x: (cid:6)wi = (cid:6) xi(cid:0) (cid:22)x (cid:6)(xi(cid:0) (cid:22)x)2 = 0; (cid:6)(xi(cid:0) (cid:22)x)2 = i (cid:0) (cid:22)x(cid:6)xi, (cid:6)wixi = (cid:6)(xi(cid:0) (cid:22)x)xi (cid:6)(xi(cid:0) (cid:22)x)2 = (cid:6)x 2 (cid:6)(xi(cid:0) (cid:22)x)2 = since (cid:6)(cid:0)xi (cid:0) (cid:22)x(cid:1)2, (cid:6)w2 i = (cid:6) 1 (cid:6)(xi(cid:0) (cid:22)x)2 : (cid:6)(xi(cid:0) (cid:22)x)2 (cid:6)(xi(cid:0) (cid:22)x)2 = 1 i (cid:0) 2(cid:6)xi (cid:22)x + n (cid:22)x 2 = (cid:6)x 2 i (cid:0) (cid:6)xi (cid:22)x: E ^(cid:12)1 = (cid:6)wieyi = (cid:6)wi((cid:12)0 + (cid:12)1xi) = (cid:12)0(cid:6)!i + (cid:12)1(cid:6)wixi: