Lecture+1+Review+SLR

Somecomments 9 1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ges when X increases by one unit. Quiz: Y= real hourly wage (in dollars), X=years of schooling yi 10 14 21 xi 12 14 16 Assume the population model is Y = α + β X + u 1. Calculate y , x , yi − y , xi − x y = 15, x = 14 yi − y 1 y1 − y = ‐5 2 y2 − y = ‐1 3 y3 − y = 6 Sum: 0 mean: 0 i xi − x x1 − x =‐2 x2 − x =0 x3 − x =2 0 0 2. Calculate the sample variance of X and the sample covariance between X and Y 3 ∑ (x − x ) i =1 i 2 = (−2) 2 + (0) 2 + (2) 2 = 8 8 3 ∑ ( x − x )( y i =1 i i − y ) = (−2)(−5) + (0)( −1) + (2)(6) = 22 ˆˆ 3. Calculate the OLS estimates of α and β : α , β ˆ β= 22 ˆ = 2.75,α = 15 − 2.75 *14 = −23.5 8 4. Fill out the following table ˆ μ ˆ y1 − y1 = 0.5 ˆ y2 − y2 = ‐1 ˆ y3 − y3 = 0.5 0 0 ˆ yi i ˆ y1 = 9.5 2 ˆ y2 = 15 3 ˆ y3 = 20.5 Sum: 45 mean: 15 1 ˆ xi μ i ˆ ui2 ˆ x1μ 1 = ‐6 ˆ x2 μ2 = ‐14 ˆ x3 μ3 = 8 0 0 Algebraic Properties of OLS estimates: n ˆ • The sum of OLS residuals is zero, ∑ ui = 0. i =1 This is the first order condition (1) ˆ o Thus, the sum of th...
View Full Document

This document was uploaded on 03/11/2014.

Ask a homework question - tutors are online