Yi yi ui bydefinition ui yi yi soeach yi

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: e true yi is the same as the sum of the fitted yi : n n i =1 i =1 ˆ ∑ yi = ∑ yi . ˆ o Thus, the mean of the true yi is the same as the mean of the fitted yi : ˆ yi = yi . (On average, you do not make any mistakes.) • The sample covariance between the regressor and the OLS residual is zero 1n ˆ ( n ∑ i =1 xi μi =0) This is the first order condition (2) • The OLS regression line always goes through the mean of the sample ( y , x ) , ˆˆ y = α + β x . Some comments: 9 ˆ 1. β is an estimate of how much Y (e.g., wage) is expected to change in response to one unit increase in X (e.g., year of schooling, what if X is ˆ measured in quarters, or months?). β is positive means that wage and education are positively correlated; the expected wage will increase given one more year of schooling. ˆ 2. β = 2.75 means that an additional year of schooling is predicted to increase hourly wage by 2.75 dollars (what if Y is logarithm of wage?). ˆ 3. α = an estimate of yi when xi = 0. But regression models give statistically meaningful estimates only near th...
View Full Document

This document was uploaded on 03/11/2014.

Ask a homework question - tutors are online