slides_Ch2_W[1]

8 here is some terminology ols ols for each i yiols o

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: The Ordinary Least Squares Approach IV ˆˆ Observe that choosing βo , β1 corresponds to “…tting” a line through the data points f(xi , yi )g: the OLS approach …ts the line that minimizes the sum of the squared ˆ OLS and slope βOLS , ˆ deviations: it has intercept βo 1 we call this line the OLS regression line (2.23) or the OLS sample regression function b/c it is the OLS-based version of the population regression function (2.8). Here is some terminology: ˆ OLS ˆ OLS for each i , yiOLS ˆ βo + β1 xi is called the OLS …tted value of yi , for each i , uiOLS = yi yiOLS is called the i th OLS residual, b ˆ OLS < 0 we say that the OLS regression line overpredicts y , if ui ˆ i Melissa Tartari (Yale) Econometrics 33 / 93 The Ordinary Least Squares Approach IV ˆˆ Observe that choosing βo , β1 corresponds to “…tting” a line through the data points f(xi , yi )g: the OLS approach …ts the line that minimizes the sum of the squared ˆ OLS and slope βOLS , ˆ deviations: it has intercept βo 1 we call this line the OLS regression line (2.23) or the OLS sample regression function b/c it is the OLS-based version of the population regression function (2.8). Here is some terminology: ˆ OLS ˆ OLS for each i , yiOLS ˆ βo + β1 xi is called the OLS …tted value of yi , for each i , uiOLS = yi yiOLS is called the i th OLS residual, b ˆ OLS < 0 we say that the OLS regression line overpredicts y , if ui ˆ i if uiOLS > 0 we say that the OLS regression line underpredicts yi . ˆ Melissa Tartari (Yale) Econometrics 33 / 93 The Ordinary Least Squares Approach: Food for thought Let g be any function. Consider the following minimization problem: 1n 1n g (ui ) , min ˆ ∑ ∑ g yi ˆˆ ˆˆ ( βo , β1 ) n i =1 ( βo , β1 ) n i =1 min Melissa Tartari (Yale) Econometrics ˆ βo ˆ β1 xi (6) 34 / 93 The Ordinary Least Squares Approach: Food for thought Let g be any function. Consider the following minimization problem: 1n 1n g (ui ) , min ˆ ∑ ∑ g yi ˆˆ ˆˆ ( βo , β1 ) n i =1 ( βo , β1 ) n i =1 min ˆ βo ˆ β1 xi (6) We see that...
View Full Document

Ask a homework question - tutors are online