slides_Ch2_W[1]

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

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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 &lt; 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 &lt; 0 we say that the OLS regression line overpredicts y , if ui ˆ i if uiOLS &gt; 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...
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