# 61155 - Basic Estimation Techniques The relationships we...

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5.1 Basic Estimation Techniques The relationships we theoretically develop in the text can be estimated statistically using regression analysis, Regression analysis is a method used to determine the coefficients of a a functional relationship. For example, if demand is P = a+bQ We need to estimate a and b.

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5.2 Ordinary Least Squares(OLS) Means to determine regression equation that “best” fits data Goal is to select the line(proper intercept & slope) that minimizes the sum of the squared vertical deviations Minimize Σ e i 2 which is equivalent to minimizing Σ (Y i -(Y-hat) i ) 2
5.3 Standard Error of the Estimate Measures variability about the regression equation Labeled SEE If SEE = 0 all points are on line and fit is perfect ) 1 ( 2 - - Σ k n e i

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5.4 Standard Error of the Slope Measures theoretical variability in estimated slope - different datasets(samples) would yield different slopes = - = n i X X SEE SE 1 2 1 ) ( ) ( β
5.5 Variability in the Dependent Variable The sum of squares of Y about its mean value is representative of the total variation in Y 2 1 ) ( Y Y TSS n i i - = =

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5.6 Variability in the Dependent Variable The sum of squares of Y about the regression line(Y-hat) is representative of the “unexplained” or residual variation in Y = - = n i i Y Y RSS 1 2 ) ˆ (
5.7 Variability in the Dependent Variable The sum of squares of Y-hat about Y-bar is representative of the “explained” variation in Y = - = n i i Y Y ESS 1 2 ) ˆ (

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Variability in the Dependent Variable Note, TSS = ESS + RSS If all data points are on the regression line, RSS=0 and TSS=ESS If the regression line is horizontal, slope =
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61155 - Basic Estimation Techniques The relationships we...

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