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handout3.26 - ECO391 Lecture Handout Over 15.3 Spring 2003...

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ECO391 Lecture Handout Over 15.3 Spring 2003, G. Hoyt I. What is The Method of Least Squares(Ordinary Least Squares) A. Theory B. Formula C. Application II. Standard Error of the Estimate I. Ordinary Least Squares (OLS) (also called The Method of Least Squares) A. The Theory Ordinary least squares is a statistical technique that uses sample data to estimate the true population relationship between two variables. Recall that : 1) E(Y i X i ) = β o + β 1 X i is the population regression line 2) Y i(hat) = b o + b 1 X i is the sample regression equation OLS allows us to find = b o and b 1 . Consider the following scatter plot diagram the shows the actual, observed data points in a sample: Y X Many lines could fit through these data points. We want to determine the line with the "best fit."
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What does it mean to say a line fits the data the best? Recall that e i(hat) , the residual, represents the distance between the sample regression line and the observed data point, (X i ,Y i ). The line that minimizes the sum of these distances is the one that gives us the best fit. However, some of the values of the residuals are negative in sign while others are positive. If we sum the
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