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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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View Full DocumentWhat 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
residuals, positive values will cancel out negative values so the sum will not accurately reflect the total
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 Spring '08
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