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Introduction to regression
ESM 206
Jan 11, 2007
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View Full Document Some questions about eutrophication
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Phosphorus
Chlorophyll A
•
If I reduce the phosphorus
concentration by 100 units, how
much should that reduce the
chlorophylla concentration?
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How certain is my answer to the
previous question?
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If I go to a new lake and find that it
has a phosphorus concentration of
150 units, what is the most likely
chlorophylla concentration?
What
is the range of likely concentrations?
A linear model of the data
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View Full Document A linear model of the data
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“Regress Y on X”
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Regression line should “go through the data”
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For any X, the most likely value of Y should be on the line
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For any X, the expected value of the residual should be zero
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The intercept (
β
0
) is the expected value of Y when X is zero
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The slope (
β
1
) is the amount that, all else being equal, Y changes in
response to a unit change in X
Ordinary Least Squares (OLS) Regression
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Also called
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“Classical Linear Regression Model” (CLRM) [economics]
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“Linear regression” [biology]
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Find the intercept and slope parameters such that the
sum of
squared residuals
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This note was uploaded on 08/06/2008 for the course ESM 206 taught by Professor Kendall,berkley during the Spring '08 term at UCSB.
 Spring '08
 KENDALL,BERKLEY
 Environmental Science

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