SimpleRegression08B - posted

SimpleRegression08B - posted - Introduction to regression...

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Introduction to regression ESM 206 Jan 11, 2007
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Some questions about eutrophication 0 20 40 60 80 100 120 140 160 180 0 100 200 300 400 500 600 700 Phosphorus Chlorophyll A If I reduce the phosphorus concentration by 100 units, how much should that reduce the chlorophyll-a concentration? How certain is my answer to the previous question? If I go to a new lake and find that it has a phosphorus concentration of 150 units, what is the most likely chlorophyll-a concentration? What is the range of likely concentrations?
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A linear model of the data
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A linear model of the data “Regress Y on X” Regression line should “go through the data” For any X, the most likely value of Y should be on the line For any X, the expected value of the residual should be zero The intercept ( β 0 ) is the expected value of Y when X is zero The slope ( β 1 ) is the amount that, all else being equal, Y changes in response to a unit change in X
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Ordinary Least Squares (OLS) Regression Also called “Classical Linear Regression Model” (CLRM) [economics] “Linear regression” [biology] 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.

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SimpleRegression08B - posted - Introduction to regression...

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