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Regression

# Regression - PSY 2801 Summer 2010 Linear Regression Je...

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PSY 2801: Summer 2010 Linear Regression Jeff Jones University of Minnesota Jeff Jones

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Scatterplot Revisited + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 An Example Scatterplot Variable 1 Variable 2 1 The linear measure of association The typical increase in y for an increase in x 2 The scatter Are the points close to the line or far away from the line? Even though we can tell the average change, does that say much about most people? Jeff Jones
Correlation versus Regression Before, we concentrated on the scatter of the points -- the shape of an oval surounding the points. Now, we want to concentrate on the best fit line -- the typical increase in y for an increase in x. How could we describe the best fit line? Jeff Jones

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Regression Vocabulary + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 An Example Scatterplot Variable 1 Variable 2 1 Criterion : The variable we are trying to predict, which is usually on the y-axis. 2 Predictor : The variable used to predict the criterion, which is usually on the x-axis. 3 The Slope : The steepness of the line. 4 The Intercept : The predicted value of the criterion when the predictor is at 0. Jeff Jones
Regression Terminology When we are running a regression, we say: “We regress the criterion (the y variable) on the predictor (the x variable).” This tends to be a point of confusion - most people think the x variable should be first, but it isn’t. Jeff Jones

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Regression Equations A regression equation must be similar to an equation for a line, since that is our ultimate objective: y i = a + bx i + error i Where i indicates person . Furthermore, no matter how we construct the line (the a + bx i portion), most people will not lie directly on that line. Jeff Jones