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Unformatted text preview: PSY 2801: Summer 2010 Linear Regression Jeff Jones University of Minnesota Jeff Jones Scatterplot Revisited + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +321 1 2 3321 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 Regression Vocabulary + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +321 1 2 3321 1 2 3 An Example Scatterplot Variable 1 Variable 2 1 Criterion : The variable we are trying to predict, which is usually on the yaxis. 2 Predictor : The variable used to predict the criterion, which is usually on the xaxis. 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 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 Error Visualized What do you notice about this picture? Jeff Jones Each Observation Observations about the observations: 1 The x i is each person’s observation on the xaxis. 2 The y i is each person’s observation on the yaxis. 3 The line accounts for part of the relation between a specific x i and a specific y i . 4 The unaccounted for stuff the distance from the line to the point, is called the error (or the residual). Jeff Jones Finding the Formula We have a generic equation for a line. What we need is a method to find what a (the intercept) and b (the slope) are for any sample of data The basic idea: If the average distance from the line to the points is small, then the line represents the points pretty well....
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This note was uploaded on 10/08/2010 for the course PSY 2801 taught by Professor Guyer during the Summer '08 term at Minnesota.
 Summer '08
 GUYER

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