lecture_2_4,6 - Looking at data relationships Caution about...

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    Looking at data: relationships Caution about correlation and regression The question of causation IPS chapters 2.4 and 2.6 © 2006 W. H. Freeman and Company
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Objectives (IPS chapters 2.4 and 2.5) Caution about correlation and regression The question of causation Residuals Outliers and influential points Lurking variables Association and causation
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The distances from each point to the least-squares regression line give us potentially useful information about the contribution of individual data points to the overall pattern of scatter. These distances are called “residuals.” The sum of these residuals is always 0. Observed y Predicted ŷ residual ) ˆ ( dist. = - y y Residuals Points above the line have a positive residual. Points below the line have a negative residual.
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Residuals are the distances between y -observed and y -predicted. We plot them in a residual plot. If residuals are scattered randomly around 0, chances are your data fit a linear model and you didn’t have outliers. Residual plots
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The x -axis in a residual plot is the same as on the scatterplot. The line on both plots is the regression line. Only the y -axis is different.
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Residuals are randomly scattered—good! Curved pattern—means the relationship you are looking at is not linear.
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