# 2.4-2.6 - 2.4 and 2.6 Regression diagnostics; residual...

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2.4 and 2.6 Regression diagnostics; residual plots Caution about correlation and regression Causation

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Residuals The vertical distances from the points in a scatter plot 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 signed distances are called “residuals.” residual = observed predicted =
Observed y Predicted ŷ

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Residual plots A residual plot is a scatter plot of the residuals against the explanatory variable. Residual plots help us assess the goodness of fit of a regression line.

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Points above the regression line have positive residuals and those below the line have negative residuals. The sum of all the residuals is equal to zero. If the residuals are scattered randomly around 0 without a distinctive pattern, chances are your data fit a line well.
Patterns to look for Curvature indicates that the relationship is not linear. Increasing or decreasing spread indicates that the prediction will be less accurate in the range of explanatory variables where the spread is larger. Outliers Influential observations.

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Residuals are randomly scattered—good! Curved pattern—means the relationship you are looking at is not linear. A change in variability across plot is a warning sign. You need to find out why it is, and remember that predictions made in areas of larger variability will not be as good.
r = 0.86, but this is misleading. The elephant is an influential point. Most

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## This note was uploaded on 09/04/2010 for the course STAT 131 taught by Professor Isber during the Spring '08 term at University of California, Berkeley.

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2.4-2.6 - 2.4 and 2.6 Regression diagnostics; residual...

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