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handout_2_4_fall11

handout_2_4_fall11 - Chapter 2.4 Cautions about Correlation...

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Chapter 2.4- Cautions about Correlation and Regression population→ error= y y ˆ sample→ residual= y y ˆ
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Residual Plots A residual plot is a scatterplot of the regression residuals against the explanatory variable. ●the mean of the residuals of a least-squares regression is always zero ●if regression line catches the overall pattern of the data (linear relationship), there should be no pattern in the residuals (irregular scatter- randomly distributed above and below zero) ●don’t have an irregular horizontal pattern in residual plot- this demonstrates regression line fails to capture overall pattern of relationship between y and x 2
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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 a 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. Lurking variables lurking variable - a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables Example private health spending and goods imported ( r = 0.97) 3
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