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Lecture30_HH_PPTX

# Lecture30_HH_PPTX - COMM 291 Applications of Statistics in...

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Click to edit Master subtitle style 5/10/10 Lecture 30 Section 201 M/W/F 10:00-11:00 COMM 291 Applications of Statistics in 1 1

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5/10/10 Examining Residuals for Groups Consider the following study of the Sugar content vs. the Calorie content of breakfast cereals: There is no obvious departure from the linearity assumption. 2 2
5/10/10 Examining Residuals for Groups The histogram of residuals looks fairly normal… …but the distribution shows signs of being a composite of three groups of cereal types. 3 3

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5/10/10 Examining Residuals for Groups 4 4 Examining the residuals of groups… …suggests factors other than sugar content that may be important in determining Calorie content. Puffing: replacing cereal with “air” lowers the Calorie content, even for high-sugar cereals Fat/oil: Fats add to the Calorie content, even for low-sugar cereals Puffed cereals (high air content per serving) Cereals with fruits and/or nuts (high fat/ oil content per serving) All others
5/10/10 Examining Residuals for Groups Conclusion: It may be better to report three regressions, one for puffed cereals, one for high-fat cereals, and one for all others. 5 5

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5/10/10 Extrapolation and Prediction Extrapolating – predicting a y value by extending the regression model to regions outside the range of the x -values of the data. 6 6
5/10/10 Extrapolation and Prediction Why is extrapolation dangerous? § It introduces the questionable and untested assumption that the relationship between x and y does not change. 7 7

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5/10/10 Extrapolation and Prediction Cautionary Example: Oil Prices in Constant Dollars 8 8 Actual Price Behavior Extrapolating the 1971-1982 model to the ’80s and ’90s lead to grossly erroneous forecasts.
5/10/10 Unusual and Extraordinary Observations In regression, an outlier can stand out in two ways. It can have… 1). a large residual: 2). a large distance from : 9 9 “High- leverage point” A high leverage point is influential if omitting it gives a regression model with a very different slope. x

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5/10/10 Unusual and Extraordinary Observations Tell whether the point is a high-leverage point, if it has a large residual, and if it is influential.
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