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UT Knoxville STAT 201 - Chapter 08 Student 0115

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Slide 1Slide 2Getting the “Bends”Getting the “Bends” (cont.)Sifting Residuals for GroupsSifting Residuals for Groups (cont.)In Class ExampleRun Time vs. BudgetRun Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Run Time vs. Budget (Cont.)Slide 17Extrapolation: Reaching Beyond the DataExtrapolation (cont.)Extrapolation (cont.)A Critical Need for ExtrapolationQuestionable Extrapolation - ExampleQuestionable Extrapolation - Example (Cont.)Questionable Extrapolation - Example (Cont.)Questionable Extrapolation - Example (Cont.)Questionable Extrapolation - Example (Cont.)Questionable Extrapolation - Example (Cont.)Slide 28Outliers and Their ImpactOutliers and Their Impact (cont.)Outliers and Their Impact (cont.)Outliers and Their Impact (cont.)Outliers and Their Impact (cont.)Outliers and Their Impact (cont.)Outliers and Their Impact (cont.)Slide 36Causation RevisitedLurking Variables and Causation – Another ExampleLurking Variables and Causation – Another Example (Cont.)Lurking Variables and Causation – Another Example (Cont.)Slide 41Is the Linear Association We See Due to “Chance”?An Example of a Linear Relationship Due to “Chance”Two Spinners DataRelationship or Chance?Standard Regression OutputStandard Regression Output (Cont.)Correlation and Regression Connections1Chapter08 Presentation 0115Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 8Regression Wisdom2Chapter08 Presentation 0115Copyright © 2014, 2012, 2009 Pearson Education, Inc.8.1Examining ResidualsChapter08 Presentation 01153Copyright © 2014, 2012, 2009 Pearson Education, Inc.Getting the “Bends”An obvious curved relationship can be spotted in a scatterplot of the data.A more subtle curved relationship might be more obvious in a plot of the residuals.Chapter08 Presentation 01154Copyright © 2014, 2012, 2009 Pearson Education, Inc.Getting the “Bends” (cont.)For this example, the “bend” in the data is easier to see in the residuals plot than in the original scatterplot.So we are checking the conditions for doing regression after we have fit a regression line to the data. Aren’t we supposed to check the conditions before doing regression?Bad plotFailsChapter08 Presentation 01155Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sifting Residuals for GroupsIt is a good idea to look at both a histogram of the residuals and a scatterplot of the residuals vs. predicted values:The small modes in the histogram are marked with different colors and symbols in the residual plot above. What do you see?Chapter08 Presentation 01156Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sifting Residuals for Groups (cont.)An examination of residuals might lead us to discover groups of observations that are different from the rest.What should we do if we do discover that we have different groups represented in our analysis? Analyze separateChapter08 Presentation 01157Copyright © 2014, 2012, 2009 Pearson Education, Inc.In Class Example(From problem 21 of Chapter 8). Data have been collected regarding major release movies in 2005.In the file Ch08_Movie Dramas.jmp, we find several variables reported for 120 different movies.Let’s open this file and take a look at it. A portion of it is reproduced on the next page.Chapter08 Presentation 01158Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. BudgetIs there a relationship between Run Time (minutes) and Budget ($million)?What might you expect this relationship to look like?Chapter08 Presentation 01159Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Which variable should be y and which variable should be x? Why?Run time(x) and budget(mil$) (y)After making your decision above, what is the next thing we should do with these data?Chapter08 Presentation 011510Copyright © 2014, 2012, 2009 Pearson Education, Inc.Look at the scatter plot of the data. Does it look fairly linear? Not perfectly linear The movie with the longest run time looks unusual. In what way? Which movie is this?Outlier(King Kong) high run time but low Budget Which movie had the largest budget? Does it also have one of the longest run times?High budget low run time (Narnia) Run Time vs. Budget (Cont.)Chapter08 Presentation 011511Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)A regression analysis on the entire data set produced the following results:Predicted Budget($Millions)= y = ÙRun Time [minutes]()r2 =Chapter08 Presentation 011512Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Someone suggested that Dramas might be different from all other types of movies regarding the relationship between Run Time and Budget.To explore this theory, we will do two separate regression analyses: one for Dramas and one for all other types of movies.Chapter08 Presentation 011513Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Some regression results for Dramas:Predicted Budget($Millions)= y = ÙRun Time [minutes]()r2 =Some regression results for Non-Dramas:Predicted Budget($Millions)= y = ÙRun Time [minutes]()r2 =….Chapter08 Presentation 011514Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Drama = YESDrama = NODramaOtherChapter08 Presentation 011515Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Did doing separate analyses for Drama and Non-Drama improve the fit of the regression (compared to the original analysis)? If so, how do you know? Yes because of the R2 went up How are the two groups (Drama and Non-Drama) different? How are they the same? Had different R2. both had positive slopesChapter08 Presentation 011516Copyright © 2014, 2012, 2009 Pearson Education, Inc.Run Time vs. Budget (Cont.)Look back at the original data set. What relationships would you be interested in exploring?17Chapter08 Presentation 0115Copyright © 2014, 2012, 2009 Pearson Education, Inc.8.2Extrapolation:Reaching Beyond the DataChapter08 Presentation 011518Copyright © 2014, 2012, 2009 Pearson Education, Inc.Extrapolation: Reaching Beyond the DataLinear models give a predicted value for each case in the data.We cannot assume that a linear relationship in the data exists


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UT Knoxville STAT 201 - Chapter 08 Student 0115

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