Chapter 8 Regression Wisdom Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 1 8 1 Examining Residuals Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 2 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 0117 Copyright 2014 2012 2009 Pearson Education Inc 3 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 Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 4 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 0117 Copyright 2014 2012 2009 Pearson Education Inc 5 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 Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 6 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 0117 Copyright 2014 2012 2009 Pearson Education Inc 7 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 0117 Copyright 2014 2012 2009 Pearson Education Inc 8 Run Time vs Budget Cont Which variable should be y and which variable should be x Why After making your decision above what is the next thing we should do with these data Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 9 Run Time vs Budget Cont Look at the scatter plot of the data Does it look fairly linear The movie with the longest run time looks unusual In what way Which movie is this Which movie had the largest budget Does it also have one of the longest run times Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 10 Run Time vs Budget Cont A regression analysis on the entire data set produced the following results Predicted Budget y Millions Run Time minutes r2 Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 11 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 0117 Copyright 2014 2012 2009 Pearson Education Inc 12 Run Time vs Budget Cont Some regression results for Dramas Predicted Budget y Millions Run Time minutes r2 Some regression results for Non Dramas Predicted Budget y Millions Run Time minutes r2 Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 13 Run Time vs Budget Cont Drama YES Drama NO Other Drama Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 14 Run Time vs Budget Cont Did doing separate analyses for Drama and NonDrama improve the fit of the regression compared to the original analysis If so how do you know How are the two groups Drama and Non Drama different How are they the same Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 15 Run Time vs Budget Cont Look back at the original data set What relationships would you be interested in exploring Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 16 8 2 Extrapolation Reaching Beyond the Data Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 17 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 beyond the range of the data Once we venture into new x territory such a prediction is called an extrapolation Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 18 Extrapolation cont Extrapolations can be inaccurate because they require the additional and many times questionable assumption that nothing about the relationship between x and y changes even at extreme values of x Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 19 Extrapolation cont Here is a timeplot of the Energy Information Administration EIA predictions and actual prices Neither forecast predicted the sharp run up in oil prices in the past few years Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 20 A Critical Need for Extrapolation Extrapolation can be dangerous but in most fields of study it is done regularly Regression Extrapolation and Forecasting Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 21 Questionable Extrapolation Example The file Ch08 Attendance 2006 xls contains the number of wins and the average home game attendance by the 14 American League baseball teams in 2006 Can the number of wins in a season be used to estimate the average home game attendance for an American League team Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 22 Questionable Extrapolation Example Cont Avg Home Attendance Avg Home Attendance vs Total Wins 55000 50000 45000 40000 35000 30000 25000 20000 15000 10000 60 65 70 75 80 85 90 95 100 Total Wins Does the scatterplot pass the Straight Enough Condition Does it pass the Outlier Condition Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 23 Questionable Extrapolation Example Cont Chapter08 Presentation 0117 Copyright 2014 2012 2009 Pearson Education Inc 24 Questionable Extrapolation Example Cont Does the residual plot pass the Does the Plot Thicken Condition What implication do you think this has regarding making predictions of average home game attendance for
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