252x0541 4 22 05 hour ECO252 QBA2 Final EXAM May 4 2005 Name and Class I 25 points Do all the following Note that answers without reasons receive no credit Most answers require a statistical test that is stating or implying a hypothesis and showing why it is true or false by citing a table value or a p value If you haven t done it lately take a fast look at ECO 252 Things That You Should Never Do on a Statistics Exam or Anywhere Else The next 12 pages contain computer output This comes from a data set on the text CD ROM called Auto2002 There are 121 observations The dependent variable is MPG miles per gallon The columns in the data set are Name The make and model SUV Yes if it s an SUV No if not Drive Type All wheel front wheel rear wheel or four wheel Horsepower An independent variable Fuel Type Premium or regular MPG The dependent variable Length In inches an independent variable Width In inches an independent variable Weight In pounds an independent variable Cargo Volume Square feet an independent variable Turning Circle Feet an independent variable I added the following SUV D A dummy variable based on SUV 1 for an SUV otherwise zero Fuel D A dummy variable based on Fuel Type 1 for a Premium fuel otherwise zero SUVwt An interaction variable the product of SUV D and Weight SUVtc An interaction variable the product of SUV D and Turning Circle HPsq AWD DA dummy variable based on Drive Type 1 for all wheel drive otherwise zero FWD D A dummy variable based on Drive Type 1 for front wheel drive otherwise zero RWD D A dummy variable based on Drive Type 1 for rear wheel drive otherwise zero SUV L An interaction variable the product of SUV D and Length Questions are included with the regressions and thus cannot be in order of difficulty It s probably a good idea to look over the questions and explanations before you do anything 4 28 2005 6 18 32 PM Welcome to Minitab press F1 for help Results for 252x0504 4 MTW MTB Stepwise MPG Horsepower Length Width Weight Cargo Volume CONT Turning Circle SUV D Fuel D SUVwt HPsq AWD D CONT FWD D RWD D SUV L SUBC AEnter 0 15 SUBC ARemove 0 15 SUBC Best 0 SUBC Constant Because I had relatively little idea of what to do I ran a stepwise regression You probably have not seen one of these before but they are relatively easy to read Note that it dropped 2 observations so that the results will not be quite the same as I got later The first numbered column represents the single independent variable that seems to have the most explanatory effect on MPG The equation reads MPG 38 31 15 34 Weight The fact that Weight entered first with a negative coefficient should surprise no one At the bottom appears s e R 2 1 252x0541 4 22 05 R 2 and the C p statistic mentioned in your text The value of the t ratio and its p value appear below the coefficient Stepwise Regression MPG versus Horsepower Length Alpha to Enter 0 15 Alpha to Remove 0 15 Response is MPG on 14 predictors with N 119 N cases with missing observations 2 N all cases 121 Step Constant Weight T Value P Value 1 38 31 2 36 75 3 41 59 4 50 06 5 50 15 6 59 00 0 00491 15 34 0 000 0 00436 11 87 0 000 0 00578 12 82 0 000 0 00495 9 31 0 000 0 00424 6 74 0 000 0 00339 5 61 0 000 1 72 2 84 0 005 33 71 4 99 0 000 35 29 5 36 0 000 35 12 5 40 0 000 18 68 2 71 0 008 0 180 4 75 0 000 0 185 5 04 0 000 0 182 5 01 0 000 0 088 2 26 0 026 0 285 2 79 0 006 0 292 2 90 0 004 0 255 2 75 0 007 0 0124 2 01 0 046 0 1619 5 04 0 000 SUV D T Value P Value SUV L T Value P Value Turning Circle T Value P Value Horsepower T Value P Value HPsq T Value P Value S R Sq R Sq adj Mallows C p 0 00040 4 73 0 000 2 50 66 78 66 50 71 5 2 43 68 94 68 40 61 4 2 23 74 04 73 36 34 8 2 17 75 70 74 85 27 4 2 14 76 55 75 51 24 7 1 96 80 45 79 41 4 8 More Yes No Subcommand or Help SUBC y I m greedy so while I was surprised that Minitab had found six explanatory independent variables that actually seemed to affect miles per gallon I wanted more For the first time ever for me Minitab found another variable 2 252x0541 4 22 05 Step Constant 7 58 50 Weight T Value P Value 0 00342 5 74 0 000 SUV D T Value P Value 19 0 2 79 0 006 SUV L T Value P Value 0 090 2 36 0 020 Turning Circle T Value P Value 0 210 2 24 0 027 Horsepower T Value P Value 0 175 5 43 0 000 HPsq T Value P Value 0 00042 5 03 0 000 Fuel D T Value P Value 0 92 2 11 0 037 S R Sq R Sq adj Mallows C p 1 93 81 21 80 02 2 5 More Yes No Subcommand or Help SUBC y No variables entered or removed More Yes No Subcommand or Help SUBC n Because I was worried about Collinearity I had the computer do a table of correlations between all the independent variables The table is triangular since the correlation between say Length and Horsepower is going to be the same as the correlation between Horsepower and Length So for example the correlation between Horsepower and Length is 648 and the p value of zero below it evaluates the null hypothesis that the correlation is insignificant The explanation of Predicted R2 that appears below the correlation table was a new one on me but could help you in comparing the regressions 3 252x0541 4 22 05 MTB Correlation Horsepower Length Width Weight Cargo Volume CONT Turning Circle SUV D Fuel D SUVwt SUVtc HPsq AWD D CONT FWD D RWD D SUV L Correlations Horsepower Length Width Weight Cargo Volume Horsepower 0 648 0 000 Length Width 0 660 0 000 0 825 0 000 Weight 0 673 0 000 0 634 0 000 0 780 0 000 Cargo Volume 0 296 0 001 0 395 0 000 0 546 0 000 0 716 0 000 Turning Circ 0 497 0 000 0 750 0 000 0 658 0 000 0 650 0 000 SUV D 0 160 0 080 0 102 0 265 0 180 0 049 0 535 0 000 Fuel …
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