PRESS Assesses your model's predictive ability. In general, the smaller the prediction sum of squares (PRESS) value, the better the model's predictive ability. PRESS is used to calculate the predicted R2. PRESS, similar to the error sum of squares (SSE), is the sum of squares of the prediction error. PRESS differs from SSE in that each fitted value, i, for PRESS is obtained by deleting the ith observation from the data set, estimating the regression equation from the remaining n - 1 observations, then using the fitted regression function to obtain the predicted value for the ith observation.Predicted R2 Similar to R2. Predicted R2 indicates how well the model predicts responses for new observations, whereas R2 indicates how well the model fits your data. Predicted R2 can prevent overfitting the model and is more useful than adjusted R2 for comparing models because it is calculated with observations not included in model calculation. Predicted R2 is between 0 and 1 and is calculated from the PRESS statistic. Larger values of predicted R2 suggest models of greater predictive ability.252x0541 4/22/05 ECO252 QBA2Final EXAMMay 4, 2005Name and Class hour:_________________________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 inthe data set are:Name The make and modelSUV ‘Yes’ if it’s an SUV, ‘No’ if not. Drive Type All wheel, front wheel, rear wheel or four wheel.Horsepower An independent variableFuel Type Premium or regularMPG The dependent variableLength In inches – an independent variableWidth In inches – an independent variable Weight In pounds – an independent variableCargo Volume Square feet – an independent variableTurning 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 zeroSUVwt An interaction variable, the product of ‘SUV_D’ and ‘Weight’SUVtc An interaction variable, the product of ‘SUV_D’ and ‘Turning Circle’HPsqAWD_DA dummy variable based on ‘Drive Type’, 1 for all wheel drive, otherwise zeroFWD_D A dummy variable based on ‘Drive Type’, 1 for front wheel drive, otherwise zeroRWD_D A dummy variable based on ‘Drive Type’, 1 for rear wheel drive, otherwise zeroSUV_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.MTWMTB > 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 ,es,2R1252x0541 4/22/05 2R and the pC 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: 0.15Response is MPG on 14 predictors, with N = 119N(cases with missing observations) = 2 N(all cases) = 121Step 1 2 3 4 5 6Constant 38.31 36.75 41.59 50.06 50.15 59.00Weight -0.00491 -0.00436 -0.00578 -0.00495 -0.00424 -0.00339T-Value -15.34 -11.87 -12.82 -9.31 -6.74 -5.61P-Value 0.000 0.000 0.000 0.000 0.000 0.000SUV_D -1.72 -33.71 -35.29 -35.12 -18.68T-Value -2.84 -4.99 -5.36 -5.40 -2.71P-Value 0.005 0.000 0.000 0.000 0.008SUV_L 0.180 0.185 0.182 0.088T-Value 4.75 5.04 5.01 2.26P-Value 0.000 0.000 0.000 0.026Turning Circle -0.285 -0.292 -0.255T-Value -2.79 -2.90 -2.75P-Value 0.006 0.004 0.007Horsepower -0.0124 -0.1619T-Value -2.01 -5.04P-Value 0.046 0.000HPsq 0.00040T-Value 4.73P-Value 0.000S 2.50 2.43 2.23 2.17 2.14 1.96R-Sq 66.78 68.94 74.04 75.70 76.55 80.45R-Sq(adj) 66.50 68.40 73.36 74.85 75.51 79.41Mallows C-p 71.5 61.4 34.8 27.4 24.7 4.8More? (Yes, No, Subcommand, or Help)SUBC> yI’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 2252x0541 4/22/05 Step 7Constant 58.50Weight -0.00342T-Value -5.74P-Value 0.000SUV_D -19.0T-Value -2.79P-Value 0.006SUV_L 0.090T-Value 2.36P-Value 0.020Turning Circle -0.210T-Value -2.24P-Value 0.027Horsepower -0.175T-Value -5.43P-Value 0.000HPsq 0.00042T-Value 5.03P-Value 0.000Fuel_D 0.92T-Value 2.11P-Value 0.037S 1.93R-Sq 81.21R-Sq(adj) 80.02Mallows C-p 2.5More? (Yes, No, Subcommand, or Help)SUBC> yNo variables entered or removedMore? (Yes, No, Subcommand, or Help)SUBC> nBecause I was worried about Collinearity, I
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