STAT 501 � Final Exam � Spring 2015

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1STAT501–Final Exam–Spring 20151)(5x2 =10points)State which of the following statements are true and which are false. Forthe statements that are false,explain why they are false.a)In a logistic regression analysis whereY=1represents survival andY=0represents death,the logit of the survival probability is the negative of the logit of death probability.b)In regression analysis, the method ofordinaryleast squares can be used in the presenceof non-normal errors.c)In multiple linear regression analysis, thewidth of aprediction intervalfora futureresponse ofYbased on a single predictorXincreaseswiththe value ofX.d)The error terms in anAR(1) modelhavezero mean.e)In model selection, theMSE(orS) criterion minimizes confidence/prediction intervalwidths, while thePRESScriterion evaluates model unbiasedness.2)(7x2 =14 points)Fill in the blanks withtermsfrom the list:non-normality, multicollinearity,heteroscadasticity,confidenceintervals, predictionintervals.[Note: there are 7 blanks butonly 5terms, so you’ll have to use some terms more than onceand there may be someterms you don’t use at all.]a)A small p-valueforthe Ryan-Joiner test indicatesnon-normality.b)A residual vs.fits plot with a non-random pattern aroundahorizontal lineatzeroindicatesheteroscedasticity.c)A large sample size ensures the validity of a confidence intervalfora mean responseeven when errorsexhibitnon-normalityd)Multicollinearityamong predictors will lead tounreliableconfidence intervalsforregression coefficients.e)Weighted least squares estimation can be used in the presence of errorheteroscadasticityandnon-normality.3)(4x3= 12points)The following ANOVA table is abstracted from a regressionfit tothemodel:Y=β0+β1X1+β2X2+β3X3+ … +β10X10+ε.SourceDFSSRegression10110.53ResidualError2839.47Total38150

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2SourceDFSeq SSX110.10X2140X311.0X4155X512.5X610.08X716.5X814.0X910.4X1010.95a)Calculate the three missing values in the upper table.b)Forthe10-predictormodel,perform a hypothesis test at significance level 0.05 todetermine whether predictorsX7,X8,X9,andX10are significantly linearly related to Yupon controlling for the remaining predictorsX1-X6usinga general linearFtest. Writethe null and alternative hypotheses, the value of the test statistic, the decision rule, andthe conclusion.[Note: an F-distribution table is provided on the last page of the exam.]c)Later it was decided to consider a regression ofY on thefirst 4 predictors ONLY. Useinformation from both tablesaboveto calculate adjusted R2for the model with only thefirst 4 predictors.d)Given the information in both tablesabove, is it possible to test whetherX1andX3canbe dropped from the 4-predictor model? Give a brief argument supporting your answer.[You do not have to do a test, even if one is possible.]4)(4+9+4+4 = 21points)Data from alocal supermarketrevealed thatthedeli usageofcustomersdepends ontheirgrocery billand also on the time of shopping. To understandthe link between these variables,a logistic regression model was fittedbased ondata from890 sales records,which yielded the following.SourceDFAdjDevAdj MeanChi-SquareP-ValueRegression217.5328.766017.530.000bill110.82410.824110.820.001lunch15.5495.54895.550.018Error887534.2900.6024Total889551.822OddsRatio95%CIBill1.0760(1.0305,1.1236)OddsRatioforlunch=1relative to lunch=0

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