STAT 501 Mid-Term Exam 2 Spring 2015

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STAT 501–Mid-Term Exam 2–Spring 2015–Due April 12Instructions: Use Word to type your answers within this document. Then, submit youranswers in the appropriate dropbox in ANGEL by the due date andwithin 3 hours ofdownloading the exam. The point distribution is located next to each question.1.(4x2=8points)State which of the following statements is TRUE and which isFALSE. For the statements that are false,explain why they are false.a.Removinganoutlier ina regressionanalysiswillresultin narrowerconfidence intervals.b.In a simple linear regression(SLR) model, ifalogtransformationisperformed on Xto remedysomenon-linearity, the mean value ofYis boundto change.c.In model selection, thehighestadjustedR2-value andthesmallest S-valuecriteria always yield the same "best" models.d.Regression models with different responses, but the samepredictorXmatrix,willhave the same leverage values.2.(3+3+4+4+3+3 = 20points)Open the “SalaryData.”The datasetconsistsof currentsalaries(Salaryin thousands of dollars)for63individuals withinformationabouttheiryears of work experience(YrsExp)andhighest degree attained(Degree).Yourgoalis tofit a regression model to express the dependenceofY (Salary)on X(YrsExp) and Degree.a.Clearly definea set ofindicator variablesthat could be used in a regressionmodelto represent the qualitative variableDegree.[Hint: Think carefullyabout the number of indicator variables needed given the number of levels ofDegreeand use “Bachelor” as the reference level.]b.Write apopulation multiple linear regression equationfor predicting thecurrent salary in terms ofYrsExpand Degree.Since education levelcouldimpact thedependence of Y on X,the model should containaninteractioneffect betweenYrsExpand Degree, together with their main effects.[Hint:Your equation should include Y, X,theindicator variablesyou defined in part(a),interaction terms,andpopulationregression coefficients (β’s).]c.Conduct a hypothesistestforwhethertheaverage annual salary increaseper year of experience differs bylevel of education (i.e., test iftheslopesfortwo or moreDegree categoriesdiffer).Write out the null and alternativehypotheses, the test statistic, the p-value, and the conclusion.[Minitab v17:SelectSalary as the Response, YrsExp as the Continuous predictor, Degreeas the categorical predictor,click “Model,” select both YrsExp and Degreetogether in the Predictors box and click the Add button next to “Interactionsthrough order 2.”Minitab v16: Create interaction terms using Calc >Calculator before fitting the regression model.]d.Writeanew population regression equationbased on your conclusion to part(c). Fit this model and conduct twoseparatehypothesis testsfor whetherthemean salaryfor a fixed number of years’ experience differsbyeducationlevel. For each test, write out the null and alternative hypotheses, the teststatistic, the p-value, and the conclusion.

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