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University of WaterlooSTAT 331: Midterm ITerm: WinterYear: 2015Student Name (Print):UW Student ID Number:UW Student Userid:Course Abbreviation and Number:STAT 331Course Title:Applied Linear ModelsSection(s):001Sections Combined Course(s):SYDE 334Section Numbers of Combined Course(s):001Instructor(s):Martin LysyDate of Exam:Feb. 12, 2015Time Period:Start time:1:30pmEnd Time:2:20pmDuration of Exam:50 minutesNumber of Exam Pages (incl. cover sheet):6Exam Type:Closed BookAdditional Materials Allowed:CalculatorInstructions:♣Read all questions before you start.♣Not all questions and parts are equally difficult.♣The exam is single-sided.Use the backs of pages if you need extra space.♣Show all your workto receive full marks.♣You may tear offthe formula sheet on the last page (page 6).Marking Scheme:Question:123TotalPoints:14101640Score:
Question 1. (14 pts)Consider the simple linear regression modelyi|xiind∼ N(β0+β1xi, σ2),i= 1, . . . , n.Suppose thatn= 25,Sxx= 9,nsummationdisplayi=1x2i= 9,¯y= 2.2,Sxy=-38.7.Moreover, suppose that ifT∼t(23), we haveP(|T|> .06) =.95andP(|T|>2.07) =.05.(a) (6 pts) Calculateˆβ0andˆβ1, the MLEs ofβ0andβ1.