STAT 331 Midterm 1 solutions Winter 2015 - University of Waterloo STAT 331 Midterm I Term Winter Year 2015 Student Name(Print UW Student ID Number UW

# STAT 331 Midterm 1 solutions Winter 2015 - University of...

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University of Waterloo STAT 331: Midterm I Term: Winter Year: 2015 Student Name (Print): UW Student ID Number: UW Student Userid: Course Abbreviation and Number: STAT 331 Course Title: Applied Linear Models Section(s): 001 Sections Combined Course(s): SYDE 334 Section Numbers of Combined Course(s): 001 Instructor(s): Martin Lysy Date of Exam: Feb. 12, 2015 Time Period: Start time: 1:30pm End Time: 2:20pm Duration of Exam: 50 minutes Number of Exam Pages (incl. cover sheet): 6 Exam Type: Closed Book Additional Materials Allowed: Calculator Instructions: 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 work to receive full marks. You may tear off the formula sheet on the last page (page 6) . Marking Scheme: Question: 1 2 3 Total Points: 14 10 16 40 Score:
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 ifTt(23), we haveP(|T|> .06) =.95andP(|T|>2.07) =.05.(a) (6 pts) Calculateˆβ0andˆβ1, the MLEs ofβ0andβ1.