{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# spr02_1 - STA 6208 Spring 2002 Exam 1 Print Name SSN All...

This preview shows pages 1–2. Sign up to view the full content.

STA 6208 – Spring 2002 – Exam 1 Print Name: SSN: All questions are based on the following two regression models, where SIMPLE REGRESSION refers to the case where p = 1 , and X is of full column rank (no linear dependencies among the predictor variables) Model 1: Y i = β 0 + β 1 X i 1 + · · · + β p X ip + ε i i = 1 , . . . , n ε i NID (0 , σ 2 ) Model 2: Y = X β + ε X n × p β p × 1 ε N ( 0 , σ 2 I ) 1) For Model 1 : a) Write out the the least squares estimate ˆ β 1 as a linear function of Y i ( i = 1 , . . . , n ). b) Derive E [ ˆ β 1 ]. c) Derive V ar [ ˆ β 1 ]. 2) A foam beverage insulator (beer hugger) manufacturer produces their product for firms that want their logo on beer huggers for marketing purposes. The firm’s cost analyst wants to estimate their cost function. She interprets β 0 as the fixed cost of a production run, and β 1 as the unit variable cost (or marginal cost). Based on n = 5 production runs she observes the following pairs ( X i , Y i ) where X i is the number of beer huggers produced in the i th production run (in 1000 s ), and Y i was the total cost of the run (in \$1000).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern