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

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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 ,...,n ε i NID (0 2 ) Model 2: Y = X β + ε X n × p ± β p ± × 1 ε N ( 0 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 ,...,n ). b) Derive E [ ˆ β 1 ]. c) Derive Var [ ˆ β 1 ]. 2) A foam beverage insulator (beer hugger) manufacturer produces their product for ±rms that want their logo on beer huggers for marketing purposes. The ±rm’s cost analyst wants to estimate their cost function. She interprets β 0 as the ±xed 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).
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This note was uploaded on 07/28/2011 for the course STA 6208 taught by Professor Park during the Fall '08 term at University of Florida.

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

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