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Quiz 1 Econ140A Winter2014 Sketched out answers

Quiz 1 Econ140A Winter2014 Sketched out answers - Economics...

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Economics 140A Winter 2014 Sketched Out Answers for Quiz 1 Note that not all the details are shown here. The sketches here are just to point you in the right direction. A good exam answer would have more details. Question: Let: X ~ N(0,4) Y = 2 – 5X (a) Find 𝐸𝐸 ( 𝑌𝑌 ) . 𝐸𝐸 ( 𝑌𝑌 ) = 𝐸𝐸 (2 5 𝑋𝑋 ) = 𝐸𝐸 (2) + 𝐸𝐸 ( 5 𝑋𝑋 ) = 2 5 𝐸𝐸 ( 𝑋𝑋 ) = 2 (5 0) = 2 (b) Find 𝑉𝑉𝑉𝑉𝑉𝑉 ( 𝑌𝑌 ) . 𝑉𝑉𝑉𝑉𝑉𝑉 ( 𝑌𝑌 ) = 𝑉𝑉𝑉𝑉𝑉𝑉 (2 5 𝑋𝑋 ) = 𝑉𝑉𝑉𝑉𝑉𝑉 ( 5 𝑋𝑋 ) = ( 5) 2 ∗ 𝑉𝑉𝑉𝑉𝑉𝑉 ( 𝑋𝑋 ) = 25 4 = 100 (c) Find 𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉 ( 𝑋𝑋 , 𝑌𝑌 ) . 𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉 ( 𝑋𝑋 , 𝑌𝑌 ) = cov( 𝑋𝑋 , 𝑌𝑌 ) var( 𝑋𝑋 ) var( 𝑌𝑌 ) What is 𝑐𝑐𝐶𝐶𝑐𝑐 ( 𝑋𝑋 , 𝑌𝑌 )? 𝑐𝑐𝐶𝐶𝑐𝑐 ( 𝑋𝑋 , 𝑌𝑌 ) = 𝑐𝑐𝐶𝐶𝑐𝑐 ( 𝑋𝑋 , 2 5 𝑋𝑋 ) = 𝑐𝑐𝐶𝐶𝑐𝑐 ( 𝑋𝑋 , 5 𝑋𝑋 ) = (1)( 5) 𝑐𝑐𝐶𝐶𝑐𝑐 ( 𝑋𝑋 , 𝑋𝑋 ) = 5 ∗ 𝑐𝑐𝑉𝑉𝑉𝑉 ( 𝑋𝑋 ) = 5 4 = 20 So 𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉 ( 𝑋𝑋 , 𝑌𝑌 ) = 20 4 100 = 20 20 = 1 Question: You work for a health insurance company, and have been asked to model the number of doctor visits elderly (65+) clients make in a year. The dataset you have is large, with 4406 elderly clients in it. Your co-worker has already started using the dataset you’ve been given and shows you the following (incomplete) table of regression results:
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page 2 a. Having one more chronic condition increases the number of doctor visits a client makes each year by 1.32, holding everything else constant.
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