STAT 231 FALL 2007 MT2-sol

STAT 231 FALL 2007 MT2-sol - Stat231-Quiz 2 Version 1 Nov...

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Stat231-Quiz 2 Version 1 Nov 15, 2007, 4:45-5:45 Family (last) Name: Given (&rst) Name: Marks Awarded = ID: Marks Available: Circle the appropriate section number: Instructor Section Time Section Riley Metzger 10-11:20 1 Grace Chiu 11:30-12:50 4 Chris Springer 1-2:20 3 Riley Metzger 2:30-3:50 2 Aids: A non programmable calculator. Pages: There are a total of 10 pages on 5 sheets of paper. A Gaussian, t n and & 2 n table is located at the end of the midterm. Page Marks Available Marks Awarded 3 6 4 8 5 6 6 9 Total 29
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The Story A large random sample was collected in 2005 from the 50 states (i.e. excluding the only &district&, DC) of the USA. The data collected were ‘fuel consumption’ (thousands of gallons, y) and ‘number of licensed drivers’ (x). The Data Alabama 3,637,414 2,629,805 Alaska 486,582 299,484 Arizona 3,943,180 2,827,962 . . . . . . . . . Possibly Useful Numbers for w=log(x) and v=log(y): 50 X i & 1 log ( x i ) = 50 X i & 1 w i = 737 : 6 50 X i & 1 log ( y i ) = 50 X i & 1 v i = 719 : 7 50 X i & 1 w 2 i = 10930 : 0 50 X i & 1 v 2 i = 10406 : 6 50 X i & 1 w i v i = 10664 : 6 S wv = 50 X i & 1 ( w i & w ) ( v i & v ) = 47 : 5 S ww = 50 X i & 1 ( w i & w ) 2 = 47 : 6 S vv = 50 X i & 1 ( v i & v ) 2 = 48 : 3 Possibly Useful Numbers for x and y: 50 X i & 1 x i = 200 ; 218 ; 609 50 X i & 1 y i = 139 ; 847 ; 755 50 X i & 1 x 2 i = 1 : 7 ± 10 14 50 X i & 1 y 2 i = 8 : 1 ± 10 14 S xy = 50 X i & 1 ( x i & x ) ( y i & y ) = 6 : 0 ± 10 14 S xx = 50 X i & 1 ( x i & x ) 2 = 8 : 7 ± 10 14 S yy = 50 X i & 1 ( y i & y ) 2 = 4 : 2 ± 10 14
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Model 1 log ( Y ) = & 1 + ± 1 log ( x ) + R where R & G (0 1 ) which we may write as V = & 1 + ± 1 w + R where R & G (0 1 ) Estimates b & 1 = v ± b ± 1 w = ± 0 : 329 b ±
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STAT 231 FALL 2007 MT2-sol - Stat231-Quiz 2 Version 1 Nov...

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