mid-term - STAT3503 A Last Name First Name Midterm Student...

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STAT3503 A Midterm June 25, 2009 Last Name First Name Student Number Nonprogrammable calculators are allowed. Total Mark=50 Question 1 . Infestation of crops by insects has long been of great concern to farmers and agri- cultural scientists. The article ”Cotton Square Damage by the Plant Bug” reports data on x = age of cotton plant(days) and y = % damaged squares. Consider the accompanying n = 12 observations. x 9 12 12 15 18 18 21 21 27 30 30 33 y 11 12 23 30 29 52 41 65 60 72 84 93 The summary statistics are n = 12 , x i /n = 20 . 5 , x 2 i = 5742 , ( x i - x ) 2 = 699 , y i /n = 47 . 67 , y 2 i = 35634 ,, ( y i - b y ) 2 = 827 . 01 , x i y i = 14022 , ( x i - x )( y i - y ) = 2296 . 00. And, assume the simple linear regression model( Y = β 0 + β 1 X + ε ) is plausible. (a) (2 points) Determine the equation of the least squares line. (b) (2 points) Find a 99% confidence interval for β 1 . (c) (4 points) Find Bonferroni joint confidence intervals for β 0 and β 1 , using a 90 percent family confidence coefficient. (d) (2 points) Predict the percentage of damaged squares when the age is 20 days by giving a interval of plausible values with 95% prediction level. (e) (4 points) Predict the percentage of damaged squares when the age is 20 and 22 days by Scheff´ e procedure and a 90 percent family confidence coefficient. (f) (2 points) Find a 95% confidence interval for the average percentage of damaged squares when the age is 20 days. (g) (4 points) Find the average percentage of damaged squares when the age is 20 and 22 days by Working-Hotelling procedure and a 90 percent family confidence coefficient. . Solution: (a) b β 1 = 3 . 28469 , b β 0 = - 19 . 66953, so, b Y = - 19 . 66953 + 3 . 28469 X (b) 3 . 28469 ± 3 . 169 × 0 . 34397 = (2 . 1946 , 4 . 3747) (c) β 0 : - 19 . 6695 ± 2 . 228139 * 7 . 524169 = ( - 36 . 4344 , - 2 . 90464) β 1 : 3 . 284692 ± 2 . 228139 * 0 . 343968 = (2 . 518285 , 4 . 0511) (d) 46 . 03 ± 2 . 228 * 9 . 4669 = (24 . 94 , 67 . 12) (e) x = 20 46 . 02432 ± 9 . 466923 * 2 * 2 . 924466 = (23 . 12898 , 68 . 91966) x = 22 52 . 59371 ± 9 . 479413 * 2 * 2 . 924466 = (29 . 66816 , 75 . 51925) (f) 46 . 03 ± 2 . 228 × 2 . 6335 = (40 . 1626 , 51 . 8974) (g) x = 20 46 . 02432 ± 2 . 630846 * 2 * 2 . 924466 = (39 . 66173 , 52 . 38691) x = 22 52 . 59371 ± 2 . 67544 * 2 * 2 . 924466 = (46 . 12327 , 59 . 06414) Page 1 of 6
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STAT3503 A Midterm June 25, 2009 Question 2 . A number of studies have shown lichens(certain plants composed of alga and a fungus) to be excellent bio-indicators of air pollution. A report give the following data on x=NO - 3 wet deposition(gN/m 2 ) and y= lichen N(% dry weight): x 0.05 0.10 0.11 0.12 0.31
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This note was uploaded on 09/30/2010 for the course STAT 3503 taught by Professor Smills during the Spring '07 term at Carleton CA.

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mid-term - STAT3503 A Last Name First Name Midterm Student...

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