mid-term

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

This preview shows pages 1–3. Sign up to view the full content.

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

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

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

## 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.

### Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online