Each box Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healt y number of employees required to process the mail in one working day. A random sample of 8 days gave the following data. ‹ (lb). 12 y (Number of employees) 7 LAUSE SALT 23 De=131: D821 D²2.4191 ²940: Day - 1,492 (a) Find yb, and the equation of the least-squares line. (Round your and y to two decimal places. Round your least-squares estimates to three decimal places.) x= 20 13 سیمیا کے سمیرا (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. 10 O 25 20 13 3 10 19 10 9 16 6 10 5 13 10 12 18 23 2 25 8 14 13 16 20 25 30 25 20 10 25 20 13 10 KK 13 20 25 10 15 20 23 (e) Find the sample correlation coefficient and the coefficient of determination. (Round your answers to three decimal places.) 2.1 O 5 10 15 20 23 What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) 30 (d) If Healthy Crunch receives 16 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to two decimal places.) employees
Each box Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healt y number of employees required to process the mail in one working day. A random sample of 8 days gave the following data. ‹ (lb). 12 y (Number of employees) 7 LAUSE SALT 23 De=131: D821 D²2.4191 ²940: Day - 1,492 (a) Find yb, and the equation of the least-squares line. (Round your and y to two decimal places. Round your least-squares estimates to three decimal places.) x= 20 13 سیمیا کے سمیرا (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. 10 O 25 20 13 3 10 19 10 9 16 6 10 5 13 10 12 18 23 2 25 8 14 13 16 20 25 30 25 20 10 25 20 13 10 KK 13 20 25 10 15 20 23 (e) Find the sample correlation coefficient and the coefficient of determination. (Round your answers to three decimal places.) 2.1 O 5 10 15 20 23 What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) 30 (d) If Healthy Crunch receives 16 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to two decimal places.) employees
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healthy Crunch has a policy c
y = number of employees required to process the mail in one working day. A random sample of 8 days gave the following data.
x (lb)
12
y (Number of employees) 7
v=
b=
USE SALT
25
20
Σx = 131; Σy = 82; Σχ? = 2,419; Σy? = 940; Σxy = 1,492
(a) Find x, y, b, and the equation of the least-squares line. (Round your x and y to two decimal places. Round your least-squares estimates to three decimal places.)
15
10
(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.
y
O
y
25
20
15
10
O
5
5
5
10
10
15
15
9
20
20
16
10
25
5
25
12
8
30
30
18 23 25
14 13. 16
20
D
15
10
y
25
25
20
15
O
10
5
5
10
10
15
15
20
20
25
25
30
What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
30
(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)
2 =
(d) If Healthy Crunch receives 16 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to two decimal places.)
employees
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