Chapter 4, Problem 9CR

In Problems 9-14,

(a) Draw a scatter diagram for the data.

(b) Find $\bar{x},\bar{y},b$, and the equations of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination $r^2$. What percentage of variation in y is explained by the least-squares model?

Marketing: Coupons 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 of answering all its mail on the day it is received.)

Let x = weight of incoming mail and 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)	11	20	16	6	12 18 23	25
y (Number of employees)	6	10	9	5	8 14 13	16

Complete parts (a) through (c), given

${\displaystyle \sum x}=131;{\displaystyle \sum y}=81:x{\displaystyle \sum {}^2}=2435; {\displaystyle \sum y^2}-927;{\displaystyle \sum xy}=1487$

(d) If Healthy Crunch receives 15 pounds of mail, how many employees should be assigned mail duty that day?