Chapter 4, Problem 12CR

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?

Sales: Insurance Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients' homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she has kept careful records of the number of visits (x) she makes each week and the number of people (y) who buy insurance that week. For a random sample of 15 such weeks, the x and y values follow:

X	11	19	16	13	28	5	20	14	22	7	15	29	8	25	16
y	3	11	8	5	8	2	5	6	8	3	5	10	6	10	7

Complete parts (a) through (c). given

${\displaystyle \sum x}=248;{\displaystyle \sum y}=97;{\displaystyle \sum x^2}=4856; {\displaystyle \sum y^2}=731;{\displaystyle \sum xy}=1825.$ (d) In a week during which Dorothy makes 18 visits, how many people do you predict will buy insurance from her?