Dorothy Kelly sells life insurance for the Prudence InsuranceCompany. She sells insurance by making visits to her clients homes.Dorothy believes that the number of sales should depend, to somedegree, on the number of visits made. For the past several years,she kept careful records of the number of visits (x) shemade each week and the number of people (y) who boughtinsurance that week. For a random sample of 15 such weeks, thex and y values follow.
| x | 11 | 17 | 17 | 14 | 28 | 5 | 20 | 14 | 22 | 7 | 15 | 29 | 8 | 25 | 16 |
| y | 2 | 13 | 9 | 3 | 8 | 2 | 5 | 6 | 8 | 3 | 5 | 10 | 6 | 10 | 7 |
Σx = 248; Σy = 97; Σx2 =4,844; Σy2 = 775; Σxy = 1,828
(a) Find x, y, b, and the equation ofthe least-squares line. (Round your answers for x andy to two decimal places. Round your least-squaresestimates to three decimal places.)
(b) Draw a scatter diagram for the data. Plot the least-squaresline on your scatter diagram.
(c) Find the sample correlation coefficient r and thecoefficient of determination. (Round your answers to three decimalplaces.)
What percentage of variation in y is explained by theleast-squares model? (Round your answer to one decimalplace.)
%
(d) In a week during which Dorothy makes 21 visits, how many peopledo you predict will buy insurance from her? (Round your answer toone decimal place.)
people
