Plymouth Rock Securities is interested in finding out if there is a relationship between the number of new clients brought into the firm by a broker and the sales performance of the broker. A random sample of 11 brokers' records are reviewed to determine the number of new clients enrolled last year and total sales in millions of dollars:
Broker 1 2 3 4 5 6 7 8 9 10 11
Clients 27 11 42 33 15 15 25 36 28 30 17
Sales, $ 52 37 64 55 29 34 58 59 44 48 31
a) How closely related is the new client base to sales performance? Draw the scatterplot and compute the correlation and describe the relationship
b) Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?
c) What does the slope represent?
d) What would a new broker who brings in 30 clients sell, on average?
e) How much of the variability in sales is not explained by the number of new clients?