Question

The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm is related to the sales generated by the broker. They sample 6 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows:

Sales No. of Clients ($1000) 27 52 11 37 42 64 33 55 15 29 25 58

Plot the data.

b)      Is there a relation between the number of clients and sales?

c)      Calculate the least squares line coefficients of bo and b1. What do these coefficients mean?

d)      What sales would you expect at 45 clients?

e)      What is the standard error for your predictions? What does it mean?

f)      What is correlation coefficient? What does it mean?

g)     What is the coefficient of determination? What does it mean?

Answer 1

let, the given date as below, No. of clients sales ($1000) 27 52 42 37 64 55 29 1404 407 2688 1815 435 729 121 1964 1089 2704 1369 4096 3025 33 15 841 28 58. 1450 625 3364 Ex? Ex= 153 Ey= 295 Sy? Eny= 8199 4553 115399

bi= C) Calculations X=25.5, y = 49.1667 Ixy - h (Ex) x(sy) Ex? to (1x)? 8199 - 5 x 153 x 295 4553 - L x C153)2 6 by= 676.5 651.5 b1 = 1,0384 The coefficient of no. of client is positive bo-y-bia bo= 49.1667- 1.03848 25.5 bo = 22, 6882 bi is the slope bo is the intercept d. The regression eqn is sale on no. of clients (y on a) is Y = bot bix = 22.6882 + 1.0384 x -

put x= 45 in above regression egn. ŷ = 22,6882 + 1.0384x 45 19=69,4149 sales (%) = 69,4149 corelath coefficient (o); Exy - x (EX)x(cy) (ex (Ex) (sy² + 18433) 8199 - &* 153 x 295 (4553-5x445393(15399- * 0295) 676.5 763,5338 r=0.88 60 coefficient of correlath is positively comelated. ... coefficient of determinath (139:- 183= 0,7850 coelficient of determinath is posi Hively correlated