The managers of a brokerage firm are interested in finding out the effects of number of new clients that a broker brings into the firm on the sales generated by them. They sample 10 brokers and identify 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:
Broker Clients(X) Sales(Y) Calculation shows that
1. 27 52 n=10 2. 11 37 X = 260 3. 40 64 Y= 480 4. 33 55 X2= 7594 5 15 29 Y2= 24276 6. 15 34 XY =13377 7. 25 58 SSX =(X-Xbar)2 =834 8. 36 59 SST=(Y-ybar)2 = 1236 9. 28 44 SSE = (Y –Yhat)2=271.241
10. 30 48 (i) Assuming a linear relationship, what is the prediction for the amount for sales (in $1,000s) for a person who brings 25 new clients into the firm? (ii) Calculate the standard error of estimate and interpret the result. (iii) Test at 5% level of significance that the number of new clients that the broker have enrolled in the last year is significant predictor of their sales amount.