Question

Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the value of sales ($1000) for each client sampled.

                        Number of`                             Sales

                        Contacts (X)                            ($1000)

10 26

8 21

12 29

9 27

10 22

a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.

b) Compute the correlation coefficient and coefficient of determination. Interpret the coefficients.

c) James would like to require 35 client contacts per month. Based upon the above data, predict what the monthly sales would be for this number of client contacts. What would be your advice to Mr. James about his proposed policy?

Answer 1

( a )

The slope indicates that every​ 1 client increase in contact increases the value of sales by 1.591, on average.

The​ y-intercept means that the value of sales is 9.409 on average.

( b )

correlation coefficient

correlation coefficient ( r ) = 0.6958

coefficient of determination( r² ) :

r² = ( 0.6958 )²

r² = 0.4841

( c )

Give x = 35 then

y = 9.409 +1.591 ( 35 )

y = 65.094

y = 65 ( app)

if 35  contacts are made.the estimated sales is $ 65.094 so which is high so decrease the contacts