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) (Y)

                        14                                            24

                        12                                            14

                        20                                            28

                        16                                            30

                        23                                            30

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 30 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

Carrying out regression in Excel (go to Data tab -> Data Analysis -> Regression, and choose Y as Y-column and X as X-column), we get the following result:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.764968621
R Square	0.585176991
Adjusted R Square	0.446902655
Standard Error	5
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	105.8	105.8	4.232	0.131851755
Residual	3	75	25
Total	4	180.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	5.65	9.762812095	0.5787267	0.60336212	-25.41962528	36.71962528
X	1.15	0.559016994	2.05718254	0.13185175	-0.629041568	2.929041568

Hence, regression equation for client contacts (X) and sales (Y) is:

Y = 5.65 + 1.15*X

The slope of 1.15 means the sales increases by 1.15*1000 = 1150 $ for each unit increase in client contacts.

The intercept of 5.65 means the sales is 5.65*1000 = 5650 $ when there are no client contacts at all (i.e. X=0).

b) Correlation coefficient, r = corr(X, Y) = 0.765 => client contacts X and sales Y are linearly correlated, the strength of the correlation being 76.5%, which is a moderately strong linear relationship.

Coefficient of determination = r² = 0.585 => 58.5% of the changes in sales Y are explained by the changes in client contacts X.

c) For 30 client contacts, predicted monthly sales, Y = 5.65 + 1.15*30 = 40.15k $

Given the massive increase in sales with client contacts, Mr. James should setup regular client contact practice, possibly through dedicated teams. Increasing and regular client contacts should help achieve much higher level of sales going forward, hence this should be a top prioirity for him.