Question

Mr. James McWhinney, president of Daniel James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample Information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled Number of Sales Number of Sales Contacts, (5 thousands), Contacts, (5 thousands) х 22 76 18 38 22 17 Y 561 х 37 41 19 29 49 34 47 95 Y $33 22 48 32 31 a. Not available in Connect b. Determine the regression equation (Do not round intermediate calculations and round the final answers to 4 decimal places. Negative answers should be indicated by a minus sign.) be YE c. Determine the estimated sales if 53 contacts are made. (Round the final answer to 4 decimal places.)

Answer 1

Q) Mr. James MaWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicate the number of client contacts last months and Y column sows the value of sales ($ thousands) last month for each client sampled.

Number of contacts(X)	Sales($ thousands) (Y)
37	61
41	76
19	34
29	47
49	95
22	33
18	22
38	48
22	32
17	31

b)

We fit the regression model to given data. Here the dependent variable is Sales(Y) and independent variable is number of contacts(X).

By using excel the coefficient of regression model is,

	Coefficients	Standard Error	t Stat	P-value
Intercept	-8.572941994	7.229141198	-1.185886644	0.269691857
Number of contacts(X)	1.934004863	0.232377406	8.32268894	3.28147E-05

and

Regression Statistics
Multiple R	0.946817362
R Square	0.896463117
Adjusted R Square	0.883521007
Standard Error	7.885781267
Observations	10

Here we can see that the independent variable, number of contact is significant at 0.05 significance level. The value of R-square and adjusted R-square is 0.89 and 0.88 respectively.

So the regression model fitted well for the data and the model for finding relationship between the number of client contacts and dollar amount of sales is

ŷ=1.9340*X-8.5729

The value of a and b can be calculated by comparing above model to ŷ=ax+b.

Therefore, b=-8.5729 and b=1.9340

c)

Determine estimated sales if 53 contacts are made.

The estimated sales if 53 contacts are made is

ŷ=1.9340*(53)-8.5729

ŷ=93.9291

Therefore,if 53 contacts are made,estimated sales is 93.9221.