The manager of a discount store would like to determine whet

The manager of a discount store would like to determine whether there is a relationship between the number of customers who visit the store each day and the dollar value of sales that day. A random sample of 20 days was taken and the number of customers in the store and the dollar value of sales were recorded for each day. The sample results are shown below.

Day

Customers

Sales

Day

Customers

Sales

1

907

11,200

11

679

7,630

2

926

11,050

12

872

9,430

3

506

6,840

13

924

9,460

4

741

9,210

14

607

7,640

5

789

9,420

15

452

6,920

6

889

10,080

16

729

8,950

7

874

9,450

17

794

9,330

8

510

6,730

18

844

10,230

9

529

7,240

19

1010

11,770

10

420

6,120

20

621

7,410

As a part of the study, the manager would like to estimate the correlation between the two variables and conduct a test to determine if the linear relationship between sales and customers is positive.

  1.      Develop a 95% C.I. for the regression model slope coefficient.

Day	Customers	Sales	Day	Customers	Sales
1	907	11,200	11	679	7,630
2	926	11,050	12	872	9,430
3	506	6,840	13	924	9,460
4	741	9,210	14	607	7,640
5	789	9,420	15	452	6,920
6	889	10,080	16	729	8,950
7	874	9,450	17	794	9,330
8	510	6,730	18	844	10,230
9	529	7,240	19	1010	11,770
10	420	6,120	20	621	7,410

Solution

From the above table obtained from Excel, the regression equation is given by

Sales (Y) = 2575.120608 +8.456015489* customers(X)

i.e., Y = 2575.12 + 8.45 X

the 95% confidence interval for the regression slope is given by ( 7.1648, 9.7472)

from the regression coefficients table the correlation coeffient is given by  

r = Sqrt( R²) = 0.9582

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2575.120608	454.59222	5.664683	2.8E-05	1616.014861	3534.226355
Customers	8.456015489	0.611990114	13.81724	1.13E-10	7.164829213	9.747201766