Question

Question 4: Consider the soft drink delivery time data (data-ex-3-1 (Delivery Time).csv).

a) Find the simple correlation between cases (x1) and distance (x2).

b) Find the variance inflation factors.

c) Find the condition number of XT X. Is there evidence of multicollinearity in these data?

Observation	Delivery Time, y	Number of Cases, x1	Distance, x2 (ft)
1	16.68	7	560
2	11.5	3	220
3	12.03	3	340
4	14.88	4	80
5	13.75	6	150
6	18.11	7	330
7	8	2	110
8	17.83	7	210
9	79.24	30	1460
10	21.5	5	605
11	40.33	16	688
12	21	10	215
13	13.5	4	255
14	19.75	6	462
15	24	9	448
16	29	10	776
17	15.35	6	200
18	19	7	132
19	9.5	3	36
20	35.1	17	770
21	17.9	10	140
22	52.32	26	810
23	18.75	9	450
24	19.83	8	635
25	10.75	4	150

Answer 1

(a)

Number of Cases, x1	Distance, x2 (ft)
7	560
3	220
3	340
4	80
6	150
7	330
2	110
7	210
30	1460
5	605
16	688
10	215
4	255
6	462
9	448
10	776
6	200
7	132
3	36
17	770
10	140
26	810
9	450
8	635
4	150
r	0.824215

The simple correlation between cases (x1) and distance (x2) is 0.824215.

(b)

variables	VIF
Number of Cases, x1	3.118
Distance, x2 (ft)	3.118

(c) The analysis is:

There is no evidence of multicollinearity in these data.