An online retailer has collected data on 150 customers to study their spending behavior. In particular, they are interested in whether their rewards program increases customer spending. Their data set includes the amount each customer spent during the previous year, whether the customer lives outside of the United States, number of children, number of previous purchases prior to this year, age, and whether the customer is female or is a member of the retailer's rewards program.

 

(A) What is dummy variable for rewards program membership and run a simple linear regression model with this variable.  Interpret your regression coefficient.

(B) Interpret the of your regression.

(C) What is a suitable dummy variables for the remaining non-numeric variables in the data set. Run a multiple regression model which includes all explanatory variables from the data file. Interpret all regression coefficients that are significant at the 5% level.

 

(D) Which model would you choose? Explain your choice.

 

(E) You also suspect that the effect of the rewards membership on purchases depends on whether the customer is female. Create a suitable interaction variable and add it to your model from part (C). Interpret the coefficient of the interaction variable.

Customer	International	Number of children	Number of previous purchases	Age	Female	Rewards member	Purchases
1	1	1	1	26	Yes	No	$603.8
2	0	2	1	38	No	No	$546.9
3	0	2	0	35	No	No	$581.0
4	0	0	7	40	No	No	$472.5
5	1	3	0	28	Yes	Yes	$634.4
6	1	2	0	24	No	No	$533.8
7	1	4	0	27	No	Yes	$765.6
8	0	0	2	33	Yes	No	$472.5
9	0	4	0	62	No	No	$595.0
10	0	2	0	31	No	No	$516.3
11	1	2	2	34	No	No	$469.0
12	0	1	8	37	No	No	$547.8
13	0	1	0	37	No	No	$546.0
14	0	0	6	58	No	No	$607.3
15	1	4	0	33	No	Yes	$739.4
16	1	3	0	27	No	Yes	$691.3
17	0	1	0	30	No	No	$472.5
18	0	0	9	37	No	No	$518.0
19	1	2	6	44	No	No	$570.5
20	0	2	3	29	No	No	$518.0
21	0	1	2	36	No	No	$516.3
22	1	3	3	28	Yes	No	$616.9
23	0	0	0	45	No	No	$498.8
24	0	3	4	33	Yes	No	$608.1
25	1	2	1	24	Yes	No	$538.1
26	1	1	1	27	Yes	No	$516.3
27	0	1	6	60	No	No	$738.5
28	1	0	0	48	No	No	$658.0
29	0	0	6	40	No	No	$595.0
30	0	1	7	33	No	No	$577.5
31	0	2	4	35	No	No	$503.3
32	0	0	0	44	No	No	$619.5
33	1	1	8	43	Yes	No	$542.5
34	0	2	2	46	No	No	$679.0
35	0	0	0	42	No	No	$600.3
36	0	0	0	47	No	No	$612.5
37	0	1	2	25	No	Yes	$605.5
38	0	2	4	30	No	No	$498.8
39	0	1	0	40	No	No	$516.3
40	1	3	2	26	Yes	No	$669.4
41	1	0	1	32	No	No	$598.5
42	0	1	0	51	No	No	$818.1
43	1	0	0	35	No	Yes	$673.8
44	1	0	1	37	No	No	$577.5
45	1	1	0	44	No	Yes	$792.8
46	1	2	3	53	Yes	No	$679.0
47	0	0	0	40	No	No	$523.3
48	1	0	10	51	Yes	No	$546.0
49	0	1	0	42	No	No	$595.0
50	0	2	0	53	No	No	$532.9
51	0	3	3	58	Yes	No	$621.3
52	0	0	10	44	No	Yes	$595.0
53	0	0	0	31	No	No	$509.3
54	0	1	0	64	No	No	$518.9
55	1	2	1	47	No	No	$511.0
56	0	2	0	37	No	Yes	$521.5
57	0	2	0	46	No	No	$586.3
58	0	1	0	55	No	No	$595.0
59	0	1	0	39	No	No	$518.0
60	1	0	0	51	No	No	$595.0
61	0	3	8	37	No	No	$651.9
62	0	4	3	30	Yes	No	$577.5
63	1	2	0	26	No	No	$500.5
64	1	0	1	41	No	Yes	$630.0
65	1	0	4	34	No	Yes	$652.8
66	0	1	4	57	Yes	No	$523.3
67	0	1	8	53	No	No	$551.3
68	1	2	4	32	No	Yes	$724.5
69	0	0	5	44	No	No	$573.0
70	1	3	1	25	Yes	No	$586.3
71	0	2	9	31	No	No	$560.0
72	0	0	0	50	No	No	$539.0
73	1	3	3	47	No	Yes	$735.0
74	1	4	0	35	Yes	No	$686.9
75	0	1	0	43	No	No	$568.8
76	0	1	10	46	No	No	$554.8
77	0	2	0	35	Yes	No	$638.8
78	1	0	0	22	Yes	No	$577.5
79	0	0	0	58	No	No	$546.0
80	1	1	0	40	No	No	$595.0
81	0	1	0	30	No	No	$577.5
82	1	4	4	29	No	No	$689.1
83	1	3	9	31	No	Yes	$682.5
84	0	1	18	52	Yes	No	$611.1
85	1	3	5	33	Yes	No	$682.5
86	0	2	0	49	No	No	$595.0
87	0	0	7	34	No	No	$558.3
88	1	0	1	26	Yes	No	$647.5
89	1	1	0	28	Yes	No	$595.0
90	1	1	2	35	No	No	$637.0
91	0	0	1	47	No	Yes	$668.5
92	0	0	0	51	No	No	$617.8
93	1	2	2	26	Yes	No	$603.8
94	1	1	0	33	No	No	$533.8
95	1	2	2	27	Yes	No	$525.0
96	1	0	0	34	No	No	$652.8
97	1	1	0	29	No	No	$703.5
98	1	2	0	27	Yes	No	$621.3
99	0	0	0	43	No	No	$612.5
100	1	0	3	36	No	No	$665.0
101	0	0	0	38	No	No	$617.8
102	0	1	0	60	No	No	$596.8
103	1	4	5	43	No	Yes	$756.0
104	0	1	5	48	No	No	$631.8
105	0	2	3	32	No	No	$605.5
106	1	5	0	31	Yes	No	$826.9
107	1	0	2	29	No	No	$633.5
108	1	3	0	35	No	No	$656.3
109	1	0	12	37	No	No	$717.5
110	0	0	0	43	No	No	$623.0
111	1	1	5	33	No	No	$696.5
112	1	1	4	58	No	Yes	$826.9
113	1	0	7	44	No	No	$743.8
114	1	0	8	37	No	Yes	$801.5
115	1	1	6	48	No	No	$610.8
116	1	2	0	26	Yes	Yes	$784.0
117	1	2	0	25	No	No	$665.0
118	1	0	0	38	No	No	$612.5
119	1	0	0	41	No	Yes	$700.0
120	1	0	0	29	Yes	No	$630.0
121	0	1	0	59	No	No	$538.1
122	1	2	4	29	Yes	No	$683.8
123	1	2	2	27	No	Yes	$708.8
124	1	2	0	30	No	No	$691.3
125	0	1	5	34	No	No	$628.3
126	0	0	2	35	No	No	$568.8
127	1	2	6	50	No	No	$647.5
128	0	3	1	33	No	No	$570.5
129	1	2	0	26	No	No	$630.0
130	0	1	0	36	No	No	$612.5
131	1	2	5	33	No	Yes	$763.0
132	1	0	0	47	No	No	$591.5
133	0	0	0	51	No	No	$617.8
134	1	1	6	42	No	No	$705.3
135	1	2	0	31	Yes	No	$691.3
136	1	3	10	62	No	No	$761.3
137	1	0	1	46	Yes	No	$735.0
138	1	4	9	60	No	No	$705.3
139	1	0	5	43	Yes	No	$770.0
140	1	0	2	53	No	No	$696.5
141	1	2	1	38	No	No	$694.8
142	1	3	5	39	No	No	$787.5
143	1	0	0	35	No	No	$768.3
144	1	0	3	40	No	No	$665.0
145	1	1	3	32	No	No	$682.9
146	1	1	3	33	Yes	Yes	$818.1
147	1	2	1	30	Yes	Yes	$987.9
148	1	2	3	37	Yes	Yes	$770.0
149	1	0	0	30	Yes	Yes	$826.9
150	1	3	4	32	No	Yes	$857.5