S_No	Weight	Failed	Failure
1	2500	No	0
2	2900	No	0
3	3500	Yes	1
4	2500	No	0
5	2900	Yes	1
6	3500	Yes	1
7	3300	No	0
8	3300	Yes	1
9	3300	Yes	1
10	2500	No	0
11	3700	Yes	1
12	2300	No	0
13	2300	No	0
14	2300	No	0
15	3300	Yes	1
16	2900	No	0
17	2700	No	0
18	4100	Yes	1
19	2500	No	0
20	2900	No	0
21	2900	Yes	1
22	2500	No	0
23	4300	Yes	1
24	3900	Yes	1
25	3100	No	0
26	2500	No	0
27	2300	No	0
28	2300	No	0
29	4300	Yes	1
30	3700	Yes	1
31	3100	No	0
32	3300	No	0
33	2700	Yes	1
34	2100	No	0
35	3100	Yes	1
36	2100	No	0
37	3900	Yes	1
38	2100	No	0
39	2900	No	0
40	2900	No	0
41	2100	No	0
42	2300	No	0
43	2100	No	0
44	2500	No	0
45	2500	No	0
46	2700	No	0
47	2100	No	0
48	2900	Yes	1
49	4300	Yes	1
50	2900	No	0
51	3700	No	0
52	2700	No	0
53	3300	No	0
54	2300	No	0
55	4100	Yes	1
56	2500	No	0
57	3700	Yes	1
58	2300	No	0
59	3500	No	0
60	3700	Yes	1
61	2500	No	0
62	2900	Yes	1
63	2900	No	0
64	3500	Yes	1
65	3100	No	0
66	4300	Yes	1
67	2100	No	0
68	4300	Yes	1
69	2900	No	0
70	2100	No	0
71	3900	Yes	1
72	3100	No	0
73	4300	Yes	1
74	2900	No	0
75	2300	No	0
76	2300	No	0
77	2300	No	0
78	4300	Yes	1
79	4300	Yes	1
80	2900	No	0
81	2900	No	0
82	2300	No	0
83	2700	No	0
84	2700	No	0
85	2100	No	0
86	4100	Yes	1
87	3300	Yes	1
88	2300	No	0
89	4100	Yes	1
90	3500	Yes	1
91	3500	Yes	1
92	2300	No	0
93	3500	No	0
94	2700	No	0
95	2500	No	0
96	3700	Yes	1
97	2300	No	0
98	2700	No	0
99	2100	No	0
100	3300	Yes	1
101	4100	Yes	1
102	3500	Yes	1
103	2500	No	0
104	2100	No	0
105	2100	No	0
106	4300	Yes	1
107	2300	No	0
108	3700	Yes	1
109	2100	No	0
110	2300	No	0
111	3700	Yes	1
112	2300	No	0
113	2300	No	0
114	3300	Yes	1
115	2100	No	0
116	4100	Yes	1
117	4300	Yes	1
118	3900	Yes	1
119	3300	No	0
120	2500	No	0
121	2300	No	0
122	2100	No	0
123	3700	Yes	1
124	4100	Yes	1
125	3300	Yes	1
126	2700	Yes	1
127	4100	Yes	1
128	2500	No	0
129	2100	No	0
130	3100	No	0
131	3100	Yes	1
132	2300	No	0
133	3300	Yes	1
134	3500	Yes	1
135	3300	No	0
136	2300	No	0
137	3500	Yes	1
138	4100	Yes	1
139	2700	No	0
140	4100	Yes	1
141	2300	No	0
142	2100	No	0
143	2100	No	0
144	2100	No	0
145	2300	No	0
146	2700	No	0
147	2900	No	0
148	3700	Yes	1
149	2900	No	0
150	2700	No	0
151	3300	No	0
152	2100	No	0
153	3900	Yes	1
154	3900	Yes	1
155	2100	No	0
156	3900	Yes	1
157	3900	No	0
158	3500	No	0
159	2100	No	0
160	3100	No	0
161	3300	Yes	1
162	2100	No	0
163	2300	No	0
164	2700	No	0
165	2300	No	0
166	2300	No	0
167	3100	Yes	1
168	2100	No	0
169	2900	No	0
170	3100	No	0
171	3900	Yes	1
172	2300	No	0
173	2500	No	0
174	3500	No	0
175	2100	No	0
176	3100	Yes	1
177	4300	Yes	1
178	4100	Yes	1
179	2500	No	0
180	2700	No	0
181	2500	No	0
182	2700	No	0
183	2900	No	0
184	2500	No	0
185	2500	No	0
186	2500	No	0
187	3900	Yes	1
188	3500	Yes	1
189	3100	Yes	1
190	3300	Yes	1
191	2300	No	0
192	2100	No	0
193	3100	No	0
194	2500	No	0
195	2900	Yes	1
196	2500	No	0
197	2700	No	0
198	4300	Yes	1
199	4100	Yes	1
200	3500	Yes	1
201	2300	Yes	1
202	3700	Yes	1
203	2700	No	0
204	3100	No	0
205	2100	No	0
206	2300	No	0
207	3500	Yes	1
208	3100	No	0
209	3300	No	0
210	2700	No	0
211	3300	Yes	1
212	2900	Yes	1
213	3500	Yes	1
214	3900	Yes	1
215	2500	No	0
216	3100	Yes	1
217	3700	Yes	1
218	2100	No	0
219	3300	Yes	1
220	3300	Yes	1
221	3100	Yes	1
222	3300	No	0
223	2700	No	0
224	2100	No	0
225	2300	No	0
226	2900	Yes	1
227	2100	No	0
228	2700	No	0
229	3700	Yes	1
230	4300	Yes	1
231	2300	No	0
232	3700	Yes	1
233	2700	No	0
234	2300	No	0
235	3700	Yes	1
236	2700	No	0
237	2100	No	0
238	3500	No	0
239	3500	Yes	1
240	2300	No	0
241	3900	Yes	1
242	3500	Yes	1
243	3500	Yes	1
244	2700	Yes	1
245	2900	Yes	1
246	3900	Yes	1
247	2900	No	0
248	2100	No	0
249	4300	Yes	1
250	2100	No	0
251	4300	Yes	1
252	4100	Yes	1
253	2900	No	0
254	4300	Yes	1
255	2500	No	0
256	2100	No	0
257	2100	No	0
258	2700	No	0
259	2300	No	0
260	2900	No	0
261	3700	Yes	1
262	2300	No	0
263	2100	Yes	1
264	2100	No	0
265	2300	No	0
266	2700	No	0
267	3700	Yes	1
268	2100	No	0
269	2900	No	0
270	2100	No	0
271	2700	No	0
272	3100	No	0
273	2300	No	0
274	2100	No	0
275	3700	Yes	1
276	3900	Yes	1
277	3700	Yes	1
278	2500	No	0
279	2300	Yes	1
280	2700	No	0
281	2100	No	0
282	2900	No	0
283	3500	No	0
284	4100	Yes	1
285	3500	Yes	1
286	2300	No	0
287	3900	Yes	1
288	2100	No	0
289	2100	No	0
290	3300	No	0
291	2700	No	0
292	4100	Yes	1
293	4300	Yes	1
294	2500	No	0
295	4300	Yes	1
296	4300	Yes	1
297	2700	No	0
298	2900	No	0
299	2700	No	0
300	2100	No	0
301	3700	Yes	1
302	2700	No	0
303	2100	No	0
304	4300	Yes	1
305	3100	No	0
306	3100	Yes	1
307	3900	Yes	1
308	2900	No	0
309	2500	No	0
310	2900	No	0
311	4100	Yes	1
312	2500	No	0
313	2500	No	0
314	2100	No	0
315	2700	No	0
316	2500	No	0
317	4100	Yes	1
318	2100	No	0
319	2300	No	0
320	2100	No	0
321	2500	No	0
322	2700	No	0
323	4300	Yes	1
324	3300	Yes	1
325	3100	No	0
326	3700	No	0
327	3500	Yes	1
328	2700	No	0

The data for this problem contains data from a campaign run by a retailer for a period of 1 month.

The retailer "bought" a set of adwords from Google and monitored the performance of those

adwords over this time period.

We have daily data on the following variables,

- Whether any sale can be attributable to the adword (SALE [Yes=1 or No=0])

- Number of Clicks (CLICKS) generated by the adword

- Number of impressions (IMPS) adword gets

- The average position (AvgPOS)occupied by the adword.

Higher the AvgPOS, lower is the adword displayed in the rankings and hence less likely to be viewed

(a) Estimate an appropriate regression model with SALE as your dependent variable and CLICKS, IMPS and AvgPOS as the independent variables.

Report and interpret the estimated coefficient on AvgPOS

(b) Notice that the CLICKS have a 'positive' impact on the likelihood of SALE, while

AvgPOS has a 'negative' impact on the likelihood of sale. Suppose the average position occupied by an adword drops by 3(i.e. the variable AvgPOS increases by 3). How much should the number of CLICKS increase so that the odds of getting a SALE do not change.

Briefly show your working in support of your answer.

c) We will now investigate the interaction between AvgPOS and CLICKS. Please introduce such an interaction variable in your model and estimate the model. Report and interpret the estimated coefficient on this interaction variable.

(d) Please use the estimated model (with interaction effects) from part(c) for this question.

An adword currently occupies an average position equal to 1.9and the number of CLICKS generated by the adword are 5.

Suppose the average position occupied by the adword increases by 3(i.e. the variable AvgPOS drops from 1.9 to 4.9). By what % do the odds of getting a SALE change? Please briefly show your calculations

PLEASE SOLVE THIS QUESTION WITH LOGISTIC REGRESSION