Q: The dataset posted below lists a sample of months and the advertising budget (in hundreds of dollars) for TV, radio and newspaper advertisements. Also included is whether a coupon was published for that month and the resulting sales (in thousands of dollars). a) Develop a multiple regression model predicting the sales based off the four predictor variables: TV, radio, and newspaper advertising budget and whether a coupon is used. Recode Coupon as 0 = No and 1 = Yes. Report the estimated regression equation (Solve in Excel) TV ($100) radio ($100) newspaper ($100) Coupon sales ($1000) 0.7 39.6 8.7 No 1.6 230.1 37.8 69.2 No 22.1 4.1 11.6 5.7 Yes 3.2 44.5 39.3 45.1 No 10.4 250.9 36.5 72.3 No 22.2 8.6 2.1 1 No 4.8 17.2 45.9 69.3 Yes 9.3 104.6 5.7 34.4 No 10.4 216.8 43.9 27.2 Yes 22.3 5.4 29.9 9.4 No 5.3 69 9.3 0.9 No 9.3 70.6 16 40.8 No 10.5 151.5 41.3 58.5 No 18.5 195.4 47.7 52.9 Yes 22.4 13.1 0.4 25.6 Yes 5.3 76.4 0.8 14.8 No 9.4 156.6 2.6 8.3 No 10.5 180.8 10.8 58.4 No 12.9 248.8 27.1 22.9 No 18.9 216.4 41.7 39.6 Yes 22.6 7.3 28.1 41.4 Yes 5.5 8.7 48.9 75 No 7.2 95.7 1.4 7.4 No 9.5 199.8 2.6 21.2 Yes 10.6 206.9 8.4 26.4 No 12.9 237.4 27.5 11 No 18.9 205 45.1 19.6 Yes 22.6 13.2 15.9 49.6 No 5.6 25 11 29.7 No 7.2 31.5 24.6 2.2 No 9.5 89.7 9.9 35.7 Yes 10.6 57.5 32.8 23.5 No 11.8 88.3 25.5 73.4 No 12.9 204.1 32.9 46 Yes 19 239.9 41.5 18.5 Yes 23.2 8.4 27.2 2.1 No 5.7 28.6 1.5 33 No 7.3 25.6 39 9.3 No 9.5 87.2 11.8 25.9 No 10.6 76.4 26.7 22.3 No 11.8 131.7 18.4 34.6 No 12.9 120.2 19.6 11.6 No 13.2 171.3 39.7 37.7 Yes 19 198.9 49.4 60 Yes 23.7 17.2 4.1 31.6 No 5.9 11.7 36.9 45.2 Yes 7.3 97.2 1.5 30 No 9.6 100.4 9.6 3.6 No 10.7 276.7 2.3 23.7 No 11.8 136.2 19.2 16.6 No 13.2 137.9 46.4 59 Yes 19.2 210.8 49.6 37.7 Yes 23.8 19.4 16 22.3 No 6.6 19.6 20.1 17 Yes 7.6 43 25.9 20.5 No 9.6 36.9 38.6 65.6 No 10.8 112.9 17.4 38.6 No 11.9 240.1 7.3 8.7 No 13.2 193.7 35.4 75.6 Yes 19.2 296.4 36.3 100.9 Yes 23.8 7.8 38.9 50.6 No 6.6 38.2 3.7 13.8 Yes 7.6 97.5 7.6 7.2 No 9.7 39.5 41.1 5.8 No 10.8 117.2 14.7 5.4 No 11.9 85.7 35.8 49.3 Yes 13.3 217.7 33.5 59 Yes 19.4 261.3 42.7 54.7 Yes 24.2 18.7 12.1 23.4 No 6.7 17.9 37.6 21.6 No 8 62.3 12.6 18.3 No 9.7 73.4 17 12.9 No 10.9 234.5 3.4 84.8 No 11.9 139.3 14.5 10.2 No 13.4 219.8 33.5 45.1 Yes 19.6 281.4 39.6 55.8 Yes 24.4 27.5 1.6 20.7 No 6.9 53.5 2 21.4 No 8.1 66.9 11.7 36.8 No 9.7 38 40.3 11.9 No 10.9 262.9 3.5 19.5 No 12 225.8 8.2 56.5 No 13.4 166.8 42 3.6 Yes 19.6 220.3 49 3.2 Yes 24.7 18.8 21.7 50.4 No 7 50 11.6 18.4 No 8.4 59.6 12 43.1 No 9.7 129.4 5.7 31.3 No 11 76.3 27.5 16 Yes 12 232.1 8.6 8.7 No 13.4 229.5 32.3 74.2 Yes 19.7 266.9 43.8 5 Yes 25.4 25.1 25.7 43.3 No 8.5 94.2 4.9 8.1 Yes 9.7 116 7.7 23.1 Yes 11 139.2 14.3 25.6 No 12.2 68.4 44.5 35.6 No 13.6 255.4 26.9 5.5 Yes 19.8 289.7 42.3 51.2 Yes 25.4 66.1 5.8 24.2 No 8.6 75.5 10.8 6 Yes 9.9 134.3 4.9 9.3 No 11.2 206.8 5.2 19.4 No 12.2 102.7 29.6 8.4 No 14 220.5 33.2 37.9 Yes 20.1 243.2 49 44.3 Yes 25.4 16.9 43.7 89.4 No 8.7 43.1 26.7 35.1 Yes 10.1 69.2 20.5 18.3 No 11.3 218.5 5.4 27.4 No 12.2 175.7 15.4 2.4 No 14.1 262.7 28.8 15.9 No 20.2 283.6 42 66.2 Yes 25.5 90.4 0.3 23.2 No 8.7 44.7 25.8 20.6 Yes 10.1 75.3 20.3 32.5 No 11.3 239.8 4.1 36.9 No 12.3 120.5 28.5 14.2 No 14.2 248.4 30.2 20.3 Yes 20.2 287.6 43 71.8 Yes 26.2 56.2 5.7 29.7 No 8.7 149.8 1.3 24.3 Yes 10.1 199.8 3.1 34.6 No 11.4 109.8 14.3 31.7 No 12.4 172.5 18.1 30.7 No 14.4 293.6 27.7 1.8 Yes 20.7 276.9 48.9 41.8 Yes 27 26.8 33 19.3 No 8.8 140.3 1.9 9 Yes 10.3 96.2 14.8 38.9 No 11.4 67.8 36.6 114 No 12.5 164.5 20.9 47.4 Yes 14.5 238.2 34.3 5.3 Yes 20.7 80.2 0 9.2 Yes 8.8 139.5 2.1 26.6 No 10.3 107.4 14 10.9 No 11.5 237.4 5.1 23.5 No 12.5 147.3 23.9 19.1 No 14.6 184.9 43.9 1.7 Yes 20.7 23.8 35.1 65.9 Yes 9.2 222.4 3.4 13.1 No 11.5 75.1 35 52.7 No 12.6 78.2 46.8 34.5 No 14.6 273.7 28.9 59.7 Yes 20.8 224 2.4 15.6 No 11.6 165.6 10 17.6 No 12.6 74.7 49.4 45.7 No 14.7 182.6 46.2 58.7 No 21.2 48.3 47 8.5 No 11.6 265.2 2.9 43 Yes 12.7 187.9 17.2 17.9 No 14.7 292.9 28.3 43.2 No 21.4 121 8.4 48.7 Yes 11.6 290.7 4.1 8.5 Yes 12.8 227.2 15.8 49.9 No 14.8 228 37.7 32 No 21.5 197.6 3.5 5.9 No 11.7 177 9.3 6.4 Yes 12.8 280.2 10.1 21.4 No 14.8 213.5 43 33.8 No 21.7 222.4 4.3 49.8 No 11.7 175.1 22.5 31.5 No 14.9 241.7 38 23.2 No 21.8 168.4 7.1 12.8 No 11.7 188.4 18.1 25.6 No 14.9 170.2 7.8 35.2 No 11.7 142.9 29.3 12.6 No 15 284.3 10.6 6.4 Yes 15 193.2 18.4 65.7 No 15.2 123.1 34.6 12.4 No 15.2 93.9 43.5 50.5 No 15.3 228.3 16.9 26.2 No 15.5 184.9 21 22 No 15.5 141.3 26.8 46.2 No 15.5 187.8 21.1 9.5 Yes 15.6 239.3 15.5 27.3 Yes 15.7 240.1 16.7 22.9 No 15.9 209.6 20.6 10.7 No 15.9 125.7 36.9 79.2 No 15.9 286 13.9 3.7 No 15.9 110.7 40.6 63.2 No 16 280.7 13.9 37 No 16.1 202.5 22.3 31.6 No 16.6 197.6 23.3 14.2 No 16.6 109.8 47.8 51.4 Yes 16.7 163.3 31.6 52.9 Yes 16.9 213.4 24.6 13.1 Yes 17 177 33.4 38.7 No 17.1 215.4 23.6 57.6 No 17.1 135.2 41.7 45.9 No 17.2 191.1 28.7 18.2 No 17.3 149.7 35.6 6 No 17.3 214.7 24 4 Yes 17.4 265.6 20 0.3 Yes 17.4 253.8 21.3 30 Yes 17.6 218.4 27.7 53.4 Yes 18 131.1 42.8 28.9 Yes 18 163.5 36.8 7.4 Yes 18 199.1 30.6 38.7 Yes 18.3 210.7 29.5 9.3 Yes 18.4
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Q: The dataset posted below lists a sample of months and the advertising budget (in hundreds of dollars) for TV, radio and newspaper advertisements. Also included is whether a coupon was published for that month and the resulting sales (in thousands of dollars).
a) Develop a multiple regression model predicting the sales based off the four predictor variables: TV, radio, and newspaper advertising budget and whether a coupon is used. Recode Coupon as 0 = No and 1 = Yes. Report the estimated regression equation (Solve in Excel)
TV ($100) | radio ($100) | newspaper ($100) | Coupon | sales ($1000) | |
0.7 | 39.6 | 8.7 | No | 1.6 | |
230.1 | 37.8 | 69.2 | No | 22.1 | |
4.1 | 11.6 | 5.7 | Yes | 3.2 | |
44.5 | 39.3 | 45.1 | No | 10.4 | |
250.9 | 36.5 | 72.3 | No | 22.2 | |
8.6 | 2.1 | 1 | No | 4.8 | |
17.2 | 45.9 | 69.3 | Yes | 9.3 | |
104.6 | 5.7 | 34.4 | No | 10.4 | |
216.8 | 43.9 | 27.2 | Yes | 22.3 | |
5.4 | 29.9 | 9.4 | No | 5.3 | |
69 | 9.3 | 0.9 | No | 9.3 | |
70.6 | 16 | 40.8 | No | 10.5 | |
151.5 | 41.3 | 58.5 | No | 18.5 | |
195.4 | 47.7 | 52.9 | Yes | 22.4 | |
13.1 | 0.4 | 25.6 | Yes | 5.3 | |
76.4 | 0.8 | 14.8 | No | 9.4 | |
156.6 | 2.6 | 8.3 | No | 10.5 | |
180.8 | 10.8 | 58.4 | No | 12.9 | |
248.8 | 27.1 | 22.9 | No | 18.9 | |
216.4 | 41.7 | 39.6 | Yes | 22.6 | |
7.3 | 28.1 | 41.4 | Yes | 5.5 | |
8.7 | 48.9 | 75 | No | 7.2 | |
95.7 | 1.4 | 7.4 | No | 9.5 | |
199.8 | 2.6 | 21.2 | Yes | 10.6 | |
206.9 | 8.4 | 26.4 | No | 12.9 | |
237.4 | 27.5 | 11 | No | 18.9 | |
205 | 45.1 | 19.6 | Yes | 22.6 | |
13.2 | 15.9 | 49.6 | No | 5.6 | |
25 | 11 | 29.7 | No | 7.2 | |
31.5 | 24.6 | 2.2 | No | 9.5 | |
89.7 | 9.9 | 35.7 | Yes | 10.6 | |
57.5 | 32.8 | 23.5 | No | 11.8 | |
88.3 | 25.5 | 73.4 | No | 12.9 | |
204.1 | 32.9 | 46 | Yes | 19 | |
239.9 | 41.5 | 18.5 | Yes | 23.2 | |
8.4 | 27.2 | 2.1 | No | 5.7 | |
28.6 | 1.5 | 33 | No | 7.3 | |
25.6 | 39 | 9.3 | No | 9.5 | |
87.2 | 11.8 | 25.9 | No | 10.6 | |
76.4 | 26.7 | 22.3 | No | 11.8 | |
131.7 | 18.4 | 34.6 | No | 12.9 | |
120.2 | 19.6 | 11.6 | No | 13.2 | |
171.3 | 39.7 | 37.7 | Yes | 19 | |
198.9 | 49.4 | 60 | Yes | 23.7 | |
17.2 | 4.1 | 31.6 | No | 5.9 | |
11.7 | 36.9 | 45.2 | Yes | 7.3 | |
97.2 | 1.5 | 30 | No | 9.6 | |
100.4 | 9.6 | 3.6 | No | 10.7 | |
276.7 | 2.3 | 23.7 | No | 11.8 | |
136.2 | 19.2 | 16.6 | No | 13.2 | |
137.9 | 46.4 | 59 | Yes | 19.2 | |
210.8 | 49.6 | 37.7 | Yes | 23.8 | |
19.4 | 16 | 22.3 | No | 6.6 | |
19.6 | 20.1 | 17 | Yes | 7.6 | |
43 | 25.9 | 20.5 | No | 9.6 | |
36.9 | 38.6 | 65.6 | No | 10.8 | |
112.9 | 17.4 | 38.6 | No | 11.9 | |
240.1 | 7.3 | 8.7 | No | 13.2 | |
193.7 | 35.4 | 75.6 | Yes | 19.2 | |
296.4 | 36.3 | 100.9 | Yes | 23.8 | |
7.8 | 38.9 | 50.6 | No | 6.6 | |
38.2 | 3.7 | 13.8 | Yes | 7.6 | |
97.5 | 7.6 | 7.2 | No | 9.7 | |
39.5 | 41.1 | 5.8 | No | 10.8 | |
117.2 | 14.7 | 5.4 | No | 11.9 | |
85.7 | 35.8 | 49.3 | Yes | 13.3 | |
217.7 | 33.5 | 59 | Yes | 19.4 | |
261.3 | 42.7 | 54.7 | Yes | 24.2 | |
18.7 | 12.1 | 23.4 | No | 6.7 | |
17.9 | 37.6 | 21.6 | No | 8 | |
62.3 | 12.6 | 18.3 | No | 9.7 | |
73.4 | 17 | 12.9 | No | 10.9 | |
234.5 | 3.4 | 84.8 | No | 11.9 | |
139.3 | 14.5 | 10.2 | No | 13.4 | |
219.8 | 33.5 | 45.1 | Yes | 19.6 | |
281.4 | 39.6 | 55.8 | Yes | 24.4 | |
27.5 | 1.6 | 20.7 | No | 6.9 | |
53.5 | 2 | 21.4 | No | 8.1 | |
66.9 | 11.7 | 36.8 | No | 9.7 | |
38 | 40.3 | 11.9 | No | 10.9 | |
262.9 | 3.5 | 19.5 | No | 12 | |
225.8 | 8.2 | 56.5 | No | 13.4 | |
166.8 | 42 | 3.6 | Yes | 19.6 | |
220.3 | 49 | 3.2 | Yes | 24.7 | |
18.8 | 21.7 | 50.4 | No | 7 | |
50 | 11.6 | 18.4 | No | 8.4 | |
59.6 | 12 | 43.1 | No | 9.7 | |
129.4 | 5.7 | 31.3 | No | 11 | |
76.3 | 27.5 | 16 | Yes | 12 | |
232.1 | 8.6 | 8.7 | No | 13.4 | |
229.5 | 32.3 | 74.2 | Yes | 19.7 | |
266.9 | 43.8 | 5 | Yes | 25.4 | |
25.1 | 25.7 | 43.3 | No | 8.5 | |
94.2 | 4.9 | 8.1 | Yes | 9.7 | |
116 | 7.7 | 23.1 | Yes | 11 | |
139.2 | 14.3 | 25.6 | No | 12.2 | |
68.4 | 44.5 | 35.6 | No | 13.6 | |
255.4 | 26.9 | 5.5 | Yes | 19.8 | |
289.7 | 42.3 | 51.2 | Yes | 25.4 | |
66.1 | 5.8 | 24.2 | No | 8.6 | |
75.5 | 10.8 | 6 | Yes | 9.9 | |
134.3 | 4.9 | 9.3 | No | 11.2 | |
206.8 | 5.2 | 19.4 | No | 12.2 | |
102.7 | 29.6 | 8.4 | No | 14 | |
220.5 | 33.2 | 37.9 | Yes | 20.1 | |
243.2 | 49 | 44.3 | Yes | 25.4 | |
16.9 | 43.7 | 89.4 | No | 8.7 | |
43.1 | 26.7 | 35.1 | Yes | 10.1 | |
69.2 | 20.5 | 18.3 | No | 11.3 | |
218.5 | 5.4 | 27.4 | No | 12.2 | |
175.7 | 15.4 | 2.4 | No | 14.1 | |
262.7 | 28.8 | 15.9 | No | 20.2 | |
283.6 | 42 | 66.2 | Yes | 25.5 | |
90.4 | 0.3 | 23.2 | No | 8.7 | |
44.7 | 25.8 | 20.6 | Yes | 10.1 | |
75.3 | 20.3 | 32.5 | No | 11.3 | |
239.8 | 4.1 | 36.9 | No | 12.3 | |
120.5 | 28.5 | 14.2 | No | 14.2 | |
248.4 | 30.2 | 20.3 | Yes | 20.2 | |
287.6 | 43 | 71.8 | Yes | 26.2 | |
56.2 | 5.7 | 29.7 | No | 8.7 | |
149.8 | 1.3 | 24.3 | Yes | 10.1 | |
199.8 | 3.1 | 34.6 | No | 11.4 | |
109.8 | 14.3 | 31.7 | No | 12.4 | |
172.5 | 18.1 | 30.7 | No | 14.4 | |
293.6 | 27.7 | 1.8 | Yes | 20.7 | |
276.9 | 48.9 | 41.8 | Yes | 27 | |
26.8 | 33 | 19.3 | No | 8.8 | |
140.3 | 1.9 | 9 | Yes | 10.3 | |
96.2 | 14.8 | 38.9 | No | 11.4 | |
67.8 | 36.6 | 114 | No | 12.5 | |
164.5 | 20.9 | 47.4 | Yes | 14.5 | |
238.2 | 34.3 | 5.3 | Yes | 20.7 | |
80.2 | 0 | 9.2 | Yes | 8.8 | |
139.5 | 2.1 | 26.6 | No | 10.3 | |
107.4 | 14 | 10.9 | No | 11.5 | |
237.4 | 5.1 | 23.5 | No | 12.5 | |
147.3 | 23.9 | 19.1 | No | 14.6 | |
184.9 | 43.9 | 1.7 | Yes | 20.7 | |
23.8 | 35.1 | 65.9 | Yes | 9.2 | |
222.4 | 3.4 | 13.1 | No | 11.5 | |
75.1 | 35 | 52.7 | No | 12.6 | |
78.2 | 46.8 | 34.5 | No | 14.6 | |
273.7 | 28.9 | 59.7 | Yes | 20.8 | |
224 | 2.4 | 15.6 | No | 11.6 | |
165.6 | 10 | 17.6 | No | 12.6 | |
74.7 | 49.4 | 45.7 | No | 14.7 | |
182.6 | 46.2 | 58.7 | No | 21.2 | |
48.3 | 47 | 8.5 | No | 11.6 | |
265.2 | 2.9 | 43 | Yes | 12.7 | |
187.9 | 17.2 | 17.9 | No | 14.7 | |
292.9 | 28.3 | 43.2 | No | 21.4 | |
121 | 8.4 | 48.7 | Yes | 11.6 | |
290.7 | 4.1 | 8.5 | Yes | 12.8 | |
227.2 | 15.8 | 49.9 | No | 14.8 | |
228 | 37.7 | 32 | No | 21.5 | |
197.6 | 3.5 | 5.9 | No | 11.7 | |
177 | 9.3 | 6.4 | Yes | 12.8 | |
280.2 | 10.1 | 21.4 | No | 14.8 | |
213.5 | 43 | 33.8 | No | 21.7 | |
222.4 | 4.3 | 49.8 | No | 11.7 | |
175.1 | 22.5 | 31.5 | No | 14.9 | |
241.7 | 38 | 23.2 | No | 21.8 | |
168.4 | 7.1 | 12.8 | No | 11.7 | |
188.4 | 18.1 | 25.6 | No | 14.9 | |
170.2 | 7.8 | 35.2 | No | 11.7 | |
142.9 | 29.3 | 12.6 | No | 15 | |
284.3 | 10.6 | 6.4 | Yes | 15 | |
193.2 | 18.4 | 65.7 | No | 15.2 | |
123.1 | 34.6 | 12.4 | No | 15.2 | |
93.9 | 43.5 | 50.5 | No | 15.3 | |
228.3 | 16.9 | 26.2 | No | 15.5 | |
184.9 | 21 | 22 | No | 15.5 | |
141.3 | 26.8 | 46.2 | No | 15.5 | |
187.8 | 21.1 | 9.5 | Yes | 15.6 | |
239.3 | 15.5 | 27.3 | Yes | 15.7 | |
240.1 | 16.7 | 22.9 | No | 15.9 | |
209.6 | 20.6 | 10.7 | No | 15.9 | |
125.7 | 36.9 | 79.2 | No | 15.9 | |
286 | 13.9 | 3.7 | No | 15.9 | |
110.7 | 40.6 | 63.2 | No | 16 | |
280.7 | 13.9 | 37 | No | 16.1 | |
202.5 | 22.3 | 31.6 | No | 16.6 | |
197.6 | 23.3 | 14.2 | No | 16.6 | |
109.8 | 47.8 | 51.4 | Yes | 16.7 | |
163.3 | 31.6 | 52.9 | Yes | 16.9 | |
213.4 | 24.6 | 13.1 | Yes | 17 | |
177 | 33.4 | 38.7 | No | 17.1 | |
215.4 | 23.6 | 57.6 | No | 17.1 | |
135.2 | 41.7 | 45.9 | No | 17.2 | |
191.1 | 28.7 | 18.2 | No | 17.3 | |
149.7 | 35.6 | 6 | No | 17.3 | |
214.7 | 24 | 4 | Yes | 17.4 | |
265.6 | 20 | 0.3 | Yes | 17.4 | |
253.8 | 21.3 | 30 | Yes | 17.6 | |
218.4 | 27.7 | 53.4 | Yes | 18 | |
131.1 | 42.8 | 28.9 | Yes | 18 | |
163.5 | 36.8 | 7.4 | Yes | 18 | |
199.1 | 30.6 | 38.7 | Yes | 18.3 | |
210.7 | 29.5 | 9.3 | Yes | 18.4 |
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 9 images