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). Interpret the coefficient for the Coupon dummy variable in context. Predict the sales for a month when a coupon was published and the advertising budgets were $1.2 hundred for TV, $25.4 hundred for Radio, and $35.3 hundred for Newspaper (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
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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).
- Interpret the coefficient for the Coupon dummy variable in context.
- Predict the sales for a month when a coupon was published and the advertising budgets were $1.2 hundred for TV, $25.4 hundred for Radio, and $35.3 hundred for Newspaper (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 |
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