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Suppose the observed unit sales (in millions) for a durable good (which lasts for 15 years before it needs to be replaced by a customer) during the first 5 years of its life are 0.625, 1.277, 1.712, 2.152 and 2.394. How many adopters are expected to adopt this product over its entire lifetime?

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FINAL EXAM – SPRING 2023 (40 POINTS TOTAL)
Please submit your answers electronically by uploading on Canvas by 1 PM on March 3 (Friday), 2023.
Question 1 (8 points)
[PART A]
Suppose the observed unit sales (in millions) for a durable good (which lasts for 15 years before it needs
to be replaced by a customer) during the first 5 years of its life are 0.625, 1.277, 1.712, 2.152 and 2.394.
How many adopters are expected to adopt this product over its entire lifetime? (2 points)
[Part B]
Estimate the Generalized Bass Model (GBM) for the SUV category whose quarterly category-level
adoptions data (from 1990 to 2000) are given in the Excel file, “FinalExam2023-Question1B.csv.” [Hint:
Use Number Analytics software].
1. Report the estimated market size for SUVs. Also report the forecasted SUV adoptions for the next
5 quarters (Q43-Q47). (2 points)
2. What is the sign of the estimated value of badv? What does it imply for SUV adoption? (2 points)
3. Among the estimated values of p and q, which is larger? Suppose we exchanged the values of p
and q. What would that imply for the shape of the SUV adoption curve? (2 points)
Question 2 (8 points)
Electronic Book Readers (“EReaders” for short) were introduced to the US market in 2004. In 2003, a
marketing consultant was tasked with developing a forecast for how many EReaders would sell during the
year of launch so that EReader production could be planned accordingly. The consultant gathered data on
a set of potential analogs for EBook Readers, and these analogs, as well as their Bass Model parameters
(estimated using historical data on their adoption in patterns in the US), are listed below.
_____________________________________________________________________________________
Product
m (in millions)
p
q
_____________________________________________________________________________________
CD Player (1986-1996)
29.6
0.055
0.378
Cable TV Service (1981-1994)
68.0
0.100
0.060
Home PC (1982-1988)
25.8
0.121
0.281
Cellular Telephone (1986-1996)
45.1
0.008
0.421
Handheld Organizer (1997-2004)
80.5
0.043
0.565
MP3 Player (1999-2004)
388
0.009
0.783
_____________________________________________________________________________________
1. Play the role of a Delphi and choose relevant analogs for the EReader from the above set. Briefly
explain the reasons for your choice of including and excluding analogs. (2 points)
2. Calculate simple average values of p and q across your chosen analogs. Do these averages
represent reasonable estimates of p and q for EReaders? (1 point)
3. Give each chosen analog two types of similarity ratings, as discussed in class. Also give relative
weights to the two types of similarity ratings. Using these similarity ratings and relative weights,
calculate the weights for each analog. Use these weights to calculate weighted average values of
p and q across your chosen analogs. Are these weighted averages more reasonable estimates of
p and q for EReaders than the estimates in the previous question? (2 points)
The marketing consultant gathered the following information from the US census and other public data
sources.
Total US population (2004 estimate)
293.7 million
Percentage of US population reading literature
46.7 %
Number of US households
111.3 million
US Household PC Penetration (2002)
74.1 million
US Internet Penetration
67.8 %
Percentage of Internet Users Likely to Buy Music Online
42 %
Percentage of Traditional Paper Books Purchased Online in 2003
8%
US Household Penetration of Cell Phones
66 %
US Household Penetration of MP3 Players
6%
Cumulative Number of Downloads from iTunes (4/03-4/05)
350 million
Amazon.com Worldwide Customer Base
47 million
Average Number of Books Purchased Per Year Per Consumer
3.25
The marketing consultant gathered the following information from consumer surveys.
Read recreational material from a PDA
12 %
Read recreational material on a dedicated eBook device
28 %
Sample a business-related publication on a computer
44 %
Read a reference book on a PC / laptop
66 %
4. Use any information from the above lists that you believe are relevant, and then use the chain
ratio method to develop an estimate of market size (M) for EReaders. (1 point)
5. Using the estimates of p, q, M obtained under questions 3 and 4 above, forecast the adoptions of
EReaders in Years 1 and 2. (2 points)
Question 3 (8 points)
Reproduced below is the AR perceptual map for beer brands that we discussed in class.
1. Between the two brands Coors and Heineken, which brand is perceived as a more “special
occasions” type of beer? Explain the reason for your choice. (2 points)
2. Suppose you are the brand manager of an existing brand of beer that is positioned in the market
as a beer meant for special occasions. The above perceptual map shows that the attribute vector
labeled “special occasions” is perpendicular to the attribute vector labeled “light.” Given this
finding, explain one strategy that you will employ in the future to market your brand of beer in
terms of its lightness. Explain the reason for your chosen strategy. (2 points)
3. There is another type of perceptual map called the OS map. What is the main strength of the OS
perceptual map compared to the AR perceptual map (such as the one shown above)? (2 points)
4. Which of the two maps is more appropriate from the standpoint of managing your “special
occasions” type of brand (do not say “it depends” or “both”!)? Explain the rationale for your
choice.
Question 4 (8 points)
You must use the Excel file titled “FinalExam2023-Question4.csv” to answer the following questions.
1. The Scan*Pro model for Brand X is given by ln (oz_x) = x + β1x * ln (px) + β2x * ln (py) + β3x
* deal_x + β4x * feat_x. Estimate this Scan*Pro model for brand X. Report the estimated
values of the 5 coefficients — x, β1x, β2x, β3x, β4x (Hint: Use brand X sales data only; ignore
brand Y sales data; use data from all stores). (1 point)
2. The Scan*Pro model for Brand Y is given by ln (oz_y) = y + β1y * ln (px) + β2y * ln (py) + β3y
* deal_y + β4y * feat_y. Estimate this Scan*Pro model for brand Y. Report the estimated
values of the 5 coefficients — y, β1y, β2y, β3y, β4y (Hint: Use brand Y sales data only; ignore
brand X sales data; use data from all stores). (1 point)
3. Which of the two brands has higher clout? (1 point)
4. If brand X cut its price by 0.5 %, by what % will its sales increase? (1 point)
5. If brand Y cut its price by 0.5 %, will its sales increase by a larger or smaller % than the
answer you calculated for brand X above? (1 point)
6. Suppose px = py = 1, deal_x = deal_y = 0, feat_x = feat_y = 0. How many more ounces will
the stronger brand sell than the weaker brand? (1 point)
7. Suppose brand X engages in both display and feature advertising, by what multiple will its
sales increase compared to when it engages in neither type of advertising? (1 point)
8. There are a total of 10 different brands in the product category that brands X and Y belong
to. In that case, why do you think that we are using only the prices of brands X and Y (and
ignoring the prices of the remaining 8 brands in the product category) in the above
Scan*Pro model? Why not additionally use other brands’ prices as well? (1 point)
Question 5 (8 points)
Given in the Excel file “FinalExam2023-Question5.xlsx” are the weekly advertising spending (thousands of
GRPs), prices ($) and unit sales (in hundreds of thousands) of a brand of perfume in the United States over
the 52 weeks of 2020.
1. Suppose Adpp1 and Adpp2 refer to the weekly advertising spending (thousands of GRPs) in the
previous week, and in the previous-to-previous week, respectively. Assume the following
Scan*Pro model for this perfume brand:
ln (Unit Sales) =  + β1 * ln (Price) + β2 * ln (Ad) + β3 * ln (Adpp1) + β4 * ln (Adpp2).
Estimate this Scan*Pro model and report the estimated coefficients — , β1, β2, β3, β4. (2 points)
2. What is the price elasticity of the perfume brand? Clearly interpret its numerical value in words.
(1 point)
3. What is the brand equity of the perfume brand? Clearly interpret its numerical value in words. (1
point)
4. Clearly interpret the estimated coefficient β 4 in words. ( 1 point)
5. What is the total advertising elasticity of the perfume brand? (Hint: Assume infinite dynamic
carryover effect of advertising). (1 point)
6. Suppose you ignored the effect of dynamic advertising carryover in the Scan*Pro model by
dropping variables Adpp1 and Adpp2 from the regression analysis. What do you think will change
in terms of your conclusions? Why? (1 point)
7. Compare the perfume brand’s price elasticity (from part 2 above) to its estimated total advertising
elasticity calculated (from part 5 above). What do you conclude on the basis of this comparison?
(1 point)
GOOD LUCK!
Quarter
Sales
1
2
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25
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27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
121154
157640
144451
164984
172697
168451
178018
199187
200796
209513
220392
264539
272156
291614
283745
278325
278638
341365
291980
351525
323118
359708
331423
369062
387187
402464
331528
383105
378938
389872
339073
402731
364452
403693
369276
411223
427109
439321
408572
431491
422275
352022
Advertising
7.35205
9.79288
7.74146
7.47065003
6.44911003
8.90226
8.44509006
9.72147006
6.95411006
9.87117006
9.13735
9.41215
7.89009
7.05407
6.11257
7.73325
5.05089
8.75479
9.26566
8.09745
5.33041
10.96397
9.17477
9.15614
7.80073
10.00208
9.83857
13.10364
10.40422
12.41814
7.95822
7.90897
4.78761
6.88859
6.72067
9.98735
6.16558
7.96756
4.22949
10.39312
6.64432
8.72444
STORE
Hval_150
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
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62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
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0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
0.09001
WEEK
OUNCES
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
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134
135
136
137
138
139
140
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142
143
144
145
146
147
148
149
150
151
152
101
UPC_X
72
72
72
72
72
72
72
72
72
72
72
72
72
72
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72
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4900000636
deal_X
feat_X
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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0
1
0
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0
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0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
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1
0
0
0
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1
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1
1
0
0
0
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1
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0
1
1
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1
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1
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1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
oz_X
13032
3384
2088
35064
26640
2304
1800
2592
2520
1728
2376
5832
2448
2592
2376
2808
6264
4824
2520
24264
2520
22896
31824
2376
20808
2304
3240
2592
2448
3384
2160
25776
14616
2232
2160
2016
3024
2232
3456
2520
2304
2448
3600
29160
2016
32976
2016
2952
2160
26280
3168
2448
2160
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0.09001
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0.09001
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102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
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126
127
128
129
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131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
72
72
72
72
72
72
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72
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72
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2016
2232
2160
3024
1584
3096
2016
2232
2088
3816
2376
3744
3888
2160
29592
2376
2304
3024
3312
2304
2304
2304
2448
3600
2016
2880
2592
2952
2952
2304
2664
2376
1008
2232
936
19512
35208
1944
2736
2952
2376
4104
1800
2376
2376
3384
24408
2016
2448
2088
2592
29880
25920
2664
1944
63
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111
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120
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136
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139
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141
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143
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145
146
147
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149
150
151
152
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2304
26568
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28728
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2520
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26352
2160
2016
3240
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25416
2160
2736
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2304
15768
2592
23688
6984
2232
2088
3024
1152
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2160
2088
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1944
50760
1512
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3240
2736
2808
1944
3600
2160
2304
2520
3600
16848
24840
2808
3312
25992
2520
26712
1656
2448
27576
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
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4900000057
4900000057
4900000057
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4900000057
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4900000636
4900000636
4900000636
4900000636
4900000636
4900000636
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2160
2736
5184
2304
2808
2232
1080
2664
26496
2088
1944
2664
28296
2376
2808
21744
2376
1584
2808
3384
2016
2088
2376
3384
2808
1944
1152
2448
11088
2232
2304
2376
3312
25416
3168
2376
2376
15048
2952
24480
2448
2448
16560
20376
2160
6408
2952
2736
14760
2232
2592
2952
15048
2016
3168
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
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67
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67
67
67
67
67
67
67
67
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.29634
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
4900000636
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4900000636
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4900000636
4900000636
4900000636
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4900000636
4900000636
4900000636
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4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1080
38952
2664
11808
2736
14472
2088
1224
3096
31464
2736
2808
2232
30096
2160
2088
14832
3312
2592
2016
2376
25200
2160
2664
3024
2232
2808
2160
21672
2448
3384
2880
2304
3096
3384
7920
2232
2880
13608
21240
2160
18000
3168
1728
35928
2736
2088
2664
1872
32472
2376
32400
28584
2664
2664
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
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72
72
72
72
72
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72
72
72
72
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4900000057
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4900000636
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4900000636
4900000636
4900000636
4900000636
4900000636
4900000636
1
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0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
15696
2232
2448
43632
27360
2808
3096
27000
2232
25920
2736
36216
1008
2088
2232
2016
20088
3024
2592
2952
1872
29160
22032
2592
2664
1872
2232
40896
3888
2160
2880
2664
7344
1152
1872
2376
2160
2448
14112
16632
3816
3240
3312
3240
2016
2376
2160
1944
1800
2160
2232
1944
2808
2880
2088
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.21453
0.25259
0.25259
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0.25259
0.25259
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0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
4900000636
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4900000057
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4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
4900000057
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
8064
2088
25560
1224
27504
1944
3168
3168
2664
6264
2088
2376
2232
2664
3888
8784
3096
3096
1872
18072
2520
3528
7128
2016
23184
6120
2088
1728
22536
2016
21816
2736
2160
2952
2448
3096
2304
2952
23832
1800
2736
2088
3600
34776
1080
2880
2232
3024
2736
2592
2592
3024
2880
36936
2088
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
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68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
68
0.25259
0.25259
0.25259
0.25259
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0.25259
0.25259
0.25259
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0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
0.25259
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
4900000057
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4900000636
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4900000636
4900000636
4900000636
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4900000636
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4900000636
4900000636
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4900000636
4900000636
4900000636
4900000636
4900000636
4900000636
4900000636
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
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0
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0
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0
1
0
0
0
0
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0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
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1
0
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1
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0
1
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0
0
0
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1
1
2304
29160
16200
2520
24480
39384
26928
2304
3096
28080
2016
2088
19008
2592
2160
2376
3168
2880
2520
2376
2736
2592
3024
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1
0
0
0
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0
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1
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1
1
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0
0
1
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1
0
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1
0
1
0
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0
1
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1
1
0
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1
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1656
3384
1800
45936
936
1512
2448
3960
432
7200
5112
2448
4680
360
1080
160992
4752
3168
648
25776
22176
1800
2592
360
9720
1728
720
7632
1296
1296
576
432
9072
864
10224
360
1512
648
36000
216
11088
11664
2304
7560
576
4032
6048
16056
9936
504
2160
4032
4104
864
1296
23
47
25
638
13
21
34
55
6
100
71
34
65
5
15
2236
66
44
9
358
308
25
36
5
135
24
10
106
18
18
8
6
126
12
142
5
21
9
500
3
154
162
32
105
8
56
84
223
138
7
30
56
57
12
18
0.039
0.021
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0.025
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0.025
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218
31
34
606
380
39
43
375
31
360
38
503
14
29
31
28
279
42
36
41
26
405
306
36
37
26
31
568
54
30
40
37
102
16
26
33
30
34
196
231
53
45
46
45
28
33
30
27
25
30
31
27
39
40
29
1200000044
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1
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1
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1
1
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1
4968
40752
5328
3456
576
5544
3888
648
576
5184
288
2664
2952
1656
34056
1224
10728
5256
1008
1944
1800
792
23976
5040
1512
45288
8424
2016
1440
1512
4176
1728
5112
41976
22824
19584
360
792
1080
45936
4680
3600
2592
648
648
1800
936
8352
14688
6264
1728
5040
5904
1080
37152
69
566
74
48
8
77
54
9
8
72
4
37
41
23
473
17
149
73
14
27
25
11
333
70
21
629
117
28
20
21
58
24
71
583
317
272
5
11
15
638
65
50
36
9
9
25
13
116
204
87
24
70
82
15
516
0.025
0.030
0.030
0.021
0.022
0.028
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0.022
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0.022
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0.039
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0.023
112
29
355
17
382
27
44
44
37
87
29
33
31
37
54
122
43
43
26
251
35
49
99
28
322
85
29
24
313
28
303
38
30
41
34
43
32
41
331
25
38
29
50
483
15
40
31
42
38
36
36
42
40
513
29
1200000281
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1
1
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1
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0
0
1
0
1
1
0
1
0
0
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0
0
0
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0
0
0
0
0
0
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0
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1
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0
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1
1
0
1
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0
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1
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0
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1
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1
1
0
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0
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1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1152
1800
1512
4320
4896
432
3528
14904
49968
2520
41256
14904
648
2304
4680
2664
7704
6696
3312
4608
1080
288
936
21600
2088
2592
864
11376
2952
35784
25488
720
9936
288
4104
1584
3456
432
4536
9720
216
1368
864
2880
2376
2520
17136
1440
1368
1080
4104
7920
288
864
50976
16
25
21
60
68
6
49
207
694
35
573
207
9
32
65
37
107
93
46
64
15
4
13
300
29
36
12
158
41
497
354
10
138
4
57
22
48
6
63
135
3
19
12
40
33
35
238
20
19
15
57
110
4
12
708
0.030
0.030
0.022
0.039
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0.028
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0.039
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0.021
32
405
225
35
340
547
374
32
43
390
28
29
264
36
30
33
44
40
35
33
38
36
42
35
41
38
37
19
63
29
33
33
16
370
34
40
26
36
44
33
30
316
41
100
34
32
37
35
40
33
40
37
14
264
418
1200000044
1200000044
1200000044
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1200000281
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1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
43992
13032
3384
6048
2232
4608
24624
11160
1152
4680
40392
3312
1224
1008
4608
3816
2304
432
1944
8712
4536
24120
4464
44928
23256
1224
360
1224
50616
6624
6048
1440
1368
32832
3240
1008
3960
504
9360
11448
1224
19368
7848
4608
5688
792
8640
1512
7632
504
1224
12168
52560
3312
3888
611
181
47
84
31
64
342
155
16
65
561
46
17
14
64
53
32
6
27
121
63
335
62
624
323
17
5
17
703
92
84
20
19
456
45
14
55
7
130
159
17
269
109
64
79
11
120
21
106
7
17
169
730
46
54
0.030
0.023
0.025
0.030
0.022
0.021
0.021
0.030
0.028
0.023
0.030
0.030
0.025
0.030
0.030
0.030
0.028
0.030
0.030
0.030
0.028
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0.028
0.028
0.028
0.030
0.028
0.039
0.030
0.030
0.030
0.030
0.039
0.022
0.030
0.028
0.030
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0.028
0.030
0.030
0.022
0.028
0.030
0.030
0.030
0.030
0.030
0.028
0.030
0.028
0.028
0.039
0.025
0.022
0.021
0.030
0.030
0.030
0.030
0.030
0.021
0.030
0.030
0.030
0.021
0.028
0.030
0.030
0.030
0.028
0.030
0.039
0.028
0.030
0.028
0.021
0.030
0.021
0.023
0.028
0.028
0.039
0.021
0.030
0.030
0.030
0.030
0.021
0.030
0.028
0.030
0.030
0.030
0.030
0.030
0.023
0.030
0.030
0.030
0.030
0.030
0.030
0.030
0.030
0.028
0.023
0.030
0.030
0.030
46
32
41
34
28
41
27
42
45
37
384
30
270
31
30
1200000281
1200000281
1200000281
1200000281
1200000281
1200000281
1200000281
1200000281
1200000281
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1200000281
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1200000281
1200000281
1200000281
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1440
2016
20016
4464
1728
432
2592
5760
7056
1800
9936
4752
2808
18432
4752
20
28
278
62
24
6
36
80
98
25
138
66
39
256
66
0.028
0.030
0.028
0.030
0.030
0.028
0.030
0.028
0.028
0.030
0.022
0.030
0.025
0.030
0.030
0.030
0.028
0.021
0.030
0.030
0.030
0.030
0.030
0.028
0.030
0.030
0.028
0.030
0.028
0.028
cx
cY
0.021
0.023
0.025
0.017
0.018
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.023
0.025
0.025
0.023
0.018
0.025
0.018
0.018
0.023
0.018
0.025
0.025
0.023
0.025
0.023
0.025
0.019
0.021
0.025
0.025
0.025
0.023
0.025
0.023
0.025
0.025
0.025
0.023
0.018
0.025
0.017
0.025
0.023
0.025
0.019
0.023
0.023
0.025
class
0.022
0.025
0.022
0.025
0.022
0.024
0.019
0.022
0.025
0.019
0.025
0.019
0.025
0.025
0.022
0.025
0.022
0.019
0.025
0.024
0.024
0.019
0.025
0.017
0.019
0.025
0.025
0.025
0.025
0.024
0.022
0.025
0.024
0.022
0.022
0.022
0.025
0.025
0.025
0.025
0.022
0.025
0.025
0.022
0.022
0.022
0.025
0.025
0.025
0.022
0.019
0.025
0.022
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
lit
reg
0.025
0.023
0.025
0.023
0.025
0.023
0.025
0.023
0.025
0.023
0.025
0.023
0.023
0.025
0.018
0.025
0.025
0.023
0.023
0.025
0.025
0.025
0.025
0.023
0.025
0.023
0.023
0.023
0.023
0.025
0.023
0.025
0.032
0.025
0.032
0.021
0.017
0.025
0.023
0.023
0.025
0.023
0.025
0.023
0.025
0.023
0.018
0.025
0.025
0.023
0.023
0.018
0.018
0.025
0.025
0.022
0.025
0.025
0.025
0.017
0.025
0.025
0.022
0.025
0.031
0.019
0.031
0.025
0.017
0.025
0.025
0.024
0.025
0.025
0.022
0.025
0.017
0.025
0.025
0.019
0.022
0.022
0.025
0.025
0.025
0.025
0.022
0.022
0.022
0.019
0.025
0.024
0.017
0.025
0.022
0.019
0.031
0.017
0.017
0.024
0.025
0.019
0.019
0.025
0.019
0.025
0.024
0.024
0.024
0.017
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
lit
lit
lit
lit
0.025
0.025
0.023
0.025
0.017
0.023
0.018
0.025
0.019
0.023
0.023
0.017
0.023
0.018
0.025
0.025
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0.023
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0.022
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
reg
Week Advertising GRPs (in thousands)
Price ($)
Unit Sales (in hundred thousands)
1
133.3928256 5.639422365
2.648133349
2
3.694304395 8.215130058
0.760499318
3
0.960336936 9.596032234
0.412447672
4
68.43348526 5.087044169
1.830883778
5
3.429925654 5.296597205
1.929689179
6
0.977225912 7.36727545
0.640444326
7
89.82531224 7.145172751
0.969151962
8
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