Double Log Model

1. By
Tuhin Chattopadhyay, Ph.D.

2.  Measure the contribution of each of the
independent variables in the model.
 Separating product sales into base and incremental
volume
 Quantification of the long-term impact of
marketing investments on sales
 ROI

3. 0
100000
200000
300000
400000
500000
600000
27/06/10
08/08/10
19/09/10
31/10/10
12/12/10
23/01/11
06/03/11
17/04/11
29/05/11
10/07/11
21/08/11
02/10/11
13/11/11
25/12/11
05/02/12
18/03/12
29/04/12
10/06/12
22/07/12
02/09/12
14/10/12
25/11/12
06/01/13
17/02/13
31/03/13
12/05/13
23/06/13
Week
TGYVolume
TGY Volume

4. 0
100000
200000
300000
400000
500000
600000
0
10000
20000
30000
40000
50000
60000
70000
27/06/10
01/08/10
05/09/10
10/10/10
14/11/10
19/12/10
23/01/11
27/02/11
03/04/11
08/05/11
12/06/11
17/07/11
21/08/11
25/09/11
30/10/11
04/12/11
08/01/12
12/02/12
18/03/12
22/04/12
27/05/12
01/07/12
05/08/12
09/09/12
14/10/12
18/11/12
23/12/12
27/01/13
03/03/13
07/04/13
12/05/13
16/06/13
TVImps
TGYVolume
TVImps And Sales

5. 0
50000
100000
150000
200000
250000
300000
350000
0
100000
200000
300000
400000
500000
600000
27/06/10
08/08/10
19/09/10
31/10/10
12/12/10
23/01/11
06/03/11
17/04/11
29/05/11
10/07/11
21/08/11
02/10/11
13/11/11
25/12/11
05/02/12
18/03/12
29/04/12
10/06/12
22/07/12
02/09/12
14/10/12
25/11/12
06/01/13
17/02/13
31/03/13
12/05/13
23/06/13
TVSpend
TGYVolume
TV Spend and Sales

6.  They have deployed 6 TV campaigns over the
Period with a total expenditure of £2,977,167.61.
 Each campaign lasted from 4 to 8 weeks.
 The exposure to TV advertising builds awareness,
carry over effects resulting in sales.

7. 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
100000
200000
300000
400000
500000
600000
27/06/10
01/08/10
05/09/10
10/10/10
14/11/10
19/12/10
23/01/11
27/02/11
03/04/11
08/05/11
12/06/11
17/07/11
21/08/11
25/09/11
30/10/11
04/12/11
08/01/12
12/02/12
18/03/12
22/04/12
27/05/12
01/07/12
05/08/12
09/09/12
14/10/12
18/11/12
23/12/12
27/01/13
03/03/13
07/04/13
12/05/13
16/06/13
TGYAvgprice
TGYVolume(Sales)
TGYVolume
TGYAvgPrice
Price And Sales

8. Christmas week seasonal dummy downs
every year in December

12. LOG(TGYVOLUME) =
3.042
- 0.7243*LOG(TGYAVGPRICE)
+ 0.6593*LOG(COMPVOLUME)
- 0.0041*LOG(COMPSSPEND)
- 0.1937*D1
+ 0.0512*M6
+ 0.0704*M7
- 0.0864*M11
+ 0.0053*LOG(TVIMPS)
+ 0.8460*UT

13.  Model:
◦ Significant F-stat and high R-squared
 Variables:
◦ Significant T-stats
◦ Coefficients must make sense
◦ Variance inflation factor low
 Residuals:
◦ Normality (Jarque-Bera)
◦ Absence of serial correlation ( Durbin Watson, correlogram)
◦ Hteroskedasticity Test: Breusch-Pagan-Godfrey

14. Normal Error
yy ˆˆ 

15. No
Hetroskedasticity
detected
No
Autocorrelation
detected

17. -400000
-200000
0
200000
400000
600000
800000
1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
CompsSpend
Tvimps
TGYAvgPrice
Base
TGY Volume

18. -20000000
-10000000
0
10000000
20000000
30000000
40000000
50000000
2010 2011 2012 2013
CompsSpend
Tvimps
TGYAvgPrice
Base value
TGY Value

19. £105,634
£436,791
£714,106
£180,336
£275,380
£770,006
£1,156,772
£775,009
£0
£200,000
£400,000
£600,000
£800,000
£1,000,000
£1,200,000
£1,400,000
2010 2011 2012 2013
Revenue
Cost

20. -0.62
-0.43
-0.38
-0.77
-0.90
-0.80
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
2010 2011 2012 2013
ROI
ROI
TOTCost
TOTCostvenueTOT
ROI


Re

21. £26,804,912
£5,097,661
£20,537,257
£331,156 £257,404
£10,776,755
£0
£5,000,000
£10,000,000
£15,000,000
£20,000,000
£25,000,000
£30,000,000
£35,000,000
2010 Inc Base Inc TV Dec TGYavg
price
Compspend 2011

22. £31,405,936
£5,297,871
£1,373,072
£10,994,652
£277,315
£26,804,912
£0
£5,000,000
£10,000,000
£15,000,000
£20,000,000
£25,000,000
£30,000,000
£35,000,000
£40,000,000
2011 Inc Base Inc TV Dec TGYavg
price
Compspend 2012

23. £17,923,363
£18,897,076
£533,770
£5,285,581
£662,692
£31,405,936
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
2012 Inc Base Inc TVDec TGYavg priceCompspend 2013

24.  Model building
 Decomposition
 Contribution effects,
 Annual Decomposition Effects
 ROI
 Water fall Charts

26. TGYVOLUME = 309470.312165
84190.05*TGYAVGPRICE
- 53225.33*D1
+ 0.3956*TVIMPS
+ 0.5313*TVIMPS(-1)
+ 0.4782*TVIMPS(-2)
+ 0.6034*TVIMPS(-3)
+ 0.0416*COMPVOLUME
- 0.0581*COMPSSPEND
- 33985.6*RW
+ 0.9363*UT

27.  Model:
◦ Significant F-stat and high R-squared
 Variables:
◦ Significant T-stats
◦ Coefficients must make sense
◦ Variance inflation factor low
 Residuals:
◦ Normality (Jarque-Bera)
◦ Absence of serial correlation ( Durbin Watson, correlogram)
◦ Hteroskedasticity Test: Breusch-Pagan-Godfrey

31. -200000
-100000
0
100000
200000
300000
400000
500000
600000
700000
Week
22/08/10
10/03/10
14/11/10
26/12/10
02/06/11
20/03/11
05/01/11
06/12/11
24/07/11
09/04/11
16/10/11
27/11/11
01/08/12
19/02/12
04/01/12
13/05/12
24/06/12
08/05/12
16/09/12
28/10/12
12/09/12
20/01/13
03/03/13
14/04/13
26/05/13
07/07/13
Base Seasonal TV TGYavg price Compspend TGY Volume

32. -10000000
-5000000
0
5000000
10000000
15000000
20000000
25000000
30000000
2010 2011 2012 2013
Compspend
TGYavg price
TV
Seasonal
Base
TGY Volume

33. £102,545.65
£599,523.29
£1,026,225.93
£515,991.52
£275,380.00
£770,006.20
£1,156,772.00
£775,009.00
2010 2011 2012 2013
Revenue Cost

34. -0.63
-0.22
-0.11
-0.33
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
2010 2011 2012 2013
ROI
ROI

35. £26,804,803.67
£5,155,713.64
£14,844,271.93
£6,756,794.73
£496,977.65
£53,354.12
£9,809,118.88
£0.00
£5,000,000.00
£10,000,000.00
£15,000,000.00
£20,000,000.00
£25,000,000.00
£30,000,000.00
£35,000,000.00
2010 Inc Base Inc
Seasonal
Inc TV Dec
TGYavg
price
Compspend 2011

36. £31,405,782.42
£2,699,682.90
£989,600.71
£2,698,702.80
£5,164,856.93
£426,702.64
£26,804,803.67
£0.00
£5,000,000.00
£10,000,000.00
£15,000,000.00
£20,000,000.00
£25,000,000.00
£30,000,000.00
£35,000,000.00
£40,000,000.00
2011 Inc Base Inc Seasonal Inc TV Inc TGYavg
price
Inc
Compspend
2012

37. £17,923,263.06
£13,044,750.20
£5,626,723.30
£510,234.42
£5,288,963.04 £410,225.51
£31,405,782.42
£0.00
£5,000,000.00
£10,000,000.00
£15,000,000.00
£20,000,000.00
£25,000,000.00
£30,000,000.00
£35,000,000.00
2012 Inc Base Seasonal TV TGYavg
price
Compspend 2013

38.  Model building
 Decomposition
 Contribution effects,
 Annual Decomposition Effects
 ROI
 Water fall Charts