Case study 3
Team members: Emeline Abumbi; Gracie Wang; Trung Phan; Abbas Farhat
Question 1
1. Mower sales forecast for NA region for January-March 2015:
Month
Jan-2015
Feb-2015
Mar-2015
Period
61
62
63
Forecast Sales
57852.51
76911.75
81322.35
2. We implemented Multiple Regression Approach to predict for sales because:
a. The data did not exhibit the linear trend
b. The data also showed a significant seasonal component
The margin of error:
Mower Sales
Mean
Standard Deviation
Margin of Error (95%)
Confidence Interval
72580.9
16730.1
4213.4
76794.3
68367.5
3. Observations: There was an upward trend in Mower Sales in North America
region from the beginning of the year to June and gradually declined at the end of
the year. This tendency repeated every year but did not exhibit the clear trend
over the time.
Question 2
Tractor Unit Sales Time Series Plot Chart
3000
2500
2000
1500
1000
500
0
Jul-09
Jan-10
Aug-10
Feb-11
Sep-11
Apr-12
Actual
Oct-12
May-13
Nov-13
Jun-14
Dec-14
Linear (Actual)
Using method: Holt-Winters multiplicative model
Reason:
1) Seasonal: The graph appears a pattern of demand movement that repeats every 4
months.
2) Linear trend: The data contains a trend that goes upward.
3) Multiplicative: The model appears to be multiplicative rather than additive because the
amplitudes increase as the level increases.
MAE 107.888
MSE 23060.82
MAPE 10.65%
Jul-15
Holt-Winters / Seasonal multiplicative (NA)
6000
5000
NA
4000
3000
2000
1000
0
0
10
20
30
40
50
60
70
Date1
NA
Holt-Winters(NA)
Validation
Prediction
Lower bound (95%)
Upper bound (95%)
Forecast 2015 sales
January
February
March
2482.139
2918.093
3266.153
Observation:
1) The sales in North America appears in a pattern that high sales occurs in April and low
volume sales occurs in December. The pattern repeats every year.
2) The overall sales increases every year. The trend sales increase approximately 11.46%.
Question 3
a) Administrative expenses:
Administrative Time Series Forecast
a=0.73
800000
750000
700000
650000
600000
550000
500000
450000
400000
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263
Actual
Forecast:
Jan-15 $639,073
Feb-15 $638,146
Mar-15 $637,898
b) interests
Forecast
Interest Time Series Forecast
a=0.27
12000
10000
8000
6000
4000
2000
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Actual
Forecast
Forecast:
Jan-15 : $9687.98
Feb-15 : $9516.63
Mar-15 : $9391.96
Method used for forecast: Exponential smoothing model
Administrative a=0.73 MAD=15725.99
Interests: a=0.27 MAD=691.31
Reason is MAD is smaller, means less error hence better forecast result.
Question 4:
1. Unit production costs (both tractor and mower) forecast from January to March
2015
Chart Title
2500
2000
1500
1000
500
0
0
10
20
30
Total Costs (Y)
40
50
60
70
Total Cost Forecast
2. We chose Double Exponential Smoothing method to predict because:
a. The data exhibited the trend
b. No significant seasonal component is found in this time serial data
The margin of error:
Total Cost Forecast
2005.736
117.3425
29.55232
2035.288
1976.183
3. The percentage increase in costs in years 2010-2014:
Mean
Standard Deviation
Margin of Error (95%)
Confidence Interval
Month
Jan-10
Feb-10
Mar-10
Apr-10
May10
Jun-10
Jul-10
Aug-10
Sep-10
Oct-10
Nov-10
Dec-10
Total Costs
(Y)
1800
1805
1814
1821
1829
Increased
Percentage
1836
1843
1846
1853
1856
1862
1865
0.38
0.38
0.16
0.38
0.16
0.32
0.16
0.28
0.50
0.39
0.44
Jan-11
Feb-11
Mar-11
Apr-11
May11
Jun-11
Jul-11
Aug-11
Sep-11
Oct-11
Nov-11
Dec-11
Jan-12
1890
1896
1903
1909
1916
1.34
0.32
0.37
0.32
0.37
1922
1928
1934
1941
1949
1954
1960
1984
0.31
0.31
0.31
0.36
0.41
0.26
0.31
1.22
Feb-12
Mar-12
Apr-12
May12
Jun-12
Jul-12
Aug-12
Sep-12
Oct-12
Nov-12
Dec-12
Jan-13
Feb-13
Mar-13
Apr-13
May13
Jun-13
1990
1997
2003
2009
0.30
0.35
0.30
0.30
2016
2023
2029
2036
2043
2051
2057
1999
2005
2011
2017
2024
0.35
0.35
0.30
0.34
0.34
0.39
0.29
-2.82
0.30
0.30
0.30
0.35
2030
0.30
Jul-13
Aug-13
Sep-13
Oct-13
Nov-13
Dec-13
Jan-14
Feb-14
Mar-14
Apr-14
May14
Jun-14
Jul-14
Aug-14
Sep-14
Oct-14
Nov-14
Dec-14
2036
2043
2050
2056
2073
2069
2136
2140
2144
2149
2155
0.30
0.34
0.34
0.29
0.83
-0.19
3.24
0.19
0.19
0.23
0.28
2161
2168
2174
2180
2186
2193
2199
0.28
0.32
0.28
0.28
0.28
0.32
0.27
4. Inflation effect:
Inflation Rate over years from 2010 to 2014
2010
2011
2012
2013
2014
2.6
1.6
2.9
1.6
1.6
2.1
2.1
2.9
2
1.1
2.3
2.7
2.7
1.5
1.5
2.2
3.2
2.3
1.1
2
2
3.6
1.7
1.4
2.1
1.1
3.6
1.7
1.8
2.1
1.2
3.6
1.4
2
2
1.1
3.8
1.7
1.5
1.7
1.1
3.9
2
1.2
1.7
1.2
3.5
2.2
1
1.7
1.1
3.4
1.8
1.2
1.3
1.5
3
1.7
1.5
0.8
1.6
3.2
2.1
1.5
1.6
Following the table, the inflation intensively occurred during 2011 and beginning of
2012, and during this period, the trend of total costs presented changes of its behavior
correspondingly.
As we can see, the inflation stared at year 2011 and continuously increasing during this
year, compared with the total costs which also jumped its increase percentage from Dec-10
(1.6%) to Jan-11 (1.34%). When the inflation rate started decreasing in next year (2012) the
costs’ increase percentage started leveled off and finally dropped to -2.82% at the end of the
year 2012 (Jan-13)
Obviously, the inflation had significantly affected to the unit production costs.