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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Dec 2017 17:00:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/17/t15135264382brk3iiwdxsopc6.htm/, Retrieved Wed, 15 May 2024 21:17:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310016, Retrieved Wed, 15 May 2024 21:17:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-12-17 16:00:26] [1fb90e819e5b19aec9e872ea972cd63e] [Current]
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Dataseries X:
58.4
64.8
73.8
65
73
71.1
58.2
64
75
74.9
75
68.3
72.5
72.4
79.6
70.7
76.4
79.7
64.2
67.9
74.1
78.5
73.4
65.4
69.9
69.6
76.8
75.6
74
76
68.1
65.5
76.9
81.7
73.6
68.7
73.3
71.5
78.3
76.5
71.8
77.6
70
64
81.3
82.5
73.1
78.1
70.7
74.9
88
81.3
75.7
89.8
74.6
74.9
90
88.1
84.9
87.7
80.5
79
89.9
86.3
81.1
92.4
71.8
76.1
92.5
87
89.5
88.7
83.8
84.9
99
84.6
92.7
97.6
78
81.9
96.5
99.9
96.2
90.5
91.4
89.7
102.7
91.5
96.2
104.5
90.3
90.3
100.4
111.3
101.3
94.4
100.4
102
104.3
108.8
101.3
108.9
98.5
88.8
111.8
109.6
92.5
94.5
80.8
83.7
94.2
86.2
89
94.7
81.9
80.2
96.5
95.6
91.9
89.9
86.3
94
108
96.3
94.6
111.7
92
91.9
109.2
106.8
105.8
103.6
97.6
102.8
124.8
103.9
112.2
108.5
92.4
101.1
114.9
106.4
104
101.6
99.4
102.3
121.3
99.3
102.9
111.4
98.5
98.5
108.5
112.1
105.3
95.2
98.2
96.6
109.6
108
106.7
111.5
104.5
94.3
109.6
116.4
106.5
100.5
101.7
104.1
112.3
111.2
108.2
115.1
102.3
93.6
120.6
118.4
106.6
105.3
101.5
100.1
119.5
111.2
103.7
117.8
101.7
97.4
120
117
110.6
105.3
100.9
108.1
119.3
113
108.6
123.3
101.4
103.5
119.4
113.1
112
115.8
105.4
110.9
128.5
109
117.2
124.4
104.7
108.6




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310016&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310016&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310016&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.201076272503187
beta0.391676265650881
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.201076272503187 \tabularnewline
beta & 0.391676265650881 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310016&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.201076272503187[/C][/ROW]
[ROW][C]beta[/C][C]0.391676265650881[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310016&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310016&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.201076272503187
beta0.391676265650881
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
373.871.22.60000000000001
46578.3275659976734-13.3275659976734
57381.2028398977403-8.2028398977403
671.184.4625451694078-13.3625451694078
758.285.6323647933317-27.4323647933317
86481.812592168229-17.812592168229
97578.5242647432451-3.52426474324511
1074.977.831421111228-2.93142111122803
117577.0269149104081-2.02691491040805
1268.376.244650105544-7.94465010554397
1372.573.6467739185435-1.14677391854347
1472.472.32547308797280.0745269120271672
1579.671.25561637738628.34438362261375
1670.772.5058086098037-1.80580860980368
1776.471.57281830904974.82718169095034
1879.772.3537383735357.34626162646505
1964.274.2197537251502-10.0197537251502
2067.971.8047516661286-3.90475166612855
2174.170.31180566770093.78819433229911
2278.570.66407465194897.83592534805106
2373.472.44737873401330.952621265986679
2465.472.9216390946293-7.52163909462932
2569.971.0995465173491-1.19954651734912
2669.670.4542043005425-0.854204300542477
2776.869.81102780916126.98897219083879
2875.671.29535712092744.30464287907257
297472.57895141398531.42104858601475
307673.39464055947192.60535944052813
3168.174.6536562986389-6.5536562986389
3265.573.5548662716936-8.05486627169361
3376.971.51984301874165.38015698125842
3481.772.61000812879379.08999187120634
3573.675.1620317139636-1.56203171396363
3668.775.449165477215-6.74916547721503
3773.374.1617470189294-0.861747018929393
3871.573.9902802782442-2.49028027824416
3978.373.29522762553255.00477237446752
4076.574.50141209702671.9985879029733
4171.875.2605265953379-3.46052659533791
4277.674.64940268599842.95059731400163
437075.5597832878452-5.55978328784524
446474.3210575206466-10.3210575206466
4581.371.31209897902669.9879010209734
4682.573.17340527771379.32659472228632
4773.175.6362713589787-2.53627135897874
4878.175.51404792231322.58595207768677
4970.776.6254434009284-5.92544340092844
5074.975.5587302211775-0.658730221177535
518875.499148609349112.5008513906509
5281.379.07017371259782.22982628740215
5375.780.7515533641106-5.05155336411062
5489.880.57097614082319.22902385917688
5574.683.9887325735933-9.38873257359334
5674.982.9234733738422-8.02347337384219
579081.50083228888568.49916771111442
5888.184.06986956675074.0301304332493
5984.986.0576896778167-1.15768967781665
6087.786.91118632003360.788813679966381
6180.588.2182030458595-7.71820304585952
627987.2067995574849-8.2067995574849
6389.985.45080960347634.4491903965237
6486.386.5900429481621-0.290042948162096
6581.186.7534860618934-5.65348606189342
6692.485.39321753552467.00678246447536
6771.887.1304604032249-15.3304604032249
6876.183.1688356791644-7.06883567916439
6992.580.311708756703312.1882912432967
708782.28664399368584.71335600631421
7189.583.1297559689466.37024403105397
7288.784.80772886973653.89227113026355
7383.886.2939830489444-2.49398304894439
7484.986.2996949095588-1.39969490955878
759986.415206653298212.5847933467018
7684.690.3338052654805-5.73380526548054
7792.790.11739217649892.58260782350111
7897.691.77661036898415.82338963101586
797894.5461044403403-16.5461044403403
8081.991.5145057295333-9.61450572953325
8196.589.11947931125197.38052068874809
8299.990.7230156740489.17698432595198
8396.293.41052820021212.78947179978795
8490.595.0333533995222-4.53335339952216
8591.494.8266997805668-3.42669978056682
8689.794.5726920249058-4.87269202490576
87102.793.64417189024099.05582810975908
8891.596.229554740937-4.72955474093699
8996.295.67053957949280.529460420507206
90104.596.21068619406178.28931380593828
9190.398.9639950613161-8.6639950613161
9290.397.6260472181617-7.32604721816172
93100.495.98015287873654.41984712126347
94111.397.044172221639314.2558277783607
95101.3101.2087173189120.0912826810880887
9694.4102.532297618501-8.13229761850133
97100.4101.561837279071-1.16183727907116
98102101.9014685320090.0985314679909663
99104.3102.5022900580511.79770994194872
100108.8103.5863579466485.21364205335234
101101.3105.767898514175-4.46789851417482
102108.9105.6508335868453.24916641315548
10398.5107.341381270588-8.84138127058795
10488.8105.904487765944-17.1044877659445
105111.8101.45898482553910.3410151744612
106109.6103.346546613716.25345338629026
10792.5104.904698713586-12.4046987135859
10894.5101.734184718048-7.23418471804814
10980.899.0335971391555-18.2335971391555
11083.792.685268883458-8.98526888345796
11194.287.48890894422786.7110910557722
11286.285.97725863316450.222741366835479
1138983.17849755001745.82150244998259
11494.781.963997400779312.7360025992207
11581.983.142886022174-1.24288602217399
11680.281.4130660955891-1.21306609558907
11796.579.59370504053516.906294959465
11895.682.749203317029612.8507966829704
11991.986.10132478644465.79867521355536
12089.988.49211708204961.40788291795045
12186.390.1109055878738-3.8109055878738
1229490.38018481132783.61981518867222
12310892.428690744152815.5713092558472
12496.398.1067050985399-1.80670509853992
12594.6100.148122784567-5.54812278456654
126111.7101.00027773233310.6997222676675
12792105.962164723818-13.9621647238183
12891.9104.865515942223-12.9655159422232
129109.2102.9481469909646.25185300903645
130106.8105.3873109148421.41268908515816
131105.8106.964692671597-1.16469267159657
132103.6107.932096639981-4.33209663998136
13397.6107.921428740965-10.321428740965
134102.8105.893565532849-3.09356553284923
135124.8105.07541478392219.7245852160782
136103.9110.39889801548-6.49889801548028
137112.2109.9376285526532.26237144734738
138108.5111.416219639386-2.91621963938577
13992.4111.623846796405-19.2238467964054
140101.1107.03838834618-5.93838834617969
141114.9104.65663187538610.2433681246142
142106.4106.3353776091180.0646223908815386
143104105.972508544896-1.97250854489644
144101.6105.044672317585-3.44467231758537
14599.4103.549527505424-4.14952750542352
146102.3101.585849516970.714150483029755
147121.3100.6563859783720.6436140216298
14899.3105.360089734648-6.06008973464847
149102.9104.217038981009-1.31703898100908
150111.4103.9239774129437.47602258705724
15198.5105.987779530912-7.48777953091194
15298.5104.45300251517-5.95300251516967
153108.5102.7579932914055.7420067085949
154112.1103.8667950234348.23320497656618
155105.3106.124938523973-0.824938523973444
15695.2106.496734772373-11.2967347723728
15798.2103.873206543789-5.67320654378881
15896.6101.933632796599-5.33363279659876
159109.699.64227940249729.95772059750284
160108101.2098925950656.79010740493469
161106.7102.6753410889444.02465891105567
162111.5103.9016927789887.59830722101204
163104.5106.445038739363-1.94503873936313
16494.3106.916259232973-12.6162592329731
165109.6104.2481342370365.35186576296398
166116.4105.61446867953910.7855313204605
167106.5108.922818309492-2.42281830949209
168100.5109.384468804357-8.8844688043574
169101.7107.847122339448-6.14712233944765
170104.1106.376063591919-2.27606359191941
171112.3105.5041274148666.79587258513432
172111.2106.9915635506494.20843644935059
173108.2108.290170675499-0.090170675498868
174115.1108.7173283485546.38267165144603
175102.3110.94869984643-8.64869984642982
17693.6109.47647523835-15.8764752383498
177120.6105.30053605495515.2994639450448
178118.4108.5982753903029.80172460969789
179106.6111.562502292196-4.96250229219592
180105.3111.167162664247-5.86716266424659
181101.5110.127838323606-8.6278383236064
182100.1107.853906644094-7.7539066440937
183119.5105.14502898699914.3549710130006
184111.2108.0122736701013.18772632989872
185103.7108.885105554449-5.18510555444945
186117.8107.66599727378910.1340027262113
187101.7110.325319845906-8.62531984590635
18897.4108.533285140093-11.133285140093
189120105.36013617099114.6398638290094
190117108.5223448064798.4776551935206
191110.6111.113152523586-0.513152523586385
192105.3111.855707885666-6.55570788566612
193100.9110.866942141226-9.9669421412257
194108.1108.40729362408-0.307293624080188
195119.3107.86576976087711.434230239123
196113110.5857111739972.41428882600327
197108.6111.682098060291-3.08209806029149
198123.3111.43055576787511.8694442321246
199101.4115.120213355133-13.720213355133
200103.5112.58383783258-9.08383783258004
201119.4110.2643133865939.13568661340686
202113.1112.3278004786640.772199521335523
203112112.770404727118-0.770404727117523
204115.8112.8421532496162.95784675038428
205105.4113.896515237542-8.49651523754167
206110.9111.978518431823-1.07851843182266
207128.5111.46716410900517.032835890995
208109115.939025113145-6.93902511314539
209117.2115.0442182241172.15578177588257
210124.4116.1479436852388.25205631476243
211104.7119.127390884651-14.4273908846511
212108.6116.410284189492-7.81028418949225

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 73.8 & 71.2 & 2.60000000000001 \tabularnewline
4 & 65 & 78.3275659976734 & -13.3275659976734 \tabularnewline
5 & 73 & 81.2028398977403 & -8.2028398977403 \tabularnewline
6 & 71.1 & 84.4625451694078 & -13.3625451694078 \tabularnewline
7 & 58.2 & 85.6323647933317 & -27.4323647933317 \tabularnewline
8 & 64 & 81.812592168229 & -17.812592168229 \tabularnewline
9 & 75 & 78.5242647432451 & -3.52426474324511 \tabularnewline
10 & 74.9 & 77.831421111228 & -2.93142111122803 \tabularnewline
11 & 75 & 77.0269149104081 & -2.02691491040805 \tabularnewline
12 & 68.3 & 76.244650105544 & -7.94465010554397 \tabularnewline
13 & 72.5 & 73.6467739185435 & -1.14677391854347 \tabularnewline
14 & 72.4 & 72.3254730879728 & 0.0745269120271672 \tabularnewline
15 & 79.6 & 71.2556163773862 & 8.34438362261375 \tabularnewline
16 & 70.7 & 72.5058086098037 & -1.80580860980368 \tabularnewline
17 & 76.4 & 71.5728183090497 & 4.82718169095034 \tabularnewline
18 & 79.7 & 72.353738373535 & 7.34626162646505 \tabularnewline
19 & 64.2 & 74.2197537251502 & -10.0197537251502 \tabularnewline
20 & 67.9 & 71.8047516661286 & -3.90475166612855 \tabularnewline
21 & 74.1 & 70.3118056677009 & 3.78819433229911 \tabularnewline
22 & 78.5 & 70.6640746519489 & 7.83592534805106 \tabularnewline
23 & 73.4 & 72.4473787340133 & 0.952621265986679 \tabularnewline
24 & 65.4 & 72.9216390946293 & -7.52163909462932 \tabularnewline
25 & 69.9 & 71.0995465173491 & -1.19954651734912 \tabularnewline
26 & 69.6 & 70.4542043005425 & -0.854204300542477 \tabularnewline
27 & 76.8 & 69.8110278091612 & 6.98897219083879 \tabularnewline
28 & 75.6 & 71.2953571209274 & 4.30464287907257 \tabularnewline
29 & 74 & 72.5789514139853 & 1.42104858601475 \tabularnewline
30 & 76 & 73.3946405594719 & 2.60535944052813 \tabularnewline
31 & 68.1 & 74.6536562986389 & -6.5536562986389 \tabularnewline
32 & 65.5 & 73.5548662716936 & -8.05486627169361 \tabularnewline
33 & 76.9 & 71.5198430187416 & 5.38015698125842 \tabularnewline
34 & 81.7 & 72.6100081287937 & 9.08999187120634 \tabularnewline
35 & 73.6 & 75.1620317139636 & -1.56203171396363 \tabularnewline
36 & 68.7 & 75.449165477215 & -6.74916547721503 \tabularnewline
37 & 73.3 & 74.1617470189294 & -0.861747018929393 \tabularnewline
38 & 71.5 & 73.9902802782442 & -2.49028027824416 \tabularnewline
39 & 78.3 & 73.2952276255325 & 5.00477237446752 \tabularnewline
40 & 76.5 & 74.5014120970267 & 1.9985879029733 \tabularnewline
41 & 71.8 & 75.2605265953379 & -3.46052659533791 \tabularnewline
42 & 77.6 & 74.6494026859984 & 2.95059731400163 \tabularnewline
43 & 70 & 75.5597832878452 & -5.55978328784524 \tabularnewline
44 & 64 & 74.3210575206466 & -10.3210575206466 \tabularnewline
45 & 81.3 & 71.3120989790266 & 9.9879010209734 \tabularnewline
46 & 82.5 & 73.1734052777137 & 9.32659472228632 \tabularnewline
47 & 73.1 & 75.6362713589787 & -2.53627135897874 \tabularnewline
48 & 78.1 & 75.5140479223132 & 2.58595207768677 \tabularnewline
49 & 70.7 & 76.6254434009284 & -5.92544340092844 \tabularnewline
50 & 74.9 & 75.5587302211775 & -0.658730221177535 \tabularnewline
51 & 88 & 75.4991486093491 & 12.5008513906509 \tabularnewline
52 & 81.3 & 79.0701737125978 & 2.22982628740215 \tabularnewline
53 & 75.7 & 80.7515533641106 & -5.05155336411062 \tabularnewline
54 & 89.8 & 80.5709761408231 & 9.22902385917688 \tabularnewline
55 & 74.6 & 83.9887325735933 & -9.38873257359334 \tabularnewline
56 & 74.9 & 82.9234733738422 & -8.02347337384219 \tabularnewline
57 & 90 & 81.5008322888856 & 8.49916771111442 \tabularnewline
58 & 88.1 & 84.0698695667507 & 4.0301304332493 \tabularnewline
59 & 84.9 & 86.0576896778167 & -1.15768967781665 \tabularnewline
60 & 87.7 & 86.9111863200336 & 0.788813679966381 \tabularnewline
61 & 80.5 & 88.2182030458595 & -7.71820304585952 \tabularnewline
62 & 79 & 87.2067995574849 & -8.2067995574849 \tabularnewline
63 & 89.9 & 85.4508096034763 & 4.4491903965237 \tabularnewline
64 & 86.3 & 86.5900429481621 & -0.290042948162096 \tabularnewline
65 & 81.1 & 86.7534860618934 & -5.65348606189342 \tabularnewline
66 & 92.4 & 85.3932175355246 & 7.00678246447536 \tabularnewline
67 & 71.8 & 87.1304604032249 & -15.3304604032249 \tabularnewline
68 & 76.1 & 83.1688356791644 & -7.06883567916439 \tabularnewline
69 & 92.5 & 80.3117087567033 & 12.1882912432967 \tabularnewline
70 & 87 & 82.2866439936858 & 4.71335600631421 \tabularnewline
71 & 89.5 & 83.129755968946 & 6.37024403105397 \tabularnewline
72 & 88.7 & 84.8077288697365 & 3.89227113026355 \tabularnewline
73 & 83.8 & 86.2939830489444 & -2.49398304894439 \tabularnewline
74 & 84.9 & 86.2996949095588 & -1.39969490955878 \tabularnewline
75 & 99 & 86.4152066532982 & 12.5847933467018 \tabularnewline
76 & 84.6 & 90.3338052654805 & -5.73380526548054 \tabularnewline
77 & 92.7 & 90.1173921764989 & 2.58260782350111 \tabularnewline
78 & 97.6 & 91.7766103689841 & 5.82338963101586 \tabularnewline
79 & 78 & 94.5461044403403 & -16.5461044403403 \tabularnewline
80 & 81.9 & 91.5145057295333 & -9.61450572953325 \tabularnewline
81 & 96.5 & 89.1194793112519 & 7.38052068874809 \tabularnewline
82 & 99.9 & 90.723015674048 & 9.17698432595198 \tabularnewline
83 & 96.2 & 93.4105282002121 & 2.78947179978795 \tabularnewline
84 & 90.5 & 95.0333533995222 & -4.53335339952216 \tabularnewline
85 & 91.4 & 94.8266997805668 & -3.42669978056682 \tabularnewline
86 & 89.7 & 94.5726920249058 & -4.87269202490576 \tabularnewline
87 & 102.7 & 93.6441718902409 & 9.05582810975908 \tabularnewline
88 & 91.5 & 96.229554740937 & -4.72955474093699 \tabularnewline
89 & 96.2 & 95.6705395794928 & 0.529460420507206 \tabularnewline
90 & 104.5 & 96.2106861940617 & 8.28931380593828 \tabularnewline
91 & 90.3 & 98.9639950613161 & -8.6639950613161 \tabularnewline
92 & 90.3 & 97.6260472181617 & -7.32604721816172 \tabularnewline
93 & 100.4 & 95.9801528787365 & 4.41984712126347 \tabularnewline
94 & 111.3 & 97.0441722216393 & 14.2558277783607 \tabularnewline
95 & 101.3 & 101.208717318912 & 0.0912826810880887 \tabularnewline
96 & 94.4 & 102.532297618501 & -8.13229761850133 \tabularnewline
97 & 100.4 & 101.561837279071 & -1.16183727907116 \tabularnewline
98 & 102 & 101.901468532009 & 0.0985314679909663 \tabularnewline
99 & 104.3 & 102.502290058051 & 1.79770994194872 \tabularnewline
100 & 108.8 & 103.586357946648 & 5.21364205335234 \tabularnewline
101 & 101.3 & 105.767898514175 & -4.46789851417482 \tabularnewline
102 & 108.9 & 105.650833586845 & 3.24916641315548 \tabularnewline
103 & 98.5 & 107.341381270588 & -8.84138127058795 \tabularnewline
104 & 88.8 & 105.904487765944 & -17.1044877659445 \tabularnewline
105 & 111.8 & 101.458984825539 & 10.3410151744612 \tabularnewline
106 & 109.6 & 103.34654661371 & 6.25345338629026 \tabularnewline
107 & 92.5 & 104.904698713586 & -12.4046987135859 \tabularnewline
108 & 94.5 & 101.734184718048 & -7.23418471804814 \tabularnewline
109 & 80.8 & 99.0335971391555 & -18.2335971391555 \tabularnewline
110 & 83.7 & 92.685268883458 & -8.98526888345796 \tabularnewline
111 & 94.2 & 87.4889089442278 & 6.7110910557722 \tabularnewline
112 & 86.2 & 85.9772586331645 & 0.222741366835479 \tabularnewline
113 & 89 & 83.1784975500174 & 5.82150244998259 \tabularnewline
114 & 94.7 & 81.9639974007793 & 12.7360025992207 \tabularnewline
115 & 81.9 & 83.142886022174 & -1.24288602217399 \tabularnewline
116 & 80.2 & 81.4130660955891 & -1.21306609558907 \tabularnewline
117 & 96.5 & 79.593705040535 & 16.906294959465 \tabularnewline
118 & 95.6 & 82.7492033170296 & 12.8507966829704 \tabularnewline
119 & 91.9 & 86.1013247864446 & 5.79867521355536 \tabularnewline
120 & 89.9 & 88.4921170820496 & 1.40788291795045 \tabularnewline
121 & 86.3 & 90.1109055878738 & -3.8109055878738 \tabularnewline
122 & 94 & 90.3801848113278 & 3.61981518867222 \tabularnewline
123 & 108 & 92.4286907441528 & 15.5713092558472 \tabularnewline
124 & 96.3 & 98.1067050985399 & -1.80670509853992 \tabularnewline
125 & 94.6 & 100.148122784567 & -5.54812278456654 \tabularnewline
126 & 111.7 & 101.000277732333 & 10.6997222676675 \tabularnewline
127 & 92 & 105.962164723818 & -13.9621647238183 \tabularnewline
128 & 91.9 & 104.865515942223 & -12.9655159422232 \tabularnewline
129 & 109.2 & 102.948146990964 & 6.25185300903645 \tabularnewline
130 & 106.8 & 105.387310914842 & 1.41268908515816 \tabularnewline
131 & 105.8 & 106.964692671597 & -1.16469267159657 \tabularnewline
132 & 103.6 & 107.932096639981 & -4.33209663998136 \tabularnewline
133 & 97.6 & 107.921428740965 & -10.321428740965 \tabularnewline
134 & 102.8 & 105.893565532849 & -3.09356553284923 \tabularnewline
135 & 124.8 & 105.075414783922 & 19.7245852160782 \tabularnewline
136 & 103.9 & 110.39889801548 & -6.49889801548028 \tabularnewline
137 & 112.2 & 109.937628552653 & 2.26237144734738 \tabularnewline
138 & 108.5 & 111.416219639386 & -2.91621963938577 \tabularnewline
139 & 92.4 & 111.623846796405 & -19.2238467964054 \tabularnewline
140 & 101.1 & 107.03838834618 & -5.93838834617969 \tabularnewline
141 & 114.9 & 104.656631875386 & 10.2433681246142 \tabularnewline
142 & 106.4 & 106.335377609118 & 0.0646223908815386 \tabularnewline
143 & 104 & 105.972508544896 & -1.97250854489644 \tabularnewline
144 & 101.6 & 105.044672317585 & -3.44467231758537 \tabularnewline
145 & 99.4 & 103.549527505424 & -4.14952750542352 \tabularnewline
146 & 102.3 & 101.58584951697 & 0.714150483029755 \tabularnewline
147 & 121.3 & 100.65638597837 & 20.6436140216298 \tabularnewline
148 & 99.3 & 105.360089734648 & -6.06008973464847 \tabularnewline
149 & 102.9 & 104.217038981009 & -1.31703898100908 \tabularnewline
150 & 111.4 & 103.923977412943 & 7.47602258705724 \tabularnewline
151 & 98.5 & 105.987779530912 & -7.48777953091194 \tabularnewline
152 & 98.5 & 104.45300251517 & -5.95300251516967 \tabularnewline
153 & 108.5 & 102.757993291405 & 5.7420067085949 \tabularnewline
154 & 112.1 & 103.866795023434 & 8.23320497656618 \tabularnewline
155 & 105.3 & 106.124938523973 & -0.824938523973444 \tabularnewline
156 & 95.2 & 106.496734772373 & -11.2967347723728 \tabularnewline
157 & 98.2 & 103.873206543789 & -5.67320654378881 \tabularnewline
158 & 96.6 & 101.933632796599 & -5.33363279659876 \tabularnewline
159 & 109.6 & 99.6422794024972 & 9.95772059750284 \tabularnewline
160 & 108 & 101.209892595065 & 6.79010740493469 \tabularnewline
161 & 106.7 & 102.675341088944 & 4.02465891105567 \tabularnewline
162 & 111.5 & 103.901692778988 & 7.59830722101204 \tabularnewline
163 & 104.5 & 106.445038739363 & -1.94503873936313 \tabularnewline
164 & 94.3 & 106.916259232973 & -12.6162592329731 \tabularnewline
165 & 109.6 & 104.248134237036 & 5.35186576296398 \tabularnewline
166 & 116.4 & 105.614468679539 & 10.7855313204605 \tabularnewline
167 & 106.5 & 108.922818309492 & -2.42281830949209 \tabularnewline
168 & 100.5 & 109.384468804357 & -8.8844688043574 \tabularnewline
169 & 101.7 & 107.847122339448 & -6.14712233944765 \tabularnewline
170 & 104.1 & 106.376063591919 & -2.27606359191941 \tabularnewline
171 & 112.3 & 105.504127414866 & 6.79587258513432 \tabularnewline
172 & 111.2 & 106.991563550649 & 4.20843644935059 \tabularnewline
173 & 108.2 & 108.290170675499 & -0.090170675498868 \tabularnewline
174 & 115.1 & 108.717328348554 & 6.38267165144603 \tabularnewline
175 & 102.3 & 110.94869984643 & -8.64869984642982 \tabularnewline
176 & 93.6 & 109.47647523835 & -15.8764752383498 \tabularnewline
177 & 120.6 & 105.300536054955 & 15.2994639450448 \tabularnewline
178 & 118.4 & 108.598275390302 & 9.80172460969789 \tabularnewline
179 & 106.6 & 111.562502292196 & -4.96250229219592 \tabularnewline
180 & 105.3 & 111.167162664247 & -5.86716266424659 \tabularnewline
181 & 101.5 & 110.127838323606 & -8.6278383236064 \tabularnewline
182 & 100.1 & 107.853906644094 & -7.7539066440937 \tabularnewline
183 & 119.5 & 105.145028986999 & 14.3549710130006 \tabularnewline
184 & 111.2 & 108.012273670101 & 3.18772632989872 \tabularnewline
185 & 103.7 & 108.885105554449 & -5.18510555444945 \tabularnewline
186 & 117.8 & 107.665997273789 & 10.1340027262113 \tabularnewline
187 & 101.7 & 110.325319845906 & -8.62531984590635 \tabularnewline
188 & 97.4 & 108.533285140093 & -11.133285140093 \tabularnewline
189 & 120 & 105.360136170991 & 14.6398638290094 \tabularnewline
190 & 117 & 108.522344806479 & 8.4776551935206 \tabularnewline
191 & 110.6 & 111.113152523586 & -0.513152523586385 \tabularnewline
192 & 105.3 & 111.855707885666 & -6.55570788566612 \tabularnewline
193 & 100.9 & 110.866942141226 & -9.9669421412257 \tabularnewline
194 & 108.1 & 108.40729362408 & -0.307293624080188 \tabularnewline
195 & 119.3 & 107.865769760877 & 11.434230239123 \tabularnewline
196 & 113 & 110.585711173997 & 2.41428882600327 \tabularnewline
197 & 108.6 & 111.682098060291 & -3.08209806029149 \tabularnewline
198 & 123.3 & 111.430555767875 & 11.8694442321246 \tabularnewline
199 & 101.4 & 115.120213355133 & -13.720213355133 \tabularnewline
200 & 103.5 & 112.58383783258 & -9.08383783258004 \tabularnewline
201 & 119.4 & 110.264313386593 & 9.13568661340686 \tabularnewline
202 & 113.1 & 112.327800478664 & 0.772199521335523 \tabularnewline
203 & 112 & 112.770404727118 & -0.770404727117523 \tabularnewline
204 & 115.8 & 112.842153249616 & 2.95784675038428 \tabularnewline
205 & 105.4 & 113.896515237542 & -8.49651523754167 \tabularnewline
206 & 110.9 & 111.978518431823 & -1.07851843182266 \tabularnewline
207 & 128.5 & 111.467164109005 & 17.032835890995 \tabularnewline
208 & 109 & 115.939025113145 & -6.93902511314539 \tabularnewline
209 & 117.2 & 115.044218224117 & 2.15578177588257 \tabularnewline
210 & 124.4 & 116.147943685238 & 8.25205631476243 \tabularnewline
211 & 104.7 & 119.127390884651 & -14.4273908846511 \tabularnewline
212 & 108.6 & 116.410284189492 & -7.81028418949225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310016&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]73.8[/C][C]71.2[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]4[/C][C]65[/C][C]78.3275659976734[/C][C]-13.3275659976734[/C][/ROW]
[ROW][C]5[/C][C]73[/C][C]81.2028398977403[/C][C]-8.2028398977403[/C][/ROW]
[ROW][C]6[/C][C]71.1[/C][C]84.4625451694078[/C][C]-13.3625451694078[/C][/ROW]
[ROW][C]7[/C][C]58.2[/C][C]85.6323647933317[/C][C]-27.4323647933317[/C][/ROW]
[ROW][C]8[/C][C]64[/C][C]81.812592168229[/C][C]-17.812592168229[/C][/ROW]
[ROW][C]9[/C][C]75[/C][C]78.5242647432451[/C][C]-3.52426474324511[/C][/ROW]
[ROW][C]10[/C][C]74.9[/C][C]77.831421111228[/C][C]-2.93142111122803[/C][/ROW]
[ROW][C]11[/C][C]75[/C][C]77.0269149104081[/C][C]-2.02691491040805[/C][/ROW]
[ROW][C]12[/C][C]68.3[/C][C]76.244650105544[/C][C]-7.94465010554397[/C][/ROW]
[ROW][C]13[/C][C]72.5[/C][C]73.6467739185435[/C][C]-1.14677391854347[/C][/ROW]
[ROW][C]14[/C][C]72.4[/C][C]72.3254730879728[/C][C]0.0745269120271672[/C][/ROW]
[ROW][C]15[/C][C]79.6[/C][C]71.2556163773862[/C][C]8.34438362261375[/C][/ROW]
[ROW][C]16[/C][C]70.7[/C][C]72.5058086098037[/C][C]-1.80580860980368[/C][/ROW]
[ROW][C]17[/C][C]76.4[/C][C]71.5728183090497[/C][C]4.82718169095034[/C][/ROW]
[ROW][C]18[/C][C]79.7[/C][C]72.353738373535[/C][C]7.34626162646505[/C][/ROW]
[ROW][C]19[/C][C]64.2[/C][C]74.2197537251502[/C][C]-10.0197537251502[/C][/ROW]
[ROW][C]20[/C][C]67.9[/C][C]71.8047516661286[/C][C]-3.90475166612855[/C][/ROW]
[ROW][C]21[/C][C]74.1[/C][C]70.3118056677009[/C][C]3.78819433229911[/C][/ROW]
[ROW][C]22[/C][C]78.5[/C][C]70.6640746519489[/C][C]7.83592534805106[/C][/ROW]
[ROW][C]23[/C][C]73.4[/C][C]72.4473787340133[/C][C]0.952621265986679[/C][/ROW]
[ROW][C]24[/C][C]65.4[/C][C]72.9216390946293[/C][C]-7.52163909462932[/C][/ROW]
[ROW][C]25[/C][C]69.9[/C][C]71.0995465173491[/C][C]-1.19954651734912[/C][/ROW]
[ROW][C]26[/C][C]69.6[/C][C]70.4542043005425[/C][C]-0.854204300542477[/C][/ROW]
[ROW][C]27[/C][C]76.8[/C][C]69.8110278091612[/C][C]6.98897219083879[/C][/ROW]
[ROW][C]28[/C][C]75.6[/C][C]71.2953571209274[/C][C]4.30464287907257[/C][/ROW]
[ROW][C]29[/C][C]74[/C][C]72.5789514139853[/C][C]1.42104858601475[/C][/ROW]
[ROW][C]30[/C][C]76[/C][C]73.3946405594719[/C][C]2.60535944052813[/C][/ROW]
[ROW][C]31[/C][C]68.1[/C][C]74.6536562986389[/C][C]-6.5536562986389[/C][/ROW]
[ROW][C]32[/C][C]65.5[/C][C]73.5548662716936[/C][C]-8.05486627169361[/C][/ROW]
[ROW][C]33[/C][C]76.9[/C][C]71.5198430187416[/C][C]5.38015698125842[/C][/ROW]
[ROW][C]34[/C][C]81.7[/C][C]72.6100081287937[/C][C]9.08999187120634[/C][/ROW]
[ROW][C]35[/C][C]73.6[/C][C]75.1620317139636[/C][C]-1.56203171396363[/C][/ROW]
[ROW][C]36[/C][C]68.7[/C][C]75.449165477215[/C][C]-6.74916547721503[/C][/ROW]
[ROW][C]37[/C][C]73.3[/C][C]74.1617470189294[/C][C]-0.861747018929393[/C][/ROW]
[ROW][C]38[/C][C]71.5[/C][C]73.9902802782442[/C][C]-2.49028027824416[/C][/ROW]
[ROW][C]39[/C][C]78.3[/C][C]73.2952276255325[/C][C]5.00477237446752[/C][/ROW]
[ROW][C]40[/C][C]76.5[/C][C]74.5014120970267[/C][C]1.9985879029733[/C][/ROW]
[ROW][C]41[/C][C]71.8[/C][C]75.2605265953379[/C][C]-3.46052659533791[/C][/ROW]
[ROW][C]42[/C][C]77.6[/C][C]74.6494026859984[/C][C]2.95059731400163[/C][/ROW]
[ROW][C]43[/C][C]70[/C][C]75.5597832878452[/C][C]-5.55978328784524[/C][/ROW]
[ROW][C]44[/C][C]64[/C][C]74.3210575206466[/C][C]-10.3210575206466[/C][/ROW]
[ROW][C]45[/C][C]81.3[/C][C]71.3120989790266[/C][C]9.9879010209734[/C][/ROW]
[ROW][C]46[/C][C]82.5[/C][C]73.1734052777137[/C][C]9.32659472228632[/C][/ROW]
[ROW][C]47[/C][C]73.1[/C][C]75.6362713589787[/C][C]-2.53627135897874[/C][/ROW]
[ROW][C]48[/C][C]78.1[/C][C]75.5140479223132[/C][C]2.58595207768677[/C][/ROW]
[ROW][C]49[/C][C]70.7[/C][C]76.6254434009284[/C][C]-5.92544340092844[/C][/ROW]
[ROW][C]50[/C][C]74.9[/C][C]75.5587302211775[/C][C]-0.658730221177535[/C][/ROW]
[ROW][C]51[/C][C]88[/C][C]75.4991486093491[/C][C]12.5008513906509[/C][/ROW]
[ROW][C]52[/C][C]81.3[/C][C]79.0701737125978[/C][C]2.22982628740215[/C][/ROW]
[ROW][C]53[/C][C]75.7[/C][C]80.7515533641106[/C][C]-5.05155336411062[/C][/ROW]
[ROW][C]54[/C][C]89.8[/C][C]80.5709761408231[/C][C]9.22902385917688[/C][/ROW]
[ROW][C]55[/C][C]74.6[/C][C]83.9887325735933[/C][C]-9.38873257359334[/C][/ROW]
[ROW][C]56[/C][C]74.9[/C][C]82.9234733738422[/C][C]-8.02347337384219[/C][/ROW]
[ROW][C]57[/C][C]90[/C][C]81.5008322888856[/C][C]8.49916771111442[/C][/ROW]
[ROW][C]58[/C][C]88.1[/C][C]84.0698695667507[/C][C]4.0301304332493[/C][/ROW]
[ROW][C]59[/C][C]84.9[/C][C]86.0576896778167[/C][C]-1.15768967781665[/C][/ROW]
[ROW][C]60[/C][C]87.7[/C][C]86.9111863200336[/C][C]0.788813679966381[/C][/ROW]
[ROW][C]61[/C][C]80.5[/C][C]88.2182030458595[/C][C]-7.71820304585952[/C][/ROW]
[ROW][C]62[/C][C]79[/C][C]87.2067995574849[/C][C]-8.2067995574849[/C][/ROW]
[ROW][C]63[/C][C]89.9[/C][C]85.4508096034763[/C][C]4.4491903965237[/C][/ROW]
[ROW][C]64[/C][C]86.3[/C][C]86.5900429481621[/C][C]-0.290042948162096[/C][/ROW]
[ROW][C]65[/C][C]81.1[/C][C]86.7534860618934[/C][C]-5.65348606189342[/C][/ROW]
[ROW][C]66[/C][C]92.4[/C][C]85.3932175355246[/C][C]7.00678246447536[/C][/ROW]
[ROW][C]67[/C][C]71.8[/C][C]87.1304604032249[/C][C]-15.3304604032249[/C][/ROW]
[ROW][C]68[/C][C]76.1[/C][C]83.1688356791644[/C][C]-7.06883567916439[/C][/ROW]
[ROW][C]69[/C][C]92.5[/C][C]80.3117087567033[/C][C]12.1882912432967[/C][/ROW]
[ROW][C]70[/C][C]87[/C][C]82.2866439936858[/C][C]4.71335600631421[/C][/ROW]
[ROW][C]71[/C][C]89.5[/C][C]83.129755968946[/C][C]6.37024403105397[/C][/ROW]
[ROW][C]72[/C][C]88.7[/C][C]84.8077288697365[/C][C]3.89227113026355[/C][/ROW]
[ROW][C]73[/C][C]83.8[/C][C]86.2939830489444[/C][C]-2.49398304894439[/C][/ROW]
[ROW][C]74[/C][C]84.9[/C][C]86.2996949095588[/C][C]-1.39969490955878[/C][/ROW]
[ROW][C]75[/C][C]99[/C][C]86.4152066532982[/C][C]12.5847933467018[/C][/ROW]
[ROW][C]76[/C][C]84.6[/C][C]90.3338052654805[/C][C]-5.73380526548054[/C][/ROW]
[ROW][C]77[/C][C]92.7[/C][C]90.1173921764989[/C][C]2.58260782350111[/C][/ROW]
[ROW][C]78[/C][C]97.6[/C][C]91.7766103689841[/C][C]5.82338963101586[/C][/ROW]
[ROW][C]79[/C][C]78[/C][C]94.5461044403403[/C][C]-16.5461044403403[/C][/ROW]
[ROW][C]80[/C][C]81.9[/C][C]91.5145057295333[/C][C]-9.61450572953325[/C][/ROW]
[ROW][C]81[/C][C]96.5[/C][C]89.1194793112519[/C][C]7.38052068874809[/C][/ROW]
[ROW][C]82[/C][C]99.9[/C][C]90.723015674048[/C][C]9.17698432595198[/C][/ROW]
[ROW][C]83[/C][C]96.2[/C][C]93.4105282002121[/C][C]2.78947179978795[/C][/ROW]
[ROW][C]84[/C][C]90.5[/C][C]95.0333533995222[/C][C]-4.53335339952216[/C][/ROW]
[ROW][C]85[/C][C]91.4[/C][C]94.8266997805668[/C][C]-3.42669978056682[/C][/ROW]
[ROW][C]86[/C][C]89.7[/C][C]94.5726920249058[/C][C]-4.87269202490576[/C][/ROW]
[ROW][C]87[/C][C]102.7[/C][C]93.6441718902409[/C][C]9.05582810975908[/C][/ROW]
[ROW][C]88[/C][C]91.5[/C][C]96.229554740937[/C][C]-4.72955474093699[/C][/ROW]
[ROW][C]89[/C][C]96.2[/C][C]95.6705395794928[/C][C]0.529460420507206[/C][/ROW]
[ROW][C]90[/C][C]104.5[/C][C]96.2106861940617[/C][C]8.28931380593828[/C][/ROW]
[ROW][C]91[/C][C]90.3[/C][C]98.9639950613161[/C][C]-8.6639950613161[/C][/ROW]
[ROW][C]92[/C][C]90.3[/C][C]97.6260472181617[/C][C]-7.32604721816172[/C][/ROW]
[ROW][C]93[/C][C]100.4[/C][C]95.9801528787365[/C][C]4.41984712126347[/C][/ROW]
[ROW][C]94[/C][C]111.3[/C][C]97.0441722216393[/C][C]14.2558277783607[/C][/ROW]
[ROW][C]95[/C][C]101.3[/C][C]101.208717318912[/C][C]0.0912826810880887[/C][/ROW]
[ROW][C]96[/C][C]94.4[/C][C]102.532297618501[/C][C]-8.13229761850133[/C][/ROW]
[ROW][C]97[/C][C]100.4[/C][C]101.561837279071[/C][C]-1.16183727907116[/C][/ROW]
[ROW][C]98[/C][C]102[/C][C]101.901468532009[/C][C]0.0985314679909663[/C][/ROW]
[ROW][C]99[/C][C]104.3[/C][C]102.502290058051[/C][C]1.79770994194872[/C][/ROW]
[ROW][C]100[/C][C]108.8[/C][C]103.586357946648[/C][C]5.21364205335234[/C][/ROW]
[ROW][C]101[/C][C]101.3[/C][C]105.767898514175[/C][C]-4.46789851417482[/C][/ROW]
[ROW][C]102[/C][C]108.9[/C][C]105.650833586845[/C][C]3.24916641315548[/C][/ROW]
[ROW][C]103[/C][C]98.5[/C][C]107.341381270588[/C][C]-8.84138127058795[/C][/ROW]
[ROW][C]104[/C][C]88.8[/C][C]105.904487765944[/C][C]-17.1044877659445[/C][/ROW]
[ROW][C]105[/C][C]111.8[/C][C]101.458984825539[/C][C]10.3410151744612[/C][/ROW]
[ROW][C]106[/C][C]109.6[/C][C]103.34654661371[/C][C]6.25345338629026[/C][/ROW]
[ROW][C]107[/C][C]92.5[/C][C]104.904698713586[/C][C]-12.4046987135859[/C][/ROW]
[ROW][C]108[/C][C]94.5[/C][C]101.734184718048[/C][C]-7.23418471804814[/C][/ROW]
[ROW][C]109[/C][C]80.8[/C][C]99.0335971391555[/C][C]-18.2335971391555[/C][/ROW]
[ROW][C]110[/C][C]83.7[/C][C]92.685268883458[/C][C]-8.98526888345796[/C][/ROW]
[ROW][C]111[/C][C]94.2[/C][C]87.4889089442278[/C][C]6.7110910557722[/C][/ROW]
[ROW][C]112[/C][C]86.2[/C][C]85.9772586331645[/C][C]0.222741366835479[/C][/ROW]
[ROW][C]113[/C][C]89[/C][C]83.1784975500174[/C][C]5.82150244998259[/C][/ROW]
[ROW][C]114[/C][C]94.7[/C][C]81.9639974007793[/C][C]12.7360025992207[/C][/ROW]
[ROW][C]115[/C][C]81.9[/C][C]83.142886022174[/C][C]-1.24288602217399[/C][/ROW]
[ROW][C]116[/C][C]80.2[/C][C]81.4130660955891[/C][C]-1.21306609558907[/C][/ROW]
[ROW][C]117[/C][C]96.5[/C][C]79.593705040535[/C][C]16.906294959465[/C][/ROW]
[ROW][C]118[/C][C]95.6[/C][C]82.7492033170296[/C][C]12.8507966829704[/C][/ROW]
[ROW][C]119[/C][C]91.9[/C][C]86.1013247864446[/C][C]5.79867521355536[/C][/ROW]
[ROW][C]120[/C][C]89.9[/C][C]88.4921170820496[/C][C]1.40788291795045[/C][/ROW]
[ROW][C]121[/C][C]86.3[/C][C]90.1109055878738[/C][C]-3.8109055878738[/C][/ROW]
[ROW][C]122[/C][C]94[/C][C]90.3801848113278[/C][C]3.61981518867222[/C][/ROW]
[ROW][C]123[/C][C]108[/C][C]92.4286907441528[/C][C]15.5713092558472[/C][/ROW]
[ROW][C]124[/C][C]96.3[/C][C]98.1067050985399[/C][C]-1.80670509853992[/C][/ROW]
[ROW][C]125[/C][C]94.6[/C][C]100.148122784567[/C][C]-5.54812278456654[/C][/ROW]
[ROW][C]126[/C][C]111.7[/C][C]101.000277732333[/C][C]10.6997222676675[/C][/ROW]
[ROW][C]127[/C][C]92[/C][C]105.962164723818[/C][C]-13.9621647238183[/C][/ROW]
[ROW][C]128[/C][C]91.9[/C][C]104.865515942223[/C][C]-12.9655159422232[/C][/ROW]
[ROW][C]129[/C][C]109.2[/C][C]102.948146990964[/C][C]6.25185300903645[/C][/ROW]
[ROW][C]130[/C][C]106.8[/C][C]105.387310914842[/C][C]1.41268908515816[/C][/ROW]
[ROW][C]131[/C][C]105.8[/C][C]106.964692671597[/C][C]-1.16469267159657[/C][/ROW]
[ROW][C]132[/C][C]103.6[/C][C]107.932096639981[/C][C]-4.33209663998136[/C][/ROW]
[ROW][C]133[/C][C]97.6[/C][C]107.921428740965[/C][C]-10.321428740965[/C][/ROW]
[ROW][C]134[/C][C]102.8[/C][C]105.893565532849[/C][C]-3.09356553284923[/C][/ROW]
[ROW][C]135[/C][C]124.8[/C][C]105.075414783922[/C][C]19.7245852160782[/C][/ROW]
[ROW][C]136[/C][C]103.9[/C][C]110.39889801548[/C][C]-6.49889801548028[/C][/ROW]
[ROW][C]137[/C][C]112.2[/C][C]109.937628552653[/C][C]2.26237144734738[/C][/ROW]
[ROW][C]138[/C][C]108.5[/C][C]111.416219639386[/C][C]-2.91621963938577[/C][/ROW]
[ROW][C]139[/C][C]92.4[/C][C]111.623846796405[/C][C]-19.2238467964054[/C][/ROW]
[ROW][C]140[/C][C]101.1[/C][C]107.03838834618[/C][C]-5.93838834617969[/C][/ROW]
[ROW][C]141[/C][C]114.9[/C][C]104.656631875386[/C][C]10.2433681246142[/C][/ROW]
[ROW][C]142[/C][C]106.4[/C][C]106.335377609118[/C][C]0.0646223908815386[/C][/ROW]
[ROW][C]143[/C][C]104[/C][C]105.972508544896[/C][C]-1.97250854489644[/C][/ROW]
[ROW][C]144[/C][C]101.6[/C][C]105.044672317585[/C][C]-3.44467231758537[/C][/ROW]
[ROW][C]145[/C][C]99.4[/C][C]103.549527505424[/C][C]-4.14952750542352[/C][/ROW]
[ROW][C]146[/C][C]102.3[/C][C]101.58584951697[/C][C]0.714150483029755[/C][/ROW]
[ROW][C]147[/C][C]121.3[/C][C]100.65638597837[/C][C]20.6436140216298[/C][/ROW]
[ROW][C]148[/C][C]99.3[/C][C]105.360089734648[/C][C]-6.06008973464847[/C][/ROW]
[ROW][C]149[/C][C]102.9[/C][C]104.217038981009[/C][C]-1.31703898100908[/C][/ROW]
[ROW][C]150[/C][C]111.4[/C][C]103.923977412943[/C][C]7.47602258705724[/C][/ROW]
[ROW][C]151[/C][C]98.5[/C][C]105.987779530912[/C][C]-7.48777953091194[/C][/ROW]
[ROW][C]152[/C][C]98.5[/C][C]104.45300251517[/C][C]-5.95300251516967[/C][/ROW]
[ROW][C]153[/C][C]108.5[/C][C]102.757993291405[/C][C]5.7420067085949[/C][/ROW]
[ROW][C]154[/C][C]112.1[/C][C]103.866795023434[/C][C]8.23320497656618[/C][/ROW]
[ROW][C]155[/C][C]105.3[/C][C]106.124938523973[/C][C]-0.824938523973444[/C][/ROW]
[ROW][C]156[/C][C]95.2[/C][C]106.496734772373[/C][C]-11.2967347723728[/C][/ROW]
[ROW][C]157[/C][C]98.2[/C][C]103.873206543789[/C][C]-5.67320654378881[/C][/ROW]
[ROW][C]158[/C][C]96.6[/C][C]101.933632796599[/C][C]-5.33363279659876[/C][/ROW]
[ROW][C]159[/C][C]109.6[/C][C]99.6422794024972[/C][C]9.95772059750284[/C][/ROW]
[ROW][C]160[/C][C]108[/C][C]101.209892595065[/C][C]6.79010740493469[/C][/ROW]
[ROW][C]161[/C][C]106.7[/C][C]102.675341088944[/C][C]4.02465891105567[/C][/ROW]
[ROW][C]162[/C][C]111.5[/C][C]103.901692778988[/C][C]7.59830722101204[/C][/ROW]
[ROW][C]163[/C][C]104.5[/C][C]106.445038739363[/C][C]-1.94503873936313[/C][/ROW]
[ROW][C]164[/C][C]94.3[/C][C]106.916259232973[/C][C]-12.6162592329731[/C][/ROW]
[ROW][C]165[/C][C]109.6[/C][C]104.248134237036[/C][C]5.35186576296398[/C][/ROW]
[ROW][C]166[/C][C]116.4[/C][C]105.614468679539[/C][C]10.7855313204605[/C][/ROW]
[ROW][C]167[/C][C]106.5[/C][C]108.922818309492[/C][C]-2.42281830949209[/C][/ROW]
[ROW][C]168[/C][C]100.5[/C][C]109.384468804357[/C][C]-8.8844688043574[/C][/ROW]
[ROW][C]169[/C][C]101.7[/C][C]107.847122339448[/C][C]-6.14712233944765[/C][/ROW]
[ROW][C]170[/C][C]104.1[/C][C]106.376063591919[/C][C]-2.27606359191941[/C][/ROW]
[ROW][C]171[/C][C]112.3[/C][C]105.504127414866[/C][C]6.79587258513432[/C][/ROW]
[ROW][C]172[/C][C]111.2[/C][C]106.991563550649[/C][C]4.20843644935059[/C][/ROW]
[ROW][C]173[/C][C]108.2[/C][C]108.290170675499[/C][C]-0.090170675498868[/C][/ROW]
[ROW][C]174[/C][C]115.1[/C][C]108.717328348554[/C][C]6.38267165144603[/C][/ROW]
[ROW][C]175[/C][C]102.3[/C][C]110.94869984643[/C][C]-8.64869984642982[/C][/ROW]
[ROW][C]176[/C][C]93.6[/C][C]109.47647523835[/C][C]-15.8764752383498[/C][/ROW]
[ROW][C]177[/C][C]120.6[/C][C]105.300536054955[/C][C]15.2994639450448[/C][/ROW]
[ROW][C]178[/C][C]118.4[/C][C]108.598275390302[/C][C]9.80172460969789[/C][/ROW]
[ROW][C]179[/C][C]106.6[/C][C]111.562502292196[/C][C]-4.96250229219592[/C][/ROW]
[ROW][C]180[/C][C]105.3[/C][C]111.167162664247[/C][C]-5.86716266424659[/C][/ROW]
[ROW][C]181[/C][C]101.5[/C][C]110.127838323606[/C][C]-8.6278383236064[/C][/ROW]
[ROW][C]182[/C][C]100.1[/C][C]107.853906644094[/C][C]-7.7539066440937[/C][/ROW]
[ROW][C]183[/C][C]119.5[/C][C]105.145028986999[/C][C]14.3549710130006[/C][/ROW]
[ROW][C]184[/C][C]111.2[/C][C]108.012273670101[/C][C]3.18772632989872[/C][/ROW]
[ROW][C]185[/C][C]103.7[/C][C]108.885105554449[/C][C]-5.18510555444945[/C][/ROW]
[ROW][C]186[/C][C]117.8[/C][C]107.665997273789[/C][C]10.1340027262113[/C][/ROW]
[ROW][C]187[/C][C]101.7[/C][C]110.325319845906[/C][C]-8.62531984590635[/C][/ROW]
[ROW][C]188[/C][C]97.4[/C][C]108.533285140093[/C][C]-11.133285140093[/C][/ROW]
[ROW][C]189[/C][C]120[/C][C]105.360136170991[/C][C]14.6398638290094[/C][/ROW]
[ROW][C]190[/C][C]117[/C][C]108.522344806479[/C][C]8.4776551935206[/C][/ROW]
[ROW][C]191[/C][C]110.6[/C][C]111.113152523586[/C][C]-0.513152523586385[/C][/ROW]
[ROW][C]192[/C][C]105.3[/C][C]111.855707885666[/C][C]-6.55570788566612[/C][/ROW]
[ROW][C]193[/C][C]100.9[/C][C]110.866942141226[/C][C]-9.9669421412257[/C][/ROW]
[ROW][C]194[/C][C]108.1[/C][C]108.40729362408[/C][C]-0.307293624080188[/C][/ROW]
[ROW][C]195[/C][C]119.3[/C][C]107.865769760877[/C][C]11.434230239123[/C][/ROW]
[ROW][C]196[/C][C]113[/C][C]110.585711173997[/C][C]2.41428882600327[/C][/ROW]
[ROW][C]197[/C][C]108.6[/C][C]111.682098060291[/C][C]-3.08209806029149[/C][/ROW]
[ROW][C]198[/C][C]123.3[/C][C]111.430555767875[/C][C]11.8694442321246[/C][/ROW]
[ROW][C]199[/C][C]101.4[/C][C]115.120213355133[/C][C]-13.720213355133[/C][/ROW]
[ROW][C]200[/C][C]103.5[/C][C]112.58383783258[/C][C]-9.08383783258004[/C][/ROW]
[ROW][C]201[/C][C]119.4[/C][C]110.264313386593[/C][C]9.13568661340686[/C][/ROW]
[ROW][C]202[/C][C]113.1[/C][C]112.327800478664[/C][C]0.772199521335523[/C][/ROW]
[ROW][C]203[/C][C]112[/C][C]112.770404727118[/C][C]-0.770404727117523[/C][/ROW]
[ROW][C]204[/C][C]115.8[/C][C]112.842153249616[/C][C]2.95784675038428[/C][/ROW]
[ROW][C]205[/C][C]105.4[/C][C]113.896515237542[/C][C]-8.49651523754167[/C][/ROW]
[ROW][C]206[/C][C]110.9[/C][C]111.978518431823[/C][C]-1.07851843182266[/C][/ROW]
[ROW][C]207[/C][C]128.5[/C][C]111.467164109005[/C][C]17.032835890995[/C][/ROW]
[ROW][C]208[/C][C]109[/C][C]115.939025113145[/C][C]-6.93902511314539[/C][/ROW]
[ROW][C]209[/C][C]117.2[/C][C]115.044218224117[/C][C]2.15578177588257[/C][/ROW]
[ROW][C]210[/C][C]124.4[/C][C]116.147943685238[/C][C]8.25205631476243[/C][/ROW]
[ROW][C]211[/C][C]104.7[/C][C]119.127390884651[/C][C]-14.4273908846511[/C][/ROW]
[ROW][C]212[/C][C]108.6[/C][C]116.410284189492[/C][C]-7.81028418949225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310016&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310016&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
373.871.22.60000000000001
46578.3275659976734-13.3275659976734
57381.2028398977403-8.2028398977403
671.184.4625451694078-13.3625451694078
758.285.6323647933317-27.4323647933317
86481.812592168229-17.812592168229
97578.5242647432451-3.52426474324511
1074.977.831421111228-2.93142111122803
117577.0269149104081-2.02691491040805
1268.376.244650105544-7.94465010554397
1372.573.6467739185435-1.14677391854347
1472.472.32547308797280.0745269120271672
1579.671.25561637738628.34438362261375
1670.772.5058086098037-1.80580860980368
1776.471.57281830904974.82718169095034
1879.772.3537383735357.34626162646505
1964.274.2197537251502-10.0197537251502
2067.971.8047516661286-3.90475166612855
2174.170.31180566770093.78819433229911
2278.570.66407465194897.83592534805106
2373.472.44737873401330.952621265986679
2465.472.9216390946293-7.52163909462932
2569.971.0995465173491-1.19954651734912
2669.670.4542043005425-0.854204300542477
2776.869.81102780916126.98897219083879
2875.671.29535712092744.30464287907257
297472.57895141398531.42104858601475
307673.39464055947192.60535944052813
3168.174.6536562986389-6.5536562986389
3265.573.5548662716936-8.05486627169361
3376.971.51984301874165.38015698125842
3481.772.61000812879379.08999187120634
3573.675.1620317139636-1.56203171396363
3668.775.449165477215-6.74916547721503
3773.374.1617470189294-0.861747018929393
3871.573.9902802782442-2.49028027824416
3978.373.29522762553255.00477237446752
4076.574.50141209702671.9985879029733
4171.875.2605265953379-3.46052659533791
4277.674.64940268599842.95059731400163
437075.5597832878452-5.55978328784524
446474.3210575206466-10.3210575206466
4581.371.31209897902669.9879010209734
4682.573.17340527771379.32659472228632
4773.175.6362713589787-2.53627135897874
4878.175.51404792231322.58595207768677
4970.776.6254434009284-5.92544340092844
5074.975.5587302211775-0.658730221177535
518875.499148609349112.5008513906509
5281.379.07017371259782.22982628740215
5375.780.7515533641106-5.05155336411062
5489.880.57097614082319.22902385917688
5574.683.9887325735933-9.38873257359334
5674.982.9234733738422-8.02347337384219
579081.50083228888568.49916771111442
5888.184.06986956675074.0301304332493
5984.986.0576896778167-1.15768967781665
6087.786.91118632003360.788813679966381
6180.588.2182030458595-7.71820304585952
627987.2067995574849-8.2067995574849
6389.985.45080960347634.4491903965237
6486.386.5900429481621-0.290042948162096
6581.186.7534860618934-5.65348606189342
6692.485.39321753552467.00678246447536
6771.887.1304604032249-15.3304604032249
6876.183.1688356791644-7.06883567916439
6992.580.311708756703312.1882912432967
708782.28664399368584.71335600631421
7189.583.1297559689466.37024403105397
7288.784.80772886973653.89227113026355
7383.886.2939830489444-2.49398304894439
7484.986.2996949095588-1.39969490955878
759986.415206653298212.5847933467018
7684.690.3338052654805-5.73380526548054
7792.790.11739217649892.58260782350111
7897.691.77661036898415.82338963101586
797894.5461044403403-16.5461044403403
8081.991.5145057295333-9.61450572953325
8196.589.11947931125197.38052068874809
8299.990.7230156740489.17698432595198
8396.293.41052820021212.78947179978795
8490.595.0333533995222-4.53335339952216
8591.494.8266997805668-3.42669978056682
8689.794.5726920249058-4.87269202490576
87102.793.64417189024099.05582810975908
8891.596.229554740937-4.72955474093699
8996.295.67053957949280.529460420507206
90104.596.21068619406178.28931380593828
9190.398.9639950613161-8.6639950613161
9290.397.6260472181617-7.32604721816172
93100.495.98015287873654.41984712126347
94111.397.044172221639314.2558277783607
95101.3101.2087173189120.0912826810880887
9694.4102.532297618501-8.13229761850133
97100.4101.561837279071-1.16183727907116
98102101.9014685320090.0985314679909663
99104.3102.5022900580511.79770994194872
100108.8103.5863579466485.21364205335234
101101.3105.767898514175-4.46789851417482
102108.9105.6508335868453.24916641315548
10398.5107.341381270588-8.84138127058795
10488.8105.904487765944-17.1044877659445
105111.8101.45898482553910.3410151744612
106109.6103.346546613716.25345338629026
10792.5104.904698713586-12.4046987135859
10894.5101.734184718048-7.23418471804814
10980.899.0335971391555-18.2335971391555
11083.792.685268883458-8.98526888345796
11194.287.48890894422786.7110910557722
11286.285.97725863316450.222741366835479
1138983.17849755001745.82150244998259
11494.781.963997400779312.7360025992207
11581.983.142886022174-1.24288602217399
11680.281.4130660955891-1.21306609558907
11796.579.59370504053516.906294959465
11895.682.749203317029612.8507966829704
11991.986.10132478644465.79867521355536
12089.988.49211708204961.40788291795045
12186.390.1109055878738-3.8109055878738
1229490.38018481132783.61981518867222
12310892.428690744152815.5713092558472
12496.398.1067050985399-1.80670509853992
12594.6100.148122784567-5.54812278456654
126111.7101.00027773233310.6997222676675
12792105.962164723818-13.9621647238183
12891.9104.865515942223-12.9655159422232
129109.2102.9481469909646.25185300903645
130106.8105.3873109148421.41268908515816
131105.8106.964692671597-1.16469267159657
132103.6107.932096639981-4.33209663998136
13397.6107.921428740965-10.321428740965
134102.8105.893565532849-3.09356553284923
135124.8105.07541478392219.7245852160782
136103.9110.39889801548-6.49889801548028
137112.2109.9376285526532.26237144734738
138108.5111.416219639386-2.91621963938577
13992.4111.623846796405-19.2238467964054
140101.1107.03838834618-5.93838834617969
141114.9104.65663187538610.2433681246142
142106.4106.3353776091180.0646223908815386
143104105.972508544896-1.97250854489644
144101.6105.044672317585-3.44467231758537
14599.4103.549527505424-4.14952750542352
146102.3101.585849516970.714150483029755
147121.3100.6563859783720.6436140216298
14899.3105.360089734648-6.06008973464847
149102.9104.217038981009-1.31703898100908
150111.4103.9239774129437.47602258705724
15198.5105.987779530912-7.48777953091194
15298.5104.45300251517-5.95300251516967
153108.5102.7579932914055.7420067085949
154112.1103.8667950234348.23320497656618
155105.3106.124938523973-0.824938523973444
15695.2106.496734772373-11.2967347723728
15798.2103.873206543789-5.67320654378881
15896.6101.933632796599-5.33363279659876
159109.699.64227940249729.95772059750284
160108101.2098925950656.79010740493469
161106.7102.6753410889444.02465891105567
162111.5103.9016927789887.59830722101204
163104.5106.445038739363-1.94503873936313
16494.3106.916259232973-12.6162592329731
165109.6104.2481342370365.35186576296398
166116.4105.61446867953910.7855313204605
167106.5108.922818309492-2.42281830949209
168100.5109.384468804357-8.8844688043574
169101.7107.847122339448-6.14712233944765
170104.1106.376063591919-2.27606359191941
171112.3105.5041274148666.79587258513432
172111.2106.9915635506494.20843644935059
173108.2108.290170675499-0.090170675498868
174115.1108.7173283485546.38267165144603
175102.3110.94869984643-8.64869984642982
17693.6109.47647523835-15.8764752383498
177120.6105.30053605495515.2994639450448
178118.4108.5982753903029.80172460969789
179106.6111.562502292196-4.96250229219592
180105.3111.167162664247-5.86716266424659
181101.5110.127838323606-8.6278383236064
182100.1107.853906644094-7.7539066440937
183119.5105.14502898699914.3549710130006
184111.2108.0122736701013.18772632989872
185103.7108.885105554449-5.18510555444945
186117.8107.66599727378910.1340027262113
187101.7110.325319845906-8.62531984590635
18897.4108.533285140093-11.133285140093
189120105.36013617099114.6398638290094
190117108.5223448064798.4776551935206
191110.6111.113152523586-0.513152523586385
192105.3111.855707885666-6.55570788566612
193100.9110.866942141226-9.9669421412257
194108.1108.40729362408-0.307293624080188
195119.3107.86576976087711.434230239123
196113110.5857111739972.41428882600327
197108.6111.682098060291-3.08209806029149
198123.3111.43055576787511.8694442321246
199101.4115.120213355133-13.720213355133
200103.5112.58383783258-9.08383783258004
201119.4110.2643133865939.13568661340686
202113.1112.3278004786640.772199521335523
203112112.770404727118-0.770404727117523
204115.8112.8421532496162.95784675038428
205105.4113.896515237542-8.49651523754167
206110.9111.978518431823-1.07851843182266
207128.5111.46716410900517.032835890995
208109115.939025113145-6.93902511314539
209117.2115.0442182241172.15578177588257
210124.4116.1479436852388.25205631476243
211104.7119.127390884651-14.4273908846511
212108.6116.410284189492-7.81028418949225







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
213114.40860762596598.28278228025130.53443297168
214113.97739389445297.2320884596539130.72269932925
215113.54618016293895.8305591337518131.261801192125
216113.11496643142594.047138556041132.182794306809
217112.68375269991291.8787619000883133.488743499735
218112.25253896839889.3425876566722135.162490280124
219111.82132523688586.4665892999921137.176061173777
220111.39011150537183.2820373642648139.498185646478
221110.95889777385879.8189659281981142.098829619518
222110.52768404234576.1041005785293144.95126750616
223110.09647031083172.16030082701148.032639794652
224109.66525657931868.0067542182547151.323758940381

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 114.408607625965 & 98.28278228025 & 130.53443297168 \tabularnewline
214 & 113.977393894452 & 97.2320884596539 & 130.72269932925 \tabularnewline
215 & 113.546180162938 & 95.8305591337518 & 131.261801192125 \tabularnewline
216 & 113.114966431425 & 94.047138556041 & 132.182794306809 \tabularnewline
217 & 112.683752699912 & 91.8787619000883 & 133.488743499735 \tabularnewline
218 & 112.252538968398 & 89.3425876566722 & 135.162490280124 \tabularnewline
219 & 111.821325236885 & 86.4665892999921 & 137.176061173777 \tabularnewline
220 & 111.390111505371 & 83.2820373642648 & 139.498185646478 \tabularnewline
221 & 110.958897773858 & 79.8189659281981 & 142.098829619518 \tabularnewline
222 & 110.527684042345 & 76.1041005785293 & 144.95126750616 \tabularnewline
223 & 110.096470310831 & 72.16030082701 & 148.032639794652 \tabularnewline
224 & 109.665256579318 & 68.0067542182547 & 151.323758940381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310016&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]213[/C][C]114.408607625965[/C][C]98.28278228025[/C][C]130.53443297168[/C][/ROW]
[ROW][C]214[/C][C]113.977393894452[/C][C]97.2320884596539[/C][C]130.72269932925[/C][/ROW]
[ROW][C]215[/C][C]113.546180162938[/C][C]95.8305591337518[/C][C]131.261801192125[/C][/ROW]
[ROW][C]216[/C][C]113.114966431425[/C][C]94.047138556041[/C][C]132.182794306809[/C][/ROW]
[ROW][C]217[/C][C]112.683752699912[/C][C]91.8787619000883[/C][C]133.488743499735[/C][/ROW]
[ROW][C]218[/C][C]112.252538968398[/C][C]89.3425876566722[/C][C]135.162490280124[/C][/ROW]
[ROW][C]219[/C][C]111.821325236885[/C][C]86.4665892999921[/C][C]137.176061173777[/C][/ROW]
[ROW][C]220[/C][C]111.390111505371[/C][C]83.2820373642648[/C][C]139.498185646478[/C][/ROW]
[ROW][C]221[/C][C]110.958897773858[/C][C]79.8189659281981[/C][C]142.098829619518[/C][/ROW]
[ROW][C]222[/C][C]110.527684042345[/C][C]76.1041005785293[/C][C]144.95126750616[/C][/ROW]
[ROW][C]223[/C][C]110.096470310831[/C][C]72.16030082701[/C][C]148.032639794652[/C][/ROW]
[ROW][C]224[/C][C]109.665256579318[/C][C]68.0067542182547[/C][C]151.323758940381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310016&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310016&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
213114.40860762596598.28278228025130.53443297168
214113.97739389445297.2320884596539130.72269932925
215113.54618016293895.8305591337518131.261801192125
216113.11496643142594.047138556041132.182794306809
217112.68375269991291.8787619000883133.488743499735
218112.25253896839889.3425876566722135.162490280124
219111.82132523688586.4665892999921137.176061173777
220111.39011150537183.2820373642648139.498185646478
221110.95889777385879.8189659281981142.098829619518
222110.52768404234576.1041005785293144.95126750616
223110.09647031083172.16030082701148.032639794652
224109.66525657931868.0067542182547151.323758940381



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')