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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 computationMon, 18 Dec 2017 13:47:56 +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/18/t1513601301qz54rw70rm5w6je.htm/, Retrieved Tue, 14 May 2024 00:29:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310143, Retrieved Tue, 14 May 2024 00:29:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact35
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-12-18 12:47:56] [eeb8783d96126a2719bfaf914027c923] [Current]
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Dataseries X:
55.5
63
77.2
71.1
90.1
91.5
76.1
87.8
81
77.2
73.8
68.9
68.4
65.2
78.7
77
97.6
88.1
98.7
93.4
68
87.9
75.8
66.3
68.4
71.3
77.4
87.1
88.5
85.9
92.7
88.5
80.2
81.8
70.4
82.2
72.8
69
83
92.4
92.3
100.5
106.9
99.5
85.9
92.6
77.4
84.1
75.3
73.8
100.1
90.7
96.5
111.8
97.4
100.8
93.7
82
86
84.3
73.1
75.4
97.9
97.5
106
112.8
99.5
100.8
102.9
88.8
91.3
88.3
77.4
80.5
96.7
93.8
105
117.1
111.1
105.8
95.7
97.1
91
90.9
83.5
82.3
101.7
108.3
114
118.2
103.4
106.8
95.4
101.8
95.6
94.8
94
82.4
95.8
106.7
114.1
103.9
117.4
105.9
101.7
98.7
91.3
102.3
80.5
86.7
102.6
107.3
108
124.3
117.1
103.9
104.7
95.9
94.2
102.7
70.3
90.2
107.3
104.6
102.7
124.5
117.8
104.2
99.9
91.5
95.7
91.4
86.2
91.5
115.5
113.9
131.9
121.2
105.2
107.5
113.8
100.5
104.8
103.8
93.1
106.2
117.5
109.9
123.6
131.7
111
122
110.9
108
103.6
107.3
94.4
85.2
113.2
111.7
124.3
124
133.4
112.6
115.8
112.3
103.6
111.4
95.1
93.4
117.3
121.5
123.1
139.3
125.8
108.6
121
111.6
99.7
116.7
90.3
90.4
117.3
121.6
114.6
133.3
127.4
115
112.6
108.3
107.6
109
89
102.5
124.5
124.2
130.8
138.7
127.6
130.9
136.9
125.2
131.3
124.1
103.2
118.1
136.5
117.8
145.1
158.8
136.9
132.7




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=310143&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=310143&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310143&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
alpha0.730179305724786
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.730179305724786 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310143&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]0.730179305724786[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310143&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310143&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
alpha0.730179305724786
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26355.57.5
377.260.976344792935916.2236552070641
471.172.8225220883483-1.72252208834827
590.171.564772105782518.5352278942175
691.585.09881194103296.40118805896709
776.189.7728269937433-13.6728269937433
887.879.78921167215678.0107883278433
98185.6385235316895-4.63852353168954
1077.282.2515696397324-5.05156963973239
1173.878.5630180273722-4.76301802737218
1268.975.0851608309909-6.18516083099092
1368.470.5688843896218-2.16888438962184
1465.268.9852098918104-3.78520989181044
1578.766.221327960985712.4786720390143
167775.33299604680051.66700395319954
1797.676.550207835988221.0497921640118
1888.191.9203304639574-3.82033046395738
1998.789.13080421814579.56919578185428
2093.496.1180329504846-2.71803295048463
216894.1333815377627-26.1333815377627
2287.975.051327150278212.8486728497218
2375.884.433162171173-8.63316217117297
2466.378.1294058108164-11.8294058108164
2568.469.4918184887377-1.09181848873773
2671.368.69459522265372.60540477734627
2777.470.59700787410856.80299212589154
2887.175.564411941443111.5355880585569
2988.583.98745962116734.5125403788327
3085.987.2824232220384-1.38242322203843
3192.786.27300639355266.42699360644741
3288.590.965864123006-2.46586412300599
3380.289.1653411696578-8.96534116965782
3481.882.6190345788112-0.819034578811241
3570.482.0209924786903-11.6209924786903
3682.273.53558425876738.66441574123274
3772.879.8621613292115-7.06216132921149
386974.7055172729314-5.70551727293142
398370.539466631781612.4605333682184
4092.479.637890235547812.7621097644522
4192.388.9565186829393.34348131706098
42100.591.39785954973449.10214045026561
43106.998.04405414431888.85594585568118
4499.5104.510482540756-5.0104825407564
4585.9100.851931877801-14.9519318778007
4692.689.93434064002392.66565935997609
4777.491.88074994079-14.48074994079
4884.181.30720600264972.79279399735026
4975.383.3464463846673-8.04644638466731
5073.877.4710977499592-3.67109774995922
51100.174.790538143646225.3094618563538
5290.793.2709834301865-2.57098343018654
5396.591.3937045341035.10629546589699
54111.895.122215812217316.6777841877827
5597.4107.29998869148-9.89998869148027
56100.8100.0712218220520.728778177948001
5793.7100.603360566053-6.90336056605344
588295.5626695407647-13.5626695407647
598685.65948891171440.340511088285581
6084.385.9081230617504-1.60812306175038
6173.184.7339048810015-11.6339048810015
6275.476.2390682921236-0.839068292123613
6397.975.626397989125122.2736020108749
6497.591.89012124141595.60987875858406
6510695.986338618559110.0136613814409
66112.8103.2981069338239.50189306617729
6799.5110.236192615955-10.7361926159552
68100.8102.396846945509-1.59684694550945
69102.9101.2308623514891.66913764851139
7088.8102.449632120838-13.6496321208378
7191.392.4829532154457-1.18295321544571
7288.391.6191852578867-3.31918525788666
7377.489.195584870711-11.795584870711
7480.580.5826928991975-0.0826928991974683
7596.780.522312255473116.1776877445269
7693.892.33492506100411.46507493899587
7710593.404692462794911.5953075372051
78117.1101.87134606997715.2286539300233
79111.1112.990994023724-1.89099402372415
80105.8111.610229320352-5.81022932035152
8195.7107.367720109115-11.6677201091155
8297.198.8481923404504-1.74819234045043
839197.5716984710269-6.57169847102695
8490.992.7731802440199-1.87318024401985
8583.591.4054227939441-7.90542279394406
8682.385.6330466668011-3.3330466668011
87101.783.19932496568818.500675034312
88108.396.708135017681811.5918649823182
89114105.1722749425268.82772505747366
90118.2111.6180970961226.58190290387824
91103.4116.424066388824-13.0240663888235
92106.8106.914162635319-0.114162635318849
9395.4106.830803441522-11.430803441522
94101.898.4842673207153.31573267928501
9595.6100.905346706444-5.30534670644431
9694.897.0314923317035-2.23149233170352
979495.4021028102101-1.40210281021007
9882.494.3783163536961-11.9783163536961
9995.885.631997634802410.1680023651976
100106.793.056462542430413.6435374575696
101114.1103.01869125082911.0813087491713
102103.9111.110033579821-7.21003357982057
103117.4105.84541626625511.5545837337452
104105.9114.2823341949-8.38233419489977
105101.7108.161727232115-6.46172723211474
10698.7103.443507727986-4.74350772798626
10791.399.9798965484651-8.67989654846509
108102.393.64201571294398.65798428705611
10980.599.9638966686426-19.4638966686426
11086.785.75176211243420.94823788756581
111102.686.444145794838916.1558542051611
112107.398.24081620175439.05918379824571
113108104.8556447379913.14435526200943
114124.3107.15158788015717.1484121198433
115117.1119.673003536106-2.57300353610637
116103.9117.794249600485-13.8942496004848
117104.7107.648956073636-2.94895607363593
11895.9105.495689375176-9.59568937517555
11994.298.4891155692592-4.28911556925917
120102.795.35729214072417.34270785927586
12170.3100.71878546755-30.4187854675501
12290.278.507617813863211.6923821861368
123107.387.045153320805420.2548466791946
124104.6101.8348232065822.76517679341829
125102.7103.853898077806-1.15389807780616
126124.5103.01134558047721.4886544195235
127117.8118.701916345484-0.901916345484025
128104.2118.043355694517-13.8433556945167
12999.9107.935223844593-8.03522384459322
13091.5102.068069676405-10.5680696764049
13195.794.35148389723641.3485161027636
13291.495.336142448911-3.93614244891103
13386.292.4620526883313-6.26205268833131
13491.587.88963140395353.61036859604647
135115.590.525847838825324.9741521611747
136113.9108.7614569249375.13854307506301
137131.9112.51351473992319.3864852600766
138121.2126.66912508757-5.46912508756992
139105.2122.675683128206-17.4756831282061
140107.5109.915300954586-2.41530095458623
141113.8108.151698180455.64830181954996
142100.5112.275971281573-11.7759712815731
143104.8103.6774007469591.12259925304096
144103.8104.497099490152-0.697099490151643
14593.1103.988091868412-10.8880918684116
146106.296.037832507267110.1621674927329
147117.5103.4580369117714.0419630882302
148109.9113.711187770547-3.81118777054679
149123.6110.92833733026212.6716626697378
150131.7120.1809231808311.51907681917
151111128.591914695242-17.591914695242
152122115.7466626367016.25333736329945
153110.9120.312720171097-9.4127201710974
154108113.439746691584-5.43974669158382
155103.6109.467756229004-5.86775622900446
156107.3105.1832420595482.1167579404523
15794.4106.728854902895-12.3288549028946
15885.297.7265801895174-12.5265801895174
159113.288.579930563629724.6200694363703
160111.7106.5569957715755.14300422842541
161124.3110.31231102842613.9876889715741
162124120.5258320503843.47416794961589
163133.4123.06259759180610.3374024081941
164112.6130.610754905219-18.0107549052188
165115.8117.459674392947-1.65967439294685
166112.3116.247814496976-3.94781449697572
167103.6113.365202048444-9.76520204844374
168111.4106.2348535964495.16514640355118
16995.1110.006336611361-14.9063366113607
17093.499.1220380935774-5.72203809357738
171117.394.943924291078322.3560757089217
172121.5111.26786813094910.2321318690505
173123.1118.7391590751774.36084092482275
174139.3121.92335487404117.3766451259595
175125.8134.61142154794-8.81142154793959
176108.6128.177503879617-19.5775038796166
177121113.8824156889747.11758431102614
178111.6119.079528459637-7.47952845963657
17999.7113.61813156183-13.9181315618304
180116.7103.45539992102713.2446000789732
18190.3113.126332811294-22.8263328112939
18290.496.4590169669004-6.05901696690043
183117.392.034848164634425.2651518353656
184121.6110.48293919081311.1170608091871
185114.6118.600386934165-4.00038693416538
186133.3115.67938717994617.620612820054
187127.4128.545594015338-1.14559401533828
188115127.709104972576-12.7091049725761
189112.6118.429179527317-5.82917952731707
190108.3114.172833267116-5.87283326711555
191107.6109.884611949496-2.28461194949568
192109108.2164355823620.783564417637621
19389108.788578104824-19.7885781048237
194102.594.33936788296288.16063211703717
195124.5100.29809257645624.2019074235436
196124.2117.9698245361956.230175463805
197130.8122.51896973098.28103026910028
198138.7128.56560666347710.1343933365227
199127.6135.965530953881-8.36553095388135
200130.9129.8571933699571.04280663004295
201136.9130.6186291910876.28137080891298
202125.2135.205156167339-10.0051561673391
203131.3127.8995981834033.40040181659666
204124.1130.382501221031-6.2825012210312
205103.2125.795148841244-22.5951488412435
206118.1109.2966387475968.80336125240386
207136.5115.72467095492120.7753290450791
208117.8130.894386293261-13.0943862932607
209145.1121.33313640075523.7668635992445
210158.8138.68720836290820.1127916370925
211136.9153.373152596667-16.473152596667
212132.7141.344797470534-8.64479747053426

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 63 & 55.5 & 7.5 \tabularnewline
3 & 77.2 & 60.9763447929359 & 16.2236552070641 \tabularnewline
4 & 71.1 & 72.8225220883483 & -1.72252208834827 \tabularnewline
5 & 90.1 & 71.5647721057825 & 18.5352278942175 \tabularnewline
6 & 91.5 & 85.0988119410329 & 6.40118805896709 \tabularnewline
7 & 76.1 & 89.7728269937433 & -13.6728269937433 \tabularnewline
8 & 87.8 & 79.7892116721567 & 8.0107883278433 \tabularnewline
9 & 81 & 85.6385235316895 & -4.63852353168954 \tabularnewline
10 & 77.2 & 82.2515696397324 & -5.05156963973239 \tabularnewline
11 & 73.8 & 78.5630180273722 & -4.76301802737218 \tabularnewline
12 & 68.9 & 75.0851608309909 & -6.18516083099092 \tabularnewline
13 & 68.4 & 70.5688843896218 & -2.16888438962184 \tabularnewline
14 & 65.2 & 68.9852098918104 & -3.78520989181044 \tabularnewline
15 & 78.7 & 66.2213279609857 & 12.4786720390143 \tabularnewline
16 & 77 & 75.3329960468005 & 1.66700395319954 \tabularnewline
17 & 97.6 & 76.5502078359882 & 21.0497921640118 \tabularnewline
18 & 88.1 & 91.9203304639574 & -3.82033046395738 \tabularnewline
19 & 98.7 & 89.1308042181457 & 9.56919578185428 \tabularnewline
20 & 93.4 & 96.1180329504846 & -2.71803295048463 \tabularnewline
21 & 68 & 94.1333815377627 & -26.1333815377627 \tabularnewline
22 & 87.9 & 75.0513271502782 & 12.8486728497218 \tabularnewline
23 & 75.8 & 84.433162171173 & -8.63316217117297 \tabularnewline
24 & 66.3 & 78.1294058108164 & -11.8294058108164 \tabularnewline
25 & 68.4 & 69.4918184887377 & -1.09181848873773 \tabularnewline
26 & 71.3 & 68.6945952226537 & 2.60540477734627 \tabularnewline
27 & 77.4 & 70.5970078741085 & 6.80299212589154 \tabularnewline
28 & 87.1 & 75.5644119414431 & 11.5355880585569 \tabularnewline
29 & 88.5 & 83.9874596211673 & 4.5125403788327 \tabularnewline
30 & 85.9 & 87.2824232220384 & -1.38242322203843 \tabularnewline
31 & 92.7 & 86.2730063935526 & 6.42699360644741 \tabularnewline
32 & 88.5 & 90.965864123006 & -2.46586412300599 \tabularnewline
33 & 80.2 & 89.1653411696578 & -8.96534116965782 \tabularnewline
34 & 81.8 & 82.6190345788112 & -0.819034578811241 \tabularnewline
35 & 70.4 & 82.0209924786903 & -11.6209924786903 \tabularnewline
36 & 82.2 & 73.5355842587673 & 8.66441574123274 \tabularnewline
37 & 72.8 & 79.8621613292115 & -7.06216132921149 \tabularnewline
38 & 69 & 74.7055172729314 & -5.70551727293142 \tabularnewline
39 & 83 & 70.5394666317816 & 12.4605333682184 \tabularnewline
40 & 92.4 & 79.6378902355478 & 12.7621097644522 \tabularnewline
41 & 92.3 & 88.956518682939 & 3.34348131706098 \tabularnewline
42 & 100.5 & 91.3978595497344 & 9.10214045026561 \tabularnewline
43 & 106.9 & 98.0440541443188 & 8.85594585568118 \tabularnewline
44 & 99.5 & 104.510482540756 & -5.0104825407564 \tabularnewline
45 & 85.9 & 100.851931877801 & -14.9519318778007 \tabularnewline
46 & 92.6 & 89.9343406400239 & 2.66565935997609 \tabularnewline
47 & 77.4 & 91.88074994079 & -14.48074994079 \tabularnewline
48 & 84.1 & 81.3072060026497 & 2.79279399735026 \tabularnewline
49 & 75.3 & 83.3464463846673 & -8.04644638466731 \tabularnewline
50 & 73.8 & 77.4710977499592 & -3.67109774995922 \tabularnewline
51 & 100.1 & 74.7905381436462 & 25.3094618563538 \tabularnewline
52 & 90.7 & 93.2709834301865 & -2.57098343018654 \tabularnewline
53 & 96.5 & 91.393704534103 & 5.10629546589699 \tabularnewline
54 & 111.8 & 95.1222158122173 & 16.6777841877827 \tabularnewline
55 & 97.4 & 107.29998869148 & -9.89998869148027 \tabularnewline
56 & 100.8 & 100.071221822052 & 0.728778177948001 \tabularnewline
57 & 93.7 & 100.603360566053 & -6.90336056605344 \tabularnewline
58 & 82 & 95.5626695407647 & -13.5626695407647 \tabularnewline
59 & 86 & 85.6594889117144 & 0.340511088285581 \tabularnewline
60 & 84.3 & 85.9081230617504 & -1.60812306175038 \tabularnewline
61 & 73.1 & 84.7339048810015 & -11.6339048810015 \tabularnewline
62 & 75.4 & 76.2390682921236 & -0.839068292123613 \tabularnewline
63 & 97.9 & 75.6263979891251 & 22.2736020108749 \tabularnewline
64 & 97.5 & 91.8901212414159 & 5.60987875858406 \tabularnewline
65 & 106 & 95.9863386185591 & 10.0136613814409 \tabularnewline
66 & 112.8 & 103.298106933823 & 9.50189306617729 \tabularnewline
67 & 99.5 & 110.236192615955 & -10.7361926159552 \tabularnewline
68 & 100.8 & 102.396846945509 & -1.59684694550945 \tabularnewline
69 & 102.9 & 101.230862351489 & 1.66913764851139 \tabularnewline
70 & 88.8 & 102.449632120838 & -13.6496321208378 \tabularnewline
71 & 91.3 & 92.4829532154457 & -1.18295321544571 \tabularnewline
72 & 88.3 & 91.6191852578867 & -3.31918525788666 \tabularnewline
73 & 77.4 & 89.195584870711 & -11.795584870711 \tabularnewline
74 & 80.5 & 80.5826928991975 & -0.0826928991974683 \tabularnewline
75 & 96.7 & 80.5223122554731 & 16.1776877445269 \tabularnewline
76 & 93.8 & 92.3349250610041 & 1.46507493899587 \tabularnewline
77 & 105 & 93.4046924627949 & 11.5953075372051 \tabularnewline
78 & 117.1 & 101.871346069977 & 15.2286539300233 \tabularnewline
79 & 111.1 & 112.990994023724 & -1.89099402372415 \tabularnewline
80 & 105.8 & 111.610229320352 & -5.81022932035152 \tabularnewline
81 & 95.7 & 107.367720109115 & -11.6677201091155 \tabularnewline
82 & 97.1 & 98.8481923404504 & -1.74819234045043 \tabularnewline
83 & 91 & 97.5716984710269 & -6.57169847102695 \tabularnewline
84 & 90.9 & 92.7731802440199 & -1.87318024401985 \tabularnewline
85 & 83.5 & 91.4054227939441 & -7.90542279394406 \tabularnewline
86 & 82.3 & 85.6330466668011 & -3.3330466668011 \tabularnewline
87 & 101.7 & 83.199324965688 & 18.500675034312 \tabularnewline
88 & 108.3 & 96.7081350176818 & 11.5918649823182 \tabularnewline
89 & 114 & 105.172274942526 & 8.82772505747366 \tabularnewline
90 & 118.2 & 111.618097096122 & 6.58190290387824 \tabularnewline
91 & 103.4 & 116.424066388824 & -13.0240663888235 \tabularnewline
92 & 106.8 & 106.914162635319 & -0.114162635318849 \tabularnewline
93 & 95.4 & 106.830803441522 & -11.430803441522 \tabularnewline
94 & 101.8 & 98.484267320715 & 3.31573267928501 \tabularnewline
95 & 95.6 & 100.905346706444 & -5.30534670644431 \tabularnewline
96 & 94.8 & 97.0314923317035 & -2.23149233170352 \tabularnewline
97 & 94 & 95.4021028102101 & -1.40210281021007 \tabularnewline
98 & 82.4 & 94.3783163536961 & -11.9783163536961 \tabularnewline
99 & 95.8 & 85.6319976348024 & 10.1680023651976 \tabularnewline
100 & 106.7 & 93.0564625424304 & 13.6435374575696 \tabularnewline
101 & 114.1 & 103.018691250829 & 11.0813087491713 \tabularnewline
102 & 103.9 & 111.110033579821 & -7.21003357982057 \tabularnewline
103 & 117.4 & 105.845416266255 & 11.5545837337452 \tabularnewline
104 & 105.9 & 114.2823341949 & -8.38233419489977 \tabularnewline
105 & 101.7 & 108.161727232115 & -6.46172723211474 \tabularnewline
106 & 98.7 & 103.443507727986 & -4.74350772798626 \tabularnewline
107 & 91.3 & 99.9798965484651 & -8.67989654846509 \tabularnewline
108 & 102.3 & 93.6420157129439 & 8.65798428705611 \tabularnewline
109 & 80.5 & 99.9638966686426 & -19.4638966686426 \tabularnewline
110 & 86.7 & 85.7517621124342 & 0.94823788756581 \tabularnewline
111 & 102.6 & 86.4441457948389 & 16.1558542051611 \tabularnewline
112 & 107.3 & 98.2408162017543 & 9.05918379824571 \tabularnewline
113 & 108 & 104.855644737991 & 3.14435526200943 \tabularnewline
114 & 124.3 & 107.151587880157 & 17.1484121198433 \tabularnewline
115 & 117.1 & 119.673003536106 & -2.57300353610637 \tabularnewline
116 & 103.9 & 117.794249600485 & -13.8942496004848 \tabularnewline
117 & 104.7 & 107.648956073636 & -2.94895607363593 \tabularnewline
118 & 95.9 & 105.495689375176 & -9.59568937517555 \tabularnewline
119 & 94.2 & 98.4891155692592 & -4.28911556925917 \tabularnewline
120 & 102.7 & 95.3572921407241 & 7.34270785927586 \tabularnewline
121 & 70.3 & 100.71878546755 & -30.4187854675501 \tabularnewline
122 & 90.2 & 78.5076178138632 & 11.6923821861368 \tabularnewline
123 & 107.3 & 87.0451533208054 & 20.2548466791946 \tabularnewline
124 & 104.6 & 101.834823206582 & 2.76517679341829 \tabularnewline
125 & 102.7 & 103.853898077806 & -1.15389807780616 \tabularnewline
126 & 124.5 & 103.011345580477 & 21.4886544195235 \tabularnewline
127 & 117.8 & 118.701916345484 & -0.901916345484025 \tabularnewline
128 & 104.2 & 118.043355694517 & -13.8433556945167 \tabularnewline
129 & 99.9 & 107.935223844593 & -8.03522384459322 \tabularnewline
130 & 91.5 & 102.068069676405 & -10.5680696764049 \tabularnewline
131 & 95.7 & 94.3514838972364 & 1.3485161027636 \tabularnewline
132 & 91.4 & 95.336142448911 & -3.93614244891103 \tabularnewline
133 & 86.2 & 92.4620526883313 & -6.26205268833131 \tabularnewline
134 & 91.5 & 87.8896314039535 & 3.61036859604647 \tabularnewline
135 & 115.5 & 90.5258478388253 & 24.9741521611747 \tabularnewline
136 & 113.9 & 108.761456924937 & 5.13854307506301 \tabularnewline
137 & 131.9 & 112.513514739923 & 19.3864852600766 \tabularnewline
138 & 121.2 & 126.66912508757 & -5.46912508756992 \tabularnewline
139 & 105.2 & 122.675683128206 & -17.4756831282061 \tabularnewline
140 & 107.5 & 109.915300954586 & -2.41530095458623 \tabularnewline
141 & 113.8 & 108.15169818045 & 5.64830181954996 \tabularnewline
142 & 100.5 & 112.275971281573 & -11.7759712815731 \tabularnewline
143 & 104.8 & 103.677400746959 & 1.12259925304096 \tabularnewline
144 & 103.8 & 104.497099490152 & -0.697099490151643 \tabularnewline
145 & 93.1 & 103.988091868412 & -10.8880918684116 \tabularnewline
146 & 106.2 & 96.0378325072671 & 10.1621674927329 \tabularnewline
147 & 117.5 & 103.45803691177 & 14.0419630882302 \tabularnewline
148 & 109.9 & 113.711187770547 & -3.81118777054679 \tabularnewline
149 & 123.6 & 110.928337330262 & 12.6716626697378 \tabularnewline
150 & 131.7 & 120.18092318083 & 11.51907681917 \tabularnewline
151 & 111 & 128.591914695242 & -17.591914695242 \tabularnewline
152 & 122 & 115.746662636701 & 6.25333736329945 \tabularnewline
153 & 110.9 & 120.312720171097 & -9.4127201710974 \tabularnewline
154 & 108 & 113.439746691584 & -5.43974669158382 \tabularnewline
155 & 103.6 & 109.467756229004 & -5.86775622900446 \tabularnewline
156 & 107.3 & 105.183242059548 & 2.1167579404523 \tabularnewline
157 & 94.4 & 106.728854902895 & -12.3288549028946 \tabularnewline
158 & 85.2 & 97.7265801895174 & -12.5265801895174 \tabularnewline
159 & 113.2 & 88.5799305636297 & 24.6200694363703 \tabularnewline
160 & 111.7 & 106.556995771575 & 5.14300422842541 \tabularnewline
161 & 124.3 & 110.312311028426 & 13.9876889715741 \tabularnewline
162 & 124 & 120.525832050384 & 3.47416794961589 \tabularnewline
163 & 133.4 & 123.062597591806 & 10.3374024081941 \tabularnewline
164 & 112.6 & 130.610754905219 & -18.0107549052188 \tabularnewline
165 & 115.8 & 117.459674392947 & -1.65967439294685 \tabularnewline
166 & 112.3 & 116.247814496976 & -3.94781449697572 \tabularnewline
167 & 103.6 & 113.365202048444 & -9.76520204844374 \tabularnewline
168 & 111.4 & 106.234853596449 & 5.16514640355118 \tabularnewline
169 & 95.1 & 110.006336611361 & -14.9063366113607 \tabularnewline
170 & 93.4 & 99.1220380935774 & -5.72203809357738 \tabularnewline
171 & 117.3 & 94.9439242910783 & 22.3560757089217 \tabularnewline
172 & 121.5 & 111.267868130949 & 10.2321318690505 \tabularnewline
173 & 123.1 & 118.739159075177 & 4.36084092482275 \tabularnewline
174 & 139.3 & 121.923354874041 & 17.3766451259595 \tabularnewline
175 & 125.8 & 134.61142154794 & -8.81142154793959 \tabularnewline
176 & 108.6 & 128.177503879617 & -19.5775038796166 \tabularnewline
177 & 121 & 113.882415688974 & 7.11758431102614 \tabularnewline
178 & 111.6 & 119.079528459637 & -7.47952845963657 \tabularnewline
179 & 99.7 & 113.61813156183 & -13.9181315618304 \tabularnewline
180 & 116.7 & 103.455399921027 & 13.2446000789732 \tabularnewline
181 & 90.3 & 113.126332811294 & -22.8263328112939 \tabularnewline
182 & 90.4 & 96.4590169669004 & -6.05901696690043 \tabularnewline
183 & 117.3 & 92.0348481646344 & 25.2651518353656 \tabularnewline
184 & 121.6 & 110.482939190813 & 11.1170608091871 \tabularnewline
185 & 114.6 & 118.600386934165 & -4.00038693416538 \tabularnewline
186 & 133.3 & 115.679387179946 & 17.620612820054 \tabularnewline
187 & 127.4 & 128.545594015338 & -1.14559401533828 \tabularnewline
188 & 115 & 127.709104972576 & -12.7091049725761 \tabularnewline
189 & 112.6 & 118.429179527317 & -5.82917952731707 \tabularnewline
190 & 108.3 & 114.172833267116 & -5.87283326711555 \tabularnewline
191 & 107.6 & 109.884611949496 & -2.28461194949568 \tabularnewline
192 & 109 & 108.216435582362 & 0.783564417637621 \tabularnewline
193 & 89 & 108.788578104824 & -19.7885781048237 \tabularnewline
194 & 102.5 & 94.3393678829628 & 8.16063211703717 \tabularnewline
195 & 124.5 & 100.298092576456 & 24.2019074235436 \tabularnewline
196 & 124.2 & 117.969824536195 & 6.230175463805 \tabularnewline
197 & 130.8 & 122.5189697309 & 8.28103026910028 \tabularnewline
198 & 138.7 & 128.565606663477 & 10.1343933365227 \tabularnewline
199 & 127.6 & 135.965530953881 & -8.36553095388135 \tabularnewline
200 & 130.9 & 129.857193369957 & 1.04280663004295 \tabularnewline
201 & 136.9 & 130.618629191087 & 6.28137080891298 \tabularnewline
202 & 125.2 & 135.205156167339 & -10.0051561673391 \tabularnewline
203 & 131.3 & 127.899598183403 & 3.40040181659666 \tabularnewline
204 & 124.1 & 130.382501221031 & -6.2825012210312 \tabularnewline
205 & 103.2 & 125.795148841244 & -22.5951488412435 \tabularnewline
206 & 118.1 & 109.296638747596 & 8.80336125240386 \tabularnewline
207 & 136.5 & 115.724670954921 & 20.7753290450791 \tabularnewline
208 & 117.8 & 130.894386293261 & -13.0943862932607 \tabularnewline
209 & 145.1 & 121.333136400755 & 23.7668635992445 \tabularnewline
210 & 158.8 & 138.687208362908 & 20.1127916370925 \tabularnewline
211 & 136.9 & 153.373152596667 & -16.473152596667 \tabularnewline
212 & 132.7 & 141.344797470534 & -8.64479747053426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310143&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]2[/C][C]63[/C][C]55.5[/C][C]7.5[/C][/ROW]
[ROW][C]3[/C][C]77.2[/C][C]60.9763447929359[/C][C]16.2236552070641[/C][/ROW]
[ROW][C]4[/C][C]71.1[/C][C]72.8225220883483[/C][C]-1.72252208834827[/C][/ROW]
[ROW][C]5[/C][C]90.1[/C][C]71.5647721057825[/C][C]18.5352278942175[/C][/ROW]
[ROW][C]6[/C][C]91.5[/C][C]85.0988119410329[/C][C]6.40118805896709[/C][/ROW]
[ROW][C]7[/C][C]76.1[/C][C]89.7728269937433[/C][C]-13.6728269937433[/C][/ROW]
[ROW][C]8[/C][C]87.8[/C][C]79.7892116721567[/C][C]8.0107883278433[/C][/ROW]
[ROW][C]9[/C][C]81[/C][C]85.6385235316895[/C][C]-4.63852353168954[/C][/ROW]
[ROW][C]10[/C][C]77.2[/C][C]82.2515696397324[/C][C]-5.05156963973239[/C][/ROW]
[ROW][C]11[/C][C]73.8[/C][C]78.5630180273722[/C][C]-4.76301802737218[/C][/ROW]
[ROW][C]12[/C][C]68.9[/C][C]75.0851608309909[/C][C]-6.18516083099092[/C][/ROW]
[ROW][C]13[/C][C]68.4[/C][C]70.5688843896218[/C][C]-2.16888438962184[/C][/ROW]
[ROW][C]14[/C][C]65.2[/C][C]68.9852098918104[/C][C]-3.78520989181044[/C][/ROW]
[ROW][C]15[/C][C]78.7[/C][C]66.2213279609857[/C][C]12.4786720390143[/C][/ROW]
[ROW][C]16[/C][C]77[/C][C]75.3329960468005[/C][C]1.66700395319954[/C][/ROW]
[ROW][C]17[/C][C]97.6[/C][C]76.5502078359882[/C][C]21.0497921640118[/C][/ROW]
[ROW][C]18[/C][C]88.1[/C][C]91.9203304639574[/C][C]-3.82033046395738[/C][/ROW]
[ROW][C]19[/C][C]98.7[/C][C]89.1308042181457[/C][C]9.56919578185428[/C][/ROW]
[ROW][C]20[/C][C]93.4[/C][C]96.1180329504846[/C][C]-2.71803295048463[/C][/ROW]
[ROW][C]21[/C][C]68[/C][C]94.1333815377627[/C][C]-26.1333815377627[/C][/ROW]
[ROW][C]22[/C][C]87.9[/C][C]75.0513271502782[/C][C]12.8486728497218[/C][/ROW]
[ROW][C]23[/C][C]75.8[/C][C]84.433162171173[/C][C]-8.63316217117297[/C][/ROW]
[ROW][C]24[/C][C]66.3[/C][C]78.1294058108164[/C][C]-11.8294058108164[/C][/ROW]
[ROW][C]25[/C][C]68.4[/C][C]69.4918184887377[/C][C]-1.09181848873773[/C][/ROW]
[ROW][C]26[/C][C]71.3[/C][C]68.6945952226537[/C][C]2.60540477734627[/C][/ROW]
[ROW][C]27[/C][C]77.4[/C][C]70.5970078741085[/C][C]6.80299212589154[/C][/ROW]
[ROW][C]28[/C][C]87.1[/C][C]75.5644119414431[/C][C]11.5355880585569[/C][/ROW]
[ROW][C]29[/C][C]88.5[/C][C]83.9874596211673[/C][C]4.5125403788327[/C][/ROW]
[ROW][C]30[/C][C]85.9[/C][C]87.2824232220384[/C][C]-1.38242322203843[/C][/ROW]
[ROW][C]31[/C][C]92.7[/C][C]86.2730063935526[/C][C]6.42699360644741[/C][/ROW]
[ROW][C]32[/C][C]88.5[/C][C]90.965864123006[/C][C]-2.46586412300599[/C][/ROW]
[ROW][C]33[/C][C]80.2[/C][C]89.1653411696578[/C][C]-8.96534116965782[/C][/ROW]
[ROW][C]34[/C][C]81.8[/C][C]82.6190345788112[/C][C]-0.819034578811241[/C][/ROW]
[ROW][C]35[/C][C]70.4[/C][C]82.0209924786903[/C][C]-11.6209924786903[/C][/ROW]
[ROW][C]36[/C][C]82.2[/C][C]73.5355842587673[/C][C]8.66441574123274[/C][/ROW]
[ROW][C]37[/C][C]72.8[/C][C]79.8621613292115[/C][C]-7.06216132921149[/C][/ROW]
[ROW][C]38[/C][C]69[/C][C]74.7055172729314[/C][C]-5.70551727293142[/C][/ROW]
[ROW][C]39[/C][C]83[/C][C]70.5394666317816[/C][C]12.4605333682184[/C][/ROW]
[ROW][C]40[/C][C]92.4[/C][C]79.6378902355478[/C][C]12.7621097644522[/C][/ROW]
[ROW][C]41[/C][C]92.3[/C][C]88.956518682939[/C][C]3.34348131706098[/C][/ROW]
[ROW][C]42[/C][C]100.5[/C][C]91.3978595497344[/C][C]9.10214045026561[/C][/ROW]
[ROW][C]43[/C][C]106.9[/C][C]98.0440541443188[/C][C]8.85594585568118[/C][/ROW]
[ROW][C]44[/C][C]99.5[/C][C]104.510482540756[/C][C]-5.0104825407564[/C][/ROW]
[ROW][C]45[/C][C]85.9[/C][C]100.851931877801[/C][C]-14.9519318778007[/C][/ROW]
[ROW][C]46[/C][C]92.6[/C][C]89.9343406400239[/C][C]2.66565935997609[/C][/ROW]
[ROW][C]47[/C][C]77.4[/C][C]91.88074994079[/C][C]-14.48074994079[/C][/ROW]
[ROW][C]48[/C][C]84.1[/C][C]81.3072060026497[/C][C]2.79279399735026[/C][/ROW]
[ROW][C]49[/C][C]75.3[/C][C]83.3464463846673[/C][C]-8.04644638466731[/C][/ROW]
[ROW][C]50[/C][C]73.8[/C][C]77.4710977499592[/C][C]-3.67109774995922[/C][/ROW]
[ROW][C]51[/C][C]100.1[/C][C]74.7905381436462[/C][C]25.3094618563538[/C][/ROW]
[ROW][C]52[/C][C]90.7[/C][C]93.2709834301865[/C][C]-2.57098343018654[/C][/ROW]
[ROW][C]53[/C][C]96.5[/C][C]91.393704534103[/C][C]5.10629546589699[/C][/ROW]
[ROW][C]54[/C][C]111.8[/C][C]95.1222158122173[/C][C]16.6777841877827[/C][/ROW]
[ROW][C]55[/C][C]97.4[/C][C]107.29998869148[/C][C]-9.89998869148027[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]100.071221822052[/C][C]0.728778177948001[/C][/ROW]
[ROW][C]57[/C][C]93.7[/C][C]100.603360566053[/C][C]-6.90336056605344[/C][/ROW]
[ROW][C]58[/C][C]82[/C][C]95.5626695407647[/C][C]-13.5626695407647[/C][/ROW]
[ROW][C]59[/C][C]86[/C][C]85.6594889117144[/C][C]0.340511088285581[/C][/ROW]
[ROW][C]60[/C][C]84.3[/C][C]85.9081230617504[/C][C]-1.60812306175038[/C][/ROW]
[ROW][C]61[/C][C]73.1[/C][C]84.7339048810015[/C][C]-11.6339048810015[/C][/ROW]
[ROW][C]62[/C][C]75.4[/C][C]76.2390682921236[/C][C]-0.839068292123613[/C][/ROW]
[ROW][C]63[/C][C]97.9[/C][C]75.6263979891251[/C][C]22.2736020108749[/C][/ROW]
[ROW][C]64[/C][C]97.5[/C][C]91.8901212414159[/C][C]5.60987875858406[/C][/ROW]
[ROW][C]65[/C][C]106[/C][C]95.9863386185591[/C][C]10.0136613814409[/C][/ROW]
[ROW][C]66[/C][C]112.8[/C][C]103.298106933823[/C][C]9.50189306617729[/C][/ROW]
[ROW][C]67[/C][C]99.5[/C][C]110.236192615955[/C][C]-10.7361926159552[/C][/ROW]
[ROW][C]68[/C][C]100.8[/C][C]102.396846945509[/C][C]-1.59684694550945[/C][/ROW]
[ROW][C]69[/C][C]102.9[/C][C]101.230862351489[/C][C]1.66913764851139[/C][/ROW]
[ROW][C]70[/C][C]88.8[/C][C]102.449632120838[/C][C]-13.6496321208378[/C][/ROW]
[ROW][C]71[/C][C]91.3[/C][C]92.4829532154457[/C][C]-1.18295321544571[/C][/ROW]
[ROW][C]72[/C][C]88.3[/C][C]91.6191852578867[/C][C]-3.31918525788666[/C][/ROW]
[ROW][C]73[/C][C]77.4[/C][C]89.195584870711[/C][C]-11.795584870711[/C][/ROW]
[ROW][C]74[/C][C]80.5[/C][C]80.5826928991975[/C][C]-0.0826928991974683[/C][/ROW]
[ROW][C]75[/C][C]96.7[/C][C]80.5223122554731[/C][C]16.1776877445269[/C][/ROW]
[ROW][C]76[/C][C]93.8[/C][C]92.3349250610041[/C][C]1.46507493899587[/C][/ROW]
[ROW][C]77[/C][C]105[/C][C]93.4046924627949[/C][C]11.5953075372051[/C][/ROW]
[ROW][C]78[/C][C]117.1[/C][C]101.871346069977[/C][C]15.2286539300233[/C][/ROW]
[ROW][C]79[/C][C]111.1[/C][C]112.990994023724[/C][C]-1.89099402372415[/C][/ROW]
[ROW][C]80[/C][C]105.8[/C][C]111.610229320352[/C][C]-5.81022932035152[/C][/ROW]
[ROW][C]81[/C][C]95.7[/C][C]107.367720109115[/C][C]-11.6677201091155[/C][/ROW]
[ROW][C]82[/C][C]97.1[/C][C]98.8481923404504[/C][C]-1.74819234045043[/C][/ROW]
[ROW][C]83[/C][C]91[/C][C]97.5716984710269[/C][C]-6.57169847102695[/C][/ROW]
[ROW][C]84[/C][C]90.9[/C][C]92.7731802440199[/C][C]-1.87318024401985[/C][/ROW]
[ROW][C]85[/C][C]83.5[/C][C]91.4054227939441[/C][C]-7.90542279394406[/C][/ROW]
[ROW][C]86[/C][C]82.3[/C][C]85.6330466668011[/C][C]-3.3330466668011[/C][/ROW]
[ROW][C]87[/C][C]101.7[/C][C]83.199324965688[/C][C]18.500675034312[/C][/ROW]
[ROW][C]88[/C][C]108.3[/C][C]96.7081350176818[/C][C]11.5918649823182[/C][/ROW]
[ROW][C]89[/C][C]114[/C][C]105.172274942526[/C][C]8.82772505747366[/C][/ROW]
[ROW][C]90[/C][C]118.2[/C][C]111.618097096122[/C][C]6.58190290387824[/C][/ROW]
[ROW][C]91[/C][C]103.4[/C][C]116.424066388824[/C][C]-13.0240663888235[/C][/ROW]
[ROW][C]92[/C][C]106.8[/C][C]106.914162635319[/C][C]-0.114162635318849[/C][/ROW]
[ROW][C]93[/C][C]95.4[/C][C]106.830803441522[/C][C]-11.430803441522[/C][/ROW]
[ROW][C]94[/C][C]101.8[/C][C]98.484267320715[/C][C]3.31573267928501[/C][/ROW]
[ROW][C]95[/C][C]95.6[/C][C]100.905346706444[/C][C]-5.30534670644431[/C][/ROW]
[ROW][C]96[/C][C]94.8[/C][C]97.0314923317035[/C][C]-2.23149233170352[/C][/ROW]
[ROW][C]97[/C][C]94[/C][C]95.4021028102101[/C][C]-1.40210281021007[/C][/ROW]
[ROW][C]98[/C][C]82.4[/C][C]94.3783163536961[/C][C]-11.9783163536961[/C][/ROW]
[ROW][C]99[/C][C]95.8[/C][C]85.6319976348024[/C][C]10.1680023651976[/C][/ROW]
[ROW][C]100[/C][C]106.7[/C][C]93.0564625424304[/C][C]13.6435374575696[/C][/ROW]
[ROW][C]101[/C][C]114.1[/C][C]103.018691250829[/C][C]11.0813087491713[/C][/ROW]
[ROW][C]102[/C][C]103.9[/C][C]111.110033579821[/C][C]-7.21003357982057[/C][/ROW]
[ROW][C]103[/C][C]117.4[/C][C]105.845416266255[/C][C]11.5545837337452[/C][/ROW]
[ROW][C]104[/C][C]105.9[/C][C]114.2823341949[/C][C]-8.38233419489977[/C][/ROW]
[ROW][C]105[/C][C]101.7[/C][C]108.161727232115[/C][C]-6.46172723211474[/C][/ROW]
[ROW][C]106[/C][C]98.7[/C][C]103.443507727986[/C][C]-4.74350772798626[/C][/ROW]
[ROW][C]107[/C][C]91.3[/C][C]99.9798965484651[/C][C]-8.67989654846509[/C][/ROW]
[ROW][C]108[/C][C]102.3[/C][C]93.6420157129439[/C][C]8.65798428705611[/C][/ROW]
[ROW][C]109[/C][C]80.5[/C][C]99.9638966686426[/C][C]-19.4638966686426[/C][/ROW]
[ROW][C]110[/C][C]86.7[/C][C]85.7517621124342[/C][C]0.94823788756581[/C][/ROW]
[ROW][C]111[/C][C]102.6[/C][C]86.4441457948389[/C][C]16.1558542051611[/C][/ROW]
[ROW][C]112[/C][C]107.3[/C][C]98.2408162017543[/C][C]9.05918379824571[/C][/ROW]
[ROW][C]113[/C][C]108[/C][C]104.855644737991[/C][C]3.14435526200943[/C][/ROW]
[ROW][C]114[/C][C]124.3[/C][C]107.151587880157[/C][C]17.1484121198433[/C][/ROW]
[ROW][C]115[/C][C]117.1[/C][C]119.673003536106[/C][C]-2.57300353610637[/C][/ROW]
[ROW][C]116[/C][C]103.9[/C][C]117.794249600485[/C][C]-13.8942496004848[/C][/ROW]
[ROW][C]117[/C][C]104.7[/C][C]107.648956073636[/C][C]-2.94895607363593[/C][/ROW]
[ROW][C]118[/C][C]95.9[/C][C]105.495689375176[/C][C]-9.59568937517555[/C][/ROW]
[ROW][C]119[/C][C]94.2[/C][C]98.4891155692592[/C][C]-4.28911556925917[/C][/ROW]
[ROW][C]120[/C][C]102.7[/C][C]95.3572921407241[/C][C]7.34270785927586[/C][/ROW]
[ROW][C]121[/C][C]70.3[/C][C]100.71878546755[/C][C]-30.4187854675501[/C][/ROW]
[ROW][C]122[/C][C]90.2[/C][C]78.5076178138632[/C][C]11.6923821861368[/C][/ROW]
[ROW][C]123[/C][C]107.3[/C][C]87.0451533208054[/C][C]20.2548466791946[/C][/ROW]
[ROW][C]124[/C][C]104.6[/C][C]101.834823206582[/C][C]2.76517679341829[/C][/ROW]
[ROW][C]125[/C][C]102.7[/C][C]103.853898077806[/C][C]-1.15389807780616[/C][/ROW]
[ROW][C]126[/C][C]124.5[/C][C]103.011345580477[/C][C]21.4886544195235[/C][/ROW]
[ROW][C]127[/C][C]117.8[/C][C]118.701916345484[/C][C]-0.901916345484025[/C][/ROW]
[ROW][C]128[/C][C]104.2[/C][C]118.043355694517[/C][C]-13.8433556945167[/C][/ROW]
[ROW][C]129[/C][C]99.9[/C][C]107.935223844593[/C][C]-8.03522384459322[/C][/ROW]
[ROW][C]130[/C][C]91.5[/C][C]102.068069676405[/C][C]-10.5680696764049[/C][/ROW]
[ROW][C]131[/C][C]95.7[/C][C]94.3514838972364[/C][C]1.3485161027636[/C][/ROW]
[ROW][C]132[/C][C]91.4[/C][C]95.336142448911[/C][C]-3.93614244891103[/C][/ROW]
[ROW][C]133[/C][C]86.2[/C][C]92.4620526883313[/C][C]-6.26205268833131[/C][/ROW]
[ROW][C]134[/C][C]91.5[/C][C]87.8896314039535[/C][C]3.61036859604647[/C][/ROW]
[ROW][C]135[/C][C]115.5[/C][C]90.5258478388253[/C][C]24.9741521611747[/C][/ROW]
[ROW][C]136[/C][C]113.9[/C][C]108.761456924937[/C][C]5.13854307506301[/C][/ROW]
[ROW][C]137[/C][C]131.9[/C][C]112.513514739923[/C][C]19.3864852600766[/C][/ROW]
[ROW][C]138[/C][C]121.2[/C][C]126.66912508757[/C][C]-5.46912508756992[/C][/ROW]
[ROW][C]139[/C][C]105.2[/C][C]122.675683128206[/C][C]-17.4756831282061[/C][/ROW]
[ROW][C]140[/C][C]107.5[/C][C]109.915300954586[/C][C]-2.41530095458623[/C][/ROW]
[ROW][C]141[/C][C]113.8[/C][C]108.15169818045[/C][C]5.64830181954996[/C][/ROW]
[ROW][C]142[/C][C]100.5[/C][C]112.275971281573[/C][C]-11.7759712815731[/C][/ROW]
[ROW][C]143[/C][C]104.8[/C][C]103.677400746959[/C][C]1.12259925304096[/C][/ROW]
[ROW][C]144[/C][C]103.8[/C][C]104.497099490152[/C][C]-0.697099490151643[/C][/ROW]
[ROW][C]145[/C][C]93.1[/C][C]103.988091868412[/C][C]-10.8880918684116[/C][/ROW]
[ROW][C]146[/C][C]106.2[/C][C]96.0378325072671[/C][C]10.1621674927329[/C][/ROW]
[ROW][C]147[/C][C]117.5[/C][C]103.45803691177[/C][C]14.0419630882302[/C][/ROW]
[ROW][C]148[/C][C]109.9[/C][C]113.711187770547[/C][C]-3.81118777054679[/C][/ROW]
[ROW][C]149[/C][C]123.6[/C][C]110.928337330262[/C][C]12.6716626697378[/C][/ROW]
[ROW][C]150[/C][C]131.7[/C][C]120.18092318083[/C][C]11.51907681917[/C][/ROW]
[ROW][C]151[/C][C]111[/C][C]128.591914695242[/C][C]-17.591914695242[/C][/ROW]
[ROW][C]152[/C][C]122[/C][C]115.746662636701[/C][C]6.25333736329945[/C][/ROW]
[ROW][C]153[/C][C]110.9[/C][C]120.312720171097[/C][C]-9.4127201710974[/C][/ROW]
[ROW][C]154[/C][C]108[/C][C]113.439746691584[/C][C]-5.43974669158382[/C][/ROW]
[ROW][C]155[/C][C]103.6[/C][C]109.467756229004[/C][C]-5.86775622900446[/C][/ROW]
[ROW][C]156[/C][C]107.3[/C][C]105.183242059548[/C][C]2.1167579404523[/C][/ROW]
[ROW][C]157[/C][C]94.4[/C][C]106.728854902895[/C][C]-12.3288549028946[/C][/ROW]
[ROW][C]158[/C][C]85.2[/C][C]97.7265801895174[/C][C]-12.5265801895174[/C][/ROW]
[ROW][C]159[/C][C]113.2[/C][C]88.5799305636297[/C][C]24.6200694363703[/C][/ROW]
[ROW][C]160[/C][C]111.7[/C][C]106.556995771575[/C][C]5.14300422842541[/C][/ROW]
[ROW][C]161[/C][C]124.3[/C][C]110.312311028426[/C][C]13.9876889715741[/C][/ROW]
[ROW][C]162[/C][C]124[/C][C]120.525832050384[/C][C]3.47416794961589[/C][/ROW]
[ROW][C]163[/C][C]133.4[/C][C]123.062597591806[/C][C]10.3374024081941[/C][/ROW]
[ROW][C]164[/C][C]112.6[/C][C]130.610754905219[/C][C]-18.0107549052188[/C][/ROW]
[ROW][C]165[/C][C]115.8[/C][C]117.459674392947[/C][C]-1.65967439294685[/C][/ROW]
[ROW][C]166[/C][C]112.3[/C][C]116.247814496976[/C][C]-3.94781449697572[/C][/ROW]
[ROW][C]167[/C][C]103.6[/C][C]113.365202048444[/C][C]-9.76520204844374[/C][/ROW]
[ROW][C]168[/C][C]111.4[/C][C]106.234853596449[/C][C]5.16514640355118[/C][/ROW]
[ROW][C]169[/C][C]95.1[/C][C]110.006336611361[/C][C]-14.9063366113607[/C][/ROW]
[ROW][C]170[/C][C]93.4[/C][C]99.1220380935774[/C][C]-5.72203809357738[/C][/ROW]
[ROW][C]171[/C][C]117.3[/C][C]94.9439242910783[/C][C]22.3560757089217[/C][/ROW]
[ROW][C]172[/C][C]121.5[/C][C]111.267868130949[/C][C]10.2321318690505[/C][/ROW]
[ROW][C]173[/C][C]123.1[/C][C]118.739159075177[/C][C]4.36084092482275[/C][/ROW]
[ROW][C]174[/C][C]139.3[/C][C]121.923354874041[/C][C]17.3766451259595[/C][/ROW]
[ROW][C]175[/C][C]125.8[/C][C]134.61142154794[/C][C]-8.81142154793959[/C][/ROW]
[ROW][C]176[/C][C]108.6[/C][C]128.177503879617[/C][C]-19.5775038796166[/C][/ROW]
[ROW][C]177[/C][C]121[/C][C]113.882415688974[/C][C]7.11758431102614[/C][/ROW]
[ROW][C]178[/C][C]111.6[/C][C]119.079528459637[/C][C]-7.47952845963657[/C][/ROW]
[ROW][C]179[/C][C]99.7[/C][C]113.61813156183[/C][C]-13.9181315618304[/C][/ROW]
[ROW][C]180[/C][C]116.7[/C][C]103.455399921027[/C][C]13.2446000789732[/C][/ROW]
[ROW][C]181[/C][C]90.3[/C][C]113.126332811294[/C][C]-22.8263328112939[/C][/ROW]
[ROW][C]182[/C][C]90.4[/C][C]96.4590169669004[/C][C]-6.05901696690043[/C][/ROW]
[ROW][C]183[/C][C]117.3[/C][C]92.0348481646344[/C][C]25.2651518353656[/C][/ROW]
[ROW][C]184[/C][C]121.6[/C][C]110.482939190813[/C][C]11.1170608091871[/C][/ROW]
[ROW][C]185[/C][C]114.6[/C][C]118.600386934165[/C][C]-4.00038693416538[/C][/ROW]
[ROW][C]186[/C][C]133.3[/C][C]115.679387179946[/C][C]17.620612820054[/C][/ROW]
[ROW][C]187[/C][C]127.4[/C][C]128.545594015338[/C][C]-1.14559401533828[/C][/ROW]
[ROW][C]188[/C][C]115[/C][C]127.709104972576[/C][C]-12.7091049725761[/C][/ROW]
[ROW][C]189[/C][C]112.6[/C][C]118.429179527317[/C][C]-5.82917952731707[/C][/ROW]
[ROW][C]190[/C][C]108.3[/C][C]114.172833267116[/C][C]-5.87283326711555[/C][/ROW]
[ROW][C]191[/C][C]107.6[/C][C]109.884611949496[/C][C]-2.28461194949568[/C][/ROW]
[ROW][C]192[/C][C]109[/C][C]108.216435582362[/C][C]0.783564417637621[/C][/ROW]
[ROW][C]193[/C][C]89[/C][C]108.788578104824[/C][C]-19.7885781048237[/C][/ROW]
[ROW][C]194[/C][C]102.5[/C][C]94.3393678829628[/C][C]8.16063211703717[/C][/ROW]
[ROW][C]195[/C][C]124.5[/C][C]100.298092576456[/C][C]24.2019074235436[/C][/ROW]
[ROW][C]196[/C][C]124.2[/C][C]117.969824536195[/C][C]6.230175463805[/C][/ROW]
[ROW][C]197[/C][C]130.8[/C][C]122.5189697309[/C][C]8.28103026910028[/C][/ROW]
[ROW][C]198[/C][C]138.7[/C][C]128.565606663477[/C][C]10.1343933365227[/C][/ROW]
[ROW][C]199[/C][C]127.6[/C][C]135.965530953881[/C][C]-8.36553095388135[/C][/ROW]
[ROW][C]200[/C][C]130.9[/C][C]129.857193369957[/C][C]1.04280663004295[/C][/ROW]
[ROW][C]201[/C][C]136.9[/C][C]130.618629191087[/C][C]6.28137080891298[/C][/ROW]
[ROW][C]202[/C][C]125.2[/C][C]135.205156167339[/C][C]-10.0051561673391[/C][/ROW]
[ROW][C]203[/C][C]131.3[/C][C]127.899598183403[/C][C]3.40040181659666[/C][/ROW]
[ROW][C]204[/C][C]124.1[/C][C]130.382501221031[/C][C]-6.2825012210312[/C][/ROW]
[ROW][C]205[/C][C]103.2[/C][C]125.795148841244[/C][C]-22.5951488412435[/C][/ROW]
[ROW][C]206[/C][C]118.1[/C][C]109.296638747596[/C][C]8.80336125240386[/C][/ROW]
[ROW][C]207[/C][C]136.5[/C][C]115.724670954921[/C][C]20.7753290450791[/C][/ROW]
[ROW][C]208[/C][C]117.8[/C][C]130.894386293261[/C][C]-13.0943862932607[/C][/ROW]
[ROW][C]209[/C][C]145.1[/C][C]121.333136400755[/C][C]23.7668635992445[/C][/ROW]
[ROW][C]210[/C][C]158.8[/C][C]138.687208362908[/C][C]20.1127916370925[/C][/ROW]
[ROW][C]211[/C][C]136.9[/C][C]153.373152596667[/C][C]-16.473152596667[/C][/ROW]
[ROW][C]212[/C][C]132.7[/C][C]141.344797470534[/C][C]-8.64479747053426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310143&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310143&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
26355.57.5
377.260.976344792935916.2236552070641
471.172.8225220883483-1.72252208834827
590.171.564772105782518.5352278942175
691.585.09881194103296.40118805896709
776.189.7728269937433-13.6728269937433
887.879.78921167215678.0107883278433
98185.6385235316895-4.63852353168954
1077.282.2515696397324-5.05156963973239
1173.878.5630180273722-4.76301802737218
1268.975.0851608309909-6.18516083099092
1368.470.5688843896218-2.16888438962184
1465.268.9852098918104-3.78520989181044
1578.766.221327960985712.4786720390143
167775.33299604680051.66700395319954
1797.676.550207835988221.0497921640118
1888.191.9203304639574-3.82033046395738
1998.789.13080421814579.56919578185428
2093.496.1180329504846-2.71803295048463
216894.1333815377627-26.1333815377627
2287.975.051327150278212.8486728497218
2375.884.433162171173-8.63316217117297
2466.378.1294058108164-11.8294058108164
2568.469.4918184887377-1.09181848873773
2671.368.69459522265372.60540477734627
2777.470.59700787410856.80299212589154
2887.175.564411941443111.5355880585569
2988.583.98745962116734.5125403788327
3085.987.2824232220384-1.38242322203843
3192.786.27300639355266.42699360644741
3288.590.965864123006-2.46586412300599
3380.289.1653411696578-8.96534116965782
3481.882.6190345788112-0.819034578811241
3570.482.0209924786903-11.6209924786903
3682.273.53558425876738.66441574123274
3772.879.8621613292115-7.06216132921149
386974.7055172729314-5.70551727293142
398370.539466631781612.4605333682184
4092.479.637890235547812.7621097644522
4192.388.9565186829393.34348131706098
42100.591.39785954973449.10214045026561
43106.998.04405414431888.85594585568118
4499.5104.510482540756-5.0104825407564
4585.9100.851931877801-14.9519318778007
4692.689.93434064002392.66565935997609
4777.491.88074994079-14.48074994079
4884.181.30720600264972.79279399735026
4975.383.3464463846673-8.04644638466731
5073.877.4710977499592-3.67109774995922
51100.174.790538143646225.3094618563538
5290.793.2709834301865-2.57098343018654
5396.591.3937045341035.10629546589699
54111.895.122215812217316.6777841877827
5597.4107.29998869148-9.89998869148027
56100.8100.0712218220520.728778177948001
5793.7100.603360566053-6.90336056605344
588295.5626695407647-13.5626695407647
598685.65948891171440.340511088285581
6084.385.9081230617504-1.60812306175038
6173.184.7339048810015-11.6339048810015
6275.476.2390682921236-0.839068292123613
6397.975.626397989125122.2736020108749
6497.591.89012124141595.60987875858406
6510695.986338618559110.0136613814409
66112.8103.2981069338239.50189306617729
6799.5110.236192615955-10.7361926159552
68100.8102.396846945509-1.59684694550945
69102.9101.2308623514891.66913764851139
7088.8102.449632120838-13.6496321208378
7191.392.4829532154457-1.18295321544571
7288.391.6191852578867-3.31918525788666
7377.489.195584870711-11.795584870711
7480.580.5826928991975-0.0826928991974683
7596.780.522312255473116.1776877445269
7693.892.33492506100411.46507493899587
7710593.404692462794911.5953075372051
78117.1101.87134606997715.2286539300233
79111.1112.990994023724-1.89099402372415
80105.8111.610229320352-5.81022932035152
8195.7107.367720109115-11.6677201091155
8297.198.8481923404504-1.74819234045043
839197.5716984710269-6.57169847102695
8490.992.7731802440199-1.87318024401985
8583.591.4054227939441-7.90542279394406
8682.385.6330466668011-3.3330466668011
87101.783.19932496568818.500675034312
88108.396.708135017681811.5918649823182
89114105.1722749425268.82772505747366
90118.2111.6180970961226.58190290387824
91103.4116.424066388824-13.0240663888235
92106.8106.914162635319-0.114162635318849
9395.4106.830803441522-11.430803441522
94101.898.4842673207153.31573267928501
9595.6100.905346706444-5.30534670644431
9694.897.0314923317035-2.23149233170352
979495.4021028102101-1.40210281021007
9882.494.3783163536961-11.9783163536961
9995.885.631997634802410.1680023651976
100106.793.056462542430413.6435374575696
101114.1103.01869125082911.0813087491713
102103.9111.110033579821-7.21003357982057
103117.4105.84541626625511.5545837337452
104105.9114.2823341949-8.38233419489977
105101.7108.161727232115-6.46172723211474
10698.7103.443507727986-4.74350772798626
10791.399.9798965484651-8.67989654846509
108102.393.64201571294398.65798428705611
10980.599.9638966686426-19.4638966686426
11086.785.75176211243420.94823788756581
111102.686.444145794838916.1558542051611
112107.398.24081620175439.05918379824571
113108104.8556447379913.14435526200943
114124.3107.15158788015717.1484121198433
115117.1119.673003536106-2.57300353610637
116103.9117.794249600485-13.8942496004848
117104.7107.648956073636-2.94895607363593
11895.9105.495689375176-9.59568937517555
11994.298.4891155692592-4.28911556925917
120102.795.35729214072417.34270785927586
12170.3100.71878546755-30.4187854675501
12290.278.507617813863211.6923821861368
123107.387.045153320805420.2548466791946
124104.6101.8348232065822.76517679341829
125102.7103.853898077806-1.15389807780616
126124.5103.01134558047721.4886544195235
127117.8118.701916345484-0.901916345484025
128104.2118.043355694517-13.8433556945167
12999.9107.935223844593-8.03522384459322
13091.5102.068069676405-10.5680696764049
13195.794.35148389723641.3485161027636
13291.495.336142448911-3.93614244891103
13386.292.4620526883313-6.26205268833131
13491.587.88963140395353.61036859604647
135115.590.525847838825324.9741521611747
136113.9108.7614569249375.13854307506301
137131.9112.51351473992319.3864852600766
138121.2126.66912508757-5.46912508756992
139105.2122.675683128206-17.4756831282061
140107.5109.915300954586-2.41530095458623
141113.8108.151698180455.64830181954996
142100.5112.275971281573-11.7759712815731
143104.8103.6774007469591.12259925304096
144103.8104.497099490152-0.697099490151643
14593.1103.988091868412-10.8880918684116
146106.296.037832507267110.1621674927329
147117.5103.4580369117714.0419630882302
148109.9113.711187770547-3.81118777054679
149123.6110.92833733026212.6716626697378
150131.7120.1809231808311.51907681917
151111128.591914695242-17.591914695242
152122115.7466626367016.25333736329945
153110.9120.312720171097-9.4127201710974
154108113.439746691584-5.43974669158382
155103.6109.467756229004-5.86775622900446
156107.3105.1832420595482.1167579404523
15794.4106.728854902895-12.3288549028946
15885.297.7265801895174-12.5265801895174
159113.288.579930563629724.6200694363703
160111.7106.5569957715755.14300422842541
161124.3110.31231102842613.9876889715741
162124120.5258320503843.47416794961589
163133.4123.06259759180610.3374024081941
164112.6130.610754905219-18.0107549052188
165115.8117.459674392947-1.65967439294685
166112.3116.247814496976-3.94781449697572
167103.6113.365202048444-9.76520204844374
168111.4106.2348535964495.16514640355118
16995.1110.006336611361-14.9063366113607
17093.499.1220380935774-5.72203809357738
171117.394.943924291078322.3560757089217
172121.5111.26786813094910.2321318690505
173123.1118.7391590751774.36084092482275
174139.3121.92335487404117.3766451259595
175125.8134.61142154794-8.81142154793959
176108.6128.177503879617-19.5775038796166
177121113.8824156889747.11758431102614
178111.6119.079528459637-7.47952845963657
17999.7113.61813156183-13.9181315618304
180116.7103.45539992102713.2446000789732
18190.3113.126332811294-22.8263328112939
18290.496.4590169669004-6.05901696690043
183117.392.034848164634425.2651518353656
184121.6110.48293919081311.1170608091871
185114.6118.600386934165-4.00038693416538
186133.3115.67938717994617.620612820054
187127.4128.545594015338-1.14559401533828
188115127.709104972576-12.7091049725761
189112.6118.429179527317-5.82917952731707
190108.3114.172833267116-5.87283326711555
191107.6109.884611949496-2.28461194949568
192109108.2164355823620.783564417637621
19389108.788578104824-19.7885781048237
194102.594.33936788296288.16063211703717
195124.5100.29809257645624.2019074235436
196124.2117.9698245361956.230175463805
197130.8122.51896973098.28103026910028
198138.7128.56560666347710.1343933365227
199127.6135.965530953881-8.36553095388135
200130.9129.8571933699571.04280663004295
201136.9130.6186291910876.28137080891298
202125.2135.205156167339-10.0051561673391
203131.3127.8995981834033.40040181659666
204124.1130.382501221031-6.2825012210312
205103.2125.795148841244-22.5951488412435
206118.1109.2966387475968.80336125240386
207136.5115.72467095492120.7753290450791
208117.8130.894386293261-13.0943862932607
209145.1121.33313640075523.7668635992445
210158.8138.68720836290820.1127916370925
211136.9153.373152596667-16.473152596667
212132.7141.344797470534-8.64479747053426







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
213135.032545255368113.111250769821156.953839740915
214135.032545255368107.889398557302162.175691953434
215135.032545255368103.521314346001166.543776164735
216135.03254525536899.6890177832254170.376072727511
217135.03254525536896.2334190419495173.831671468787
218135.03254525536893.0613711512824177.003719359454
219135.03254525536890.1127643517823179.952326158954
220135.03254525536887.3461323353671182.718958175369
221135.03254525536884.7314395227153185.333650988021
222135.03254525536882.2461028797144187.818987631022
223135.03254525536879.872634455686190.19245605505
224135.03254525536877.5971639979971192.467926512739

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 135.032545255368 & 113.111250769821 & 156.953839740915 \tabularnewline
214 & 135.032545255368 & 107.889398557302 & 162.175691953434 \tabularnewline
215 & 135.032545255368 & 103.521314346001 & 166.543776164735 \tabularnewline
216 & 135.032545255368 & 99.6890177832254 & 170.376072727511 \tabularnewline
217 & 135.032545255368 & 96.2334190419495 & 173.831671468787 \tabularnewline
218 & 135.032545255368 & 93.0613711512824 & 177.003719359454 \tabularnewline
219 & 135.032545255368 & 90.1127643517823 & 179.952326158954 \tabularnewline
220 & 135.032545255368 & 87.3461323353671 & 182.718958175369 \tabularnewline
221 & 135.032545255368 & 84.7314395227153 & 185.333650988021 \tabularnewline
222 & 135.032545255368 & 82.2461028797144 & 187.818987631022 \tabularnewline
223 & 135.032545255368 & 79.872634455686 & 190.19245605505 \tabularnewline
224 & 135.032545255368 & 77.5971639979971 & 192.467926512739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310143&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]135.032545255368[/C][C]113.111250769821[/C][C]156.953839740915[/C][/ROW]
[ROW][C]214[/C][C]135.032545255368[/C][C]107.889398557302[/C][C]162.175691953434[/C][/ROW]
[ROW][C]215[/C][C]135.032545255368[/C][C]103.521314346001[/C][C]166.543776164735[/C][/ROW]
[ROW][C]216[/C][C]135.032545255368[/C][C]99.6890177832254[/C][C]170.376072727511[/C][/ROW]
[ROW][C]217[/C][C]135.032545255368[/C][C]96.2334190419495[/C][C]173.831671468787[/C][/ROW]
[ROW][C]218[/C][C]135.032545255368[/C][C]93.0613711512824[/C][C]177.003719359454[/C][/ROW]
[ROW][C]219[/C][C]135.032545255368[/C][C]90.1127643517823[/C][C]179.952326158954[/C][/ROW]
[ROW][C]220[/C][C]135.032545255368[/C][C]87.3461323353671[/C][C]182.718958175369[/C][/ROW]
[ROW][C]221[/C][C]135.032545255368[/C][C]84.7314395227153[/C][C]185.333650988021[/C][/ROW]
[ROW][C]222[/C][C]135.032545255368[/C][C]82.2461028797144[/C][C]187.818987631022[/C][/ROW]
[ROW][C]223[/C][C]135.032545255368[/C][C]79.872634455686[/C][C]190.19245605505[/C][/ROW]
[ROW][C]224[/C][C]135.032545255368[/C][C]77.5971639979971[/C][C]192.467926512739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310143&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310143&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
213135.032545255368113.111250769821156.953839740915
214135.032545255368107.889398557302162.175691953434
215135.032545255368103.521314346001166.543776164735
216135.03254525536899.6890177832254170.376072727511
217135.03254525536896.2334190419495173.831671468787
218135.03254525536893.0613711512824177.003719359454
219135.03254525536890.1127643517823179.952326158954
220135.03254525536887.3461323353671182.718958175369
221135.03254525536884.7314395227153185.333650988021
222135.03254525536882.2461028797144187.818987631022
223135.03254525536879.872634455686190.19245605505
224135.03254525536877.5971639979971192.467926512739



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; 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')