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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 computationTue, 19 Dec 2017 19:30:51 +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/19/t1513708277f8keim4ybvj2ya3.htm/, Retrieved Wed, 15 May 2024 12:55:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310394, Retrieved Wed, 15 May 2024 12:55:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Non-durable consu...] [2017-12-19 18:30:51] [a98cfedcb2213d624216c666f97af8d4] [Current]
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Dataseries X:
50
52.4
57.5
52.5
57.5
57.6
48.3
52
62.1
59.1
62.6
57.9
59.3
61.5
66
61.1
63.8
69.6
57
59.9
63.8
69.8
64.6
60.8
64.7
63.6
68.8
66.4
64.4
65.3
63
61.1
67.7
72.3
65.4
63.2
69.4
62.3
71
68.6
62
68.2
66.8
65.5
76.9
78.1
67.6
80.1
64.7
70.4
84.6
75.1
69.6
81.8
74.2
72.9
84.9
80.5
79.6
90.8
76.5
70.9
82.3
77.8
75.6
81.3
71
75.1
89.2
84.1
82.7
82.4
78.2
78.5
91.5
76.6
80.6
85.9
74.5
79.4
89.7
92.7
89.6
87
80.9
76.2
89.7
79.1
82.4
90.3
85.8
83.5
85.1
90.6
87.7
86
89.7
86.2
91.1
91.3
85.5
92
91.5
80
100.9
97.3
89.1
104
80.2
83.3
97.5
86.8
84.3
93.4
90.2
82.5
93.7
93.9
91.1
96.9
88.2
100.9
109.5
91
89.5
109.6
97.9
94.9
103.5
100
107.1
108
95
102.2
131.4
104.5
105.6
106.1
98
113
113.2
105.4
100.1
100.7
96.1
98.2
123.5
93.9
94.8
103.5
105.3
105.8
112
114.5
108.3
103.8
103
97.7
118.7
115.1
110
117.3
119.1
105.9
114.1
124.6
117.3
115
103.6
113.4
122
122.5
119.6
132.6
113
107.5
139.3
134.6
125.6
124
111.9
101.5
130.2
121.9
111.3
122
116.4
119.1
133
128.9
126.1
122.3
110.2
113.6
131
123.2
120.7
142.8
131.7
131.6
139
128.5
122.7
148.4
118.6
126.3
141
120.9
127
138.5
131.9
136.3




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=310394&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=310394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310394&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
alpha0.211362431091643
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.211362431091643 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310394&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]0.211362431091643[/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=310394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310394&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
alpha0.211362431091643
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
252.4502.4
357.550.50726983461996.99273016538005
452.551.98527028234250.51472971765746
557.552.09406480682175.40593519317827
657.653.23667641157584.36332358842423
748.354.1589190928646-5.85891909286463
85252.9205637098275-0.920563709827519
962.152.72599112614369.37400887385636
1059.154.70730443079664.39269556920344
1162.655.63575524534896.96424475465111
1257.957.10773494740920.792265052590814
1359.357.27519001499372.02480998500626
1461.557.70315877592333.7968412240767
156658.50566836751317.49433163248688
1661.160.08968852076261.01031147923744
1763.860.3032304111743.49676958882602
1869.661.04231613243568.55768386756442
195762.8510889991977-5.85108899919773
2059.961.6143886037937-1.71438860379373
2163.861.25203126066012.54796873933991
2269.861.79057612775258.00942387224752
2364.663.48346742903421.11653257096584
2460.863.7194604676265-2.91946046762651
2564.763.1023962057131.59760379428698
2663.663.44006962759480.159930372405249
2768.863.47387289991175.32612710008828
2866.464.59961607208951.80038392791054
2964.464.980149595991-0.580149595990946
3065.364.85752776698550.442472233014527
316364.951049773846-1.95104977384597
3261.164.5386711504651-3.43867115046509
3367.763.81186525637813.8881347436219
3472.364.63367086820197.66632913179809
3565.466.2540448310474-0.854044831047432
3663.266.073531839296-2.87353183929601
3769.465.46617516392323.93382483607684
3862.366.2976379447651-3.99763794476506
397165.45268747013535.54731252986468
4068.666.62518093247271.97481906752733
416267.0425834915514-5.04258349155137
4268.265.97677078579452.22322921420552
4366.866.44667791738290.353322082617069
4465.566.5213569317232-1.02135693172323
4576.966.305480447621910.5945195523781
4678.168.54476385646059.55523614353949
4767.670.5643817974137-2.96438179741375
4880.169.937822854028610.1621771459714
4964.772.085725320785-7.38572532078503
5070.470.5246604616088-0.124660461608798
5184.670.498311923382214.1016880766178
5275.173.47887899775211.62112100224785
5369.673.821523073881-4.22152307388099
5481.872.9292516940768.87074830592397
5574.274.8041946216182-0.604194621618191
5672.974.6764905775405-1.77649057754047
5784.974.301007210260110.5989927897399
5880.576.54123609342233.95876390657766
5979.677.37797005683442.22202994316555
6090.877.847623707580312.9523762924197
6176.580.5852694491599-4.08526944915992
6270.979.7217969667211-8.82179696672105
6382.377.8572005132384.44279948676198
6477.878.7962414136127-0.996241413612736
6575.678.5856734064774-2.98567340647737
6681.377.95461421683863.34538578316135
677178.661703088907-7.66170308890705
6875.177.0423068977333-1.94230689773332
6989.276.631776189902312.5682238100977
7084.179.28822652890854.81177347109153
7182.780.30525466762072.39474533237934
7282.480.81141386291771.58858613708229
7378.281.1471812908499-2.94718129084991
7478.580.5242578883481-2.02425788834807
7591.580.096405819910411.4035941800896
7676.682.5066972089966-5.90669720899665
7780.681.2582433271809-0.658243327180898
7885.981.11911541729814.78088458270192
7974.582.1296148054665-7.62961480546653
8079.480.5170008718903-1.11700087189033
8189.780.28090885207619.41909114792389
8292.782.271750855775110.4282491442249
8389.684.47589094692785.12410905307217
848785.55893509356391.44106490643614
8580.985.8635220755491-4.96352207554905
8676.284.814419982884-8.61441998288396
8789.782.99365523285726.70634476714282
8879.184.4111245665792-5.31112456657922
8982.483.2885523663565-0.888552366356492
9090.383.10074577805127.19925422194883
9185.884.62239765244911.17760234755094
9283.584.8712985474866-1.37129854748665
9385.184.58145755273740.518542447262561
9490.684.69105794501515.90894205498492
9587.785.93998630293631.76001369706366
968686.3119870767023-0.311987076702323
9789.786.24604472970143.45395527029865
9886.286.9760811125135-0.776081112513467
9991.186.81204672184834.28795327815168
10091.387.71835895112583.58164104887416
10185.588.4753833105135-2.97538331051351
1029287.84649906057394.15350093942614
10391.588.72439311667242.7756068833276
1048089.3110521352872-9.31105213528723
105100.987.343045519951913.5569544800481
10697.390.20847637705367.0915236229464
10789.191.7073580501434-2.60735805014338
10810491.156260513938712.8437394860613
10980.293.8709445160203-13.6709445160203
11083.390.9814204477953-7.6814204477953
11197.589.35785674771228.14214325228777
11286.891.0787999398122-4.2787999398122
11384.390.1744223823787-5.87442238237871
11493.488.932790186384.46720981362002
11590.289.87699051278320.323009487216851
11682.589.945262583267-7.44526258326697
11793.788.3716137835525.328386216448
11893.989.49783444805574.40216555194434
11991.190.42828686118250.671713138817481
12096.990.57026178319926.32973821680083
12188.291.9081306408759-3.70813064087588
122100.991.12437113381499.77562886618506
123109.593.190571816421516.3094281835785
1249196.6377722070172-5.63777220701719
12589.595.4461589674011-5.94615896740115
126109.694.189364352393915.4106356476061
12797.997.44659376753940.453406232460566
12894.997.5424268111044-2.6424268111044
129103.596.98391705632766.51608294367236
13010098.3611721884971.63882781150298
131107.198.70755881887698.3924411811231
132108100.4814055897137.51859441028731
13395102.070553982663-7.07055398266306
134102.2100.5761045037231.6238954962773
135131.4100.91933500365530.4806649963454
136104.5107.361802458572-2.86180245857216
137105.6106.756924933624-1.15692493362431
138106.1106.512394467063-0.412394467062953
13998106.425229769936-8.42522976993578
140113104.6444527232568.35554727674352
141113.2106.410501508776.78949849122985
142105.4107.84554641577-2.44554641576954
143100.1107.328649779985-7.22864977998506
144100.7105.800784788977-5.10078478897734
14596.1104.722670515504-8.62267051550381
14698.2102.900161912845-4.70016191284468
147123.5101.90672426442121.5932757355785
14893.9106.470731519126-12.5707315191256
14994.8103.813751144643-9.01375114464284
150103.5101.9085827894561.59141721054395
151105.3102.2449485999583.0550514000423
152105.8102.8906716909812.90932830901944
153112103.5055943952198.49440560478135
154114.5105.3009926145249.19900738547628
155108.3107.2453171791481.05468282085202
156103.8107.468237504194-3.66823750419387
157103106.692909907486-3.69290990748591
15897.7105.912367491637-8.21236749163727
159118.7104.17658153358714.5234184664132
160115.1107.2462865684097.8537134315908
161110108.9062665324071.09373346759268
162117.3109.1374406970848.16255930291599
163119.1110.8626990752788.23730092472195
164105.9112.603755024361-6.70375502436072
165114.1111.1868330649692.91316693503097
166124.6111.80256711053312.797432889467
167117.3114.5074636377832.79253636221712
168115115.097700912213-0.0977009122129004
169103.6115.077050609888-11.4770506098877
170113.4112.651233291220.748766708779982
171122112.8094944431089.19050555689175
172122.5114.7520220405747.74797795942585
173119.6116.3896534981233.21034650187713
174132.6117.06820013940615.5317998605938
175113120.35103911717-7.35103911717013
176107.5118.797305618315-11.2973056183153
177139.3116.40947963804322.8905203619571
178134.6121.24767567069913.3523243293011
179125.6124.0698554016641.53014459833592
180124124.39327048389-0.393270483890092
181111.9124.310147878338-12.4101478783385
182101.5121.687108852566-20.1871088525661
183130.2117.42031244877612.7796875512239
184121.9120.1214582781941.77854172180562
185111.3120.497375180313-9.19737518031314
186122118.553395602543.44660439745979
187116.4119.281878286998-2.88187828699844
188119.1118.6727574861480.427242513851752
189133118.76306050254214.2369394974583
190128.9121.7722146460297.12778535397091
191126.1123.2787606867442.8212393132562
192122.3123.875064686685-1.57506468668495
193110.2123.542155185381-13.3421551853806
194113.6120.722124829397-7.12212482939663
195131119.21677521091711.7832247890828
196123.2121.7073062484371.49269375156294
197120.7122.022805628643-1.32280562864271
198142.8121.74321421511121.0567857848889
199131.7126.1938276495815.50617235041882
200131.6127.3576256235754.24237437642471
201139128.25430418537710.7456958146227
202128.5130.525540576527-2.02554057652728
203122.7130.097417395998-7.39741739599769
204148.4128.5338812713819.86611872862
205118.6132.732832422216-14.1328324222164
206126.3129.745682603246-3.44568260324591
207141129.01739475145411.9826052485463
208120.9131.550067327598-10.6500673275979
209127129.299043205947-2.29904320594713
210138.5128.8131118447539.68688815524658
211131.9130.8605560749591.03944392504081
212136.3131.0802554699395.21974453006075

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 52.4 & 50 & 2.4 \tabularnewline
3 & 57.5 & 50.5072698346199 & 6.99273016538005 \tabularnewline
4 & 52.5 & 51.9852702823425 & 0.51472971765746 \tabularnewline
5 & 57.5 & 52.0940648068217 & 5.40593519317827 \tabularnewline
6 & 57.6 & 53.2366764115758 & 4.36332358842423 \tabularnewline
7 & 48.3 & 54.1589190928646 & -5.85891909286463 \tabularnewline
8 & 52 & 52.9205637098275 & -0.920563709827519 \tabularnewline
9 & 62.1 & 52.7259911261436 & 9.37400887385636 \tabularnewline
10 & 59.1 & 54.7073044307966 & 4.39269556920344 \tabularnewline
11 & 62.6 & 55.6357552453489 & 6.96424475465111 \tabularnewline
12 & 57.9 & 57.1077349474092 & 0.792265052590814 \tabularnewline
13 & 59.3 & 57.2751900149937 & 2.02480998500626 \tabularnewline
14 & 61.5 & 57.7031587759233 & 3.7968412240767 \tabularnewline
15 & 66 & 58.5056683675131 & 7.49433163248688 \tabularnewline
16 & 61.1 & 60.0896885207626 & 1.01031147923744 \tabularnewline
17 & 63.8 & 60.303230411174 & 3.49676958882602 \tabularnewline
18 & 69.6 & 61.0423161324356 & 8.55768386756442 \tabularnewline
19 & 57 & 62.8510889991977 & -5.85108899919773 \tabularnewline
20 & 59.9 & 61.6143886037937 & -1.71438860379373 \tabularnewline
21 & 63.8 & 61.2520312606601 & 2.54796873933991 \tabularnewline
22 & 69.8 & 61.7905761277525 & 8.00942387224752 \tabularnewline
23 & 64.6 & 63.4834674290342 & 1.11653257096584 \tabularnewline
24 & 60.8 & 63.7194604676265 & -2.91946046762651 \tabularnewline
25 & 64.7 & 63.102396205713 & 1.59760379428698 \tabularnewline
26 & 63.6 & 63.4400696275948 & 0.159930372405249 \tabularnewline
27 & 68.8 & 63.4738728999117 & 5.32612710008828 \tabularnewline
28 & 66.4 & 64.5996160720895 & 1.80038392791054 \tabularnewline
29 & 64.4 & 64.980149595991 & -0.580149595990946 \tabularnewline
30 & 65.3 & 64.8575277669855 & 0.442472233014527 \tabularnewline
31 & 63 & 64.951049773846 & -1.95104977384597 \tabularnewline
32 & 61.1 & 64.5386711504651 & -3.43867115046509 \tabularnewline
33 & 67.7 & 63.8118652563781 & 3.8881347436219 \tabularnewline
34 & 72.3 & 64.6336708682019 & 7.66632913179809 \tabularnewline
35 & 65.4 & 66.2540448310474 & -0.854044831047432 \tabularnewline
36 & 63.2 & 66.073531839296 & -2.87353183929601 \tabularnewline
37 & 69.4 & 65.4661751639232 & 3.93382483607684 \tabularnewline
38 & 62.3 & 66.2976379447651 & -3.99763794476506 \tabularnewline
39 & 71 & 65.4526874701353 & 5.54731252986468 \tabularnewline
40 & 68.6 & 66.6251809324727 & 1.97481906752733 \tabularnewline
41 & 62 & 67.0425834915514 & -5.04258349155137 \tabularnewline
42 & 68.2 & 65.9767707857945 & 2.22322921420552 \tabularnewline
43 & 66.8 & 66.4466779173829 & 0.353322082617069 \tabularnewline
44 & 65.5 & 66.5213569317232 & -1.02135693172323 \tabularnewline
45 & 76.9 & 66.3054804476219 & 10.5945195523781 \tabularnewline
46 & 78.1 & 68.5447638564605 & 9.55523614353949 \tabularnewline
47 & 67.6 & 70.5643817974137 & -2.96438179741375 \tabularnewline
48 & 80.1 & 69.9378228540286 & 10.1621771459714 \tabularnewline
49 & 64.7 & 72.085725320785 & -7.38572532078503 \tabularnewline
50 & 70.4 & 70.5246604616088 & -0.124660461608798 \tabularnewline
51 & 84.6 & 70.4983119233822 & 14.1016880766178 \tabularnewline
52 & 75.1 & 73.4788789977521 & 1.62112100224785 \tabularnewline
53 & 69.6 & 73.821523073881 & -4.22152307388099 \tabularnewline
54 & 81.8 & 72.929251694076 & 8.87074830592397 \tabularnewline
55 & 74.2 & 74.8041946216182 & -0.604194621618191 \tabularnewline
56 & 72.9 & 74.6764905775405 & -1.77649057754047 \tabularnewline
57 & 84.9 & 74.3010072102601 & 10.5989927897399 \tabularnewline
58 & 80.5 & 76.5412360934223 & 3.95876390657766 \tabularnewline
59 & 79.6 & 77.3779700568344 & 2.22202994316555 \tabularnewline
60 & 90.8 & 77.8476237075803 & 12.9523762924197 \tabularnewline
61 & 76.5 & 80.5852694491599 & -4.08526944915992 \tabularnewline
62 & 70.9 & 79.7217969667211 & -8.82179696672105 \tabularnewline
63 & 82.3 & 77.857200513238 & 4.44279948676198 \tabularnewline
64 & 77.8 & 78.7962414136127 & -0.996241413612736 \tabularnewline
65 & 75.6 & 78.5856734064774 & -2.98567340647737 \tabularnewline
66 & 81.3 & 77.9546142168386 & 3.34538578316135 \tabularnewline
67 & 71 & 78.661703088907 & -7.66170308890705 \tabularnewline
68 & 75.1 & 77.0423068977333 & -1.94230689773332 \tabularnewline
69 & 89.2 & 76.6317761899023 & 12.5682238100977 \tabularnewline
70 & 84.1 & 79.2882265289085 & 4.81177347109153 \tabularnewline
71 & 82.7 & 80.3052546676207 & 2.39474533237934 \tabularnewline
72 & 82.4 & 80.8114138629177 & 1.58858613708229 \tabularnewline
73 & 78.2 & 81.1471812908499 & -2.94718129084991 \tabularnewline
74 & 78.5 & 80.5242578883481 & -2.02425788834807 \tabularnewline
75 & 91.5 & 80.0964058199104 & 11.4035941800896 \tabularnewline
76 & 76.6 & 82.5066972089966 & -5.90669720899665 \tabularnewline
77 & 80.6 & 81.2582433271809 & -0.658243327180898 \tabularnewline
78 & 85.9 & 81.1191154172981 & 4.78088458270192 \tabularnewline
79 & 74.5 & 82.1296148054665 & -7.62961480546653 \tabularnewline
80 & 79.4 & 80.5170008718903 & -1.11700087189033 \tabularnewline
81 & 89.7 & 80.2809088520761 & 9.41909114792389 \tabularnewline
82 & 92.7 & 82.2717508557751 & 10.4282491442249 \tabularnewline
83 & 89.6 & 84.4758909469278 & 5.12410905307217 \tabularnewline
84 & 87 & 85.5589350935639 & 1.44106490643614 \tabularnewline
85 & 80.9 & 85.8635220755491 & -4.96352207554905 \tabularnewline
86 & 76.2 & 84.814419982884 & -8.61441998288396 \tabularnewline
87 & 89.7 & 82.9936552328572 & 6.70634476714282 \tabularnewline
88 & 79.1 & 84.4111245665792 & -5.31112456657922 \tabularnewline
89 & 82.4 & 83.2885523663565 & -0.888552366356492 \tabularnewline
90 & 90.3 & 83.1007457780512 & 7.19925422194883 \tabularnewline
91 & 85.8 & 84.6223976524491 & 1.17760234755094 \tabularnewline
92 & 83.5 & 84.8712985474866 & -1.37129854748665 \tabularnewline
93 & 85.1 & 84.5814575527374 & 0.518542447262561 \tabularnewline
94 & 90.6 & 84.6910579450151 & 5.90894205498492 \tabularnewline
95 & 87.7 & 85.9399863029363 & 1.76001369706366 \tabularnewline
96 & 86 & 86.3119870767023 & -0.311987076702323 \tabularnewline
97 & 89.7 & 86.2460447297014 & 3.45395527029865 \tabularnewline
98 & 86.2 & 86.9760811125135 & -0.776081112513467 \tabularnewline
99 & 91.1 & 86.8120467218483 & 4.28795327815168 \tabularnewline
100 & 91.3 & 87.7183589511258 & 3.58164104887416 \tabularnewline
101 & 85.5 & 88.4753833105135 & -2.97538331051351 \tabularnewline
102 & 92 & 87.8464990605739 & 4.15350093942614 \tabularnewline
103 & 91.5 & 88.7243931166724 & 2.7756068833276 \tabularnewline
104 & 80 & 89.3110521352872 & -9.31105213528723 \tabularnewline
105 & 100.9 & 87.3430455199519 & 13.5569544800481 \tabularnewline
106 & 97.3 & 90.2084763770536 & 7.0915236229464 \tabularnewline
107 & 89.1 & 91.7073580501434 & -2.60735805014338 \tabularnewline
108 & 104 & 91.1562605139387 & 12.8437394860613 \tabularnewline
109 & 80.2 & 93.8709445160203 & -13.6709445160203 \tabularnewline
110 & 83.3 & 90.9814204477953 & -7.6814204477953 \tabularnewline
111 & 97.5 & 89.3578567477122 & 8.14214325228777 \tabularnewline
112 & 86.8 & 91.0787999398122 & -4.2787999398122 \tabularnewline
113 & 84.3 & 90.1744223823787 & -5.87442238237871 \tabularnewline
114 & 93.4 & 88.93279018638 & 4.46720981362002 \tabularnewline
115 & 90.2 & 89.8769905127832 & 0.323009487216851 \tabularnewline
116 & 82.5 & 89.945262583267 & -7.44526258326697 \tabularnewline
117 & 93.7 & 88.371613783552 & 5.328386216448 \tabularnewline
118 & 93.9 & 89.4978344480557 & 4.40216555194434 \tabularnewline
119 & 91.1 & 90.4282868611825 & 0.671713138817481 \tabularnewline
120 & 96.9 & 90.5702617831992 & 6.32973821680083 \tabularnewline
121 & 88.2 & 91.9081306408759 & -3.70813064087588 \tabularnewline
122 & 100.9 & 91.1243711338149 & 9.77562886618506 \tabularnewline
123 & 109.5 & 93.1905718164215 & 16.3094281835785 \tabularnewline
124 & 91 & 96.6377722070172 & -5.63777220701719 \tabularnewline
125 & 89.5 & 95.4461589674011 & -5.94615896740115 \tabularnewline
126 & 109.6 & 94.1893643523939 & 15.4106356476061 \tabularnewline
127 & 97.9 & 97.4465937675394 & 0.453406232460566 \tabularnewline
128 & 94.9 & 97.5424268111044 & -2.6424268111044 \tabularnewline
129 & 103.5 & 96.9839170563276 & 6.51608294367236 \tabularnewline
130 & 100 & 98.361172188497 & 1.63882781150298 \tabularnewline
131 & 107.1 & 98.7075588188769 & 8.3924411811231 \tabularnewline
132 & 108 & 100.481405589713 & 7.51859441028731 \tabularnewline
133 & 95 & 102.070553982663 & -7.07055398266306 \tabularnewline
134 & 102.2 & 100.576104503723 & 1.6238954962773 \tabularnewline
135 & 131.4 & 100.919335003655 & 30.4806649963454 \tabularnewline
136 & 104.5 & 107.361802458572 & -2.86180245857216 \tabularnewline
137 & 105.6 & 106.756924933624 & -1.15692493362431 \tabularnewline
138 & 106.1 & 106.512394467063 & -0.412394467062953 \tabularnewline
139 & 98 & 106.425229769936 & -8.42522976993578 \tabularnewline
140 & 113 & 104.644452723256 & 8.35554727674352 \tabularnewline
141 & 113.2 & 106.41050150877 & 6.78949849122985 \tabularnewline
142 & 105.4 & 107.84554641577 & -2.44554641576954 \tabularnewline
143 & 100.1 & 107.328649779985 & -7.22864977998506 \tabularnewline
144 & 100.7 & 105.800784788977 & -5.10078478897734 \tabularnewline
145 & 96.1 & 104.722670515504 & -8.62267051550381 \tabularnewline
146 & 98.2 & 102.900161912845 & -4.70016191284468 \tabularnewline
147 & 123.5 & 101.906724264421 & 21.5932757355785 \tabularnewline
148 & 93.9 & 106.470731519126 & -12.5707315191256 \tabularnewline
149 & 94.8 & 103.813751144643 & -9.01375114464284 \tabularnewline
150 & 103.5 & 101.908582789456 & 1.59141721054395 \tabularnewline
151 & 105.3 & 102.244948599958 & 3.0550514000423 \tabularnewline
152 & 105.8 & 102.890671690981 & 2.90932830901944 \tabularnewline
153 & 112 & 103.505594395219 & 8.49440560478135 \tabularnewline
154 & 114.5 & 105.300992614524 & 9.19900738547628 \tabularnewline
155 & 108.3 & 107.245317179148 & 1.05468282085202 \tabularnewline
156 & 103.8 & 107.468237504194 & -3.66823750419387 \tabularnewline
157 & 103 & 106.692909907486 & -3.69290990748591 \tabularnewline
158 & 97.7 & 105.912367491637 & -8.21236749163727 \tabularnewline
159 & 118.7 & 104.176581533587 & 14.5234184664132 \tabularnewline
160 & 115.1 & 107.246286568409 & 7.8537134315908 \tabularnewline
161 & 110 & 108.906266532407 & 1.09373346759268 \tabularnewline
162 & 117.3 & 109.137440697084 & 8.16255930291599 \tabularnewline
163 & 119.1 & 110.862699075278 & 8.23730092472195 \tabularnewline
164 & 105.9 & 112.603755024361 & -6.70375502436072 \tabularnewline
165 & 114.1 & 111.186833064969 & 2.91316693503097 \tabularnewline
166 & 124.6 & 111.802567110533 & 12.797432889467 \tabularnewline
167 & 117.3 & 114.507463637783 & 2.79253636221712 \tabularnewline
168 & 115 & 115.097700912213 & -0.0977009122129004 \tabularnewline
169 & 103.6 & 115.077050609888 & -11.4770506098877 \tabularnewline
170 & 113.4 & 112.65123329122 & 0.748766708779982 \tabularnewline
171 & 122 & 112.809494443108 & 9.19050555689175 \tabularnewline
172 & 122.5 & 114.752022040574 & 7.74797795942585 \tabularnewline
173 & 119.6 & 116.389653498123 & 3.21034650187713 \tabularnewline
174 & 132.6 & 117.068200139406 & 15.5317998605938 \tabularnewline
175 & 113 & 120.35103911717 & -7.35103911717013 \tabularnewline
176 & 107.5 & 118.797305618315 & -11.2973056183153 \tabularnewline
177 & 139.3 & 116.409479638043 & 22.8905203619571 \tabularnewline
178 & 134.6 & 121.247675670699 & 13.3523243293011 \tabularnewline
179 & 125.6 & 124.069855401664 & 1.53014459833592 \tabularnewline
180 & 124 & 124.39327048389 & -0.393270483890092 \tabularnewline
181 & 111.9 & 124.310147878338 & -12.4101478783385 \tabularnewline
182 & 101.5 & 121.687108852566 & -20.1871088525661 \tabularnewline
183 & 130.2 & 117.420312448776 & 12.7796875512239 \tabularnewline
184 & 121.9 & 120.121458278194 & 1.77854172180562 \tabularnewline
185 & 111.3 & 120.497375180313 & -9.19737518031314 \tabularnewline
186 & 122 & 118.55339560254 & 3.44660439745979 \tabularnewline
187 & 116.4 & 119.281878286998 & -2.88187828699844 \tabularnewline
188 & 119.1 & 118.672757486148 & 0.427242513851752 \tabularnewline
189 & 133 & 118.763060502542 & 14.2369394974583 \tabularnewline
190 & 128.9 & 121.772214646029 & 7.12778535397091 \tabularnewline
191 & 126.1 & 123.278760686744 & 2.8212393132562 \tabularnewline
192 & 122.3 & 123.875064686685 & -1.57506468668495 \tabularnewline
193 & 110.2 & 123.542155185381 & -13.3421551853806 \tabularnewline
194 & 113.6 & 120.722124829397 & -7.12212482939663 \tabularnewline
195 & 131 & 119.216775210917 & 11.7832247890828 \tabularnewline
196 & 123.2 & 121.707306248437 & 1.49269375156294 \tabularnewline
197 & 120.7 & 122.022805628643 & -1.32280562864271 \tabularnewline
198 & 142.8 & 121.743214215111 & 21.0567857848889 \tabularnewline
199 & 131.7 & 126.193827649581 & 5.50617235041882 \tabularnewline
200 & 131.6 & 127.357625623575 & 4.24237437642471 \tabularnewline
201 & 139 & 128.254304185377 & 10.7456958146227 \tabularnewline
202 & 128.5 & 130.525540576527 & -2.02554057652728 \tabularnewline
203 & 122.7 & 130.097417395998 & -7.39741739599769 \tabularnewline
204 & 148.4 & 128.53388127138 & 19.86611872862 \tabularnewline
205 & 118.6 & 132.732832422216 & -14.1328324222164 \tabularnewline
206 & 126.3 & 129.745682603246 & -3.44568260324591 \tabularnewline
207 & 141 & 129.017394751454 & 11.9826052485463 \tabularnewline
208 & 120.9 & 131.550067327598 & -10.6500673275979 \tabularnewline
209 & 127 & 129.299043205947 & -2.29904320594713 \tabularnewline
210 & 138.5 & 128.813111844753 & 9.68688815524658 \tabularnewline
211 & 131.9 & 130.860556074959 & 1.03944392504081 \tabularnewline
212 & 136.3 & 131.080255469939 & 5.21974453006075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310394&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]52.4[/C][C]50[/C][C]2.4[/C][/ROW]
[ROW][C]3[/C][C]57.5[/C][C]50.5072698346199[/C][C]6.99273016538005[/C][/ROW]
[ROW][C]4[/C][C]52.5[/C][C]51.9852702823425[/C][C]0.51472971765746[/C][/ROW]
[ROW][C]5[/C][C]57.5[/C][C]52.0940648068217[/C][C]5.40593519317827[/C][/ROW]
[ROW][C]6[/C][C]57.6[/C][C]53.2366764115758[/C][C]4.36332358842423[/C][/ROW]
[ROW][C]7[/C][C]48.3[/C][C]54.1589190928646[/C][C]-5.85891909286463[/C][/ROW]
[ROW][C]8[/C][C]52[/C][C]52.9205637098275[/C][C]-0.920563709827519[/C][/ROW]
[ROW][C]9[/C][C]62.1[/C][C]52.7259911261436[/C][C]9.37400887385636[/C][/ROW]
[ROW][C]10[/C][C]59.1[/C][C]54.7073044307966[/C][C]4.39269556920344[/C][/ROW]
[ROW][C]11[/C][C]62.6[/C][C]55.6357552453489[/C][C]6.96424475465111[/C][/ROW]
[ROW][C]12[/C][C]57.9[/C][C]57.1077349474092[/C][C]0.792265052590814[/C][/ROW]
[ROW][C]13[/C][C]59.3[/C][C]57.2751900149937[/C][C]2.02480998500626[/C][/ROW]
[ROW][C]14[/C][C]61.5[/C][C]57.7031587759233[/C][C]3.7968412240767[/C][/ROW]
[ROW][C]15[/C][C]66[/C][C]58.5056683675131[/C][C]7.49433163248688[/C][/ROW]
[ROW][C]16[/C][C]61.1[/C][C]60.0896885207626[/C][C]1.01031147923744[/C][/ROW]
[ROW][C]17[/C][C]63.8[/C][C]60.303230411174[/C][C]3.49676958882602[/C][/ROW]
[ROW][C]18[/C][C]69.6[/C][C]61.0423161324356[/C][C]8.55768386756442[/C][/ROW]
[ROW][C]19[/C][C]57[/C][C]62.8510889991977[/C][C]-5.85108899919773[/C][/ROW]
[ROW][C]20[/C][C]59.9[/C][C]61.6143886037937[/C][C]-1.71438860379373[/C][/ROW]
[ROW][C]21[/C][C]63.8[/C][C]61.2520312606601[/C][C]2.54796873933991[/C][/ROW]
[ROW][C]22[/C][C]69.8[/C][C]61.7905761277525[/C][C]8.00942387224752[/C][/ROW]
[ROW][C]23[/C][C]64.6[/C][C]63.4834674290342[/C][C]1.11653257096584[/C][/ROW]
[ROW][C]24[/C][C]60.8[/C][C]63.7194604676265[/C][C]-2.91946046762651[/C][/ROW]
[ROW][C]25[/C][C]64.7[/C][C]63.102396205713[/C][C]1.59760379428698[/C][/ROW]
[ROW][C]26[/C][C]63.6[/C][C]63.4400696275948[/C][C]0.159930372405249[/C][/ROW]
[ROW][C]27[/C][C]68.8[/C][C]63.4738728999117[/C][C]5.32612710008828[/C][/ROW]
[ROW][C]28[/C][C]66.4[/C][C]64.5996160720895[/C][C]1.80038392791054[/C][/ROW]
[ROW][C]29[/C][C]64.4[/C][C]64.980149595991[/C][C]-0.580149595990946[/C][/ROW]
[ROW][C]30[/C][C]65.3[/C][C]64.8575277669855[/C][C]0.442472233014527[/C][/ROW]
[ROW][C]31[/C][C]63[/C][C]64.951049773846[/C][C]-1.95104977384597[/C][/ROW]
[ROW][C]32[/C][C]61.1[/C][C]64.5386711504651[/C][C]-3.43867115046509[/C][/ROW]
[ROW][C]33[/C][C]67.7[/C][C]63.8118652563781[/C][C]3.8881347436219[/C][/ROW]
[ROW][C]34[/C][C]72.3[/C][C]64.6336708682019[/C][C]7.66632913179809[/C][/ROW]
[ROW][C]35[/C][C]65.4[/C][C]66.2540448310474[/C][C]-0.854044831047432[/C][/ROW]
[ROW][C]36[/C][C]63.2[/C][C]66.073531839296[/C][C]-2.87353183929601[/C][/ROW]
[ROW][C]37[/C][C]69.4[/C][C]65.4661751639232[/C][C]3.93382483607684[/C][/ROW]
[ROW][C]38[/C][C]62.3[/C][C]66.2976379447651[/C][C]-3.99763794476506[/C][/ROW]
[ROW][C]39[/C][C]71[/C][C]65.4526874701353[/C][C]5.54731252986468[/C][/ROW]
[ROW][C]40[/C][C]68.6[/C][C]66.6251809324727[/C][C]1.97481906752733[/C][/ROW]
[ROW][C]41[/C][C]62[/C][C]67.0425834915514[/C][C]-5.04258349155137[/C][/ROW]
[ROW][C]42[/C][C]68.2[/C][C]65.9767707857945[/C][C]2.22322921420552[/C][/ROW]
[ROW][C]43[/C][C]66.8[/C][C]66.4466779173829[/C][C]0.353322082617069[/C][/ROW]
[ROW][C]44[/C][C]65.5[/C][C]66.5213569317232[/C][C]-1.02135693172323[/C][/ROW]
[ROW][C]45[/C][C]76.9[/C][C]66.3054804476219[/C][C]10.5945195523781[/C][/ROW]
[ROW][C]46[/C][C]78.1[/C][C]68.5447638564605[/C][C]9.55523614353949[/C][/ROW]
[ROW][C]47[/C][C]67.6[/C][C]70.5643817974137[/C][C]-2.96438179741375[/C][/ROW]
[ROW][C]48[/C][C]80.1[/C][C]69.9378228540286[/C][C]10.1621771459714[/C][/ROW]
[ROW][C]49[/C][C]64.7[/C][C]72.085725320785[/C][C]-7.38572532078503[/C][/ROW]
[ROW][C]50[/C][C]70.4[/C][C]70.5246604616088[/C][C]-0.124660461608798[/C][/ROW]
[ROW][C]51[/C][C]84.6[/C][C]70.4983119233822[/C][C]14.1016880766178[/C][/ROW]
[ROW][C]52[/C][C]75.1[/C][C]73.4788789977521[/C][C]1.62112100224785[/C][/ROW]
[ROW][C]53[/C][C]69.6[/C][C]73.821523073881[/C][C]-4.22152307388099[/C][/ROW]
[ROW][C]54[/C][C]81.8[/C][C]72.929251694076[/C][C]8.87074830592397[/C][/ROW]
[ROW][C]55[/C][C]74.2[/C][C]74.8041946216182[/C][C]-0.604194621618191[/C][/ROW]
[ROW][C]56[/C][C]72.9[/C][C]74.6764905775405[/C][C]-1.77649057754047[/C][/ROW]
[ROW][C]57[/C][C]84.9[/C][C]74.3010072102601[/C][C]10.5989927897399[/C][/ROW]
[ROW][C]58[/C][C]80.5[/C][C]76.5412360934223[/C][C]3.95876390657766[/C][/ROW]
[ROW][C]59[/C][C]79.6[/C][C]77.3779700568344[/C][C]2.22202994316555[/C][/ROW]
[ROW][C]60[/C][C]90.8[/C][C]77.8476237075803[/C][C]12.9523762924197[/C][/ROW]
[ROW][C]61[/C][C]76.5[/C][C]80.5852694491599[/C][C]-4.08526944915992[/C][/ROW]
[ROW][C]62[/C][C]70.9[/C][C]79.7217969667211[/C][C]-8.82179696672105[/C][/ROW]
[ROW][C]63[/C][C]82.3[/C][C]77.857200513238[/C][C]4.44279948676198[/C][/ROW]
[ROW][C]64[/C][C]77.8[/C][C]78.7962414136127[/C][C]-0.996241413612736[/C][/ROW]
[ROW][C]65[/C][C]75.6[/C][C]78.5856734064774[/C][C]-2.98567340647737[/C][/ROW]
[ROW][C]66[/C][C]81.3[/C][C]77.9546142168386[/C][C]3.34538578316135[/C][/ROW]
[ROW][C]67[/C][C]71[/C][C]78.661703088907[/C][C]-7.66170308890705[/C][/ROW]
[ROW][C]68[/C][C]75.1[/C][C]77.0423068977333[/C][C]-1.94230689773332[/C][/ROW]
[ROW][C]69[/C][C]89.2[/C][C]76.6317761899023[/C][C]12.5682238100977[/C][/ROW]
[ROW][C]70[/C][C]84.1[/C][C]79.2882265289085[/C][C]4.81177347109153[/C][/ROW]
[ROW][C]71[/C][C]82.7[/C][C]80.3052546676207[/C][C]2.39474533237934[/C][/ROW]
[ROW][C]72[/C][C]82.4[/C][C]80.8114138629177[/C][C]1.58858613708229[/C][/ROW]
[ROW][C]73[/C][C]78.2[/C][C]81.1471812908499[/C][C]-2.94718129084991[/C][/ROW]
[ROW][C]74[/C][C]78.5[/C][C]80.5242578883481[/C][C]-2.02425788834807[/C][/ROW]
[ROW][C]75[/C][C]91.5[/C][C]80.0964058199104[/C][C]11.4035941800896[/C][/ROW]
[ROW][C]76[/C][C]76.6[/C][C]82.5066972089966[/C][C]-5.90669720899665[/C][/ROW]
[ROW][C]77[/C][C]80.6[/C][C]81.2582433271809[/C][C]-0.658243327180898[/C][/ROW]
[ROW][C]78[/C][C]85.9[/C][C]81.1191154172981[/C][C]4.78088458270192[/C][/ROW]
[ROW][C]79[/C][C]74.5[/C][C]82.1296148054665[/C][C]-7.62961480546653[/C][/ROW]
[ROW][C]80[/C][C]79.4[/C][C]80.5170008718903[/C][C]-1.11700087189033[/C][/ROW]
[ROW][C]81[/C][C]89.7[/C][C]80.2809088520761[/C][C]9.41909114792389[/C][/ROW]
[ROW][C]82[/C][C]92.7[/C][C]82.2717508557751[/C][C]10.4282491442249[/C][/ROW]
[ROW][C]83[/C][C]89.6[/C][C]84.4758909469278[/C][C]5.12410905307217[/C][/ROW]
[ROW][C]84[/C][C]87[/C][C]85.5589350935639[/C][C]1.44106490643614[/C][/ROW]
[ROW][C]85[/C][C]80.9[/C][C]85.8635220755491[/C][C]-4.96352207554905[/C][/ROW]
[ROW][C]86[/C][C]76.2[/C][C]84.814419982884[/C][C]-8.61441998288396[/C][/ROW]
[ROW][C]87[/C][C]89.7[/C][C]82.9936552328572[/C][C]6.70634476714282[/C][/ROW]
[ROW][C]88[/C][C]79.1[/C][C]84.4111245665792[/C][C]-5.31112456657922[/C][/ROW]
[ROW][C]89[/C][C]82.4[/C][C]83.2885523663565[/C][C]-0.888552366356492[/C][/ROW]
[ROW][C]90[/C][C]90.3[/C][C]83.1007457780512[/C][C]7.19925422194883[/C][/ROW]
[ROW][C]91[/C][C]85.8[/C][C]84.6223976524491[/C][C]1.17760234755094[/C][/ROW]
[ROW][C]92[/C][C]83.5[/C][C]84.8712985474866[/C][C]-1.37129854748665[/C][/ROW]
[ROW][C]93[/C][C]85.1[/C][C]84.5814575527374[/C][C]0.518542447262561[/C][/ROW]
[ROW][C]94[/C][C]90.6[/C][C]84.6910579450151[/C][C]5.90894205498492[/C][/ROW]
[ROW][C]95[/C][C]87.7[/C][C]85.9399863029363[/C][C]1.76001369706366[/C][/ROW]
[ROW][C]96[/C][C]86[/C][C]86.3119870767023[/C][C]-0.311987076702323[/C][/ROW]
[ROW][C]97[/C][C]89.7[/C][C]86.2460447297014[/C][C]3.45395527029865[/C][/ROW]
[ROW][C]98[/C][C]86.2[/C][C]86.9760811125135[/C][C]-0.776081112513467[/C][/ROW]
[ROW][C]99[/C][C]91.1[/C][C]86.8120467218483[/C][C]4.28795327815168[/C][/ROW]
[ROW][C]100[/C][C]91.3[/C][C]87.7183589511258[/C][C]3.58164104887416[/C][/ROW]
[ROW][C]101[/C][C]85.5[/C][C]88.4753833105135[/C][C]-2.97538331051351[/C][/ROW]
[ROW][C]102[/C][C]92[/C][C]87.8464990605739[/C][C]4.15350093942614[/C][/ROW]
[ROW][C]103[/C][C]91.5[/C][C]88.7243931166724[/C][C]2.7756068833276[/C][/ROW]
[ROW][C]104[/C][C]80[/C][C]89.3110521352872[/C][C]-9.31105213528723[/C][/ROW]
[ROW][C]105[/C][C]100.9[/C][C]87.3430455199519[/C][C]13.5569544800481[/C][/ROW]
[ROW][C]106[/C][C]97.3[/C][C]90.2084763770536[/C][C]7.0915236229464[/C][/ROW]
[ROW][C]107[/C][C]89.1[/C][C]91.7073580501434[/C][C]-2.60735805014338[/C][/ROW]
[ROW][C]108[/C][C]104[/C][C]91.1562605139387[/C][C]12.8437394860613[/C][/ROW]
[ROW][C]109[/C][C]80.2[/C][C]93.8709445160203[/C][C]-13.6709445160203[/C][/ROW]
[ROW][C]110[/C][C]83.3[/C][C]90.9814204477953[/C][C]-7.6814204477953[/C][/ROW]
[ROW][C]111[/C][C]97.5[/C][C]89.3578567477122[/C][C]8.14214325228777[/C][/ROW]
[ROW][C]112[/C][C]86.8[/C][C]91.0787999398122[/C][C]-4.2787999398122[/C][/ROW]
[ROW][C]113[/C][C]84.3[/C][C]90.1744223823787[/C][C]-5.87442238237871[/C][/ROW]
[ROW][C]114[/C][C]93.4[/C][C]88.93279018638[/C][C]4.46720981362002[/C][/ROW]
[ROW][C]115[/C][C]90.2[/C][C]89.8769905127832[/C][C]0.323009487216851[/C][/ROW]
[ROW][C]116[/C][C]82.5[/C][C]89.945262583267[/C][C]-7.44526258326697[/C][/ROW]
[ROW][C]117[/C][C]93.7[/C][C]88.371613783552[/C][C]5.328386216448[/C][/ROW]
[ROW][C]118[/C][C]93.9[/C][C]89.4978344480557[/C][C]4.40216555194434[/C][/ROW]
[ROW][C]119[/C][C]91.1[/C][C]90.4282868611825[/C][C]0.671713138817481[/C][/ROW]
[ROW][C]120[/C][C]96.9[/C][C]90.5702617831992[/C][C]6.32973821680083[/C][/ROW]
[ROW][C]121[/C][C]88.2[/C][C]91.9081306408759[/C][C]-3.70813064087588[/C][/ROW]
[ROW][C]122[/C][C]100.9[/C][C]91.1243711338149[/C][C]9.77562886618506[/C][/ROW]
[ROW][C]123[/C][C]109.5[/C][C]93.1905718164215[/C][C]16.3094281835785[/C][/ROW]
[ROW][C]124[/C][C]91[/C][C]96.6377722070172[/C][C]-5.63777220701719[/C][/ROW]
[ROW][C]125[/C][C]89.5[/C][C]95.4461589674011[/C][C]-5.94615896740115[/C][/ROW]
[ROW][C]126[/C][C]109.6[/C][C]94.1893643523939[/C][C]15.4106356476061[/C][/ROW]
[ROW][C]127[/C][C]97.9[/C][C]97.4465937675394[/C][C]0.453406232460566[/C][/ROW]
[ROW][C]128[/C][C]94.9[/C][C]97.5424268111044[/C][C]-2.6424268111044[/C][/ROW]
[ROW][C]129[/C][C]103.5[/C][C]96.9839170563276[/C][C]6.51608294367236[/C][/ROW]
[ROW][C]130[/C][C]100[/C][C]98.361172188497[/C][C]1.63882781150298[/C][/ROW]
[ROW][C]131[/C][C]107.1[/C][C]98.7075588188769[/C][C]8.3924411811231[/C][/ROW]
[ROW][C]132[/C][C]108[/C][C]100.481405589713[/C][C]7.51859441028731[/C][/ROW]
[ROW][C]133[/C][C]95[/C][C]102.070553982663[/C][C]-7.07055398266306[/C][/ROW]
[ROW][C]134[/C][C]102.2[/C][C]100.576104503723[/C][C]1.6238954962773[/C][/ROW]
[ROW][C]135[/C][C]131.4[/C][C]100.919335003655[/C][C]30.4806649963454[/C][/ROW]
[ROW][C]136[/C][C]104.5[/C][C]107.361802458572[/C][C]-2.86180245857216[/C][/ROW]
[ROW][C]137[/C][C]105.6[/C][C]106.756924933624[/C][C]-1.15692493362431[/C][/ROW]
[ROW][C]138[/C][C]106.1[/C][C]106.512394467063[/C][C]-0.412394467062953[/C][/ROW]
[ROW][C]139[/C][C]98[/C][C]106.425229769936[/C][C]-8.42522976993578[/C][/ROW]
[ROW][C]140[/C][C]113[/C][C]104.644452723256[/C][C]8.35554727674352[/C][/ROW]
[ROW][C]141[/C][C]113.2[/C][C]106.41050150877[/C][C]6.78949849122985[/C][/ROW]
[ROW][C]142[/C][C]105.4[/C][C]107.84554641577[/C][C]-2.44554641576954[/C][/ROW]
[ROW][C]143[/C][C]100.1[/C][C]107.328649779985[/C][C]-7.22864977998506[/C][/ROW]
[ROW][C]144[/C][C]100.7[/C][C]105.800784788977[/C][C]-5.10078478897734[/C][/ROW]
[ROW][C]145[/C][C]96.1[/C][C]104.722670515504[/C][C]-8.62267051550381[/C][/ROW]
[ROW][C]146[/C][C]98.2[/C][C]102.900161912845[/C][C]-4.70016191284468[/C][/ROW]
[ROW][C]147[/C][C]123.5[/C][C]101.906724264421[/C][C]21.5932757355785[/C][/ROW]
[ROW][C]148[/C][C]93.9[/C][C]106.470731519126[/C][C]-12.5707315191256[/C][/ROW]
[ROW][C]149[/C][C]94.8[/C][C]103.813751144643[/C][C]-9.01375114464284[/C][/ROW]
[ROW][C]150[/C][C]103.5[/C][C]101.908582789456[/C][C]1.59141721054395[/C][/ROW]
[ROW][C]151[/C][C]105.3[/C][C]102.244948599958[/C][C]3.0550514000423[/C][/ROW]
[ROW][C]152[/C][C]105.8[/C][C]102.890671690981[/C][C]2.90932830901944[/C][/ROW]
[ROW][C]153[/C][C]112[/C][C]103.505594395219[/C][C]8.49440560478135[/C][/ROW]
[ROW][C]154[/C][C]114.5[/C][C]105.300992614524[/C][C]9.19900738547628[/C][/ROW]
[ROW][C]155[/C][C]108.3[/C][C]107.245317179148[/C][C]1.05468282085202[/C][/ROW]
[ROW][C]156[/C][C]103.8[/C][C]107.468237504194[/C][C]-3.66823750419387[/C][/ROW]
[ROW][C]157[/C][C]103[/C][C]106.692909907486[/C][C]-3.69290990748591[/C][/ROW]
[ROW][C]158[/C][C]97.7[/C][C]105.912367491637[/C][C]-8.21236749163727[/C][/ROW]
[ROW][C]159[/C][C]118.7[/C][C]104.176581533587[/C][C]14.5234184664132[/C][/ROW]
[ROW][C]160[/C][C]115.1[/C][C]107.246286568409[/C][C]7.8537134315908[/C][/ROW]
[ROW][C]161[/C][C]110[/C][C]108.906266532407[/C][C]1.09373346759268[/C][/ROW]
[ROW][C]162[/C][C]117.3[/C][C]109.137440697084[/C][C]8.16255930291599[/C][/ROW]
[ROW][C]163[/C][C]119.1[/C][C]110.862699075278[/C][C]8.23730092472195[/C][/ROW]
[ROW][C]164[/C][C]105.9[/C][C]112.603755024361[/C][C]-6.70375502436072[/C][/ROW]
[ROW][C]165[/C][C]114.1[/C][C]111.186833064969[/C][C]2.91316693503097[/C][/ROW]
[ROW][C]166[/C][C]124.6[/C][C]111.802567110533[/C][C]12.797432889467[/C][/ROW]
[ROW][C]167[/C][C]117.3[/C][C]114.507463637783[/C][C]2.79253636221712[/C][/ROW]
[ROW][C]168[/C][C]115[/C][C]115.097700912213[/C][C]-0.0977009122129004[/C][/ROW]
[ROW][C]169[/C][C]103.6[/C][C]115.077050609888[/C][C]-11.4770506098877[/C][/ROW]
[ROW][C]170[/C][C]113.4[/C][C]112.65123329122[/C][C]0.748766708779982[/C][/ROW]
[ROW][C]171[/C][C]122[/C][C]112.809494443108[/C][C]9.19050555689175[/C][/ROW]
[ROW][C]172[/C][C]122.5[/C][C]114.752022040574[/C][C]7.74797795942585[/C][/ROW]
[ROW][C]173[/C][C]119.6[/C][C]116.389653498123[/C][C]3.21034650187713[/C][/ROW]
[ROW][C]174[/C][C]132.6[/C][C]117.068200139406[/C][C]15.5317998605938[/C][/ROW]
[ROW][C]175[/C][C]113[/C][C]120.35103911717[/C][C]-7.35103911717013[/C][/ROW]
[ROW][C]176[/C][C]107.5[/C][C]118.797305618315[/C][C]-11.2973056183153[/C][/ROW]
[ROW][C]177[/C][C]139.3[/C][C]116.409479638043[/C][C]22.8905203619571[/C][/ROW]
[ROW][C]178[/C][C]134.6[/C][C]121.247675670699[/C][C]13.3523243293011[/C][/ROW]
[ROW][C]179[/C][C]125.6[/C][C]124.069855401664[/C][C]1.53014459833592[/C][/ROW]
[ROW][C]180[/C][C]124[/C][C]124.39327048389[/C][C]-0.393270483890092[/C][/ROW]
[ROW][C]181[/C][C]111.9[/C][C]124.310147878338[/C][C]-12.4101478783385[/C][/ROW]
[ROW][C]182[/C][C]101.5[/C][C]121.687108852566[/C][C]-20.1871088525661[/C][/ROW]
[ROW][C]183[/C][C]130.2[/C][C]117.420312448776[/C][C]12.7796875512239[/C][/ROW]
[ROW][C]184[/C][C]121.9[/C][C]120.121458278194[/C][C]1.77854172180562[/C][/ROW]
[ROW][C]185[/C][C]111.3[/C][C]120.497375180313[/C][C]-9.19737518031314[/C][/ROW]
[ROW][C]186[/C][C]122[/C][C]118.55339560254[/C][C]3.44660439745979[/C][/ROW]
[ROW][C]187[/C][C]116.4[/C][C]119.281878286998[/C][C]-2.88187828699844[/C][/ROW]
[ROW][C]188[/C][C]119.1[/C][C]118.672757486148[/C][C]0.427242513851752[/C][/ROW]
[ROW][C]189[/C][C]133[/C][C]118.763060502542[/C][C]14.2369394974583[/C][/ROW]
[ROW][C]190[/C][C]128.9[/C][C]121.772214646029[/C][C]7.12778535397091[/C][/ROW]
[ROW][C]191[/C][C]126.1[/C][C]123.278760686744[/C][C]2.8212393132562[/C][/ROW]
[ROW][C]192[/C][C]122.3[/C][C]123.875064686685[/C][C]-1.57506468668495[/C][/ROW]
[ROW][C]193[/C][C]110.2[/C][C]123.542155185381[/C][C]-13.3421551853806[/C][/ROW]
[ROW][C]194[/C][C]113.6[/C][C]120.722124829397[/C][C]-7.12212482939663[/C][/ROW]
[ROW][C]195[/C][C]131[/C][C]119.216775210917[/C][C]11.7832247890828[/C][/ROW]
[ROW][C]196[/C][C]123.2[/C][C]121.707306248437[/C][C]1.49269375156294[/C][/ROW]
[ROW][C]197[/C][C]120.7[/C][C]122.022805628643[/C][C]-1.32280562864271[/C][/ROW]
[ROW][C]198[/C][C]142.8[/C][C]121.743214215111[/C][C]21.0567857848889[/C][/ROW]
[ROW][C]199[/C][C]131.7[/C][C]126.193827649581[/C][C]5.50617235041882[/C][/ROW]
[ROW][C]200[/C][C]131.6[/C][C]127.357625623575[/C][C]4.24237437642471[/C][/ROW]
[ROW][C]201[/C][C]139[/C][C]128.254304185377[/C][C]10.7456958146227[/C][/ROW]
[ROW][C]202[/C][C]128.5[/C][C]130.525540576527[/C][C]-2.02554057652728[/C][/ROW]
[ROW][C]203[/C][C]122.7[/C][C]130.097417395998[/C][C]-7.39741739599769[/C][/ROW]
[ROW][C]204[/C][C]148.4[/C][C]128.53388127138[/C][C]19.86611872862[/C][/ROW]
[ROW][C]205[/C][C]118.6[/C][C]132.732832422216[/C][C]-14.1328324222164[/C][/ROW]
[ROW][C]206[/C][C]126.3[/C][C]129.745682603246[/C][C]-3.44568260324591[/C][/ROW]
[ROW][C]207[/C][C]141[/C][C]129.017394751454[/C][C]11.9826052485463[/C][/ROW]
[ROW][C]208[/C][C]120.9[/C][C]131.550067327598[/C][C]-10.6500673275979[/C][/ROW]
[ROW][C]209[/C][C]127[/C][C]129.299043205947[/C][C]-2.29904320594713[/C][/ROW]
[ROW][C]210[/C][C]138.5[/C][C]128.813111844753[/C][C]9.68688815524658[/C][/ROW]
[ROW][C]211[/C][C]131.9[/C][C]130.860556074959[/C][C]1.03944392504081[/C][/ROW]
[ROW][C]212[/C][C]136.3[/C][C]131.080255469939[/C][C]5.21974453006075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310394&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
252.4502.4
357.550.50726983461996.99273016538005
452.551.98527028234250.51472971765746
557.552.09406480682175.40593519317827
657.653.23667641157584.36332358842423
748.354.1589190928646-5.85891909286463
85252.9205637098275-0.920563709827519
962.152.72599112614369.37400887385636
1059.154.70730443079664.39269556920344
1162.655.63575524534896.96424475465111
1257.957.10773494740920.792265052590814
1359.357.27519001499372.02480998500626
1461.557.70315877592333.7968412240767
156658.50566836751317.49433163248688
1661.160.08968852076261.01031147923744
1763.860.3032304111743.49676958882602
1869.661.04231613243568.55768386756442
195762.8510889991977-5.85108899919773
2059.961.6143886037937-1.71438860379373
2163.861.25203126066012.54796873933991
2269.861.79057612775258.00942387224752
2364.663.48346742903421.11653257096584
2460.863.7194604676265-2.91946046762651
2564.763.1023962057131.59760379428698
2663.663.44006962759480.159930372405249
2768.863.47387289991175.32612710008828
2866.464.59961607208951.80038392791054
2964.464.980149595991-0.580149595990946
3065.364.85752776698550.442472233014527
316364.951049773846-1.95104977384597
3261.164.5386711504651-3.43867115046509
3367.763.81186525637813.8881347436219
3472.364.63367086820197.66632913179809
3565.466.2540448310474-0.854044831047432
3663.266.073531839296-2.87353183929601
3769.465.46617516392323.93382483607684
3862.366.2976379447651-3.99763794476506
397165.45268747013535.54731252986468
4068.666.62518093247271.97481906752733
416267.0425834915514-5.04258349155137
4268.265.97677078579452.22322921420552
4366.866.44667791738290.353322082617069
4465.566.5213569317232-1.02135693172323
4576.966.305480447621910.5945195523781
4678.168.54476385646059.55523614353949
4767.670.5643817974137-2.96438179741375
4880.169.937822854028610.1621771459714
4964.772.085725320785-7.38572532078503
5070.470.5246604616088-0.124660461608798
5184.670.498311923382214.1016880766178
5275.173.47887899775211.62112100224785
5369.673.821523073881-4.22152307388099
5481.872.9292516940768.87074830592397
5574.274.8041946216182-0.604194621618191
5672.974.6764905775405-1.77649057754047
5784.974.301007210260110.5989927897399
5880.576.54123609342233.95876390657766
5979.677.37797005683442.22202994316555
6090.877.847623707580312.9523762924197
6176.580.5852694491599-4.08526944915992
6270.979.7217969667211-8.82179696672105
6382.377.8572005132384.44279948676198
6477.878.7962414136127-0.996241413612736
6575.678.5856734064774-2.98567340647737
6681.377.95461421683863.34538578316135
677178.661703088907-7.66170308890705
6875.177.0423068977333-1.94230689773332
6989.276.631776189902312.5682238100977
7084.179.28822652890854.81177347109153
7182.780.30525466762072.39474533237934
7282.480.81141386291771.58858613708229
7378.281.1471812908499-2.94718129084991
7478.580.5242578883481-2.02425788834807
7591.580.096405819910411.4035941800896
7676.682.5066972089966-5.90669720899665
7780.681.2582433271809-0.658243327180898
7885.981.11911541729814.78088458270192
7974.582.1296148054665-7.62961480546653
8079.480.5170008718903-1.11700087189033
8189.780.28090885207619.41909114792389
8292.782.271750855775110.4282491442249
8389.684.47589094692785.12410905307217
848785.55893509356391.44106490643614
8580.985.8635220755491-4.96352207554905
8676.284.814419982884-8.61441998288396
8789.782.99365523285726.70634476714282
8879.184.4111245665792-5.31112456657922
8982.483.2885523663565-0.888552366356492
9090.383.10074577805127.19925422194883
9185.884.62239765244911.17760234755094
9283.584.8712985474866-1.37129854748665
9385.184.58145755273740.518542447262561
9490.684.69105794501515.90894205498492
9587.785.93998630293631.76001369706366
968686.3119870767023-0.311987076702323
9789.786.24604472970143.45395527029865
9886.286.9760811125135-0.776081112513467
9991.186.81204672184834.28795327815168
10091.387.71835895112583.58164104887416
10185.588.4753833105135-2.97538331051351
1029287.84649906057394.15350093942614
10391.588.72439311667242.7756068833276
1048089.3110521352872-9.31105213528723
105100.987.343045519951913.5569544800481
10697.390.20847637705367.0915236229464
10789.191.7073580501434-2.60735805014338
10810491.156260513938712.8437394860613
10980.293.8709445160203-13.6709445160203
11083.390.9814204477953-7.6814204477953
11197.589.35785674771228.14214325228777
11286.891.0787999398122-4.2787999398122
11384.390.1744223823787-5.87442238237871
11493.488.932790186384.46720981362002
11590.289.87699051278320.323009487216851
11682.589.945262583267-7.44526258326697
11793.788.3716137835525.328386216448
11893.989.49783444805574.40216555194434
11991.190.42828686118250.671713138817481
12096.990.57026178319926.32973821680083
12188.291.9081306408759-3.70813064087588
122100.991.12437113381499.77562886618506
123109.593.190571816421516.3094281835785
1249196.6377722070172-5.63777220701719
12589.595.4461589674011-5.94615896740115
126109.694.189364352393915.4106356476061
12797.997.44659376753940.453406232460566
12894.997.5424268111044-2.6424268111044
129103.596.98391705632766.51608294367236
13010098.3611721884971.63882781150298
131107.198.70755881887698.3924411811231
132108100.4814055897137.51859441028731
13395102.070553982663-7.07055398266306
134102.2100.5761045037231.6238954962773
135131.4100.91933500365530.4806649963454
136104.5107.361802458572-2.86180245857216
137105.6106.756924933624-1.15692493362431
138106.1106.512394467063-0.412394467062953
13998106.425229769936-8.42522976993578
140113104.6444527232568.35554727674352
141113.2106.410501508776.78949849122985
142105.4107.84554641577-2.44554641576954
143100.1107.328649779985-7.22864977998506
144100.7105.800784788977-5.10078478897734
14596.1104.722670515504-8.62267051550381
14698.2102.900161912845-4.70016191284468
147123.5101.90672426442121.5932757355785
14893.9106.470731519126-12.5707315191256
14994.8103.813751144643-9.01375114464284
150103.5101.9085827894561.59141721054395
151105.3102.2449485999583.0550514000423
152105.8102.8906716909812.90932830901944
153112103.5055943952198.49440560478135
154114.5105.3009926145249.19900738547628
155108.3107.2453171791481.05468282085202
156103.8107.468237504194-3.66823750419387
157103106.692909907486-3.69290990748591
15897.7105.912367491637-8.21236749163727
159118.7104.17658153358714.5234184664132
160115.1107.2462865684097.8537134315908
161110108.9062665324071.09373346759268
162117.3109.1374406970848.16255930291599
163119.1110.8626990752788.23730092472195
164105.9112.603755024361-6.70375502436072
165114.1111.1868330649692.91316693503097
166124.6111.80256711053312.797432889467
167117.3114.5074636377832.79253636221712
168115115.097700912213-0.0977009122129004
169103.6115.077050609888-11.4770506098877
170113.4112.651233291220.748766708779982
171122112.8094944431089.19050555689175
172122.5114.7520220405747.74797795942585
173119.6116.3896534981233.21034650187713
174132.6117.06820013940615.5317998605938
175113120.35103911717-7.35103911717013
176107.5118.797305618315-11.2973056183153
177139.3116.40947963804322.8905203619571
178134.6121.24767567069913.3523243293011
179125.6124.0698554016641.53014459833592
180124124.39327048389-0.393270483890092
181111.9124.310147878338-12.4101478783385
182101.5121.687108852566-20.1871088525661
183130.2117.42031244877612.7796875512239
184121.9120.1214582781941.77854172180562
185111.3120.497375180313-9.19737518031314
186122118.553395602543.44660439745979
187116.4119.281878286998-2.88187828699844
188119.1118.6727574861480.427242513851752
189133118.76306050254214.2369394974583
190128.9121.7722146460297.12778535397091
191126.1123.2787606867442.8212393132562
192122.3123.875064686685-1.57506468668495
193110.2123.542155185381-13.3421551853806
194113.6120.722124829397-7.12212482939663
195131119.21677521091711.7832247890828
196123.2121.7073062484371.49269375156294
197120.7122.022805628643-1.32280562864271
198142.8121.74321421511121.0567857848889
199131.7126.1938276495815.50617235041882
200131.6127.3576256235754.24237437642471
201139128.25430418537710.7456958146227
202128.5130.525540576527-2.02554057652728
203122.7130.097417395998-7.39741739599769
204148.4128.5338812713819.86611872862
205118.6132.732832422216-14.1328324222164
206126.3129.745682603246-3.44568260324591
207141129.01739475145411.9826052485463
208120.9131.550067327598-10.6500673275979
209127129.299043205947-2.29904320594713
210138.5128.8131118447539.68688815524658
211131.9130.8605560749591.03944392504081
212136.3131.0802554699395.21974453006075







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
213132.18351336349117.573613639121146.793413087859
214132.18351336349117.250837291552147.116189435429
215132.18351336349116.934891806682147.432134920299
216132.18351336349116.625361027943147.741665699038
217132.18351336349116.321869413085148.045157313895
218132.18351336349116.024076692531148.34295003445
219132.18351336349115.731673398426148.635353328554
220132.18351336349115.444377096962148.922649630018
221132.18351336349115.161929193304149.205097533676
222132.18351336349114.884092206236149.482934520744
223132.18351336349114.61064743077149.756379296211
224132.18351336349114.341392923288150.025633803693

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 132.18351336349 & 117.573613639121 & 146.793413087859 \tabularnewline
214 & 132.18351336349 & 117.250837291552 & 147.116189435429 \tabularnewline
215 & 132.18351336349 & 116.934891806682 & 147.432134920299 \tabularnewline
216 & 132.18351336349 & 116.625361027943 & 147.741665699038 \tabularnewline
217 & 132.18351336349 & 116.321869413085 & 148.045157313895 \tabularnewline
218 & 132.18351336349 & 116.024076692531 & 148.34295003445 \tabularnewline
219 & 132.18351336349 & 115.731673398426 & 148.635353328554 \tabularnewline
220 & 132.18351336349 & 115.444377096962 & 148.922649630018 \tabularnewline
221 & 132.18351336349 & 115.161929193304 & 149.205097533676 \tabularnewline
222 & 132.18351336349 & 114.884092206236 & 149.482934520744 \tabularnewline
223 & 132.18351336349 & 114.61064743077 & 149.756379296211 \tabularnewline
224 & 132.18351336349 & 114.341392923288 & 150.025633803693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310394&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]132.18351336349[/C][C]117.573613639121[/C][C]146.793413087859[/C][/ROW]
[ROW][C]214[/C][C]132.18351336349[/C][C]117.250837291552[/C][C]147.116189435429[/C][/ROW]
[ROW][C]215[/C][C]132.18351336349[/C][C]116.934891806682[/C][C]147.432134920299[/C][/ROW]
[ROW][C]216[/C][C]132.18351336349[/C][C]116.625361027943[/C][C]147.741665699038[/C][/ROW]
[ROW][C]217[/C][C]132.18351336349[/C][C]116.321869413085[/C][C]148.045157313895[/C][/ROW]
[ROW][C]218[/C][C]132.18351336349[/C][C]116.024076692531[/C][C]148.34295003445[/C][/ROW]
[ROW][C]219[/C][C]132.18351336349[/C][C]115.731673398426[/C][C]148.635353328554[/C][/ROW]
[ROW][C]220[/C][C]132.18351336349[/C][C]115.444377096962[/C][C]148.922649630018[/C][/ROW]
[ROW][C]221[/C][C]132.18351336349[/C][C]115.161929193304[/C][C]149.205097533676[/C][/ROW]
[ROW][C]222[/C][C]132.18351336349[/C][C]114.884092206236[/C][C]149.482934520744[/C][/ROW]
[ROW][C]223[/C][C]132.18351336349[/C][C]114.61064743077[/C][C]149.756379296211[/C][/ROW]
[ROW][C]224[/C][C]132.18351336349[/C][C]114.341392923288[/C][C]150.025633803693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310394&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310394&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
213132.18351336349117.573613639121146.793413087859
214132.18351336349117.250837291552147.116189435429
215132.18351336349116.934891806682147.432134920299
216132.18351336349116.625361027943147.741665699038
217132.18351336349116.321869413085148.045157313895
218132.18351336349116.024076692531148.34295003445
219132.18351336349115.731673398426148.635353328554
220132.18351336349115.444377096962148.922649630018
221132.18351336349115.161929193304149.205097533676
222132.18351336349114.884092206236149.482934520744
223132.18351336349114.61064743077149.756379296211
224132.18351336349114.341392923288150.025633803693



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')