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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 computationThu, 14 Dec 2017 15:56:54 +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/14/t1513263554ibqqq758ztnck5r.htm/, Retrieved Tue, 14 May 2024 00:58:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309522, Retrieved Tue, 14 May 2024 00:58:15 +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] [] [2017-12-14 14:56:54] [d2d54f927b4b6a5dbf001a3c29aa1f74] [Current]
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Dataseries X:
122.2
136.1
145.5
116.7
137.1
125.5
112.4
106.3
145.7
151.5
144.6
116.4
137.7
138.8
149.5
125
133.4
134.4
124.8
110.6
142.4
149.6
134.6
103.3
136.5
137.1
140.7
131.4
126.2
125.3
126.6
107.7
144.5
154.2
131.4
105.7
136.2
133.3
130
129.3
113.1
117.7
116.3
97.3
140.6
141.2
120.8
106.2
121.5
122.6
137.2
118.9
107.2
127.4
111.8
100
138.3
128
121.2
105.9
112.5
123.1
129
115.5
105.7
122.3
106.4
101.1
131.6
119.5
127
106.9
115.9
122.7
137.2
108.5
115.2
129.4
112.3
104.3
140
139.9
134.9
105.1
127
135.5
143.9
115.8
117.5
129.3
117.9
108.1
131.7
143.7
126.2
96.9
125.8
129.6
124.9
136.8
107.5
114.3
110.3
85.5
116.8
115.1
95.2
83.4
95.4
96.3
100.5
90.9
80.6
94.8
93.9
75.9
101.6
103.3
91.8
83.5
92
101.2
109.1
99.8
90.8
110.6
97.8
81.9
114.4
108.8
103.1
90.4
94.4
100.5
115.1
93.9
102.5
97.1
91.2
82.3
107.1
99.2
94.8
81.1
92.5
97.7
98.5
81.2
86.2
92
86.3
74.8
90
101.1
87.8
66.3
88.6
90
92
85.1
85.9
88.5
92.3
68
93.6
97.7
85.1
69.9
96.1
97
95.9
91.3
83.5
91.4
96.8
71
106.9
102.7
84.9
75.8
93.6
100.7
100.5
95.9
85.7
104.1
93.5
81.5
102.1
98.2
88.4
77.8
90.1
101
98.6
91.5
86.4
98.9
85.2
77.3
93
86.8
91.3
74.9
93.9
95
103.1
81.4
93.1
97.2
86.4
75.5




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=309522&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=309522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309522&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
alpha0.158887024244763
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.158887024244763 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309522&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]0.158887024244763[/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=309522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309522&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
alpha0.158887024244763
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2136.1122.213.9
3145.5124.40852963700221.0914703629978
4116.7127.759690599926-11.0596905999255
5137.1126.00244927143611.0975507285644
6125.5127.765706083102-2.26570608310249
7112.4127.405714785745-15.0057147857451
8106.3125.021501416772-18.7215014167724
9145.7122.04689776726723.6531022327327
10151.5125.80506879518325.6949312048166
11144.6129.88765995249114.7123400475094
12116.4132.225259882316-15.8252598823164
13137.7129.7108314317157.98916856828487
14138.8130.980206651727.81979334828031
15149.5132.22267034703717.2773296529631
16125134.967813842492-9.96781384249203
17133.4133.3840575628330.0159424371672969
18134.4133.3865906092331.01340939076658
19124.8133.547608211674-8.74760821167401
20110.6132.157726773662-21.5577267736621
21142.4128.73248371711313.6675162828868
22149.6130.90407470811818.695925291882
23134.6133.8746146432470.725385356752497
24103.3133.989868964013-30.6898689640126
25136.5129.1136470098597.38635299014106
26137.1130.2872426564846.81275734351613
27140.7131.3697013976979.33029860230317
28131.4132.852164777932-1.45216477793184
29126.2132.621434637653-6.42143463765318
30125.3131.601151996694-6.3011519966942
31126.6130.599980706626-3.99998070662551
32107.7129.964435675113-22.2644356751133
33144.5126.42690574420618.0730942557944
34154.2129.29848590940424.9015140905961
35131.4133.255013382448-1.85501338244774
36105.7132.960275826176-27.2602758261764
37136.2128.6289717200647.57102827993623
38133.3129.8319098739363.46809012606423
39130130.382944393879-0.382944393878773
40129.3130.322099498684-1.02209949868413
41113.1130.159701150856-17.0597011508562
42117.7127.449136000492-9.74913600049166
43116.3125.900124792416-9.60012479241604
4497.3124.374789531771-27.0747895317707
45140.6120.07295679101420.5270432089856
46141.2123.33443760303417.8655623969662
47120.8126.173043648747-5.37304364874686
48106.2125.31933673226-19.1193367322602
49121.5122.281522213338-0.781522213337809
50122.6122.1573484744790.442651525520603
51137.2122.22768005814714.9723199418532
52118.9124.606587419748-5.70658741974835
53107.2123.699884726032-16.4998847260319
54127.4121.0782671415316.32173285846891
55111.8122.082708463484-10.2827084634836
56100120.448919514544-20.4489195145442
57138.3117.19985154385821.1001484561424
58128120.5523913431777.44760865682319
59121.2121.735719720399-0.535719720398987
60105.9121.650600808196-15.7506008081955
61112.5119.148034715714-6.64803471571419
62123.1118.0917482626585.00825173734152
63129118.88749447787310.1125055221267
64115.5120.494240387943-4.99424038794277
65105.7119.70072039434-14.0007203943395
66122.3117.47618759364.82381240640005
67106.4118.242628792368-11.8426287923678
68101.1116.360988744313-15.2609887443131
69131.6113.93621565569617.6637843443036
70119.5116.7427617870642.75723821293596
71127117.1808511618519.81914883814862
72106.9118.740986501361-11.8409865013612
73115.9116.859607392038-0.959607392037526
74122.7116.7071382290735.9928617709266
75137.2117.65932620256619.5406737974339
76108.5120.764085713978-12.264085713978
77115.2118.815481629801-3.61548162980132
78129.4118.24102851243111.1589714875694
79112.3120.014044285723-7.71404428572264
80104.3118.788382744272-14.4883827442718
81140116.48636672391523.5136332760847
82139.9120.22237794433519.677622055665
83134.9123.34889675697311.5511032430272
84105.1125.184217178001-20.0842171780014
85127121.9930956763035.0069043236968
86135.5122.78862780497412.7113721950264
87143.9124.80829990710919.091700092891
88115.8127.841723322642-12.0417233226419
89117.5125.928449737129-8.42844973712857
90129.3124.58927843944.71072156060036
91117.9125.337750970209-7.43775097020908
92108.1124.155988851479-16.055988851479
93131.7121.6049005615610.0950994384396
94143.7123.20888087078920.491119129211
95126.2126.464653812674-0.264653812674283
9696.9126.422603755923-29.5226037559234
97125.8121.7318450971874.06815490281252
98129.6122.3782221238627.22177787613791
99124.9123.5256689203581.37433107964171
100136.8123.7440322959313.0559677040703
101107.5125.818456153065-18.3184561530651
102114.3122.907891166146-8.60789116614644
103110.3121.540208953735-11.2402089537347
10485.5119.754285601186-34.2542856011864
105116.8114.3117240943842.48827590561633
106115.1114.7070788485270.392921151473018
10795.2114.769508921047-19.5695089210473
10883.4111.660167882651-28.2601678826508
10995.4107.169993903119-11.769993903119
11096.3105.299894596473-8.99989459647338
111100.5103.869928125523-3.36992812552319
11290.9103.33449027374-12.4344902737401
11380.6101.358811116145-20.7588111161451
11494.898.0605053910417-3.26050539104166
11593.997.542453391925-3.64245339192503
11675.996.9637148115318-21.0637148115318
117101.693.61696384558727.98303615441282
118103.394.88536470460028.4146352953998
11991.896.2223410667912-4.42234106679122
12083.595.5196884544933-12.0196884544933
1219293.6099159236098-1.60991592360976
122101.293.35412117322317.84587882677685
123109.194.600729512594714.4992704874053
12499.896.90447545405852.89552454594154
12590.897.3645367327908-6.56453673279078
126110.696.321517025772214.2784829742278
12797.898.5901826962768-0.790182696276787
12881.998.4646329190557-16.5646329190557
129114.495.832727686840118.5672723131599
130108.898.782826333020210.0171736669798
131103.1100.374425248312.72557475169035
13290.4100.807483709962-10.4074837099624
13394.499.1538695934106-4.7538695934106
134100.598.39854140006592.10145859993408
135115.198.73243590358316.367564096417
13693.9101.333029456998-7.43302945699813
137102.5100.1520175254522.34798247454798
13897.1100.525081473812-3.42508147381182
13991.299.980880470642-8.78088047064197
14082.398.5857125024127-16.2857125024127
141107.195.998124105198611.1018758948014
14299.297.76206812965831.43793187034171
14394.897.9905368456036-3.1905368456036
14481.197.4836019404624-16.3836019404624
14592.594.8804601817316-2.38046018173158
14697.794.50223594712313.19776405287691
14798.595.01031916172163.48968083827843
14881.295.5647841656796-14.3647841656796
14986.293.2824063556765-7.08240635567647
1509292.1571038853308-0.157103885330841
15186.392.1321421164933-5.83214211649333
15274.891.2054904106311-16.4054904106311
1539088.598870858011.40112914199004
154101.188.821492097963412.2785079020366
15587.890.7723876806838-2.97238768068378
15666.390.3001138471981-24.0001138471981
15788.686.48680717648132.11319282351872
1589086.82256609586563.17743390413445
1599287.32741911362794.6725808863721
16085.188.0698315862065-2.96983158620652
16185.987.5979638829661-1.69796388296605
16288.587.32817945432651.1718205456735
16392.387.51436653377744.78563346622256
1646888.2747415943517-20.2747415943517
16593.685.05334823509368.54665176490639
16697.786.411300301275811.2886996987242
16785.188.2049282039989-3.10492820399887
16869.987.7115954011718-17.8115954011718
16996.184.881564010827911.2184359891721
1709786.664027921827810.3359720781722
17195.988.30627976800567.59372023199444
17291.389.51282337861441.78717662138558
17383.589.7967825537862-6.29678255378617
17491.488.79630551149872.60369448850126
17596.889.20999878081927.59000121918081
1767190.4159514885489-19.4159514885489
177106.987.331008733652719.5689912663473
178102.790.440267523434412.2597324765656
17984.992.3881799346728-7.48817993467277
18075.891.1984053078433-15.3984053078433
18193.688.75179851036534.84820148963472
182100.789.522114817992411.1778851820076
183100.591.29813573191129.20186426808883
18495.992.7601925629723.139807437028
18585.793.259067223343-7.55906722334295
186104.192.058029526159912.0419704738401
18793.593.9713423807916-0.47134238079164
18881.593.8964521925072-12.3964521925072
189102.191.926816792447310.1731832075527
19098.293.54320359939214.65679640060789
19188.494.2831081219984-5.88310812199842
19277.893.3483585791839-15.5483585791839
19390.190.8779261526468-0.777926152646842
19410190.754323781170610.2456762188294
19598.692.38222878695576.21777121304424
19691.593.3701519524311-1.8701519524311
19786.493.0730090738238-6.67300907382378
19898.992.01275451932566.88724548067439
19985.293.1070484589931-7.90704845899315
20077.391.8507210587846-14.5507210587846
2019389.53880028913873.46119971086131
20286.890.0887400115143-3.28874001151428
20391.389.56620189757011.73379810242992
20474.989.8416799187064-14.9416799187064
20593.987.46764085920546.43235914079462
2069588.48965926195986.51034073804016
207103.189.524067928646513.5759320713535
20881.491.6811073768129-10.2811073768129
20993.190.04757281977023.05242718022978
21097.290.53256389116076.66743610883925
21186.491.5919329738363-5.19193297383629
21275.590.7670021935452-15.2670021935452

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 136.1 & 122.2 & 13.9 \tabularnewline
3 & 145.5 & 124.408529637002 & 21.0914703629978 \tabularnewline
4 & 116.7 & 127.759690599926 & -11.0596905999255 \tabularnewline
5 & 137.1 & 126.002449271436 & 11.0975507285644 \tabularnewline
6 & 125.5 & 127.765706083102 & -2.26570608310249 \tabularnewline
7 & 112.4 & 127.405714785745 & -15.0057147857451 \tabularnewline
8 & 106.3 & 125.021501416772 & -18.7215014167724 \tabularnewline
9 & 145.7 & 122.046897767267 & 23.6531022327327 \tabularnewline
10 & 151.5 & 125.805068795183 & 25.6949312048166 \tabularnewline
11 & 144.6 & 129.887659952491 & 14.7123400475094 \tabularnewline
12 & 116.4 & 132.225259882316 & -15.8252598823164 \tabularnewline
13 & 137.7 & 129.710831431715 & 7.98916856828487 \tabularnewline
14 & 138.8 & 130.98020665172 & 7.81979334828031 \tabularnewline
15 & 149.5 & 132.222670347037 & 17.2773296529631 \tabularnewline
16 & 125 & 134.967813842492 & -9.96781384249203 \tabularnewline
17 & 133.4 & 133.384057562833 & 0.0159424371672969 \tabularnewline
18 & 134.4 & 133.386590609233 & 1.01340939076658 \tabularnewline
19 & 124.8 & 133.547608211674 & -8.74760821167401 \tabularnewline
20 & 110.6 & 132.157726773662 & -21.5577267736621 \tabularnewline
21 & 142.4 & 128.732483717113 & 13.6675162828868 \tabularnewline
22 & 149.6 & 130.904074708118 & 18.695925291882 \tabularnewline
23 & 134.6 & 133.874614643247 & 0.725385356752497 \tabularnewline
24 & 103.3 & 133.989868964013 & -30.6898689640126 \tabularnewline
25 & 136.5 & 129.113647009859 & 7.38635299014106 \tabularnewline
26 & 137.1 & 130.287242656484 & 6.81275734351613 \tabularnewline
27 & 140.7 & 131.369701397697 & 9.33029860230317 \tabularnewline
28 & 131.4 & 132.852164777932 & -1.45216477793184 \tabularnewline
29 & 126.2 & 132.621434637653 & -6.42143463765318 \tabularnewline
30 & 125.3 & 131.601151996694 & -6.3011519966942 \tabularnewline
31 & 126.6 & 130.599980706626 & -3.99998070662551 \tabularnewline
32 & 107.7 & 129.964435675113 & -22.2644356751133 \tabularnewline
33 & 144.5 & 126.426905744206 & 18.0730942557944 \tabularnewline
34 & 154.2 & 129.298485909404 & 24.9015140905961 \tabularnewline
35 & 131.4 & 133.255013382448 & -1.85501338244774 \tabularnewline
36 & 105.7 & 132.960275826176 & -27.2602758261764 \tabularnewline
37 & 136.2 & 128.628971720064 & 7.57102827993623 \tabularnewline
38 & 133.3 & 129.831909873936 & 3.46809012606423 \tabularnewline
39 & 130 & 130.382944393879 & -0.382944393878773 \tabularnewline
40 & 129.3 & 130.322099498684 & -1.02209949868413 \tabularnewline
41 & 113.1 & 130.159701150856 & -17.0597011508562 \tabularnewline
42 & 117.7 & 127.449136000492 & -9.74913600049166 \tabularnewline
43 & 116.3 & 125.900124792416 & -9.60012479241604 \tabularnewline
44 & 97.3 & 124.374789531771 & -27.0747895317707 \tabularnewline
45 & 140.6 & 120.072956791014 & 20.5270432089856 \tabularnewline
46 & 141.2 & 123.334437603034 & 17.8655623969662 \tabularnewline
47 & 120.8 & 126.173043648747 & -5.37304364874686 \tabularnewline
48 & 106.2 & 125.31933673226 & -19.1193367322602 \tabularnewline
49 & 121.5 & 122.281522213338 & -0.781522213337809 \tabularnewline
50 & 122.6 & 122.157348474479 & 0.442651525520603 \tabularnewline
51 & 137.2 & 122.227680058147 & 14.9723199418532 \tabularnewline
52 & 118.9 & 124.606587419748 & -5.70658741974835 \tabularnewline
53 & 107.2 & 123.699884726032 & -16.4998847260319 \tabularnewline
54 & 127.4 & 121.078267141531 & 6.32173285846891 \tabularnewline
55 & 111.8 & 122.082708463484 & -10.2827084634836 \tabularnewline
56 & 100 & 120.448919514544 & -20.4489195145442 \tabularnewline
57 & 138.3 & 117.199851543858 & 21.1001484561424 \tabularnewline
58 & 128 & 120.552391343177 & 7.44760865682319 \tabularnewline
59 & 121.2 & 121.735719720399 & -0.535719720398987 \tabularnewline
60 & 105.9 & 121.650600808196 & -15.7506008081955 \tabularnewline
61 & 112.5 & 119.148034715714 & -6.64803471571419 \tabularnewline
62 & 123.1 & 118.091748262658 & 5.00825173734152 \tabularnewline
63 & 129 & 118.887494477873 & 10.1125055221267 \tabularnewline
64 & 115.5 & 120.494240387943 & -4.99424038794277 \tabularnewline
65 & 105.7 & 119.70072039434 & -14.0007203943395 \tabularnewline
66 & 122.3 & 117.4761875936 & 4.82381240640005 \tabularnewline
67 & 106.4 & 118.242628792368 & -11.8426287923678 \tabularnewline
68 & 101.1 & 116.360988744313 & -15.2609887443131 \tabularnewline
69 & 131.6 & 113.936215655696 & 17.6637843443036 \tabularnewline
70 & 119.5 & 116.742761787064 & 2.75723821293596 \tabularnewline
71 & 127 & 117.180851161851 & 9.81914883814862 \tabularnewline
72 & 106.9 & 118.740986501361 & -11.8409865013612 \tabularnewline
73 & 115.9 & 116.859607392038 & -0.959607392037526 \tabularnewline
74 & 122.7 & 116.707138229073 & 5.9928617709266 \tabularnewline
75 & 137.2 & 117.659326202566 & 19.5406737974339 \tabularnewline
76 & 108.5 & 120.764085713978 & -12.264085713978 \tabularnewline
77 & 115.2 & 118.815481629801 & -3.61548162980132 \tabularnewline
78 & 129.4 & 118.241028512431 & 11.1589714875694 \tabularnewline
79 & 112.3 & 120.014044285723 & -7.71404428572264 \tabularnewline
80 & 104.3 & 118.788382744272 & -14.4883827442718 \tabularnewline
81 & 140 & 116.486366723915 & 23.5136332760847 \tabularnewline
82 & 139.9 & 120.222377944335 & 19.677622055665 \tabularnewline
83 & 134.9 & 123.348896756973 & 11.5511032430272 \tabularnewline
84 & 105.1 & 125.184217178001 & -20.0842171780014 \tabularnewline
85 & 127 & 121.993095676303 & 5.0069043236968 \tabularnewline
86 & 135.5 & 122.788627804974 & 12.7113721950264 \tabularnewline
87 & 143.9 & 124.808299907109 & 19.091700092891 \tabularnewline
88 & 115.8 & 127.841723322642 & -12.0417233226419 \tabularnewline
89 & 117.5 & 125.928449737129 & -8.42844973712857 \tabularnewline
90 & 129.3 & 124.5892784394 & 4.71072156060036 \tabularnewline
91 & 117.9 & 125.337750970209 & -7.43775097020908 \tabularnewline
92 & 108.1 & 124.155988851479 & -16.055988851479 \tabularnewline
93 & 131.7 & 121.60490056156 & 10.0950994384396 \tabularnewline
94 & 143.7 & 123.208880870789 & 20.491119129211 \tabularnewline
95 & 126.2 & 126.464653812674 & -0.264653812674283 \tabularnewline
96 & 96.9 & 126.422603755923 & -29.5226037559234 \tabularnewline
97 & 125.8 & 121.731845097187 & 4.06815490281252 \tabularnewline
98 & 129.6 & 122.378222123862 & 7.22177787613791 \tabularnewline
99 & 124.9 & 123.525668920358 & 1.37433107964171 \tabularnewline
100 & 136.8 & 123.74403229593 & 13.0559677040703 \tabularnewline
101 & 107.5 & 125.818456153065 & -18.3184561530651 \tabularnewline
102 & 114.3 & 122.907891166146 & -8.60789116614644 \tabularnewline
103 & 110.3 & 121.540208953735 & -11.2402089537347 \tabularnewline
104 & 85.5 & 119.754285601186 & -34.2542856011864 \tabularnewline
105 & 116.8 & 114.311724094384 & 2.48827590561633 \tabularnewline
106 & 115.1 & 114.707078848527 & 0.392921151473018 \tabularnewline
107 & 95.2 & 114.769508921047 & -19.5695089210473 \tabularnewline
108 & 83.4 & 111.660167882651 & -28.2601678826508 \tabularnewline
109 & 95.4 & 107.169993903119 & -11.769993903119 \tabularnewline
110 & 96.3 & 105.299894596473 & -8.99989459647338 \tabularnewline
111 & 100.5 & 103.869928125523 & -3.36992812552319 \tabularnewline
112 & 90.9 & 103.33449027374 & -12.4344902737401 \tabularnewline
113 & 80.6 & 101.358811116145 & -20.7588111161451 \tabularnewline
114 & 94.8 & 98.0605053910417 & -3.26050539104166 \tabularnewline
115 & 93.9 & 97.542453391925 & -3.64245339192503 \tabularnewline
116 & 75.9 & 96.9637148115318 & -21.0637148115318 \tabularnewline
117 & 101.6 & 93.6169638455872 & 7.98303615441282 \tabularnewline
118 & 103.3 & 94.8853647046002 & 8.4146352953998 \tabularnewline
119 & 91.8 & 96.2223410667912 & -4.42234106679122 \tabularnewline
120 & 83.5 & 95.5196884544933 & -12.0196884544933 \tabularnewline
121 & 92 & 93.6099159236098 & -1.60991592360976 \tabularnewline
122 & 101.2 & 93.3541211732231 & 7.84587882677685 \tabularnewline
123 & 109.1 & 94.6007295125947 & 14.4992704874053 \tabularnewline
124 & 99.8 & 96.9044754540585 & 2.89552454594154 \tabularnewline
125 & 90.8 & 97.3645367327908 & -6.56453673279078 \tabularnewline
126 & 110.6 & 96.3215170257722 & 14.2784829742278 \tabularnewline
127 & 97.8 & 98.5901826962768 & -0.790182696276787 \tabularnewline
128 & 81.9 & 98.4646329190557 & -16.5646329190557 \tabularnewline
129 & 114.4 & 95.8327276868401 & 18.5672723131599 \tabularnewline
130 & 108.8 & 98.7828263330202 & 10.0171736669798 \tabularnewline
131 & 103.1 & 100.37442524831 & 2.72557475169035 \tabularnewline
132 & 90.4 & 100.807483709962 & -10.4074837099624 \tabularnewline
133 & 94.4 & 99.1538695934106 & -4.7538695934106 \tabularnewline
134 & 100.5 & 98.3985414000659 & 2.10145859993408 \tabularnewline
135 & 115.1 & 98.732435903583 & 16.367564096417 \tabularnewline
136 & 93.9 & 101.333029456998 & -7.43302945699813 \tabularnewline
137 & 102.5 & 100.152017525452 & 2.34798247454798 \tabularnewline
138 & 97.1 & 100.525081473812 & -3.42508147381182 \tabularnewline
139 & 91.2 & 99.980880470642 & -8.78088047064197 \tabularnewline
140 & 82.3 & 98.5857125024127 & -16.2857125024127 \tabularnewline
141 & 107.1 & 95.9981241051986 & 11.1018758948014 \tabularnewline
142 & 99.2 & 97.7620681296583 & 1.43793187034171 \tabularnewline
143 & 94.8 & 97.9905368456036 & -3.1905368456036 \tabularnewline
144 & 81.1 & 97.4836019404624 & -16.3836019404624 \tabularnewline
145 & 92.5 & 94.8804601817316 & -2.38046018173158 \tabularnewline
146 & 97.7 & 94.5022359471231 & 3.19776405287691 \tabularnewline
147 & 98.5 & 95.0103191617216 & 3.48968083827843 \tabularnewline
148 & 81.2 & 95.5647841656796 & -14.3647841656796 \tabularnewline
149 & 86.2 & 93.2824063556765 & -7.08240635567647 \tabularnewline
150 & 92 & 92.1571038853308 & -0.157103885330841 \tabularnewline
151 & 86.3 & 92.1321421164933 & -5.83214211649333 \tabularnewline
152 & 74.8 & 91.2054904106311 & -16.4054904106311 \tabularnewline
153 & 90 & 88.59887085801 & 1.40112914199004 \tabularnewline
154 & 101.1 & 88.8214920979634 & 12.2785079020366 \tabularnewline
155 & 87.8 & 90.7723876806838 & -2.97238768068378 \tabularnewline
156 & 66.3 & 90.3001138471981 & -24.0001138471981 \tabularnewline
157 & 88.6 & 86.4868071764813 & 2.11319282351872 \tabularnewline
158 & 90 & 86.8225660958656 & 3.17743390413445 \tabularnewline
159 & 92 & 87.3274191136279 & 4.6725808863721 \tabularnewline
160 & 85.1 & 88.0698315862065 & -2.96983158620652 \tabularnewline
161 & 85.9 & 87.5979638829661 & -1.69796388296605 \tabularnewline
162 & 88.5 & 87.3281794543265 & 1.1718205456735 \tabularnewline
163 & 92.3 & 87.5143665337774 & 4.78563346622256 \tabularnewline
164 & 68 & 88.2747415943517 & -20.2747415943517 \tabularnewline
165 & 93.6 & 85.0533482350936 & 8.54665176490639 \tabularnewline
166 & 97.7 & 86.4113003012758 & 11.2886996987242 \tabularnewline
167 & 85.1 & 88.2049282039989 & -3.10492820399887 \tabularnewline
168 & 69.9 & 87.7115954011718 & -17.8115954011718 \tabularnewline
169 & 96.1 & 84.8815640108279 & 11.2184359891721 \tabularnewline
170 & 97 & 86.6640279218278 & 10.3359720781722 \tabularnewline
171 & 95.9 & 88.3062797680056 & 7.59372023199444 \tabularnewline
172 & 91.3 & 89.5128233786144 & 1.78717662138558 \tabularnewline
173 & 83.5 & 89.7967825537862 & -6.29678255378617 \tabularnewline
174 & 91.4 & 88.7963055114987 & 2.60369448850126 \tabularnewline
175 & 96.8 & 89.2099987808192 & 7.59000121918081 \tabularnewline
176 & 71 & 90.4159514885489 & -19.4159514885489 \tabularnewline
177 & 106.9 & 87.3310087336527 & 19.5689912663473 \tabularnewline
178 & 102.7 & 90.4402675234344 & 12.2597324765656 \tabularnewline
179 & 84.9 & 92.3881799346728 & -7.48817993467277 \tabularnewline
180 & 75.8 & 91.1984053078433 & -15.3984053078433 \tabularnewline
181 & 93.6 & 88.7517985103653 & 4.84820148963472 \tabularnewline
182 & 100.7 & 89.5221148179924 & 11.1778851820076 \tabularnewline
183 & 100.5 & 91.2981357319112 & 9.20186426808883 \tabularnewline
184 & 95.9 & 92.760192562972 & 3.139807437028 \tabularnewline
185 & 85.7 & 93.259067223343 & -7.55906722334295 \tabularnewline
186 & 104.1 & 92.0580295261599 & 12.0419704738401 \tabularnewline
187 & 93.5 & 93.9713423807916 & -0.47134238079164 \tabularnewline
188 & 81.5 & 93.8964521925072 & -12.3964521925072 \tabularnewline
189 & 102.1 & 91.9268167924473 & 10.1731832075527 \tabularnewline
190 & 98.2 & 93.5432035993921 & 4.65679640060789 \tabularnewline
191 & 88.4 & 94.2831081219984 & -5.88310812199842 \tabularnewline
192 & 77.8 & 93.3483585791839 & -15.5483585791839 \tabularnewline
193 & 90.1 & 90.8779261526468 & -0.777926152646842 \tabularnewline
194 & 101 & 90.7543237811706 & 10.2456762188294 \tabularnewline
195 & 98.6 & 92.3822287869557 & 6.21777121304424 \tabularnewline
196 & 91.5 & 93.3701519524311 & -1.8701519524311 \tabularnewline
197 & 86.4 & 93.0730090738238 & -6.67300907382378 \tabularnewline
198 & 98.9 & 92.0127545193256 & 6.88724548067439 \tabularnewline
199 & 85.2 & 93.1070484589931 & -7.90704845899315 \tabularnewline
200 & 77.3 & 91.8507210587846 & -14.5507210587846 \tabularnewline
201 & 93 & 89.5388002891387 & 3.46119971086131 \tabularnewline
202 & 86.8 & 90.0887400115143 & -3.28874001151428 \tabularnewline
203 & 91.3 & 89.5662018975701 & 1.73379810242992 \tabularnewline
204 & 74.9 & 89.8416799187064 & -14.9416799187064 \tabularnewline
205 & 93.9 & 87.4676408592054 & 6.43235914079462 \tabularnewline
206 & 95 & 88.4896592619598 & 6.51034073804016 \tabularnewline
207 & 103.1 & 89.5240679286465 & 13.5759320713535 \tabularnewline
208 & 81.4 & 91.6811073768129 & -10.2811073768129 \tabularnewline
209 & 93.1 & 90.0475728197702 & 3.05242718022978 \tabularnewline
210 & 97.2 & 90.5325638911607 & 6.66743610883925 \tabularnewline
211 & 86.4 & 91.5919329738363 & -5.19193297383629 \tabularnewline
212 & 75.5 & 90.7670021935452 & -15.2670021935452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309522&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]136.1[/C][C]122.2[/C][C]13.9[/C][/ROW]
[ROW][C]3[/C][C]145.5[/C][C]124.408529637002[/C][C]21.0914703629978[/C][/ROW]
[ROW][C]4[/C][C]116.7[/C][C]127.759690599926[/C][C]-11.0596905999255[/C][/ROW]
[ROW][C]5[/C][C]137.1[/C][C]126.002449271436[/C][C]11.0975507285644[/C][/ROW]
[ROW][C]6[/C][C]125.5[/C][C]127.765706083102[/C][C]-2.26570608310249[/C][/ROW]
[ROW][C]7[/C][C]112.4[/C][C]127.405714785745[/C][C]-15.0057147857451[/C][/ROW]
[ROW][C]8[/C][C]106.3[/C][C]125.021501416772[/C][C]-18.7215014167724[/C][/ROW]
[ROW][C]9[/C][C]145.7[/C][C]122.046897767267[/C][C]23.6531022327327[/C][/ROW]
[ROW][C]10[/C][C]151.5[/C][C]125.805068795183[/C][C]25.6949312048166[/C][/ROW]
[ROW][C]11[/C][C]144.6[/C][C]129.887659952491[/C][C]14.7123400475094[/C][/ROW]
[ROW][C]12[/C][C]116.4[/C][C]132.225259882316[/C][C]-15.8252598823164[/C][/ROW]
[ROW][C]13[/C][C]137.7[/C][C]129.710831431715[/C][C]7.98916856828487[/C][/ROW]
[ROW][C]14[/C][C]138.8[/C][C]130.98020665172[/C][C]7.81979334828031[/C][/ROW]
[ROW][C]15[/C][C]149.5[/C][C]132.222670347037[/C][C]17.2773296529631[/C][/ROW]
[ROW][C]16[/C][C]125[/C][C]134.967813842492[/C][C]-9.96781384249203[/C][/ROW]
[ROW][C]17[/C][C]133.4[/C][C]133.384057562833[/C][C]0.0159424371672969[/C][/ROW]
[ROW][C]18[/C][C]134.4[/C][C]133.386590609233[/C][C]1.01340939076658[/C][/ROW]
[ROW][C]19[/C][C]124.8[/C][C]133.547608211674[/C][C]-8.74760821167401[/C][/ROW]
[ROW][C]20[/C][C]110.6[/C][C]132.157726773662[/C][C]-21.5577267736621[/C][/ROW]
[ROW][C]21[/C][C]142.4[/C][C]128.732483717113[/C][C]13.6675162828868[/C][/ROW]
[ROW][C]22[/C][C]149.6[/C][C]130.904074708118[/C][C]18.695925291882[/C][/ROW]
[ROW][C]23[/C][C]134.6[/C][C]133.874614643247[/C][C]0.725385356752497[/C][/ROW]
[ROW][C]24[/C][C]103.3[/C][C]133.989868964013[/C][C]-30.6898689640126[/C][/ROW]
[ROW][C]25[/C][C]136.5[/C][C]129.113647009859[/C][C]7.38635299014106[/C][/ROW]
[ROW][C]26[/C][C]137.1[/C][C]130.287242656484[/C][C]6.81275734351613[/C][/ROW]
[ROW][C]27[/C][C]140.7[/C][C]131.369701397697[/C][C]9.33029860230317[/C][/ROW]
[ROW][C]28[/C][C]131.4[/C][C]132.852164777932[/C][C]-1.45216477793184[/C][/ROW]
[ROW][C]29[/C][C]126.2[/C][C]132.621434637653[/C][C]-6.42143463765318[/C][/ROW]
[ROW][C]30[/C][C]125.3[/C][C]131.601151996694[/C][C]-6.3011519966942[/C][/ROW]
[ROW][C]31[/C][C]126.6[/C][C]130.599980706626[/C][C]-3.99998070662551[/C][/ROW]
[ROW][C]32[/C][C]107.7[/C][C]129.964435675113[/C][C]-22.2644356751133[/C][/ROW]
[ROW][C]33[/C][C]144.5[/C][C]126.426905744206[/C][C]18.0730942557944[/C][/ROW]
[ROW][C]34[/C][C]154.2[/C][C]129.298485909404[/C][C]24.9015140905961[/C][/ROW]
[ROW][C]35[/C][C]131.4[/C][C]133.255013382448[/C][C]-1.85501338244774[/C][/ROW]
[ROW][C]36[/C][C]105.7[/C][C]132.960275826176[/C][C]-27.2602758261764[/C][/ROW]
[ROW][C]37[/C][C]136.2[/C][C]128.628971720064[/C][C]7.57102827993623[/C][/ROW]
[ROW][C]38[/C][C]133.3[/C][C]129.831909873936[/C][C]3.46809012606423[/C][/ROW]
[ROW][C]39[/C][C]130[/C][C]130.382944393879[/C][C]-0.382944393878773[/C][/ROW]
[ROW][C]40[/C][C]129.3[/C][C]130.322099498684[/C][C]-1.02209949868413[/C][/ROW]
[ROW][C]41[/C][C]113.1[/C][C]130.159701150856[/C][C]-17.0597011508562[/C][/ROW]
[ROW][C]42[/C][C]117.7[/C][C]127.449136000492[/C][C]-9.74913600049166[/C][/ROW]
[ROW][C]43[/C][C]116.3[/C][C]125.900124792416[/C][C]-9.60012479241604[/C][/ROW]
[ROW][C]44[/C][C]97.3[/C][C]124.374789531771[/C][C]-27.0747895317707[/C][/ROW]
[ROW][C]45[/C][C]140.6[/C][C]120.072956791014[/C][C]20.5270432089856[/C][/ROW]
[ROW][C]46[/C][C]141.2[/C][C]123.334437603034[/C][C]17.8655623969662[/C][/ROW]
[ROW][C]47[/C][C]120.8[/C][C]126.173043648747[/C][C]-5.37304364874686[/C][/ROW]
[ROW][C]48[/C][C]106.2[/C][C]125.31933673226[/C][C]-19.1193367322602[/C][/ROW]
[ROW][C]49[/C][C]121.5[/C][C]122.281522213338[/C][C]-0.781522213337809[/C][/ROW]
[ROW][C]50[/C][C]122.6[/C][C]122.157348474479[/C][C]0.442651525520603[/C][/ROW]
[ROW][C]51[/C][C]137.2[/C][C]122.227680058147[/C][C]14.9723199418532[/C][/ROW]
[ROW][C]52[/C][C]118.9[/C][C]124.606587419748[/C][C]-5.70658741974835[/C][/ROW]
[ROW][C]53[/C][C]107.2[/C][C]123.699884726032[/C][C]-16.4998847260319[/C][/ROW]
[ROW][C]54[/C][C]127.4[/C][C]121.078267141531[/C][C]6.32173285846891[/C][/ROW]
[ROW][C]55[/C][C]111.8[/C][C]122.082708463484[/C][C]-10.2827084634836[/C][/ROW]
[ROW][C]56[/C][C]100[/C][C]120.448919514544[/C][C]-20.4489195145442[/C][/ROW]
[ROW][C]57[/C][C]138.3[/C][C]117.199851543858[/C][C]21.1001484561424[/C][/ROW]
[ROW][C]58[/C][C]128[/C][C]120.552391343177[/C][C]7.44760865682319[/C][/ROW]
[ROW][C]59[/C][C]121.2[/C][C]121.735719720399[/C][C]-0.535719720398987[/C][/ROW]
[ROW][C]60[/C][C]105.9[/C][C]121.650600808196[/C][C]-15.7506008081955[/C][/ROW]
[ROW][C]61[/C][C]112.5[/C][C]119.148034715714[/C][C]-6.64803471571419[/C][/ROW]
[ROW][C]62[/C][C]123.1[/C][C]118.091748262658[/C][C]5.00825173734152[/C][/ROW]
[ROW][C]63[/C][C]129[/C][C]118.887494477873[/C][C]10.1125055221267[/C][/ROW]
[ROW][C]64[/C][C]115.5[/C][C]120.494240387943[/C][C]-4.99424038794277[/C][/ROW]
[ROW][C]65[/C][C]105.7[/C][C]119.70072039434[/C][C]-14.0007203943395[/C][/ROW]
[ROW][C]66[/C][C]122.3[/C][C]117.4761875936[/C][C]4.82381240640005[/C][/ROW]
[ROW][C]67[/C][C]106.4[/C][C]118.242628792368[/C][C]-11.8426287923678[/C][/ROW]
[ROW][C]68[/C][C]101.1[/C][C]116.360988744313[/C][C]-15.2609887443131[/C][/ROW]
[ROW][C]69[/C][C]131.6[/C][C]113.936215655696[/C][C]17.6637843443036[/C][/ROW]
[ROW][C]70[/C][C]119.5[/C][C]116.742761787064[/C][C]2.75723821293596[/C][/ROW]
[ROW][C]71[/C][C]127[/C][C]117.180851161851[/C][C]9.81914883814862[/C][/ROW]
[ROW][C]72[/C][C]106.9[/C][C]118.740986501361[/C][C]-11.8409865013612[/C][/ROW]
[ROW][C]73[/C][C]115.9[/C][C]116.859607392038[/C][C]-0.959607392037526[/C][/ROW]
[ROW][C]74[/C][C]122.7[/C][C]116.707138229073[/C][C]5.9928617709266[/C][/ROW]
[ROW][C]75[/C][C]137.2[/C][C]117.659326202566[/C][C]19.5406737974339[/C][/ROW]
[ROW][C]76[/C][C]108.5[/C][C]120.764085713978[/C][C]-12.264085713978[/C][/ROW]
[ROW][C]77[/C][C]115.2[/C][C]118.815481629801[/C][C]-3.61548162980132[/C][/ROW]
[ROW][C]78[/C][C]129.4[/C][C]118.241028512431[/C][C]11.1589714875694[/C][/ROW]
[ROW][C]79[/C][C]112.3[/C][C]120.014044285723[/C][C]-7.71404428572264[/C][/ROW]
[ROW][C]80[/C][C]104.3[/C][C]118.788382744272[/C][C]-14.4883827442718[/C][/ROW]
[ROW][C]81[/C][C]140[/C][C]116.486366723915[/C][C]23.5136332760847[/C][/ROW]
[ROW][C]82[/C][C]139.9[/C][C]120.222377944335[/C][C]19.677622055665[/C][/ROW]
[ROW][C]83[/C][C]134.9[/C][C]123.348896756973[/C][C]11.5511032430272[/C][/ROW]
[ROW][C]84[/C][C]105.1[/C][C]125.184217178001[/C][C]-20.0842171780014[/C][/ROW]
[ROW][C]85[/C][C]127[/C][C]121.993095676303[/C][C]5.0069043236968[/C][/ROW]
[ROW][C]86[/C][C]135.5[/C][C]122.788627804974[/C][C]12.7113721950264[/C][/ROW]
[ROW][C]87[/C][C]143.9[/C][C]124.808299907109[/C][C]19.091700092891[/C][/ROW]
[ROW][C]88[/C][C]115.8[/C][C]127.841723322642[/C][C]-12.0417233226419[/C][/ROW]
[ROW][C]89[/C][C]117.5[/C][C]125.928449737129[/C][C]-8.42844973712857[/C][/ROW]
[ROW][C]90[/C][C]129.3[/C][C]124.5892784394[/C][C]4.71072156060036[/C][/ROW]
[ROW][C]91[/C][C]117.9[/C][C]125.337750970209[/C][C]-7.43775097020908[/C][/ROW]
[ROW][C]92[/C][C]108.1[/C][C]124.155988851479[/C][C]-16.055988851479[/C][/ROW]
[ROW][C]93[/C][C]131.7[/C][C]121.60490056156[/C][C]10.0950994384396[/C][/ROW]
[ROW][C]94[/C][C]143.7[/C][C]123.208880870789[/C][C]20.491119129211[/C][/ROW]
[ROW][C]95[/C][C]126.2[/C][C]126.464653812674[/C][C]-0.264653812674283[/C][/ROW]
[ROW][C]96[/C][C]96.9[/C][C]126.422603755923[/C][C]-29.5226037559234[/C][/ROW]
[ROW][C]97[/C][C]125.8[/C][C]121.731845097187[/C][C]4.06815490281252[/C][/ROW]
[ROW][C]98[/C][C]129.6[/C][C]122.378222123862[/C][C]7.22177787613791[/C][/ROW]
[ROW][C]99[/C][C]124.9[/C][C]123.525668920358[/C][C]1.37433107964171[/C][/ROW]
[ROW][C]100[/C][C]136.8[/C][C]123.74403229593[/C][C]13.0559677040703[/C][/ROW]
[ROW][C]101[/C][C]107.5[/C][C]125.818456153065[/C][C]-18.3184561530651[/C][/ROW]
[ROW][C]102[/C][C]114.3[/C][C]122.907891166146[/C][C]-8.60789116614644[/C][/ROW]
[ROW][C]103[/C][C]110.3[/C][C]121.540208953735[/C][C]-11.2402089537347[/C][/ROW]
[ROW][C]104[/C][C]85.5[/C][C]119.754285601186[/C][C]-34.2542856011864[/C][/ROW]
[ROW][C]105[/C][C]116.8[/C][C]114.311724094384[/C][C]2.48827590561633[/C][/ROW]
[ROW][C]106[/C][C]115.1[/C][C]114.707078848527[/C][C]0.392921151473018[/C][/ROW]
[ROW][C]107[/C][C]95.2[/C][C]114.769508921047[/C][C]-19.5695089210473[/C][/ROW]
[ROW][C]108[/C][C]83.4[/C][C]111.660167882651[/C][C]-28.2601678826508[/C][/ROW]
[ROW][C]109[/C][C]95.4[/C][C]107.169993903119[/C][C]-11.769993903119[/C][/ROW]
[ROW][C]110[/C][C]96.3[/C][C]105.299894596473[/C][C]-8.99989459647338[/C][/ROW]
[ROW][C]111[/C][C]100.5[/C][C]103.869928125523[/C][C]-3.36992812552319[/C][/ROW]
[ROW][C]112[/C][C]90.9[/C][C]103.33449027374[/C][C]-12.4344902737401[/C][/ROW]
[ROW][C]113[/C][C]80.6[/C][C]101.358811116145[/C][C]-20.7588111161451[/C][/ROW]
[ROW][C]114[/C][C]94.8[/C][C]98.0605053910417[/C][C]-3.26050539104166[/C][/ROW]
[ROW][C]115[/C][C]93.9[/C][C]97.542453391925[/C][C]-3.64245339192503[/C][/ROW]
[ROW][C]116[/C][C]75.9[/C][C]96.9637148115318[/C][C]-21.0637148115318[/C][/ROW]
[ROW][C]117[/C][C]101.6[/C][C]93.6169638455872[/C][C]7.98303615441282[/C][/ROW]
[ROW][C]118[/C][C]103.3[/C][C]94.8853647046002[/C][C]8.4146352953998[/C][/ROW]
[ROW][C]119[/C][C]91.8[/C][C]96.2223410667912[/C][C]-4.42234106679122[/C][/ROW]
[ROW][C]120[/C][C]83.5[/C][C]95.5196884544933[/C][C]-12.0196884544933[/C][/ROW]
[ROW][C]121[/C][C]92[/C][C]93.6099159236098[/C][C]-1.60991592360976[/C][/ROW]
[ROW][C]122[/C][C]101.2[/C][C]93.3541211732231[/C][C]7.84587882677685[/C][/ROW]
[ROW][C]123[/C][C]109.1[/C][C]94.6007295125947[/C][C]14.4992704874053[/C][/ROW]
[ROW][C]124[/C][C]99.8[/C][C]96.9044754540585[/C][C]2.89552454594154[/C][/ROW]
[ROW][C]125[/C][C]90.8[/C][C]97.3645367327908[/C][C]-6.56453673279078[/C][/ROW]
[ROW][C]126[/C][C]110.6[/C][C]96.3215170257722[/C][C]14.2784829742278[/C][/ROW]
[ROW][C]127[/C][C]97.8[/C][C]98.5901826962768[/C][C]-0.790182696276787[/C][/ROW]
[ROW][C]128[/C][C]81.9[/C][C]98.4646329190557[/C][C]-16.5646329190557[/C][/ROW]
[ROW][C]129[/C][C]114.4[/C][C]95.8327276868401[/C][C]18.5672723131599[/C][/ROW]
[ROW][C]130[/C][C]108.8[/C][C]98.7828263330202[/C][C]10.0171736669798[/C][/ROW]
[ROW][C]131[/C][C]103.1[/C][C]100.37442524831[/C][C]2.72557475169035[/C][/ROW]
[ROW][C]132[/C][C]90.4[/C][C]100.807483709962[/C][C]-10.4074837099624[/C][/ROW]
[ROW][C]133[/C][C]94.4[/C][C]99.1538695934106[/C][C]-4.7538695934106[/C][/ROW]
[ROW][C]134[/C][C]100.5[/C][C]98.3985414000659[/C][C]2.10145859993408[/C][/ROW]
[ROW][C]135[/C][C]115.1[/C][C]98.732435903583[/C][C]16.367564096417[/C][/ROW]
[ROW][C]136[/C][C]93.9[/C][C]101.333029456998[/C][C]-7.43302945699813[/C][/ROW]
[ROW][C]137[/C][C]102.5[/C][C]100.152017525452[/C][C]2.34798247454798[/C][/ROW]
[ROW][C]138[/C][C]97.1[/C][C]100.525081473812[/C][C]-3.42508147381182[/C][/ROW]
[ROW][C]139[/C][C]91.2[/C][C]99.980880470642[/C][C]-8.78088047064197[/C][/ROW]
[ROW][C]140[/C][C]82.3[/C][C]98.5857125024127[/C][C]-16.2857125024127[/C][/ROW]
[ROW][C]141[/C][C]107.1[/C][C]95.9981241051986[/C][C]11.1018758948014[/C][/ROW]
[ROW][C]142[/C][C]99.2[/C][C]97.7620681296583[/C][C]1.43793187034171[/C][/ROW]
[ROW][C]143[/C][C]94.8[/C][C]97.9905368456036[/C][C]-3.1905368456036[/C][/ROW]
[ROW][C]144[/C][C]81.1[/C][C]97.4836019404624[/C][C]-16.3836019404624[/C][/ROW]
[ROW][C]145[/C][C]92.5[/C][C]94.8804601817316[/C][C]-2.38046018173158[/C][/ROW]
[ROW][C]146[/C][C]97.7[/C][C]94.5022359471231[/C][C]3.19776405287691[/C][/ROW]
[ROW][C]147[/C][C]98.5[/C][C]95.0103191617216[/C][C]3.48968083827843[/C][/ROW]
[ROW][C]148[/C][C]81.2[/C][C]95.5647841656796[/C][C]-14.3647841656796[/C][/ROW]
[ROW][C]149[/C][C]86.2[/C][C]93.2824063556765[/C][C]-7.08240635567647[/C][/ROW]
[ROW][C]150[/C][C]92[/C][C]92.1571038853308[/C][C]-0.157103885330841[/C][/ROW]
[ROW][C]151[/C][C]86.3[/C][C]92.1321421164933[/C][C]-5.83214211649333[/C][/ROW]
[ROW][C]152[/C][C]74.8[/C][C]91.2054904106311[/C][C]-16.4054904106311[/C][/ROW]
[ROW][C]153[/C][C]90[/C][C]88.59887085801[/C][C]1.40112914199004[/C][/ROW]
[ROW][C]154[/C][C]101.1[/C][C]88.8214920979634[/C][C]12.2785079020366[/C][/ROW]
[ROW][C]155[/C][C]87.8[/C][C]90.7723876806838[/C][C]-2.97238768068378[/C][/ROW]
[ROW][C]156[/C][C]66.3[/C][C]90.3001138471981[/C][C]-24.0001138471981[/C][/ROW]
[ROW][C]157[/C][C]88.6[/C][C]86.4868071764813[/C][C]2.11319282351872[/C][/ROW]
[ROW][C]158[/C][C]90[/C][C]86.8225660958656[/C][C]3.17743390413445[/C][/ROW]
[ROW][C]159[/C][C]92[/C][C]87.3274191136279[/C][C]4.6725808863721[/C][/ROW]
[ROW][C]160[/C][C]85.1[/C][C]88.0698315862065[/C][C]-2.96983158620652[/C][/ROW]
[ROW][C]161[/C][C]85.9[/C][C]87.5979638829661[/C][C]-1.69796388296605[/C][/ROW]
[ROW][C]162[/C][C]88.5[/C][C]87.3281794543265[/C][C]1.1718205456735[/C][/ROW]
[ROW][C]163[/C][C]92.3[/C][C]87.5143665337774[/C][C]4.78563346622256[/C][/ROW]
[ROW][C]164[/C][C]68[/C][C]88.2747415943517[/C][C]-20.2747415943517[/C][/ROW]
[ROW][C]165[/C][C]93.6[/C][C]85.0533482350936[/C][C]8.54665176490639[/C][/ROW]
[ROW][C]166[/C][C]97.7[/C][C]86.4113003012758[/C][C]11.2886996987242[/C][/ROW]
[ROW][C]167[/C][C]85.1[/C][C]88.2049282039989[/C][C]-3.10492820399887[/C][/ROW]
[ROW][C]168[/C][C]69.9[/C][C]87.7115954011718[/C][C]-17.8115954011718[/C][/ROW]
[ROW][C]169[/C][C]96.1[/C][C]84.8815640108279[/C][C]11.2184359891721[/C][/ROW]
[ROW][C]170[/C][C]97[/C][C]86.6640279218278[/C][C]10.3359720781722[/C][/ROW]
[ROW][C]171[/C][C]95.9[/C][C]88.3062797680056[/C][C]7.59372023199444[/C][/ROW]
[ROW][C]172[/C][C]91.3[/C][C]89.5128233786144[/C][C]1.78717662138558[/C][/ROW]
[ROW][C]173[/C][C]83.5[/C][C]89.7967825537862[/C][C]-6.29678255378617[/C][/ROW]
[ROW][C]174[/C][C]91.4[/C][C]88.7963055114987[/C][C]2.60369448850126[/C][/ROW]
[ROW][C]175[/C][C]96.8[/C][C]89.2099987808192[/C][C]7.59000121918081[/C][/ROW]
[ROW][C]176[/C][C]71[/C][C]90.4159514885489[/C][C]-19.4159514885489[/C][/ROW]
[ROW][C]177[/C][C]106.9[/C][C]87.3310087336527[/C][C]19.5689912663473[/C][/ROW]
[ROW][C]178[/C][C]102.7[/C][C]90.4402675234344[/C][C]12.2597324765656[/C][/ROW]
[ROW][C]179[/C][C]84.9[/C][C]92.3881799346728[/C][C]-7.48817993467277[/C][/ROW]
[ROW][C]180[/C][C]75.8[/C][C]91.1984053078433[/C][C]-15.3984053078433[/C][/ROW]
[ROW][C]181[/C][C]93.6[/C][C]88.7517985103653[/C][C]4.84820148963472[/C][/ROW]
[ROW][C]182[/C][C]100.7[/C][C]89.5221148179924[/C][C]11.1778851820076[/C][/ROW]
[ROW][C]183[/C][C]100.5[/C][C]91.2981357319112[/C][C]9.20186426808883[/C][/ROW]
[ROW][C]184[/C][C]95.9[/C][C]92.760192562972[/C][C]3.139807437028[/C][/ROW]
[ROW][C]185[/C][C]85.7[/C][C]93.259067223343[/C][C]-7.55906722334295[/C][/ROW]
[ROW][C]186[/C][C]104.1[/C][C]92.0580295261599[/C][C]12.0419704738401[/C][/ROW]
[ROW][C]187[/C][C]93.5[/C][C]93.9713423807916[/C][C]-0.47134238079164[/C][/ROW]
[ROW][C]188[/C][C]81.5[/C][C]93.8964521925072[/C][C]-12.3964521925072[/C][/ROW]
[ROW][C]189[/C][C]102.1[/C][C]91.9268167924473[/C][C]10.1731832075527[/C][/ROW]
[ROW][C]190[/C][C]98.2[/C][C]93.5432035993921[/C][C]4.65679640060789[/C][/ROW]
[ROW][C]191[/C][C]88.4[/C][C]94.2831081219984[/C][C]-5.88310812199842[/C][/ROW]
[ROW][C]192[/C][C]77.8[/C][C]93.3483585791839[/C][C]-15.5483585791839[/C][/ROW]
[ROW][C]193[/C][C]90.1[/C][C]90.8779261526468[/C][C]-0.777926152646842[/C][/ROW]
[ROW][C]194[/C][C]101[/C][C]90.7543237811706[/C][C]10.2456762188294[/C][/ROW]
[ROW][C]195[/C][C]98.6[/C][C]92.3822287869557[/C][C]6.21777121304424[/C][/ROW]
[ROW][C]196[/C][C]91.5[/C][C]93.3701519524311[/C][C]-1.8701519524311[/C][/ROW]
[ROW][C]197[/C][C]86.4[/C][C]93.0730090738238[/C][C]-6.67300907382378[/C][/ROW]
[ROW][C]198[/C][C]98.9[/C][C]92.0127545193256[/C][C]6.88724548067439[/C][/ROW]
[ROW][C]199[/C][C]85.2[/C][C]93.1070484589931[/C][C]-7.90704845899315[/C][/ROW]
[ROW][C]200[/C][C]77.3[/C][C]91.8507210587846[/C][C]-14.5507210587846[/C][/ROW]
[ROW][C]201[/C][C]93[/C][C]89.5388002891387[/C][C]3.46119971086131[/C][/ROW]
[ROW][C]202[/C][C]86.8[/C][C]90.0887400115143[/C][C]-3.28874001151428[/C][/ROW]
[ROW][C]203[/C][C]91.3[/C][C]89.5662018975701[/C][C]1.73379810242992[/C][/ROW]
[ROW][C]204[/C][C]74.9[/C][C]89.8416799187064[/C][C]-14.9416799187064[/C][/ROW]
[ROW][C]205[/C][C]93.9[/C][C]87.4676408592054[/C][C]6.43235914079462[/C][/ROW]
[ROW][C]206[/C][C]95[/C][C]88.4896592619598[/C][C]6.51034073804016[/C][/ROW]
[ROW][C]207[/C][C]103.1[/C][C]89.5240679286465[/C][C]13.5759320713535[/C][/ROW]
[ROW][C]208[/C][C]81.4[/C][C]91.6811073768129[/C][C]-10.2811073768129[/C][/ROW]
[ROW][C]209[/C][C]93.1[/C][C]90.0475728197702[/C][C]3.05242718022978[/C][/ROW]
[ROW][C]210[/C][C]97.2[/C][C]90.5325638911607[/C][C]6.66743610883925[/C][/ROW]
[ROW][C]211[/C][C]86.4[/C][C]91.5919329738363[/C][C]-5.19193297383629[/C][/ROW]
[ROW][C]212[/C][C]75.5[/C][C]90.7670021935452[/C][C]-15.2670021935452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309522&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
2136.1122.213.9
3145.5124.40852963700221.0914703629978
4116.7127.759690599926-11.0596905999255
5137.1126.00244927143611.0975507285644
6125.5127.765706083102-2.26570608310249
7112.4127.405714785745-15.0057147857451
8106.3125.021501416772-18.7215014167724
9145.7122.04689776726723.6531022327327
10151.5125.80506879518325.6949312048166
11144.6129.88765995249114.7123400475094
12116.4132.225259882316-15.8252598823164
13137.7129.7108314317157.98916856828487
14138.8130.980206651727.81979334828031
15149.5132.22267034703717.2773296529631
16125134.967813842492-9.96781384249203
17133.4133.3840575628330.0159424371672969
18134.4133.3865906092331.01340939076658
19124.8133.547608211674-8.74760821167401
20110.6132.157726773662-21.5577267736621
21142.4128.73248371711313.6675162828868
22149.6130.90407470811818.695925291882
23134.6133.8746146432470.725385356752497
24103.3133.989868964013-30.6898689640126
25136.5129.1136470098597.38635299014106
26137.1130.2872426564846.81275734351613
27140.7131.3697013976979.33029860230317
28131.4132.852164777932-1.45216477793184
29126.2132.621434637653-6.42143463765318
30125.3131.601151996694-6.3011519966942
31126.6130.599980706626-3.99998070662551
32107.7129.964435675113-22.2644356751133
33144.5126.42690574420618.0730942557944
34154.2129.29848590940424.9015140905961
35131.4133.255013382448-1.85501338244774
36105.7132.960275826176-27.2602758261764
37136.2128.6289717200647.57102827993623
38133.3129.8319098739363.46809012606423
39130130.382944393879-0.382944393878773
40129.3130.322099498684-1.02209949868413
41113.1130.159701150856-17.0597011508562
42117.7127.449136000492-9.74913600049166
43116.3125.900124792416-9.60012479241604
4497.3124.374789531771-27.0747895317707
45140.6120.07295679101420.5270432089856
46141.2123.33443760303417.8655623969662
47120.8126.173043648747-5.37304364874686
48106.2125.31933673226-19.1193367322602
49121.5122.281522213338-0.781522213337809
50122.6122.1573484744790.442651525520603
51137.2122.22768005814714.9723199418532
52118.9124.606587419748-5.70658741974835
53107.2123.699884726032-16.4998847260319
54127.4121.0782671415316.32173285846891
55111.8122.082708463484-10.2827084634836
56100120.448919514544-20.4489195145442
57138.3117.19985154385821.1001484561424
58128120.5523913431777.44760865682319
59121.2121.735719720399-0.535719720398987
60105.9121.650600808196-15.7506008081955
61112.5119.148034715714-6.64803471571419
62123.1118.0917482626585.00825173734152
63129118.88749447787310.1125055221267
64115.5120.494240387943-4.99424038794277
65105.7119.70072039434-14.0007203943395
66122.3117.47618759364.82381240640005
67106.4118.242628792368-11.8426287923678
68101.1116.360988744313-15.2609887443131
69131.6113.93621565569617.6637843443036
70119.5116.7427617870642.75723821293596
71127117.1808511618519.81914883814862
72106.9118.740986501361-11.8409865013612
73115.9116.859607392038-0.959607392037526
74122.7116.7071382290735.9928617709266
75137.2117.65932620256619.5406737974339
76108.5120.764085713978-12.264085713978
77115.2118.815481629801-3.61548162980132
78129.4118.24102851243111.1589714875694
79112.3120.014044285723-7.71404428572264
80104.3118.788382744272-14.4883827442718
81140116.48636672391523.5136332760847
82139.9120.22237794433519.677622055665
83134.9123.34889675697311.5511032430272
84105.1125.184217178001-20.0842171780014
85127121.9930956763035.0069043236968
86135.5122.78862780497412.7113721950264
87143.9124.80829990710919.091700092891
88115.8127.841723322642-12.0417233226419
89117.5125.928449737129-8.42844973712857
90129.3124.58927843944.71072156060036
91117.9125.337750970209-7.43775097020908
92108.1124.155988851479-16.055988851479
93131.7121.6049005615610.0950994384396
94143.7123.20888087078920.491119129211
95126.2126.464653812674-0.264653812674283
9696.9126.422603755923-29.5226037559234
97125.8121.7318450971874.06815490281252
98129.6122.3782221238627.22177787613791
99124.9123.5256689203581.37433107964171
100136.8123.7440322959313.0559677040703
101107.5125.818456153065-18.3184561530651
102114.3122.907891166146-8.60789116614644
103110.3121.540208953735-11.2402089537347
10485.5119.754285601186-34.2542856011864
105116.8114.3117240943842.48827590561633
106115.1114.7070788485270.392921151473018
10795.2114.769508921047-19.5695089210473
10883.4111.660167882651-28.2601678826508
10995.4107.169993903119-11.769993903119
11096.3105.299894596473-8.99989459647338
111100.5103.869928125523-3.36992812552319
11290.9103.33449027374-12.4344902737401
11380.6101.358811116145-20.7588111161451
11494.898.0605053910417-3.26050539104166
11593.997.542453391925-3.64245339192503
11675.996.9637148115318-21.0637148115318
117101.693.61696384558727.98303615441282
118103.394.88536470460028.4146352953998
11991.896.2223410667912-4.42234106679122
12083.595.5196884544933-12.0196884544933
1219293.6099159236098-1.60991592360976
122101.293.35412117322317.84587882677685
123109.194.600729512594714.4992704874053
12499.896.90447545405852.89552454594154
12590.897.3645367327908-6.56453673279078
126110.696.321517025772214.2784829742278
12797.898.5901826962768-0.790182696276787
12881.998.4646329190557-16.5646329190557
129114.495.832727686840118.5672723131599
130108.898.782826333020210.0171736669798
131103.1100.374425248312.72557475169035
13290.4100.807483709962-10.4074837099624
13394.499.1538695934106-4.7538695934106
134100.598.39854140006592.10145859993408
135115.198.73243590358316.367564096417
13693.9101.333029456998-7.43302945699813
137102.5100.1520175254522.34798247454798
13897.1100.525081473812-3.42508147381182
13991.299.980880470642-8.78088047064197
14082.398.5857125024127-16.2857125024127
141107.195.998124105198611.1018758948014
14299.297.76206812965831.43793187034171
14394.897.9905368456036-3.1905368456036
14481.197.4836019404624-16.3836019404624
14592.594.8804601817316-2.38046018173158
14697.794.50223594712313.19776405287691
14798.595.01031916172163.48968083827843
14881.295.5647841656796-14.3647841656796
14986.293.2824063556765-7.08240635567647
1509292.1571038853308-0.157103885330841
15186.392.1321421164933-5.83214211649333
15274.891.2054904106311-16.4054904106311
1539088.598870858011.40112914199004
154101.188.821492097963412.2785079020366
15587.890.7723876806838-2.97238768068378
15666.390.3001138471981-24.0001138471981
15788.686.48680717648132.11319282351872
1589086.82256609586563.17743390413445
1599287.32741911362794.6725808863721
16085.188.0698315862065-2.96983158620652
16185.987.5979638829661-1.69796388296605
16288.587.32817945432651.1718205456735
16392.387.51436653377744.78563346622256
1646888.2747415943517-20.2747415943517
16593.685.05334823509368.54665176490639
16697.786.411300301275811.2886996987242
16785.188.2049282039989-3.10492820399887
16869.987.7115954011718-17.8115954011718
16996.184.881564010827911.2184359891721
1709786.664027921827810.3359720781722
17195.988.30627976800567.59372023199444
17291.389.51282337861441.78717662138558
17383.589.7967825537862-6.29678255378617
17491.488.79630551149872.60369448850126
17596.889.20999878081927.59000121918081
1767190.4159514885489-19.4159514885489
177106.987.331008733652719.5689912663473
178102.790.440267523434412.2597324765656
17984.992.3881799346728-7.48817993467277
18075.891.1984053078433-15.3984053078433
18193.688.75179851036534.84820148963472
182100.789.522114817992411.1778851820076
183100.591.29813573191129.20186426808883
18495.992.7601925629723.139807437028
18585.793.259067223343-7.55906722334295
186104.192.058029526159912.0419704738401
18793.593.9713423807916-0.47134238079164
18881.593.8964521925072-12.3964521925072
189102.191.926816792447310.1731832075527
19098.293.54320359939214.65679640060789
19188.494.2831081219984-5.88310812199842
19277.893.3483585791839-15.5483585791839
19390.190.8779261526468-0.777926152646842
19410190.754323781170610.2456762188294
19598.692.38222878695576.21777121304424
19691.593.3701519524311-1.8701519524311
19786.493.0730090738238-6.67300907382378
19898.992.01275451932566.88724548067439
19985.293.1070484589931-7.90704845899315
20077.391.8507210587846-14.5507210587846
2019389.53880028913873.46119971086131
20286.890.0887400115143-3.28874001151428
20391.389.56620189757011.73379810242992
20474.989.8416799187064-14.9416799187064
20593.987.46764085920546.43235914079462
2069588.48965926195986.51034073804016
207103.189.524067928646513.5759320713535
20881.491.6811073768129-10.2811073768129
20993.190.04757281977023.05242718022978
21097.290.53256389116076.66743610883925
21186.491.5919329738363-5.19193297383629
21275.590.7670021935452-15.2670021935452







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21388.341273645874564.110073275382112.572474016367
21488.341273645874563.8061202743294112.87642701742
21588.341273645874563.5058869862001113.176660305549
21688.341273645874563.2092401008981113.473307190851
21788.341273645874562.9160540858371113.766493205912
21888.341273645874562.6262105651352114.056336726614
21988.341273645874562.3395977611034114.342949530646
22088.341273645874562.0561099905541114.626437301195
22188.341273645874561.775647209495114.906900082254
22288.341273645874561.4981146006437115.184432691105
22388.341273645874561.223422198943115.459125092806
22488.341273645874560.9514845508826115.731062740866

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 88.3412736458745 & 64.110073275382 & 112.572474016367 \tabularnewline
214 & 88.3412736458745 & 63.8061202743294 & 112.87642701742 \tabularnewline
215 & 88.3412736458745 & 63.5058869862001 & 113.176660305549 \tabularnewline
216 & 88.3412736458745 & 63.2092401008981 & 113.473307190851 \tabularnewline
217 & 88.3412736458745 & 62.9160540858371 & 113.766493205912 \tabularnewline
218 & 88.3412736458745 & 62.6262105651352 & 114.056336726614 \tabularnewline
219 & 88.3412736458745 & 62.3395977611034 & 114.342949530646 \tabularnewline
220 & 88.3412736458745 & 62.0561099905541 & 114.626437301195 \tabularnewline
221 & 88.3412736458745 & 61.775647209495 & 114.906900082254 \tabularnewline
222 & 88.3412736458745 & 61.4981146006437 & 115.184432691105 \tabularnewline
223 & 88.3412736458745 & 61.223422198943 & 115.459125092806 \tabularnewline
224 & 88.3412736458745 & 60.9514845508826 & 115.731062740866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309522&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]88.3412736458745[/C][C]64.110073275382[/C][C]112.572474016367[/C][/ROW]
[ROW][C]214[/C][C]88.3412736458745[/C][C]63.8061202743294[/C][C]112.87642701742[/C][/ROW]
[ROW][C]215[/C][C]88.3412736458745[/C][C]63.5058869862001[/C][C]113.176660305549[/C][/ROW]
[ROW][C]216[/C][C]88.3412736458745[/C][C]63.2092401008981[/C][C]113.473307190851[/C][/ROW]
[ROW][C]217[/C][C]88.3412736458745[/C][C]62.9160540858371[/C][C]113.766493205912[/C][/ROW]
[ROW][C]218[/C][C]88.3412736458745[/C][C]62.6262105651352[/C][C]114.056336726614[/C][/ROW]
[ROW][C]219[/C][C]88.3412736458745[/C][C]62.3395977611034[/C][C]114.342949530646[/C][/ROW]
[ROW][C]220[/C][C]88.3412736458745[/C][C]62.0561099905541[/C][C]114.626437301195[/C][/ROW]
[ROW][C]221[/C][C]88.3412736458745[/C][C]61.775647209495[/C][C]114.906900082254[/C][/ROW]
[ROW][C]222[/C][C]88.3412736458745[/C][C]61.4981146006437[/C][C]115.184432691105[/C][/ROW]
[ROW][C]223[/C][C]88.3412736458745[/C][C]61.223422198943[/C][C]115.459125092806[/C][/ROW]
[ROW][C]224[/C][C]88.3412736458745[/C][C]60.9514845508826[/C][C]115.731062740866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309522&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309522&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
21388.341273645874564.110073275382112.572474016367
21488.341273645874563.8061202743294112.87642701742
21588.341273645874563.5058869862001113.176660305549
21688.341273645874563.2092401008981113.473307190851
21788.341273645874562.9160540858371113.766493205912
21888.341273645874562.6262105651352114.056336726614
21988.341273645874562.3395977611034114.342949530646
22088.341273645874562.0561099905541114.626437301195
22188.341273645874561.775647209495114.906900082254
22288.341273645874561.4981146006437115.184432691105
22388.341273645874561.223422198943115.459125092806
22488.341273645874560.9514845508826115.731062740866



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')