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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 computationWed, 20 Dec 2017 15:50:58 +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/20/t1513781896phpqd9jjjcwen8k.htm/, Retrieved Tue, 14 May 2024 22:46:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310513, Retrieved Tue, 14 May 2024 22:46:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [dataset 3 - doubl...] [2017-12-20 14:50:58] [6bf860cf1a792f74e81bfd3c0354928d] [Current]
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Dataseries X:
46.8
52.8
58.3
54.5
64.7
58.3
57.5
56.7
56
66.2
58.2
53.9
53.1
54.4
59.2
57.8
61.5
60.1
60.1
58.4
56.8
63.8
53.9
63.1
55.7
54.9
64.6
60.2
63.9
69.9
58.5
52
66.7
72
68.4
70.8
56.5
62.6
66.5
69.2
63.7
73.6
64.1
53.8
72.2
80.2
69.1
72
66.3
72.5
88.9
88.6
73.7
86
70
71.6
90.5
85.7
84.8
81.1
70.8
65.7
86.2
76.1
79.8
85.2
75.8
69.4
85
75
77.7
68.5
68.4
65
73.2
67.9
76.5
85.5
71.7
57.9
75.5
78.2
75.7
67.1
74.6
66.2
74.9
69.5
76.1
82.3
82.1
60.5
71.2
81.4
74.5
61.4
83.8
85.4
91.6
91.9
86.3
96.8
81
70.8
98.8
94.5
84.5
92.8
81.2
75.7
86.7
87.5
87.8
103.1
96.4
77.1
106.5
95.7
95.3
86.6
89.6
81.9
98.4
92.9
83.9
121.8
103.9
87.5
118.9
109
112.2
100.1
111.3
102.7
122.6
124.8
120.3
118.3
108.7
100.7
124
103.1
115
112.7
101.7
111.5
114.4
112.5
107.2
136.7
107.8
94.6
110.7
126.6
127.9
109.2
87.1
90.8
94.5
103.3
103.2
105.4
103.9
79.8
105.6
113
87.7
110
90.3
108.9
105.1
113
100.4
110.1
114.7
88.6
117.2
127.7
107.8
102.8
100.2
108.4
114.2
94.4
92.2
115.3
102
86.3
112
112.5
109.5
105.9
115.3
126.2
112.2
112.5
106.9
90.6
75.6
78.8
101.8
93.9
100
89.2
97.7
121.1
108.8
92.9
113.6
112.6
98.8
78




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=310513&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=310513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310513&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
alpha0.334390833260281
beta0.102714459560635
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.334390833260281 \tabularnewline
beta & 0.102714459560635 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310513&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]0.334390833260281[/C][/ROW]
[ROW][C]beta[/C][C]0.102714459560635[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310513&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
alpha0.334390833260281
beta0.102714459560635
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
358.358.8-0.5
454.564.6156311965097-10.1156311965097
564.766.8684441691498-2.16844416914981
658.371.7042445727411-13.4042445727411
757.572.322503761797-14.822503761797
856.771.9574048961697-15.2574048961697
95670.9228364443051-14.9228364443051
1066.269.4875933292236-3.28759332922361
1158.271.8301506304168-13.6301506304168
1253.970.2460998781444-16.3460998781444
1353.167.1924248001067-14.0924248001067
1454.464.4083286835315-10.0083286835315
1559.262.6461630698807-3.44616306988068
1657.862.9599609006059-5.15996090060591
1761.562.5234524372162-1.02345243721623
1860.163.435002196413-3.33500219641301
1960.163.4590443397123-3.35904433971228
2058.463.3596746748276-4.9596746748276
2156.862.5547200746591-5.75472007465911
2263.861.28625351253292.51374648746712
2353.962.8690254556962-8.96902545569618
2463.160.30400663282842.79599336717161
2555.761.7691356089681-6.06913560896812
2654.960.0613914923772-5.16139149237721
2764.658.47991154164946.12008845835061
2860.260.8810603654821-0.681060365482139
2963.960.98457514072322.91542485927683
3069.962.39085704501997.50914295498007
3158.565.5911510050103-7.09115100501027
325263.6656823428884-11.6656823428884
3366.759.80985378319346.8901462168066
347262.39557849041869.60442150958141
3568.466.21881286679712.18118713320291
3670.867.63470245547793.16529754452209
3756.569.4883873031392-12.9883873031392
3862.665.4943188146737-2.8943188146737
3966.564.77620378565041.72379621434965
4069.265.66155092778823.53844907221178
4163.767.275235660749-3.57523566074904
4273.666.38737161806747.21262838193255
4364.169.3546009366801-5.25460093668008
4453.867.9724244656319-14.1724244656319
4572.263.12143249767949.07856750232064
4680.266.357178611725813.8428213882742
4769.171.6615038064343-2.56150380643426
487271.39239363858810.607606361411939
4966.372.2038741786681-5.90387417866806
5072.570.63519628470441.86480371529559
5188.971.728343056276117.1716569437239
5288.678.529752248944510.0702477510554
5373.783.3023958251678-9.6023958251678
548681.16687640692494.8331235930751
557084.0244645579071-14.0244645579071
5671.680.0945529830835-8.49455298308351
5790.577.722032658455312.7779673415447
5885.782.90173008361192.79826991638809
5984.884.8404197147116-0.0404197147116321
6081.185.8284892679055-4.72848926790554
6170.885.0865029859009-14.2865029859009
6265.780.6577092471106-14.9577092471106
6386.275.490721232459410.7092787675406
6476.179.274367901846-3.17436790184604
6579.878.30642109673531.49357890326472
6685.278.95069253002416.24930746997589
6775.881.3998795510754-5.59987955107545
6869.479.6944692548985-10.2944692548984
698576.06564938977578.93435061022427
707579.173636740711-4.17363674071098
7177.777.7550823222776-0.0550823222775847
7268.577.7118428475927-9.21184284759269
7368.474.290269509049-5.89026950904903
746571.7770880929369-6.77708809293689
7573.268.73459156039674.46540843960327
7667.969.6048551845425-1.70485518454254
7776.568.35328293872528.14671706127484
7885.570.675799592577914.8242004074221
7971.775.7403689236095-4.04036892360951
8057.974.3580255597751-16.4580255597751
8175.568.25805156644777.24194843355228
8278.270.33186918913787.86813081086218
8375.772.88532136731232.81467863268766
8467.173.8456205908786-6.74562059087859
8574.671.37735308682063.22264691317942
8666.272.3530703839135-6.1530703839135
8774.969.9822956454574.91770435454303
8869.571.4823937753189-1.9823937753189
8976.170.6070735115335.49292648846695
9082.372.4200961228049.87990387719603
9182.176.0394265814356.06057341856501
9260.578.5897690893311-18.0897690893311
9371.272.4431332369258-1.2431332369258
9481.471.88716036884599.51283963115411
9574.575.2546215808975-0.754621580897535
9661.475.1628190661-13.7628190661
9783.870.248486122793813.5515138772062
9885.474.933266513057110.4667334869429
9991.678.946023144862712.6539768551373
10091.984.12479718880797.77520281119207
10186.387.9392070464956-1.6392070464956
10296.888.54922307371058.25077692628952
1038192.7497466506202-11.7497466506202
10470.889.8587125935248-19.0587125935248
10598.883.869022035659414.9309779643406
10694.589.75800334726254.74199665273748
10784.592.4027549940195-7.90275499401955
10892.890.54778346370122.25221653629885
10981.292.1658976968819-10.9658976968819
11075.788.9873524906643-13.2873524906643
11186.784.57615639223822.1238436077618
11287.585.39127017451562.10872982548436
11387.886.27375811269691.5262418873031
114103.187.013888908611416.0861110913886
11596.493.17521251753733.22478748246274
11677.195.1465884540007-18.0465884540007
117106.589.385169176423417.1148308235766
11895.795.9692454112489-0.269245411248889
11995.396.7309981972355-1.43099819723545
12086.697.0551213297988-10.4551213297988
12189.694.0025607220874-4.40256072208743
12281.992.8227071424353-10.9227071424353
12398.489.0874166176699.31258338233097
12492.992.43847894692810.461521053071877
12583.992.8456789278446-8.94567892784463
126121.889.799942258586732.0000577414133
127103.9101.5451833349012.35481666509925
12887.5103.458207900653-15.9582079006533
129118.998.699411966601720.2005880333983
130109106.7256109608272.27438903917256
131112.2108.8355712618653.36442873813506
132100.1111.425588118692-11.3255881186923
133111.3108.7144005857952.58559941420516
134102.7110.743793641674-8.04379364167418
135122.6108.94253673648313.6574632635168
136124.8114.8670710109219.93292898907947
137120.3119.8873192301910.412680769809384
138118.3121.738257967594-3.43825796759366
139108.7122.183385023357-13.4833850233571
140100.7118.806402898357-18.1064028983566
141124113.26162945071810.7383705492817
142103.1117.731112214821-14.6311122148214
143115113.2147409975341.78525900246592
144112.7114.249171717695-1.54917171769547
145101.7114.115390320452-12.4153903204517
146111.5109.9216164282571.57838357174253
147114.4110.4614446317133.93855536828742
148112.5111.9257693188710.574230681128569
149107.2112.284817641801-5.0848176418011
150136.7110.57688499961426.1231150003861
151107.8120.201843677768-12.4018436777676
15294.6116.5184460037-21.9184460037
153110.7108.8999558428661.80004415713384
154126.6109.27453707994117.325462920059
155127.9115.43574978838112.464250211619
156109.2120.399524310203-11.1995243102027
15787.1117.065682024331-29.9656820243308
15890.8106.427384123472-15.6273841234719
15994.5100.046931378885-5.5469313788852
160103.396.84677043028886.45322956971117
161103.297.88100091634755.31899908365253
162105.498.71864558300886.68135441699124
163103.9100.2413323530883.65866764691229
16479.8100.878923805222-21.0789238052216
165105.692.520498412617413.0795015873826
16611396.033576031302216.9664239686978
16787.7101.42914678879-13.7291467887896
16811096.088848165152713.9111518348473
16990.3100.469015214098-10.1690152140978
170108.996.447722273981812.4522777260182
171105.1100.4184778948954.68152210510516
172113101.9515592490811.0484407509204
173100.4105.993158128974-5.59315812897363
174110.1104.2778519559985.82214804400152
175114.7106.5796915275598.12030847244053
17688.6109.928921277394-21.3289212773945
177117.2102.69801891949514.5019810805054
178127.7107.9467381201919.7532618798103
179107.8115.629898299073-7.82989829907297
180102.8113.820570816656-11.0205708166559
181100.2110.565790640315-10.3657906403148
182108.4107.1739314871871.22606851281287
183114.2107.7003952730856.49960472691511
18494.4110.213521680672-15.8135216806717
18592.2104.722199705296-12.5221997052956
186115.399.901368468034415.3986315319656
187102104.945900566352-2.94590056635225
18886.3103.755007110388-17.4550071103885
18911297.112878247794414.8871217522056
190112.5101.79698540714510.703014592855
191109.5105.4495795073774.0504204926234
192105.9107.016725999222-1.11672599922173
193115.3106.8176701348788.48232986512207
194126.2110.11979122402316.0802087759772
195112.2116.514876665384-4.31487666538395
196112.5115.941830399136-3.44183039913649
197106.9115.542507031431-8.64250703143129
19890.6113.107282837751-22.5072828377506
19975.6105.262752158539-29.6627521585394
20078.894.0066782944688-15.2066782944688
201101.887.062282677058514.7377173229415
20293.990.63721150367523.26278849632477
20310090.48709557653799.51290442346215
20489.292.7536986979053-3.55369869790535
20597.790.52889142859017.17110857140992
206121.192.136665842043428.9633341579566
207108.8102.0263578124896.77364218751137
20892.9104.728672950625-11.8286729506248
209113.6100.80426767590212.7957323240979
210112.6105.5535299222557.04647007774517
21198.8108.622315088705-9.82231508870539
21278105.712968293496-27.712968293496

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 58.3 & 58.8 & -0.5 \tabularnewline
4 & 54.5 & 64.6156311965097 & -10.1156311965097 \tabularnewline
5 & 64.7 & 66.8684441691498 & -2.16844416914981 \tabularnewline
6 & 58.3 & 71.7042445727411 & -13.4042445727411 \tabularnewline
7 & 57.5 & 72.322503761797 & -14.822503761797 \tabularnewline
8 & 56.7 & 71.9574048961697 & -15.2574048961697 \tabularnewline
9 & 56 & 70.9228364443051 & -14.9228364443051 \tabularnewline
10 & 66.2 & 69.4875933292236 & -3.28759332922361 \tabularnewline
11 & 58.2 & 71.8301506304168 & -13.6301506304168 \tabularnewline
12 & 53.9 & 70.2460998781444 & -16.3460998781444 \tabularnewline
13 & 53.1 & 67.1924248001067 & -14.0924248001067 \tabularnewline
14 & 54.4 & 64.4083286835315 & -10.0083286835315 \tabularnewline
15 & 59.2 & 62.6461630698807 & -3.44616306988068 \tabularnewline
16 & 57.8 & 62.9599609006059 & -5.15996090060591 \tabularnewline
17 & 61.5 & 62.5234524372162 & -1.02345243721623 \tabularnewline
18 & 60.1 & 63.435002196413 & -3.33500219641301 \tabularnewline
19 & 60.1 & 63.4590443397123 & -3.35904433971228 \tabularnewline
20 & 58.4 & 63.3596746748276 & -4.9596746748276 \tabularnewline
21 & 56.8 & 62.5547200746591 & -5.75472007465911 \tabularnewline
22 & 63.8 & 61.2862535125329 & 2.51374648746712 \tabularnewline
23 & 53.9 & 62.8690254556962 & -8.96902545569618 \tabularnewline
24 & 63.1 & 60.3040066328284 & 2.79599336717161 \tabularnewline
25 & 55.7 & 61.7691356089681 & -6.06913560896812 \tabularnewline
26 & 54.9 & 60.0613914923772 & -5.16139149237721 \tabularnewline
27 & 64.6 & 58.4799115416494 & 6.12008845835061 \tabularnewline
28 & 60.2 & 60.8810603654821 & -0.681060365482139 \tabularnewline
29 & 63.9 & 60.9845751407232 & 2.91542485927683 \tabularnewline
30 & 69.9 & 62.3908570450199 & 7.50914295498007 \tabularnewline
31 & 58.5 & 65.5911510050103 & -7.09115100501027 \tabularnewline
32 & 52 & 63.6656823428884 & -11.6656823428884 \tabularnewline
33 & 66.7 & 59.8098537831934 & 6.8901462168066 \tabularnewline
34 & 72 & 62.3955784904186 & 9.60442150958141 \tabularnewline
35 & 68.4 & 66.2188128667971 & 2.18118713320291 \tabularnewline
36 & 70.8 & 67.6347024554779 & 3.16529754452209 \tabularnewline
37 & 56.5 & 69.4883873031392 & -12.9883873031392 \tabularnewline
38 & 62.6 & 65.4943188146737 & -2.8943188146737 \tabularnewline
39 & 66.5 & 64.7762037856504 & 1.72379621434965 \tabularnewline
40 & 69.2 & 65.6615509277882 & 3.53844907221178 \tabularnewline
41 & 63.7 & 67.275235660749 & -3.57523566074904 \tabularnewline
42 & 73.6 & 66.3873716180674 & 7.21262838193255 \tabularnewline
43 & 64.1 & 69.3546009366801 & -5.25460093668008 \tabularnewline
44 & 53.8 & 67.9724244656319 & -14.1724244656319 \tabularnewline
45 & 72.2 & 63.1214324976794 & 9.07856750232064 \tabularnewline
46 & 80.2 & 66.3571786117258 & 13.8428213882742 \tabularnewline
47 & 69.1 & 71.6615038064343 & -2.56150380643426 \tabularnewline
48 & 72 & 71.3923936385881 & 0.607606361411939 \tabularnewline
49 & 66.3 & 72.2038741786681 & -5.90387417866806 \tabularnewline
50 & 72.5 & 70.6351962847044 & 1.86480371529559 \tabularnewline
51 & 88.9 & 71.7283430562761 & 17.1716569437239 \tabularnewline
52 & 88.6 & 78.5297522489445 & 10.0702477510554 \tabularnewline
53 & 73.7 & 83.3023958251678 & -9.6023958251678 \tabularnewline
54 & 86 & 81.1668764069249 & 4.8331235930751 \tabularnewline
55 & 70 & 84.0244645579071 & -14.0244645579071 \tabularnewline
56 & 71.6 & 80.0945529830835 & -8.49455298308351 \tabularnewline
57 & 90.5 & 77.7220326584553 & 12.7779673415447 \tabularnewline
58 & 85.7 & 82.9017300836119 & 2.79826991638809 \tabularnewline
59 & 84.8 & 84.8404197147116 & -0.0404197147116321 \tabularnewline
60 & 81.1 & 85.8284892679055 & -4.72848926790554 \tabularnewline
61 & 70.8 & 85.0865029859009 & -14.2865029859009 \tabularnewline
62 & 65.7 & 80.6577092471106 & -14.9577092471106 \tabularnewline
63 & 86.2 & 75.4907212324594 & 10.7092787675406 \tabularnewline
64 & 76.1 & 79.274367901846 & -3.17436790184604 \tabularnewline
65 & 79.8 & 78.3064210967353 & 1.49357890326472 \tabularnewline
66 & 85.2 & 78.9506925300241 & 6.24930746997589 \tabularnewline
67 & 75.8 & 81.3998795510754 & -5.59987955107545 \tabularnewline
68 & 69.4 & 79.6944692548985 & -10.2944692548984 \tabularnewline
69 & 85 & 76.0656493897757 & 8.93435061022427 \tabularnewline
70 & 75 & 79.173636740711 & -4.17363674071098 \tabularnewline
71 & 77.7 & 77.7550823222776 & -0.0550823222775847 \tabularnewline
72 & 68.5 & 77.7118428475927 & -9.21184284759269 \tabularnewline
73 & 68.4 & 74.290269509049 & -5.89026950904903 \tabularnewline
74 & 65 & 71.7770880929369 & -6.77708809293689 \tabularnewline
75 & 73.2 & 68.7345915603967 & 4.46540843960327 \tabularnewline
76 & 67.9 & 69.6048551845425 & -1.70485518454254 \tabularnewline
77 & 76.5 & 68.3532829387252 & 8.14671706127484 \tabularnewline
78 & 85.5 & 70.6757995925779 & 14.8242004074221 \tabularnewline
79 & 71.7 & 75.7403689236095 & -4.04036892360951 \tabularnewline
80 & 57.9 & 74.3580255597751 & -16.4580255597751 \tabularnewline
81 & 75.5 & 68.2580515664477 & 7.24194843355228 \tabularnewline
82 & 78.2 & 70.3318691891378 & 7.86813081086218 \tabularnewline
83 & 75.7 & 72.8853213673123 & 2.81467863268766 \tabularnewline
84 & 67.1 & 73.8456205908786 & -6.74562059087859 \tabularnewline
85 & 74.6 & 71.3773530868206 & 3.22264691317942 \tabularnewline
86 & 66.2 & 72.3530703839135 & -6.1530703839135 \tabularnewline
87 & 74.9 & 69.982295645457 & 4.91770435454303 \tabularnewline
88 & 69.5 & 71.4823937753189 & -1.9823937753189 \tabularnewline
89 & 76.1 & 70.607073511533 & 5.49292648846695 \tabularnewline
90 & 82.3 & 72.420096122804 & 9.87990387719603 \tabularnewline
91 & 82.1 & 76.039426581435 & 6.06057341856501 \tabularnewline
92 & 60.5 & 78.5897690893311 & -18.0897690893311 \tabularnewline
93 & 71.2 & 72.4431332369258 & -1.2431332369258 \tabularnewline
94 & 81.4 & 71.8871603688459 & 9.51283963115411 \tabularnewline
95 & 74.5 & 75.2546215808975 & -0.754621580897535 \tabularnewline
96 & 61.4 & 75.1628190661 & -13.7628190661 \tabularnewline
97 & 83.8 & 70.2484861227938 & 13.5515138772062 \tabularnewline
98 & 85.4 & 74.9332665130571 & 10.4667334869429 \tabularnewline
99 & 91.6 & 78.9460231448627 & 12.6539768551373 \tabularnewline
100 & 91.9 & 84.1247971888079 & 7.77520281119207 \tabularnewline
101 & 86.3 & 87.9392070464956 & -1.6392070464956 \tabularnewline
102 & 96.8 & 88.5492230737105 & 8.25077692628952 \tabularnewline
103 & 81 & 92.7497466506202 & -11.7497466506202 \tabularnewline
104 & 70.8 & 89.8587125935248 & -19.0587125935248 \tabularnewline
105 & 98.8 & 83.8690220356594 & 14.9309779643406 \tabularnewline
106 & 94.5 & 89.7580033472625 & 4.74199665273748 \tabularnewline
107 & 84.5 & 92.4027549940195 & -7.90275499401955 \tabularnewline
108 & 92.8 & 90.5477834637012 & 2.25221653629885 \tabularnewline
109 & 81.2 & 92.1658976968819 & -10.9658976968819 \tabularnewline
110 & 75.7 & 88.9873524906643 & -13.2873524906643 \tabularnewline
111 & 86.7 & 84.5761563922382 & 2.1238436077618 \tabularnewline
112 & 87.5 & 85.3912701745156 & 2.10872982548436 \tabularnewline
113 & 87.8 & 86.2737581126969 & 1.5262418873031 \tabularnewline
114 & 103.1 & 87.0138889086114 & 16.0861110913886 \tabularnewline
115 & 96.4 & 93.1752125175373 & 3.22478748246274 \tabularnewline
116 & 77.1 & 95.1465884540007 & -18.0465884540007 \tabularnewline
117 & 106.5 & 89.3851691764234 & 17.1148308235766 \tabularnewline
118 & 95.7 & 95.9692454112489 & -0.269245411248889 \tabularnewline
119 & 95.3 & 96.7309981972355 & -1.43099819723545 \tabularnewline
120 & 86.6 & 97.0551213297988 & -10.4551213297988 \tabularnewline
121 & 89.6 & 94.0025607220874 & -4.40256072208743 \tabularnewline
122 & 81.9 & 92.8227071424353 & -10.9227071424353 \tabularnewline
123 & 98.4 & 89.087416617669 & 9.31258338233097 \tabularnewline
124 & 92.9 & 92.4384789469281 & 0.461521053071877 \tabularnewline
125 & 83.9 & 92.8456789278446 & -8.94567892784463 \tabularnewline
126 & 121.8 & 89.7999422585867 & 32.0000577414133 \tabularnewline
127 & 103.9 & 101.545183334901 & 2.35481666509925 \tabularnewline
128 & 87.5 & 103.458207900653 & -15.9582079006533 \tabularnewline
129 & 118.9 & 98.6994119666017 & 20.2005880333983 \tabularnewline
130 & 109 & 106.725610960827 & 2.27438903917256 \tabularnewline
131 & 112.2 & 108.835571261865 & 3.36442873813506 \tabularnewline
132 & 100.1 & 111.425588118692 & -11.3255881186923 \tabularnewline
133 & 111.3 & 108.714400585795 & 2.58559941420516 \tabularnewline
134 & 102.7 & 110.743793641674 & -8.04379364167418 \tabularnewline
135 & 122.6 & 108.942536736483 & 13.6574632635168 \tabularnewline
136 & 124.8 & 114.867071010921 & 9.93292898907947 \tabularnewline
137 & 120.3 & 119.887319230191 & 0.412680769809384 \tabularnewline
138 & 118.3 & 121.738257967594 & -3.43825796759366 \tabularnewline
139 & 108.7 & 122.183385023357 & -13.4833850233571 \tabularnewline
140 & 100.7 & 118.806402898357 & -18.1064028983566 \tabularnewline
141 & 124 & 113.261629450718 & 10.7383705492817 \tabularnewline
142 & 103.1 & 117.731112214821 & -14.6311122148214 \tabularnewline
143 & 115 & 113.214740997534 & 1.78525900246592 \tabularnewline
144 & 112.7 & 114.249171717695 & -1.54917171769547 \tabularnewline
145 & 101.7 & 114.115390320452 & -12.4153903204517 \tabularnewline
146 & 111.5 & 109.921616428257 & 1.57838357174253 \tabularnewline
147 & 114.4 & 110.461444631713 & 3.93855536828742 \tabularnewline
148 & 112.5 & 111.925769318871 & 0.574230681128569 \tabularnewline
149 & 107.2 & 112.284817641801 & -5.0848176418011 \tabularnewline
150 & 136.7 & 110.576884999614 & 26.1231150003861 \tabularnewline
151 & 107.8 & 120.201843677768 & -12.4018436777676 \tabularnewline
152 & 94.6 & 116.5184460037 & -21.9184460037 \tabularnewline
153 & 110.7 & 108.899955842866 & 1.80004415713384 \tabularnewline
154 & 126.6 & 109.274537079941 & 17.325462920059 \tabularnewline
155 & 127.9 & 115.435749788381 & 12.464250211619 \tabularnewline
156 & 109.2 & 120.399524310203 & -11.1995243102027 \tabularnewline
157 & 87.1 & 117.065682024331 & -29.9656820243308 \tabularnewline
158 & 90.8 & 106.427384123472 & -15.6273841234719 \tabularnewline
159 & 94.5 & 100.046931378885 & -5.5469313788852 \tabularnewline
160 & 103.3 & 96.8467704302888 & 6.45322956971117 \tabularnewline
161 & 103.2 & 97.8810009163475 & 5.31899908365253 \tabularnewline
162 & 105.4 & 98.7186455830088 & 6.68135441699124 \tabularnewline
163 & 103.9 & 100.241332353088 & 3.65866764691229 \tabularnewline
164 & 79.8 & 100.878923805222 & -21.0789238052216 \tabularnewline
165 & 105.6 & 92.5204984126174 & 13.0795015873826 \tabularnewline
166 & 113 & 96.0335760313022 & 16.9664239686978 \tabularnewline
167 & 87.7 & 101.42914678879 & -13.7291467887896 \tabularnewline
168 & 110 & 96.0888481651527 & 13.9111518348473 \tabularnewline
169 & 90.3 & 100.469015214098 & -10.1690152140978 \tabularnewline
170 & 108.9 & 96.4477222739818 & 12.4522777260182 \tabularnewline
171 & 105.1 & 100.418477894895 & 4.68152210510516 \tabularnewline
172 & 113 & 101.95155924908 & 11.0484407509204 \tabularnewline
173 & 100.4 & 105.993158128974 & -5.59315812897363 \tabularnewline
174 & 110.1 & 104.277851955998 & 5.82214804400152 \tabularnewline
175 & 114.7 & 106.579691527559 & 8.12030847244053 \tabularnewline
176 & 88.6 & 109.928921277394 & -21.3289212773945 \tabularnewline
177 & 117.2 & 102.698018919495 & 14.5019810805054 \tabularnewline
178 & 127.7 & 107.94673812019 & 19.7532618798103 \tabularnewline
179 & 107.8 & 115.629898299073 & -7.82989829907297 \tabularnewline
180 & 102.8 & 113.820570816656 & -11.0205708166559 \tabularnewline
181 & 100.2 & 110.565790640315 & -10.3657906403148 \tabularnewline
182 & 108.4 & 107.173931487187 & 1.22606851281287 \tabularnewline
183 & 114.2 & 107.700395273085 & 6.49960472691511 \tabularnewline
184 & 94.4 & 110.213521680672 & -15.8135216806717 \tabularnewline
185 & 92.2 & 104.722199705296 & -12.5221997052956 \tabularnewline
186 & 115.3 & 99.9013684680344 & 15.3986315319656 \tabularnewline
187 & 102 & 104.945900566352 & -2.94590056635225 \tabularnewline
188 & 86.3 & 103.755007110388 & -17.4550071103885 \tabularnewline
189 & 112 & 97.1128782477944 & 14.8871217522056 \tabularnewline
190 & 112.5 & 101.796985407145 & 10.703014592855 \tabularnewline
191 & 109.5 & 105.449579507377 & 4.0504204926234 \tabularnewline
192 & 105.9 & 107.016725999222 & -1.11672599922173 \tabularnewline
193 & 115.3 & 106.817670134878 & 8.48232986512207 \tabularnewline
194 & 126.2 & 110.119791224023 & 16.0802087759772 \tabularnewline
195 & 112.2 & 116.514876665384 & -4.31487666538395 \tabularnewline
196 & 112.5 & 115.941830399136 & -3.44183039913649 \tabularnewline
197 & 106.9 & 115.542507031431 & -8.64250703143129 \tabularnewline
198 & 90.6 & 113.107282837751 & -22.5072828377506 \tabularnewline
199 & 75.6 & 105.262752158539 & -29.6627521585394 \tabularnewline
200 & 78.8 & 94.0066782944688 & -15.2066782944688 \tabularnewline
201 & 101.8 & 87.0622826770585 & 14.7377173229415 \tabularnewline
202 & 93.9 & 90.6372115036752 & 3.26278849632477 \tabularnewline
203 & 100 & 90.4870955765379 & 9.51290442346215 \tabularnewline
204 & 89.2 & 92.7536986979053 & -3.55369869790535 \tabularnewline
205 & 97.7 & 90.5288914285901 & 7.17110857140992 \tabularnewline
206 & 121.1 & 92.1366658420434 & 28.9633341579566 \tabularnewline
207 & 108.8 & 102.026357812489 & 6.77364218751137 \tabularnewline
208 & 92.9 & 104.728672950625 & -11.8286729506248 \tabularnewline
209 & 113.6 & 100.804267675902 & 12.7957323240979 \tabularnewline
210 & 112.6 & 105.553529922255 & 7.04647007774517 \tabularnewline
211 & 98.8 & 108.622315088705 & -9.82231508870539 \tabularnewline
212 & 78 & 105.712968293496 & -27.712968293496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310513&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]58.3[/C][C]58.8[/C][C]-0.5[/C][/ROW]
[ROW][C]4[/C][C]54.5[/C][C]64.6156311965097[/C][C]-10.1156311965097[/C][/ROW]
[ROW][C]5[/C][C]64.7[/C][C]66.8684441691498[/C][C]-2.16844416914981[/C][/ROW]
[ROW][C]6[/C][C]58.3[/C][C]71.7042445727411[/C][C]-13.4042445727411[/C][/ROW]
[ROW][C]7[/C][C]57.5[/C][C]72.322503761797[/C][C]-14.822503761797[/C][/ROW]
[ROW][C]8[/C][C]56.7[/C][C]71.9574048961697[/C][C]-15.2574048961697[/C][/ROW]
[ROW][C]9[/C][C]56[/C][C]70.9228364443051[/C][C]-14.9228364443051[/C][/ROW]
[ROW][C]10[/C][C]66.2[/C][C]69.4875933292236[/C][C]-3.28759332922361[/C][/ROW]
[ROW][C]11[/C][C]58.2[/C][C]71.8301506304168[/C][C]-13.6301506304168[/C][/ROW]
[ROW][C]12[/C][C]53.9[/C][C]70.2460998781444[/C][C]-16.3460998781444[/C][/ROW]
[ROW][C]13[/C][C]53.1[/C][C]67.1924248001067[/C][C]-14.0924248001067[/C][/ROW]
[ROW][C]14[/C][C]54.4[/C][C]64.4083286835315[/C][C]-10.0083286835315[/C][/ROW]
[ROW][C]15[/C][C]59.2[/C][C]62.6461630698807[/C][C]-3.44616306988068[/C][/ROW]
[ROW][C]16[/C][C]57.8[/C][C]62.9599609006059[/C][C]-5.15996090060591[/C][/ROW]
[ROW][C]17[/C][C]61.5[/C][C]62.5234524372162[/C][C]-1.02345243721623[/C][/ROW]
[ROW][C]18[/C][C]60.1[/C][C]63.435002196413[/C][C]-3.33500219641301[/C][/ROW]
[ROW][C]19[/C][C]60.1[/C][C]63.4590443397123[/C][C]-3.35904433971228[/C][/ROW]
[ROW][C]20[/C][C]58.4[/C][C]63.3596746748276[/C][C]-4.9596746748276[/C][/ROW]
[ROW][C]21[/C][C]56.8[/C][C]62.5547200746591[/C][C]-5.75472007465911[/C][/ROW]
[ROW][C]22[/C][C]63.8[/C][C]61.2862535125329[/C][C]2.51374648746712[/C][/ROW]
[ROW][C]23[/C][C]53.9[/C][C]62.8690254556962[/C][C]-8.96902545569618[/C][/ROW]
[ROW][C]24[/C][C]63.1[/C][C]60.3040066328284[/C][C]2.79599336717161[/C][/ROW]
[ROW][C]25[/C][C]55.7[/C][C]61.7691356089681[/C][C]-6.06913560896812[/C][/ROW]
[ROW][C]26[/C][C]54.9[/C][C]60.0613914923772[/C][C]-5.16139149237721[/C][/ROW]
[ROW][C]27[/C][C]64.6[/C][C]58.4799115416494[/C][C]6.12008845835061[/C][/ROW]
[ROW][C]28[/C][C]60.2[/C][C]60.8810603654821[/C][C]-0.681060365482139[/C][/ROW]
[ROW][C]29[/C][C]63.9[/C][C]60.9845751407232[/C][C]2.91542485927683[/C][/ROW]
[ROW][C]30[/C][C]69.9[/C][C]62.3908570450199[/C][C]7.50914295498007[/C][/ROW]
[ROW][C]31[/C][C]58.5[/C][C]65.5911510050103[/C][C]-7.09115100501027[/C][/ROW]
[ROW][C]32[/C][C]52[/C][C]63.6656823428884[/C][C]-11.6656823428884[/C][/ROW]
[ROW][C]33[/C][C]66.7[/C][C]59.8098537831934[/C][C]6.8901462168066[/C][/ROW]
[ROW][C]34[/C][C]72[/C][C]62.3955784904186[/C][C]9.60442150958141[/C][/ROW]
[ROW][C]35[/C][C]68.4[/C][C]66.2188128667971[/C][C]2.18118713320291[/C][/ROW]
[ROW][C]36[/C][C]70.8[/C][C]67.6347024554779[/C][C]3.16529754452209[/C][/ROW]
[ROW][C]37[/C][C]56.5[/C][C]69.4883873031392[/C][C]-12.9883873031392[/C][/ROW]
[ROW][C]38[/C][C]62.6[/C][C]65.4943188146737[/C][C]-2.8943188146737[/C][/ROW]
[ROW][C]39[/C][C]66.5[/C][C]64.7762037856504[/C][C]1.72379621434965[/C][/ROW]
[ROW][C]40[/C][C]69.2[/C][C]65.6615509277882[/C][C]3.53844907221178[/C][/ROW]
[ROW][C]41[/C][C]63.7[/C][C]67.275235660749[/C][C]-3.57523566074904[/C][/ROW]
[ROW][C]42[/C][C]73.6[/C][C]66.3873716180674[/C][C]7.21262838193255[/C][/ROW]
[ROW][C]43[/C][C]64.1[/C][C]69.3546009366801[/C][C]-5.25460093668008[/C][/ROW]
[ROW][C]44[/C][C]53.8[/C][C]67.9724244656319[/C][C]-14.1724244656319[/C][/ROW]
[ROW][C]45[/C][C]72.2[/C][C]63.1214324976794[/C][C]9.07856750232064[/C][/ROW]
[ROW][C]46[/C][C]80.2[/C][C]66.3571786117258[/C][C]13.8428213882742[/C][/ROW]
[ROW][C]47[/C][C]69.1[/C][C]71.6615038064343[/C][C]-2.56150380643426[/C][/ROW]
[ROW][C]48[/C][C]72[/C][C]71.3923936385881[/C][C]0.607606361411939[/C][/ROW]
[ROW][C]49[/C][C]66.3[/C][C]72.2038741786681[/C][C]-5.90387417866806[/C][/ROW]
[ROW][C]50[/C][C]72.5[/C][C]70.6351962847044[/C][C]1.86480371529559[/C][/ROW]
[ROW][C]51[/C][C]88.9[/C][C]71.7283430562761[/C][C]17.1716569437239[/C][/ROW]
[ROW][C]52[/C][C]88.6[/C][C]78.5297522489445[/C][C]10.0702477510554[/C][/ROW]
[ROW][C]53[/C][C]73.7[/C][C]83.3023958251678[/C][C]-9.6023958251678[/C][/ROW]
[ROW][C]54[/C][C]86[/C][C]81.1668764069249[/C][C]4.8331235930751[/C][/ROW]
[ROW][C]55[/C][C]70[/C][C]84.0244645579071[/C][C]-14.0244645579071[/C][/ROW]
[ROW][C]56[/C][C]71.6[/C][C]80.0945529830835[/C][C]-8.49455298308351[/C][/ROW]
[ROW][C]57[/C][C]90.5[/C][C]77.7220326584553[/C][C]12.7779673415447[/C][/ROW]
[ROW][C]58[/C][C]85.7[/C][C]82.9017300836119[/C][C]2.79826991638809[/C][/ROW]
[ROW][C]59[/C][C]84.8[/C][C]84.8404197147116[/C][C]-0.0404197147116321[/C][/ROW]
[ROW][C]60[/C][C]81.1[/C][C]85.8284892679055[/C][C]-4.72848926790554[/C][/ROW]
[ROW][C]61[/C][C]70.8[/C][C]85.0865029859009[/C][C]-14.2865029859009[/C][/ROW]
[ROW][C]62[/C][C]65.7[/C][C]80.6577092471106[/C][C]-14.9577092471106[/C][/ROW]
[ROW][C]63[/C][C]86.2[/C][C]75.4907212324594[/C][C]10.7092787675406[/C][/ROW]
[ROW][C]64[/C][C]76.1[/C][C]79.274367901846[/C][C]-3.17436790184604[/C][/ROW]
[ROW][C]65[/C][C]79.8[/C][C]78.3064210967353[/C][C]1.49357890326472[/C][/ROW]
[ROW][C]66[/C][C]85.2[/C][C]78.9506925300241[/C][C]6.24930746997589[/C][/ROW]
[ROW][C]67[/C][C]75.8[/C][C]81.3998795510754[/C][C]-5.59987955107545[/C][/ROW]
[ROW][C]68[/C][C]69.4[/C][C]79.6944692548985[/C][C]-10.2944692548984[/C][/ROW]
[ROW][C]69[/C][C]85[/C][C]76.0656493897757[/C][C]8.93435061022427[/C][/ROW]
[ROW][C]70[/C][C]75[/C][C]79.173636740711[/C][C]-4.17363674071098[/C][/ROW]
[ROW][C]71[/C][C]77.7[/C][C]77.7550823222776[/C][C]-0.0550823222775847[/C][/ROW]
[ROW][C]72[/C][C]68.5[/C][C]77.7118428475927[/C][C]-9.21184284759269[/C][/ROW]
[ROW][C]73[/C][C]68.4[/C][C]74.290269509049[/C][C]-5.89026950904903[/C][/ROW]
[ROW][C]74[/C][C]65[/C][C]71.7770880929369[/C][C]-6.77708809293689[/C][/ROW]
[ROW][C]75[/C][C]73.2[/C][C]68.7345915603967[/C][C]4.46540843960327[/C][/ROW]
[ROW][C]76[/C][C]67.9[/C][C]69.6048551845425[/C][C]-1.70485518454254[/C][/ROW]
[ROW][C]77[/C][C]76.5[/C][C]68.3532829387252[/C][C]8.14671706127484[/C][/ROW]
[ROW][C]78[/C][C]85.5[/C][C]70.6757995925779[/C][C]14.8242004074221[/C][/ROW]
[ROW][C]79[/C][C]71.7[/C][C]75.7403689236095[/C][C]-4.04036892360951[/C][/ROW]
[ROW][C]80[/C][C]57.9[/C][C]74.3580255597751[/C][C]-16.4580255597751[/C][/ROW]
[ROW][C]81[/C][C]75.5[/C][C]68.2580515664477[/C][C]7.24194843355228[/C][/ROW]
[ROW][C]82[/C][C]78.2[/C][C]70.3318691891378[/C][C]7.86813081086218[/C][/ROW]
[ROW][C]83[/C][C]75.7[/C][C]72.8853213673123[/C][C]2.81467863268766[/C][/ROW]
[ROW][C]84[/C][C]67.1[/C][C]73.8456205908786[/C][C]-6.74562059087859[/C][/ROW]
[ROW][C]85[/C][C]74.6[/C][C]71.3773530868206[/C][C]3.22264691317942[/C][/ROW]
[ROW][C]86[/C][C]66.2[/C][C]72.3530703839135[/C][C]-6.1530703839135[/C][/ROW]
[ROW][C]87[/C][C]74.9[/C][C]69.982295645457[/C][C]4.91770435454303[/C][/ROW]
[ROW][C]88[/C][C]69.5[/C][C]71.4823937753189[/C][C]-1.9823937753189[/C][/ROW]
[ROW][C]89[/C][C]76.1[/C][C]70.607073511533[/C][C]5.49292648846695[/C][/ROW]
[ROW][C]90[/C][C]82.3[/C][C]72.420096122804[/C][C]9.87990387719603[/C][/ROW]
[ROW][C]91[/C][C]82.1[/C][C]76.039426581435[/C][C]6.06057341856501[/C][/ROW]
[ROW][C]92[/C][C]60.5[/C][C]78.5897690893311[/C][C]-18.0897690893311[/C][/ROW]
[ROW][C]93[/C][C]71.2[/C][C]72.4431332369258[/C][C]-1.2431332369258[/C][/ROW]
[ROW][C]94[/C][C]81.4[/C][C]71.8871603688459[/C][C]9.51283963115411[/C][/ROW]
[ROW][C]95[/C][C]74.5[/C][C]75.2546215808975[/C][C]-0.754621580897535[/C][/ROW]
[ROW][C]96[/C][C]61.4[/C][C]75.1628190661[/C][C]-13.7628190661[/C][/ROW]
[ROW][C]97[/C][C]83.8[/C][C]70.2484861227938[/C][C]13.5515138772062[/C][/ROW]
[ROW][C]98[/C][C]85.4[/C][C]74.9332665130571[/C][C]10.4667334869429[/C][/ROW]
[ROW][C]99[/C][C]91.6[/C][C]78.9460231448627[/C][C]12.6539768551373[/C][/ROW]
[ROW][C]100[/C][C]91.9[/C][C]84.1247971888079[/C][C]7.77520281119207[/C][/ROW]
[ROW][C]101[/C][C]86.3[/C][C]87.9392070464956[/C][C]-1.6392070464956[/C][/ROW]
[ROW][C]102[/C][C]96.8[/C][C]88.5492230737105[/C][C]8.25077692628952[/C][/ROW]
[ROW][C]103[/C][C]81[/C][C]92.7497466506202[/C][C]-11.7497466506202[/C][/ROW]
[ROW][C]104[/C][C]70.8[/C][C]89.8587125935248[/C][C]-19.0587125935248[/C][/ROW]
[ROW][C]105[/C][C]98.8[/C][C]83.8690220356594[/C][C]14.9309779643406[/C][/ROW]
[ROW][C]106[/C][C]94.5[/C][C]89.7580033472625[/C][C]4.74199665273748[/C][/ROW]
[ROW][C]107[/C][C]84.5[/C][C]92.4027549940195[/C][C]-7.90275499401955[/C][/ROW]
[ROW][C]108[/C][C]92.8[/C][C]90.5477834637012[/C][C]2.25221653629885[/C][/ROW]
[ROW][C]109[/C][C]81.2[/C][C]92.1658976968819[/C][C]-10.9658976968819[/C][/ROW]
[ROW][C]110[/C][C]75.7[/C][C]88.9873524906643[/C][C]-13.2873524906643[/C][/ROW]
[ROW][C]111[/C][C]86.7[/C][C]84.5761563922382[/C][C]2.1238436077618[/C][/ROW]
[ROW][C]112[/C][C]87.5[/C][C]85.3912701745156[/C][C]2.10872982548436[/C][/ROW]
[ROW][C]113[/C][C]87.8[/C][C]86.2737581126969[/C][C]1.5262418873031[/C][/ROW]
[ROW][C]114[/C][C]103.1[/C][C]87.0138889086114[/C][C]16.0861110913886[/C][/ROW]
[ROW][C]115[/C][C]96.4[/C][C]93.1752125175373[/C][C]3.22478748246274[/C][/ROW]
[ROW][C]116[/C][C]77.1[/C][C]95.1465884540007[/C][C]-18.0465884540007[/C][/ROW]
[ROW][C]117[/C][C]106.5[/C][C]89.3851691764234[/C][C]17.1148308235766[/C][/ROW]
[ROW][C]118[/C][C]95.7[/C][C]95.9692454112489[/C][C]-0.269245411248889[/C][/ROW]
[ROW][C]119[/C][C]95.3[/C][C]96.7309981972355[/C][C]-1.43099819723545[/C][/ROW]
[ROW][C]120[/C][C]86.6[/C][C]97.0551213297988[/C][C]-10.4551213297988[/C][/ROW]
[ROW][C]121[/C][C]89.6[/C][C]94.0025607220874[/C][C]-4.40256072208743[/C][/ROW]
[ROW][C]122[/C][C]81.9[/C][C]92.8227071424353[/C][C]-10.9227071424353[/C][/ROW]
[ROW][C]123[/C][C]98.4[/C][C]89.087416617669[/C][C]9.31258338233097[/C][/ROW]
[ROW][C]124[/C][C]92.9[/C][C]92.4384789469281[/C][C]0.461521053071877[/C][/ROW]
[ROW][C]125[/C][C]83.9[/C][C]92.8456789278446[/C][C]-8.94567892784463[/C][/ROW]
[ROW][C]126[/C][C]121.8[/C][C]89.7999422585867[/C][C]32.0000577414133[/C][/ROW]
[ROW][C]127[/C][C]103.9[/C][C]101.545183334901[/C][C]2.35481666509925[/C][/ROW]
[ROW][C]128[/C][C]87.5[/C][C]103.458207900653[/C][C]-15.9582079006533[/C][/ROW]
[ROW][C]129[/C][C]118.9[/C][C]98.6994119666017[/C][C]20.2005880333983[/C][/ROW]
[ROW][C]130[/C][C]109[/C][C]106.725610960827[/C][C]2.27438903917256[/C][/ROW]
[ROW][C]131[/C][C]112.2[/C][C]108.835571261865[/C][C]3.36442873813506[/C][/ROW]
[ROW][C]132[/C][C]100.1[/C][C]111.425588118692[/C][C]-11.3255881186923[/C][/ROW]
[ROW][C]133[/C][C]111.3[/C][C]108.714400585795[/C][C]2.58559941420516[/C][/ROW]
[ROW][C]134[/C][C]102.7[/C][C]110.743793641674[/C][C]-8.04379364167418[/C][/ROW]
[ROW][C]135[/C][C]122.6[/C][C]108.942536736483[/C][C]13.6574632635168[/C][/ROW]
[ROW][C]136[/C][C]124.8[/C][C]114.867071010921[/C][C]9.93292898907947[/C][/ROW]
[ROW][C]137[/C][C]120.3[/C][C]119.887319230191[/C][C]0.412680769809384[/C][/ROW]
[ROW][C]138[/C][C]118.3[/C][C]121.738257967594[/C][C]-3.43825796759366[/C][/ROW]
[ROW][C]139[/C][C]108.7[/C][C]122.183385023357[/C][C]-13.4833850233571[/C][/ROW]
[ROW][C]140[/C][C]100.7[/C][C]118.806402898357[/C][C]-18.1064028983566[/C][/ROW]
[ROW][C]141[/C][C]124[/C][C]113.261629450718[/C][C]10.7383705492817[/C][/ROW]
[ROW][C]142[/C][C]103.1[/C][C]117.731112214821[/C][C]-14.6311122148214[/C][/ROW]
[ROW][C]143[/C][C]115[/C][C]113.214740997534[/C][C]1.78525900246592[/C][/ROW]
[ROW][C]144[/C][C]112.7[/C][C]114.249171717695[/C][C]-1.54917171769547[/C][/ROW]
[ROW][C]145[/C][C]101.7[/C][C]114.115390320452[/C][C]-12.4153903204517[/C][/ROW]
[ROW][C]146[/C][C]111.5[/C][C]109.921616428257[/C][C]1.57838357174253[/C][/ROW]
[ROW][C]147[/C][C]114.4[/C][C]110.461444631713[/C][C]3.93855536828742[/C][/ROW]
[ROW][C]148[/C][C]112.5[/C][C]111.925769318871[/C][C]0.574230681128569[/C][/ROW]
[ROW][C]149[/C][C]107.2[/C][C]112.284817641801[/C][C]-5.0848176418011[/C][/ROW]
[ROW][C]150[/C][C]136.7[/C][C]110.576884999614[/C][C]26.1231150003861[/C][/ROW]
[ROW][C]151[/C][C]107.8[/C][C]120.201843677768[/C][C]-12.4018436777676[/C][/ROW]
[ROW][C]152[/C][C]94.6[/C][C]116.5184460037[/C][C]-21.9184460037[/C][/ROW]
[ROW][C]153[/C][C]110.7[/C][C]108.899955842866[/C][C]1.80004415713384[/C][/ROW]
[ROW][C]154[/C][C]126.6[/C][C]109.274537079941[/C][C]17.325462920059[/C][/ROW]
[ROW][C]155[/C][C]127.9[/C][C]115.435749788381[/C][C]12.464250211619[/C][/ROW]
[ROW][C]156[/C][C]109.2[/C][C]120.399524310203[/C][C]-11.1995243102027[/C][/ROW]
[ROW][C]157[/C][C]87.1[/C][C]117.065682024331[/C][C]-29.9656820243308[/C][/ROW]
[ROW][C]158[/C][C]90.8[/C][C]106.427384123472[/C][C]-15.6273841234719[/C][/ROW]
[ROW][C]159[/C][C]94.5[/C][C]100.046931378885[/C][C]-5.5469313788852[/C][/ROW]
[ROW][C]160[/C][C]103.3[/C][C]96.8467704302888[/C][C]6.45322956971117[/C][/ROW]
[ROW][C]161[/C][C]103.2[/C][C]97.8810009163475[/C][C]5.31899908365253[/C][/ROW]
[ROW][C]162[/C][C]105.4[/C][C]98.7186455830088[/C][C]6.68135441699124[/C][/ROW]
[ROW][C]163[/C][C]103.9[/C][C]100.241332353088[/C][C]3.65866764691229[/C][/ROW]
[ROW][C]164[/C][C]79.8[/C][C]100.878923805222[/C][C]-21.0789238052216[/C][/ROW]
[ROW][C]165[/C][C]105.6[/C][C]92.5204984126174[/C][C]13.0795015873826[/C][/ROW]
[ROW][C]166[/C][C]113[/C][C]96.0335760313022[/C][C]16.9664239686978[/C][/ROW]
[ROW][C]167[/C][C]87.7[/C][C]101.42914678879[/C][C]-13.7291467887896[/C][/ROW]
[ROW][C]168[/C][C]110[/C][C]96.0888481651527[/C][C]13.9111518348473[/C][/ROW]
[ROW][C]169[/C][C]90.3[/C][C]100.469015214098[/C][C]-10.1690152140978[/C][/ROW]
[ROW][C]170[/C][C]108.9[/C][C]96.4477222739818[/C][C]12.4522777260182[/C][/ROW]
[ROW][C]171[/C][C]105.1[/C][C]100.418477894895[/C][C]4.68152210510516[/C][/ROW]
[ROW][C]172[/C][C]113[/C][C]101.95155924908[/C][C]11.0484407509204[/C][/ROW]
[ROW][C]173[/C][C]100.4[/C][C]105.993158128974[/C][C]-5.59315812897363[/C][/ROW]
[ROW][C]174[/C][C]110.1[/C][C]104.277851955998[/C][C]5.82214804400152[/C][/ROW]
[ROW][C]175[/C][C]114.7[/C][C]106.579691527559[/C][C]8.12030847244053[/C][/ROW]
[ROW][C]176[/C][C]88.6[/C][C]109.928921277394[/C][C]-21.3289212773945[/C][/ROW]
[ROW][C]177[/C][C]117.2[/C][C]102.698018919495[/C][C]14.5019810805054[/C][/ROW]
[ROW][C]178[/C][C]127.7[/C][C]107.94673812019[/C][C]19.7532618798103[/C][/ROW]
[ROW][C]179[/C][C]107.8[/C][C]115.629898299073[/C][C]-7.82989829907297[/C][/ROW]
[ROW][C]180[/C][C]102.8[/C][C]113.820570816656[/C][C]-11.0205708166559[/C][/ROW]
[ROW][C]181[/C][C]100.2[/C][C]110.565790640315[/C][C]-10.3657906403148[/C][/ROW]
[ROW][C]182[/C][C]108.4[/C][C]107.173931487187[/C][C]1.22606851281287[/C][/ROW]
[ROW][C]183[/C][C]114.2[/C][C]107.700395273085[/C][C]6.49960472691511[/C][/ROW]
[ROW][C]184[/C][C]94.4[/C][C]110.213521680672[/C][C]-15.8135216806717[/C][/ROW]
[ROW][C]185[/C][C]92.2[/C][C]104.722199705296[/C][C]-12.5221997052956[/C][/ROW]
[ROW][C]186[/C][C]115.3[/C][C]99.9013684680344[/C][C]15.3986315319656[/C][/ROW]
[ROW][C]187[/C][C]102[/C][C]104.945900566352[/C][C]-2.94590056635225[/C][/ROW]
[ROW][C]188[/C][C]86.3[/C][C]103.755007110388[/C][C]-17.4550071103885[/C][/ROW]
[ROW][C]189[/C][C]112[/C][C]97.1128782477944[/C][C]14.8871217522056[/C][/ROW]
[ROW][C]190[/C][C]112.5[/C][C]101.796985407145[/C][C]10.703014592855[/C][/ROW]
[ROW][C]191[/C][C]109.5[/C][C]105.449579507377[/C][C]4.0504204926234[/C][/ROW]
[ROW][C]192[/C][C]105.9[/C][C]107.016725999222[/C][C]-1.11672599922173[/C][/ROW]
[ROW][C]193[/C][C]115.3[/C][C]106.817670134878[/C][C]8.48232986512207[/C][/ROW]
[ROW][C]194[/C][C]126.2[/C][C]110.119791224023[/C][C]16.0802087759772[/C][/ROW]
[ROW][C]195[/C][C]112.2[/C][C]116.514876665384[/C][C]-4.31487666538395[/C][/ROW]
[ROW][C]196[/C][C]112.5[/C][C]115.941830399136[/C][C]-3.44183039913649[/C][/ROW]
[ROW][C]197[/C][C]106.9[/C][C]115.542507031431[/C][C]-8.64250703143129[/C][/ROW]
[ROW][C]198[/C][C]90.6[/C][C]113.107282837751[/C][C]-22.5072828377506[/C][/ROW]
[ROW][C]199[/C][C]75.6[/C][C]105.262752158539[/C][C]-29.6627521585394[/C][/ROW]
[ROW][C]200[/C][C]78.8[/C][C]94.0066782944688[/C][C]-15.2066782944688[/C][/ROW]
[ROW][C]201[/C][C]101.8[/C][C]87.0622826770585[/C][C]14.7377173229415[/C][/ROW]
[ROW][C]202[/C][C]93.9[/C][C]90.6372115036752[/C][C]3.26278849632477[/C][/ROW]
[ROW][C]203[/C][C]100[/C][C]90.4870955765379[/C][C]9.51290442346215[/C][/ROW]
[ROW][C]204[/C][C]89.2[/C][C]92.7536986979053[/C][C]-3.55369869790535[/C][/ROW]
[ROW][C]205[/C][C]97.7[/C][C]90.5288914285901[/C][C]7.17110857140992[/C][/ROW]
[ROW][C]206[/C][C]121.1[/C][C]92.1366658420434[/C][C]28.9633341579566[/C][/ROW]
[ROW][C]207[/C][C]108.8[/C][C]102.026357812489[/C][C]6.77364218751137[/C][/ROW]
[ROW][C]208[/C][C]92.9[/C][C]104.728672950625[/C][C]-11.8286729506248[/C][/ROW]
[ROW][C]209[/C][C]113.6[/C][C]100.804267675902[/C][C]12.7957323240979[/C][/ROW]
[ROW][C]210[/C][C]112.6[/C][C]105.553529922255[/C][C]7.04647007774517[/C][/ROW]
[ROW][C]211[/C][C]98.8[/C][C]108.622315088705[/C][C]-9.82231508870539[/C][/ROW]
[ROW][C]212[/C][C]78[/C][C]105.712968293496[/C][C]-27.712968293496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310513&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310513&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
358.358.8-0.5
454.564.6156311965097-10.1156311965097
564.766.8684441691498-2.16844416914981
658.371.7042445727411-13.4042445727411
757.572.322503761797-14.822503761797
856.771.9574048961697-15.2574048961697
95670.9228364443051-14.9228364443051
1066.269.4875933292236-3.28759332922361
1158.271.8301506304168-13.6301506304168
1253.970.2460998781444-16.3460998781444
1353.167.1924248001067-14.0924248001067
1454.464.4083286835315-10.0083286835315
1559.262.6461630698807-3.44616306988068
1657.862.9599609006059-5.15996090060591
1761.562.5234524372162-1.02345243721623
1860.163.435002196413-3.33500219641301
1960.163.4590443397123-3.35904433971228
2058.463.3596746748276-4.9596746748276
2156.862.5547200746591-5.75472007465911
2263.861.28625351253292.51374648746712
2353.962.8690254556962-8.96902545569618
2463.160.30400663282842.79599336717161
2555.761.7691356089681-6.06913560896812
2654.960.0613914923772-5.16139149237721
2764.658.47991154164946.12008845835061
2860.260.8810603654821-0.681060365482139
2963.960.98457514072322.91542485927683
3069.962.39085704501997.50914295498007
3158.565.5911510050103-7.09115100501027
325263.6656823428884-11.6656823428884
3366.759.80985378319346.8901462168066
347262.39557849041869.60442150958141
3568.466.21881286679712.18118713320291
3670.867.63470245547793.16529754452209
3756.569.4883873031392-12.9883873031392
3862.665.4943188146737-2.8943188146737
3966.564.77620378565041.72379621434965
4069.265.66155092778823.53844907221178
4163.767.275235660749-3.57523566074904
4273.666.38737161806747.21262838193255
4364.169.3546009366801-5.25460093668008
4453.867.9724244656319-14.1724244656319
4572.263.12143249767949.07856750232064
4680.266.357178611725813.8428213882742
4769.171.6615038064343-2.56150380643426
487271.39239363858810.607606361411939
4966.372.2038741786681-5.90387417866806
5072.570.63519628470441.86480371529559
5188.971.728343056276117.1716569437239
5288.678.529752248944510.0702477510554
5373.783.3023958251678-9.6023958251678
548681.16687640692494.8331235930751
557084.0244645579071-14.0244645579071
5671.680.0945529830835-8.49455298308351
5790.577.722032658455312.7779673415447
5885.782.90173008361192.79826991638809
5984.884.8404197147116-0.0404197147116321
6081.185.8284892679055-4.72848926790554
6170.885.0865029859009-14.2865029859009
6265.780.6577092471106-14.9577092471106
6386.275.490721232459410.7092787675406
6476.179.274367901846-3.17436790184604
6579.878.30642109673531.49357890326472
6685.278.95069253002416.24930746997589
6775.881.3998795510754-5.59987955107545
6869.479.6944692548985-10.2944692548984
698576.06564938977578.93435061022427
707579.173636740711-4.17363674071098
7177.777.7550823222776-0.0550823222775847
7268.577.7118428475927-9.21184284759269
7368.474.290269509049-5.89026950904903
746571.7770880929369-6.77708809293689
7573.268.73459156039674.46540843960327
7667.969.6048551845425-1.70485518454254
7776.568.35328293872528.14671706127484
7885.570.675799592577914.8242004074221
7971.775.7403689236095-4.04036892360951
8057.974.3580255597751-16.4580255597751
8175.568.25805156644777.24194843355228
8278.270.33186918913787.86813081086218
8375.772.88532136731232.81467863268766
8467.173.8456205908786-6.74562059087859
8574.671.37735308682063.22264691317942
8666.272.3530703839135-6.1530703839135
8774.969.9822956454574.91770435454303
8869.571.4823937753189-1.9823937753189
8976.170.6070735115335.49292648846695
9082.372.4200961228049.87990387719603
9182.176.0394265814356.06057341856501
9260.578.5897690893311-18.0897690893311
9371.272.4431332369258-1.2431332369258
9481.471.88716036884599.51283963115411
9574.575.2546215808975-0.754621580897535
9661.475.1628190661-13.7628190661
9783.870.248486122793813.5515138772062
9885.474.933266513057110.4667334869429
9991.678.946023144862712.6539768551373
10091.984.12479718880797.77520281119207
10186.387.9392070464956-1.6392070464956
10296.888.54922307371058.25077692628952
1038192.7497466506202-11.7497466506202
10470.889.8587125935248-19.0587125935248
10598.883.869022035659414.9309779643406
10694.589.75800334726254.74199665273748
10784.592.4027549940195-7.90275499401955
10892.890.54778346370122.25221653629885
10981.292.1658976968819-10.9658976968819
11075.788.9873524906643-13.2873524906643
11186.784.57615639223822.1238436077618
11287.585.39127017451562.10872982548436
11387.886.27375811269691.5262418873031
114103.187.013888908611416.0861110913886
11596.493.17521251753733.22478748246274
11677.195.1465884540007-18.0465884540007
117106.589.385169176423417.1148308235766
11895.795.9692454112489-0.269245411248889
11995.396.7309981972355-1.43099819723545
12086.697.0551213297988-10.4551213297988
12189.694.0025607220874-4.40256072208743
12281.992.8227071424353-10.9227071424353
12398.489.0874166176699.31258338233097
12492.992.43847894692810.461521053071877
12583.992.8456789278446-8.94567892784463
126121.889.799942258586732.0000577414133
127103.9101.5451833349012.35481666509925
12887.5103.458207900653-15.9582079006533
129118.998.699411966601720.2005880333983
130109106.7256109608272.27438903917256
131112.2108.8355712618653.36442873813506
132100.1111.425588118692-11.3255881186923
133111.3108.7144005857952.58559941420516
134102.7110.743793641674-8.04379364167418
135122.6108.94253673648313.6574632635168
136124.8114.8670710109219.93292898907947
137120.3119.8873192301910.412680769809384
138118.3121.738257967594-3.43825796759366
139108.7122.183385023357-13.4833850233571
140100.7118.806402898357-18.1064028983566
141124113.26162945071810.7383705492817
142103.1117.731112214821-14.6311122148214
143115113.2147409975341.78525900246592
144112.7114.249171717695-1.54917171769547
145101.7114.115390320452-12.4153903204517
146111.5109.9216164282571.57838357174253
147114.4110.4614446317133.93855536828742
148112.5111.9257693188710.574230681128569
149107.2112.284817641801-5.0848176418011
150136.7110.57688499961426.1231150003861
151107.8120.201843677768-12.4018436777676
15294.6116.5184460037-21.9184460037
153110.7108.8999558428661.80004415713384
154126.6109.27453707994117.325462920059
155127.9115.43574978838112.464250211619
156109.2120.399524310203-11.1995243102027
15787.1117.065682024331-29.9656820243308
15890.8106.427384123472-15.6273841234719
15994.5100.046931378885-5.5469313788852
160103.396.84677043028886.45322956971117
161103.297.88100091634755.31899908365253
162105.498.71864558300886.68135441699124
163103.9100.2413323530883.65866764691229
16479.8100.878923805222-21.0789238052216
165105.692.520498412617413.0795015873826
16611396.033576031302216.9664239686978
16787.7101.42914678879-13.7291467887896
16811096.088848165152713.9111518348473
16990.3100.469015214098-10.1690152140978
170108.996.447722273981812.4522777260182
171105.1100.4184778948954.68152210510516
172113101.9515592490811.0484407509204
173100.4105.993158128974-5.59315812897363
174110.1104.2778519559985.82214804400152
175114.7106.5796915275598.12030847244053
17688.6109.928921277394-21.3289212773945
177117.2102.69801891949514.5019810805054
178127.7107.9467381201919.7532618798103
179107.8115.629898299073-7.82989829907297
180102.8113.820570816656-11.0205708166559
181100.2110.565790640315-10.3657906403148
182108.4107.1739314871871.22606851281287
183114.2107.7003952730856.49960472691511
18494.4110.213521680672-15.8135216806717
18592.2104.722199705296-12.5221997052956
186115.399.901368468034415.3986315319656
187102104.945900566352-2.94590056635225
18886.3103.755007110388-17.4550071103885
18911297.112878247794414.8871217522056
190112.5101.79698540714510.703014592855
191109.5105.4495795073774.0504204926234
192105.9107.016725999222-1.11672599922173
193115.3106.8176701348788.48232986512207
194126.2110.11979122402316.0802087759772
195112.2116.514876665384-4.31487666538395
196112.5115.941830399136-3.44183039913649
197106.9115.542507031431-8.64250703143129
19890.6113.107282837751-22.5072828377506
19975.6105.262752158539-29.6627521585394
20078.894.0066782944688-15.2066782944688
201101.887.062282677058514.7377173229415
20293.990.63721150367523.26278849632477
20310090.48709557653799.51290442346215
20489.292.7536986979053-3.55369869790535
20597.790.52889142859017.17110857140992
206121.192.136665842043428.9633341579566
207108.8102.0263578124896.77364218751137
20892.9104.728672950625-11.8286729506248
209113.6100.80426767590212.7957323240979
210112.6105.5535299222557.04647007774517
21198.8108.622315088705-9.82231508870539
21278105.712968293496-27.712968293496







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21395.869300014469874.3568422033124117.381757825627
21495.292594295221572.3642354530101118.220953137433
21594.715888575973170.2025921307406119.229185021206
21694.139182856724867.8817281241199120.39663758933
21793.562477137476465.4118427542143121.713111520739
21892.985771418228162.8028878289846123.168655007472
21992.409065698979760.0641965000787124.753934897881
22091.832359979731457.2043017163702126.460418243093
22191.25565426048354.2308797673679128.280428753598
22290.678948541234751.150768938147130.207128144322
22390.102242821986447.9700284699187132.234457174054
22489.52553710273844.6940154421483134.357058763328

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 95.8693000144698 & 74.3568422033124 & 117.381757825627 \tabularnewline
214 & 95.2925942952215 & 72.3642354530101 & 118.220953137433 \tabularnewline
215 & 94.7158885759731 & 70.2025921307406 & 119.229185021206 \tabularnewline
216 & 94.1391828567248 & 67.8817281241199 & 120.39663758933 \tabularnewline
217 & 93.5624771374764 & 65.4118427542143 & 121.713111520739 \tabularnewline
218 & 92.9857714182281 & 62.8028878289846 & 123.168655007472 \tabularnewline
219 & 92.4090656989797 & 60.0641965000787 & 124.753934897881 \tabularnewline
220 & 91.8323599797314 & 57.2043017163702 & 126.460418243093 \tabularnewline
221 & 91.255654260483 & 54.2308797673679 & 128.280428753598 \tabularnewline
222 & 90.6789485412347 & 51.150768938147 & 130.207128144322 \tabularnewline
223 & 90.1022428219864 & 47.9700284699187 & 132.234457174054 \tabularnewline
224 & 89.525537102738 & 44.6940154421483 & 134.357058763328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310513&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]95.8693000144698[/C][C]74.3568422033124[/C][C]117.381757825627[/C][/ROW]
[ROW][C]214[/C][C]95.2925942952215[/C][C]72.3642354530101[/C][C]118.220953137433[/C][/ROW]
[ROW][C]215[/C][C]94.7158885759731[/C][C]70.2025921307406[/C][C]119.229185021206[/C][/ROW]
[ROW][C]216[/C][C]94.1391828567248[/C][C]67.8817281241199[/C][C]120.39663758933[/C][/ROW]
[ROW][C]217[/C][C]93.5624771374764[/C][C]65.4118427542143[/C][C]121.713111520739[/C][/ROW]
[ROW][C]218[/C][C]92.9857714182281[/C][C]62.8028878289846[/C][C]123.168655007472[/C][/ROW]
[ROW][C]219[/C][C]92.4090656989797[/C][C]60.0641965000787[/C][C]124.753934897881[/C][/ROW]
[ROW][C]220[/C][C]91.8323599797314[/C][C]57.2043017163702[/C][C]126.460418243093[/C][/ROW]
[ROW][C]221[/C][C]91.255654260483[/C][C]54.2308797673679[/C][C]128.280428753598[/C][/ROW]
[ROW][C]222[/C][C]90.6789485412347[/C][C]51.150768938147[/C][C]130.207128144322[/C][/ROW]
[ROW][C]223[/C][C]90.1022428219864[/C][C]47.9700284699187[/C][C]132.234457174054[/C][/ROW]
[ROW][C]224[/C][C]89.525537102738[/C][C]44.6940154421483[/C][C]134.357058763328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310513&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310513&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
21395.869300014469874.3568422033124117.381757825627
21495.292594295221572.3642354530101118.220953137433
21594.715888575973170.2025921307406119.229185021206
21694.139182856724867.8817281241199120.39663758933
21793.562477137476465.4118427542143121.713111520739
21892.985771418228162.8028878289846123.168655007472
21992.409065698979760.0641965000787124.753934897881
22091.832359979731457.2043017163702126.460418243093
22191.25565426048354.2308797673679128.280428753598
22290.678948541234751.150768938147130.207128144322
22390.102242821986447.9700284699187132.234457174054
22489.52553710273844.6940154421483134.357058763328



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')