FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 May 2014 15:39:53 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/16/t14002692225luq9zpjuyw6hdg.htm/, Retrieved Tue, 14 May 2024 20:45:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234886, Retrieved Tue, 14 May 2024 20:45:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-16 19:39:53] [6d333a1ec28e0cb62f7dec9ea64dd0e6] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
329,6
327,2
326,3
315,4
308,6
302,6
295,6
291,5
288,1
281,1
282,4
284,9
274,2
265,7
259,7
253,7
249,5
244,6
243
239,2
235,7
231,1
226,7
221,7
219,4
214,2
211,7
207,7
204,7
201,2
199,9
197,8
195,2
194,3
192,8
188,5
183,2
181,4
180,5
180,2
179,2
177,1
174,2
172,1
171,1
169,8
169,5
165,5
167,2
167,6
171,8
175,9
180
184,9
184,6
187,6
191,5
195,5
201,6
203,5
209,1
217,1
227,6
237,2
245,6
253,2
260,5
266,1
273
280,8
284,4
288,5
284,8
288,9
299,6
307,8
311,4
322
317,8
319,1
322,3
323,1
322,8
325
323,2
318,8
328,2
329,2
326,5
330,1
323,8
321,8
319,6
315,5
310,7
306,5
295,1
288
293,9
289,3
287,4
282,6
276,9
272,7
267,9
262,8
256,6
250,7
243,2
235,1
229,6
222,9
217,6
214,1
210,8
208
202,6
199
195,5
192,1
189,4
182,4
179,2
176,5
174
171,7
169,8
168,3
166,4
165,9
166,4
170,6
177,6
183,4
191,9
201,7
210,6
221,6
232,2
240,4
248,4
258,5
265
271,7
273,9
277,8
273,4
270,9
268,3
264,7
264,1
264,5
262,2
258,6
259,4
262,7
264,9
260,5
256,4
254,7
254,8
255,3
256,8
258,7
259,8
261,7
264,7
269,1
279
283,4
285,5
288,2
292,1
295,6
302,4
308,5
314,1
319,8
329,7
339,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234886&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234886&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.444346038397632
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.444346038397632 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234886&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.444346038397632[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234886&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.444346038397632
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3326.3324.81.50000000000006
4315.4324.566519057596-9.16651905759647
5308.6309.593412628457-0.993412628457008
6302.6302.3519936625080.248006337491972
7295.6296.46219429607-0.862194296070072
8291.5289.0790816762822.42091832371767
9288.1286.0548071427112.04519285728952
10281.1283.563580486606-2.46358048660625
11282.4275.4688982571096.93110174289092
12284.9279.8487058582935.05129414170648
13274.2284.593228398942-10.393228398942
14265.7269.27503853371-3.57503853371037
15259.7259.1864843241370.51351567586272
16253.7253.4146629803620.285337019638035
17249.5247.5414513546461.95854864535369
18244.6244.2117246862180.388275313781719
19243239.4842532837053.51574671629521
20239.2239.4464614091-0.24646140910005
21235.7235.5369472583490.163052741651455
22231.1232.109399098151-1.00939909815122
23226.7227.060876607726-0.360876607725601
24221.7222.500522516732-0.800522516732343
25219.4217.1448135077742.25518649222579
26214.2215.846896691443-1.64689669144263
27211.7209.915104670951.7848953290501
28207.7208.208215839368-0.50821583936775
29204.7203.9823921444940.71760785550623
30201.2201.301258352211-0.101258352210976
31199.9197.7562646045512.14373539544866
32197.8197.4088249348920.391175065108257
33195.2195.482642025393-0.282642025392562
34194.3192.7570511611251.54294883887536
35192.8192.5426543651290.257345634870831
36188.5191.157004878483-2.65700487848295
37183.2185.676375286726-2.47637528672587
38181.4179.2760077384832.12399226151661
39180.5178.4197952854762.08020471452446
40180.2178.4441260094311.75587399056943
41179.2178.9243416610660.275658338934477
42177.1178.046829351922-0.946829351922332
43174.2175.526109480357-1.32610948035705
44172.1172.0368579862790.0631420137211478
45171.1169.9649148899321.13508511006771
46169.8169.4692854618350.330714538165012
47169.5168.3162371567091.18376284329085
48165.5168.542237486528-3.04223748652774
49167.2163.1904313115244.00956868847561
50167.6166.6720672739320.927932726068292
51171.8167.484390504664.31560949534034
52175.9173.6020144871852.29798551281465
53180178.72311524611.2768847539003
54184.9183.3904939279861.50950607201437
55184.6188.961236971022-4.36123697102241
56187.6186.7233386004350.876661399564711
57191.5190.1128796203481.387120379652
58195.5194.6292410658270.870758934173011
59201.6199.0161593486262.58384065137389
60203.5206.264278705915-2.76427870591485
61209.1206.9359824139152.16401758608535
62217.1213.4975550553143.60244494468552
63227.6223.0982871950314.50171280496895
64237.2235.5986054459231.6013945540771
65245.6245.910178771939-0.31017877193861
66253.2254.172352063433-0.972352063432652
67260.5261.340291276119-0.840291276118592
68266.1268.266911176475-2.1669111764752
69273272.9040527796490.0959472203510927
70280.8279.8466865469070.953313453092846
71284.4288.07028760314-3.6702876031402
72288.5290.039409846905-1.53940984690485
73284.8293.455379179962-8.65537917996238
74288.9285.9093957305172.99060426948319
75299.6291.3382588900778.26174110992338
76307.8305.7093308225382.09066917746202
77311.4314.838311389143-3.43831138914328
78322316.91051134465.08948865540003
79317.8329.772005466097-11.9720054660967
80319.1320.252292265562-1.15229226556181
81322.3321.0402757622831.2597242377168
82323.1324.800029236786-1.70002923678612
83322.8324.84462798026-2.04462798026009
84325323.6361056372351.36389436276545
85323.2326.442146694122-3.24214669412225
86318.8323.201511654685-4.40151165468501
87328.2316.84571738796511.3542826120352
88329.2331.29094788547-2.09094788546969
89326.5331.361843476065-4.8618434760653
90330.1326.5015025881663.5984974118337
91323.8331.700480657299-7.90048065729877
92321.8321.889933375791-0.0899333757909631
93319.6319.849971836539-0.249971836538521
94315.5317.538897841262-2.03889784126164
95310.7312.5329216628-1.83292166279955
96306.5306.918470183241-0.418470183241368
97295.1302.532524615131-7.43252461513049
98288287.8299117471040.170088252895539
99293.9280.80548978845713.0945102115434
100289.3292.523983525713-3.22398352571315
101287.4286.4914192182030.908580781796616
102282.6284.995143489159-2.39514348915884
103276.9279.130870968357-2.23087096835729
104272.7272.4395922913910.260407708608625
105267.9268.35530342508-0.455303425079876
106262.8263.352991151877-0.552991151876711
107256.6258.007271724271-1.40727172427137
108250.7251.181956108642-0.481956108642436
109243.2245.067800821086-1.86780082108558
110235.1236.73785092572-1.63785092572036
111229.6227.9100783553911.68992164460937
112222.9223.160988343375-0.260988343375203
113217.6216.3450192069281.2549807930715
114214.1211.6026649505952.49733504940508
115210.8209.212345886351.58765411365039
116208206.6178137020961.3821862979041
117202.6204.431982707897-1.83198270789705
118199198.217948449230.782051550769978
119195.5194.9654499576370.534550042362611
120192.1191.7029751512860.3970248487135
121189.4188.4793915699580.92060843004225
122182.4186.188460278763-3.7884602787625
123179.2177.5050729622681.69492703773238
124176.5175.0582070768571.441792923143
125174172.9988620504451.00113794955465
126171.7170.9437137322190.756286267780496
127169.8168.9797665392020.820233460797738
128168.3167.4442340280690.855765971931049
129166.4166.3244902474920.0755097525079975
130165.9164.4580427068791.44195729312068
131166.4164.5987707176161.80122928238393
132170.6165.8991398134894.70086018651082
133177.6172.1879484144265.41205158557358
134183.4181.592772096081.80722790392036
135191.9188.1958066556683.70419334433169
136201.7198.3417502936813.35824970631901
137210.6209.6339752466340.966024753366156
138221.6218.9632245187862.63677548121385
139232.2231.1348652580081.06513474199247
140240.4242.208153660972-1.80815366097156
141248.4249.604707744905-1.20470774490468
142258.5257.0694006310291.43059936897066
143265267.805081793166-2.80508179316558
144271.7273.058654810991-1.35865481099114
145273.9279.154941928177-5.25494192817735
146277.8279.019929300382-1.21992930038209
147273.4282.377858548632-8.97785854863218
148270.9273.988582669253-3.08858266925313
149268.3270.116183195907-1.81618319590689
150264.7266.709169387801-2.00916938780136
151264.1262.2164029298621.88359707013802
152264.5262.4533718259152.04662817408473
153262.2263.762782947143-1.56278294714275
154258.6260.768366535705-2.16836653570448
155259.4256.204861455773.19513854422974
156262.7258.424608610034.27539138996974
157264.9263.6243618367631.27563816323732
158260.5266.391186601026-5.89118660102599
159256.4259.373461173399-2.9734611733989
160254.7253.952215480670.747784519330082
161254.8252.5844905694092.21550943059071
162255.3253.6689434079251.63105659207511
163256.8254.8936969430161.9063030569842
164258.7257.2407551543721.45924484562795
165259.8259.7891648205790.0108351794210648
166261.7260.893979389630.806020610369956
167264.7263.1521314547151.54786854528521
168269.1266.8399207107732.26007928922746
169279272.2441779894056.75582201059467
170283.4285.146100735933-1.7461007359326
171285.5288.770227791278-3.2702277912777
172288.2289.417115027566-1.21711502756568
173292.1291.5762947867930.523705213207393
174295.6295.70900112357-0.109001123569499
175302.4299.1605669061313.23943309386942
176308.5307.3999961680461.10000383195444
177314.1313.9887785129970.111221487003263
178319.8319.6381993401310.161800659868618
179329.7325.4100948223544.28990517764589
180339.7337.2162971931432.48370280685748

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 326.3 & 324.8 & 1.50000000000006 \tabularnewline
4 & 315.4 & 324.566519057596 & -9.16651905759647 \tabularnewline
5 & 308.6 & 309.593412628457 & -0.993412628457008 \tabularnewline
6 & 302.6 & 302.351993662508 & 0.248006337491972 \tabularnewline
7 & 295.6 & 296.46219429607 & -0.862194296070072 \tabularnewline
8 & 291.5 & 289.079081676282 & 2.42091832371767 \tabularnewline
9 & 288.1 & 286.054807142711 & 2.04519285728952 \tabularnewline
10 & 281.1 & 283.563580486606 & -2.46358048660625 \tabularnewline
11 & 282.4 & 275.468898257109 & 6.93110174289092 \tabularnewline
12 & 284.9 & 279.848705858293 & 5.05129414170648 \tabularnewline
13 & 274.2 & 284.593228398942 & -10.393228398942 \tabularnewline
14 & 265.7 & 269.27503853371 & -3.57503853371037 \tabularnewline
15 & 259.7 & 259.186484324137 & 0.51351567586272 \tabularnewline
16 & 253.7 & 253.414662980362 & 0.285337019638035 \tabularnewline
17 & 249.5 & 247.541451354646 & 1.95854864535369 \tabularnewline
18 & 244.6 & 244.211724686218 & 0.388275313781719 \tabularnewline
19 & 243 & 239.484253283705 & 3.51574671629521 \tabularnewline
20 & 239.2 & 239.4464614091 & -0.24646140910005 \tabularnewline
21 & 235.7 & 235.536947258349 & 0.163052741651455 \tabularnewline
22 & 231.1 & 232.109399098151 & -1.00939909815122 \tabularnewline
23 & 226.7 & 227.060876607726 & -0.360876607725601 \tabularnewline
24 & 221.7 & 222.500522516732 & -0.800522516732343 \tabularnewline
25 & 219.4 & 217.144813507774 & 2.25518649222579 \tabularnewline
26 & 214.2 & 215.846896691443 & -1.64689669144263 \tabularnewline
27 & 211.7 & 209.91510467095 & 1.7848953290501 \tabularnewline
28 & 207.7 & 208.208215839368 & -0.50821583936775 \tabularnewline
29 & 204.7 & 203.982392144494 & 0.71760785550623 \tabularnewline
30 & 201.2 & 201.301258352211 & -0.101258352210976 \tabularnewline
31 & 199.9 & 197.756264604551 & 2.14373539544866 \tabularnewline
32 & 197.8 & 197.408824934892 & 0.391175065108257 \tabularnewline
33 & 195.2 & 195.482642025393 & -0.282642025392562 \tabularnewline
34 & 194.3 & 192.757051161125 & 1.54294883887536 \tabularnewline
35 & 192.8 & 192.542654365129 & 0.257345634870831 \tabularnewline
36 & 188.5 & 191.157004878483 & -2.65700487848295 \tabularnewline
37 & 183.2 & 185.676375286726 & -2.47637528672587 \tabularnewline
38 & 181.4 & 179.276007738483 & 2.12399226151661 \tabularnewline
39 & 180.5 & 178.419795285476 & 2.08020471452446 \tabularnewline
40 & 180.2 & 178.444126009431 & 1.75587399056943 \tabularnewline
41 & 179.2 & 178.924341661066 & 0.275658338934477 \tabularnewline
42 & 177.1 & 178.046829351922 & -0.946829351922332 \tabularnewline
43 & 174.2 & 175.526109480357 & -1.32610948035705 \tabularnewline
44 & 172.1 & 172.036857986279 & 0.0631420137211478 \tabularnewline
45 & 171.1 & 169.964914889932 & 1.13508511006771 \tabularnewline
46 & 169.8 & 169.469285461835 & 0.330714538165012 \tabularnewline
47 & 169.5 & 168.316237156709 & 1.18376284329085 \tabularnewline
48 & 165.5 & 168.542237486528 & -3.04223748652774 \tabularnewline
49 & 167.2 & 163.190431311524 & 4.00956868847561 \tabularnewline
50 & 167.6 & 166.672067273932 & 0.927932726068292 \tabularnewline
51 & 171.8 & 167.48439050466 & 4.31560949534034 \tabularnewline
52 & 175.9 & 173.602014487185 & 2.29798551281465 \tabularnewline
53 & 180 & 178.7231152461 & 1.2768847539003 \tabularnewline
54 & 184.9 & 183.390493927986 & 1.50950607201437 \tabularnewline
55 & 184.6 & 188.961236971022 & -4.36123697102241 \tabularnewline
56 & 187.6 & 186.723338600435 & 0.876661399564711 \tabularnewline
57 & 191.5 & 190.112879620348 & 1.387120379652 \tabularnewline
58 & 195.5 & 194.629241065827 & 0.870758934173011 \tabularnewline
59 & 201.6 & 199.016159348626 & 2.58384065137389 \tabularnewline
60 & 203.5 & 206.264278705915 & -2.76427870591485 \tabularnewline
61 & 209.1 & 206.935982413915 & 2.16401758608535 \tabularnewline
62 & 217.1 & 213.497555055314 & 3.60244494468552 \tabularnewline
63 & 227.6 & 223.098287195031 & 4.50171280496895 \tabularnewline
64 & 237.2 & 235.598605445923 & 1.6013945540771 \tabularnewline
65 & 245.6 & 245.910178771939 & -0.31017877193861 \tabularnewline
66 & 253.2 & 254.172352063433 & -0.972352063432652 \tabularnewline
67 & 260.5 & 261.340291276119 & -0.840291276118592 \tabularnewline
68 & 266.1 & 268.266911176475 & -2.1669111764752 \tabularnewline
69 & 273 & 272.904052779649 & 0.0959472203510927 \tabularnewline
70 & 280.8 & 279.846686546907 & 0.953313453092846 \tabularnewline
71 & 284.4 & 288.07028760314 & -3.6702876031402 \tabularnewline
72 & 288.5 & 290.039409846905 & -1.53940984690485 \tabularnewline
73 & 284.8 & 293.455379179962 & -8.65537917996238 \tabularnewline
74 & 288.9 & 285.909395730517 & 2.99060426948319 \tabularnewline
75 & 299.6 & 291.338258890077 & 8.26174110992338 \tabularnewline
76 & 307.8 & 305.709330822538 & 2.09066917746202 \tabularnewline
77 & 311.4 & 314.838311389143 & -3.43831138914328 \tabularnewline
78 & 322 & 316.9105113446 & 5.08948865540003 \tabularnewline
79 & 317.8 & 329.772005466097 & -11.9720054660967 \tabularnewline
80 & 319.1 & 320.252292265562 & -1.15229226556181 \tabularnewline
81 & 322.3 & 321.040275762283 & 1.2597242377168 \tabularnewline
82 & 323.1 & 324.800029236786 & -1.70002923678612 \tabularnewline
83 & 322.8 & 324.84462798026 & -2.04462798026009 \tabularnewline
84 & 325 & 323.636105637235 & 1.36389436276545 \tabularnewline
85 & 323.2 & 326.442146694122 & -3.24214669412225 \tabularnewline
86 & 318.8 & 323.201511654685 & -4.40151165468501 \tabularnewline
87 & 328.2 & 316.845717387965 & 11.3542826120352 \tabularnewline
88 & 329.2 & 331.29094788547 & -2.09094788546969 \tabularnewline
89 & 326.5 & 331.361843476065 & -4.8618434760653 \tabularnewline
90 & 330.1 & 326.501502588166 & 3.5984974118337 \tabularnewline
91 & 323.8 & 331.700480657299 & -7.90048065729877 \tabularnewline
92 & 321.8 & 321.889933375791 & -0.0899333757909631 \tabularnewline
93 & 319.6 & 319.849971836539 & -0.249971836538521 \tabularnewline
94 & 315.5 & 317.538897841262 & -2.03889784126164 \tabularnewline
95 & 310.7 & 312.5329216628 & -1.83292166279955 \tabularnewline
96 & 306.5 & 306.918470183241 & -0.418470183241368 \tabularnewline
97 & 295.1 & 302.532524615131 & -7.43252461513049 \tabularnewline
98 & 288 & 287.829911747104 & 0.170088252895539 \tabularnewline
99 & 293.9 & 280.805489788457 & 13.0945102115434 \tabularnewline
100 & 289.3 & 292.523983525713 & -3.22398352571315 \tabularnewline
101 & 287.4 & 286.491419218203 & 0.908580781796616 \tabularnewline
102 & 282.6 & 284.995143489159 & -2.39514348915884 \tabularnewline
103 & 276.9 & 279.130870968357 & -2.23087096835729 \tabularnewline
104 & 272.7 & 272.439592291391 & 0.260407708608625 \tabularnewline
105 & 267.9 & 268.35530342508 & -0.455303425079876 \tabularnewline
106 & 262.8 & 263.352991151877 & -0.552991151876711 \tabularnewline
107 & 256.6 & 258.007271724271 & -1.40727172427137 \tabularnewline
108 & 250.7 & 251.181956108642 & -0.481956108642436 \tabularnewline
109 & 243.2 & 245.067800821086 & -1.86780082108558 \tabularnewline
110 & 235.1 & 236.73785092572 & -1.63785092572036 \tabularnewline
111 & 229.6 & 227.910078355391 & 1.68992164460937 \tabularnewline
112 & 222.9 & 223.160988343375 & -0.260988343375203 \tabularnewline
113 & 217.6 & 216.345019206928 & 1.2549807930715 \tabularnewline
114 & 214.1 & 211.602664950595 & 2.49733504940508 \tabularnewline
115 & 210.8 & 209.21234588635 & 1.58765411365039 \tabularnewline
116 & 208 & 206.617813702096 & 1.3821862979041 \tabularnewline
117 & 202.6 & 204.431982707897 & -1.83198270789705 \tabularnewline
118 & 199 & 198.21794844923 & 0.782051550769978 \tabularnewline
119 & 195.5 & 194.965449957637 & 0.534550042362611 \tabularnewline
120 & 192.1 & 191.702975151286 & 0.3970248487135 \tabularnewline
121 & 189.4 & 188.479391569958 & 0.92060843004225 \tabularnewline
122 & 182.4 & 186.188460278763 & -3.7884602787625 \tabularnewline
123 & 179.2 & 177.505072962268 & 1.69492703773238 \tabularnewline
124 & 176.5 & 175.058207076857 & 1.441792923143 \tabularnewline
125 & 174 & 172.998862050445 & 1.00113794955465 \tabularnewline
126 & 171.7 & 170.943713732219 & 0.756286267780496 \tabularnewline
127 & 169.8 & 168.979766539202 & 0.820233460797738 \tabularnewline
128 & 168.3 & 167.444234028069 & 0.855765971931049 \tabularnewline
129 & 166.4 & 166.324490247492 & 0.0755097525079975 \tabularnewline
130 & 165.9 & 164.458042706879 & 1.44195729312068 \tabularnewline
131 & 166.4 & 164.598770717616 & 1.80122928238393 \tabularnewline
132 & 170.6 & 165.899139813489 & 4.70086018651082 \tabularnewline
133 & 177.6 & 172.187948414426 & 5.41205158557358 \tabularnewline
134 & 183.4 & 181.59277209608 & 1.80722790392036 \tabularnewline
135 & 191.9 & 188.195806655668 & 3.70419334433169 \tabularnewline
136 & 201.7 & 198.341750293681 & 3.35824970631901 \tabularnewline
137 & 210.6 & 209.633975246634 & 0.966024753366156 \tabularnewline
138 & 221.6 & 218.963224518786 & 2.63677548121385 \tabularnewline
139 & 232.2 & 231.134865258008 & 1.06513474199247 \tabularnewline
140 & 240.4 & 242.208153660972 & -1.80815366097156 \tabularnewline
141 & 248.4 & 249.604707744905 & -1.20470774490468 \tabularnewline
142 & 258.5 & 257.069400631029 & 1.43059936897066 \tabularnewline
143 & 265 & 267.805081793166 & -2.80508179316558 \tabularnewline
144 & 271.7 & 273.058654810991 & -1.35865481099114 \tabularnewline
145 & 273.9 & 279.154941928177 & -5.25494192817735 \tabularnewline
146 & 277.8 & 279.019929300382 & -1.21992930038209 \tabularnewline
147 & 273.4 & 282.377858548632 & -8.97785854863218 \tabularnewline
148 & 270.9 & 273.988582669253 & -3.08858266925313 \tabularnewline
149 & 268.3 & 270.116183195907 & -1.81618319590689 \tabularnewline
150 & 264.7 & 266.709169387801 & -2.00916938780136 \tabularnewline
151 & 264.1 & 262.216402929862 & 1.88359707013802 \tabularnewline
152 & 264.5 & 262.453371825915 & 2.04662817408473 \tabularnewline
153 & 262.2 & 263.762782947143 & -1.56278294714275 \tabularnewline
154 & 258.6 & 260.768366535705 & -2.16836653570448 \tabularnewline
155 & 259.4 & 256.20486145577 & 3.19513854422974 \tabularnewline
156 & 262.7 & 258.42460861003 & 4.27539138996974 \tabularnewline
157 & 264.9 & 263.624361836763 & 1.27563816323732 \tabularnewline
158 & 260.5 & 266.391186601026 & -5.89118660102599 \tabularnewline
159 & 256.4 & 259.373461173399 & -2.9734611733989 \tabularnewline
160 & 254.7 & 253.95221548067 & 0.747784519330082 \tabularnewline
161 & 254.8 & 252.584490569409 & 2.21550943059071 \tabularnewline
162 & 255.3 & 253.668943407925 & 1.63105659207511 \tabularnewline
163 & 256.8 & 254.893696943016 & 1.9063030569842 \tabularnewline
164 & 258.7 & 257.240755154372 & 1.45924484562795 \tabularnewline
165 & 259.8 & 259.789164820579 & 0.0108351794210648 \tabularnewline
166 & 261.7 & 260.89397938963 & 0.806020610369956 \tabularnewline
167 & 264.7 & 263.152131454715 & 1.54786854528521 \tabularnewline
168 & 269.1 & 266.839920710773 & 2.26007928922746 \tabularnewline
169 & 279 & 272.244177989405 & 6.75582201059467 \tabularnewline
170 & 283.4 & 285.146100735933 & -1.7461007359326 \tabularnewline
171 & 285.5 & 288.770227791278 & -3.2702277912777 \tabularnewline
172 & 288.2 & 289.417115027566 & -1.21711502756568 \tabularnewline
173 & 292.1 & 291.576294786793 & 0.523705213207393 \tabularnewline
174 & 295.6 & 295.70900112357 & -0.109001123569499 \tabularnewline
175 & 302.4 & 299.160566906131 & 3.23943309386942 \tabularnewline
176 & 308.5 & 307.399996168046 & 1.10000383195444 \tabularnewline
177 & 314.1 & 313.988778512997 & 0.111221487003263 \tabularnewline
178 & 319.8 & 319.638199340131 & 0.161800659868618 \tabularnewline
179 & 329.7 & 325.410094822354 & 4.28990517764589 \tabularnewline
180 & 339.7 & 337.216297193143 & 2.48370280685748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234886&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]326.3[/C][C]324.8[/C][C]1.50000000000006[/C][/ROW]
[ROW][C]4[/C][C]315.4[/C][C]324.566519057596[/C][C]-9.16651905759647[/C][/ROW]
[ROW][C]5[/C][C]308.6[/C][C]309.593412628457[/C][C]-0.993412628457008[/C][/ROW]
[ROW][C]6[/C][C]302.6[/C][C]302.351993662508[/C][C]0.248006337491972[/C][/ROW]
[ROW][C]7[/C][C]295.6[/C][C]296.46219429607[/C][C]-0.862194296070072[/C][/ROW]
[ROW][C]8[/C][C]291.5[/C][C]289.079081676282[/C][C]2.42091832371767[/C][/ROW]
[ROW][C]9[/C][C]288.1[/C][C]286.054807142711[/C][C]2.04519285728952[/C][/ROW]
[ROW][C]10[/C][C]281.1[/C][C]283.563580486606[/C][C]-2.46358048660625[/C][/ROW]
[ROW][C]11[/C][C]282.4[/C][C]275.468898257109[/C][C]6.93110174289092[/C][/ROW]
[ROW][C]12[/C][C]284.9[/C][C]279.848705858293[/C][C]5.05129414170648[/C][/ROW]
[ROW][C]13[/C][C]274.2[/C][C]284.593228398942[/C][C]-10.393228398942[/C][/ROW]
[ROW][C]14[/C][C]265.7[/C][C]269.27503853371[/C][C]-3.57503853371037[/C][/ROW]
[ROW][C]15[/C][C]259.7[/C][C]259.186484324137[/C][C]0.51351567586272[/C][/ROW]
[ROW][C]16[/C][C]253.7[/C][C]253.414662980362[/C][C]0.285337019638035[/C][/ROW]
[ROW][C]17[/C][C]249.5[/C][C]247.541451354646[/C][C]1.95854864535369[/C][/ROW]
[ROW][C]18[/C][C]244.6[/C][C]244.211724686218[/C][C]0.388275313781719[/C][/ROW]
[ROW][C]19[/C][C]243[/C][C]239.484253283705[/C][C]3.51574671629521[/C][/ROW]
[ROW][C]20[/C][C]239.2[/C][C]239.4464614091[/C][C]-0.24646140910005[/C][/ROW]
[ROW][C]21[/C][C]235.7[/C][C]235.536947258349[/C][C]0.163052741651455[/C][/ROW]
[ROW][C]22[/C][C]231.1[/C][C]232.109399098151[/C][C]-1.00939909815122[/C][/ROW]
[ROW][C]23[/C][C]226.7[/C][C]227.060876607726[/C][C]-0.360876607725601[/C][/ROW]
[ROW][C]24[/C][C]221.7[/C][C]222.500522516732[/C][C]-0.800522516732343[/C][/ROW]
[ROW][C]25[/C][C]219.4[/C][C]217.144813507774[/C][C]2.25518649222579[/C][/ROW]
[ROW][C]26[/C][C]214.2[/C][C]215.846896691443[/C][C]-1.64689669144263[/C][/ROW]
[ROW][C]27[/C][C]211.7[/C][C]209.91510467095[/C][C]1.7848953290501[/C][/ROW]
[ROW][C]28[/C][C]207.7[/C][C]208.208215839368[/C][C]-0.50821583936775[/C][/ROW]
[ROW][C]29[/C][C]204.7[/C][C]203.982392144494[/C][C]0.71760785550623[/C][/ROW]
[ROW][C]30[/C][C]201.2[/C][C]201.301258352211[/C][C]-0.101258352210976[/C][/ROW]
[ROW][C]31[/C][C]199.9[/C][C]197.756264604551[/C][C]2.14373539544866[/C][/ROW]
[ROW][C]32[/C][C]197.8[/C][C]197.408824934892[/C][C]0.391175065108257[/C][/ROW]
[ROW][C]33[/C][C]195.2[/C][C]195.482642025393[/C][C]-0.282642025392562[/C][/ROW]
[ROW][C]34[/C][C]194.3[/C][C]192.757051161125[/C][C]1.54294883887536[/C][/ROW]
[ROW][C]35[/C][C]192.8[/C][C]192.542654365129[/C][C]0.257345634870831[/C][/ROW]
[ROW][C]36[/C][C]188.5[/C][C]191.157004878483[/C][C]-2.65700487848295[/C][/ROW]
[ROW][C]37[/C][C]183.2[/C][C]185.676375286726[/C][C]-2.47637528672587[/C][/ROW]
[ROW][C]38[/C][C]181.4[/C][C]179.276007738483[/C][C]2.12399226151661[/C][/ROW]
[ROW][C]39[/C][C]180.5[/C][C]178.419795285476[/C][C]2.08020471452446[/C][/ROW]
[ROW][C]40[/C][C]180.2[/C][C]178.444126009431[/C][C]1.75587399056943[/C][/ROW]
[ROW][C]41[/C][C]179.2[/C][C]178.924341661066[/C][C]0.275658338934477[/C][/ROW]
[ROW][C]42[/C][C]177.1[/C][C]178.046829351922[/C][C]-0.946829351922332[/C][/ROW]
[ROW][C]43[/C][C]174.2[/C][C]175.526109480357[/C][C]-1.32610948035705[/C][/ROW]
[ROW][C]44[/C][C]172.1[/C][C]172.036857986279[/C][C]0.0631420137211478[/C][/ROW]
[ROW][C]45[/C][C]171.1[/C][C]169.964914889932[/C][C]1.13508511006771[/C][/ROW]
[ROW][C]46[/C][C]169.8[/C][C]169.469285461835[/C][C]0.330714538165012[/C][/ROW]
[ROW][C]47[/C][C]169.5[/C][C]168.316237156709[/C][C]1.18376284329085[/C][/ROW]
[ROW][C]48[/C][C]165.5[/C][C]168.542237486528[/C][C]-3.04223748652774[/C][/ROW]
[ROW][C]49[/C][C]167.2[/C][C]163.190431311524[/C][C]4.00956868847561[/C][/ROW]
[ROW][C]50[/C][C]167.6[/C][C]166.672067273932[/C][C]0.927932726068292[/C][/ROW]
[ROW][C]51[/C][C]171.8[/C][C]167.48439050466[/C][C]4.31560949534034[/C][/ROW]
[ROW][C]52[/C][C]175.9[/C][C]173.602014487185[/C][C]2.29798551281465[/C][/ROW]
[ROW][C]53[/C][C]180[/C][C]178.7231152461[/C][C]1.2768847539003[/C][/ROW]
[ROW][C]54[/C][C]184.9[/C][C]183.390493927986[/C][C]1.50950607201437[/C][/ROW]
[ROW][C]55[/C][C]184.6[/C][C]188.961236971022[/C][C]-4.36123697102241[/C][/ROW]
[ROW][C]56[/C][C]187.6[/C][C]186.723338600435[/C][C]0.876661399564711[/C][/ROW]
[ROW][C]57[/C][C]191.5[/C][C]190.112879620348[/C][C]1.387120379652[/C][/ROW]
[ROW][C]58[/C][C]195.5[/C][C]194.629241065827[/C][C]0.870758934173011[/C][/ROW]
[ROW][C]59[/C][C]201.6[/C][C]199.016159348626[/C][C]2.58384065137389[/C][/ROW]
[ROW][C]60[/C][C]203.5[/C][C]206.264278705915[/C][C]-2.76427870591485[/C][/ROW]
[ROW][C]61[/C][C]209.1[/C][C]206.935982413915[/C][C]2.16401758608535[/C][/ROW]
[ROW][C]62[/C][C]217.1[/C][C]213.497555055314[/C][C]3.60244494468552[/C][/ROW]
[ROW][C]63[/C][C]227.6[/C][C]223.098287195031[/C][C]4.50171280496895[/C][/ROW]
[ROW][C]64[/C][C]237.2[/C][C]235.598605445923[/C][C]1.6013945540771[/C][/ROW]
[ROW][C]65[/C][C]245.6[/C][C]245.910178771939[/C][C]-0.31017877193861[/C][/ROW]
[ROW][C]66[/C][C]253.2[/C][C]254.172352063433[/C][C]-0.972352063432652[/C][/ROW]
[ROW][C]67[/C][C]260.5[/C][C]261.340291276119[/C][C]-0.840291276118592[/C][/ROW]
[ROW][C]68[/C][C]266.1[/C][C]268.266911176475[/C][C]-2.1669111764752[/C][/ROW]
[ROW][C]69[/C][C]273[/C][C]272.904052779649[/C][C]0.0959472203510927[/C][/ROW]
[ROW][C]70[/C][C]280.8[/C][C]279.846686546907[/C][C]0.953313453092846[/C][/ROW]
[ROW][C]71[/C][C]284.4[/C][C]288.07028760314[/C][C]-3.6702876031402[/C][/ROW]
[ROW][C]72[/C][C]288.5[/C][C]290.039409846905[/C][C]-1.53940984690485[/C][/ROW]
[ROW][C]73[/C][C]284.8[/C][C]293.455379179962[/C][C]-8.65537917996238[/C][/ROW]
[ROW][C]74[/C][C]288.9[/C][C]285.909395730517[/C][C]2.99060426948319[/C][/ROW]
[ROW][C]75[/C][C]299.6[/C][C]291.338258890077[/C][C]8.26174110992338[/C][/ROW]
[ROW][C]76[/C][C]307.8[/C][C]305.709330822538[/C][C]2.09066917746202[/C][/ROW]
[ROW][C]77[/C][C]311.4[/C][C]314.838311389143[/C][C]-3.43831138914328[/C][/ROW]
[ROW][C]78[/C][C]322[/C][C]316.9105113446[/C][C]5.08948865540003[/C][/ROW]
[ROW][C]79[/C][C]317.8[/C][C]329.772005466097[/C][C]-11.9720054660967[/C][/ROW]
[ROW][C]80[/C][C]319.1[/C][C]320.252292265562[/C][C]-1.15229226556181[/C][/ROW]
[ROW][C]81[/C][C]322.3[/C][C]321.040275762283[/C][C]1.2597242377168[/C][/ROW]
[ROW][C]82[/C][C]323.1[/C][C]324.800029236786[/C][C]-1.70002923678612[/C][/ROW]
[ROW][C]83[/C][C]322.8[/C][C]324.84462798026[/C][C]-2.04462798026009[/C][/ROW]
[ROW][C]84[/C][C]325[/C][C]323.636105637235[/C][C]1.36389436276545[/C][/ROW]
[ROW][C]85[/C][C]323.2[/C][C]326.442146694122[/C][C]-3.24214669412225[/C][/ROW]
[ROW][C]86[/C][C]318.8[/C][C]323.201511654685[/C][C]-4.40151165468501[/C][/ROW]
[ROW][C]87[/C][C]328.2[/C][C]316.845717387965[/C][C]11.3542826120352[/C][/ROW]
[ROW][C]88[/C][C]329.2[/C][C]331.29094788547[/C][C]-2.09094788546969[/C][/ROW]
[ROW][C]89[/C][C]326.5[/C][C]331.361843476065[/C][C]-4.8618434760653[/C][/ROW]
[ROW][C]90[/C][C]330.1[/C][C]326.501502588166[/C][C]3.5984974118337[/C][/ROW]
[ROW][C]91[/C][C]323.8[/C][C]331.700480657299[/C][C]-7.90048065729877[/C][/ROW]
[ROW][C]92[/C][C]321.8[/C][C]321.889933375791[/C][C]-0.0899333757909631[/C][/ROW]
[ROW][C]93[/C][C]319.6[/C][C]319.849971836539[/C][C]-0.249971836538521[/C][/ROW]
[ROW][C]94[/C][C]315.5[/C][C]317.538897841262[/C][C]-2.03889784126164[/C][/ROW]
[ROW][C]95[/C][C]310.7[/C][C]312.5329216628[/C][C]-1.83292166279955[/C][/ROW]
[ROW][C]96[/C][C]306.5[/C][C]306.918470183241[/C][C]-0.418470183241368[/C][/ROW]
[ROW][C]97[/C][C]295.1[/C][C]302.532524615131[/C][C]-7.43252461513049[/C][/ROW]
[ROW][C]98[/C][C]288[/C][C]287.829911747104[/C][C]0.170088252895539[/C][/ROW]
[ROW][C]99[/C][C]293.9[/C][C]280.805489788457[/C][C]13.0945102115434[/C][/ROW]
[ROW][C]100[/C][C]289.3[/C][C]292.523983525713[/C][C]-3.22398352571315[/C][/ROW]
[ROW][C]101[/C][C]287.4[/C][C]286.491419218203[/C][C]0.908580781796616[/C][/ROW]
[ROW][C]102[/C][C]282.6[/C][C]284.995143489159[/C][C]-2.39514348915884[/C][/ROW]
[ROW][C]103[/C][C]276.9[/C][C]279.130870968357[/C][C]-2.23087096835729[/C][/ROW]
[ROW][C]104[/C][C]272.7[/C][C]272.439592291391[/C][C]0.260407708608625[/C][/ROW]
[ROW][C]105[/C][C]267.9[/C][C]268.35530342508[/C][C]-0.455303425079876[/C][/ROW]
[ROW][C]106[/C][C]262.8[/C][C]263.352991151877[/C][C]-0.552991151876711[/C][/ROW]
[ROW][C]107[/C][C]256.6[/C][C]258.007271724271[/C][C]-1.40727172427137[/C][/ROW]
[ROW][C]108[/C][C]250.7[/C][C]251.181956108642[/C][C]-0.481956108642436[/C][/ROW]
[ROW][C]109[/C][C]243.2[/C][C]245.067800821086[/C][C]-1.86780082108558[/C][/ROW]
[ROW][C]110[/C][C]235.1[/C][C]236.73785092572[/C][C]-1.63785092572036[/C][/ROW]
[ROW][C]111[/C][C]229.6[/C][C]227.910078355391[/C][C]1.68992164460937[/C][/ROW]
[ROW][C]112[/C][C]222.9[/C][C]223.160988343375[/C][C]-0.260988343375203[/C][/ROW]
[ROW][C]113[/C][C]217.6[/C][C]216.345019206928[/C][C]1.2549807930715[/C][/ROW]
[ROW][C]114[/C][C]214.1[/C][C]211.602664950595[/C][C]2.49733504940508[/C][/ROW]
[ROW][C]115[/C][C]210.8[/C][C]209.21234588635[/C][C]1.58765411365039[/C][/ROW]
[ROW][C]116[/C][C]208[/C][C]206.617813702096[/C][C]1.3821862979041[/C][/ROW]
[ROW][C]117[/C][C]202.6[/C][C]204.431982707897[/C][C]-1.83198270789705[/C][/ROW]
[ROW][C]118[/C][C]199[/C][C]198.21794844923[/C][C]0.782051550769978[/C][/ROW]
[ROW][C]119[/C][C]195.5[/C][C]194.965449957637[/C][C]0.534550042362611[/C][/ROW]
[ROW][C]120[/C][C]192.1[/C][C]191.702975151286[/C][C]0.3970248487135[/C][/ROW]
[ROW][C]121[/C][C]189.4[/C][C]188.479391569958[/C][C]0.92060843004225[/C][/ROW]
[ROW][C]122[/C][C]182.4[/C][C]186.188460278763[/C][C]-3.7884602787625[/C][/ROW]
[ROW][C]123[/C][C]179.2[/C][C]177.505072962268[/C][C]1.69492703773238[/C][/ROW]
[ROW][C]124[/C][C]176.5[/C][C]175.058207076857[/C][C]1.441792923143[/C][/ROW]
[ROW][C]125[/C][C]174[/C][C]172.998862050445[/C][C]1.00113794955465[/C][/ROW]
[ROW][C]126[/C][C]171.7[/C][C]170.943713732219[/C][C]0.756286267780496[/C][/ROW]
[ROW][C]127[/C][C]169.8[/C][C]168.979766539202[/C][C]0.820233460797738[/C][/ROW]
[ROW][C]128[/C][C]168.3[/C][C]167.444234028069[/C][C]0.855765971931049[/C][/ROW]
[ROW][C]129[/C][C]166.4[/C][C]166.324490247492[/C][C]0.0755097525079975[/C][/ROW]
[ROW][C]130[/C][C]165.9[/C][C]164.458042706879[/C][C]1.44195729312068[/C][/ROW]
[ROW][C]131[/C][C]166.4[/C][C]164.598770717616[/C][C]1.80122928238393[/C][/ROW]
[ROW][C]132[/C][C]170.6[/C][C]165.899139813489[/C][C]4.70086018651082[/C][/ROW]
[ROW][C]133[/C][C]177.6[/C][C]172.187948414426[/C][C]5.41205158557358[/C][/ROW]
[ROW][C]134[/C][C]183.4[/C][C]181.59277209608[/C][C]1.80722790392036[/C][/ROW]
[ROW][C]135[/C][C]191.9[/C][C]188.195806655668[/C][C]3.70419334433169[/C][/ROW]
[ROW][C]136[/C][C]201.7[/C][C]198.341750293681[/C][C]3.35824970631901[/C][/ROW]
[ROW][C]137[/C][C]210.6[/C][C]209.633975246634[/C][C]0.966024753366156[/C][/ROW]
[ROW][C]138[/C][C]221.6[/C][C]218.963224518786[/C][C]2.63677548121385[/C][/ROW]
[ROW][C]139[/C][C]232.2[/C][C]231.134865258008[/C][C]1.06513474199247[/C][/ROW]
[ROW][C]140[/C][C]240.4[/C][C]242.208153660972[/C][C]-1.80815366097156[/C][/ROW]
[ROW][C]141[/C][C]248.4[/C][C]249.604707744905[/C][C]-1.20470774490468[/C][/ROW]
[ROW][C]142[/C][C]258.5[/C][C]257.069400631029[/C][C]1.43059936897066[/C][/ROW]
[ROW][C]143[/C][C]265[/C][C]267.805081793166[/C][C]-2.80508179316558[/C][/ROW]
[ROW][C]144[/C][C]271.7[/C][C]273.058654810991[/C][C]-1.35865481099114[/C][/ROW]
[ROW][C]145[/C][C]273.9[/C][C]279.154941928177[/C][C]-5.25494192817735[/C][/ROW]
[ROW][C]146[/C][C]277.8[/C][C]279.019929300382[/C][C]-1.21992930038209[/C][/ROW]
[ROW][C]147[/C][C]273.4[/C][C]282.377858548632[/C][C]-8.97785854863218[/C][/ROW]
[ROW][C]148[/C][C]270.9[/C][C]273.988582669253[/C][C]-3.08858266925313[/C][/ROW]
[ROW][C]149[/C][C]268.3[/C][C]270.116183195907[/C][C]-1.81618319590689[/C][/ROW]
[ROW][C]150[/C][C]264.7[/C][C]266.709169387801[/C][C]-2.00916938780136[/C][/ROW]
[ROW][C]151[/C][C]264.1[/C][C]262.216402929862[/C][C]1.88359707013802[/C][/ROW]
[ROW][C]152[/C][C]264.5[/C][C]262.453371825915[/C][C]2.04662817408473[/C][/ROW]
[ROW][C]153[/C][C]262.2[/C][C]263.762782947143[/C][C]-1.56278294714275[/C][/ROW]
[ROW][C]154[/C][C]258.6[/C][C]260.768366535705[/C][C]-2.16836653570448[/C][/ROW]
[ROW][C]155[/C][C]259.4[/C][C]256.20486145577[/C][C]3.19513854422974[/C][/ROW]
[ROW][C]156[/C][C]262.7[/C][C]258.42460861003[/C][C]4.27539138996974[/C][/ROW]
[ROW][C]157[/C][C]264.9[/C][C]263.624361836763[/C][C]1.27563816323732[/C][/ROW]
[ROW][C]158[/C][C]260.5[/C][C]266.391186601026[/C][C]-5.89118660102599[/C][/ROW]
[ROW][C]159[/C][C]256.4[/C][C]259.373461173399[/C][C]-2.9734611733989[/C][/ROW]
[ROW][C]160[/C][C]254.7[/C][C]253.95221548067[/C][C]0.747784519330082[/C][/ROW]
[ROW][C]161[/C][C]254.8[/C][C]252.584490569409[/C][C]2.21550943059071[/C][/ROW]
[ROW][C]162[/C][C]255.3[/C][C]253.668943407925[/C][C]1.63105659207511[/C][/ROW]
[ROW][C]163[/C][C]256.8[/C][C]254.893696943016[/C][C]1.9063030569842[/C][/ROW]
[ROW][C]164[/C][C]258.7[/C][C]257.240755154372[/C][C]1.45924484562795[/C][/ROW]
[ROW][C]165[/C][C]259.8[/C][C]259.789164820579[/C][C]0.0108351794210648[/C][/ROW]
[ROW][C]166[/C][C]261.7[/C][C]260.89397938963[/C][C]0.806020610369956[/C][/ROW]
[ROW][C]167[/C][C]264.7[/C][C]263.152131454715[/C][C]1.54786854528521[/C][/ROW]
[ROW][C]168[/C][C]269.1[/C][C]266.839920710773[/C][C]2.26007928922746[/C][/ROW]
[ROW][C]169[/C][C]279[/C][C]272.244177989405[/C][C]6.75582201059467[/C][/ROW]
[ROW][C]170[/C][C]283.4[/C][C]285.146100735933[/C][C]-1.7461007359326[/C][/ROW]
[ROW][C]171[/C][C]285.5[/C][C]288.770227791278[/C][C]-3.2702277912777[/C][/ROW]
[ROW][C]172[/C][C]288.2[/C][C]289.417115027566[/C][C]-1.21711502756568[/C][/ROW]
[ROW][C]173[/C][C]292.1[/C][C]291.576294786793[/C][C]0.523705213207393[/C][/ROW]
[ROW][C]174[/C][C]295.6[/C][C]295.70900112357[/C][C]-0.109001123569499[/C][/ROW]
[ROW][C]175[/C][C]302.4[/C][C]299.160566906131[/C][C]3.23943309386942[/C][/ROW]
[ROW][C]176[/C][C]308.5[/C][C]307.399996168046[/C][C]1.10000383195444[/C][/ROW]
[ROW][C]177[/C][C]314.1[/C][C]313.988778512997[/C][C]0.111221487003263[/C][/ROW]
[ROW][C]178[/C][C]319.8[/C][C]319.638199340131[/C][C]0.161800659868618[/C][/ROW]
[ROW][C]179[/C][C]329.7[/C][C]325.410094822354[/C][C]4.28990517764589[/C][/ROW]
[ROW][C]180[/C][C]339.7[/C][C]337.216297193143[/C][C]2.48370280685748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234886&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234886&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3326.3324.81.50000000000006
4315.4324.566519057596-9.16651905759647
5308.6309.593412628457-0.993412628457008
6302.6302.3519936625080.248006337491972
7295.6296.46219429607-0.862194296070072
8291.5289.0790816762822.42091832371767
9288.1286.0548071427112.04519285728952
10281.1283.563580486606-2.46358048660625
11282.4275.4688982571096.93110174289092
12284.9279.8487058582935.05129414170648
13274.2284.593228398942-10.393228398942
14265.7269.27503853371-3.57503853371037
15259.7259.1864843241370.51351567586272
16253.7253.4146629803620.285337019638035
17249.5247.5414513546461.95854864535369
18244.6244.2117246862180.388275313781719
19243239.4842532837053.51574671629521
20239.2239.4464614091-0.24646140910005
21235.7235.5369472583490.163052741651455
22231.1232.109399098151-1.00939909815122
23226.7227.060876607726-0.360876607725601
24221.7222.500522516732-0.800522516732343
25219.4217.1448135077742.25518649222579
26214.2215.846896691443-1.64689669144263
27211.7209.915104670951.7848953290501
28207.7208.208215839368-0.50821583936775
29204.7203.9823921444940.71760785550623
30201.2201.301258352211-0.101258352210976
31199.9197.7562646045512.14373539544866
32197.8197.4088249348920.391175065108257
33195.2195.482642025393-0.282642025392562
34194.3192.7570511611251.54294883887536
35192.8192.5426543651290.257345634870831
36188.5191.157004878483-2.65700487848295
37183.2185.676375286726-2.47637528672587
38181.4179.2760077384832.12399226151661
39180.5178.4197952854762.08020471452446
40180.2178.4441260094311.75587399056943
41179.2178.9243416610660.275658338934477
42177.1178.046829351922-0.946829351922332
43174.2175.526109480357-1.32610948035705
44172.1172.0368579862790.0631420137211478
45171.1169.9649148899321.13508511006771
46169.8169.4692854618350.330714538165012
47169.5168.3162371567091.18376284329085
48165.5168.542237486528-3.04223748652774
49167.2163.1904313115244.00956868847561
50167.6166.6720672739320.927932726068292
51171.8167.484390504664.31560949534034
52175.9173.6020144871852.29798551281465
53180178.72311524611.2768847539003
54184.9183.3904939279861.50950607201437
55184.6188.961236971022-4.36123697102241
56187.6186.7233386004350.876661399564711
57191.5190.1128796203481.387120379652
58195.5194.6292410658270.870758934173011
59201.6199.0161593486262.58384065137389
60203.5206.264278705915-2.76427870591485
61209.1206.9359824139152.16401758608535
62217.1213.4975550553143.60244494468552
63227.6223.0982871950314.50171280496895
64237.2235.5986054459231.6013945540771
65245.6245.910178771939-0.31017877193861
66253.2254.172352063433-0.972352063432652
67260.5261.340291276119-0.840291276118592
68266.1268.266911176475-2.1669111764752
69273272.9040527796490.0959472203510927
70280.8279.8466865469070.953313453092846
71284.4288.07028760314-3.6702876031402
72288.5290.039409846905-1.53940984690485
73284.8293.455379179962-8.65537917996238
74288.9285.9093957305172.99060426948319
75299.6291.3382588900778.26174110992338
76307.8305.7093308225382.09066917746202
77311.4314.838311389143-3.43831138914328
78322316.91051134465.08948865540003
79317.8329.772005466097-11.9720054660967
80319.1320.252292265562-1.15229226556181
81322.3321.0402757622831.2597242377168
82323.1324.800029236786-1.70002923678612
83322.8324.84462798026-2.04462798026009
84325323.6361056372351.36389436276545
85323.2326.442146694122-3.24214669412225
86318.8323.201511654685-4.40151165468501
87328.2316.84571738796511.3542826120352
88329.2331.29094788547-2.09094788546969
89326.5331.361843476065-4.8618434760653
90330.1326.5015025881663.5984974118337
91323.8331.700480657299-7.90048065729877
92321.8321.889933375791-0.0899333757909631
93319.6319.849971836539-0.249971836538521
94315.5317.538897841262-2.03889784126164
95310.7312.5329216628-1.83292166279955
96306.5306.918470183241-0.418470183241368
97295.1302.532524615131-7.43252461513049
98288287.8299117471040.170088252895539
99293.9280.80548978845713.0945102115434
100289.3292.523983525713-3.22398352571315
101287.4286.4914192182030.908580781796616
102282.6284.995143489159-2.39514348915884
103276.9279.130870968357-2.23087096835729
104272.7272.4395922913910.260407708608625
105267.9268.35530342508-0.455303425079876
106262.8263.352991151877-0.552991151876711
107256.6258.007271724271-1.40727172427137
108250.7251.181956108642-0.481956108642436
109243.2245.067800821086-1.86780082108558
110235.1236.73785092572-1.63785092572036
111229.6227.9100783553911.68992164460937
112222.9223.160988343375-0.260988343375203
113217.6216.3450192069281.2549807930715
114214.1211.6026649505952.49733504940508
115210.8209.212345886351.58765411365039
116208206.6178137020961.3821862979041
117202.6204.431982707897-1.83198270789705
118199198.217948449230.782051550769978
119195.5194.9654499576370.534550042362611
120192.1191.7029751512860.3970248487135
121189.4188.4793915699580.92060843004225
122182.4186.188460278763-3.7884602787625
123179.2177.5050729622681.69492703773238
124176.5175.0582070768571.441792923143
125174172.9988620504451.00113794955465
126171.7170.9437137322190.756286267780496
127169.8168.9797665392020.820233460797738
128168.3167.4442340280690.855765971931049
129166.4166.3244902474920.0755097525079975
130165.9164.4580427068791.44195729312068
131166.4164.5987707176161.80122928238393
132170.6165.8991398134894.70086018651082
133177.6172.1879484144265.41205158557358
134183.4181.592772096081.80722790392036
135191.9188.1958066556683.70419334433169
136201.7198.3417502936813.35824970631901
137210.6209.6339752466340.966024753366156
138221.6218.9632245187862.63677548121385
139232.2231.1348652580081.06513474199247
140240.4242.208153660972-1.80815366097156
141248.4249.604707744905-1.20470774490468
142258.5257.0694006310291.43059936897066
143265267.805081793166-2.80508179316558
144271.7273.058654810991-1.35865481099114
145273.9279.154941928177-5.25494192817735
146277.8279.019929300382-1.21992930038209
147273.4282.377858548632-8.97785854863218
148270.9273.988582669253-3.08858266925313
149268.3270.116183195907-1.81618319590689
150264.7266.709169387801-2.00916938780136
151264.1262.2164029298621.88359707013802
152264.5262.4533718259152.04662817408473
153262.2263.762782947143-1.56278294714275
154258.6260.768366535705-2.16836653570448
155259.4256.204861455773.19513854422974
156262.7258.424608610034.27539138996974
157264.9263.6243618367631.27563816323732
158260.5266.391186601026-5.89118660102599
159256.4259.373461173399-2.9734611733989
160254.7253.952215480670.747784519330082
161254.8252.5844905694092.21550943059071
162255.3253.6689434079251.63105659207511
163256.8254.8936969430161.9063030569842
164258.7257.2407551543721.45924484562795
165259.8259.7891648205790.0108351794210648
166261.7260.893979389630.806020610369956
167264.7263.1521314547151.54786854528521
168269.1266.8399207107732.26007928922746
169279272.2441779894056.75582201059467
170283.4285.146100735933-1.7461007359326
171285.5288.770227791278-3.2702277912777
172288.2289.417115027566-1.21711502756568
173292.1291.5762947867930.523705213207393
174295.6295.70900112357-0.109001123569499
175302.4299.1605669061313.23943309386942
176308.5307.3999961680461.10000383195444
177314.1313.9887785129970.111221487003263
178319.8319.6381993401310.161800659868618
179329.7325.4100948223544.28990517764589
180339.7337.2162971931432.48370280685748






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
181348.319920695927341.927829888392354.712011503461
182356.939841391853345.710599693777368.16908308993
183365.55976208778349.072016837754382.047507337806
184374.179682783707351.948104823445396.411260743969
185382.799603479634354.349253299052411.249953660215
186391.41952417556356.298042791983426.541005559137
187400.039444871487357.817818222286442.261071520688
188408.659365567414358.930109156887458.388621977941
189417.279286263341359.654182150125474.904390376556
190425.899206959267360.007163354497491.791250564038
191434.519127655194360.004297500588509.0339578098
192443.139048351121359.659214004777526.618882697464

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
181 & 348.319920695927 & 341.927829888392 & 354.712011503461 \tabularnewline
182 & 356.939841391853 & 345.710599693777 & 368.16908308993 \tabularnewline
183 & 365.55976208778 & 349.072016837754 & 382.047507337806 \tabularnewline
184 & 374.179682783707 & 351.948104823445 & 396.411260743969 \tabularnewline
185 & 382.799603479634 & 354.349253299052 & 411.249953660215 \tabularnewline
186 & 391.41952417556 & 356.298042791983 & 426.541005559137 \tabularnewline
187 & 400.039444871487 & 357.817818222286 & 442.261071520688 \tabularnewline
188 & 408.659365567414 & 358.930109156887 & 458.388621977941 \tabularnewline
189 & 417.279286263341 & 359.654182150125 & 474.904390376556 \tabularnewline
190 & 425.899206959267 & 360.007163354497 & 491.791250564038 \tabularnewline
191 & 434.519127655194 & 360.004297500588 & 509.0339578098 \tabularnewline
192 & 443.139048351121 & 359.659214004777 & 526.618882697464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234886&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]181[/C][C]348.319920695927[/C][C]341.927829888392[/C][C]354.712011503461[/C][/ROW]
[ROW][C]182[/C][C]356.939841391853[/C][C]345.710599693777[/C][C]368.16908308993[/C][/ROW]
[ROW][C]183[/C][C]365.55976208778[/C][C]349.072016837754[/C][C]382.047507337806[/C][/ROW]
[ROW][C]184[/C][C]374.179682783707[/C][C]351.948104823445[/C][C]396.411260743969[/C][/ROW]
[ROW][C]185[/C][C]382.799603479634[/C][C]354.349253299052[/C][C]411.249953660215[/C][/ROW]
[ROW][C]186[/C][C]391.41952417556[/C][C]356.298042791983[/C][C]426.541005559137[/C][/ROW]
[ROW][C]187[/C][C]400.039444871487[/C][C]357.817818222286[/C][C]442.261071520688[/C][/ROW]
[ROW][C]188[/C][C]408.659365567414[/C][C]358.930109156887[/C][C]458.388621977941[/C][/ROW]
[ROW][C]189[/C][C]417.279286263341[/C][C]359.654182150125[/C][C]474.904390376556[/C][/ROW]
[ROW][C]190[/C][C]425.899206959267[/C][C]360.007163354497[/C][C]491.791250564038[/C][/ROW]
[ROW][C]191[/C][C]434.519127655194[/C][C]360.004297500588[/C][C]509.0339578098[/C][/ROW]
[ROW][C]192[/C][C]443.139048351121[/C][C]359.659214004777[/C][C]526.618882697464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234886&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234886&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
181348.319920695927341.927829888392354.712011503461
182356.939841391853345.710599693777368.16908308993
183365.55976208778349.072016837754382.047507337806
184374.179682783707351.948104823445396.411260743969
185382.799603479634354.349253299052411.249953660215
186391.41952417556356.298042791983426.541005559137
187400.039444871487357.817818222286442.261071520688
188408.659365567414358.930109156887458.388621977941
189417.279286263341359.654182150125474.904390376556
190425.899206959267360.007163354497491.791250564038
191434.519127655194360.004297500588509.0339578098
192443.139048351121359.659214004777526.618882697464


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')