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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 18:09:42 +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/2016/Apr/25/t1461604196t1csaw26ukylbkd.htm/, Retrieved Sun, 05 May 2024 23:20:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294747, Retrieved Sun, 05 May 2024 23:20:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 17:09:42] [e2ca982fef5d38be90899c2ec1ea6fcf] [Current]
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Dataseries X:
250785
250140
255755
254671
253919
253741
252729
253810
256653
255231
258405
251061
254811
254895
258325
257608
258759
258621
257852
260560
262358
260812
261165
257164
260720
259581
264743
261845
262262
261631
258953
259966
262850
262204
263418
262752
266433
267722
266003
262971
265521
264676
270223
269508
268457
265814
266680
263018
269285
269829
270911
266844
271244
269907
271296
270157
271322
267179
264101
265518
269419
268714
272482
268351
268175
270674
272764
272599
270333
270846
270491
269160
274027
273784
276663
274525
271344
271115
270798
273911
273985
271917
273338
270601
273547
275363
281229
277793
279913
282500
280041
282166
290304
283519
287816
285226
287595
289741
289148
288301
290155
289648
288225
289351
294735
305333
309030
310215
321935
325734
320846
323023
319753
321753
320757
324479
324641
322767
324181
321389
327897
334287
332653
334819
335264
339622
342440
346585
335378
337010
339130
341193
343507
348915
346431
348322
348288
346597
351076
355215
350562
355266
361565
363462
366183
365423
369208
366713
369354
371970
371824
373187
367270
368140
373742
364815
368558
371503
372611
370197
375441
375888
375132
381142
372024
376070
376864
371401
375687
384304
380738
379908
384007
384499
385106
387935
380435
379281
384153
380599




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294747&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294747&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294747&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.789051318979081
beta0.0123448757276883
gamma0.937438792723424

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.789051318979081 \tabularnewline
beta & 0.0123448757276883 \tabularnewline
gamma & 0.937438792723424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294747&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]0.789051318979081[/C][/ROW]
[ROW][C]beta[/C][C]0.0123448757276883[/C][/ROW]
[ROW][C]gamma[/C][C]0.937438792723424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294747&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294747&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
alpha0.789051318979081
beta0.0123448757276883
gamma0.937438792723424







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13254811252774.6456389162036.35436108371
14254895254389.011531162505.98846883775
15258325258119.678338033205.321661967086
16257608257518.6675888689.3324111398833
17258759258817.697836457-58.6978364574607
18258621258688.461047099-67.4610470992338
19257852257389.174968921462.825031079119
20260560258911.7830185831648.21698141668
21262358263259.402882181-901.402882181399
22260812261294.545844435-482.545844434935
23261165264259.30868544-3094.30868543976
24257164254367.6800158042796.31998419634
25260720260821.597389182-101.597389182163
26259581260440.342745724-859.342745723727
27264743263086.0520308481656.94796915207
28261845263590.539059669-1745.5390596686
29262262263419.887874012-1157.88787401165
30261631262397.126764529-766.126764529094
31258953260608.375303099-1655.37530309873
32259966260653.278517283-687.278517282859
33262850262582.09543888267.904561120202
34262204261563.840781186640.159218814457
35263418264858.123404223-1440.12340422289
36262752257338.6525348855413.34746511461
37266433265337.6505744861095.34942551446
38267722265740.343885191981.65611481032
39266003271261.005620253-5258.00562025298
40262971265586.493722252-2615.4937222522
41265521264811.076486724709.923513276211
42264676265312.828400023-636.828400022583
43270223263407.4597049416815.54029505863
44269508270434.365484084-926.36548408441
45268457272509.84966396-4052.84966395982
46265814268136.820481195-2322.82048119511
47266680268701.696121599-2021.69612159906
48263018261970.3871603111047.61283968919
49269285265612.4469978443672.55300215638
50269829268182.5358377951646.4641622054
51270911271967.573643649-1056.57364364946
52266844270103.560725537-3259.56072553695
53271244269501.5280808451742.47191915492
54269907270544.456360187-637.456360187382
55271296270085.9046702251210.09532977507
56270157271109.730983951-952.730983950605
57271322272493.938660007-1171.93866000738
58267179270698.931691925-3519.93169192463
59264101270360.600639402-6259.60063940211
60265518260843.2286675094674.77133249136
61269419267838.6818324111580.31816758896
62268714268298.994085366415.005914633861
63272482270500.7669973781981.2330026222
64268351270544.156226871-2193.15622687084
65268175271759.782042445-3584.78204244492
66270674268057.0901678022616.90983219806
67272764270481.2509339382282.74906606169
68272599271881.301176385717.698823614512
69270333274530.756634036-4197.75663403596
70270846269825.2808211911020.71917880914
71270491272516.369302882-2025.36930288246
72269160268452.889336164707.110663836473
73274027271729.6148015722297.38519842771
74273784272504.9109402261279.08905977436
75276663275737.856422206925.143577793613
76274525274078.52208615446.477913849521
77271344277171.243459224-5827.24345922424
78271115272924.938293017-1809.93829301669
79270798271746.492451573-948.492451572733
80273911270222.3420606883688.65793931187
81273985274192.537049651-207.537049650913
82271917273653.625463103-1736.62546310329
83273338273538.348896005-200.348896004551
84270601271418.119943608-817.119943607715
85273547273791.650478789-244.650478789001
86275363272308.3748624473054.62513755326
87281229276842.3449454464386.65505455388
88277793277779.94694674213.0530532576377
89279913279277.584504775635.415495224705
90282500281005.3790140221494.62098597828
91280041282698.060952567-2657.0609525675
92282166280801.5675143231364.43248567695
93290304282215.7259065158088.27409348538
94283519287994.952196359-4475.95219635888
95287816286183.2314805811632.76851941907
96285226285384.084940447-158.084940447472
97287595288672.34822578-1077.34822578024
98289741287249.8984728492491.10152715136
99289148291810.285374573-2662.28537457326
100288301286252.536140142048.46385985956
101290155289589.798261433565.201738566975
102289648291532.99375209-1884.99375209044
103288225289747.469516244-1522.46951624408
104289351289602.800705373-251.800705373113
105294735291095.8043584733639.19564152666
106305333290806.7792485514526.2207514502
107309030305531.6582202843498.34177971602
108310215305833.2138407414381.78615925863
109321935312991.2667383148943.73326168628
110325734320476.8815860145257.11841398611
111320846326692.253392215-5846.2533922146
112323023319541.8395035723481.16049642791
113319753324173.261228593-4420.26122859272
114321753322048.184532212-295.18453221157
115320757321822.263773436-1065.26377343648
116324479322703.9932450091775.00675499148
117324641327138.669686719-2497.66968671884
118322767324163.10686174-1396.10686173983
119324181324282.773137531-101.773137530894
120321389321845.99673172-456.996731719642
121327897326225.1841742231671.81582577695
122334287327174.0044867037112.99551329698
123332653332601.20582118851.7941788121825
124334819331928.2989063682890.70109363174
125335264334537.447692512726.552307488455
126339622337440.4253254752181.57467452477
127342440339074.6608031473365.33919685293
128346585344264.4352922732320.56470772653
129335378348533.904432846-13155.9044328463
130337010337354.662070446-344.662070445542
131339130338656.322463962473.677536037983
132341193336527.3348846294665.66511537059
133343507345747.896849813-2240.89684981306
134348915344740.435035614174.56496438978
135346431346406.00862866524.9913713351707
136348322346281.4719122572040.52808774315
137348288347798.430056503489.569943497481
138346597350909.526131588-4312.52613158769
139351076347609.1887779823466.8112220178
140355215352681.416920812533.58307918982
141350562353921.087777465-3359.08777746494
142355266353125.4269174452140.57308255485
143361565356700.1933256414864.80667435884
144363462358841.4061742754620.59382572491
145366183367010.058545713-827.05854571308
146365423368616.380466374-3193.38046637387
147369208363568.9441133735639.05588662741
148366713368372.763245092-1659.76324509218
149369354366697.383773222656.61622678005
150371970370737.0215313691232.97846863122
151371824373582.020259049-1758.0202590492
152373187374549.192863841-1362.19286384102
153367270371488.431594531-4218.43159453053
154368140371285.357039348-3145.35703934811
155373742371305.4102855162436.58971448388
156364815371391.515220752-6576.51522075187
157368558369561.341247027-1003.34124702687
158371503370454.8443480141048.15565198619
159372611370394.4191136162216.58088638441
160370197370937.758232108-740.758232107793
161375441370743.9043373474697.09566265263
162375888376051.038703879-163.03870387905
163375132377121.249347184-1989.24934718397
164381142377911.7813790283230.21862097183
165372024377792.989408566-5768.98940856609
166376070376556.731633529-486.731633528543
167376864379803.749945469-2939.74994546897
168371401373718.551584172-2317.55158417212
169375687376378.188777664-691.188777663745
170384304377909.1477584396394.85224156111
171380738382263.391002235-1525.39100223483
172379908379185.708232784722.291767216404
173384007381219.1483273592787.85167264129
174384499384025.61758791473.382412090315
175385106385212.519898181-106.519898180908
176387935388580.029927821-645.029927820957
177380435383471.601912214-3036.60191221396
178379281385506.450887645-6225.45088764542
179384153383693.924930087459.075069913291
180380599380289.953680948309.046319051646

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 254811 & 252774.645638916 & 2036.35436108371 \tabularnewline
14 & 254895 & 254389.011531162 & 505.98846883775 \tabularnewline
15 & 258325 & 258119.678338033 & 205.321661967086 \tabularnewline
16 & 257608 & 257518.66758886 & 89.3324111398833 \tabularnewline
17 & 258759 & 258817.697836457 & -58.6978364574607 \tabularnewline
18 & 258621 & 258688.461047099 & -67.4610470992338 \tabularnewline
19 & 257852 & 257389.174968921 & 462.825031079119 \tabularnewline
20 & 260560 & 258911.783018583 & 1648.21698141668 \tabularnewline
21 & 262358 & 263259.402882181 & -901.402882181399 \tabularnewline
22 & 260812 & 261294.545844435 & -482.545844434935 \tabularnewline
23 & 261165 & 264259.30868544 & -3094.30868543976 \tabularnewline
24 & 257164 & 254367.680015804 & 2796.31998419634 \tabularnewline
25 & 260720 & 260821.597389182 & -101.597389182163 \tabularnewline
26 & 259581 & 260440.342745724 & -859.342745723727 \tabularnewline
27 & 264743 & 263086.052030848 & 1656.94796915207 \tabularnewline
28 & 261845 & 263590.539059669 & -1745.5390596686 \tabularnewline
29 & 262262 & 263419.887874012 & -1157.88787401165 \tabularnewline
30 & 261631 & 262397.126764529 & -766.126764529094 \tabularnewline
31 & 258953 & 260608.375303099 & -1655.37530309873 \tabularnewline
32 & 259966 & 260653.278517283 & -687.278517282859 \tabularnewline
33 & 262850 & 262582.09543888 & 267.904561120202 \tabularnewline
34 & 262204 & 261563.840781186 & 640.159218814457 \tabularnewline
35 & 263418 & 264858.123404223 & -1440.12340422289 \tabularnewline
36 & 262752 & 257338.652534885 & 5413.34746511461 \tabularnewline
37 & 266433 & 265337.650574486 & 1095.34942551446 \tabularnewline
38 & 267722 & 265740.34388519 & 1981.65611481032 \tabularnewline
39 & 266003 & 271261.005620253 & -5258.00562025298 \tabularnewline
40 & 262971 & 265586.493722252 & -2615.4937222522 \tabularnewline
41 & 265521 & 264811.076486724 & 709.923513276211 \tabularnewline
42 & 264676 & 265312.828400023 & -636.828400022583 \tabularnewline
43 & 270223 & 263407.459704941 & 6815.54029505863 \tabularnewline
44 & 269508 & 270434.365484084 & -926.36548408441 \tabularnewline
45 & 268457 & 272509.84966396 & -4052.84966395982 \tabularnewline
46 & 265814 & 268136.820481195 & -2322.82048119511 \tabularnewline
47 & 266680 & 268701.696121599 & -2021.69612159906 \tabularnewline
48 & 263018 & 261970.387160311 & 1047.61283968919 \tabularnewline
49 & 269285 & 265612.446997844 & 3672.55300215638 \tabularnewline
50 & 269829 & 268182.535837795 & 1646.4641622054 \tabularnewline
51 & 270911 & 271967.573643649 & -1056.57364364946 \tabularnewline
52 & 266844 & 270103.560725537 & -3259.56072553695 \tabularnewline
53 & 271244 & 269501.528080845 & 1742.47191915492 \tabularnewline
54 & 269907 & 270544.456360187 & -637.456360187382 \tabularnewline
55 & 271296 & 270085.904670225 & 1210.09532977507 \tabularnewline
56 & 270157 & 271109.730983951 & -952.730983950605 \tabularnewline
57 & 271322 & 272493.938660007 & -1171.93866000738 \tabularnewline
58 & 267179 & 270698.931691925 & -3519.93169192463 \tabularnewline
59 & 264101 & 270360.600639402 & -6259.60063940211 \tabularnewline
60 & 265518 & 260843.228667509 & 4674.77133249136 \tabularnewline
61 & 269419 & 267838.681832411 & 1580.31816758896 \tabularnewline
62 & 268714 & 268298.994085366 & 415.005914633861 \tabularnewline
63 & 272482 & 270500.766997378 & 1981.2330026222 \tabularnewline
64 & 268351 & 270544.156226871 & -2193.15622687084 \tabularnewline
65 & 268175 & 271759.782042445 & -3584.78204244492 \tabularnewline
66 & 270674 & 268057.090167802 & 2616.90983219806 \tabularnewline
67 & 272764 & 270481.250933938 & 2282.74906606169 \tabularnewline
68 & 272599 & 271881.301176385 & 717.698823614512 \tabularnewline
69 & 270333 & 274530.756634036 & -4197.75663403596 \tabularnewline
70 & 270846 & 269825.280821191 & 1020.71917880914 \tabularnewline
71 & 270491 & 272516.369302882 & -2025.36930288246 \tabularnewline
72 & 269160 & 268452.889336164 & 707.110663836473 \tabularnewline
73 & 274027 & 271729.614801572 & 2297.38519842771 \tabularnewline
74 & 273784 & 272504.910940226 & 1279.08905977436 \tabularnewline
75 & 276663 & 275737.856422206 & 925.143577793613 \tabularnewline
76 & 274525 & 274078.52208615 & 446.477913849521 \tabularnewline
77 & 271344 & 277171.243459224 & -5827.24345922424 \tabularnewline
78 & 271115 & 272924.938293017 & -1809.93829301669 \tabularnewline
79 & 270798 & 271746.492451573 & -948.492451572733 \tabularnewline
80 & 273911 & 270222.342060688 & 3688.65793931187 \tabularnewline
81 & 273985 & 274192.537049651 & -207.537049650913 \tabularnewline
82 & 271917 & 273653.625463103 & -1736.62546310329 \tabularnewline
83 & 273338 & 273538.348896005 & -200.348896004551 \tabularnewline
84 & 270601 & 271418.119943608 & -817.119943607715 \tabularnewline
85 & 273547 & 273791.650478789 & -244.650478789001 \tabularnewline
86 & 275363 & 272308.374862447 & 3054.62513755326 \tabularnewline
87 & 281229 & 276842.344945446 & 4386.65505455388 \tabularnewline
88 & 277793 & 277779.946946742 & 13.0530532576377 \tabularnewline
89 & 279913 & 279277.584504775 & 635.415495224705 \tabularnewline
90 & 282500 & 281005.379014022 & 1494.62098597828 \tabularnewline
91 & 280041 & 282698.060952567 & -2657.0609525675 \tabularnewline
92 & 282166 & 280801.567514323 & 1364.43248567695 \tabularnewline
93 & 290304 & 282215.725906515 & 8088.27409348538 \tabularnewline
94 & 283519 & 287994.952196359 & -4475.95219635888 \tabularnewline
95 & 287816 & 286183.231480581 & 1632.76851941907 \tabularnewline
96 & 285226 & 285384.084940447 & -158.084940447472 \tabularnewline
97 & 287595 & 288672.34822578 & -1077.34822578024 \tabularnewline
98 & 289741 & 287249.898472849 & 2491.10152715136 \tabularnewline
99 & 289148 & 291810.285374573 & -2662.28537457326 \tabularnewline
100 & 288301 & 286252.53614014 & 2048.46385985956 \tabularnewline
101 & 290155 & 289589.798261433 & 565.201738566975 \tabularnewline
102 & 289648 & 291532.99375209 & -1884.99375209044 \tabularnewline
103 & 288225 & 289747.469516244 & -1522.46951624408 \tabularnewline
104 & 289351 & 289602.800705373 & -251.800705373113 \tabularnewline
105 & 294735 & 291095.804358473 & 3639.19564152666 \tabularnewline
106 & 305333 & 290806.77924855 & 14526.2207514502 \tabularnewline
107 & 309030 & 305531.658220284 & 3498.34177971602 \tabularnewline
108 & 310215 & 305833.213840741 & 4381.78615925863 \tabularnewline
109 & 321935 & 312991.266738314 & 8943.73326168628 \tabularnewline
110 & 325734 & 320476.881586014 & 5257.11841398611 \tabularnewline
111 & 320846 & 326692.253392215 & -5846.2533922146 \tabularnewline
112 & 323023 & 319541.839503572 & 3481.16049642791 \tabularnewline
113 & 319753 & 324173.261228593 & -4420.26122859272 \tabularnewline
114 & 321753 & 322048.184532212 & -295.18453221157 \tabularnewline
115 & 320757 & 321822.263773436 & -1065.26377343648 \tabularnewline
116 & 324479 & 322703.993245009 & 1775.00675499148 \tabularnewline
117 & 324641 & 327138.669686719 & -2497.66968671884 \tabularnewline
118 & 322767 & 324163.10686174 & -1396.10686173983 \tabularnewline
119 & 324181 & 324282.773137531 & -101.773137530894 \tabularnewline
120 & 321389 & 321845.99673172 & -456.996731719642 \tabularnewline
121 & 327897 & 326225.184174223 & 1671.81582577695 \tabularnewline
122 & 334287 & 327174.004486703 & 7112.99551329698 \tabularnewline
123 & 332653 & 332601.205821188 & 51.7941788121825 \tabularnewline
124 & 334819 & 331928.298906368 & 2890.70109363174 \tabularnewline
125 & 335264 & 334537.447692512 & 726.552307488455 \tabularnewline
126 & 339622 & 337440.425325475 & 2181.57467452477 \tabularnewline
127 & 342440 & 339074.660803147 & 3365.33919685293 \tabularnewline
128 & 346585 & 344264.435292273 & 2320.56470772653 \tabularnewline
129 & 335378 & 348533.904432846 & -13155.9044328463 \tabularnewline
130 & 337010 & 337354.662070446 & -344.662070445542 \tabularnewline
131 & 339130 & 338656.322463962 & 473.677536037983 \tabularnewline
132 & 341193 & 336527.334884629 & 4665.66511537059 \tabularnewline
133 & 343507 & 345747.896849813 & -2240.89684981306 \tabularnewline
134 & 348915 & 344740.43503561 & 4174.56496438978 \tabularnewline
135 & 346431 & 346406.008628665 & 24.9913713351707 \tabularnewline
136 & 348322 & 346281.471912257 & 2040.52808774315 \tabularnewline
137 & 348288 & 347798.430056503 & 489.569943497481 \tabularnewline
138 & 346597 & 350909.526131588 & -4312.52613158769 \tabularnewline
139 & 351076 & 347609.188777982 & 3466.8112220178 \tabularnewline
140 & 355215 & 352681.41692081 & 2533.58307918982 \tabularnewline
141 & 350562 & 353921.087777465 & -3359.08777746494 \tabularnewline
142 & 355266 & 353125.426917445 & 2140.57308255485 \tabularnewline
143 & 361565 & 356700.193325641 & 4864.80667435884 \tabularnewline
144 & 363462 & 358841.406174275 & 4620.59382572491 \tabularnewline
145 & 366183 & 367010.058545713 & -827.05854571308 \tabularnewline
146 & 365423 & 368616.380466374 & -3193.38046637387 \tabularnewline
147 & 369208 & 363568.944113373 & 5639.05588662741 \tabularnewline
148 & 366713 & 368372.763245092 & -1659.76324509218 \tabularnewline
149 & 369354 & 366697.38377322 & 2656.61622678005 \tabularnewline
150 & 371970 & 370737.021531369 & 1232.97846863122 \tabularnewline
151 & 371824 & 373582.020259049 & -1758.0202590492 \tabularnewline
152 & 373187 & 374549.192863841 & -1362.19286384102 \tabularnewline
153 & 367270 & 371488.431594531 & -4218.43159453053 \tabularnewline
154 & 368140 & 371285.357039348 & -3145.35703934811 \tabularnewline
155 & 373742 & 371305.410285516 & 2436.58971448388 \tabularnewline
156 & 364815 & 371391.515220752 & -6576.51522075187 \tabularnewline
157 & 368558 & 369561.341247027 & -1003.34124702687 \tabularnewline
158 & 371503 & 370454.844348014 & 1048.15565198619 \tabularnewline
159 & 372611 & 370394.419113616 & 2216.58088638441 \tabularnewline
160 & 370197 & 370937.758232108 & -740.758232107793 \tabularnewline
161 & 375441 & 370743.904337347 & 4697.09566265263 \tabularnewline
162 & 375888 & 376051.038703879 & -163.03870387905 \tabularnewline
163 & 375132 & 377121.249347184 & -1989.24934718397 \tabularnewline
164 & 381142 & 377911.781379028 & 3230.21862097183 \tabularnewline
165 & 372024 & 377792.989408566 & -5768.98940856609 \tabularnewline
166 & 376070 & 376556.731633529 & -486.731633528543 \tabularnewline
167 & 376864 & 379803.749945469 & -2939.74994546897 \tabularnewline
168 & 371401 & 373718.551584172 & -2317.55158417212 \tabularnewline
169 & 375687 & 376378.188777664 & -691.188777663745 \tabularnewline
170 & 384304 & 377909.147758439 & 6394.85224156111 \tabularnewline
171 & 380738 & 382263.391002235 & -1525.39100223483 \tabularnewline
172 & 379908 & 379185.708232784 & 722.291767216404 \tabularnewline
173 & 384007 & 381219.148327359 & 2787.85167264129 \tabularnewline
174 & 384499 & 384025.61758791 & 473.382412090315 \tabularnewline
175 & 385106 & 385212.519898181 & -106.519898180908 \tabularnewline
176 & 387935 & 388580.029927821 & -645.029927820957 \tabularnewline
177 & 380435 & 383471.601912214 & -3036.60191221396 \tabularnewline
178 & 379281 & 385506.450887645 & -6225.45088764542 \tabularnewline
179 & 384153 & 383693.924930087 & 459.075069913291 \tabularnewline
180 & 380599 & 380289.953680948 & 309.046319051646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294747&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]13[/C][C]254811[/C][C]252774.645638916[/C][C]2036.35436108371[/C][/ROW]
[ROW][C]14[/C][C]254895[/C][C]254389.011531162[/C][C]505.98846883775[/C][/ROW]
[ROW][C]15[/C][C]258325[/C][C]258119.678338033[/C][C]205.321661967086[/C][/ROW]
[ROW][C]16[/C][C]257608[/C][C]257518.66758886[/C][C]89.3324111398833[/C][/ROW]
[ROW][C]17[/C][C]258759[/C][C]258817.697836457[/C][C]-58.6978364574607[/C][/ROW]
[ROW][C]18[/C][C]258621[/C][C]258688.461047099[/C][C]-67.4610470992338[/C][/ROW]
[ROW][C]19[/C][C]257852[/C][C]257389.174968921[/C][C]462.825031079119[/C][/ROW]
[ROW][C]20[/C][C]260560[/C][C]258911.783018583[/C][C]1648.21698141668[/C][/ROW]
[ROW][C]21[/C][C]262358[/C][C]263259.402882181[/C][C]-901.402882181399[/C][/ROW]
[ROW][C]22[/C][C]260812[/C][C]261294.545844435[/C][C]-482.545844434935[/C][/ROW]
[ROW][C]23[/C][C]261165[/C][C]264259.30868544[/C][C]-3094.30868543976[/C][/ROW]
[ROW][C]24[/C][C]257164[/C][C]254367.680015804[/C][C]2796.31998419634[/C][/ROW]
[ROW][C]25[/C][C]260720[/C][C]260821.597389182[/C][C]-101.597389182163[/C][/ROW]
[ROW][C]26[/C][C]259581[/C][C]260440.342745724[/C][C]-859.342745723727[/C][/ROW]
[ROW][C]27[/C][C]264743[/C][C]263086.052030848[/C][C]1656.94796915207[/C][/ROW]
[ROW][C]28[/C][C]261845[/C][C]263590.539059669[/C][C]-1745.5390596686[/C][/ROW]
[ROW][C]29[/C][C]262262[/C][C]263419.887874012[/C][C]-1157.88787401165[/C][/ROW]
[ROW][C]30[/C][C]261631[/C][C]262397.126764529[/C][C]-766.126764529094[/C][/ROW]
[ROW][C]31[/C][C]258953[/C][C]260608.375303099[/C][C]-1655.37530309873[/C][/ROW]
[ROW][C]32[/C][C]259966[/C][C]260653.278517283[/C][C]-687.278517282859[/C][/ROW]
[ROW][C]33[/C][C]262850[/C][C]262582.09543888[/C][C]267.904561120202[/C][/ROW]
[ROW][C]34[/C][C]262204[/C][C]261563.840781186[/C][C]640.159218814457[/C][/ROW]
[ROW][C]35[/C][C]263418[/C][C]264858.123404223[/C][C]-1440.12340422289[/C][/ROW]
[ROW][C]36[/C][C]262752[/C][C]257338.652534885[/C][C]5413.34746511461[/C][/ROW]
[ROW][C]37[/C][C]266433[/C][C]265337.650574486[/C][C]1095.34942551446[/C][/ROW]
[ROW][C]38[/C][C]267722[/C][C]265740.34388519[/C][C]1981.65611481032[/C][/ROW]
[ROW][C]39[/C][C]266003[/C][C]271261.005620253[/C][C]-5258.00562025298[/C][/ROW]
[ROW][C]40[/C][C]262971[/C][C]265586.493722252[/C][C]-2615.4937222522[/C][/ROW]
[ROW][C]41[/C][C]265521[/C][C]264811.076486724[/C][C]709.923513276211[/C][/ROW]
[ROW][C]42[/C][C]264676[/C][C]265312.828400023[/C][C]-636.828400022583[/C][/ROW]
[ROW][C]43[/C][C]270223[/C][C]263407.459704941[/C][C]6815.54029505863[/C][/ROW]
[ROW][C]44[/C][C]269508[/C][C]270434.365484084[/C][C]-926.36548408441[/C][/ROW]
[ROW][C]45[/C][C]268457[/C][C]272509.84966396[/C][C]-4052.84966395982[/C][/ROW]
[ROW][C]46[/C][C]265814[/C][C]268136.820481195[/C][C]-2322.82048119511[/C][/ROW]
[ROW][C]47[/C][C]266680[/C][C]268701.696121599[/C][C]-2021.69612159906[/C][/ROW]
[ROW][C]48[/C][C]263018[/C][C]261970.387160311[/C][C]1047.61283968919[/C][/ROW]
[ROW][C]49[/C][C]269285[/C][C]265612.446997844[/C][C]3672.55300215638[/C][/ROW]
[ROW][C]50[/C][C]269829[/C][C]268182.535837795[/C][C]1646.4641622054[/C][/ROW]
[ROW][C]51[/C][C]270911[/C][C]271967.573643649[/C][C]-1056.57364364946[/C][/ROW]
[ROW][C]52[/C][C]266844[/C][C]270103.560725537[/C][C]-3259.56072553695[/C][/ROW]
[ROW][C]53[/C][C]271244[/C][C]269501.528080845[/C][C]1742.47191915492[/C][/ROW]
[ROW][C]54[/C][C]269907[/C][C]270544.456360187[/C][C]-637.456360187382[/C][/ROW]
[ROW][C]55[/C][C]271296[/C][C]270085.904670225[/C][C]1210.09532977507[/C][/ROW]
[ROW][C]56[/C][C]270157[/C][C]271109.730983951[/C][C]-952.730983950605[/C][/ROW]
[ROW][C]57[/C][C]271322[/C][C]272493.938660007[/C][C]-1171.93866000738[/C][/ROW]
[ROW][C]58[/C][C]267179[/C][C]270698.931691925[/C][C]-3519.93169192463[/C][/ROW]
[ROW][C]59[/C][C]264101[/C][C]270360.600639402[/C][C]-6259.60063940211[/C][/ROW]
[ROW][C]60[/C][C]265518[/C][C]260843.228667509[/C][C]4674.77133249136[/C][/ROW]
[ROW][C]61[/C][C]269419[/C][C]267838.681832411[/C][C]1580.31816758896[/C][/ROW]
[ROW][C]62[/C][C]268714[/C][C]268298.994085366[/C][C]415.005914633861[/C][/ROW]
[ROW][C]63[/C][C]272482[/C][C]270500.766997378[/C][C]1981.2330026222[/C][/ROW]
[ROW][C]64[/C][C]268351[/C][C]270544.156226871[/C][C]-2193.15622687084[/C][/ROW]
[ROW][C]65[/C][C]268175[/C][C]271759.782042445[/C][C]-3584.78204244492[/C][/ROW]
[ROW][C]66[/C][C]270674[/C][C]268057.090167802[/C][C]2616.90983219806[/C][/ROW]
[ROW][C]67[/C][C]272764[/C][C]270481.250933938[/C][C]2282.74906606169[/C][/ROW]
[ROW][C]68[/C][C]272599[/C][C]271881.301176385[/C][C]717.698823614512[/C][/ROW]
[ROW][C]69[/C][C]270333[/C][C]274530.756634036[/C][C]-4197.75663403596[/C][/ROW]
[ROW][C]70[/C][C]270846[/C][C]269825.280821191[/C][C]1020.71917880914[/C][/ROW]
[ROW][C]71[/C][C]270491[/C][C]272516.369302882[/C][C]-2025.36930288246[/C][/ROW]
[ROW][C]72[/C][C]269160[/C][C]268452.889336164[/C][C]707.110663836473[/C][/ROW]
[ROW][C]73[/C][C]274027[/C][C]271729.614801572[/C][C]2297.38519842771[/C][/ROW]
[ROW][C]74[/C][C]273784[/C][C]272504.910940226[/C][C]1279.08905977436[/C][/ROW]
[ROW][C]75[/C][C]276663[/C][C]275737.856422206[/C][C]925.143577793613[/C][/ROW]
[ROW][C]76[/C][C]274525[/C][C]274078.52208615[/C][C]446.477913849521[/C][/ROW]
[ROW][C]77[/C][C]271344[/C][C]277171.243459224[/C][C]-5827.24345922424[/C][/ROW]
[ROW][C]78[/C][C]271115[/C][C]272924.938293017[/C][C]-1809.93829301669[/C][/ROW]
[ROW][C]79[/C][C]270798[/C][C]271746.492451573[/C][C]-948.492451572733[/C][/ROW]
[ROW][C]80[/C][C]273911[/C][C]270222.342060688[/C][C]3688.65793931187[/C][/ROW]
[ROW][C]81[/C][C]273985[/C][C]274192.537049651[/C][C]-207.537049650913[/C][/ROW]
[ROW][C]82[/C][C]271917[/C][C]273653.625463103[/C][C]-1736.62546310329[/C][/ROW]
[ROW][C]83[/C][C]273338[/C][C]273538.348896005[/C][C]-200.348896004551[/C][/ROW]
[ROW][C]84[/C][C]270601[/C][C]271418.119943608[/C][C]-817.119943607715[/C][/ROW]
[ROW][C]85[/C][C]273547[/C][C]273791.650478789[/C][C]-244.650478789001[/C][/ROW]
[ROW][C]86[/C][C]275363[/C][C]272308.374862447[/C][C]3054.62513755326[/C][/ROW]
[ROW][C]87[/C][C]281229[/C][C]276842.344945446[/C][C]4386.65505455388[/C][/ROW]
[ROW][C]88[/C][C]277793[/C][C]277779.946946742[/C][C]13.0530532576377[/C][/ROW]
[ROW][C]89[/C][C]279913[/C][C]279277.584504775[/C][C]635.415495224705[/C][/ROW]
[ROW][C]90[/C][C]282500[/C][C]281005.379014022[/C][C]1494.62098597828[/C][/ROW]
[ROW][C]91[/C][C]280041[/C][C]282698.060952567[/C][C]-2657.0609525675[/C][/ROW]
[ROW][C]92[/C][C]282166[/C][C]280801.567514323[/C][C]1364.43248567695[/C][/ROW]
[ROW][C]93[/C][C]290304[/C][C]282215.725906515[/C][C]8088.27409348538[/C][/ROW]
[ROW][C]94[/C][C]283519[/C][C]287994.952196359[/C][C]-4475.95219635888[/C][/ROW]
[ROW][C]95[/C][C]287816[/C][C]286183.231480581[/C][C]1632.76851941907[/C][/ROW]
[ROW][C]96[/C][C]285226[/C][C]285384.084940447[/C][C]-158.084940447472[/C][/ROW]
[ROW][C]97[/C][C]287595[/C][C]288672.34822578[/C][C]-1077.34822578024[/C][/ROW]
[ROW][C]98[/C][C]289741[/C][C]287249.898472849[/C][C]2491.10152715136[/C][/ROW]
[ROW][C]99[/C][C]289148[/C][C]291810.285374573[/C][C]-2662.28537457326[/C][/ROW]
[ROW][C]100[/C][C]288301[/C][C]286252.53614014[/C][C]2048.46385985956[/C][/ROW]
[ROW][C]101[/C][C]290155[/C][C]289589.798261433[/C][C]565.201738566975[/C][/ROW]
[ROW][C]102[/C][C]289648[/C][C]291532.99375209[/C][C]-1884.99375209044[/C][/ROW]
[ROW][C]103[/C][C]288225[/C][C]289747.469516244[/C][C]-1522.46951624408[/C][/ROW]
[ROW][C]104[/C][C]289351[/C][C]289602.800705373[/C][C]-251.800705373113[/C][/ROW]
[ROW][C]105[/C][C]294735[/C][C]291095.804358473[/C][C]3639.19564152666[/C][/ROW]
[ROW][C]106[/C][C]305333[/C][C]290806.77924855[/C][C]14526.2207514502[/C][/ROW]
[ROW][C]107[/C][C]309030[/C][C]305531.658220284[/C][C]3498.34177971602[/C][/ROW]
[ROW][C]108[/C][C]310215[/C][C]305833.213840741[/C][C]4381.78615925863[/C][/ROW]
[ROW][C]109[/C][C]321935[/C][C]312991.266738314[/C][C]8943.73326168628[/C][/ROW]
[ROW][C]110[/C][C]325734[/C][C]320476.881586014[/C][C]5257.11841398611[/C][/ROW]
[ROW][C]111[/C][C]320846[/C][C]326692.253392215[/C][C]-5846.2533922146[/C][/ROW]
[ROW][C]112[/C][C]323023[/C][C]319541.839503572[/C][C]3481.16049642791[/C][/ROW]
[ROW][C]113[/C][C]319753[/C][C]324173.261228593[/C][C]-4420.26122859272[/C][/ROW]
[ROW][C]114[/C][C]321753[/C][C]322048.184532212[/C][C]-295.18453221157[/C][/ROW]
[ROW][C]115[/C][C]320757[/C][C]321822.263773436[/C][C]-1065.26377343648[/C][/ROW]
[ROW][C]116[/C][C]324479[/C][C]322703.993245009[/C][C]1775.00675499148[/C][/ROW]
[ROW][C]117[/C][C]324641[/C][C]327138.669686719[/C][C]-2497.66968671884[/C][/ROW]
[ROW][C]118[/C][C]322767[/C][C]324163.10686174[/C][C]-1396.10686173983[/C][/ROW]
[ROW][C]119[/C][C]324181[/C][C]324282.773137531[/C][C]-101.773137530894[/C][/ROW]
[ROW][C]120[/C][C]321389[/C][C]321845.99673172[/C][C]-456.996731719642[/C][/ROW]
[ROW][C]121[/C][C]327897[/C][C]326225.184174223[/C][C]1671.81582577695[/C][/ROW]
[ROW][C]122[/C][C]334287[/C][C]327174.004486703[/C][C]7112.99551329698[/C][/ROW]
[ROW][C]123[/C][C]332653[/C][C]332601.205821188[/C][C]51.7941788121825[/C][/ROW]
[ROW][C]124[/C][C]334819[/C][C]331928.298906368[/C][C]2890.70109363174[/C][/ROW]
[ROW][C]125[/C][C]335264[/C][C]334537.447692512[/C][C]726.552307488455[/C][/ROW]
[ROW][C]126[/C][C]339622[/C][C]337440.425325475[/C][C]2181.57467452477[/C][/ROW]
[ROW][C]127[/C][C]342440[/C][C]339074.660803147[/C][C]3365.33919685293[/C][/ROW]
[ROW][C]128[/C][C]346585[/C][C]344264.435292273[/C][C]2320.56470772653[/C][/ROW]
[ROW][C]129[/C][C]335378[/C][C]348533.904432846[/C][C]-13155.9044328463[/C][/ROW]
[ROW][C]130[/C][C]337010[/C][C]337354.662070446[/C][C]-344.662070445542[/C][/ROW]
[ROW][C]131[/C][C]339130[/C][C]338656.322463962[/C][C]473.677536037983[/C][/ROW]
[ROW][C]132[/C][C]341193[/C][C]336527.334884629[/C][C]4665.66511537059[/C][/ROW]
[ROW][C]133[/C][C]343507[/C][C]345747.896849813[/C][C]-2240.89684981306[/C][/ROW]
[ROW][C]134[/C][C]348915[/C][C]344740.43503561[/C][C]4174.56496438978[/C][/ROW]
[ROW][C]135[/C][C]346431[/C][C]346406.008628665[/C][C]24.9913713351707[/C][/ROW]
[ROW][C]136[/C][C]348322[/C][C]346281.471912257[/C][C]2040.52808774315[/C][/ROW]
[ROW][C]137[/C][C]348288[/C][C]347798.430056503[/C][C]489.569943497481[/C][/ROW]
[ROW][C]138[/C][C]346597[/C][C]350909.526131588[/C][C]-4312.52613158769[/C][/ROW]
[ROW][C]139[/C][C]351076[/C][C]347609.188777982[/C][C]3466.8112220178[/C][/ROW]
[ROW][C]140[/C][C]355215[/C][C]352681.41692081[/C][C]2533.58307918982[/C][/ROW]
[ROW][C]141[/C][C]350562[/C][C]353921.087777465[/C][C]-3359.08777746494[/C][/ROW]
[ROW][C]142[/C][C]355266[/C][C]353125.426917445[/C][C]2140.57308255485[/C][/ROW]
[ROW][C]143[/C][C]361565[/C][C]356700.193325641[/C][C]4864.80667435884[/C][/ROW]
[ROW][C]144[/C][C]363462[/C][C]358841.406174275[/C][C]4620.59382572491[/C][/ROW]
[ROW][C]145[/C][C]366183[/C][C]367010.058545713[/C][C]-827.05854571308[/C][/ROW]
[ROW][C]146[/C][C]365423[/C][C]368616.380466374[/C][C]-3193.38046637387[/C][/ROW]
[ROW][C]147[/C][C]369208[/C][C]363568.944113373[/C][C]5639.05588662741[/C][/ROW]
[ROW][C]148[/C][C]366713[/C][C]368372.763245092[/C][C]-1659.76324509218[/C][/ROW]
[ROW][C]149[/C][C]369354[/C][C]366697.38377322[/C][C]2656.61622678005[/C][/ROW]
[ROW][C]150[/C][C]371970[/C][C]370737.021531369[/C][C]1232.97846863122[/C][/ROW]
[ROW][C]151[/C][C]371824[/C][C]373582.020259049[/C][C]-1758.0202590492[/C][/ROW]
[ROW][C]152[/C][C]373187[/C][C]374549.192863841[/C][C]-1362.19286384102[/C][/ROW]
[ROW][C]153[/C][C]367270[/C][C]371488.431594531[/C][C]-4218.43159453053[/C][/ROW]
[ROW][C]154[/C][C]368140[/C][C]371285.357039348[/C][C]-3145.35703934811[/C][/ROW]
[ROW][C]155[/C][C]373742[/C][C]371305.410285516[/C][C]2436.58971448388[/C][/ROW]
[ROW][C]156[/C][C]364815[/C][C]371391.515220752[/C][C]-6576.51522075187[/C][/ROW]
[ROW][C]157[/C][C]368558[/C][C]369561.341247027[/C][C]-1003.34124702687[/C][/ROW]
[ROW][C]158[/C][C]371503[/C][C]370454.844348014[/C][C]1048.15565198619[/C][/ROW]
[ROW][C]159[/C][C]372611[/C][C]370394.419113616[/C][C]2216.58088638441[/C][/ROW]
[ROW][C]160[/C][C]370197[/C][C]370937.758232108[/C][C]-740.758232107793[/C][/ROW]
[ROW][C]161[/C][C]375441[/C][C]370743.904337347[/C][C]4697.09566265263[/C][/ROW]
[ROW][C]162[/C][C]375888[/C][C]376051.038703879[/C][C]-163.03870387905[/C][/ROW]
[ROW][C]163[/C][C]375132[/C][C]377121.249347184[/C][C]-1989.24934718397[/C][/ROW]
[ROW][C]164[/C][C]381142[/C][C]377911.781379028[/C][C]3230.21862097183[/C][/ROW]
[ROW][C]165[/C][C]372024[/C][C]377792.989408566[/C][C]-5768.98940856609[/C][/ROW]
[ROW][C]166[/C][C]376070[/C][C]376556.731633529[/C][C]-486.731633528543[/C][/ROW]
[ROW][C]167[/C][C]376864[/C][C]379803.749945469[/C][C]-2939.74994546897[/C][/ROW]
[ROW][C]168[/C][C]371401[/C][C]373718.551584172[/C][C]-2317.55158417212[/C][/ROW]
[ROW][C]169[/C][C]375687[/C][C]376378.188777664[/C][C]-691.188777663745[/C][/ROW]
[ROW][C]170[/C][C]384304[/C][C]377909.147758439[/C][C]6394.85224156111[/C][/ROW]
[ROW][C]171[/C][C]380738[/C][C]382263.391002235[/C][C]-1525.39100223483[/C][/ROW]
[ROW][C]172[/C][C]379908[/C][C]379185.708232784[/C][C]722.291767216404[/C][/ROW]
[ROW][C]173[/C][C]384007[/C][C]381219.148327359[/C][C]2787.85167264129[/C][/ROW]
[ROW][C]174[/C][C]384499[/C][C]384025.61758791[/C][C]473.382412090315[/C][/ROW]
[ROW][C]175[/C][C]385106[/C][C]385212.519898181[/C][C]-106.519898180908[/C][/ROW]
[ROW][C]176[/C][C]387935[/C][C]388580.029927821[/C][C]-645.029927820957[/C][/ROW]
[ROW][C]177[/C][C]380435[/C][C]383471.601912214[/C][C]-3036.60191221396[/C][/ROW]
[ROW][C]178[/C][C]379281[/C][C]385506.450887645[/C][C]-6225.45088764542[/C][/ROW]
[ROW][C]179[/C][C]384153[/C][C]383693.924930087[/C][C]459.075069913291[/C][/ROW]
[ROW][C]180[/C][C]380599[/C][C]380289.953680948[/C][C]309.046319051646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294747&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294747&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
13254811252774.6456389162036.35436108371
14254895254389.011531162505.98846883775
15258325258119.678338033205.321661967086
16257608257518.6675888689.3324111398833
17258759258817.697836457-58.6978364574607
18258621258688.461047099-67.4610470992338
19257852257389.174968921462.825031079119
20260560258911.7830185831648.21698141668
21262358263259.402882181-901.402882181399
22260812261294.545844435-482.545844434935
23261165264259.30868544-3094.30868543976
24257164254367.6800158042796.31998419634
25260720260821.597389182-101.597389182163
26259581260440.342745724-859.342745723727
27264743263086.0520308481656.94796915207
28261845263590.539059669-1745.5390596686
29262262263419.887874012-1157.88787401165
30261631262397.126764529-766.126764529094
31258953260608.375303099-1655.37530309873
32259966260653.278517283-687.278517282859
33262850262582.09543888267.904561120202
34262204261563.840781186640.159218814457
35263418264858.123404223-1440.12340422289
36262752257338.6525348855413.34746511461
37266433265337.6505744861095.34942551446
38267722265740.343885191981.65611481032
39266003271261.005620253-5258.00562025298
40262971265586.493722252-2615.4937222522
41265521264811.076486724709.923513276211
42264676265312.828400023-636.828400022583
43270223263407.4597049416815.54029505863
44269508270434.365484084-926.36548408441
45268457272509.84966396-4052.84966395982
46265814268136.820481195-2322.82048119511
47266680268701.696121599-2021.69612159906
48263018261970.3871603111047.61283968919
49269285265612.4469978443672.55300215638
50269829268182.5358377951646.4641622054
51270911271967.573643649-1056.57364364946
52266844270103.560725537-3259.56072553695
53271244269501.5280808451742.47191915492
54269907270544.456360187-637.456360187382
55271296270085.9046702251210.09532977507
56270157271109.730983951-952.730983950605
57271322272493.938660007-1171.93866000738
58267179270698.931691925-3519.93169192463
59264101270360.600639402-6259.60063940211
60265518260843.2286675094674.77133249136
61269419267838.6818324111580.31816758896
62268714268298.994085366415.005914633861
63272482270500.7669973781981.2330026222
64268351270544.156226871-2193.15622687084
65268175271759.782042445-3584.78204244492
66270674268057.0901678022616.90983219806
67272764270481.2509339382282.74906606169
68272599271881.301176385717.698823614512
69270333274530.756634036-4197.75663403596
70270846269825.2808211911020.71917880914
71270491272516.369302882-2025.36930288246
72269160268452.889336164707.110663836473
73274027271729.6148015722297.38519842771
74273784272504.9109402261279.08905977436
75276663275737.856422206925.143577793613
76274525274078.52208615446.477913849521
77271344277171.243459224-5827.24345922424
78271115272924.938293017-1809.93829301669
79270798271746.492451573-948.492451572733
80273911270222.3420606883688.65793931187
81273985274192.537049651-207.537049650913
82271917273653.625463103-1736.62546310329
83273338273538.348896005-200.348896004551
84270601271418.119943608-817.119943607715
85273547273791.650478789-244.650478789001
86275363272308.3748624473054.62513755326
87281229276842.3449454464386.65505455388
88277793277779.94694674213.0530532576377
89279913279277.584504775635.415495224705
90282500281005.3790140221494.62098597828
91280041282698.060952567-2657.0609525675
92282166280801.5675143231364.43248567695
93290304282215.7259065158088.27409348538
94283519287994.952196359-4475.95219635888
95287816286183.2314805811632.76851941907
96285226285384.084940447-158.084940447472
97287595288672.34822578-1077.34822578024
98289741287249.8984728492491.10152715136
99289148291810.285374573-2662.28537457326
100288301286252.536140142048.46385985956
101290155289589.798261433565.201738566975
102289648291532.99375209-1884.99375209044
103288225289747.469516244-1522.46951624408
104289351289602.800705373-251.800705373113
105294735291095.8043584733639.19564152666
106305333290806.7792485514526.2207514502
107309030305531.6582202843498.34177971602
108310215305833.2138407414381.78615925863
109321935312991.2667383148943.73326168628
110325734320476.8815860145257.11841398611
111320846326692.253392215-5846.2533922146
112323023319541.8395035723481.16049642791
113319753324173.261228593-4420.26122859272
114321753322048.184532212-295.18453221157
115320757321822.263773436-1065.26377343648
116324479322703.9932450091775.00675499148
117324641327138.669686719-2497.66968671884
118322767324163.10686174-1396.10686173983
119324181324282.773137531-101.773137530894
120321389321845.99673172-456.996731719642
121327897326225.1841742231671.81582577695
122334287327174.0044867037112.99551329698
123332653332601.20582118851.7941788121825
124334819331928.2989063682890.70109363174
125335264334537.447692512726.552307488455
126339622337440.4253254752181.57467452477
127342440339074.6608031473365.33919685293
128346585344264.4352922732320.56470772653
129335378348533.904432846-13155.9044328463
130337010337354.662070446-344.662070445542
131339130338656.322463962473.677536037983
132341193336527.3348846294665.66511537059
133343507345747.896849813-2240.89684981306
134348915344740.435035614174.56496438978
135346431346406.00862866524.9913713351707
136348322346281.4719122572040.52808774315
137348288347798.430056503489.569943497481
138346597350909.526131588-4312.52613158769
139351076347609.1887779823466.8112220178
140355215352681.416920812533.58307918982
141350562353921.087777465-3359.08777746494
142355266353125.4269174452140.57308255485
143361565356700.1933256414864.80667435884
144363462358841.4061742754620.59382572491
145366183367010.058545713-827.05854571308
146365423368616.380466374-3193.38046637387
147369208363568.9441133735639.05588662741
148366713368372.763245092-1659.76324509218
149369354366697.383773222656.61622678005
150371970370737.0215313691232.97846863122
151371824373582.020259049-1758.0202590492
152373187374549.192863841-1362.19286384102
153367270371488.431594531-4218.43159453053
154368140371285.357039348-3145.35703934811
155373742371305.4102855162436.58971448388
156364815371391.515220752-6576.51522075187
157368558369561.341247027-1003.34124702687
158371503370454.8443480141048.15565198619
159372611370394.4191136162216.58088638441
160370197370937.758232108-740.758232107793
161375441370743.9043373474697.09566265263
162375888376051.038703879-163.03870387905
163375132377121.249347184-1989.24934718397
164381142377911.7813790283230.21862097183
165372024377792.989408566-5768.98940856609
166376070376556.731633529-486.731633528543
167376864379803.749945469-2939.74994546897
168371401373718.551584172-2317.55158417212
169375687376378.188777664-691.188777663745
170384304377909.1477584396394.85224156111
171380738382263.391002235-1525.39100223483
172379908379185.708232784722.291767216404
173384007381219.1483273592787.85167264129
174384499384025.61758791473.382412090315
175385106385212.519898181-106.519898180908
176387935388580.029927821-645.029927820957
177380435383471.601912214-3036.60191221396
178379281385506.450887645-6225.45088764542
179384153383693.924930087459.075069913291
180380599380289.953680948309.046319051646







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
181385430.416126095379197.768053312391663.064198879
182388955.661866123380914.4580425396996.865689747
183386591.905311813377109.863885542396073.946738083
184385075.983448729374320.338293702395831.628603757
185386900.159239238374918.504118912398881.814359565
186386957.977002676373879.918288005400036.035717347
187387565.374746591373440.776704896401689.972788286
188390836.309083483375630.460349512406042.157817454
189385633.718660506369681.751560089401585.685760924
190389405.033536157372410.540301693406399.52677062
191393930.210947571375887.933144597411972.488750544
192390020.709079309372378.747798454407662.670360164

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
181 & 385430.416126095 & 379197.768053312 & 391663.064198879 \tabularnewline
182 & 388955.661866123 & 380914.4580425 & 396996.865689747 \tabularnewline
183 & 386591.905311813 & 377109.863885542 & 396073.946738083 \tabularnewline
184 & 385075.983448729 & 374320.338293702 & 395831.628603757 \tabularnewline
185 & 386900.159239238 & 374918.504118912 & 398881.814359565 \tabularnewline
186 & 386957.977002676 & 373879.918288005 & 400036.035717347 \tabularnewline
187 & 387565.374746591 & 373440.776704896 & 401689.972788286 \tabularnewline
188 & 390836.309083483 & 375630.460349512 & 406042.157817454 \tabularnewline
189 & 385633.718660506 & 369681.751560089 & 401585.685760924 \tabularnewline
190 & 389405.033536157 & 372410.540301693 & 406399.52677062 \tabularnewline
191 & 393930.210947571 & 375887.933144597 & 411972.488750544 \tabularnewline
192 & 390020.709079309 & 372378.747798454 & 407662.670360164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294747&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]385430.416126095[/C][C]379197.768053312[/C][C]391663.064198879[/C][/ROW]
[ROW][C]182[/C][C]388955.661866123[/C][C]380914.4580425[/C][C]396996.865689747[/C][/ROW]
[ROW][C]183[/C][C]386591.905311813[/C][C]377109.863885542[/C][C]396073.946738083[/C][/ROW]
[ROW][C]184[/C][C]385075.983448729[/C][C]374320.338293702[/C][C]395831.628603757[/C][/ROW]
[ROW][C]185[/C][C]386900.159239238[/C][C]374918.504118912[/C][C]398881.814359565[/C][/ROW]
[ROW][C]186[/C][C]386957.977002676[/C][C]373879.918288005[/C][C]400036.035717347[/C][/ROW]
[ROW][C]187[/C][C]387565.374746591[/C][C]373440.776704896[/C][C]401689.972788286[/C][/ROW]
[ROW][C]188[/C][C]390836.309083483[/C][C]375630.460349512[/C][C]406042.157817454[/C][/ROW]
[ROW][C]189[/C][C]385633.718660506[/C][C]369681.751560089[/C][C]401585.685760924[/C][/ROW]
[ROW][C]190[/C][C]389405.033536157[/C][C]372410.540301693[/C][C]406399.52677062[/C][/ROW]
[ROW][C]191[/C][C]393930.210947571[/C][C]375887.933144597[/C][C]411972.488750544[/C][/ROW]
[ROW][C]192[/C][C]390020.709079309[/C][C]372378.747798454[/C][C]407662.670360164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294747&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294747&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
181385430.416126095379197.768053312391663.064198879
182388955.661866123380914.4580425396996.865689747
183386591.905311813377109.863885542396073.946738083
184385075.983448729374320.338293702395831.628603757
185386900.159239238374918.504118912398881.814359565
186386957.977002676373879.918288005400036.035717347
187387565.374746591373440.776704896401689.972788286
188390836.309083483375630.460349512406042.157817454
189385633.718660506369681.751560089401585.685760924
190389405.033536157372410.540301693406399.52677062
191393930.210947571375887.933144597411972.488750544
192390020.709079309372378.747798454407662.670360164



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')