Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 09:51:04 +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/Aug/15/t1471251083b82nimmf1lz5oli.htm/, Retrieved Sun, 28 Apr 2024 17:09:35 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 17:09:35 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
58109
57087
56064
54019
74712
73689
58109
47763
48785
48785
49808
51964
45718
39462
34339
34339
54019
56064
40484
22859
32183
32183
39462
43663
42640
32183
37417
35362
52987
48785
32183
19782
31160
34339
37417
41507
33205
26038
29116
30138
57087
57087
41507
39462
45718
42640
50942
61288
63343
48785
44685
40484
68567
70622
65388
70622
69589
61288
70622
80968
85169
72667
64365
70622
97570
105872
103827
107916
106894
96548
114173
118374
124519
105872
98593
106894
126675
144300
140099
140099
142154
134976
153634
153634
150455
132820
135999
138054
151579
169204
156701
162958
157724
154656
178538
173304
166025
155679
166025
171259
177505
185806
177505
182628
176381
175359
201285
203441
195140
180583
192984
198208
204464
213788
204464
211743
208564
197185
221066
221066




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.14114221711203
beta0.189181833960606
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.14114221711203 \tabularnewline
beta & 0.189181833960606 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.14114221711203[/C][/ROW]
[ROW][C]beta[/C][C]0.189181833960606[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.14114221711203
beta0.189181833960606
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35606456065-1
45401955042.8321562394-1023.83215623941
57471253848.961615375120863.0383846249
67368956301.327834896817387.6721651032
75810958727.4508452954-618.450845295367
84776358595.6361402768-10832.6361402768
94878556732.9205718016-7947.92057180163
104878555065.138407655-6280.13840765502
114980853465.0613270477-3657.06132704771
125196452137.5619792107-173.561979210666
134571851297.0970799008-5579.09707990084
143946249544.7124685305-10082.7124685305
153433946887.453610789-12548.453610789
163433943547.1115016778-9208.11150167785
175401940432.361894105413586.6381058946
185606440897.697992825115166.3020071749
194048441990.9550293769-1506.95502937691
202285940690.673576068-17831.673576068
213218336610.1519459917-4427.1519459917
223218334303.3624279209-2120.36242792094
233946232265.54134727367196.45865272636
244366331734.873604020911928.1263959791
254264032190.543322315610449.4566776844
263218332716.5269400416-533.526940041636
273741731678.10190666815738.89809333189
283536231678.21828615483683.78171384523
295298731486.633641029821500.3663589702
304878534383.81422130614401.185778694
313218336663.5346030731-4480.53460307308
321978236158.6099177392-16376.6099177392
333116033537.3660257469-2377.36602574693
343433932828.52711225211510.47288774788
353741732708.75836027384708.24163972624
364150733166.04709863068340.95290136945
373320534358.7810751651-1153.78107516507
382603834180.5995118148-8142.59951181476
392911632798.5806443968-3682.58064439682
403013831947.7281410835-1809.72814108348
415708731312.891657760925774.1083422391
425708735259.507486773721827.4925132263
434150739231.91694804642275.08305195358
443946240505.404217111-1043.40421711099
454571841282.65233248874435.34766751129
464264042951.6142644729-311.614264472875
475094243942.25888299786999.7411170022
486128846151.748301960115136.2516980399
496334349913.804146763113429.1958532369
504878553793.5026019071-5008.50260190709
514468554937.1286686418-10252.1286686418
524048455066.9100671771-14582.9100671771
536856754196.049170035114370.9508299649
547062257795.526962340612826.4730376594
556538861519.50036230213868.49963769785
567062264082.42044705076539.57955294933
576958967196.95954091172392.04045908834
586128869789.9769438366-8501.97694383659
597062270618.37267020243.62732979757129
608096872647.36509693098320.63490306913
618516976072.41220695499096.58779304514
627266779849.8719627431-7182.87196274311
636436581137.8189071708-16772.8189071708
647062280624.359324501-10002.359324501
659757080799.418985765616770.5810142344
6610587285201.071203226120670.9287967739
6710382790705.172858313413121.8271416866
6810791695494.150606591412421.8493934086
69106894100516.014495266377.98550474019
7096548104855.136092044-8307.13609204389
71114173106899.7537125217273.2462874788
72118374111337.6279475027036.37205249828
73124519115929.9512220998589.04877790065
74105872120970.763591595-15098.7635915951
7598593122265.065312153-23672.0653121532
76106894121717.231538648-14823.2315386479
77126675122022.538621314652.46137868978
78144300125200.91608192219099.0839180775
79140099130928.2968972399170.70310276061
80140099135499.2359596144599.76404038642
81142154139547.8433479742606.15665202599
82134976143384.656974657-8408.65697465662
83153634145442.2912651558191.7087348449
84153634150061.6692437433572.33075625729
85150455154124.444717776-3669.44471777615
86132820157067.120107889-24247.1201078886
87135999156457.981238542-20458.9812385422
88138054155837.222310795-17783.2223107947
89151579155119.286446776-3540.28644677572
90169204156317.0990162912886.9009837103
91156701160177.581387629-3476.58138762877
92162958161635.6554883111322.34451168883
93157724163806.369269657-6082.3692696573
94154656164769.556683294-10113.5566832937
95178538164893.72579423413644.2742057664
96173304168735.4510116214568.54898837933
97166025171418.195559391-5393.19555939143
98155679172550.910749647-16871.9107496474
99166025171612.988569838-5587.98856983811
100171259172118.496264429-859.496264429385
101177505173268.4439697254236.55603027451
102185806175250.78237947310555.2176205265
103177505178406.791297512-901.791297512216
104182628179921.6533558442706.34664415603
105176381182018.039635507-5637.03963550652
106175359182786.304218495-7427.30421849524
107201285183103.56640247618181.4335975242
108203441187520.77495902915920.2250409712
109195140192043.926107743096.07389225982
110180583194839.718082402-14256.718082402
111192984194805.622146881-1821.62214688087
112198208196478.0030987361729.99690126369
113204464198697.8610248685766.13897513205
114213788201641.35380245512146.6461975448
115204464205809.739717324-1345.73971732371
116211743208037.8470424583705.15295754175
117208564211077.781860923-2513.78186092337
118197185213172.84057537-15987.8405753702
119221066212939.2407490478126.7592509526
120221066216326.2260224924739.77397750752

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 56064 & 56065 & -1 \tabularnewline
4 & 54019 & 55042.8321562394 & -1023.83215623941 \tabularnewline
5 & 74712 & 53848.9616153751 & 20863.0383846249 \tabularnewline
6 & 73689 & 56301.3278348968 & 17387.6721651032 \tabularnewline
7 & 58109 & 58727.4508452954 & -618.450845295367 \tabularnewline
8 & 47763 & 58595.6361402768 & -10832.6361402768 \tabularnewline
9 & 48785 & 56732.9205718016 & -7947.92057180163 \tabularnewline
10 & 48785 & 55065.138407655 & -6280.13840765502 \tabularnewline
11 & 49808 & 53465.0613270477 & -3657.06132704771 \tabularnewline
12 & 51964 & 52137.5619792107 & -173.561979210666 \tabularnewline
13 & 45718 & 51297.0970799008 & -5579.09707990084 \tabularnewline
14 & 39462 & 49544.7124685305 & -10082.7124685305 \tabularnewline
15 & 34339 & 46887.453610789 & -12548.453610789 \tabularnewline
16 & 34339 & 43547.1115016778 & -9208.11150167785 \tabularnewline
17 & 54019 & 40432.3618941054 & 13586.6381058946 \tabularnewline
18 & 56064 & 40897.6979928251 & 15166.3020071749 \tabularnewline
19 & 40484 & 41990.9550293769 & -1506.95502937691 \tabularnewline
20 & 22859 & 40690.673576068 & -17831.673576068 \tabularnewline
21 & 32183 & 36610.1519459917 & -4427.1519459917 \tabularnewline
22 & 32183 & 34303.3624279209 & -2120.36242792094 \tabularnewline
23 & 39462 & 32265.5413472736 & 7196.45865272636 \tabularnewline
24 & 43663 & 31734.8736040209 & 11928.1263959791 \tabularnewline
25 & 42640 & 32190.5433223156 & 10449.4566776844 \tabularnewline
26 & 32183 & 32716.5269400416 & -533.526940041636 \tabularnewline
27 & 37417 & 31678.1019066681 & 5738.89809333189 \tabularnewline
28 & 35362 & 31678.2182861548 & 3683.78171384523 \tabularnewline
29 & 52987 & 31486.6336410298 & 21500.3663589702 \tabularnewline
30 & 48785 & 34383.814221306 & 14401.185778694 \tabularnewline
31 & 32183 & 36663.5346030731 & -4480.53460307308 \tabularnewline
32 & 19782 & 36158.6099177392 & -16376.6099177392 \tabularnewline
33 & 31160 & 33537.3660257469 & -2377.36602574693 \tabularnewline
34 & 34339 & 32828.5271122521 & 1510.47288774788 \tabularnewline
35 & 37417 & 32708.7583602738 & 4708.24163972624 \tabularnewline
36 & 41507 & 33166.0470986306 & 8340.95290136945 \tabularnewline
37 & 33205 & 34358.7810751651 & -1153.78107516507 \tabularnewline
38 & 26038 & 34180.5995118148 & -8142.59951181476 \tabularnewline
39 & 29116 & 32798.5806443968 & -3682.58064439682 \tabularnewline
40 & 30138 & 31947.7281410835 & -1809.72814108348 \tabularnewline
41 & 57087 & 31312.8916577609 & 25774.1083422391 \tabularnewline
42 & 57087 & 35259.5074867737 & 21827.4925132263 \tabularnewline
43 & 41507 & 39231.9169480464 & 2275.08305195358 \tabularnewline
44 & 39462 & 40505.404217111 & -1043.40421711099 \tabularnewline
45 & 45718 & 41282.6523324887 & 4435.34766751129 \tabularnewline
46 & 42640 & 42951.6142644729 & -311.614264472875 \tabularnewline
47 & 50942 & 43942.2588829978 & 6999.7411170022 \tabularnewline
48 & 61288 & 46151.7483019601 & 15136.2516980399 \tabularnewline
49 & 63343 & 49913.8041467631 & 13429.1958532369 \tabularnewline
50 & 48785 & 53793.5026019071 & -5008.50260190709 \tabularnewline
51 & 44685 & 54937.1286686418 & -10252.1286686418 \tabularnewline
52 & 40484 & 55066.9100671771 & -14582.9100671771 \tabularnewline
53 & 68567 & 54196.0491700351 & 14370.9508299649 \tabularnewline
54 & 70622 & 57795.5269623406 & 12826.4730376594 \tabularnewline
55 & 65388 & 61519.5003623021 & 3868.49963769785 \tabularnewline
56 & 70622 & 64082.4204470507 & 6539.57955294933 \tabularnewline
57 & 69589 & 67196.9595409117 & 2392.04045908834 \tabularnewline
58 & 61288 & 69789.9769438366 & -8501.97694383659 \tabularnewline
59 & 70622 & 70618.3726702024 & 3.62732979757129 \tabularnewline
60 & 80968 & 72647.3650969309 & 8320.63490306913 \tabularnewline
61 & 85169 & 76072.4122069549 & 9096.58779304514 \tabularnewline
62 & 72667 & 79849.8719627431 & -7182.87196274311 \tabularnewline
63 & 64365 & 81137.8189071708 & -16772.8189071708 \tabularnewline
64 & 70622 & 80624.359324501 & -10002.359324501 \tabularnewline
65 & 97570 & 80799.4189857656 & 16770.5810142344 \tabularnewline
66 & 105872 & 85201.0712032261 & 20670.9287967739 \tabularnewline
67 & 103827 & 90705.1728583134 & 13121.8271416866 \tabularnewline
68 & 107916 & 95494.1506065914 & 12421.8493934086 \tabularnewline
69 & 106894 & 100516.01449526 & 6377.98550474019 \tabularnewline
70 & 96548 & 104855.136092044 & -8307.13609204389 \tabularnewline
71 & 114173 & 106899.753712521 & 7273.2462874788 \tabularnewline
72 & 118374 & 111337.627947502 & 7036.37205249828 \tabularnewline
73 & 124519 & 115929.951222099 & 8589.04877790065 \tabularnewline
74 & 105872 & 120970.763591595 & -15098.7635915951 \tabularnewline
75 & 98593 & 122265.065312153 & -23672.0653121532 \tabularnewline
76 & 106894 & 121717.231538648 & -14823.2315386479 \tabularnewline
77 & 126675 & 122022.53862131 & 4652.46137868978 \tabularnewline
78 & 144300 & 125200.916081922 & 19099.0839180775 \tabularnewline
79 & 140099 & 130928.296897239 & 9170.70310276061 \tabularnewline
80 & 140099 & 135499.235959614 & 4599.76404038642 \tabularnewline
81 & 142154 & 139547.843347974 & 2606.15665202599 \tabularnewline
82 & 134976 & 143384.656974657 & -8408.65697465662 \tabularnewline
83 & 153634 & 145442.291265155 & 8191.7087348449 \tabularnewline
84 & 153634 & 150061.669243743 & 3572.33075625729 \tabularnewline
85 & 150455 & 154124.444717776 & -3669.44471777615 \tabularnewline
86 & 132820 & 157067.120107889 & -24247.1201078886 \tabularnewline
87 & 135999 & 156457.981238542 & -20458.9812385422 \tabularnewline
88 & 138054 & 155837.222310795 & -17783.2223107947 \tabularnewline
89 & 151579 & 155119.286446776 & -3540.28644677572 \tabularnewline
90 & 169204 & 156317.09901629 & 12886.9009837103 \tabularnewline
91 & 156701 & 160177.581387629 & -3476.58138762877 \tabularnewline
92 & 162958 & 161635.655488311 & 1322.34451168883 \tabularnewline
93 & 157724 & 163806.369269657 & -6082.3692696573 \tabularnewline
94 & 154656 & 164769.556683294 & -10113.5566832937 \tabularnewline
95 & 178538 & 164893.725794234 & 13644.2742057664 \tabularnewline
96 & 173304 & 168735.451011621 & 4568.54898837933 \tabularnewline
97 & 166025 & 171418.195559391 & -5393.19555939143 \tabularnewline
98 & 155679 & 172550.910749647 & -16871.9107496474 \tabularnewline
99 & 166025 & 171612.988569838 & -5587.98856983811 \tabularnewline
100 & 171259 & 172118.496264429 & -859.496264429385 \tabularnewline
101 & 177505 & 173268.443969725 & 4236.55603027451 \tabularnewline
102 & 185806 & 175250.782379473 & 10555.2176205265 \tabularnewline
103 & 177505 & 178406.791297512 & -901.791297512216 \tabularnewline
104 & 182628 & 179921.653355844 & 2706.34664415603 \tabularnewline
105 & 176381 & 182018.039635507 & -5637.03963550652 \tabularnewline
106 & 175359 & 182786.304218495 & -7427.30421849524 \tabularnewline
107 & 201285 & 183103.566402476 & 18181.4335975242 \tabularnewline
108 & 203441 & 187520.774959029 & 15920.2250409712 \tabularnewline
109 & 195140 & 192043.92610774 & 3096.07389225982 \tabularnewline
110 & 180583 & 194839.718082402 & -14256.718082402 \tabularnewline
111 & 192984 & 194805.622146881 & -1821.62214688087 \tabularnewline
112 & 198208 & 196478.003098736 & 1729.99690126369 \tabularnewline
113 & 204464 & 198697.861024868 & 5766.13897513205 \tabularnewline
114 & 213788 & 201641.353802455 & 12146.6461975448 \tabularnewline
115 & 204464 & 205809.739717324 & -1345.73971732371 \tabularnewline
116 & 211743 & 208037.847042458 & 3705.15295754175 \tabularnewline
117 & 208564 & 211077.781860923 & -2513.78186092337 \tabularnewline
118 & 197185 & 213172.84057537 & -15987.8405753702 \tabularnewline
119 & 221066 & 212939.240749047 & 8126.7592509526 \tabularnewline
120 & 221066 & 216326.226022492 & 4739.77397750752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]56064[/C][C]56065[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]54019[/C][C]55042.8321562394[/C][C]-1023.83215623941[/C][/ROW]
[ROW][C]5[/C][C]74712[/C][C]53848.9616153751[/C][C]20863.0383846249[/C][/ROW]
[ROW][C]6[/C][C]73689[/C][C]56301.3278348968[/C][C]17387.6721651032[/C][/ROW]
[ROW][C]7[/C][C]58109[/C][C]58727.4508452954[/C][C]-618.450845295367[/C][/ROW]
[ROW][C]8[/C][C]47763[/C][C]58595.6361402768[/C][C]-10832.6361402768[/C][/ROW]
[ROW][C]9[/C][C]48785[/C][C]56732.9205718016[/C][C]-7947.92057180163[/C][/ROW]
[ROW][C]10[/C][C]48785[/C][C]55065.138407655[/C][C]-6280.13840765502[/C][/ROW]
[ROW][C]11[/C][C]49808[/C][C]53465.0613270477[/C][C]-3657.06132704771[/C][/ROW]
[ROW][C]12[/C][C]51964[/C][C]52137.5619792107[/C][C]-173.561979210666[/C][/ROW]
[ROW][C]13[/C][C]45718[/C][C]51297.0970799008[/C][C]-5579.09707990084[/C][/ROW]
[ROW][C]14[/C][C]39462[/C][C]49544.7124685305[/C][C]-10082.7124685305[/C][/ROW]
[ROW][C]15[/C][C]34339[/C][C]46887.453610789[/C][C]-12548.453610789[/C][/ROW]
[ROW][C]16[/C][C]34339[/C][C]43547.1115016778[/C][C]-9208.11150167785[/C][/ROW]
[ROW][C]17[/C][C]54019[/C][C]40432.3618941054[/C][C]13586.6381058946[/C][/ROW]
[ROW][C]18[/C][C]56064[/C][C]40897.6979928251[/C][C]15166.3020071749[/C][/ROW]
[ROW][C]19[/C][C]40484[/C][C]41990.9550293769[/C][C]-1506.95502937691[/C][/ROW]
[ROW][C]20[/C][C]22859[/C][C]40690.673576068[/C][C]-17831.673576068[/C][/ROW]
[ROW][C]21[/C][C]32183[/C][C]36610.1519459917[/C][C]-4427.1519459917[/C][/ROW]
[ROW][C]22[/C][C]32183[/C][C]34303.3624279209[/C][C]-2120.36242792094[/C][/ROW]
[ROW][C]23[/C][C]39462[/C][C]32265.5413472736[/C][C]7196.45865272636[/C][/ROW]
[ROW][C]24[/C][C]43663[/C][C]31734.8736040209[/C][C]11928.1263959791[/C][/ROW]
[ROW][C]25[/C][C]42640[/C][C]32190.5433223156[/C][C]10449.4566776844[/C][/ROW]
[ROW][C]26[/C][C]32183[/C][C]32716.5269400416[/C][C]-533.526940041636[/C][/ROW]
[ROW][C]27[/C][C]37417[/C][C]31678.1019066681[/C][C]5738.89809333189[/C][/ROW]
[ROW][C]28[/C][C]35362[/C][C]31678.2182861548[/C][C]3683.78171384523[/C][/ROW]
[ROW][C]29[/C][C]52987[/C][C]31486.6336410298[/C][C]21500.3663589702[/C][/ROW]
[ROW][C]30[/C][C]48785[/C][C]34383.814221306[/C][C]14401.185778694[/C][/ROW]
[ROW][C]31[/C][C]32183[/C][C]36663.5346030731[/C][C]-4480.53460307308[/C][/ROW]
[ROW][C]32[/C][C]19782[/C][C]36158.6099177392[/C][C]-16376.6099177392[/C][/ROW]
[ROW][C]33[/C][C]31160[/C][C]33537.3660257469[/C][C]-2377.36602574693[/C][/ROW]
[ROW][C]34[/C][C]34339[/C][C]32828.5271122521[/C][C]1510.47288774788[/C][/ROW]
[ROW][C]35[/C][C]37417[/C][C]32708.7583602738[/C][C]4708.24163972624[/C][/ROW]
[ROW][C]36[/C][C]41507[/C][C]33166.0470986306[/C][C]8340.95290136945[/C][/ROW]
[ROW][C]37[/C][C]33205[/C][C]34358.7810751651[/C][C]-1153.78107516507[/C][/ROW]
[ROW][C]38[/C][C]26038[/C][C]34180.5995118148[/C][C]-8142.59951181476[/C][/ROW]
[ROW][C]39[/C][C]29116[/C][C]32798.5806443968[/C][C]-3682.58064439682[/C][/ROW]
[ROW][C]40[/C][C]30138[/C][C]31947.7281410835[/C][C]-1809.72814108348[/C][/ROW]
[ROW][C]41[/C][C]57087[/C][C]31312.8916577609[/C][C]25774.1083422391[/C][/ROW]
[ROW][C]42[/C][C]57087[/C][C]35259.5074867737[/C][C]21827.4925132263[/C][/ROW]
[ROW][C]43[/C][C]41507[/C][C]39231.9169480464[/C][C]2275.08305195358[/C][/ROW]
[ROW][C]44[/C][C]39462[/C][C]40505.404217111[/C][C]-1043.40421711099[/C][/ROW]
[ROW][C]45[/C][C]45718[/C][C]41282.6523324887[/C][C]4435.34766751129[/C][/ROW]
[ROW][C]46[/C][C]42640[/C][C]42951.6142644729[/C][C]-311.614264472875[/C][/ROW]
[ROW][C]47[/C][C]50942[/C][C]43942.2588829978[/C][C]6999.7411170022[/C][/ROW]
[ROW][C]48[/C][C]61288[/C][C]46151.7483019601[/C][C]15136.2516980399[/C][/ROW]
[ROW][C]49[/C][C]63343[/C][C]49913.8041467631[/C][C]13429.1958532369[/C][/ROW]
[ROW][C]50[/C][C]48785[/C][C]53793.5026019071[/C][C]-5008.50260190709[/C][/ROW]
[ROW][C]51[/C][C]44685[/C][C]54937.1286686418[/C][C]-10252.1286686418[/C][/ROW]
[ROW][C]52[/C][C]40484[/C][C]55066.9100671771[/C][C]-14582.9100671771[/C][/ROW]
[ROW][C]53[/C][C]68567[/C][C]54196.0491700351[/C][C]14370.9508299649[/C][/ROW]
[ROW][C]54[/C][C]70622[/C][C]57795.5269623406[/C][C]12826.4730376594[/C][/ROW]
[ROW][C]55[/C][C]65388[/C][C]61519.5003623021[/C][C]3868.49963769785[/C][/ROW]
[ROW][C]56[/C][C]70622[/C][C]64082.4204470507[/C][C]6539.57955294933[/C][/ROW]
[ROW][C]57[/C][C]69589[/C][C]67196.9595409117[/C][C]2392.04045908834[/C][/ROW]
[ROW][C]58[/C][C]61288[/C][C]69789.9769438366[/C][C]-8501.97694383659[/C][/ROW]
[ROW][C]59[/C][C]70622[/C][C]70618.3726702024[/C][C]3.62732979757129[/C][/ROW]
[ROW][C]60[/C][C]80968[/C][C]72647.3650969309[/C][C]8320.63490306913[/C][/ROW]
[ROW][C]61[/C][C]85169[/C][C]76072.4122069549[/C][C]9096.58779304514[/C][/ROW]
[ROW][C]62[/C][C]72667[/C][C]79849.8719627431[/C][C]-7182.87196274311[/C][/ROW]
[ROW][C]63[/C][C]64365[/C][C]81137.8189071708[/C][C]-16772.8189071708[/C][/ROW]
[ROW][C]64[/C][C]70622[/C][C]80624.359324501[/C][C]-10002.359324501[/C][/ROW]
[ROW][C]65[/C][C]97570[/C][C]80799.4189857656[/C][C]16770.5810142344[/C][/ROW]
[ROW][C]66[/C][C]105872[/C][C]85201.0712032261[/C][C]20670.9287967739[/C][/ROW]
[ROW][C]67[/C][C]103827[/C][C]90705.1728583134[/C][C]13121.8271416866[/C][/ROW]
[ROW][C]68[/C][C]107916[/C][C]95494.1506065914[/C][C]12421.8493934086[/C][/ROW]
[ROW][C]69[/C][C]106894[/C][C]100516.01449526[/C][C]6377.98550474019[/C][/ROW]
[ROW][C]70[/C][C]96548[/C][C]104855.136092044[/C][C]-8307.13609204389[/C][/ROW]
[ROW][C]71[/C][C]114173[/C][C]106899.753712521[/C][C]7273.2462874788[/C][/ROW]
[ROW][C]72[/C][C]118374[/C][C]111337.627947502[/C][C]7036.37205249828[/C][/ROW]
[ROW][C]73[/C][C]124519[/C][C]115929.951222099[/C][C]8589.04877790065[/C][/ROW]
[ROW][C]74[/C][C]105872[/C][C]120970.763591595[/C][C]-15098.7635915951[/C][/ROW]
[ROW][C]75[/C][C]98593[/C][C]122265.065312153[/C][C]-23672.0653121532[/C][/ROW]
[ROW][C]76[/C][C]106894[/C][C]121717.231538648[/C][C]-14823.2315386479[/C][/ROW]
[ROW][C]77[/C][C]126675[/C][C]122022.53862131[/C][C]4652.46137868978[/C][/ROW]
[ROW][C]78[/C][C]144300[/C][C]125200.916081922[/C][C]19099.0839180775[/C][/ROW]
[ROW][C]79[/C][C]140099[/C][C]130928.296897239[/C][C]9170.70310276061[/C][/ROW]
[ROW][C]80[/C][C]140099[/C][C]135499.235959614[/C][C]4599.76404038642[/C][/ROW]
[ROW][C]81[/C][C]142154[/C][C]139547.843347974[/C][C]2606.15665202599[/C][/ROW]
[ROW][C]82[/C][C]134976[/C][C]143384.656974657[/C][C]-8408.65697465662[/C][/ROW]
[ROW][C]83[/C][C]153634[/C][C]145442.291265155[/C][C]8191.7087348449[/C][/ROW]
[ROW][C]84[/C][C]153634[/C][C]150061.669243743[/C][C]3572.33075625729[/C][/ROW]
[ROW][C]85[/C][C]150455[/C][C]154124.444717776[/C][C]-3669.44471777615[/C][/ROW]
[ROW][C]86[/C][C]132820[/C][C]157067.120107889[/C][C]-24247.1201078886[/C][/ROW]
[ROW][C]87[/C][C]135999[/C][C]156457.981238542[/C][C]-20458.9812385422[/C][/ROW]
[ROW][C]88[/C][C]138054[/C][C]155837.222310795[/C][C]-17783.2223107947[/C][/ROW]
[ROW][C]89[/C][C]151579[/C][C]155119.286446776[/C][C]-3540.28644677572[/C][/ROW]
[ROW][C]90[/C][C]169204[/C][C]156317.09901629[/C][C]12886.9009837103[/C][/ROW]
[ROW][C]91[/C][C]156701[/C][C]160177.581387629[/C][C]-3476.58138762877[/C][/ROW]
[ROW][C]92[/C][C]162958[/C][C]161635.655488311[/C][C]1322.34451168883[/C][/ROW]
[ROW][C]93[/C][C]157724[/C][C]163806.369269657[/C][C]-6082.3692696573[/C][/ROW]
[ROW][C]94[/C][C]154656[/C][C]164769.556683294[/C][C]-10113.5566832937[/C][/ROW]
[ROW][C]95[/C][C]178538[/C][C]164893.725794234[/C][C]13644.2742057664[/C][/ROW]
[ROW][C]96[/C][C]173304[/C][C]168735.451011621[/C][C]4568.54898837933[/C][/ROW]
[ROW][C]97[/C][C]166025[/C][C]171418.195559391[/C][C]-5393.19555939143[/C][/ROW]
[ROW][C]98[/C][C]155679[/C][C]172550.910749647[/C][C]-16871.9107496474[/C][/ROW]
[ROW][C]99[/C][C]166025[/C][C]171612.988569838[/C][C]-5587.98856983811[/C][/ROW]
[ROW][C]100[/C][C]171259[/C][C]172118.496264429[/C][C]-859.496264429385[/C][/ROW]
[ROW][C]101[/C][C]177505[/C][C]173268.443969725[/C][C]4236.55603027451[/C][/ROW]
[ROW][C]102[/C][C]185806[/C][C]175250.782379473[/C][C]10555.2176205265[/C][/ROW]
[ROW][C]103[/C][C]177505[/C][C]178406.791297512[/C][C]-901.791297512216[/C][/ROW]
[ROW][C]104[/C][C]182628[/C][C]179921.653355844[/C][C]2706.34664415603[/C][/ROW]
[ROW][C]105[/C][C]176381[/C][C]182018.039635507[/C][C]-5637.03963550652[/C][/ROW]
[ROW][C]106[/C][C]175359[/C][C]182786.304218495[/C][C]-7427.30421849524[/C][/ROW]
[ROW][C]107[/C][C]201285[/C][C]183103.566402476[/C][C]18181.4335975242[/C][/ROW]
[ROW][C]108[/C][C]203441[/C][C]187520.774959029[/C][C]15920.2250409712[/C][/ROW]
[ROW][C]109[/C][C]195140[/C][C]192043.92610774[/C][C]3096.07389225982[/C][/ROW]
[ROW][C]110[/C][C]180583[/C][C]194839.718082402[/C][C]-14256.718082402[/C][/ROW]
[ROW][C]111[/C][C]192984[/C][C]194805.622146881[/C][C]-1821.62214688087[/C][/ROW]
[ROW][C]112[/C][C]198208[/C][C]196478.003098736[/C][C]1729.99690126369[/C][/ROW]
[ROW][C]113[/C][C]204464[/C][C]198697.861024868[/C][C]5766.13897513205[/C][/ROW]
[ROW][C]114[/C][C]213788[/C][C]201641.353802455[/C][C]12146.6461975448[/C][/ROW]
[ROW][C]115[/C][C]204464[/C][C]205809.739717324[/C][C]-1345.73971732371[/C][/ROW]
[ROW][C]116[/C][C]211743[/C][C]208037.847042458[/C][C]3705.15295754175[/C][/ROW]
[ROW][C]117[/C][C]208564[/C][C]211077.781860923[/C][C]-2513.78186092337[/C][/ROW]
[ROW][C]118[/C][C]197185[/C][C]213172.84057537[/C][C]-15987.8405753702[/C][/ROW]
[ROW][C]119[/C][C]221066[/C][C]212939.240749047[/C][C]8126.7592509526[/C][/ROW]
[ROW][C]120[/C][C]221066[/C][C]216326.226022492[/C][C]4739.77397750752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
35606456065-1
45401955042.8321562394-1023.83215623941
57471253848.961615375120863.0383846249
67368956301.327834896817387.6721651032
75810958727.4508452954-618.450845295367
84776358595.6361402768-10832.6361402768
94878556732.9205718016-7947.92057180163
104878555065.138407655-6280.13840765502
114980853465.0613270477-3657.06132704771
125196452137.5619792107-173.561979210666
134571851297.0970799008-5579.09707990084
143946249544.7124685305-10082.7124685305
153433946887.453610789-12548.453610789
163433943547.1115016778-9208.11150167785
175401940432.361894105413586.6381058946
185606440897.697992825115166.3020071749
194048441990.9550293769-1506.95502937691
202285940690.673576068-17831.673576068
213218336610.1519459917-4427.1519459917
223218334303.3624279209-2120.36242792094
233946232265.54134727367196.45865272636
244366331734.873604020911928.1263959791
254264032190.543322315610449.4566776844
263218332716.5269400416-533.526940041636
273741731678.10190666815738.89809333189
283536231678.21828615483683.78171384523
295298731486.633641029821500.3663589702
304878534383.81422130614401.185778694
313218336663.5346030731-4480.53460307308
321978236158.6099177392-16376.6099177392
333116033537.3660257469-2377.36602574693
343433932828.52711225211510.47288774788
353741732708.75836027384708.24163972624
364150733166.04709863068340.95290136945
373320534358.7810751651-1153.78107516507
382603834180.5995118148-8142.59951181476
392911632798.5806443968-3682.58064439682
403013831947.7281410835-1809.72814108348
415708731312.891657760925774.1083422391
425708735259.507486773721827.4925132263
434150739231.91694804642275.08305195358
443946240505.404217111-1043.40421711099
454571841282.65233248874435.34766751129
464264042951.6142644729-311.614264472875
475094243942.25888299786999.7411170022
486128846151.748301960115136.2516980399
496334349913.804146763113429.1958532369
504878553793.5026019071-5008.50260190709
514468554937.1286686418-10252.1286686418
524048455066.9100671771-14582.9100671771
536856754196.049170035114370.9508299649
547062257795.526962340612826.4730376594
556538861519.50036230213868.49963769785
567062264082.42044705076539.57955294933
576958967196.95954091172392.04045908834
586128869789.9769438366-8501.97694383659
597062270618.37267020243.62732979757129
608096872647.36509693098320.63490306913
618516976072.41220695499096.58779304514
627266779849.8719627431-7182.87196274311
636436581137.8189071708-16772.8189071708
647062280624.359324501-10002.359324501
659757080799.418985765616770.5810142344
6610587285201.071203226120670.9287967739
6710382790705.172858313413121.8271416866
6810791695494.150606591412421.8493934086
69106894100516.014495266377.98550474019
7096548104855.136092044-8307.13609204389
71114173106899.7537125217273.2462874788
72118374111337.6279475027036.37205249828
73124519115929.9512220998589.04877790065
74105872120970.763591595-15098.7635915951
7598593122265.065312153-23672.0653121532
76106894121717.231538648-14823.2315386479
77126675122022.538621314652.46137868978
78144300125200.91608192219099.0839180775
79140099130928.2968972399170.70310276061
80140099135499.2359596144599.76404038642
81142154139547.8433479742606.15665202599
82134976143384.656974657-8408.65697465662
83153634145442.2912651558191.7087348449
84153634150061.6692437433572.33075625729
85150455154124.444717776-3669.44471777615
86132820157067.120107889-24247.1201078886
87135999156457.981238542-20458.9812385422
88138054155837.222310795-17783.2223107947
89151579155119.286446776-3540.28644677572
90169204156317.0990162912886.9009837103
91156701160177.581387629-3476.58138762877
92162958161635.6554883111322.34451168883
93157724163806.369269657-6082.3692696573
94154656164769.556683294-10113.5566832937
95178538164893.72579423413644.2742057664
96173304168735.4510116214568.54898837933
97166025171418.195559391-5393.19555939143
98155679172550.910749647-16871.9107496474
99166025171612.988569838-5587.98856983811
100171259172118.496264429-859.496264429385
101177505173268.4439697254236.55603027451
102185806175250.78237947310555.2176205265
103177505178406.791297512-901.791297512216
104182628179921.6533558442706.34664415603
105176381182018.039635507-5637.03963550652
106175359182786.304218495-7427.30421849524
107201285183103.56640247618181.4335975242
108203441187520.77495902915920.2250409712
109195140192043.926107743096.07389225982
110180583194839.718082402-14256.718082402
111192984194805.622146881-1821.62214688087
112198208196478.0030987361729.99690126369
113204464198697.8610248685766.13897513205
114213788201641.35380245512146.6461975448
115204464205809.739717324-1345.73971732371
116211743208037.8470424583705.15295754175
117208564211077.781860923-2513.78186092337
118197185213172.84057537-15987.8405753702
119221066212939.2407490478126.7592509526
120221066216326.2260224924739.77397750752







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121219361.723966075198468.891367427240254.556564724
122221728.239701863200543.159563726242913.319840001
123224094.755437651202523.278582645245666.232292656
124226461.271173438204400.086400887248522.455945989
125228827.786909226206166.545992622251489.02782583
126231194.302645014207817.841140446254570.764149581
127233560.818380801209351.323318236257770.313443367
128235927.334116589210766.325077936261088.343155242
129238293.849852377212063.875275869264523.824428885
130240660.365588164213246.360730413268074.370445916
131243026.881323952214317.177322583271736.585325321
132245393.39705974215280.404338429275506.38978105

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 219361.723966075 & 198468.891367427 & 240254.556564724 \tabularnewline
122 & 221728.239701863 & 200543.159563726 & 242913.319840001 \tabularnewline
123 & 224094.755437651 & 202523.278582645 & 245666.232292656 \tabularnewline
124 & 226461.271173438 & 204400.086400887 & 248522.455945989 \tabularnewline
125 & 228827.786909226 & 206166.545992622 & 251489.02782583 \tabularnewline
126 & 231194.302645014 & 207817.841140446 & 254570.764149581 \tabularnewline
127 & 233560.818380801 & 209351.323318236 & 257770.313443367 \tabularnewline
128 & 235927.334116589 & 210766.325077936 & 261088.343155242 \tabularnewline
129 & 238293.849852377 & 212063.875275869 & 264523.824428885 \tabularnewline
130 & 240660.365588164 & 213246.360730413 & 268074.370445916 \tabularnewline
131 & 243026.881323952 & 214317.177322583 & 271736.585325321 \tabularnewline
132 & 245393.39705974 & 215280.404338429 & 275506.38978105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121[/C][C]219361.723966075[/C][C]198468.891367427[/C][C]240254.556564724[/C][/ROW]
[ROW][C]122[/C][C]221728.239701863[/C][C]200543.159563726[/C][C]242913.319840001[/C][/ROW]
[ROW][C]123[/C][C]224094.755437651[/C][C]202523.278582645[/C][C]245666.232292656[/C][/ROW]
[ROW][C]124[/C][C]226461.271173438[/C][C]204400.086400887[/C][C]248522.455945989[/C][/ROW]
[ROW][C]125[/C][C]228827.786909226[/C][C]206166.545992622[/C][C]251489.02782583[/C][/ROW]
[ROW][C]126[/C][C]231194.302645014[/C][C]207817.841140446[/C][C]254570.764149581[/C][/ROW]
[ROW][C]127[/C][C]233560.818380801[/C][C]209351.323318236[/C][C]257770.313443367[/C][/ROW]
[ROW][C]128[/C][C]235927.334116589[/C][C]210766.325077936[/C][C]261088.343155242[/C][/ROW]
[ROW][C]129[/C][C]238293.849852377[/C][C]212063.875275869[/C][C]264523.824428885[/C][/ROW]
[ROW][C]130[/C][C]240660.365588164[/C][C]213246.360730413[/C][C]268074.370445916[/C][/ROW]
[ROW][C]131[/C][C]243026.881323952[/C][C]214317.177322583[/C][C]271736.585325321[/C][/ROW]
[ROW][C]132[/C][C]245393.39705974[/C][C]215280.404338429[/C][C]275506.38978105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
121219361.723966075198468.891367427240254.556564724
122221728.239701863200543.159563726242913.319840001
123224094.755437651202523.278582645245666.232292656
124226461.271173438204400.086400887248522.455945989
125228827.786909226206166.545992622251489.02782583
126231194.302645014207817.841140446254570.764149581
127233560.818380801209351.323318236257770.313443367
128235927.334116589210766.325077936261088.343155242
129238293.849852377212063.875275869264523.824428885
130240660.365588164213246.360730413268074.370445916
131243026.881323952214317.177322583271736.585325321
132245393.39705974215280.404338429275506.38978105



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')