Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 13:52:41 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502884917mpej3iier2ji6c8.htm/, Retrieved Sat, 11 May 2024 19:33:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307372, Retrieved Sat, 11 May 2024 19:33:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2017-08-16 11:52:41] [7f8e680169e3605c7c9c65666ad372ce] [Current]
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Dataseries X:
209704
208923
208131
206492
222706
221848
209704
201630
202411
202411
203280
204842
207273
207273
205711
201630
222706
225918
221067
209704
214566
207273
210562
212135
213774
209704
210562
204842
222706
228349
223498
214566
224279
213774
223498
222706
225137
216205
225918
225137
239712
236423
223498
216986
225918
213774
222706
224279
227568
220286
224279
226710
235642
228349
218636
208131
217855
191125
204061
211343
218636
208131
208131
208131
213774
205711
195129
186274
192698
167618
182985
191917
193556
184624
185405
182985
191125
185405
174130
165979
179762
149831
169268
178123
178123
167618
157905
157124
165979
157905
142549
131967
143330
116611
140899
153824
157905
148973
137687
145761
148973
146542
122243
110968
119031
94743
119823
128755
136037
123893
112530
119031
122243
115819
91531
80949
90662
63943
93093
110968




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307372&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307372&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307372&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.659004759562618
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.659004759562618 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307372&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]0.659004759562618[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307372&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307372&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
alpha0.659004759562618
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3208131208142-11
4206492207353.750947645-861.750947644818
5222706206004.85297158916701.1470284107
6221848216229.9883534675618.01164653298
7209704219151.28476781-9447.28476781049
8201630212144.47914088-10514.4791408799
9202411204434.387342718-2023.3873427182
10202411202319.96545342891.0345465718419
11203280201598.9576529041681.04234709637
12204842201925.7725606662916.22743933357
13207273203066.5803231544206.41967684563
14207273205057.6309109142215.36908908648
15205711205736.569684809-25.5696848094231
16201630204938.71914082-3308.71914081951
17222706201977.25747896420728.7425210365
18225918214856.59746007511061.4025399254
19221067221365.114381323-298.114381323452
20209704220387.655585137-10683.6555851373
21214566212566.0757050041999.92429499596
22207273213103.035334171-5830.03533417129
23210562208480.0143005342081.98569946582
24212135209071.0527858233063.94721417653
25213774210309.2085830143464.79141698556
26209704211811.5226177-2107.52261769964
27210562209641.65518175920.344818250305
28204842209467.166797415-4625.16679741547
29222706205638.15986414817067.8401358523
30228349216104.94774912812244.0522508718
31223498223392.836458786105.1635412139
32214566222681.139732979-8115.13973297854
33224279216552.224024437726.77597557002
34213774220863.206168405-7089.20616840469
35223498215410.3855619058087.61443809466
36222706219959.1619701172746.83802988293
37225137220988.3413055584148.65869444248
38216205222941.327130996-6736.32713099598
39225918217721.0554896998196.94451030117
40225137222341.8809358582795.11906414205
41239712223402.87770267216309.1222973282
42236423233369.66692093053.33307910012
43223498234600.827952557-11102.8279525568
44216986226503.011487217-9517.01148721704
45225918219450.2556203296467.74437967109
46213774222931.529950167-9157.52995016653
47222706216115.674127176590.32587283044
48224279219677.7302444344601.26975556649
49227568221928.9889133835639.01108661667
50220286224864.12405869-4578.1240586901
51224279221066.1185141453212.8814858548
52226710222402.4227052344307.57729476588
53235642224460.13664466911181.8633553313
54228349231048.037816611-2699.03781661086
55218636228488.359049225-9852.35904922482
56208131221214.607542866-13083.6075428659
57217855211811.4478998686043.5521001321
58191125215013.17749852-23888.1774985196
59204061198489.7548297195571.24517028144
60211343201380.2319136249962.76808637573
61218636207164.74350096411471.2564990356
62208131213943.356131992-5812.35613199248
63208131209331.985776736-1200.98577673646
64208131207759.5304337371.469566299871
65213774207223.3306459246550.6693540756
66205711210759.252928581-5048.25292858121
67195129206651.43022117-11522.4302211702
68186274198277.093863691-12003.0938636909
69192698189585.9978780423112.00212195824
70167618190855.822088181-23237.8220881812
71182985174760.98673028224.01326979953
72191917179399.65061770412517.3493822955
73193556186867.6434377456688.35656225457
74184624190494.302245923-5870.30224592306
75185405185844.745125789-439.745125788642
76182985184773.950994899-1788.95099489947
77191125182814.0237746368310.97622536356
78185405187509.996663763-2104.99666376278
79174130185341.79384348-11211.7938434797
80165979177172.168337392-11193.1683373917
81179762169014.81712846510747.182871535
82149831175316.261792696-25485.2617926964
83169268157740.3529726111527.6470273898
84178123164556.12723021813566.8727697821
85178123172715.7609578855407.23904211522
86167618175498.157222732-7880.1572227315
87157905169524.09610685-11619.0961068497
88157124161086.05647062-3962.05647062027
89165979157694.0423988268284.95760117436
90157905162372.868890774-4467.86889077403
91142549158647.522026652-16098.5220266522
92131967147257.519389165-15290.5193891648
93143330136399.9943355216930.00566447931
94116611140185.901052208-23574.9010522084
95140899123868.92905258517030.0709474147
96153824134310.82686262119513.1731373793
97157905146389.10083432311515.8991656769
98148973153197.133195147-4224.13319514733
99137687149632.409314519-11945.4093145188
100145761140979.3277213274781.67227867272
101148973143349.4725116415623.52748835878
102146542146274.403892001267.596107999154
103122243145669.751000813-23426.7510008127
104110968129450.410590189-18482.4105901888
105119031116489.4140430642541.58595693615
10694743117383.331285522-22640.3312855223
107119823101682.24521028918140.7547897113
108128755112856.08895876715898.9110412332
109136037122552.54700680213484.4529931979
110123893130657.865709418-6764.86570941791
111112530125418.78700911-12888.7870091096
112119031116144.0150251182886.98497488248
113122243117265.5518643514977.44813564917
114115819119764.71387622-3945.71387621971
11591531116383.469651919-24852.4696519187
1168094999224.5738644188-18275.5738644188
1179066286399.88370402864262.11629597138
1186394388427.6386288832-24484.6386288832
1199309371511.145236278421581.8547637216
12011096884952.690245760126015.3097542399

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 208131 & 208142 & -11 \tabularnewline
4 & 206492 & 207353.750947645 & -861.750947644818 \tabularnewline
5 & 222706 & 206004.852971589 & 16701.1470284107 \tabularnewline
6 & 221848 & 216229.988353467 & 5618.01164653298 \tabularnewline
7 & 209704 & 219151.28476781 & -9447.28476781049 \tabularnewline
8 & 201630 & 212144.47914088 & -10514.4791408799 \tabularnewline
9 & 202411 & 204434.387342718 & -2023.3873427182 \tabularnewline
10 & 202411 & 202319.965453428 & 91.0345465718419 \tabularnewline
11 & 203280 & 201598.957652904 & 1681.04234709637 \tabularnewline
12 & 204842 & 201925.772560666 & 2916.22743933357 \tabularnewline
13 & 207273 & 203066.580323154 & 4206.41967684563 \tabularnewline
14 & 207273 & 205057.630910914 & 2215.36908908648 \tabularnewline
15 & 205711 & 205736.569684809 & -25.5696848094231 \tabularnewline
16 & 201630 & 204938.71914082 & -3308.71914081951 \tabularnewline
17 & 222706 & 201977.257478964 & 20728.7425210365 \tabularnewline
18 & 225918 & 214856.597460075 & 11061.4025399254 \tabularnewline
19 & 221067 & 221365.114381323 & -298.114381323452 \tabularnewline
20 & 209704 & 220387.655585137 & -10683.6555851373 \tabularnewline
21 & 214566 & 212566.075705004 & 1999.92429499596 \tabularnewline
22 & 207273 & 213103.035334171 & -5830.03533417129 \tabularnewline
23 & 210562 & 208480.014300534 & 2081.98569946582 \tabularnewline
24 & 212135 & 209071.052785823 & 3063.94721417653 \tabularnewline
25 & 213774 & 210309.208583014 & 3464.79141698556 \tabularnewline
26 & 209704 & 211811.5226177 & -2107.52261769964 \tabularnewline
27 & 210562 & 209641.65518175 & 920.344818250305 \tabularnewline
28 & 204842 & 209467.166797415 & -4625.16679741547 \tabularnewline
29 & 222706 & 205638.159864148 & 17067.8401358523 \tabularnewline
30 & 228349 & 216104.947749128 & 12244.0522508718 \tabularnewline
31 & 223498 & 223392.836458786 & 105.1635412139 \tabularnewline
32 & 214566 & 222681.139732979 & -8115.13973297854 \tabularnewline
33 & 224279 & 216552.22402443 & 7726.77597557002 \tabularnewline
34 & 213774 & 220863.206168405 & -7089.20616840469 \tabularnewline
35 & 223498 & 215410.385561905 & 8087.61443809466 \tabularnewline
36 & 222706 & 219959.161970117 & 2746.83802988293 \tabularnewline
37 & 225137 & 220988.341305558 & 4148.65869444248 \tabularnewline
38 & 216205 & 222941.327130996 & -6736.32713099598 \tabularnewline
39 & 225918 & 217721.055489699 & 8196.94451030117 \tabularnewline
40 & 225137 & 222341.880935858 & 2795.11906414205 \tabularnewline
41 & 239712 & 223402.877702672 & 16309.1222973282 \tabularnewline
42 & 236423 & 233369.6669209 & 3053.33307910012 \tabularnewline
43 & 223498 & 234600.827952557 & -11102.8279525568 \tabularnewline
44 & 216986 & 226503.011487217 & -9517.01148721704 \tabularnewline
45 & 225918 & 219450.255620329 & 6467.74437967109 \tabularnewline
46 & 213774 & 222931.529950167 & -9157.52995016653 \tabularnewline
47 & 222706 & 216115.67412717 & 6590.32587283044 \tabularnewline
48 & 224279 & 219677.730244434 & 4601.26975556649 \tabularnewline
49 & 227568 & 221928.988913383 & 5639.01108661667 \tabularnewline
50 & 220286 & 224864.12405869 & -4578.1240586901 \tabularnewline
51 & 224279 & 221066.118514145 & 3212.8814858548 \tabularnewline
52 & 226710 & 222402.422705234 & 4307.57729476588 \tabularnewline
53 & 235642 & 224460.136644669 & 11181.8633553313 \tabularnewline
54 & 228349 & 231048.037816611 & -2699.03781661086 \tabularnewline
55 & 218636 & 228488.359049225 & -9852.35904922482 \tabularnewline
56 & 208131 & 221214.607542866 & -13083.6075428659 \tabularnewline
57 & 217855 & 211811.447899868 & 6043.5521001321 \tabularnewline
58 & 191125 & 215013.17749852 & -23888.1774985196 \tabularnewline
59 & 204061 & 198489.754829719 & 5571.24517028144 \tabularnewline
60 & 211343 & 201380.231913624 & 9962.76808637573 \tabularnewline
61 & 218636 & 207164.743500964 & 11471.2564990356 \tabularnewline
62 & 208131 & 213943.356131992 & -5812.35613199248 \tabularnewline
63 & 208131 & 209331.985776736 & -1200.98577673646 \tabularnewline
64 & 208131 & 207759.5304337 & 371.469566299871 \tabularnewline
65 & 213774 & 207223.330645924 & 6550.6693540756 \tabularnewline
66 & 205711 & 210759.252928581 & -5048.25292858121 \tabularnewline
67 & 195129 & 206651.43022117 & -11522.4302211702 \tabularnewline
68 & 186274 & 198277.093863691 & -12003.0938636909 \tabularnewline
69 & 192698 & 189585.997878042 & 3112.00212195824 \tabularnewline
70 & 167618 & 190855.822088181 & -23237.8220881812 \tabularnewline
71 & 182985 & 174760.9867302 & 8224.01326979953 \tabularnewline
72 & 191917 & 179399.650617704 & 12517.3493822955 \tabularnewline
73 & 193556 & 186867.643437745 & 6688.35656225457 \tabularnewline
74 & 184624 & 190494.302245923 & -5870.30224592306 \tabularnewline
75 & 185405 & 185844.745125789 & -439.745125788642 \tabularnewline
76 & 182985 & 184773.950994899 & -1788.95099489947 \tabularnewline
77 & 191125 & 182814.023774636 & 8310.97622536356 \tabularnewline
78 & 185405 & 187509.996663763 & -2104.99666376278 \tabularnewline
79 & 174130 & 185341.79384348 & -11211.7938434797 \tabularnewline
80 & 165979 & 177172.168337392 & -11193.1683373917 \tabularnewline
81 & 179762 & 169014.817128465 & 10747.182871535 \tabularnewline
82 & 149831 & 175316.261792696 & -25485.2617926964 \tabularnewline
83 & 169268 & 157740.35297261 & 11527.6470273898 \tabularnewline
84 & 178123 & 164556.127230218 & 13566.8727697821 \tabularnewline
85 & 178123 & 172715.760957885 & 5407.23904211522 \tabularnewline
86 & 167618 & 175498.157222732 & -7880.1572227315 \tabularnewline
87 & 157905 & 169524.09610685 & -11619.0961068497 \tabularnewline
88 & 157124 & 161086.05647062 & -3962.05647062027 \tabularnewline
89 & 165979 & 157694.042398826 & 8284.95760117436 \tabularnewline
90 & 157905 & 162372.868890774 & -4467.86889077403 \tabularnewline
91 & 142549 & 158647.522026652 & -16098.5220266522 \tabularnewline
92 & 131967 & 147257.519389165 & -15290.5193891648 \tabularnewline
93 & 143330 & 136399.994335521 & 6930.00566447931 \tabularnewline
94 & 116611 & 140185.901052208 & -23574.9010522084 \tabularnewline
95 & 140899 & 123868.929052585 & 17030.0709474147 \tabularnewline
96 & 153824 & 134310.826862621 & 19513.1731373793 \tabularnewline
97 & 157905 & 146389.100834323 & 11515.8991656769 \tabularnewline
98 & 148973 & 153197.133195147 & -4224.13319514733 \tabularnewline
99 & 137687 & 149632.409314519 & -11945.4093145188 \tabularnewline
100 & 145761 & 140979.327721327 & 4781.67227867272 \tabularnewline
101 & 148973 & 143349.472511641 & 5623.52748835878 \tabularnewline
102 & 146542 & 146274.403892001 & 267.596107999154 \tabularnewline
103 & 122243 & 145669.751000813 & -23426.7510008127 \tabularnewline
104 & 110968 & 129450.410590189 & -18482.4105901888 \tabularnewline
105 & 119031 & 116489.414043064 & 2541.58595693615 \tabularnewline
106 & 94743 & 117383.331285522 & -22640.3312855223 \tabularnewline
107 & 119823 & 101682.245210289 & 18140.7547897113 \tabularnewline
108 & 128755 & 112856.088958767 & 15898.9110412332 \tabularnewline
109 & 136037 & 122552.547006802 & 13484.4529931979 \tabularnewline
110 & 123893 & 130657.865709418 & -6764.86570941791 \tabularnewline
111 & 112530 & 125418.78700911 & -12888.7870091096 \tabularnewline
112 & 119031 & 116144.015025118 & 2886.98497488248 \tabularnewline
113 & 122243 & 117265.551864351 & 4977.44813564917 \tabularnewline
114 & 115819 & 119764.71387622 & -3945.71387621971 \tabularnewline
115 & 91531 & 116383.469651919 & -24852.4696519187 \tabularnewline
116 & 80949 & 99224.5738644188 & -18275.5738644188 \tabularnewline
117 & 90662 & 86399.8837040286 & 4262.11629597138 \tabularnewline
118 & 63943 & 88427.6386288832 & -24484.6386288832 \tabularnewline
119 & 93093 & 71511.1452362784 & 21581.8547637216 \tabularnewline
120 & 110968 & 84952.6902457601 & 26015.3097542399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307372&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]208131[/C][C]208142[/C][C]-11[/C][/ROW]
[ROW][C]4[/C][C]206492[/C][C]207353.750947645[/C][C]-861.750947644818[/C][/ROW]
[ROW][C]5[/C][C]222706[/C][C]206004.852971589[/C][C]16701.1470284107[/C][/ROW]
[ROW][C]6[/C][C]221848[/C][C]216229.988353467[/C][C]5618.01164653298[/C][/ROW]
[ROW][C]7[/C][C]209704[/C][C]219151.28476781[/C][C]-9447.28476781049[/C][/ROW]
[ROW][C]8[/C][C]201630[/C][C]212144.47914088[/C][C]-10514.4791408799[/C][/ROW]
[ROW][C]9[/C][C]202411[/C][C]204434.387342718[/C][C]-2023.3873427182[/C][/ROW]
[ROW][C]10[/C][C]202411[/C][C]202319.965453428[/C][C]91.0345465718419[/C][/ROW]
[ROW][C]11[/C][C]203280[/C][C]201598.957652904[/C][C]1681.04234709637[/C][/ROW]
[ROW][C]12[/C][C]204842[/C][C]201925.772560666[/C][C]2916.22743933357[/C][/ROW]
[ROW][C]13[/C][C]207273[/C][C]203066.580323154[/C][C]4206.41967684563[/C][/ROW]
[ROW][C]14[/C][C]207273[/C][C]205057.630910914[/C][C]2215.36908908648[/C][/ROW]
[ROW][C]15[/C][C]205711[/C][C]205736.569684809[/C][C]-25.5696848094231[/C][/ROW]
[ROW][C]16[/C][C]201630[/C][C]204938.71914082[/C][C]-3308.71914081951[/C][/ROW]
[ROW][C]17[/C][C]222706[/C][C]201977.257478964[/C][C]20728.7425210365[/C][/ROW]
[ROW][C]18[/C][C]225918[/C][C]214856.597460075[/C][C]11061.4025399254[/C][/ROW]
[ROW][C]19[/C][C]221067[/C][C]221365.114381323[/C][C]-298.114381323452[/C][/ROW]
[ROW][C]20[/C][C]209704[/C][C]220387.655585137[/C][C]-10683.6555851373[/C][/ROW]
[ROW][C]21[/C][C]214566[/C][C]212566.075705004[/C][C]1999.92429499596[/C][/ROW]
[ROW][C]22[/C][C]207273[/C][C]213103.035334171[/C][C]-5830.03533417129[/C][/ROW]
[ROW][C]23[/C][C]210562[/C][C]208480.014300534[/C][C]2081.98569946582[/C][/ROW]
[ROW][C]24[/C][C]212135[/C][C]209071.052785823[/C][C]3063.94721417653[/C][/ROW]
[ROW][C]25[/C][C]213774[/C][C]210309.208583014[/C][C]3464.79141698556[/C][/ROW]
[ROW][C]26[/C][C]209704[/C][C]211811.5226177[/C][C]-2107.52261769964[/C][/ROW]
[ROW][C]27[/C][C]210562[/C][C]209641.65518175[/C][C]920.344818250305[/C][/ROW]
[ROW][C]28[/C][C]204842[/C][C]209467.166797415[/C][C]-4625.16679741547[/C][/ROW]
[ROW][C]29[/C][C]222706[/C][C]205638.159864148[/C][C]17067.8401358523[/C][/ROW]
[ROW][C]30[/C][C]228349[/C][C]216104.947749128[/C][C]12244.0522508718[/C][/ROW]
[ROW][C]31[/C][C]223498[/C][C]223392.836458786[/C][C]105.1635412139[/C][/ROW]
[ROW][C]32[/C][C]214566[/C][C]222681.139732979[/C][C]-8115.13973297854[/C][/ROW]
[ROW][C]33[/C][C]224279[/C][C]216552.22402443[/C][C]7726.77597557002[/C][/ROW]
[ROW][C]34[/C][C]213774[/C][C]220863.206168405[/C][C]-7089.20616840469[/C][/ROW]
[ROW][C]35[/C][C]223498[/C][C]215410.385561905[/C][C]8087.61443809466[/C][/ROW]
[ROW][C]36[/C][C]222706[/C][C]219959.161970117[/C][C]2746.83802988293[/C][/ROW]
[ROW][C]37[/C][C]225137[/C][C]220988.341305558[/C][C]4148.65869444248[/C][/ROW]
[ROW][C]38[/C][C]216205[/C][C]222941.327130996[/C][C]-6736.32713099598[/C][/ROW]
[ROW][C]39[/C][C]225918[/C][C]217721.055489699[/C][C]8196.94451030117[/C][/ROW]
[ROW][C]40[/C][C]225137[/C][C]222341.880935858[/C][C]2795.11906414205[/C][/ROW]
[ROW][C]41[/C][C]239712[/C][C]223402.877702672[/C][C]16309.1222973282[/C][/ROW]
[ROW][C]42[/C][C]236423[/C][C]233369.6669209[/C][C]3053.33307910012[/C][/ROW]
[ROW][C]43[/C][C]223498[/C][C]234600.827952557[/C][C]-11102.8279525568[/C][/ROW]
[ROW][C]44[/C][C]216986[/C][C]226503.011487217[/C][C]-9517.01148721704[/C][/ROW]
[ROW][C]45[/C][C]225918[/C][C]219450.255620329[/C][C]6467.74437967109[/C][/ROW]
[ROW][C]46[/C][C]213774[/C][C]222931.529950167[/C][C]-9157.52995016653[/C][/ROW]
[ROW][C]47[/C][C]222706[/C][C]216115.67412717[/C][C]6590.32587283044[/C][/ROW]
[ROW][C]48[/C][C]224279[/C][C]219677.730244434[/C][C]4601.26975556649[/C][/ROW]
[ROW][C]49[/C][C]227568[/C][C]221928.988913383[/C][C]5639.01108661667[/C][/ROW]
[ROW][C]50[/C][C]220286[/C][C]224864.12405869[/C][C]-4578.1240586901[/C][/ROW]
[ROW][C]51[/C][C]224279[/C][C]221066.118514145[/C][C]3212.8814858548[/C][/ROW]
[ROW][C]52[/C][C]226710[/C][C]222402.422705234[/C][C]4307.57729476588[/C][/ROW]
[ROW][C]53[/C][C]235642[/C][C]224460.136644669[/C][C]11181.8633553313[/C][/ROW]
[ROW][C]54[/C][C]228349[/C][C]231048.037816611[/C][C]-2699.03781661086[/C][/ROW]
[ROW][C]55[/C][C]218636[/C][C]228488.359049225[/C][C]-9852.35904922482[/C][/ROW]
[ROW][C]56[/C][C]208131[/C][C]221214.607542866[/C][C]-13083.6075428659[/C][/ROW]
[ROW][C]57[/C][C]217855[/C][C]211811.447899868[/C][C]6043.5521001321[/C][/ROW]
[ROW][C]58[/C][C]191125[/C][C]215013.17749852[/C][C]-23888.1774985196[/C][/ROW]
[ROW][C]59[/C][C]204061[/C][C]198489.754829719[/C][C]5571.24517028144[/C][/ROW]
[ROW][C]60[/C][C]211343[/C][C]201380.231913624[/C][C]9962.76808637573[/C][/ROW]
[ROW][C]61[/C][C]218636[/C][C]207164.743500964[/C][C]11471.2564990356[/C][/ROW]
[ROW][C]62[/C][C]208131[/C][C]213943.356131992[/C][C]-5812.35613199248[/C][/ROW]
[ROW][C]63[/C][C]208131[/C][C]209331.985776736[/C][C]-1200.98577673646[/C][/ROW]
[ROW][C]64[/C][C]208131[/C][C]207759.5304337[/C][C]371.469566299871[/C][/ROW]
[ROW][C]65[/C][C]213774[/C][C]207223.330645924[/C][C]6550.6693540756[/C][/ROW]
[ROW][C]66[/C][C]205711[/C][C]210759.252928581[/C][C]-5048.25292858121[/C][/ROW]
[ROW][C]67[/C][C]195129[/C][C]206651.43022117[/C][C]-11522.4302211702[/C][/ROW]
[ROW][C]68[/C][C]186274[/C][C]198277.093863691[/C][C]-12003.0938636909[/C][/ROW]
[ROW][C]69[/C][C]192698[/C][C]189585.997878042[/C][C]3112.00212195824[/C][/ROW]
[ROW][C]70[/C][C]167618[/C][C]190855.822088181[/C][C]-23237.8220881812[/C][/ROW]
[ROW][C]71[/C][C]182985[/C][C]174760.9867302[/C][C]8224.01326979953[/C][/ROW]
[ROW][C]72[/C][C]191917[/C][C]179399.650617704[/C][C]12517.3493822955[/C][/ROW]
[ROW][C]73[/C][C]193556[/C][C]186867.643437745[/C][C]6688.35656225457[/C][/ROW]
[ROW][C]74[/C][C]184624[/C][C]190494.302245923[/C][C]-5870.30224592306[/C][/ROW]
[ROW][C]75[/C][C]185405[/C][C]185844.745125789[/C][C]-439.745125788642[/C][/ROW]
[ROW][C]76[/C][C]182985[/C][C]184773.950994899[/C][C]-1788.95099489947[/C][/ROW]
[ROW][C]77[/C][C]191125[/C][C]182814.023774636[/C][C]8310.97622536356[/C][/ROW]
[ROW][C]78[/C][C]185405[/C][C]187509.996663763[/C][C]-2104.99666376278[/C][/ROW]
[ROW][C]79[/C][C]174130[/C][C]185341.79384348[/C][C]-11211.7938434797[/C][/ROW]
[ROW][C]80[/C][C]165979[/C][C]177172.168337392[/C][C]-11193.1683373917[/C][/ROW]
[ROW][C]81[/C][C]179762[/C][C]169014.817128465[/C][C]10747.182871535[/C][/ROW]
[ROW][C]82[/C][C]149831[/C][C]175316.261792696[/C][C]-25485.2617926964[/C][/ROW]
[ROW][C]83[/C][C]169268[/C][C]157740.35297261[/C][C]11527.6470273898[/C][/ROW]
[ROW][C]84[/C][C]178123[/C][C]164556.127230218[/C][C]13566.8727697821[/C][/ROW]
[ROW][C]85[/C][C]178123[/C][C]172715.760957885[/C][C]5407.23904211522[/C][/ROW]
[ROW][C]86[/C][C]167618[/C][C]175498.157222732[/C][C]-7880.1572227315[/C][/ROW]
[ROW][C]87[/C][C]157905[/C][C]169524.09610685[/C][C]-11619.0961068497[/C][/ROW]
[ROW][C]88[/C][C]157124[/C][C]161086.05647062[/C][C]-3962.05647062027[/C][/ROW]
[ROW][C]89[/C][C]165979[/C][C]157694.042398826[/C][C]8284.95760117436[/C][/ROW]
[ROW][C]90[/C][C]157905[/C][C]162372.868890774[/C][C]-4467.86889077403[/C][/ROW]
[ROW][C]91[/C][C]142549[/C][C]158647.522026652[/C][C]-16098.5220266522[/C][/ROW]
[ROW][C]92[/C][C]131967[/C][C]147257.519389165[/C][C]-15290.5193891648[/C][/ROW]
[ROW][C]93[/C][C]143330[/C][C]136399.994335521[/C][C]6930.00566447931[/C][/ROW]
[ROW][C]94[/C][C]116611[/C][C]140185.901052208[/C][C]-23574.9010522084[/C][/ROW]
[ROW][C]95[/C][C]140899[/C][C]123868.929052585[/C][C]17030.0709474147[/C][/ROW]
[ROW][C]96[/C][C]153824[/C][C]134310.826862621[/C][C]19513.1731373793[/C][/ROW]
[ROW][C]97[/C][C]157905[/C][C]146389.100834323[/C][C]11515.8991656769[/C][/ROW]
[ROW][C]98[/C][C]148973[/C][C]153197.133195147[/C][C]-4224.13319514733[/C][/ROW]
[ROW][C]99[/C][C]137687[/C][C]149632.409314519[/C][C]-11945.4093145188[/C][/ROW]
[ROW][C]100[/C][C]145761[/C][C]140979.327721327[/C][C]4781.67227867272[/C][/ROW]
[ROW][C]101[/C][C]148973[/C][C]143349.472511641[/C][C]5623.52748835878[/C][/ROW]
[ROW][C]102[/C][C]146542[/C][C]146274.403892001[/C][C]267.596107999154[/C][/ROW]
[ROW][C]103[/C][C]122243[/C][C]145669.751000813[/C][C]-23426.7510008127[/C][/ROW]
[ROW][C]104[/C][C]110968[/C][C]129450.410590189[/C][C]-18482.4105901888[/C][/ROW]
[ROW][C]105[/C][C]119031[/C][C]116489.414043064[/C][C]2541.58595693615[/C][/ROW]
[ROW][C]106[/C][C]94743[/C][C]117383.331285522[/C][C]-22640.3312855223[/C][/ROW]
[ROW][C]107[/C][C]119823[/C][C]101682.245210289[/C][C]18140.7547897113[/C][/ROW]
[ROW][C]108[/C][C]128755[/C][C]112856.088958767[/C][C]15898.9110412332[/C][/ROW]
[ROW][C]109[/C][C]136037[/C][C]122552.547006802[/C][C]13484.4529931979[/C][/ROW]
[ROW][C]110[/C][C]123893[/C][C]130657.865709418[/C][C]-6764.86570941791[/C][/ROW]
[ROW][C]111[/C][C]112530[/C][C]125418.78700911[/C][C]-12888.7870091096[/C][/ROW]
[ROW][C]112[/C][C]119031[/C][C]116144.015025118[/C][C]2886.98497488248[/C][/ROW]
[ROW][C]113[/C][C]122243[/C][C]117265.551864351[/C][C]4977.44813564917[/C][/ROW]
[ROW][C]114[/C][C]115819[/C][C]119764.71387622[/C][C]-3945.71387621971[/C][/ROW]
[ROW][C]115[/C][C]91531[/C][C]116383.469651919[/C][C]-24852.4696519187[/C][/ROW]
[ROW][C]116[/C][C]80949[/C][C]99224.5738644188[/C][C]-18275.5738644188[/C][/ROW]
[ROW][C]117[/C][C]90662[/C][C]86399.8837040286[/C][C]4262.11629597138[/C][/ROW]
[ROW][C]118[/C][C]63943[/C][C]88427.6386288832[/C][C]-24484.6386288832[/C][/ROW]
[ROW][C]119[/C][C]93093[/C][C]71511.1452362784[/C][C]21581.8547637216[/C][/ROW]
[ROW][C]120[/C][C]110968[/C][C]84952.6902457601[/C][C]26015.3097542399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307372&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307372&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
3208131208142-11
4206492207353.750947645-861.750947644818
5222706206004.85297158916701.1470284107
6221848216229.9883534675618.01164653298
7209704219151.28476781-9447.28476781049
8201630212144.47914088-10514.4791408799
9202411204434.387342718-2023.3873427182
10202411202319.96545342891.0345465718419
11203280201598.9576529041681.04234709637
12204842201925.7725606662916.22743933357
13207273203066.5803231544206.41967684563
14207273205057.6309109142215.36908908648
15205711205736.569684809-25.5696848094231
16201630204938.71914082-3308.71914081951
17222706201977.25747896420728.7425210365
18225918214856.59746007511061.4025399254
19221067221365.114381323-298.114381323452
20209704220387.655585137-10683.6555851373
21214566212566.0757050041999.92429499596
22207273213103.035334171-5830.03533417129
23210562208480.0143005342081.98569946582
24212135209071.0527858233063.94721417653
25213774210309.2085830143464.79141698556
26209704211811.5226177-2107.52261769964
27210562209641.65518175920.344818250305
28204842209467.166797415-4625.16679741547
29222706205638.15986414817067.8401358523
30228349216104.94774912812244.0522508718
31223498223392.836458786105.1635412139
32214566222681.139732979-8115.13973297854
33224279216552.224024437726.77597557002
34213774220863.206168405-7089.20616840469
35223498215410.3855619058087.61443809466
36222706219959.1619701172746.83802988293
37225137220988.3413055584148.65869444248
38216205222941.327130996-6736.32713099598
39225918217721.0554896998196.94451030117
40225137222341.8809358582795.11906414205
41239712223402.87770267216309.1222973282
42236423233369.66692093053.33307910012
43223498234600.827952557-11102.8279525568
44216986226503.011487217-9517.01148721704
45225918219450.2556203296467.74437967109
46213774222931.529950167-9157.52995016653
47222706216115.674127176590.32587283044
48224279219677.7302444344601.26975556649
49227568221928.9889133835639.01108661667
50220286224864.12405869-4578.1240586901
51224279221066.1185141453212.8814858548
52226710222402.4227052344307.57729476588
53235642224460.13664466911181.8633553313
54228349231048.037816611-2699.03781661086
55218636228488.359049225-9852.35904922482
56208131221214.607542866-13083.6075428659
57217855211811.4478998686043.5521001321
58191125215013.17749852-23888.1774985196
59204061198489.7548297195571.24517028144
60211343201380.2319136249962.76808637573
61218636207164.74350096411471.2564990356
62208131213943.356131992-5812.35613199248
63208131209331.985776736-1200.98577673646
64208131207759.5304337371.469566299871
65213774207223.3306459246550.6693540756
66205711210759.252928581-5048.25292858121
67195129206651.43022117-11522.4302211702
68186274198277.093863691-12003.0938636909
69192698189585.9978780423112.00212195824
70167618190855.822088181-23237.8220881812
71182985174760.98673028224.01326979953
72191917179399.65061770412517.3493822955
73193556186867.6434377456688.35656225457
74184624190494.302245923-5870.30224592306
75185405185844.745125789-439.745125788642
76182985184773.950994899-1788.95099489947
77191125182814.0237746368310.97622536356
78185405187509.996663763-2104.99666376278
79174130185341.79384348-11211.7938434797
80165979177172.168337392-11193.1683373917
81179762169014.81712846510747.182871535
82149831175316.261792696-25485.2617926964
83169268157740.3529726111527.6470273898
84178123164556.12723021813566.8727697821
85178123172715.7609578855407.23904211522
86167618175498.157222732-7880.1572227315
87157905169524.09610685-11619.0961068497
88157124161086.05647062-3962.05647062027
89165979157694.0423988268284.95760117436
90157905162372.868890774-4467.86889077403
91142549158647.522026652-16098.5220266522
92131967147257.519389165-15290.5193891648
93143330136399.9943355216930.00566447931
94116611140185.901052208-23574.9010522084
95140899123868.92905258517030.0709474147
96153824134310.82686262119513.1731373793
97157905146389.10083432311515.8991656769
98148973153197.133195147-4224.13319514733
99137687149632.409314519-11945.4093145188
100145761140979.3277213274781.67227867272
101148973143349.4725116415623.52748835878
102146542146274.403892001267.596107999154
103122243145669.751000813-23426.7510008127
104110968129450.410590189-18482.4105901888
105119031116489.4140430642541.58595693615
10694743117383.331285522-22640.3312855223
107119823101682.24521028918140.7547897113
108128755112856.08895876715898.9110412332
109136037122552.54700680213484.4529931979
110123893130657.865709418-6764.86570941791
111112530125418.78700911-12888.7870091096
112119031116144.0150251182886.98497488248
113122243117265.5518643514977.44813564917
114115819119764.71387622-3945.71387621971
11591531116383.469651919-24852.4696519187
1168094999224.5738644188-18275.5738644188
1179066286399.88370402864262.11629597138
1186394388427.6386288832-24484.6386288832
1199309371511.145236278421581.8547637216
12011096884952.690245760126015.3097542399







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121101315.903195379567.5868791262123064.219511474
122100534.903195374488.7426403198126581.06375028
12399753.903195370024.865257229129482.941133371
12498972.903195365969.434986781131976.371403819
12598191.903195362210.7674314281134173.038959172
12697410.903195358680.3552011696136141.45118943
12796629.903195355332.5840935338137927.222297066
12895848.903195352135.2693717369139562.537018863
12995067.903195349064.696794789141071.109595811
13094286.903195346102.7956888257142471.010701774
13193505.903195343235.4204717083143776.385918892
13292724.903195340451.2516074265144998.554783173

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 101315.9031953 & 79567.5868791262 & 123064.219511474 \tabularnewline
122 & 100534.9031953 & 74488.7426403198 & 126581.06375028 \tabularnewline
123 & 99753.9031953 & 70024.865257229 & 129482.941133371 \tabularnewline
124 & 98972.9031953 & 65969.434986781 & 131976.371403819 \tabularnewline
125 & 98191.9031953 & 62210.7674314281 & 134173.038959172 \tabularnewline
126 & 97410.9031953 & 58680.3552011696 & 136141.45118943 \tabularnewline
127 & 96629.9031953 & 55332.5840935338 & 137927.222297066 \tabularnewline
128 & 95848.9031953 & 52135.2693717369 & 139562.537018863 \tabularnewline
129 & 95067.9031953 & 49064.696794789 & 141071.109595811 \tabularnewline
130 & 94286.9031953 & 46102.7956888257 & 142471.010701774 \tabularnewline
131 & 93505.9031953 & 43235.4204717083 & 143776.385918892 \tabularnewline
132 & 92724.9031953 & 40451.2516074265 & 144998.554783173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307372&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]101315.9031953[/C][C]79567.5868791262[/C][C]123064.219511474[/C][/ROW]
[ROW][C]122[/C][C]100534.9031953[/C][C]74488.7426403198[/C][C]126581.06375028[/C][/ROW]
[ROW][C]123[/C][C]99753.9031953[/C][C]70024.865257229[/C][C]129482.941133371[/C][/ROW]
[ROW][C]124[/C][C]98972.9031953[/C][C]65969.434986781[/C][C]131976.371403819[/C][/ROW]
[ROW][C]125[/C][C]98191.9031953[/C][C]62210.7674314281[/C][C]134173.038959172[/C][/ROW]
[ROW][C]126[/C][C]97410.9031953[/C][C]58680.3552011696[/C][C]136141.45118943[/C][/ROW]
[ROW][C]127[/C][C]96629.9031953[/C][C]55332.5840935338[/C][C]137927.222297066[/C][/ROW]
[ROW][C]128[/C][C]95848.9031953[/C][C]52135.2693717369[/C][C]139562.537018863[/C][/ROW]
[ROW][C]129[/C][C]95067.9031953[/C][C]49064.696794789[/C][C]141071.109595811[/C][/ROW]
[ROW][C]130[/C][C]94286.9031953[/C][C]46102.7956888257[/C][C]142471.010701774[/C][/ROW]
[ROW][C]131[/C][C]93505.9031953[/C][C]43235.4204717083[/C][C]143776.385918892[/C][/ROW]
[ROW][C]132[/C][C]92724.9031953[/C][C]40451.2516074265[/C][C]144998.554783173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307372&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307372&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
121101315.903195379567.5868791262123064.219511474
122100534.903195374488.7426403198126581.06375028
12399753.903195370024.865257229129482.941133371
12498972.903195365969.434986781131976.371403819
12598191.903195362210.7674314281134173.038959172
12697410.903195358680.3552011696136141.45118943
12796629.903195355332.5840935338137927.222297066
12895848.903195352135.2693717369139562.537018863
12995067.903195349064.696794789141071.109595811
13094286.903195346102.7956888257142471.010701774
13193505.903195343235.4204717083143776.385918892
13292724.903195340451.2516074265144998.554783173



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')