Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 15:40:04 +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/Apr/26/t1461681615u94lgw1mssgxmqx.htm/, Retrieved Mon, 13 May 2024 09:06:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294889, Retrieved Mon, 13 May 2024 09:06:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 14:40:04] [f9cf779ce6533af8ecf1f6ee8a638c60] [Current]
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Dataseries X:
93166
93517
94547
95299
95121
95583
96138
96647
97311
97644
100299
101130
102239
103667
104494
105944
106956
109156
109528
109813
110939
112182
113137
114506
115197
116142
117478
118678
119808
121210
122372
123266
124020
124922
125863
126898
127522
128062
129630
130919
131175
133387
134512
135423
136395
137384
138344
139342
139885
140560
141457
144577
145505
146767
147602
148490
149516
150688
151012
151614
151779
152062
152432
153634
153989
155114
155448
155514
156552
157472
158928
154948
155178
155396
156479
157562
158255
159138
160067
161112
162009
162941
163463
165473
165805
166524
167426
168593
169452
170386
171281
171950
172842
173644
174380
175639
176169
176642
177225
178180
178771
180337
180740
181299
181768
182304
182670
183241
183106
183039
183447
184915
185144
185787
186243
186518
187156
186083
186350
187010
187057
187019
187487
188280
188756
189574
189996
190251
190925
191499
192172
191639




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294889&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294889&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294889&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.897256558700387
beta0.0457181124023206
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.897256558700387 \tabularnewline
beta & 0.0457181124023206 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294889&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]0.897256558700387[/C][/ROW]
[ROW][C]beta[/C][C]0.0457181124023206[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294889&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294889&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
alpha0.897256558700387
beta0.0457181124023206
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310223996425.91960470095813.08039529914
14103667103240.732798366426.267201634109
15104494104628.761710963-134.761710962717
16105944106073.709041982-129.709041982365
17106956107112.785801496-156.785801496488
18109156109357.552936661-201.552936661101
19109528108672.676254788855.323745211732
20109813110452.67523693-639.675236930358
21110939110983.619871723-44.6198717232619
22112182111695.026489504486.973510496144
23113137115146.718169465-2009.71816946474
24114506114329.796464293176.203535707275
25115197116291.899587015-1094.89958701454
26116142116253.826079488-111.826079488208
27117478116978.135537851499.864462148806
28118678118895.787727895-217.787727894669
29119808119752.20351874755.7964812527061
30121210122090.982452759-880.98245275885
31122372120785.0700155591586.92998444117
32123266122977.916969882288.083030118039
33124020124350.505103489-330.505103488889
34124922124796.358065624125.641934376225
35125863127588.84279626-1725.84279625973
36126898127184.38293877-286.38293876953
37127522128515.017790542-993.017790541693
38128062128587.730015203-525.730015203007
39129630128904.897208601725.102791398778
40130919130861.53994956357.4600504366535
41131175131914.951541355-739.951541354647
42133387133332.76911389654.2308861035563
43134512133047.1847283021464.81527169814
44135423134919.646130283503.353869717335
45136395136353.29284187441.7071581264026
46137384137126.711565336257.288434663642
47138344139799.219075793-1455.21907579293
48139342139748.704414685-406.704414684878
49139885140857.07347314-972.073473140132
50140560140955.743568838-395.743568838341
51141457141482.54366951-25.5436695099925
52144577142630.7627105351946.23728946503
53145505145308.137227339196.862772660883
54146767147697.717537478-930.7175374777
55147602146682.509479956919.490520043502
56148490147953.720586742536.279413257696
57149516149357.659189021158.340810979425
58150688150250.842601948437.157398052455
59151012152909.133004361-1897.13300436127
60151614152552.051680168-938.051680168457
61151779153085.997129821-1306.99712982099
62152062152890.049206501-828.049206501484
63152432152995.942604909-563.942604908749
64153634153770.528389953-136.528389952757
65153989154220.815268375-231.815268375474
66155114155913.749450056-799.749450055679
67155448155015.362073443432.63792655713
68155514155599.609912319-85.6099123186723
69156552156170.453923374381.546076626168
70157472157065.44277359406.557226409612
71158928159228.075169615-300.07516961504
72154948160239.647716988-5291.64771698773
73155178156487.949458435-1309.94945843465
74155396155996.995804553-600.995804553269
75156479156001.49801545477.501984550472
76157562157464.9102030997.0897969101206
77158255157835.075059706419.924940294353
78159138159801.223489942-663.223489941825
79160067158904.3426450861162.65735491432
80161112159872.6926727431239.30732725686
81162009161517.007881858491.99211814205
82162941162354.87879339586.12120660959
83163463164454.604070641-991.604070640722
84165473164153.0590799691319.94092003102
85165805166834.171274649-1029.17127464927
86166524166770.931596888-246.931596887909
87167426167321.396409687104.603590312559
88168593168513.3091863279.6908136804122
89169452169002.489139405449.510860594513
90170386170986.568228573-600.568228573393
91171281170438.743578099842.256421901169
92171950171219.5849909730.415009100252
93172842172401.734226541440.26577345893
94173644173271.965355528372.034644472471
95174380175077.817991001-697.817991001124
96175639175349.740791245289.259208754607
97176169176894.80193983-725.801939829631
98176642177226.667609946-584.667609945551
99177225177538.895503697-313.895503696753
100178180178364.261398394-184.261398394417
101178771178655.291330658115.708669342072
102180337180218.968865158118.031134842284
103180740180480.623941894259.376058105787
104181299180719.541855993579.458144007396
105181768181722.80144279545.1985572053818
106182304182201.70793591102.292064089706
107182670183614.709169562-944.709169561771
108183241183715.492495456-474.492495455954
109183106184388.621325142-1282.62132514166
110183039184130.176339898-1091.17633989762
111183447183889.777143141-442.777143141488
112184915184481.55648934433.44351065965
113185144185251.719249946-107.719249945832
114185787186500.071117854-713.071117853542
115186243185881.351849901361.648150098714
116186518186099.931033808418.068966192019
117187156186751.881757824404.118242175638
118186083187421.810779672-1338.81077967177
119186350187238.198727827-888.198727826762
120187010187244.314407912-234.314407912083
121187057187866.083290979-809.083290978713
122187019187887.786700414-868.786700413853
123187487187758.263020081-271.263020081446
124188280188445.712312024-165.712312023621
125188756188449.851608494306.148391505587
126189574189851.504163086-277.504163086443
127189996189596.039061267399.960938733042
128190251189718.381642218532.618357781699
129190925190339.968257505585.031742494699
130191499190868.858852492630.141147508111
131192172192454.677671296-282.677671295649
132191639193052.600827647-1413.60082764697

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102239 & 96425.9196047009 & 5813.08039529914 \tabularnewline
14 & 103667 & 103240.732798366 & 426.267201634109 \tabularnewline
15 & 104494 & 104628.761710963 & -134.761710962717 \tabularnewline
16 & 105944 & 106073.709041982 & -129.709041982365 \tabularnewline
17 & 106956 & 107112.785801496 & -156.785801496488 \tabularnewline
18 & 109156 & 109357.552936661 & -201.552936661101 \tabularnewline
19 & 109528 & 108672.676254788 & 855.323745211732 \tabularnewline
20 & 109813 & 110452.67523693 & -639.675236930358 \tabularnewline
21 & 110939 & 110983.619871723 & -44.6198717232619 \tabularnewline
22 & 112182 & 111695.026489504 & 486.973510496144 \tabularnewline
23 & 113137 & 115146.718169465 & -2009.71816946474 \tabularnewline
24 & 114506 & 114329.796464293 & 176.203535707275 \tabularnewline
25 & 115197 & 116291.899587015 & -1094.89958701454 \tabularnewline
26 & 116142 & 116253.826079488 & -111.826079488208 \tabularnewline
27 & 117478 & 116978.135537851 & 499.864462148806 \tabularnewline
28 & 118678 & 118895.787727895 & -217.787727894669 \tabularnewline
29 & 119808 & 119752.203518747 & 55.7964812527061 \tabularnewline
30 & 121210 & 122090.982452759 & -880.98245275885 \tabularnewline
31 & 122372 & 120785.070015559 & 1586.92998444117 \tabularnewline
32 & 123266 & 122977.916969882 & 288.083030118039 \tabularnewline
33 & 124020 & 124350.505103489 & -330.505103488889 \tabularnewline
34 & 124922 & 124796.358065624 & 125.641934376225 \tabularnewline
35 & 125863 & 127588.84279626 & -1725.84279625973 \tabularnewline
36 & 126898 & 127184.38293877 & -286.38293876953 \tabularnewline
37 & 127522 & 128515.017790542 & -993.017790541693 \tabularnewline
38 & 128062 & 128587.730015203 & -525.730015203007 \tabularnewline
39 & 129630 & 128904.897208601 & 725.102791398778 \tabularnewline
40 & 130919 & 130861.539949563 & 57.4600504366535 \tabularnewline
41 & 131175 & 131914.951541355 & -739.951541354647 \tabularnewline
42 & 133387 & 133332.769113896 & 54.2308861035563 \tabularnewline
43 & 134512 & 133047.184728302 & 1464.81527169814 \tabularnewline
44 & 135423 & 134919.646130283 & 503.353869717335 \tabularnewline
45 & 136395 & 136353.292841874 & 41.7071581264026 \tabularnewline
46 & 137384 & 137126.711565336 & 257.288434663642 \tabularnewline
47 & 138344 & 139799.219075793 & -1455.21907579293 \tabularnewline
48 & 139342 & 139748.704414685 & -406.704414684878 \tabularnewline
49 & 139885 & 140857.07347314 & -972.073473140132 \tabularnewline
50 & 140560 & 140955.743568838 & -395.743568838341 \tabularnewline
51 & 141457 & 141482.54366951 & -25.5436695099925 \tabularnewline
52 & 144577 & 142630.762710535 & 1946.23728946503 \tabularnewline
53 & 145505 & 145308.137227339 & 196.862772660883 \tabularnewline
54 & 146767 & 147697.717537478 & -930.7175374777 \tabularnewline
55 & 147602 & 146682.509479956 & 919.490520043502 \tabularnewline
56 & 148490 & 147953.720586742 & 536.279413257696 \tabularnewline
57 & 149516 & 149357.659189021 & 158.340810979425 \tabularnewline
58 & 150688 & 150250.842601948 & 437.157398052455 \tabularnewline
59 & 151012 & 152909.133004361 & -1897.13300436127 \tabularnewline
60 & 151614 & 152552.051680168 & -938.051680168457 \tabularnewline
61 & 151779 & 153085.997129821 & -1306.99712982099 \tabularnewline
62 & 152062 & 152890.049206501 & -828.049206501484 \tabularnewline
63 & 152432 & 152995.942604909 & -563.942604908749 \tabularnewline
64 & 153634 & 153770.528389953 & -136.528389952757 \tabularnewline
65 & 153989 & 154220.815268375 & -231.815268375474 \tabularnewline
66 & 155114 & 155913.749450056 & -799.749450055679 \tabularnewline
67 & 155448 & 155015.362073443 & 432.63792655713 \tabularnewline
68 & 155514 & 155599.609912319 & -85.6099123186723 \tabularnewline
69 & 156552 & 156170.453923374 & 381.546076626168 \tabularnewline
70 & 157472 & 157065.44277359 & 406.557226409612 \tabularnewline
71 & 158928 & 159228.075169615 & -300.07516961504 \tabularnewline
72 & 154948 & 160239.647716988 & -5291.64771698773 \tabularnewline
73 & 155178 & 156487.949458435 & -1309.94945843465 \tabularnewline
74 & 155396 & 155996.995804553 & -600.995804553269 \tabularnewline
75 & 156479 & 156001.49801545 & 477.501984550472 \tabularnewline
76 & 157562 & 157464.91020309 & 97.0897969101206 \tabularnewline
77 & 158255 & 157835.075059706 & 419.924940294353 \tabularnewline
78 & 159138 & 159801.223489942 & -663.223489941825 \tabularnewline
79 & 160067 & 158904.342645086 & 1162.65735491432 \tabularnewline
80 & 161112 & 159872.692672743 & 1239.30732725686 \tabularnewline
81 & 162009 & 161517.007881858 & 491.99211814205 \tabularnewline
82 & 162941 & 162354.87879339 & 586.12120660959 \tabularnewline
83 & 163463 & 164454.604070641 & -991.604070640722 \tabularnewline
84 & 165473 & 164153.059079969 & 1319.94092003102 \tabularnewline
85 & 165805 & 166834.171274649 & -1029.17127464927 \tabularnewline
86 & 166524 & 166770.931596888 & -246.931596887909 \tabularnewline
87 & 167426 & 167321.396409687 & 104.603590312559 \tabularnewline
88 & 168593 & 168513.30918632 & 79.6908136804122 \tabularnewline
89 & 169452 & 169002.489139405 & 449.510860594513 \tabularnewline
90 & 170386 & 170986.568228573 & -600.568228573393 \tabularnewline
91 & 171281 & 170438.743578099 & 842.256421901169 \tabularnewline
92 & 171950 & 171219.5849909 & 730.415009100252 \tabularnewline
93 & 172842 & 172401.734226541 & 440.26577345893 \tabularnewline
94 & 173644 & 173271.965355528 & 372.034644472471 \tabularnewline
95 & 174380 & 175077.817991001 & -697.817991001124 \tabularnewline
96 & 175639 & 175349.740791245 & 289.259208754607 \tabularnewline
97 & 176169 & 176894.80193983 & -725.801939829631 \tabularnewline
98 & 176642 & 177226.667609946 & -584.667609945551 \tabularnewline
99 & 177225 & 177538.895503697 & -313.895503696753 \tabularnewline
100 & 178180 & 178364.261398394 & -184.261398394417 \tabularnewline
101 & 178771 & 178655.291330658 & 115.708669342072 \tabularnewline
102 & 180337 & 180218.968865158 & 118.031134842284 \tabularnewline
103 & 180740 & 180480.623941894 & 259.376058105787 \tabularnewline
104 & 181299 & 180719.541855993 & 579.458144007396 \tabularnewline
105 & 181768 & 181722.801442795 & 45.1985572053818 \tabularnewline
106 & 182304 & 182201.70793591 & 102.292064089706 \tabularnewline
107 & 182670 & 183614.709169562 & -944.709169561771 \tabularnewline
108 & 183241 & 183715.492495456 & -474.492495455954 \tabularnewline
109 & 183106 & 184388.621325142 & -1282.62132514166 \tabularnewline
110 & 183039 & 184130.176339898 & -1091.17633989762 \tabularnewline
111 & 183447 & 183889.777143141 & -442.777143141488 \tabularnewline
112 & 184915 & 184481.55648934 & 433.44351065965 \tabularnewline
113 & 185144 & 185251.719249946 & -107.719249945832 \tabularnewline
114 & 185787 & 186500.071117854 & -713.071117853542 \tabularnewline
115 & 186243 & 185881.351849901 & 361.648150098714 \tabularnewline
116 & 186518 & 186099.931033808 & 418.068966192019 \tabularnewline
117 & 187156 & 186751.881757824 & 404.118242175638 \tabularnewline
118 & 186083 & 187421.810779672 & -1338.81077967177 \tabularnewline
119 & 186350 & 187238.198727827 & -888.198727826762 \tabularnewline
120 & 187010 & 187244.314407912 & -234.314407912083 \tabularnewline
121 & 187057 & 187866.083290979 & -809.083290978713 \tabularnewline
122 & 187019 & 187887.786700414 & -868.786700413853 \tabularnewline
123 & 187487 & 187758.263020081 & -271.263020081446 \tabularnewline
124 & 188280 & 188445.712312024 & -165.712312023621 \tabularnewline
125 & 188756 & 188449.851608494 & 306.148391505587 \tabularnewline
126 & 189574 & 189851.504163086 & -277.504163086443 \tabularnewline
127 & 189996 & 189596.039061267 & 399.960938733042 \tabularnewline
128 & 190251 & 189718.381642218 & 532.618357781699 \tabularnewline
129 & 190925 & 190339.968257505 & 585.031742494699 \tabularnewline
130 & 191499 & 190868.858852492 & 630.141147508111 \tabularnewline
131 & 192172 & 192454.677671296 & -282.677671295649 \tabularnewline
132 & 191639 & 193052.600827647 & -1413.60082764697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294889&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]102239[/C][C]96425.9196047009[/C][C]5813.08039529914[/C][/ROW]
[ROW][C]14[/C][C]103667[/C][C]103240.732798366[/C][C]426.267201634109[/C][/ROW]
[ROW][C]15[/C][C]104494[/C][C]104628.761710963[/C][C]-134.761710962717[/C][/ROW]
[ROW][C]16[/C][C]105944[/C][C]106073.709041982[/C][C]-129.709041982365[/C][/ROW]
[ROW][C]17[/C][C]106956[/C][C]107112.785801496[/C][C]-156.785801496488[/C][/ROW]
[ROW][C]18[/C][C]109156[/C][C]109357.552936661[/C][C]-201.552936661101[/C][/ROW]
[ROW][C]19[/C][C]109528[/C][C]108672.676254788[/C][C]855.323745211732[/C][/ROW]
[ROW][C]20[/C][C]109813[/C][C]110452.67523693[/C][C]-639.675236930358[/C][/ROW]
[ROW][C]21[/C][C]110939[/C][C]110983.619871723[/C][C]-44.6198717232619[/C][/ROW]
[ROW][C]22[/C][C]112182[/C][C]111695.026489504[/C][C]486.973510496144[/C][/ROW]
[ROW][C]23[/C][C]113137[/C][C]115146.718169465[/C][C]-2009.71816946474[/C][/ROW]
[ROW][C]24[/C][C]114506[/C][C]114329.796464293[/C][C]176.203535707275[/C][/ROW]
[ROW][C]25[/C][C]115197[/C][C]116291.899587015[/C][C]-1094.89958701454[/C][/ROW]
[ROW][C]26[/C][C]116142[/C][C]116253.826079488[/C][C]-111.826079488208[/C][/ROW]
[ROW][C]27[/C][C]117478[/C][C]116978.135537851[/C][C]499.864462148806[/C][/ROW]
[ROW][C]28[/C][C]118678[/C][C]118895.787727895[/C][C]-217.787727894669[/C][/ROW]
[ROW][C]29[/C][C]119808[/C][C]119752.203518747[/C][C]55.7964812527061[/C][/ROW]
[ROW][C]30[/C][C]121210[/C][C]122090.982452759[/C][C]-880.98245275885[/C][/ROW]
[ROW][C]31[/C][C]122372[/C][C]120785.070015559[/C][C]1586.92998444117[/C][/ROW]
[ROW][C]32[/C][C]123266[/C][C]122977.916969882[/C][C]288.083030118039[/C][/ROW]
[ROW][C]33[/C][C]124020[/C][C]124350.505103489[/C][C]-330.505103488889[/C][/ROW]
[ROW][C]34[/C][C]124922[/C][C]124796.358065624[/C][C]125.641934376225[/C][/ROW]
[ROW][C]35[/C][C]125863[/C][C]127588.84279626[/C][C]-1725.84279625973[/C][/ROW]
[ROW][C]36[/C][C]126898[/C][C]127184.38293877[/C][C]-286.38293876953[/C][/ROW]
[ROW][C]37[/C][C]127522[/C][C]128515.017790542[/C][C]-993.017790541693[/C][/ROW]
[ROW][C]38[/C][C]128062[/C][C]128587.730015203[/C][C]-525.730015203007[/C][/ROW]
[ROW][C]39[/C][C]129630[/C][C]128904.897208601[/C][C]725.102791398778[/C][/ROW]
[ROW][C]40[/C][C]130919[/C][C]130861.539949563[/C][C]57.4600504366535[/C][/ROW]
[ROW][C]41[/C][C]131175[/C][C]131914.951541355[/C][C]-739.951541354647[/C][/ROW]
[ROW][C]42[/C][C]133387[/C][C]133332.769113896[/C][C]54.2308861035563[/C][/ROW]
[ROW][C]43[/C][C]134512[/C][C]133047.184728302[/C][C]1464.81527169814[/C][/ROW]
[ROW][C]44[/C][C]135423[/C][C]134919.646130283[/C][C]503.353869717335[/C][/ROW]
[ROW][C]45[/C][C]136395[/C][C]136353.292841874[/C][C]41.7071581264026[/C][/ROW]
[ROW][C]46[/C][C]137384[/C][C]137126.711565336[/C][C]257.288434663642[/C][/ROW]
[ROW][C]47[/C][C]138344[/C][C]139799.219075793[/C][C]-1455.21907579293[/C][/ROW]
[ROW][C]48[/C][C]139342[/C][C]139748.704414685[/C][C]-406.704414684878[/C][/ROW]
[ROW][C]49[/C][C]139885[/C][C]140857.07347314[/C][C]-972.073473140132[/C][/ROW]
[ROW][C]50[/C][C]140560[/C][C]140955.743568838[/C][C]-395.743568838341[/C][/ROW]
[ROW][C]51[/C][C]141457[/C][C]141482.54366951[/C][C]-25.5436695099925[/C][/ROW]
[ROW][C]52[/C][C]144577[/C][C]142630.762710535[/C][C]1946.23728946503[/C][/ROW]
[ROW][C]53[/C][C]145505[/C][C]145308.137227339[/C][C]196.862772660883[/C][/ROW]
[ROW][C]54[/C][C]146767[/C][C]147697.717537478[/C][C]-930.7175374777[/C][/ROW]
[ROW][C]55[/C][C]147602[/C][C]146682.509479956[/C][C]919.490520043502[/C][/ROW]
[ROW][C]56[/C][C]148490[/C][C]147953.720586742[/C][C]536.279413257696[/C][/ROW]
[ROW][C]57[/C][C]149516[/C][C]149357.659189021[/C][C]158.340810979425[/C][/ROW]
[ROW][C]58[/C][C]150688[/C][C]150250.842601948[/C][C]437.157398052455[/C][/ROW]
[ROW][C]59[/C][C]151012[/C][C]152909.133004361[/C][C]-1897.13300436127[/C][/ROW]
[ROW][C]60[/C][C]151614[/C][C]152552.051680168[/C][C]-938.051680168457[/C][/ROW]
[ROW][C]61[/C][C]151779[/C][C]153085.997129821[/C][C]-1306.99712982099[/C][/ROW]
[ROW][C]62[/C][C]152062[/C][C]152890.049206501[/C][C]-828.049206501484[/C][/ROW]
[ROW][C]63[/C][C]152432[/C][C]152995.942604909[/C][C]-563.942604908749[/C][/ROW]
[ROW][C]64[/C][C]153634[/C][C]153770.528389953[/C][C]-136.528389952757[/C][/ROW]
[ROW][C]65[/C][C]153989[/C][C]154220.815268375[/C][C]-231.815268375474[/C][/ROW]
[ROW][C]66[/C][C]155114[/C][C]155913.749450056[/C][C]-799.749450055679[/C][/ROW]
[ROW][C]67[/C][C]155448[/C][C]155015.362073443[/C][C]432.63792655713[/C][/ROW]
[ROW][C]68[/C][C]155514[/C][C]155599.609912319[/C][C]-85.6099123186723[/C][/ROW]
[ROW][C]69[/C][C]156552[/C][C]156170.453923374[/C][C]381.546076626168[/C][/ROW]
[ROW][C]70[/C][C]157472[/C][C]157065.44277359[/C][C]406.557226409612[/C][/ROW]
[ROW][C]71[/C][C]158928[/C][C]159228.075169615[/C][C]-300.07516961504[/C][/ROW]
[ROW][C]72[/C][C]154948[/C][C]160239.647716988[/C][C]-5291.64771698773[/C][/ROW]
[ROW][C]73[/C][C]155178[/C][C]156487.949458435[/C][C]-1309.94945843465[/C][/ROW]
[ROW][C]74[/C][C]155396[/C][C]155996.995804553[/C][C]-600.995804553269[/C][/ROW]
[ROW][C]75[/C][C]156479[/C][C]156001.49801545[/C][C]477.501984550472[/C][/ROW]
[ROW][C]76[/C][C]157562[/C][C]157464.91020309[/C][C]97.0897969101206[/C][/ROW]
[ROW][C]77[/C][C]158255[/C][C]157835.075059706[/C][C]419.924940294353[/C][/ROW]
[ROW][C]78[/C][C]159138[/C][C]159801.223489942[/C][C]-663.223489941825[/C][/ROW]
[ROW][C]79[/C][C]160067[/C][C]158904.342645086[/C][C]1162.65735491432[/C][/ROW]
[ROW][C]80[/C][C]161112[/C][C]159872.692672743[/C][C]1239.30732725686[/C][/ROW]
[ROW][C]81[/C][C]162009[/C][C]161517.007881858[/C][C]491.99211814205[/C][/ROW]
[ROW][C]82[/C][C]162941[/C][C]162354.87879339[/C][C]586.12120660959[/C][/ROW]
[ROW][C]83[/C][C]163463[/C][C]164454.604070641[/C][C]-991.604070640722[/C][/ROW]
[ROW][C]84[/C][C]165473[/C][C]164153.059079969[/C][C]1319.94092003102[/C][/ROW]
[ROW][C]85[/C][C]165805[/C][C]166834.171274649[/C][C]-1029.17127464927[/C][/ROW]
[ROW][C]86[/C][C]166524[/C][C]166770.931596888[/C][C]-246.931596887909[/C][/ROW]
[ROW][C]87[/C][C]167426[/C][C]167321.396409687[/C][C]104.603590312559[/C][/ROW]
[ROW][C]88[/C][C]168593[/C][C]168513.30918632[/C][C]79.6908136804122[/C][/ROW]
[ROW][C]89[/C][C]169452[/C][C]169002.489139405[/C][C]449.510860594513[/C][/ROW]
[ROW][C]90[/C][C]170386[/C][C]170986.568228573[/C][C]-600.568228573393[/C][/ROW]
[ROW][C]91[/C][C]171281[/C][C]170438.743578099[/C][C]842.256421901169[/C][/ROW]
[ROW][C]92[/C][C]171950[/C][C]171219.5849909[/C][C]730.415009100252[/C][/ROW]
[ROW][C]93[/C][C]172842[/C][C]172401.734226541[/C][C]440.26577345893[/C][/ROW]
[ROW][C]94[/C][C]173644[/C][C]173271.965355528[/C][C]372.034644472471[/C][/ROW]
[ROW][C]95[/C][C]174380[/C][C]175077.817991001[/C][C]-697.817991001124[/C][/ROW]
[ROW][C]96[/C][C]175639[/C][C]175349.740791245[/C][C]289.259208754607[/C][/ROW]
[ROW][C]97[/C][C]176169[/C][C]176894.80193983[/C][C]-725.801939829631[/C][/ROW]
[ROW][C]98[/C][C]176642[/C][C]177226.667609946[/C][C]-584.667609945551[/C][/ROW]
[ROW][C]99[/C][C]177225[/C][C]177538.895503697[/C][C]-313.895503696753[/C][/ROW]
[ROW][C]100[/C][C]178180[/C][C]178364.261398394[/C][C]-184.261398394417[/C][/ROW]
[ROW][C]101[/C][C]178771[/C][C]178655.291330658[/C][C]115.708669342072[/C][/ROW]
[ROW][C]102[/C][C]180337[/C][C]180218.968865158[/C][C]118.031134842284[/C][/ROW]
[ROW][C]103[/C][C]180740[/C][C]180480.623941894[/C][C]259.376058105787[/C][/ROW]
[ROW][C]104[/C][C]181299[/C][C]180719.541855993[/C][C]579.458144007396[/C][/ROW]
[ROW][C]105[/C][C]181768[/C][C]181722.801442795[/C][C]45.1985572053818[/C][/ROW]
[ROW][C]106[/C][C]182304[/C][C]182201.70793591[/C][C]102.292064089706[/C][/ROW]
[ROW][C]107[/C][C]182670[/C][C]183614.709169562[/C][C]-944.709169561771[/C][/ROW]
[ROW][C]108[/C][C]183241[/C][C]183715.492495456[/C][C]-474.492495455954[/C][/ROW]
[ROW][C]109[/C][C]183106[/C][C]184388.621325142[/C][C]-1282.62132514166[/C][/ROW]
[ROW][C]110[/C][C]183039[/C][C]184130.176339898[/C][C]-1091.17633989762[/C][/ROW]
[ROW][C]111[/C][C]183447[/C][C]183889.777143141[/C][C]-442.777143141488[/C][/ROW]
[ROW][C]112[/C][C]184915[/C][C]184481.55648934[/C][C]433.44351065965[/C][/ROW]
[ROW][C]113[/C][C]185144[/C][C]185251.719249946[/C][C]-107.719249945832[/C][/ROW]
[ROW][C]114[/C][C]185787[/C][C]186500.071117854[/C][C]-713.071117853542[/C][/ROW]
[ROW][C]115[/C][C]186243[/C][C]185881.351849901[/C][C]361.648150098714[/C][/ROW]
[ROW][C]116[/C][C]186518[/C][C]186099.931033808[/C][C]418.068966192019[/C][/ROW]
[ROW][C]117[/C][C]187156[/C][C]186751.881757824[/C][C]404.118242175638[/C][/ROW]
[ROW][C]118[/C][C]186083[/C][C]187421.810779672[/C][C]-1338.81077967177[/C][/ROW]
[ROW][C]119[/C][C]186350[/C][C]187238.198727827[/C][C]-888.198727826762[/C][/ROW]
[ROW][C]120[/C][C]187010[/C][C]187244.314407912[/C][C]-234.314407912083[/C][/ROW]
[ROW][C]121[/C][C]187057[/C][C]187866.083290979[/C][C]-809.083290978713[/C][/ROW]
[ROW][C]122[/C][C]187019[/C][C]187887.786700414[/C][C]-868.786700413853[/C][/ROW]
[ROW][C]123[/C][C]187487[/C][C]187758.263020081[/C][C]-271.263020081446[/C][/ROW]
[ROW][C]124[/C][C]188280[/C][C]188445.712312024[/C][C]-165.712312023621[/C][/ROW]
[ROW][C]125[/C][C]188756[/C][C]188449.851608494[/C][C]306.148391505587[/C][/ROW]
[ROW][C]126[/C][C]189574[/C][C]189851.504163086[/C][C]-277.504163086443[/C][/ROW]
[ROW][C]127[/C][C]189996[/C][C]189596.039061267[/C][C]399.960938733042[/C][/ROW]
[ROW][C]128[/C][C]190251[/C][C]189718.381642218[/C][C]532.618357781699[/C][/ROW]
[ROW][C]129[/C][C]190925[/C][C]190339.968257505[/C][C]585.031742494699[/C][/ROW]
[ROW][C]130[/C][C]191499[/C][C]190868.858852492[/C][C]630.141147508111[/C][/ROW]
[ROW][C]131[/C][C]192172[/C][C]192454.677671296[/C][C]-282.677671295649[/C][/ROW]
[ROW][C]132[/C][C]191639[/C][C]193052.600827647[/C][C]-1413.60082764697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294889&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294889&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
1310223996425.91960470095813.08039529914
14103667103240.732798366426.267201634109
15104494104628.761710963-134.761710962717
16105944106073.709041982-129.709041982365
17106956107112.785801496-156.785801496488
18109156109357.552936661-201.552936661101
19109528108672.676254788855.323745211732
20109813110452.67523693-639.675236930358
21110939110983.619871723-44.6198717232619
22112182111695.026489504486.973510496144
23113137115146.718169465-2009.71816946474
24114506114329.796464293176.203535707275
25115197116291.899587015-1094.89958701454
26116142116253.826079488-111.826079488208
27117478116978.135537851499.864462148806
28118678118895.787727895-217.787727894669
29119808119752.20351874755.7964812527061
30121210122090.982452759-880.98245275885
31122372120785.0700155591586.92998444117
32123266122977.916969882288.083030118039
33124020124350.505103489-330.505103488889
34124922124796.358065624125.641934376225
35125863127588.84279626-1725.84279625973
36126898127184.38293877-286.38293876953
37127522128515.017790542-993.017790541693
38128062128587.730015203-525.730015203007
39129630128904.897208601725.102791398778
40130919130861.53994956357.4600504366535
41131175131914.951541355-739.951541354647
42133387133332.76911389654.2308861035563
43134512133047.1847283021464.81527169814
44135423134919.646130283503.353869717335
45136395136353.29284187441.7071581264026
46137384137126.711565336257.288434663642
47138344139799.219075793-1455.21907579293
48139342139748.704414685-406.704414684878
49139885140857.07347314-972.073473140132
50140560140955.743568838-395.743568838341
51141457141482.54366951-25.5436695099925
52144577142630.7627105351946.23728946503
53145505145308.137227339196.862772660883
54146767147697.717537478-930.7175374777
55147602146682.509479956919.490520043502
56148490147953.720586742536.279413257696
57149516149357.659189021158.340810979425
58150688150250.842601948437.157398052455
59151012152909.133004361-1897.13300436127
60151614152552.051680168-938.051680168457
61151779153085.997129821-1306.99712982099
62152062152890.049206501-828.049206501484
63152432152995.942604909-563.942604908749
64153634153770.528389953-136.528389952757
65153989154220.815268375-231.815268375474
66155114155913.749450056-799.749450055679
67155448155015.362073443432.63792655713
68155514155599.609912319-85.6099123186723
69156552156170.453923374381.546076626168
70157472157065.44277359406.557226409612
71158928159228.075169615-300.07516961504
72154948160239.647716988-5291.64771698773
73155178156487.949458435-1309.94945843465
74155396155996.995804553-600.995804553269
75156479156001.49801545477.501984550472
76157562157464.9102030997.0897969101206
77158255157835.075059706419.924940294353
78159138159801.223489942-663.223489941825
79160067158904.3426450861162.65735491432
80161112159872.6926727431239.30732725686
81162009161517.007881858491.99211814205
82162941162354.87879339586.12120660959
83163463164454.604070641-991.604070640722
84165473164153.0590799691319.94092003102
85165805166834.171274649-1029.17127464927
86166524166770.931596888-246.931596887909
87167426167321.396409687104.603590312559
88168593168513.3091863279.6908136804122
89169452169002.489139405449.510860594513
90170386170986.568228573-600.568228573393
91171281170438.743578099842.256421901169
92171950171219.5849909730.415009100252
93172842172401.734226541440.26577345893
94173644173271.965355528372.034644472471
95174380175077.817991001-697.817991001124
96175639175349.740791245289.259208754607
97176169176894.80193983-725.801939829631
98176642177226.667609946-584.667609945551
99177225177538.895503697-313.895503696753
100178180178364.261398394-184.261398394417
101178771178655.291330658115.708669342072
102180337180218.968865158118.031134842284
103180740180480.623941894259.376058105787
104181299180719.541855993579.458144007396
105181768181722.80144279545.1985572053818
106182304182201.70793591102.292064089706
107182670183614.709169562-944.709169561771
108183241183715.492495456-474.492495455954
109183106184388.621325142-1282.62132514166
110183039184130.176339898-1091.17633989762
111183447183889.777143141-442.777143141488
112184915184481.55648934433.44351065965
113185144185251.719249946-107.719249945832
114185787186500.071117854-713.071117853542
115186243185881.351849901361.648150098714
116186518186099.931033808418.068966192019
117187156186751.881757824404.118242175638
118186083187421.810779672-1338.81077967177
119186350187238.198727827-888.198727826762
120187010187244.314407912-234.314407912083
121187057187866.083290979-809.083290978713
122187019187887.786700414-868.786700413853
123187487187758.263020081-271.263020081446
124188280188445.712312024-165.712312023621
125188756188449.851608494306.148391505587
126189574189851.504163086-277.504163086443
127189996189596.039061267399.960938733042
128190251189718.381642218532.618357781699
129190925190339.968257505585.031742494699
130191499190868.858852492630.141147508111
131192172192454.677671296-282.677671295649
132191639193052.600827647-1413.60082764697







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133192490.135552411190487.604009033194492.667095789
134193197.791472376190451.792359527195943.790585225
135193910.95374287190536.590209128197285.317276612
136194865.537395049190920.783566078198810.291224019
137195086.53860043190605.660621007199567.416579853
138196160.667413154191165.531865197201155.802961111
139196242.319683899190747.420813323201737.218554475
140196021.537467188190036.609177612202006.465756765
141196150.878525562189682.398484491202619.358566633
142196115.746359743189167.868149264203063.624570222
143196972.797923998189547.961549515204397.634298481
144197650.173393435189749.52275434205550.82403253

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 192490.135552411 & 190487.604009033 & 194492.667095789 \tabularnewline
134 & 193197.791472376 & 190451.792359527 & 195943.790585225 \tabularnewline
135 & 193910.95374287 & 190536.590209128 & 197285.317276612 \tabularnewline
136 & 194865.537395049 & 190920.783566078 & 198810.291224019 \tabularnewline
137 & 195086.53860043 & 190605.660621007 & 199567.416579853 \tabularnewline
138 & 196160.667413154 & 191165.531865197 & 201155.802961111 \tabularnewline
139 & 196242.319683899 & 190747.420813323 & 201737.218554475 \tabularnewline
140 & 196021.537467188 & 190036.609177612 & 202006.465756765 \tabularnewline
141 & 196150.878525562 & 189682.398484491 & 202619.358566633 \tabularnewline
142 & 196115.746359743 & 189167.868149264 & 203063.624570222 \tabularnewline
143 & 196972.797923998 & 189547.961549515 & 204397.634298481 \tabularnewline
144 & 197650.173393435 & 189749.52275434 & 205550.82403253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294889&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]133[/C][C]192490.135552411[/C][C]190487.604009033[/C][C]194492.667095789[/C][/ROW]
[ROW][C]134[/C][C]193197.791472376[/C][C]190451.792359527[/C][C]195943.790585225[/C][/ROW]
[ROW][C]135[/C][C]193910.95374287[/C][C]190536.590209128[/C][C]197285.317276612[/C][/ROW]
[ROW][C]136[/C][C]194865.537395049[/C][C]190920.783566078[/C][C]198810.291224019[/C][/ROW]
[ROW][C]137[/C][C]195086.53860043[/C][C]190605.660621007[/C][C]199567.416579853[/C][/ROW]
[ROW][C]138[/C][C]196160.667413154[/C][C]191165.531865197[/C][C]201155.802961111[/C][/ROW]
[ROW][C]139[/C][C]196242.319683899[/C][C]190747.420813323[/C][C]201737.218554475[/C][/ROW]
[ROW][C]140[/C][C]196021.537467188[/C][C]190036.609177612[/C][C]202006.465756765[/C][/ROW]
[ROW][C]141[/C][C]196150.878525562[/C][C]189682.398484491[/C][C]202619.358566633[/C][/ROW]
[ROW][C]142[/C][C]196115.746359743[/C][C]189167.868149264[/C][C]203063.624570222[/C][/ROW]
[ROW][C]143[/C][C]196972.797923998[/C][C]189547.961549515[/C][C]204397.634298481[/C][/ROW]
[ROW][C]144[/C][C]197650.173393435[/C][C]189749.52275434[/C][C]205550.82403253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294889&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294889&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
133192490.135552411190487.604009033194492.667095789
134193197.791472376190451.792359527195943.790585225
135193910.95374287190536.590209128197285.317276612
136194865.537395049190920.783566078198810.291224019
137195086.53860043190605.660621007199567.416579853
138196160.667413154191165.531865197201155.802961111
139196242.319683899190747.420813323201737.218554475
140196021.537467188190036.609177612202006.465756765
141196150.878525562189682.398484491202619.358566633
142196115.746359743189167.868149264203063.624570222
143196972.797923998189547.961549515204397.634298481
144197650.173393435189749.52275434205550.82403253



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