Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 02 Jul 2010 15:49:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jul/02/t1278085924ww7qcejslkw1ujw.htm/, Retrieved Sat, 04 May 2024 04:04:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77922, Retrieved Sat, 04 May 2024 04:04:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsthomas talboom
Estimated Impact188
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [forcast] [2010-07-02 15:49:39] [58d9ccda37eeb031a0ffa1e9ea016ece] [Current]
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Dataseries X:
68
67
66
64
84
83
68
58
59
59
60
62
58
58
59
62
87
83
68
58
68
63
65
68
62
69
74
72
94
102
92
81
99
95
92
93
85
92
99
107
125
137
125
115
135
128
120
123
119
128
139
155
164
176
162
155
174
171
162
160
156
163
180
195
203
212
203
184
200
198
195
177
176
180
194
204
206
219
213
196
214
209
213
194
197
211
240
251
254
273
271
245
264
264
262
237
237
251
272
282
278
291
293
271
284
290
288
262
263
275
297
301
296
309
310
292
300
314
310
288




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77922&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77922&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.370054769208693
beta0.326909085417736
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.370054769208693 \tabularnewline
beta & 0.326909085417736 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77922&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]0.370054769208693[/C][/ROW]
[ROW][C]beta[/C][C]0.326909085417736[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77922&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
alpha0.370054769208693
beta0.326909085417736
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135858.8875534188034-0.887553418803435
145858.4961736516680-0.496173651668045
155958.81460159053620.185398409463829
166261.24101029105030.758989708949656
178786.1381640772430.861835922756953
188382.09430323031970.905696769680318
196867.71790596772090.282094032279119
205858.8532009899306-0.8532009899306
216860.34015931107197.65984068892813
226364.6123862454992-1.61238624549921
236565.8416574721796-0.841657472179648
246868.170988328808-0.170988328807979
256264.2937082696555-2.29370826965550
266964.15908375898234.84091624101774
277468.05809261639455.94190738360550
287274.8486577497965-2.84865774979653
299499.911741095756-5.91174109575591
3010294.00565641640477.99434358359525
319283.33389570709028.6661042929098
328179.34509407818031.65490592181966
339989.91488977353739.0851102264627
349591.8379207426713.16207925732904
359298.8614814556668-6.86148145566678
3693102.199347618506-9.19934761850621
378595.365398756152-10.3653987561520
389297.4832784492366-5.48327844923662
399997.75142114626461.24857885373540
4010796.195938320812510.8040616791875
41125124.9616438016280.0383561983715737
42137131.3172443224755.68275567752482
43125121.2333508850603.76664911494028
44115111.4422124762163.55778752378355
45135128.0544010057136.94559899428674
46128125.8532853841022.14671461589765
47120126.462753165306-6.46275316530604
48123128.799620719379-5.79962071937931
49119123.224665849066-4.22466584906618
50128132.168749293474-4.16874929347395
51139138.8013932253190.198606774681167
52155144.38712650561810.6128734943816
53164167.787480660072-3.78748066007182
54176177.307350328411-1.30735032841122
55162163.608445481613-1.60844548161310
56155151.2251610409593.77483895904066
57174169.6065685278354.39343147216474
58171162.6839925823968.3160074176036
59162160.1452848553241.85471514467565
60160166.976349408252-6.97634940825168
61156162.814262955529-6.81426295552896
62163171.378190569990-8.3781905699905
63180179.2379843008150.762015699185383
64195191.694463866853.30553613315016
65203202.5371052583700.462894741629583
66212214.924215633429-2.92421563342899
67203199.9737322640403.02626773595952
68184192.793824593662-8.79382459366195
69200205.490437424686-5.49043742468552
70198194.7622227093553.23777729064463
71195183.04062233397611.9593776660238
72177186.036873460918-9.03687346091812
73176178.954110472808-2.95411047280848
74180186.168020924693-6.16802092469288
75194199.077605215509-5.0776052155093
76204208.743017317973-4.74301731797345
77206211.610510424352-5.61051042435156
78219215.675674184563.32432581544012
79213203.6011246737889.39887532621213
80196188.9194942460697.08050575393102
81214209.0778913894424.9221086105577
82209208.4672960094130.532703990587322
83213201.67766644436111.322333555639
84194191.5734876791172.42651232088303
85197194.3131870688302.68681293117049
86211204.0209414005786.97905859942239
87240226.50400647640513.4959935235950
88251249.5218060316911.47819396830926
89254261.165987977382-7.16598797738231
90273277.116797650029-4.11679765002856
91271272.047874277667-1.04787427766666
92245256.708756485545-11.7087564855445
93264270.950236334135-6.9502363341345
94264264.140701155495-0.140701155495435
95262264.77684837389-2.77684837389018
96237243.023779628400-6.02377962839955
97237240.950575137248-3.95057513724763
98251248.2532507246672.74674927533331
99272270.1106797879571.88932021204255
100282276.6939483915645.30605160843623
101278280.203487767387-2.2034877673874
102291296.406053680970-5.40605368097027
103293289.1318582720173.8681417279829
104271265.8294448384155.17055516158536
105284288.290044970731-4.29004497073146
106290286.0516186335823.94838136641818
107288286.3320538611141.66794613888607
108262264.50785130725-2.50785130724972
109263265.796512632208-2.79651263220774
110275278.639588482012-3.63958848201156
111297297.715393283297-0.715393283297374
112301305.293829411977-4.29382941197736
113296299.165650483880-3.16565048388048
114309311.523687410122-2.52368741012225
115310310.036017736218-0.0360177362176728
116292284.5146549606327.48534503936833
117300300.557578556411-0.557578556411499
118314304.0270433457819.97295665421882
119310304.9660874183315.03391258166931
120288282.0298837570165.97011624298364

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 58 & 58.8875534188034 & -0.887553418803435 \tabularnewline
14 & 58 & 58.4961736516680 & -0.496173651668045 \tabularnewline
15 & 59 & 58.8146015905362 & 0.185398409463829 \tabularnewline
16 & 62 & 61.2410102910503 & 0.758989708949656 \tabularnewline
17 & 87 & 86.138164077243 & 0.861835922756953 \tabularnewline
18 & 83 & 82.0943032303197 & 0.905696769680318 \tabularnewline
19 & 68 & 67.7179059677209 & 0.282094032279119 \tabularnewline
20 & 58 & 58.8532009899306 & -0.8532009899306 \tabularnewline
21 & 68 & 60.3401593110719 & 7.65984068892813 \tabularnewline
22 & 63 & 64.6123862454992 & -1.61238624549921 \tabularnewline
23 & 65 & 65.8416574721796 & -0.841657472179648 \tabularnewline
24 & 68 & 68.170988328808 & -0.170988328807979 \tabularnewline
25 & 62 & 64.2937082696555 & -2.29370826965550 \tabularnewline
26 & 69 & 64.1590837589823 & 4.84091624101774 \tabularnewline
27 & 74 & 68.0580926163945 & 5.94190738360550 \tabularnewline
28 & 72 & 74.8486577497965 & -2.84865774979653 \tabularnewline
29 & 94 & 99.911741095756 & -5.91174109575591 \tabularnewline
30 & 102 & 94.0056564164047 & 7.99434358359525 \tabularnewline
31 & 92 & 83.3338957070902 & 8.6661042929098 \tabularnewline
32 & 81 & 79.3450940781803 & 1.65490592181966 \tabularnewline
33 & 99 & 89.9148897735373 & 9.0851102264627 \tabularnewline
34 & 95 & 91.837920742671 & 3.16207925732904 \tabularnewline
35 & 92 & 98.8614814556668 & -6.86148145566678 \tabularnewline
36 & 93 & 102.199347618506 & -9.19934761850621 \tabularnewline
37 & 85 & 95.365398756152 & -10.3653987561520 \tabularnewline
38 & 92 & 97.4832784492366 & -5.48327844923662 \tabularnewline
39 & 99 & 97.7514211462646 & 1.24857885373540 \tabularnewline
40 & 107 & 96.1959383208125 & 10.8040616791875 \tabularnewline
41 & 125 & 124.961643801628 & 0.0383561983715737 \tabularnewline
42 & 137 & 131.317244322475 & 5.68275567752482 \tabularnewline
43 & 125 & 121.233350885060 & 3.76664911494028 \tabularnewline
44 & 115 & 111.442212476216 & 3.55778752378355 \tabularnewline
45 & 135 & 128.054401005713 & 6.94559899428674 \tabularnewline
46 & 128 & 125.853285384102 & 2.14671461589765 \tabularnewline
47 & 120 & 126.462753165306 & -6.46275316530604 \tabularnewline
48 & 123 & 128.799620719379 & -5.79962071937931 \tabularnewline
49 & 119 & 123.224665849066 & -4.22466584906618 \tabularnewline
50 & 128 & 132.168749293474 & -4.16874929347395 \tabularnewline
51 & 139 & 138.801393225319 & 0.198606774681167 \tabularnewline
52 & 155 & 144.387126505618 & 10.6128734943816 \tabularnewline
53 & 164 & 167.787480660072 & -3.78748066007182 \tabularnewline
54 & 176 & 177.307350328411 & -1.30735032841122 \tabularnewline
55 & 162 & 163.608445481613 & -1.60844548161310 \tabularnewline
56 & 155 & 151.225161040959 & 3.77483895904066 \tabularnewline
57 & 174 & 169.606568527835 & 4.39343147216474 \tabularnewline
58 & 171 & 162.683992582396 & 8.3160074176036 \tabularnewline
59 & 162 & 160.145284855324 & 1.85471514467565 \tabularnewline
60 & 160 & 166.976349408252 & -6.97634940825168 \tabularnewline
61 & 156 & 162.814262955529 & -6.81426295552896 \tabularnewline
62 & 163 & 171.378190569990 & -8.3781905699905 \tabularnewline
63 & 180 & 179.237984300815 & 0.762015699185383 \tabularnewline
64 & 195 & 191.69446386685 & 3.30553613315016 \tabularnewline
65 & 203 & 202.537105258370 & 0.462894741629583 \tabularnewline
66 & 212 & 214.924215633429 & -2.92421563342899 \tabularnewline
67 & 203 & 199.973732264040 & 3.02626773595952 \tabularnewline
68 & 184 & 192.793824593662 & -8.79382459366195 \tabularnewline
69 & 200 & 205.490437424686 & -5.49043742468552 \tabularnewline
70 & 198 & 194.762222709355 & 3.23777729064463 \tabularnewline
71 & 195 & 183.040622333976 & 11.9593776660238 \tabularnewline
72 & 177 & 186.036873460918 & -9.03687346091812 \tabularnewline
73 & 176 & 178.954110472808 & -2.95411047280848 \tabularnewline
74 & 180 & 186.168020924693 & -6.16802092469288 \tabularnewline
75 & 194 & 199.077605215509 & -5.0776052155093 \tabularnewline
76 & 204 & 208.743017317973 & -4.74301731797345 \tabularnewline
77 & 206 & 211.610510424352 & -5.61051042435156 \tabularnewline
78 & 219 & 215.67567418456 & 3.32432581544012 \tabularnewline
79 & 213 & 203.601124673788 & 9.39887532621213 \tabularnewline
80 & 196 & 188.919494246069 & 7.08050575393102 \tabularnewline
81 & 214 & 209.077891389442 & 4.9221086105577 \tabularnewline
82 & 209 & 208.467296009413 & 0.532703990587322 \tabularnewline
83 & 213 & 201.677666444361 & 11.322333555639 \tabularnewline
84 & 194 & 191.573487679117 & 2.42651232088303 \tabularnewline
85 & 197 & 194.313187068830 & 2.68681293117049 \tabularnewline
86 & 211 & 204.020941400578 & 6.97905859942239 \tabularnewline
87 & 240 & 226.504006476405 & 13.4959935235950 \tabularnewline
88 & 251 & 249.521806031691 & 1.47819396830926 \tabularnewline
89 & 254 & 261.165987977382 & -7.16598797738231 \tabularnewline
90 & 273 & 277.116797650029 & -4.11679765002856 \tabularnewline
91 & 271 & 272.047874277667 & -1.04787427766666 \tabularnewline
92 & 245 & 256.708756485545 & -11.7087564855445 \tabularnewline
93 & 264 & 270.950236334135 & -6.9502363341345 \tabularnewline
94 & 264 & 264.140701155495 & -0.140701155495435 \tabularnewline
95 & 262 & 264.77684837389 & -2.77684837389018 \tabularnewline
96 & 237 & 243.023779628400 & -6.02377962839955 \tabularnewline
97 & 237 & 240.950575137248 & -3.95057513724763 \tabularnewline
98 & 251 & 248.253250724667 & 2.74674927533331 \tabularnewline
99 & 272 & 270.110679787957 & 1.88932021204255 \tabularnewline
100 & 282 & 276.693948391564 & 5.30605160843623 \tabularnewline
101 & 278 & 280.203487767387 & -2.2034877673874 \tabularnewline
102 & 291 & 296.406053680970 & -5.40605368097027 \tabularnewline
103 & 293 & 289.131858272017 & 3.8681417279829 \tabularnewline
104 & 271 & 265.829444838415 & 5.17055516158536 \tabularnewline
105 & 284 & 288.290044970731 & -4.29004497073146 \tabularnewline
106 & 290 & 286.051618633582 & 3.94838136641818 \tabularnewline
107 & 288 & 286.332053861114 & 1.66794613888607 \tabularnewline
108 & 262 & 264.50785130725 & -2.50785130724972 \tabularnewline
109 & 263 & 265.796512632208 & -2.79651263220774 \tabularnewline
110 & 275 & 278.639588482012 & -3.63958848201156 \tabularnewline
111 & 297 & 297.715393283297 & -0.715393283297374 \tabularnewline
112 & 301 & 305.293829411977 & -4.29382941197736 \tabularnewline
113 & 296 & 299.165650483880 & -3.16565048388048 \tabularnewline
114 & 309 & 311.523687410122 & -2.52368741012225 \tabularnewline
115 & 310 & 310.036017736218 & -0.0360177362176728 \tabularnewline
116 & 292 & 284.514654960632 & 7.48534503936833 \tabularnewline
117 & 300 & 300.557578556411 & -0.557578556411499 \tabularnewline
118 & 314 & 304.027043345781 & 9.97295665421882 \tabularnewline
119 & 310 & 304.966087418331 & 5.03391258166931 \tabularnewline
120 & 288 & 282.029883757016 & 5.97011624298364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77922&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]58[/C][C]58.8875534188034[/C][C]-0.887553418803435[/C][/ROW]
[ROW][C]14[/C][C]58[/C][C]58.4961736516680[/C][C]-0.496173651668045[/C][/ROW]
[ROW][C]15[/C][C]59[/C][C]58.8146015905362[/C][C]0.185398409463829[/C][/ROW]
[ROW][C]16[/C][C]62[/C][C]61.2410102910503[/C][C]0.758989708949656[/C][/ROW]
[ROW][C]17[/C][C]87[/C][C]86.138164077243[/C][C]0.861835922756953[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]82.0943032303197[/C][C]0.905696769680318[/C][/ROW]
[ROW][C]19[/C][C]68[/C][C]67.7179059677209[/C][C]0.282094032279119[/C][/ROW]
[ROW][C]20[/C][C]58[/C][C]58.8532009899306[/C][C]-0.8532009899306[/C][/ROW]
[ROW][C]21[/C][C]68[/C][C]60.3401593110719[/C][C]7.65984068892813[/C][/ROW]
[ROW][C]22[/C][C]63[/C][C]64.6123862454992[/C][C]-1.61238624549921[/C][/ROW]
[ROW][C]23[/C][C]65[/C][C]65.8416574721796[/C][C]-0.841657472179648[/C][/ROW]
[ROW][C]24[/C][C]68[/C][C]68.170988328808[/C][C]-0.170988328807979[/C][/ROW]
[ROW][C]25[/C][C]62[/C][C]64.2937082696555[/C][C]-2.29370826965550[/C][/ROW]
[ROW][C]26[/C][C]69[/C][C]64.1590837589823[/C][C]4.84091624101774[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]68.0580926163945[/C][C]5.94190738360550[/C][/ROW]
[ROW][C]28[/C][C]72[/C][C]74.8486577497965[/C][C]-2.84865774979653[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]99.911741095756[/C][C]-5.91174109575591[/C][/ROW]
[ROW][C]30[/C][C]102[/C][C]94.0056564164047[/C][C]7.99434358359525[/C][/ROW]
[ROW][C]31[/C][C]92[/C][C]83.3338957070902[/C][C]8.6661042929098[/C][/ROW]
[ROW][C]32[/C][C]81[/C][C]79.3450940781803[/C][C]1.65490592181966[/C][/ROW]
[ROW][C]33[/C][C]99[/C][C]89.9148897735373[/C][C]9.0851102264627[/C][/ROW]
[ROW][C]34[/C][C]95[/C][C]91.837920742671[/C][C]3.16207925732904[/C][/ROW]
[ROW][C]35[/C][C]92[/C][C]98.8614814556668[/C][C]-6.86148145566678[/C][/ROW]
[ROW][C]36[/C][C]93[/C][C]102.199347618506[/C][C]-9.19934761850621[/C][/ROW]
[ROW][C]37[/C][C]85[/C][C]95.365398756152[/C][C]-10.3653987561520[/C][/ROW]
[ROW][C]38[/C][C]92[/C][C]97.4832784492366[/C][C]-5.48327844923662[/C][/ROW]
[ROW][C]39[/C][C]99[/C][C]97.7514211462646[/C][C]1.24857885373540[/C][/ROW]
[ROW][C]40[/C][C]107[/C][C]96.1959383208125[/C][C]10.8040616791875[/C][/ROW]
[ROW][C]41[/C][C]125[/C][C]124.961643801628[/C][C]0.0383561983715737[/C][/ROW]
[ROW][C]42[/C][C]137[/C][C]131.317244322475[/C][C]5.68275567752482[/C][/ROW]
[ROW][C]43[/C][C]125[/C][C]121.233350885060[/C][C]3.76664911494028[/C][/ROW]
[ROW][C]44[/C][C]115[/C][C]111.442212476216[/C][C]3.55778752378355[/C][/ROW]
[ROW][C]45[/C][C]135[/C][C]128.054401005713[/C][C]6.94559899428674[/C][/ROW]
[ROW][C]46[/C][C]128[/C][C]125.853285384102[/C][C]2.14671461589765[/C][/ROW]
[ROW][C]47[/C][C]120[/C][C]126.462753165306[/C][C]-6.46275316530604[/C][/ROW]
[ROW][C]48[/C][C]123[/C][C]128.799620719379[/C][C]-5.79962071937931[/C][/ROW]
[ROW][C]49[/C][C]119[/C][C]123.224665849066[/C][C]-4.22466584906618[/C][/ROW]
[ROW][C]50[/C][C]128[/C][C]132.168749293474[/C][C]-4.16874929347395[/C][/ROW]
[ROW][C]51[/C][C]139[/C][C]138.801393225319[/C][C]0.198606774681167[/C][/ROW]
[ROW][C]52[/C][C]155[/C][C]144.387126505618[/C][C]10.6128734943816[/C][/ROW]
[ROW][C]53[/C][C]164[/C][C]167.787480660072[/C][C]-3.78748066007182[/C][/ROW]
[ROW][C]54[/C][C]176[/C][C]177.307350328411[/C][C]-1.30735032841122[/C][/ROW]
[ROW][C]55[/C][C]162[/C][C]163.608445481613[/C][C]-1.60844548161310[/C][/ROW]
[ROW][C]56[/C][C]155[/C][C]151.225161040959[/C][C]3.77483895904066[/C][/ROW]
[ROW][C]57[/C][C]174[/C][C]169.606568527835[/C][C]4.39343147216474[/C][/ROW]
[ROW][C]58[/C][C]171[/C][C]162.683992582396[/C][C]8.3160074176036[/C][/ROW]
[ROW][C]59[/C][C]162[/C][C]160.145284855324[/C][C]1.85471514467565[/C][/ROW]
[ROW][C]60[/C][C]160[/C][C]166.976349408252[/C][C]-6.97634940825168[/C][/ROW]
[ROW][C]61[/C][C]156[/C][C]162.814262955529[/C][C]-6.81426295552896[/C][/ROW]
[ROW][C]62[/C][C]163[/C][C]171.378190569990[/C][C]-8.3781905699905[/C][/ROW]
[ROW][C]63[/C][C]180[/C][C]179.237984300815[/C][C]0.762015699185383[/C][/ROW]
[ROW][C]64[/C][C]195[/C][C]191.69446386685[/C][C]3.30553613315016[/C][/ROW]
[ROW][C]65[/C][C]203[/C][C]202.537105258370[/C][C]0.462894741629583[/C][/ROW]
[ROW][C]66[/C][C]212[/C][C]214.924215633429[/C][C]-2.92421563342899[/C][/ROW]
[ROW][C]67[/C][C]203[/C][C]199.973732264040[/C][C]3.02626773595952[/C][/ROW]
[ROW][C]68[/C][C]184[/C][C]192.793824593662[/C][C]-8.79382459366195[/C][/ROW]
[ROW][C]69[/C][C]200[/C][C]205.490437424686[/C][C]-5.49043742468552[/C][/ROW]
[ROW][C]70[/C][C]198[/C][C]194.762222709355[/C][C]3.23777729064463[/C][/ROW]
[ROW][C]71[/C][C]195[/C][C]183.040622333976[/C][C]11.9593776660238[/C][/ROW]
[ROW][C]72[/C][C]177[/C][C]186.036873460918[/C][C]-9.03687346091812[/C][/ROW]
[ROW][C]73[/C][C]176[/C][C]178.954110472808[/C][C]-2.95411047280848[/C][/ROW]
[ROW][C]74[/C][C]180[/C][C]186.168020924693[/C][C]-6.16802092469288[/C][/ROW]
[ROW][C]75[/C][C]194[/C][C]199.077605215509[/C][C]-5.0776052155093[/C][/ROW]
[ROW][C]76[/C][C]204[/C][C]208.743017317973[/C][C]-4.74301731797345[/C][/ROW]
[ROW][C]77[/C][C]206[/C][C]211.610510424352[/C][C]-5.61051042435156[/C][/ROW]
[ROW][C]78[/C][C]219[/C][C]215.67567418456[/C][C]3.32432581544012[/C][/ROW]
[ROW][C]79[/C][C]213[/C][C]203.601124673788[/C][C]9.39887532621213[/C][/ROW]
[ROW][C]80[/C][C]196[/C][C]188.919494246069[/C][C]7.08050575393102[/C][/ROW]
[ROW][C]81[/C][C]214[/C][C]209.077891389442[/C][C]4.9221086105577[/C][/ROW]
[ROW][C]82[/C][C]209[/C][C]208.467296009413[/C][C]0.532703990587322[/C][/ROW]
[ROW][C]83[/C][C]213[/C][C]201.677666444361[/C][C]11.322333555639[/C][/ROW]
[ROW][C]84[/C][C]194[/C][C]191.573487679117[/C][C]2.42651232088303[/C][/ROW]
[ROW][C]85[/C][C]197[/C][C]194.313187068830[/C][C]2.68681293117049[/C][/ROW]
[ROW][C]86[/C][C]211[/C][C]204.020941400578[/C][C]6.97905859942239[/C][/ROW]
[ROW][C]87[/C][C]240[/C][C]226.504006476405[/C][C]13.4959935235950[/C][/ROW]
[ROW][C]88[/C][C]251[/C][C]249.521806031691[/C][C]1.47819396830926[/C][/ROW]
[ROW][C]89[/C][C]254[/C][C]261.165987977382[/C][C]-7.16598797738231[/C][/ROW]
[ROW][C]90[/C][C]273[/C][C]277.116797650029[/C][C]-4.11679765002856[/C][/ROW]
[ROW][C]91[/C][C]271[/C][C]272.047874277667[/C][C]-1.04787427766666[/C][/ROW]
[ROW][C]92[/C][C]245[/C][C]256.708756485545[/C][C]-11.7087564855445[/C][/ROW]
[ROW][C]93[/C][C]264[/C][C]270.950236334135[/C][C]-6.9502363341345[/C][/ROW]
[ROW][C]94[/C][C]264[/C][C]264.140701155495[/C][C]-0.140701155495435[/C][/ROW]
[ROW][C]95[/C][C]262[/C][C]264.77684837389[/C][C]-2.77684837389018[/C][/ROW]
[ROW][C]96[/C][C]237[/C][C]243.023779628400[/C][C]-6.02377962839955[/C][/ROW]
[ROW][C]97[/C][C]237[/C][C]240.950575137248[/C][C]-3.95057513724763[/C][/ROW]
[ROW][C]98[/C][C]251[/C][C]248.253250724667[/C][C]2.74674927533331[/C][/ROW]
[ROW][C]99[/C][C]272[/C][C]270.110679787957[/C][C]1.88932021204255[/C][/ROW]
[ROW][C]100[/C][C]282[/C][C]276.693948391564[/C][C]5.30605160843623[/C][/ROW]
[ROW][C]101[/C][C]278[/C][C]280.203487767387[/C][C]-2.2034877673874[/C][/ROW]
[ROW][C]102[/C][C]291[/C][C]296.406053680970[/C][C]-5.40605368097027[/C][/ROW]
[ROW][C]103[/C][C]293[/C][C]289.131858272017[/C][C]3.8681417279829[/C][/ROW]
[ROW][C]104[/C][C]271[/C][C]265.829444838415[/C][C]5.17055516158536[/C][/ROW]
[ROW][C]105[/C][C]284[/C][C]288.290044970731[/C][C]-4.29004497073146[/C][/ROW]
[ROW][C]106[/C][C]290[/C][C]286.051618633582[/C][C]3.94838136641818[/C][/ROW]
[ROW][C]107[/C][C]288[/C][C]286.332053861114[/C][C]1.66794613888607[/C][/ROW]
[ROW][C]108[/C][C]262[/C][C]264.50785130725[/C][C]-2.50785130724972[/C][/ROW]
[ROW][C]109[/C][C]263[/C][C]265.796512632208[/C][C]-2.79651263220774[/C][/ROW]
[ROW][C]110[/C][C]275[/C][C]278.639588482012[/C][C]-3.63958848201156[/C][/ROW]
[ROW][C]111[/C][C]297[/C][C]297.715393283297[/C][C]-0.715393283297374[/C][/ROW]
[ROW][C]112[/C][C]301[/C][C]305.293829411977[/C][C]-4.29382941197736[/C][/ROW]
[ROW][C]113[/C][C]296[/C][C]299.165650483880[/C][C]-3.16565048388048[/C][/ROW]
[ROW][C]114[/C][C]309[/C][C]311.523687410122[/C][C]-2.52368741012225[/C][/ROW]
[ROW][C]115[/C][C]310[/C][C]310.036017736218[/C][C]-0.0360177362176728[/C][/ROW]
[ROW][C]116[/C][C]292[/C][C]284.514654960632[/C][C]7.48534503936833[/C][/ROW]
[ROW][C]117[/C][C]300[/C][C]300.557578556411[/C][C]-0.557578556411499[/C][/ROW]
[ROW][C]118[/C][C]314[/C][C]304.027043345781[/C][C]9.97295665421882[/C][/ROW]
[ROW][C]119[/C][C]310[/C][C]304.966087418331[/C][C]5.03391258166931[/C][/ROW]
[ROW][C]120[/C][C]288[/C][C]282.029883757016[/C][C]5.97011624298364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77922&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
135858.8875534188034-0.887553418803435
145858.4961736516680-0.496173651668045
155958.81460159053620.185398409463829
166261.24101029105030.758989708949656
178786.1381640772430.861835922756953
188382.09430323031970.905696769680318
196867.71790596772090.282094032279119
205858.8532009899306-0.8532009899306
216860.34015931107197.65984068892813
226364.6123862454992-1.61238624549921
236565.8416574721796-0.841657472179648
246868.170988328808-0.170988328807979
256264.2937082696555-2.29370826965550
266964.15908375898234.84091624101774
277468.05809261639455.94190738360550
287274.8486577497965-2.84865774979653
299499.911741095756-5.91174109575591
3010294.00565641640477.99434358359525
319283.33389570709028.6661042929098
328179.34509407818031.65490592181966
339989.91488977353739.0851102264627
349591.8379207426713.16207925732904
359298.8614814556668-6.86148145566678
3693102.199347618506-9.19934761850621
378595.365398756152-10.3653987561520
389297.4832784492366-5.48327844923662
399997.75142114626461.24857885373540
4010796.195938320812510.8040616791875
41125124.9616438016280.0383561983715737
42137131.3172443224755.68275567752482
43125121.2333508850603.76664911494028
44115111.4422124762163.55778752378355
45135128.0544010057136.94559899428674
46128125.8532853841022.14671461589765
47120126.462753165306-6.46275316530604
48123128.799620719379-5.79962071937931
49119123.224665849066-4.22466584906618
50128132.168749293474-4.16874929347395
51139138.8013932253190.198606774681167
52155144.38712650561810.6128734943816
53164167.787480660072-3.78748066007182
54176177.307350328411-1.30735032841122
55162163.608445481613-1.60844548161310
56155151.2251610409593.77483895904066
57174169.6065685278354.39343147216474
58171162.6839925823968.3160074176036
59162160.1452848553241.85471514467565
60160166.976349408252-6.97634940825168
61156162.814262955529-6.81426295552896
62163171.378190569990-8.3781905699905
63180179.2379843008150.762015699185383
64195191.694463866853.30553613315016
65203202.5371052583700.462894741629583
66212214.924215633429-2.92421563342899
67203199.9737322640403.02626773595952
68184192.793824593662-8.79382459366195
69200205.490437424686-5.49043742468552
70198194.7622227093553.23777729064463
71195183.04062233397611.9593776660238
72177186.036873460918-9.03687346091812
73176178.954110472808-2.95411047280848
74180186.168020924693-6.16802092469288
75194199.077605215509-5.0776052155093
76204208.743017317973-4.74301731797345
77206211.610510424352-5.61051042435156
78219215.675674184563.32432581544012
79213203.6011246737889.39887532621213
80196188.9194942460697.08050575393102
81214209.0778913894424.9221086105577
82209208.4672960094130.532703990587322
83213201.67766644436111.322333555639
84194191.5734876791172.42651232088303
85197194.3131870688302.68681293117049
86211204.0209414005786.97905859942239
87240226.50400647640513.4959935235950
88251249.5218060316911.47819396830926
89254261.165987977382-7.16598797738231
90273277.116797650029-4.11679765002856
91271272.047874277667-1.04787427766666
92245256.708756485545-11.7087564855445
93264270.950236334135-6.9502363341345
94264264.140701155495-0.140701155495435
95262264.77684837389-2.77684837389018
96237243.023779628400-6.02377962839955
97237240.950575137248-3.95057513724763
98251248.2532507246672.74674927533331
99272270.1106797879571.88932021204255
100282276.6939483915645.30605160843623
101278280.203487767387-2.2034877673874
102291296.406053680970-5.40605368097027
103293289.1318582720173.8681417279829
104271265.8294448384155.17055516158536
105284288.290044970731-4.29004497073146
106290286.0516186335823.94838136641818
107288286.3320538611141.66794613888607
108262264.50785130725-2.50785130724972
109263265.796512632208-2.79651263220774
110275278.639588482012-3.63958848201156
111297297.715393283297-0.715393283297374
112301305.293829411977-4.29382941197736
113296299.165650483880-3.16565048388048
114309311.523687410122-2.52368741012225
115310310.036017736218-0.0360177362176728
116292284.5146549606327.48534503936833
117300300.557578556411-0.557578556411499
118314304.0270433457819.97295665421882
119310304.9660874183315.03391258166931
120288282.0298837570165.97011624298364







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121287.572563128397276.846972692500298.298153564294
122302.556262813834290.607408626486314.505117001182
123326.898146665613313.265007532133340.531285799093
124334.650792050579318.913336491661350.388247609496
125333.505392304797315.296677099104351.714107510489
126350.50539330611329.507798036758371.502988575462
127354.890121512827330.826461795886378.953781229768
128337.495890772697310.120599657954364.87118188744
129348.172448144501317.264412626670379.080483662331
130361.019583395977326.376732396389395.662434395565
131356.487964349178317.923277398746395.05265129961
132333.000924792096290.339494427769375.662355156422

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 287.572563128397 & 276.846972692500 & 298.298153564294 \tabularnewline
122 & 302.556262813834 & 290.607408626486 & 314.505117001182 \tabularnewline
123 & 326.898146665613 & 313.265007532133 & 340.531285799093 \tabularnewline
124 & 334.650792050579 & 318.913336491661 & 350.388247609496 \tabularnewline
125 & 333.505392304797 & 315.296677099104 & 351.714107510489 \tabularnewline
126 & 350.50539330611 & 329.507798036758 & 371.502988575462 \tabularnewline
127 & 354.890121512827 & 330.826461795886 & 378.953781229768 \tabularnewline
128 & 337.495890772697 & 310.120599657954 & 364.87118188744 \tabularnewline
129 & 348.172448144501 & 317.264412626670 & 379.080483662331 \tabularnewline
130 & 361.019583395977 & 326.376732396389 & 395.662434395565 \tabularnewline
131 & 356.487964349178 & 317.923277398746 & 395.05265129961 \tabularnewline
132 & 333.000924792096 & 290.339494427769 & 375.662355156422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77922&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]287.572563128397[/C][C]276.846972692500[/C][C]298.298153564294[/C][/ROW]
[ROW][C]122[/C][C]302.556262813834[/C][C]290.607408626486[/C][C]314.505117001182[/C][/ROW]
[ROW][C]123[/C][C]326.898146665613[/C][C]313.265007532133[/C][C]340.531285799093[/C][/ROW]
[ROW][C]124[/C][C]334.650792050579[/C][C]318.913336491661[/C][C]350.388247609496[/C][/ROW]
[ROW][C]125[/C][C]333.505392304797[/C][C]315.296677099104[/C][C]351.714107510489[/C][/ROW]
[ROW][C]126[/C][C]350.50539330611[/C][C]329.507798036758[/C][C]371.502988575462[/C][/ROW]
[ROW][C]127[/C][C]354.890121512827[/C][C]330.826461795886[/C][C]378.953781229768[/C][/ROW]
[ROW][C]128[/C][C]337.495890772697[/C][C]310.120599657954[/C][C]364.87118188744[/C][/ROW]
[ROW][C]129[/C][C]348.172448144501[/C][C]317.264412626670[/C][C]379.080483662331[/C][/ROW]
[ROW][C]130[/C][C]361.019583395977[/C][C]326.376732396389[/C][C]395.662434395565[/C][/ROW]
[ROW][C]131[/C][C]356.487964349178[/C][C]317.923277398746[/C][C]395.05265129961[/C][/ROW]
[ROW][C]132[/C][C]333.000924792096[/C][C]290.339494427769[/C][C]375.662355156422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77922&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77922&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
121287.572563128397276.846972692500298.298153564294
122302.556262813834290.607408626486314.505117001182
123326.898146665613313.265007532133340.531285799093
124334.650792050579318.913336491661350.388247609496
125333.505392304797315.296677099104351.714107510489
126350.50539330611329.507798036758371.502988575462
127354.890121512827330.826461795886378.953781229768
128337.495890772697310.120599657954364.87118188744
129348.172448144501317.264412626670379.080483662331
130361.019583395977326.376732396389395.662434395565
131356.487964349178317.923277398746395.05265129961
132333.000924792096290.339494427769375.662355156422



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')