Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 05 Aug 2010 14:12:26 +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/Aug/05/t1281017511z3vod4puanlqvg6.htm/, Retrieved Sun, 05 May 2024 17:30:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78412, Retrieved Sun, 05 May 2024 17:30:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-08-05 14:12:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
390
389
388
386
406
405
390
380
381
381
382
384
394
393
388
381
399
396
378
368
369
373
374
379
385
385
395
387
400
390
365
350
365
374
367
375
382
380
378
363
375
366
341
326
338
345
336
342
347
360
360
334
347
336
305
289
303
308
294
299
306
313
321
287
296
283
248
235
241
244
237
241
251
259
264
229
237
228
197
182
182
176
172
175
185
195
206
175
185
174
140
130
133
130
131
136
149
155
161
131
145
134
93
87
86
80
79
91
108
105
112
78
87
74
32
25
26
25
22
36




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78412&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78412&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0112924114735404
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0112924114735404 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78412&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0112924114735404[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78412&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
alpha1
beta0.0112924114735404
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33883880
4386387-1
5406384.98870758852621.0112924114736
6405405.225975748028-0.225975748027679
7390404.223423936898-14.2234239368979
8380389.06280718124-9.06280718123986
9381378.9604662334442.03953376655602
10381379.983497487951.01650251204990
11382379.994976252582.00502374741995
12384381.017617805752.98238219424985
13394383.05129609265910.9487039073410
14393393.174933362283-0.174933362282616
15388392.172957942775-4.17295794277527
16381387.125835184624-6.12583518462367
17399380.056659733118.9433402669002
18396398.270575726077-2.27057572607691
19378395.244935450696-17.2449354506962
20368377.050198543752-9.05019854375234
21369366.9479999778792.05200002212098
22373367.9711720064735.02882799352744
23374372.0279596014051.97204039859486
24379373.0502286930285.94977130697151
25385378.11741595886.88258404119972
26385384.1951369297950.804863070205272
27395384.20422577476310.7957742252366
28387394.32613609949-7.32613609949016
29400386.24340635614413.7565936438564
30390399.398751472044-9.3987514720443
31365389.292616903084-24.2926169030844
32350364.018294677246-14.0182946772457
33365348.85999432559316.1400056744071
34374364.0422539108549.95774608914644
35367373.154700877041-6.15470087704125
36375366.0851994622418.91480053775888
37382374.1858690581187.81413094188196
38380381.274109440022-1.27410944002190
39378379.259721671963-1.25972167196289
40363377.245496376501-14.2454963765009
41375362.08463036977312.9153696302274
42366374.23047603797-8.23047603797005
43341365.137534115926-24.1375341159261
44326339.864963148732-13.8649631487325
45338324.70839427979213.2916057202085
46345336.8584885607288.14151143927177
47336343.950425857917-7.95042585791703
48342334.8606463777397.1393536222605
49347340.9412668964976.05873310350279
50360346.0096846037113.9903153962897
51360359.167669001810.832330998190173
52334359.177068025924-25.1770680259236
53347332.89275821407814.1072417859225
54336346.052062993081-10.0520629930809
55305334.938550961605-29.9385509616051
56289303.600472525225-14.6004725252251
57303287.43559798176215.5644020182379
58308301.6113576136926.38864238630833
59294306.683500792275-12.6835007922751
60299292.5402734824046.45972651759621
61306297.6132193722478.38678062775296
62313304.7079263500348.29207364996608
63321311.8015638576589.19843614234173
64287319.905436383491-32.9054363834907
65296285.53385465613210.4661453438681
66283294.652042675897-11.6520426758967
67248281.520463015493-33.5204630154932
68235246.141936154339-11.1419361543387
69241233.0161168266727.98388317332802
70244239.1062741206224.89372587937811
71237242.161536086891-5.16153608689055
72241235.1032498975625.89675010243815
73251239.16983842607511.8301615739248
74259249.3034294783669.69657052163356
75264257.4129271425796.58707285742105
76229262.487311079691-33.4873110796911
77237227.1091585838379.8908414161632
78228235.220850034928-7.22085003492765
79197226.139309225145-29.1393092251445
80182194.810256155319-12.8102561553195
81182179.6655974717322.33440252826787
82176179.691958505626-3.69195850562619
83172173.650267391037-1.65026739103743
84175169.6316318926165.36836810738353
85185172.69225371422612.3077462857735
86195182.83123784959712.1687621504026
87206192.96865251892313.0313474810766
88175204.115807856734-29.1158078567344
89185172.78702017403212.2129798259684
90174182.924934167544-8.92493416754445
91140171.824150138550-31.8241501385503
92130137.46477874039-7.46477874039005
93133127.3804833872955.61951661270537
94130130.443941281168-0.443941281167696
95131127.4389281135513.56107188644934
96136128.4791412025797.52085879742069
97149133.56406983475415.4359301652458
98155146.7383787096578.26162129034304
99161152.8316723367068.16832766329392
100131158.923912453731-27.9239124537307
101145128.60858414435216.3914158556479
102134142.793682756828-8.79368275682793
10393131.69438087277-38.6943808727701
1048790.2574280022409-3.25742800224086
1058684.22064378489411.77935621510588
1068083.2407370074331-3.2407370074331
1077977.20414127166761.79585872833236
1089176.224420847376314.7755791526237
10910888.391272766927619.6087272330724
110105105.612702583316-0.612702583315865
111112102.6057836936349.39421630636583
11278109.711867049637-31.7118670496371
1138775.353763598318411.6462364016816
1147484.4852776918843-10.4852776918843
1153271.3668736217732-39.3668736217732
1162528.9223266864093-3.92232668640928
1172621.87803415953274.1219658404673
1182522.92458109388312.07541890611687
1192221.94801757815100.0519824218490292
1203618.948604585047917.0513954149521

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 388 & 388 & 0 \tabularnewline
4 & 386 & 387 & -1 \tabularnewline
5 & 406 & 384.988707588526 & 21.0112924114736 \tabularnewline
6 & 405 & 405.225975748028 & -0.225975748027679 \tabularnewline
7 & 390 & 404.223423936898 & -14.2234239368979 \tabularnewline
8 & 380 & 389.06280718124 & -9.06280718123986 \tabularnewline
9 & 381 & 378.960466233444 & 2.03953376655602 \tabularnewline
10 & 381 & 379.98349748795 & 1.01650251204990 \tabularnewline
11 & 382 & 379.99497625258 & 2.00502374741995 \tabularnewline
12 & 384 & 381.01761780575 & 2.98238219424985 \tabularnewline
13 & 394 & 383.051296092659 & 10.9487039073410 \tabularnewline
14 & 393 & 393.174933362283 & -0.174933362282616 \tabularnewline
15 & 388 & 392.172957942775 & -4.17295794277527 \tabularnewline
16 & 381 & 387.125835184624 & -6.12583518462367 \tabularnewline
17 & 399 & 380.0566597331 & 18.9433402669002 \tabularnewline
18 & 396 & 398.270575726077 & -2.27057572607691 \tabularnewline
19 & 378 & 395.244935450696 & -17.2449354506962 \tabularnewline
20 & 368 & 377.050198543752 & -9.05019854375234 \tabularnewline
21 & 369 & 366.947999977879 & 2.05200002212098 \tabularnewline
22 & 373 & 367.971172006473 & 5.02882799352744 \tabularnewline
23 & 374 & 372.027959601405 & 1.97204039859486 \tabularnewline
24 & 379 & 373.050228693028 & 5.94977130697151 \tabularnewline
25 & 385 & 378.1174159588 & 6.88258404119972 \tabularnewline
26 & 385 & 384.195136929795 & 0.804863070205272 \tabularnewline
27 & 395 & 384.204225774763 & 10.7957742252366 \tabularnewline
28 & 387 & 394.32613609949 & -7.32613609949016 \tabularnewline
29 & 400 & 386.243406356144 & 13.7565936438564 \tabularnewline
30 & 390 & 399.398751472044 & -9.3987514720443 \tabularnewline
31 & 365 & 389.292616903084 & -24.2926169030844 \tabularnewline
32 & 350 & 364.018294677246 & -14.0182946772457 \tabularnewline
33 & 365 & 348.859994325593 & 16.1400056744071 \tabularnewline
34 & 374 & 364.042253910854 & 9.95774608914644 \tabularnewline
35 & 367 & 373.154700877041 & -6.15470087704125 \tabularnewline
36 & 375 & 366.085199462241 & 8.91480053775888 \tabularnewline
37 & 382 & 374.185869058118 & 7.81413094188196 \tabularnewline
38 & 380 & 381.274109440022 & -1.27410944002190 \tabularnewline
39 & 378 & 379.259721671963 & -1.25972167196289 \tabularnewline
40 & 363 & 377.245496376501 & -14.2454963765009 \tabularnewline
41 & 375 & 362.084630369773 & 12.9153696302274 \tabularnewline
42 & 366 & 374.23047603797 & -8.23047603797005 \tabularnewline
43 & 341 & 365.137534115926 & -24.1375341159261 \tabularnewline
44 & 326 & 339.864963148732 & -13.8649631487325 \tabularnewline
45 & 338 & 324.708394279792 & 13.2916057202085 \tabularnewline
46 & 345 & 336.858488560728 & 8.14151143927177 \tabularnewline
47 & 336 & 343.950425857917 & -7.95042585791703 \tabularnewline
48 & 342 & 334.860646377739 & 7.1393536222605 \tabularnewline
49 & 347 & 340.941266896497 & 6.05873310350279 \tabularnewline
50 & 360 & 346.00968460371 & 13.9903153962897 \tabularnewline
51 & 360 & 359.16766900181 & 0.832330998190173 \tabularnewline
52 & 334 & 359.177068025924 & -25.1770680259236 \tabularnewline
53 & 347 & 332.892758214078 & 14.1072417859225 \tabularnewline
54 & 336 & 346.052062993081 & -10.0520629930809 \tabularnewline
55 & 305 & 334.938550961605 & -29.9385509616051 \tabularnewline
56 & 289 & 303.600472525225 & -14.6004725252251 \tabularnewline
57 & 303 & 287.435597981762 & 15.5644020182379 \tabularnewline
58 & 308 & 301.611357613692 & 6.38864238630833 \tabularnewline
59 & 294 & 306.683500792275 & -12.6835007922751 \tabularnewline
60 & 299 & 292.540273482404 & 6.45972651759621 \tabularnewline
61 & 306 & 297.613219372247 & 8.38678062775296 \tabularnewline
62 & 313 & 304.707926350034 & 8.29207364996608 \tabularnewline
63 & 321 & 311.801563857658 & 9.19843614234173 \tabularnewline
64 & 287 & 319.905436383491 & -32.9054363834907 \tabularnewline
65 & 296 & 285.533854656132 & 10.4661453438681 \tabularnewline
66 & 283 & 294.652042675897 & -11.6520426758967 \tabularnewline
67 & 248 & 281.520463015493 & -33.5204630154932 \tabularnewline
68 & 235 & 246.141936154339 & -11.1419361543387 \tabularnewline
69 & 241 & 233.016116826672 & 7.98388317332802 \tabularnewline
70 & 244 & 239.106274120622 & 4.89372587937811 \tabularnewline
71 & 237 & 242.161536086891 & -5.16153608689055 \tabularnewline
72 & 241 & 235.103249897562 & 5.89675010243815 \tabularnewline
73 & 251 & 239.169838426075 & 11.8301615739248 \tabularnewline
74 & 259 & 249.303429478366 & 9.69657052163356 \tabularnewline
75 & 264 & 257.412927142579 & 6.58707285742105 \tabularnewline
76 & 229 & 262.487311079691 & -33.4873110796911 \tabularnewline
77 & 237 & 227.109158583837 & 9.8908414161632 \tabularnewline
78 & 228 & 235.220850034928 & -7.22085003492765 \tabularnewline
79 & 197 & 226.139309225145 & -29.1393092251445 \tabularnewline
80 & 182 & 194.810256155319 & -12.8102561553195 \tabularnewline
81 & 182 & 179.665597471732 & 2.33440252826787 \tabularnewline
82 & 176 & 179.691958505626 & -3.69195850562619 \tabularnewline
83 & 172 & 173.650267391037 & -1.65026739103743 \tabularnewline
84 & 175 & 169.631631892616 & 5.36836810738353 \tabularnewline
85 & 185 & 172.692253714226 & 12.3077462857735 \tabularnewline
86 & 195 & 182.831237849597 & 12.1687621504026 \tabularnewline
87 & 206 & 192.968652518923 & 13.0313474810766 \tabularnewline
88 & 175 & 204.115807856734 & -29.1158078567344 \tabularnewline
89 & 185 & 172.787020174032 & 12.2129798259684 \tabularnewline
90 & 174 & 182.924934167544 & -8.92493416754445 \tabularnewline
91 & 140 & 171.824150138550 & -31.8241501385503 \tabularnewline
92 & 130 & 137.46477874039 & -7.46477874039005 \tabularnewline
93 & 133 & 127.380483387295 & 5.61951661270537 \tabularnewline
94 & 130 & 130.443941281168 & -0.443941281167696 \tabularnewline
95 & 131 & 127.438928113551 & 3.56107188644934 \tabularnewline
96 & 136 & 128.479141202579 & 7.52085879742069 \tabularnewline
97 & 149 & 133.564069834754 & 15.4359301652458 \tabularnewline
98 & 155 & 146.738378709657 & 8.26162129034304 \tabularnewline
99 & 161 & 152.831672336706 & 8.16832766329392 \tabularnewline
100 & 131 & 158.923912453731 & -27.9239124537307 \tabularnewline
101 & 145 & 128.608584144352 & 16.3914158556479 \tabularnewline
102 & 134 & 142.793682756828 & -8.79368275682793 \tabularnewline
103 & 93 & 131.69438087277 & -38.6943808727701 \tabularnewline
104 & 87 & 90.2574280022409 & -3.25742800224086 \tabularnewline
105 & 86 & 84.2206437848941 & 1.77935621510588 \tabularnewline
106 & 80 & 83.2407370074331 & -3.2407370074331 \tabularnewline
107 & 79 & 77.2041412716676 & 1.79585872833236 \tabularnewline
108 & 91 & 76.2244208473763 & 14.7755791526237 \tabularnewline
109 & 108 & 88.3912727669276 & 19.6087272330724 \tabularnewline
110 & 105 & 105.612702583316 & -0.612702583315865 \tabularnewline
111 & 112 & 102.605783693634 & 9.39421630636583 \tabularnewline
112 & 78 & 109.711867049637 & -31.7118670496371 \tabularnewline
113 & 87 & 75.3537635983184 & 11.6462364016816 \tabularnewline
114 & 74 & 84.4852776918843 & -10.4852776918843 \tabularnewline
115 & 32 & 71.3668736217732 & -39.3668736217732 \tabularnewline
116 & 25 & 28.9223266864093 & -3.92232668640928 \tabularnewline
117 & 26 & 21.8780341595327 & 4.1219658404673 \tabularnewline
118 & 25 & 22.9245810938831 & 2.07541890611687 \tabularnewline
119 & 22 & 21.9480175781510 & 0.0519824218490292 \tabularnewline
120 & 36 & 18.9486045850479 & 17.0513954149521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78412&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]388[/C][C]388[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]386[/C][C]387[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]406[/C][C]384.988707588526[/C][C]21.0112924114736[/C][/ROW]
[ROW][C]6[/C][C]405[/C][C]405.225975748028[/C][C]-0.225975748027679[/C][/ROW]
[ROW][C]7[/C][C]390[/C][C]404.223423936898[/C][C]-14.2234239368979[/C][/ROW]
[ROW][C]8[/C][C]380[/C][C]389.06280718124[/C][C]-9.06280718123986[/C][/ROW]
[ROW][C]9[/C][C]381[/C][C]378.960466233444[/C][C]2.03953376655602[/C][/ROW]
[ROW][C]10[/C][C]381[/C][C]379.98349748795[/C][C]1.01650251204990[/C][/ROW]
[ROW][C]11[/C][C]382[/C][C]379.99497625258[/C][C]2.00502374741995[/C][/ROW]
[ROW][C]12[/C][C]384[/C][C]381.01761780575[/C][C]2.98238219424985[/C][/ROW]
[ROW][C]13[/C][C]394[/C][C]383.051296092659[/C][C]10.9487039073410[/C][/ROW]
[ROW][C]14[/C][C]393[/C][C]393.174933362283[/C][C]-0.174933362282616[/C][/ROW]
[ROW][C]15[/C][C]388[/C][C]392.172957942775[/C][C]-4.17295794277527[/C][/ROW]
[ROW][C]16[/C][C]381[/C][C]387.125835184624[/C][C]-6.12583518462367[/C][/ROW]
[ROW][C]17[/C][C]399[/C][C]380.0566597331[/C][C]18.9433402669002[/C][/ROW]
[ROW][C]18[/C][C]396[/C][C]398.270575726077[/C][C]-2.27057572607691[/C][/ROW]
[ROW][C]19[/C][C]378[/C][C]395.244935450696[/C][C]-17.2449354506962[/C][/ROW]
[ROW][C]20[/C][C]368[/C][C]377.050198543752[/C][C]-9.05019854375234[/C][/ROW]
[ROW][C]21[/C][C]369[/C][C]366.947999977879[/C][C]2.05200002212098[/C][/ROW]
[ROW][C]22[/C][C]373[/C][C]367.971172006473[/C][C]5.02882799352744[/C][/ROW]
[ROW][C]23[/C][C]374[/C][C]372.027959601405[/C][C]1.97204039859486[/C][/ROW]
[ROW][C]24[/C][C]379[/C][C]373.050228693028[/C][C]5.94977130697151[/C][/ROW]
[ROW][C]25[/C][C]385[/C][C]378.1174159588[/C][C]6.88258404119972[/C][/ROW]
[ROW][C]26[/C][C]385[/C][C]384.195136929795[/C][C]0.804863070205272[/C][/ROW]
[ROW][C]27[/C][C]395[/C][C]384.204225774763[/C][C]10.7957742252366[/C][/ROW]
[ROW][C]28[/C][C]387[/C][C]394.32613609949[/C][C]-7.32613609949016[/C][/ROW]
[ROW][C]29[/C][C]400[/C][C]386.243406356144[/C][C]13.7565936438564[/C][/ROW]
[ROW][C]30[/C][C]390[/C][C]399.398751472044[/C][C]-9.3987514720443[/C][/ROW]
[ROW][C]31[/C][C]365[/C][C]389.292616903084[/C][C]-24.2926169030844[/C][/ROW]
[ROW][C]32[/C][C]350[/C][C]364.018294677246[/C][C]-14.0182946772457[/C][/ROW]
[ROW][C]33[/C][C]365[/C][C]348.859994325593[/C][C]16.1400056744071[/C][/ROW]
[ROW][C]34[/C][C]374[/C][C]364.042253910854[/C][C]9.95774608914644[/C][/ROW]
[ROW][C]35[/C][C]367[/C][C]373.154700877041[/C][C]-6.15470087704125[/C][/ROW]
[ROW][C]36[/C][C]375[/C][C]366.085199462241[/C][C]8.91480053775888[/C][/ROW]
[ROW][C]37[/C][C]382[/C][C]374.185869058118[/C][C]7.81413094188196[/C][/ROW]
[ROW][C]38[/C][C]380[/C][C]381.274109440022[/C][C]-1.27410944002190[/C][/ROW]
[ROW][C]39[/C][C]378[/C][C]379.259721671963[/C][C]-1.25972167196289[/C][/ROW]
[ROW][C]40[/C][C]363[/C][C]377.245496376501[/C][C]-14.2454963765009[/C][/ROW]
[ROW][C]41[/C][C]375[/C][C]362.084630369773[/C][C]12.9153696302274[/C][/ROW]
[ROW][C]42[/C][C]366[/C][C]374.23047603797[/C][C]-8.23047603797005[/C][/ROW]
[ROW][C]43[/C][C]341[/C][C]365.137534115926[/C][C]-24.1375341159261[/C][/ROW]
[ROW][C]44[/C][C]326[/C][C]339.864963148732[/C][C]-13.8649631487325[/C][/ROW]
[ROW][C]45[/C][C]338[/C][C]324.708394279792[/C][C]13.2916057202085[/C][/ROW]
[ROW][C]46[/C][C]345[/C][C]336.858488560728[/C][C]8.14151143927177[/C][/ROW]
[ROW][C]47[/C][C]336[/C][C]343.950425857917[/C][C]-7.95042585791703[/C][/ROW]
[ROW][C]48[/C][C]342[/C][C]334.860646377739[/C][C]7.1393536222605[/C][/ROW]
[ROW][C]49[/C][C]347[/C][C]340.941266896497[/C][C]6.05873310350279[/C][/ROW]
[ROW][C]50[/C][C]360[/C][C]346.00968460371[/C][C]13.9903153962897[/C][/ROW]
[ROW][C]51[/C][C]360[/C][C]359.16766900181[/C][C]0.832330998190173[/C][/ROW]
[ROW][C]52[/C][C]334[/C][C]359.177068025924[/C][C]-25.1770680259236[/C][/ROW]
[ROW][C]53[/C][C]347[/C][C]332.892758214078[/C][C]14.1072417859225[/C][/ROW]
[ROW][C]54[/C][C]336[/C][C]346.052062993081[/C][C]-10.0520629930809[/C][/ROW]
[ROW][C]55[/C][C]305[/C][C]334.938550961605[/C][C]-29.9385509616051[/C][/ROW]
[ROW][C]56[/C][C]289[/C][C]303.600472525225[/C][C]-14.6004725252251[/C][/ROW]
[ROW][C]57[/C][C]303[/C][C]287.435597981762[/C][C]15.5644020182379[/C][/ROW]
[ROW][C]58[/C][C]308[/C][C]301.611357613692[/C][C]6.38864238630833[/C][/ROW]
[ROW][C]59[/C][C]294[/C][C]306.683500792275[/C][C]-12.6835007922751[/C][/ROW]
[ROW][C]60[/C][C]299[/C][C]292.540273482404[/C][C]6.45972651759621[/C][/ROW]
[ROW][C]61[/C][C]306[/C][C]297.613219372247[/C][C]8.38678062775296[/C][/ROW]
[ROW][C]62[/C][C]313[/C][C]304.707926350034[/C][C]8.29207364996608[/C][/ROW]
[ROW][C]63[/C][C]321[/C][C]311.801563857658[/C][C]9.19843614234173[/C][/ROW]
[ROW][C]64[/C][C]287[/C][C]319.905436383491[/C][C]-32.9054363834907[/C][/ROW]
[ROW][C]65[/C][C]296[/C][C]285.533854656132[/C][C]10.4661453438681[/C][/ROW]
[ROW][C]66[/C][C]283[/C][C]294.652042675897[/C][C]-11.6520426758967[/C][/ROW]
[ROW][C]67[/C][C]248[/C][C]281.520463015493[/C][C]-33.5204630154932[/C][/ROW]
[ROW][C]68[/C][C]235[/C][C]246.141936154339[/C][C]-11.1419361543387[/C][/ROW]
[ROW][C]69[/C][C]241[/C][C]233.016116826672[/C][C]7.98388317332802[/C][/ROW]
[ROW][C]70[/C][C]244[/C][C]239.106274120622[/C][C]4.89372587937811[/C][/ROW]
[ROW][C]71[/C][C]237[/C][C]242.161536086891[/C][C]-5.16153608689055[/C][/ROW]
[ROW][C]72[/C][C]241[/C][C]235.103249897562[/C][C]5.89675010243815[/C][/ROW]
[ROW][C]73[/C][C]251[/C][C]239.169838426075[/C][C]11.8301615739248[/C][/ROW]
[ROW][C]74[/C][C]259[/C][C]249.303429478366[/C][C]9.69657052163356[/C][/ROW]
[ROW][C]75[/C][C]264[/C][C]257.412927142579[/C][C]6.58707285742105[/C][/ROW]
[ROW][C]76[/C][C]229[/C][C]262.487311079691[/C][C]-33.4873110796911[/C][/ROW]
[ROW][C]77[/C][C]237[/C][C]227.109158583837[/C][C]9.8908414161632[/C][/ROW]
[ROW][C]78[/C][C]228[/C][C]235.220850034928[/C][C]-7.22085003492765[/C][/ROW]
[ROW][C]79[/C][C]197[/C][C]226.139309225145[/C][C]-29.1393092251445[/C][/ROW]
[ROW][C]80[/C][C]182[/C][C]194.810256155319[/C][C]-12.8102561553195[/C][/ROW]
[ROW][C]81[/C][C]182[/C][C]179.665597471732[/C][C]2.33440252826787[/C][/ROW]
[ROW][C]82[/C][C]176[/C][C]179.691958505626[/C][C]-3.69195850562619[/C][/ROW]
[ROW][C]83[/C][C]172[/C][C]173.650267391037[/C][C]-1.65026739103743[/C][/ROW]
[ROW][C]84[/C][C]175[/C][C]169.631631892616[/C][C]5.36836810738353[/C][/ROW]
[ROW][C]85[/C][C]185[/C][C]172.692253714226[/C][C]12.3077462857735[/C][/ROW]
[ROW][C]86[/C][C]195[/C][C]182.831237849597[/C][C]12.1687621504026[/C][/ROW]
[ROW][C]87[/C][C]206[/C][C]192.968652518923[/C][C]13.0313474810766[/C][/ROW]
[ROW][C]88[/C][C]175[/C][C]204.115807856734[/C][C]-29.1158078567344[/C][/ROW]
[ROW][C]89[/C][C]185[/C][C]172.787020174032[/C][C]12.2129798259684[/C][/ROW]
[ROW][C]90[/C][C]174[/C][C]182.924934167544[/C][C]-8.92493416754445[/C][/ROW]
[ROW][C]91[/C][C]140[/C][C]171.824150138550[/C][C]-31.8241501385503[/C][/ROW]
[ROW][C]92[/C][C]130[/C][C]137.46477874039[/C][C]-7.46477874039005[/C][/ROW]
[ROW][C]93[/C][C]133[/C][C]127.380483387295[/C][C]5.61951661270537[/C][/ROW]
[ROW][C]94[/C][C]130[/C][C]130.443941281168[/C][C]-0.443941281167696[/C][/ROW]
[ROW][C]95[/C][C]131[/C][C]127.438928113551[/C][C]3.56107188644934[/C][/ROW]
[ROW][C]96[/C][C]136[/C][C]128.479141202579[/C][C]7.52085879742069[/C][/ROW]
[ROW][C]97[/C][C]149[/C][C]133.564069834754[/C][C]15.4359301652458[/C][/ROW]
[ROW][C]98[/C][C]155[/C][C]146.738378709657[/C][C]8.26162129034304[/C][/ROW]
[ROW][C]99[/C][C]161[/C][C]152.831672336706[/C][C]8.16832766329392[/C][/ROW]
[ROW][C]100[/C][C]131[/C][C]158.923912453731[/C][C]-27.9239124537307[/C][/ROW]
[ROW][C]101[/C][C]145[/C][C]128.608584144352[/C][C]16.3914158556479[/C][/ROW]
[ROW][C]102[/C][C]134[/C][C]142.793682756828[/C][C]-8.79368275682793[/C][/ROW]
[ROW][C]103[/C][C]93[/C][C]131.69438087277[/C][C]-38.6943808727701[/C][/ROW]
[ROW][C]104[/C][C]87[/C][C]90.2574280022409[/C][C]-3.25742800224086[/C][/ROW]
[ROW][C]105[/C][C]86[/C][C]84.2206437848941[/C][C]1.77935621510588[/C][/ROW]
[ROW][C]106[/C][C]80[/C][C]83.2407370074331[/C][C]-3.2407370074331[/C][/ROW]
[ROW][C]107[/C][C]79[/C][C]77.2041412716676[/C][C]1.79585872833236[/C][/ROW]
[ROW][C]108[/C][C]91[/C][C]76.2244208473763[/C][C]14.7755791526237[/C][/ROW]
[ROW][C]109[/C][C]108[/C][C]88.3912727669276[/C][C]19.6087272330724[/C][/ROW]
[ROW][C]110[/C][C]105[/C][C]105.612702583316[/C][C]-0.612702583315865[/C][/ROW]
[ROW][C]111[/C][C]112[/C][C]102.605783693634[/C][C]9.39421630636583[/C][/ROW]
[ROW][C]112[/C][C]78[/C][C]109.711867049637[/C][C]-31.7118670496371[/C][/ROW]
[ROW][C]113[/C][C]87[/C][C]75.3537635983184[/C][C]11.6462364016816[/C][/ROW]
[ROW][C]114[/C][C]74[/C][C]84.4852776918843[/C][C]-10.4852776918843[/C][/ROW]
[ROW][C]115[/C][C]32[/C][C]71.3668736217732[/C][C]-39.3668736217732[/C][/ROW]
[ROW][C]116[/C][C]25[/C][C]28.9223266864093[/C][C]-3.92232668640928[/C][/ROW]
[ROW][C]117[/C][C]26[/C][C]21.8780341595327[/C][C]4.1219658404673[/C][/ROW]
[ROW][C]118[/C][C]25[/C][C]22.9245810938831[/C][C]2.07541890611687[/C][/ROW]
[ROW][C]119[/C][C]22[/C][C]21.9480175781510[/C][C]0.0519824218490292[/C][/ROW]
[ROW][C]120[/C][C]36[/C][C]18.9486045850479[/C][C]17.0513954149521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78412&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
33883880
4386387-1
5406384.98870758852621.0112924114736
6405405.225975748028-0.225975748027679
7390404.223423936898-14.2234239368979
8380389.06280718124-9.06280718123986
9381378.9604662334442.03953376655602
10381379.983497487951.01650251204990
11382379.994976252582.00502374741995
12384381.017617805752.98238219424985
13394383.05129609265910.9487039073410
14393393.174933362283-0.174933362282616
15388392.172957942775-4.17295794277527
16381387.125835184624-6.12583518462367
17399380.056659733118.9433402669002
18396398.270575726077-2.27057572607691
19378395.244935450696-17.2449354506962
20368377.050198543752-9.05019854375234
21369366.9479999778792.05200002212098
22373367.9711720064735.02882799352744
23374372.0279596014051.97204039859486
24379373.0502286930285.94977130697151
25385378.11741595886.88258404119972
26385384.1951369297950.804863070205272
27395384.20422577476310.7957742252366
28387394.32613609949-7.32613609949016
29400386.24340635614413.7565936438564
30390399.398751472044-9.3987514720443
31365389.292616903084-24.2926169030844
32350364.018294677246-14.0182946772457
33365348.85999432559316.1400056744071
34374364.0422539108549.95774608914644
35367373.154700877041-6.15470087704125
36375366.0851994622418.91480053775888
37382374.1858690581187.81413094188196
38380381.274109440022-1.27410944002190
39378379.259721671963-1.25972167196289
40363377.245496376501-14.2454963765009
41375362.08463036977312.9153696302274
42366374.23047603797-8.23047603797005
43341365.137534115926-24.1375341159261
44326339.864963148732-13.8649631487325
45338324.70839427979213.2916057202085
46345336.8584885607288.14151143927177
47336343.950425857917-7.95042585791703
48342334.8606463777397.1393536222605
49347340.9412668964976.05873310350279
50360346.0096846037113.9903153962897
51360359.167669001810.832330998190173
52334359.177068025924-25.1770680259236
53347332.89275821407814.1072417859225
54336346.052062993081-10.0520629930809
55305334.938550961605-29.9385509616051
56289303.600472525225-14.6004725252251
57303287.43559798176215.5644020182379
58308301.6113576136926.38864238630833
59294306.683500792275-12.6835007922751
60299292.5402734824046.45972651759621
61306297.6132193722478.38678062775296
62313304.7079263500348.29207364996608
63321311.8015638576589.19843614234173
64287319.905436383491-32.9054363834907
65296285.53385465613210.4661453438681
66283294.652042675897-11.6520426758967
67248281.520463015493-33.5204630154932
68235246.141936154339-11.1419361543387
69241233.0161168266727.98388317332802
70244239.1062741206224.89372587937811
71237242.161536086891-5.16153608689055
72241235.1032498975625.89675010243815
73251239.16983842607511.8301615739248
74259249.3034294783669.69657052163356
75264257.4129271425796.58707285742105
76229262.487311079691-33.4873110796911
77237227.1091585838379.8908414161632
78228235.220850034928-7.22085003492765
79197226.139309225145-29.1393092251445
80182194.810256155319-12.8102561553195
81182179.6655974717322.33440252826787
82176179.691958505626-3.69195850562619
83172173.650267391037-1.65026739103743
84175169.6316318926165.36836810738353
85185172.69225371422612.3077462857735
86195182.83123784959712.1687621504026
87206192.96865251892313.0313474810766
88175204.115807856734-29.1158078567344
89185172.78702017403212.2129798259684
90174182.924934167544-8.92493416754445
91140171.824150138550-31.8241501385503
92130137.46477874039-7.46477874039005
93133127.3804833872955.61951661270537
94130130.443941281168-0.443941281167696
95131127.4389281135513.56107188644934
96136128.4791412025797.52085879742069
97149133.56406983475415.4359301652458
98155146.7383787096578.26162129034304
99161152.8316723367068.16832766329392
100131158.923912453731-27.9239124537307
101145128.60858414435216.3914158556479
102134142.793682756828-8.79368275682793
10393131.69438087277-38.6943808727701
1048790.2574280022409-3.25742800224086
1058684.22064378489411.77935621510588
1068083.2407370074331-3.2407370074331
1077977.20414127166761.79585872833236
1089176.224420847376314.7755791526237
10910888.391272766927619.6087272330724
110105105.612702583316-0.612702583315865
111112102.6057836936349.39421630636583
11278109.711867049637-31.7118670496371
1138775.353763598318411.6462364016816
1147484.4852776918843-10.4852776918843
1153271.3668736217732-39.3668736217732
1162528.9223266864093-3.92232668640928
1172621.87803415953274.1219658404673
1182522.92458109388312.07541890611687
1192221.94801757815100.0519824218490292
1203618.948604585047917.0513954149521







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12133.14115595827165.7939052762246460.4884066403185
12230.2823119165431-8.6115200715901869.1761439046764
12327.4234678748147-20.480236321314075.3271720709434
12424.5646238330862-31.060613083090780.1898607492632
12521.7057797913578-40.833225802590784.2447853853062
12618.8469357496294-50.043094929376987.7369664286356
12715.9880917079009-58.83493306356490.8111164793658
12813.1292476661725-67.302487879054693.5609832113995
12910.2704036244440-75.510504523579296.0513117724673
1307.4115595827156-83.5058542099498.3289733753712
1314.55271554098716-91.3237184879251100.429149569899
1321.69387149925872-98.9912731443912102.379016142909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 33.1411559582716 & 5.79390527622464 & 60.4884066403185 \tabularnewline
122 & 30.2823119165431 & -8.61152007159018 & 69.1761439046764 \tabularnewline
123 & 27.4234678748147 & -20.4802363213140 & 75.3271720709434 \tabularnewline
124 & 24.5646238330862 & -31.0606130830907 & 80.1898607492632 \tabularnewline
125 & 21.7057797913578 & -40.8332258025907 & 84.2447853853062 \tabularnewline
126 & 18.8469357496294 & -50.0430949293769 & 87.7369664286356 \tabularnewline
127 & 15.9880917079009 & -58.834933063564 & 90.8111164793658 \tabularnewline
128 & 13.1292476661725 & -67.3024878790546 & 93.5609832113995 \tabularnewline
129 & 10.2704036244440 & -75.5105045235792 & 96.0513117724673 \tabularnewline
130 & 7.4115595827156 & -83.50585420994 & 98.3289733753712 \tabularnewline
131 & 4.55271554098716 & -91.3237184879251 & 100.429149569899 \tabularnewline
132 & 1.69387149925872 & -98.9912731443912 & 102.379016142909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78412&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]33.1411559582716[/C][C]5.79390527622464[/C][C]60.4884066403185[/C][/ROW]
[ROW][C]122[/C][C]30.2823119165431[/C][C]-8.61152007159018[/C][C]69.1761439046764[/C][/ROW]
[ROW][C]123[/C][C]27.4234678748147[/C][C]-20.4802363213140[/C][C]75.3271720709434[/C][/ROW]
[ROW][C]124[/C][C]24.5646238330862[/C][C]-31.0606130830907[/C][C]80.1898607492632[/C][/ROW]
[ROW][C]125[/C][C]21.7057797913578[/C][C]-40.8332258025907[/C][C]84.2447853853062[/C][/ROW]
[ROW][C]126[/C][C]18.8469357496294[/C][C]-50.0430949293769[/C][C]87.7369664286356[/C][/ROW]
[ROW][C]127[/C][C]15.9880917079009[/C][C]-58.834933063564[/C][C]90.8111164793658[/C][/ROW]
[ROW][C]128[/C][C]13.1292476661725[/C][C]-67.3024878790546[/C][C]93.5609832113995[/C][/ROW]
[ROW][C]129[/C][C]10.2704036244440[/C][C]-75.5105045235792[/C][C]96.0513117724673[/C][/ROW]
[ROW][C]130[/C][C]7.4115595827156[/C][C]-83.50585420994[/C][C]98.3289733753712[/C][/ROW]
[ROW][C]131[/C][C]4.55271554098716[/C][C]-91.3237184879251[/C][C]100.429149569899[/C][/ROW]
[ROW][C]132[/C][C]1.69387149925872[/C][C]-98.9912731443912[/C][C]102.379016142909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78412&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78412&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
12133.14115595827165.7939052762246460.4884066403185
12230.2823119165431-8.6115200715901869.1761439046764
12327.4234678748147-20.480236321314075.3271720709434
12424.5646238330862-31.060613083090780.1898607492632
12521.7057797913578-40.833225802590784.2447853853062
12618.8469357496294-50.043094929376987.7369664286356
12715.9880917079009-58.83493306356490.8111164793658
12813.1292476661725-67.302487879054693.5609832113995
12910.2704036244440-75.510504523579296.0513117724673
1307.4115595827156-83.5058542099498.3289733753712
1314.55271554098716-91.3237184879251100.429149569899
1321.69387149925872-98.9912731443912102.379016142909



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