Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 03 Aug 2010 16:11:26 +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/03/t1280852115u744kx1qt87wzyk.htm/, Retrieved Thu, 02 May 2024 14:41:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78269, Retrieved Thu, 02 May 2024 14:41:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLisa Bruggeman
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [Tijdreeks 1 - Stap 8] [2010-07-15 13:59:40] [e35b30db8ce3563ce7b9c1c6d8c0e4ae]
- RM D    [Exponential Smoothing] [TIJDREEKS A - STA...] [2010-08-03 16:11:26] [0e6aef37627b8cf9d1bd74110cef2cca] [Current]
Feedback Forum

Post a new message
Dataseries X:
95
94
93
91
111
110
95
85
86
86
87
89
93
96
99
92
109
110
97
88
93
93
89
89
91
97
99
85
101
105
88
80
87
84
87
87
85
96
102
93
111
117
101
88
98
89
93
93
95
105
109
94
113
125
106
95
109
100
94
94
94
103
103
80
106
117
99
95
116
118
100
100
105
121
131
108
136
149
131
137
164
169
154
160
166
186
197
166
191
207
187
191
222
230
210
224
234
251
258
227
254
281
261
264
286
293
276
292
299
319
329
293
318
346
327
329
353
355
332
346




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78269&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78269&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.222642629632828
beta0.178363459675705
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.222642629632828 \tabularnewline
beta & 0.178363459675705 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78269&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]0.222642629632828[/C][/ROW]
[ROW][C]beta[/C][C]0.178363459675705[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78269&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78269&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
alpha0.222642629632828
beta0.178363459675705
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
393930
49192-1
511190.737646060674620.2623539393254
611095.013843126970314.9861568730297
79598.7104537206517-3.71045372065174
88598.0970547897341-13.0970547897341
98694.8736971146655-8.87369711466548
108692.2382527640152-6.23825276401523
118789.9418414863921-2.94184148639215
128988.26252750563770.737472494362294
139387.43167166341675.56832833658333
149687.8974958803298.10250411967098
159989.24929670792179.75070329207828
169291.35527013157030.644729868429721
1710991.459468754284417.5405312457156
1811096.021950493862813.9780495061372
1997100.346358583759-3.34635858375943
2088100.680726617627-12.6807266176270
219398.4332981446338-5.43329814463382
229397.5836928196699-4.58369281966986
238996.7412214133082-7.74122141330822
248994.8883354967752-5.88833549677517
259193.2141474586223-2.21414745862225
269792.27006361161474.72993638838527
279993.05986082144135.9401391785587
288594.354991469398-9.35499146939802
2910191.8732750459039.12672495409697
3010593.868810768194611.1311892318054
318896.7526597911115-8.75265979111145
328094.8619367967451-14.8619367967451
338791.0208413299216-4.02084132992162
348489.4337629906549-5.43376299065487
358787.3163262124592-0.316326212459174
368786.32568728735390.674312712646142
378585.5823846585122-0.582384658512183
389684.536160364768811.4638396352312
3910286.627183210952315.3728167890477
409390.19898569819382.80101430180625
4111191.083000966843719.9169990331563
4211796.568694201589820.4313057984102
43101102.980247958975-1.98024795897503
4488104.323396213692-16.3233962136915
4598101.824924781487-3.82492478148735
4689101.957253122791-12.9572531227913
479399.5417863759923-6.54178637599232
489398.2948931113027-5.29489311130268
499597.1153443018028-2.11534430180281
5010596.55969550762058.44030449237947
5110998.689359664052410.3106403359476
5294101.644889342503-7.6448893425027
53113100.29916410864712.7008358913533
54125103.98763147008021.0123685299201
55106110.361028988510-4.36102898850956
5695110.912044387976-15.9120443879758
57109108.2594232214420.740576778557809
58100109.343794695509-9.34379469550936
5994107.811900861538-13.8119008615384
6094104.736727448728-10.7367274487280
6194101.919849222321-7.91984922232103
6210399.41562058641043.58437941358956
6310399.61506406684513.38493593315488
648099.9045231654639-19.9045231654639
6510694.218321163932511.7816788360675
6611796.05468439605720.945315603943
6799100.763029729739-1.76302972973896
6895100.345517124125-5.34551712412465
6911698.918112618414617.0818873815854
70118103.16234854763914.8376514523606
71100107.496144460001-7.49614446000074
72100106.559803606599-6.55980360659943
73105105.571433750488-0.571433750487699
74121105.89363792372015.1063620762798
75131110.30628120941120.6937187905894
76108116.784682962256-8.78468296225641
77136116.3510845658119.6489154341899
78149123.02830145220325.9716985477967
79131132.144609561883-1.14460956188259
80137135.17821758331.82178241670010
81164138.94461628109325.0553837189073
82169148.87878717097820.1212128290218
83154158.513440992926-4.51344099292609
84160162.484136054812-2.48413605481167
85166166.807992608255-0.807992608254693
86186171.47294370158514.5270562984147
87197180.12901884063316.8709811593669
88166189.976920332023-23.9769203320228
89191189.7781827116071.22181728839314
90207195.23827826315511.7617217368449
91187203.512079231596-16.5120792315956
92191204.835210510672-13.8352105106725
93222206.20491255170615.7950874482942
94230214.79882565640915.2011743435912
95210223.864166927757-13.8641669277569
96224225.907759960778-1.90775996077838
97234230.5375992352673.46240076473342
98251236.50056168428214.4994383157181
99258245.49663088232912.5033691176709
100227254.544815148427-27.5448151484268
101254253.5827256727160.417274327284417
102281258.86275983794322.1372401620573
103261269.857683111974-8.85768311197404
104264273.600064965789-9.60006496578859
105286276.7959298185539.20407018144738
106293284.5439024498768.45609755012367
107276292.461147196273-16.4611471962726
108292294.177057334920-2.17705733491965
109299298.9867610041640.0132389958356498
110319304.28464374602714.7153562539728
111329313.44021060485015.5597893951496
112293323.401683894197-30.401683894197
113318321.922883224305-3.92288322430511
114346326.18360953447319.8163904655268
115327336.516644983285-9.516644983285
116329339.940977848495-10.9409778484946
117353342.6137129394410.3862870605601
118355350.4472594346314.55274056536859
119332357.162805088589-25.1628050885895
120346356.263155571568-10.2631555715683

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 93 & 93 & 0 \tabularnewline
4 & 91 & 92 & -1 \tabularnewline
5 & 111 & 90.7376460606746 & 20.2623539393254 \tabularnewline
6 & 110 & 95.0138431269703 & 14.9861568730297 \tabularnewline
7 & 95 & 98.7104537206517 & -3.71045372065174 \tabularnewline
8 & 85 & 98.0970547897341 & -13.0970547897341 \tabularnewline
9 & 86 & 94.8736971146655 & -8.87369711466548 \tabularnewline
10 & 86 & 92.2382527640152 & -6.23825276401523 \tabularnewline
11 & 87 & 89.9418414863921 & -2.94184148639215 \tabularnewline
12 & 89 & 88.2625275056377 & 0.737472494362294 \tabularnewline
13 & 93 & 87.4316716634167 & 5.56832833658333 \tabularnewline
14 & 96 & 87.897495880329 & 8.10250411967098 \tabularnewline
15 & 99 & 89.2492967079217 & 9.75070329207828 \tabularnewline
16 & 92 & 91.3552701315703 & 0.644729868429721 \tabularnewline
17 & 109 & 91.4594687542844 & 17.5405312457156 \tabularnewline
18 & 110 & 96.0219504938628 & 13.9780495061372 \tabularnewline
19 & 97 & 100.346358583759 & -3.34635858375943 \tabularnewline
20 & 88 & 100.680726617627 & -12.6807266176270 \tabularnewline
21 & 93 & 98.4332981446338 & -5.43329814463382 \tabularnewline
22 & 93 & 97.5836928196699 & -4.58369281966986 \tabularnewline
23 & 89 & 96.7412214133082 & -7.74122141330822 \tabularnewline
24 & 89 & 94.8883354967752 & -5.88833549677517 \tabularnewline
25 & 91 & 93.2141474586223 & -2.21414745862225 \tabularnewline
26 & 97 & 92.2700636116147 & 4.72993638838527 \tabularnewline
27 & 99 & 93.0598608214413 & 5.9401391785587 \tabularnewline
28 & 85 & 94.354991469398 & -9.35499146939802 \tabularnewline
29 & 101 & 91.873275045903 & 9.12672495409697 \tabularnewline
30 & 105 & 93.8688107681946 & 11.1311892318054 \tabularnewline
31 & 88 & 96.7526597911115 & -8.75265979111145 \tabularnewline
32 & 80 & 94.8619367967451 & -14.8619367967451 \tabularnewline
33 & 87 & 91.0208413299216 & -4.02084132992162 \tabularnewline
34 & 84 & 89.4337629906549 & -5.43376299065487 \tabularnewline
35 & 87 & 87.3163262124592 & -0.316326212459174 \tabularnewline
36 & 87 & 86.3256872873539 & 0.674312712646142 \tabularnewline
37 & 85 & 85.5823846585122 & -0.582384658512183 \tabularnewline
38 & 96 & 84.5361603647688 & 11.4638396352312 \tabularnewline
39 & 102 & 86.6271832109523 & 15.3728167890477 \tabularnewline
40 & 93 & 90.1989856981938 & 2.80101430180625 \tabularnewline
41 & 111 & 91.0830009668437 & 19.9169990331563 \tabularnewline
42 & 117 & 96.5686942015898 & 20.4313057984102 \tabularnewline
43 & 101 & 102.980247958975 & -1.98024795897503 \tabularnewline
44 & 88 & 104.323396213692 & -16.3233962136915 \tabularnewline
45 & 98 & 101.824924781487 & -3.82492478148735 \tabularnewline
46 & 89 & 101.957253122791 & -12.9572531227913 \tabularnewline
47 & 93 & 99.5417863759923 & -6.54178637599232 \tabularnewline
48 & 93 & 98.2948931113027 & -5.29489311130268 \tabularnewline
49 & 95 & 97.1153443018028 & -2.11534430180281 \tabularnewline
50 & 105 & 96.5596955076205 & 8.44030449237947 \tabularnewline
51 & 109 & 98.6893596640524 & 10.3106403359476 \tabularnewline
52 & 94 & 101.644889342503 & -7.6448893425027 \tabularnewline
53 & 113 & 100.299164108647 & 12.7008358913533 \tabularnewline
54 & 125 & 103.987631470080 & 21.0123685299201 \tabularnewline
55 & 106 & 110.361028988510 & -4.36102898850956 \tabularnewline
56 & 95 & 110.912044387976 & -15.9120443879758 \tabularnewline
57 & 109 & 108.259423221442 & 0.740576778557809 \tabularnewline
58 & 100 & 109.343794695509 & -9.34379469550936 \tabularnewline
59 & 94 & 107.811900861538 & -13.8119008615384 \tabularnewline
60 & 94 & 104.736727448728 & -10.7367274487280 \tabularnewline
61 & 94 & 101.919849222321 & -7.91984922232103 \tabularnewline
62 & 103 & 99.4156205864104 & 3.58437941358956 \tabularnewline
63 & 103 & 99.6150640668451 & 3.38493593315488 \tabularnewline
64 & 80 & 99.9045231654639 & -19.9045231654639 \tabularnewline
65 & 106 & 94.2183211639325 & 11.7816788360675 \tabularnewline
66 & 117 & 96.054684396057 & 20.945315603943 \tabularnewline
67 & 99 & 100.763029729739 & -1.76302972973896 \tabularnewline
68 & 95 & 100.345517124125 & -5.34551712412465 \tabularnewline
69 & 116 & 98.9181126184146 & 17.0818873815854 \tabularnewline
70 & 118 & 103.162348547639 & 14.8376514523606 \tabularnewline
71 & 100 & 107.496144460001 & -7.49614446000074 \tabularnewline
72 & 100 & 106.559803606599 & -6.55980360659943 \tabularnewline
73 & 105 & 105.571433750488 & -0.571433750487699 \tabularnewline
74 & 121 & 105.893637923720 & 15.1063620762798 \tabularnewline
75 & 131 & 110.306281209411 & 20.6937187905894 \tabularnewline
76 & 108 & 116.784682962256 & -8.78468296225641 \tabularnewline
77 & 136 & 116.35108456581 & 19.6489154341899 \tabularnewline
78 & 149 & 123.028301452203 & 25.9716985477967 \tabularnewline
79 & 131 & 132.144609561883 & -1.14460956188259 \tabularnewline
80 & 137 & 135.1782175833 & 1.82178241670010 \tabularnewline
81 & 164 & 138.944616281093 & 25.0553837189073 \tabularnewline
82 & 169 & 148.878787170978 & 20.1212128290218 \tabularnewline
83 & 154 & 158.513440992926 & -4.51344099292609 \tabularnewline
84 & 160 & 162.484136054812 & -2.48413605481167 \tabularnewline
85 & 166 & 166.807992608255 & -0.807992608254693 \tabularnewline
86 & 186 & 171.472943701585 & 14.5270562984147 \tabularnewline
87 & 197 & 180.129018840633 & 16.8709811593669 \tabularnewline
88 & 166 & 189.976920332023 & -23.9769203320228 \tabularnewline
89 & 191 & 189.778182711607 & 1.22181728839314 \tabularnewline
90 & 207 & 195.238278263155 & 11.7617217368449 \tabularnewline
91 & 187 & 203.512079231596 & -16.5120792315956 \tabularnewline
92 & 191 & 204.835210510672 & -13.8352105106725 \tabularnewline
93 & 222 & 206.204912551706 & 15.7950874482942 \tabularnewline
94 & 230 & 214.798825656409 & 15.2011743435912 \tabularnewline
95 & 210 & 223.864166927757 & -13.8641669277569 \tabularnewline
96 & 224 & 225.907759960778 & -1.90775996077838 \tabularnewline
97 & 234 & 230.537599235267 & 3.46240076473342 \tabularnewline
98 & 251 & 236.500561684282 & 14.4994383157181 \tabularnewline
99 & 258 & 245.496630882329 & 12.5033691176709 \tabularnewline
100 & 227 & 254.544815148427 & -27.5448151484268 \tabularnewline
101 & 254 & 253.582725672716 & 0.417274327284417 \tabularnewline
102 & 281 & 258.862759837943 & 22.1372401620573 \tabularnewline
103 & 261 & 269.857683111974 & -8.85768311197404 \tabularnewline
104 & 264 & 273.600064965789 & -9.60006496578859 \tabularnewline
105 & 286 & 276.795929818553 & 9.20407018144738 \tabularnewline
106 & 293 & 284.543902449876 & 8.45609755012367 \tabularnewline
107 & 276 & 292.461147196273 & -16.4611471962726 \tabularnewline
108 & 292 & 294.177057334920 & -2.17705733491965 \tabularnewline
109 & 299 & 298.986761004164 & 0.0132389958356498 \tabularnewline
110 & 319 & 304.284643746027 & 14.7153562539728 \tabularnewline
111 & 329 & 313.440210604850 & 15.5597893951496 \tabularnewline
112 & 293 & 323.401683894197 & -30.401683894197 \tabularnewline
113 & 318 & 321.922883224305 & -3.92288322430511 \tabularnewline
114 & 346 & 326.183609534473 & 19.8163904655268 \tabularnewline
115 & 327 & 336.516644983285 & -9.516644983285 \tabularnewline
116 & 329 & 339.940977848495 & -10.9409778484946 \tabularnewline
117 & 353 & 342.61371293944 & 10.3862870605601 \tabularnewline
118 & 355 & 350.447259434631 & 4.55274056536859 \tabularnewline
119 & 332 & 357.162805088589 & -25.1628050885895 \tabularnewline
120 & 346 & 356.263155571568 & -10.2631555715683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78269&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]93[/C][C]93[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]91[/C][C]92[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]111[/C][C]90.7376460606746[/C][C]20.2623539393254[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]95.0138431269703[/C][C]14.9861568730297[/C][/ROW]
[ROW][C]7[/C][C]95[/C][C]98.7104537206517[/C][C]-3.71045372065174[/C][/ROW]
[ROW][C]8[/C][C]85[/C][C]98.0970547897341[/C][C]-13.0970547897341[/C][/ROW]
[ROW][C]9[/C][C]86[/C][C]94.8736971146655[/C][C]-8.87369711466548[/C][/ROW]
[ROW][C]10[/C][C]86[/C][C]92.2382527640152[/C][C]-6.23825276401523[/C][/ROW]
[ROW][C]11[/C][C]87[/C][C]89.9418414863921[/C][C]-2.94184148639215[/C][/ROW]
[ROW][C]12[/C][C]89[/C][C]88.2625275056377[/C][C]0.737472494362294[/C][/ROW]
[ROW][C]13[/C][C]93[/C][C]87.4316716634167[/C][C]5.56832833658333[/C][/ROW]
[ROW][C]14[/C][C]96[/C][C]87.897495880329[/C][C]8.10250411967098[/C][/ROW]
[ROW][C]15[/C][C]99[/C][C]89.2492967079217[/C][C]9.75070329207828[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]91.3552701315703[/C][C]0.644729868429721[/C][/ROW]
[ROW][C]17[/C][C]109[/C][C]91.4594687542844[/C][C]17.5405312457156[/C][/ROW]
[ROW][C]18[/C][C]110[/C][C]96.0219504938628[/C][C]13.9780495061372[/C][/ROW]
[ROW][C]19[/C][C]97[/C][C]100.346358583759[/C][C]-3.34635858375943[/C][/ROW]
[ROW][C]20[/C][C]88[/C][C]100.680726617627[/C][C]-12.6807266176270[/C][/ROW]
[ROW][C]21[/C][C]93[/C][C]98.4332981446338[/C][C]-5.43329814463382[/C][/ROW]
[ROW][C]22[/C][C]93[/C][C]97.5836928196699[/C][C]-4.58369281966986[/C][/ROW]
[ROW][C]23[/C][C]89[/C][C]96.7412214133082[/C][C]-7.74122141330822[/C][/ROW]
[ROW][C]24[/C][C]89[/C][C]94.8883354967752[/C][C]-5.88833549677517[/C][/ROW]
[ROW][C]25[/C][C]91[/C][C]93.2141474586223[/C][C]-2.21414745862225[/C][/ROW]
[ROW][C]26[/C][C]97[/C][C]92.2700636116147[/C][C]4.72993638838527[/C][/ROW]
[ROW][C]27[/C][C]99[/C][C]93.0598608214413[/C][C]5.9401391785587[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]94.354991469398[/C][C]-9.35499146939802[/C][/ROW]
[ROW][C]29[/C][C]101[/C][C]91.873275045903[/C][C]9.12672495409697[/C][/ROW]
[ROW][C]30[/C][C]105[/C][C]93.8688107681946[/C][C]11.1311892318054[/C][/ROW]
[ROW][C]31[/C][C]88[/C][C]96.7526597911115[/C][C]-8.75265979111145[/C][/ROW]
[ROW][C]32[/C][C]80[/C][C]94.8619367967451[/C][C]-14.8619367967451[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]91.0208413299216[/C][C]-4.02084132992162[/C][/ROW]
[ROW][C]34[/C][C]84[/C][C]89.4337629906549[/C][C]-5.43376299065487[/C][/ROW]
[ROW][C]35[/C][C]87[/C][C]87.3163262124592[/C][C]-0.316326212459174[/C][/ROW]
[ROW][C]36[/C][C]87[/C][C]86.3256872873539[/C][C]0.674312712646142[/C][/ROW]
[ROW][C]37[/C][C]85[/C][C]85.5823846585122[/C][C]-0.582384658512183[/C][/ROW]
[ROW][C]38[/C][C]96[/C][C]84.5361603647688[/C][C]11.4638396352312[/C][/ROW]
[ROW][C]39[/C][C]102[/C][C]86.6271832109523[/C][C]15.3728167890477[/C][/ROW]
[ROW][C]40[/C][C]93[/C][C]90.1989856981938[/C][C]2.80101430180625[/C][/ROW]
[ROW][C]41[/C][C]111[/C][C]91.0830009668437[/C][C]19.9169990331563[/C][/ROW]
[ROW][C]42[/C][C]117[/C][C]96.5686942015898[/C][C]20.4313057984102[/C][/ROW]
[ROW][C]43[/C][C]101[/C][C]102.980247958975[/C][C]-1.98024795897503[/C][/ROW]
[ROW][C]44[/C][C]88[/C][C]104.323396213692[/C][C]-16.3233962136915[/C][/ROW]
[ROW][C]45[/C][C]98[/C][C]101.824924781487[/C][C]-3.82492478148735[/C][/ROW]
[ROW][C]46[/C][C]89[/C][C]101.957253122791[/C][C]-12.9572531227913[/C][/ROW]
[ROW][C]47[/C][C]93[/C][C]99.5417863759923[/C][C]-6.54178637599232[/C][/ROW]
[ROW][C]48[/C][C]93[/C][C]98.2948931113027[/C][C]-5.29489311130268[/C][/ROW]
[ROW][C]49[/C][C]95[/C][C]97.1153443018028[/C][C]-2.11534430180281[/C][/ROW]
[ROW][C]50[/C][C]105[/C][C]96.5596955076205[/C][C]8.44030449237947[/C][/ROW]
[ROW][C]51[/C][C]109[/C][C]98.6893596640524[/C][C]10.3106403359476[/C][/ROW]
[ROW][C]52[/C][C]94[/C][C]101.644889342503[/C][C]-7.6448893425027[/C][/ROW]
[ROW][C]53[/C][C]113[/C][C]100.299164108647[/C][C]12.7008358913533[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]103.987631470080[/C][C]21.0123685299201[/C][/ROW]
[ROW][C]55[/C][C]106[/C][C]110.361028988510[/C][C]-4.36102898850956[/C][/ROW]
[ROW][C]56[/C][C]95[/C][C]110.912044387976[/C][C]-15.9120443879758[/C][/ROW]
[ROW][C]57[/C][C]109[/C][C]108.259423221442[/C][C]0.740576778557809[/C][/ROW]
[ROW][C]58[/C][C]100[/C][C]109.343794695509[/C][C]-9.34379469550936[/C][/ROW]
[ROW][C]59[/C][C]94[/C][C]107.811900861538[/C][C]-13.8119008615384[/C][/ROW]
[ROW][C]60[/C][C]94[/C][C]104.736727448728[/C][C]-10.7367274487280[/C][/ROW]
[ROW][C]61[/C][C]94[/C][C]101.919849222321[/C][C]-7.91984922232103[/C][/ROW]
[ROW][C]62[/C][C]103[/C][C]99.4156205864104[/C][C]3.58437941358956[/C][/ROW]
[ROW][C]63[/C][C]103[/C][C]99.6150640668451[/C][C]3.38493593315488[/C][/ROW]
[ROW][C]64[/C][C]80[/C][C]99.9045231654639[/C][C]-19.9045231654639[/C][/ROW]
[ROW][C]65[/C][C]106[/C][C]94.2183211639325[/C][C]11.7816788360675[/C][/ROW]
[ROW][C]66[/C][C]117[/C][C]96.054684396057[/C][C]20.945315603943[/C][/ROW]
[ROW][C]67[/C][C]99[/C][C]100.763029729739[/C][C]-1.76302972973896[/C][/ROW]
[ROW][C]68[/C][C]95[/C][C]100.345517124125[/C][C]-5.34551712412465[/C][/ROW]
[ROW][C]69[/C][C]116[/C][C]98.9181126184146[/C][C]17.0818873815854[/C][/ROW]
[ROW][C]70[/C][C]118[/C][C]103.162348547639[/C][C]14.8376514523606[/C][/ROW]
[ROW][C]71[/C][C]100[/C][C]107.496144460001[/C][C]-7.49614446000074[/C][/ROW]
[ROW][C]72[/C][C]100[/C][C]106.559803606599[/C][C]-6.55980360659943[/C][/ROW]
[ROW][C]73[/C][C]105[/C][C]105.571433750488[/C][C]-0.571433750487699[/C][/ROW]
[ROW][C]74[/C][C]121[/C][C]105.893637923720[/C][C]15.1063620762798[/C][/ROW]
[ROW][C]75[/C][C]131[/C][C]110.306281209411[/C][C]20.6937187905894[/C][/ROW]
[ROW][C]76[/C][C]108[/C][C]116.784682962256[/C][C]-8.78468296225641[/C][/ROW]
[ROW][C]77[/C][C]136[/C][C]116.35108456581[/C][C]19.6489154341899[/C][/ROW]
[ROW][C]78[/C][C]149[/C][C]123.028301452203[/C][C]25.9716985477967[/C][/ROW]
[ROW][C]79[/C][C]131[/C][C]132.144609561883[/C][C]-1.14460956188259[/C][/ROW]
[ROW][C]80[/C][C]137[/C][C]135.1782175833[/C][C]1.82178241670010[/C][/ROW]
[ROW][C]81[/C][C]164[/C][C]138.944616281093[/C][C]25.0553837189073[/C][/ROW]
[ROW][C]82[/C][C]169[/C][C]148.878787170978[/C][C]20.1212128290218[/C][/ROW]
[ROW][C]83[/C][C]154[/C][C]158.513440992926[/C][C]-4.51344099292609[/C][/ROW]
[ROW][C]84[/C][C]160[/C][C]162.484136054812[/C][C]-2.48413605481167[/C][/ROW]
[ROW][C]85[/C][C]166[/C][C]166.807992608255[/C][C]-0.807992608254693[/C][/ROW]
[ROW][C]86[/C][C]186[/C][C]171.472943701585[/C][C]14.5270562984147[/C][/ROW]
[ROW][C]87[/C][C]197[/C][C]180.129018840633[/C][C]16.8709811593669[/C][/ROW]
[ROW][C]88[/C][C]166[/C][C]189.976920332023[/C][C]-23.9769203320228[/C][/ROW]
[ROW][C]89[/C][C]191[/C][C]189.778182711607[/C][C]1.22181728839314[/C][/ROW]
[ROW][C]90[/C][C]207[/C][C]195.238278263155[/C][C]11.7617217368449[/C][/ROW]
[ROW][C]91[/C][C]187[/C][C]203.512079231596[/C][C]-16.5120792315956[/C][/ROW]
[ROW][C]92[/C][C]191[/C][C]204.835210510672[/C][C]-13.8352105106725[/C][/ROW]
[ROW][C]93[/C][C]222[/C][C]206.204912551706[/C][C]15.7950874482942[/C][/ROW]
[ROW][C]94[/C][C]230[/C][C]214.798825656409[/C][C]15.2011743435912[/C][/ROW]
[ROW][C]95[/C][C]210[/C][C]223.864166927757[/C][C]-13.8641669277569[/C][/ROW]
[ROW][C]96[/C][C]224[/C][C]225.907759960778[/C][C]-1.90775996077838[/C][/ROW]
[ROW][C]97[/C][C]234[/C][C]230.537599235267[/C][C]3.46240076473342[/C][/ROW]
[ROW][C]98[/C][C]251[/C][C]236.500561684282[/C][C]14.4994383157181[/C][/ROW]
[ROW][C]99[/C][C]258[/C][C]245.496630882329[/C][C]12.5033691176709[/C][/ROW]
[ROW][C]100[/C][C]227[/C][C]254.544815148427[/C][C]-27.5448151484268[/C][/ROW]
[ROW][C]101[/C][C]254[/C][C]253.582725672716[/C][C]0.417274327284417[/C][/ROW]
[ROW][C]102[/C][C]281[/C][C]258.862759837943[/C][C]22.1372401620573[/C][/ROW]
[ROW][C]103[/C][C]261[/C][C]269.857683111974[/C][C]-8.85768311197404[/C][/ROW]
[ROW][C]104[/C][C]264[/C][C]273.600064965789[/C][C]-9.60006496578859[/C][/ROW]
[ROW][C]105[/C][C]286[/C][C]276.795929818553[/C][C]9.20407018144738[/C][/ROW]
[ROW][C]106[/C][C]293[/C][C]284.543902449876[/C][C]8.45609755012367[/C][/ROW]
[ROW][C]107[/C][C]276[/C][C]292.461147196273[/C][C]-16.4611471962726[/C][/ROW]
[ROW][C]108[/C][C]292[/C][C]294.177057334920[/C][C]-2.17705733491965[/C][/ROW]
[ROW][C]109[/C][C]299[/C][C]298.986761004164[/C][C]0.0132389958356498[/C][/ROW]
[ROW][C]110[/C][C]319[/C][C]304.284643746027[/C][C]14.7153562539728[/C][/ROW]
[ROW][C]111[/C][C]329[/C][C]313.440210604850[/C][C]15.5597893951496[/C][/ROW]
[ROW][C]112[/C][C]293[/C][C]323.401683894197[/C][C]-30.401683894197[/C][/ROW]
[ROW][C]113[/C][C]318[/C][C]321.922883224305[/C][C]-3.92288322430511[/C][/ROW]
[ROW][C]114[/C][C]346[/C][C]326.183609534473[/C][C]19.8163904655268[/C][/ROW]
[ROW][C]115[/C][C]327[/C][C]336.516644983285[/C][C]-9.516644983285[/C][/ROW]
[ROW][C]116[/C][C]329[/C][C]339.940977848495[/C][C]-10.9409778484946[/C][/ROW]
[ROW][C]117[/C][C]353[/C][C]342.61371293944[/C][C]10.3862870605601[/C][/ROW]
[ROW][C]118[/C][C]355[/C][C]350.447259434631[/C][C]4.55274056536859[/C][/ROW]
[ROW][C]119[/C][C]332[/C][C]357.162805088589[/C][C]-25.1628050885895[/C][/ROW]
[ROW][C]120[/C][C]346[/C][C]356.263155571568[/C][C]-10.2631555715683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78269&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78269&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
393930
49192-1
511190.737646060674620.2623539393254
611095.013843126970314.9861568730297
79598.7104537206517-3.71045372065174
88598.0970547897341-13.0970547897341
98694.8736971146655-8.87369711466548
108692.2382527640152-6.23825276401523
118789.9418414863921-2.94184148639215
128988.26252750563770.737472494362294
139387.43167166341675.56832833658333
149687.8974958803298.10250411967098
159989.24929670792179.75070329207828
169291.35527013157030.644729868429721
1710991.459468754284417.5405312457156
1811096.021950493862813.9780495061372
1997100.346358583759-3.34635858375943
2088100.680726617627-12.6807266176270
219398.4332981446338-5.43329814463382
229397.5836928196699-4.58369281966986
238996.7412214133082-7.74122141330822
248994.8883354967752-5.88833549677517
259193.2141474586223-2.21414745862225
269792.27006361161474.72993638838527
279993.05986082144135.9401391785587
288594.354991469398-9.35499146939802
2910191.8732750459039.12672495409697
3010593.868810768194611.1311892318054
318896.7526597911115-8.75265979111145
328094.8619367967451-14.8619367967451
338791.0208413299216-4.02084132992162
348489.4337629906549-5.43376299065487
358787.3163262124592-0.316326212459174
368786.32568728735390.674312712646142
378585.5823846585122-0.582384658512183
389684.536160364768811.4638396352312
3910286.627183210952315.3728167890477
409390.19898569819382.80101430180625
4111191.083000966843719.9169990331563
4211796.568694201589820.4313057984102
43101102.980247958975-1.98024795897503
4488104.323396213692-16.3233962136915
4598101.824924781487-3.82492478148735
4689101.957253122791-12.9572531227913
479399.5417863759923-6.54178637599232
489398.2948931113027-5.29489311130268
499597.1153443018028-2.11534430180281
5010596.55969550762058.44030449237947
5110998.689359664052410.3106403359476
5294101.644889342503-7.6448893425027
53113100.29916410864712.7008358913533
54125103.98763147008021.0123685299201
55106110.361028988510-4.36102898850956
5695110.912044387976-15.9120443879758
57109108.2594232214420.740576778557809
58100109.343794695509-9.34379469550936
5994107.811900861538-13.8119008615384
6094104.736727448728-10.7367274487280
6194101.919849222321-7.91984922232103
6210399.41562058641043.58437941358956
6310399.61506406684513.38493593315488
648099.9045231654639-19.9045231654639
6510694.218321163932511.7816788360675
6611796.05468439605720.945315603943
6799100.763029729739-1.76302972973896
6895100.345517124125-5.34551712412465
6911698.918112618414617.0818873815854
70118103.16234854763914.8376514523606
71100107.496144460001-7.49614446000074
72100106.559803606599-6.55980360659943
73105105.571433750488-0.571433750487699
74121105.89363792372015.1063620762798
75131110.30628120941120.6937187905894
76108116.784682962256-8.78468296225641
77136116.3510845658119.6489154341899
78149123.02830145220325.9716985477967
79131132.144609561883-1.14460956188259
80137135.17821758331.82178241670010
81164138.94461628109325.0553837189073
82169148.87878717097820.1212128290218
83154158.513440992926-4.51344099292609
84160162.484136054812-2.48413605481167
85166166.807992608255-0.807992608254693
86186171.47294370158514.5270562984147
87197180.12901884063316.8709811593669
88166189.976920332023-23.9769203320228
89191189.7781827116071.22181728839314
90207195.23827826315511.7617217368449
91187203.512079231596-16.5120792315956
92191204.835210510672-13.8352105106725
93222206.20491255170615.7950874482942
94230214.79882565640915.2011743435912
95210223.864166927757-13.8641669277569
96224225.907759960778-1.90775996077838
97234230.5375992352673.46240076473342
98251236.50056168428214.4994383157181
99258245.49663088232912.5033691176709
100227254.544815148427-27.5448151484268
101254253.5827256727160.417274327284417
102281258.86275983794322.1372401620573
103261269.857683111974-8.85768311197404
104264273.600064965789-9.60006496578859
105286276.7959298185539.20407018144738
106293284.5439024498768.45609755012367
107276292.461147196273-16.4611471962726
108292294.177057334920-2.17705733491965
109299298.9867610041640.0132389958356498
110319304.28464374602714.7153562539728
111329313.44021060485015.5597893951496
112293323.401683894197-30.401683894197
113318321.922883224305-3.92288322430511
114346326.18360953447319.8163904655268
115327336.516644983285-9.516644983285
116329339.940977848495-10.9409778484946
117353342.6137129394410.3862870605601
118355350.4472594346314.55274056536859
119332357.162805088589-25.1628050885895
120346356.263155571568-10.2631555715683







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121358.273239854298334.134989736376382.411489972221
122362.568340081813337.613199701773387.523480461853
123366.863440309328340.864931236798392.861949381857
124371.158540536842343.882486442201398.434594631484
125375.453640764357346.665124464909404.242157063805
126379.748740991872349.2176619798410.279820003944
127384.043841219386351.548839263316416.538843175457
128388.338941446901353.669769974652423.00811291915
129392.634041674416355.59266803114429.675415317691
130396.929141901931357.329917604624436.528366199237
131401.224242129445358.893464417798443.555019841092
132405.51934235696360.294464557766450.744220156153

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 358.273239854298 & 334.134989736376 & 382.411489972221 \tabularnewline
122 & 362.568340081813 & 337.613199701773 & 387.523480461853 \tabularnewline
123 & 366.863440309328 & 340.864931236798 & 392.861949381857 \tabularnewline
124 & 371.158540536842 & 343.882486442201 & 398.434594631484 \tabularnewline
125 & 375.453640764357 & 346.665124464909 & 404.242157063805 \tabularnewline
126 & 379.748740991872 & 349.2176619798 & 410.279820003944 \tabularnewline
127 & 384.043841219386 & 351.548839263316 & 416.538843175457 \tabularnewline
128 & 388.338941446901 & 353.669769974652 & 423.00811291915 \tabularnewline
129 & 392.634041674416 & 355.59266803114 & 429.675415317691 \tabularnewline
130 & 396.929141901931 & 357.329917604624 & 436.528366199237 \tabularnewline
131 & 401.224242129445 & 358.893464417798 & 443.555019841092 \tabularnewline
132 & 405.51934235696 & 360.294464557766 & 450.744220156153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78269&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]358.273239854298[/C][C]334.134989736376[/C][C]382.411489972221[/C][/ROW]
[ROW][C]122[/C][C]362.568340081813[/C][C]337.613199701773[/C][C]387.523480461853[/C][/ROW]
[ROW][C]123[/C][C]366.863440309328[/C][C]340.864931236798[/C][C]392.861949381857[/C][/ROW]
[ROW][C]124[/C][C]371.158540536842[/C][C]343.882486442201[/C][C]398.434594631484[/C][/ROW]
[ROW][C]125[/C][C]375.453640764357[/C][C]346.665124464909[/C][C]404.242157063805[/C][/ROW]
[ROW][C]126[/C][C]379.748740991872[/C][C]349.2176619798[/C][C]410.279820003944[/C][/ROW]
[ROW][C]127[/C][C]384.043841219386[/C][C]351.548839263316[/C][C]416.538843175457[/C][/ROW]
[ROW][C]128[/C][C]388.338941446901[/C][C]353.669769974652[/C][C]423.00811291915[/C][/ROW]
[ROW][C]129[/C][C]392.634041674416[/C][C]355.59266803114[/C][C]429.675415317691[/C][/ROW]
[ROW][C]130[/C][C]396.929141901931[/C][C]357.329917604624[/C][C]436.528366199237[/C][/ROW]
[ROW][C]131[/C][C]401.224242129445[/C][C]358.893464417798[/C][C]443.555019841092[/C][/ROW]
[ROW][C]132[/C][C]405.51934235696[/C][C]360.294464557766[/C][C]450.744220156153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78269&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78269&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
121358.273239854298334.134989736376382.411489972221
122362.568340081813337.613199701773387.523480461853
123366.863440309328340.864931236798392.861949381857
124371.158540536842343.882486442201398.434594631484
125375.453640764357346.665124464909404.242157063805
126379.748740991872349.2176619798410.279820003944
127384.043841219386351.548839263316416.538843175457
128388.338941446901353.669769974652423.00811291915
129392.634041674416355.59266803114429.675415317691
130396.929141901931357.329917604624436.528366199237
131401.224242129445358.893464417798443.555019841092
132405.51934235696360.294464557766450.744220156153



Parameters (Session):
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')