Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 Jun 2009 06:04:30 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/03/t1244030698c6kfh8rfemsp72j.htm/, Retrieved Sun, 12 May 2024 02:46:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41467, Retrieved Sun, 12 May 2024 02:46:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10, oefeni...] [2009-06-03 12:04:30] [ef3a18d597c5c4b11c910aafede28e07] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41467&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41467&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.211758486366268
beta0.00338345770218744
gamma0.436282320230838

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.211758486366268 \tabularnewline
beta & 0.00338345770218744 \tabularnewline
gamma & 0.436282320230838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41467&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]0.211758486366268[/C][/ROW]
[ROW][C]beta[/C][C]0.00338345770218744[/C][/ROW]
[ROW][C]gamma[/C][C]0.436282320230838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41467&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
alpha0.211758486366268
beta0.00338345770218744
gamma0.436282320230838







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135044.98187815845335.01812184154671
145954.29453003654974.70546996345035
156359.12290921706873.87709078293130
163230.14848539289341.85151460710664
174742.79370501932434.20629498067568
185347.52829180551325.47170819448682
196059.26605015560750.733949844392491
205747.10881827908759.8911817209125
215254.3911775331105-2.3911775331105
227049.296529701070720.7034702989293
239045.636208132833244.3637918671668
247492.9972836592548-18.9972836592548
256293.2273628458895-31.2273628458895
265599.8920133561325-44.8920133561325
278494.9056693010717-10.9056693010717
289446.044778684406447.9552213155936
297078.7271848301798-8.72718483017984
3010883.187233553906824.8127664460932
31139102.99714096911636.0028590308844
3212092.349355917214627.6506440827854
339798.968774832317-1.96877483231704
34126102.66659783647623.3334021635236
35149102.28770881136946.7122911886312
36158136.70111460453221.2988853954675
37124138.942725926159-14.9427259261588
38140147.113941927190-7.11394192719041
39109175.358308233225-66.3583082332254
40114107.2414308118786.75856918812161
4177112.530655571416-35.5306555714160
42120129.048900838430-9.04890083842955
43133149.610080578132-16.6100805781318
44110120.021859777717-10.0218597777165
4592107.427038899669-15.4270388996686
4697117.269087621380-20.2690876213804
4778114.214210369593-36.2142103695933
4899119.609962720668-20.6099627206684
49107103.9149018388293.08509816117078
50112115.955690292417-3.95569029241652
5190121.240818319716-31.2408183197158
529890.78020586521437.21979413478573
5312582.795255781984642.2047442180154
54155124.40947332343930.5905266765607
55190151.57569467286038.4243053271405
56236132.351631649902103.648368350098
57189137.07063300523351.9293669947672
58174164.2393521375769.76064786242446
59178157.63453171991120.3654682800888
60136192.326069971329-56.326069971329
61161174.29687080369-13.2968708036901
62171185.236946979371-14.2369469793711
63149175.285000998686-26.2850009986861
64184151.63638839987632.3636116001242
65155159.634391727341-4.63439172734067
66276200.04744809362775.9525519063732
67224250.039308392898-26.0393083928978
68213229.784089747381-16.7840897473808
69279182.69116345223896.3088365477616
70268204.79224168246563.207758317535
71287211.14191286179275.8580871382076
72238230.4780089487477.52199105125348
73213243.992291100576-30.9922911005764
74257255.9057516330041.09424836699591
75293239.20568784691553.794312153085
76212252.491739446472-40.4917394464719
77246226.80065006415119.1993499358493
78353328.9157829461524.0842170538502
79339331.5758645846117.42413541538883
80308316.113103317822-8.1131033178217
81247302.478464059447-55.4784640594471
82257276.864482290498-19.8644822904984
83322267.29967801787254.7003219821281
84298256.43169125584441.5683087441556
85273263.2219768854519.77802311454889
86312299.57185318309512.4281468169047
87249302.366843781185-53.3668437811846
88286257.37757120958428.6224287904157
89279267.02091424160711.9790857583935
90309382.363034867825-73.3630348678246
91401357.88523134466243.1147686553378
92309342.348465368962-33.3484653689624
93328303.95886266752124.0411373324789
94353306.88446876452446.1155312354764
95354339.61187003829714.388129961703
96327310.86521330632516.1347866936754
97324299.52513948375924.4748605162409
98285344.375760255379-59.3757602553791
99243306.569038451894-63.5690384518942
100241286.829349354318-45.829349354318
101287274.83302281321212.1669771867881
102355360.817478409014-5.81747840901437
103460391.79431987725368.2056801227468
104364351.61903473423912.380965265761
105487341.247215884008145.752784115992
106452377.66567604967674.334323950324
107391407.361668786917-16.3616687869167
108500367.373824315778132.626175684222
109451380.3242650370370.6757349629697
110375407.70415901952-32.70415901952
111372364.8789558729647.12104412703633
112302365.085961335209-63.085961335209
113316375.101472657518-59.1014726575185
114398461.649595401111-63.649595401111
115394519.019844851991-125.019844851991
116431407.67759764510423.3224023548963
117431445.427876451213-14.4278764512130

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 44.9818781584533 & 5.01812184154671 \tabularnewline
14 & 59 & 54.2945300365497 & 4.70546996345035 \tabularnewline
15 & 63 & 59.1229092170687 & 3.87709078293130 \tabularnewline
16 & 32 & 30.1484853928934 & 1.85151460710664 \tabularnewline
17 & 47 & 42.7937050193243 & 4.20629498067568 \tabularnewline
18 & 53 & 47.5282918055132 & 5.47170819448682 \tabularnewline
19 & 60 & 59.2660501556075 & 0.733949844392491 \tabularnewline
20 & 57 & 47.1088182790875 & 9.8911817209125 \tabularnewline
21 & 52 & 54.3911775331105 & -2.3911775331105 \tabularnewline
22 & 70 & 49.2965297010707 & 20.7034702989293 \tabularnewline
23 & 90 & 45.6362081328332 & 44.3637918671668 \tabularnewline
24 & 74 & 92.9972836592548 & -18.9972836592548 \tabularnewline
25 & 62 & 93.2273628458895 & -31.2273628458895 \tabularnewline
26 & 55 & 99.8920133561325 & -44.8920133561325 \tabularnewline
27 & 84 & 94.9056693010717 & -10.9056693010717 \tabularnewline
28 & 94 & 46.0447786844064 & 47.9552213155936 \tabularnewline
29 & 70 & 78.7271848301798 & -8.72718483017984 \tabularnewline
30 & 108 & 83.1872335539068 & 24.8127664460932 \tabularnewline
31 & 139 & 102.997140969116 & 36.0028590308844 \tabularnewline
32 & 120 & 92.3493559172146 & 27.6506440827854 \tabularnewline
33 & 97 & 98.968774832317 & -1.96877483231704 \tabularnewline
34 & 126 & 102.666597836476 & 23.3334021635236 \tabularnewline
35 & 149 & 102.287708811369 & 46.7122911886312 \tabularnewline
36 & 158 & 136.701114604532 & 21.2988853954675 \tabularnewline
37 & 124 & 138.942725926159 & -14.9427259261588 \tabularnewline
38 & 140 & 147.113941927190 & -7.11394192719041 \tabularnewline
39 & 109 & 175.358308233225 & -66.3583082332254 \tabularnewline
40 & 114 & 107.241430811878 & 6.75856918812161 \tabularnewline
41 & 77 & 112.530655571416 & -35.5306555714160 \tabularnewline
42 & 120 & 129.048900838430 & -9.04890083842955 \tabularnewline
43 & 133 & 149.610080578132 & -16.6100805781318 \tabularnewline
44 & 110 & 120.021859777717 & -10.0218597777165 \tabularnewline
45 & 92 & 107.427038899669 & -15.4270388996686 \tabularnewline
46 & 97 & 117.269087621380 & -20.2690876213804 \tabularnewline
47 & 78 & 114.214210369593 & -36.2142103695933 \tabularnewline
48 & 99 & 119.609962720668 & -20.6099627206684 \tabularnewline
49 & 107 & 103.914901838829 & 3.08509816117078 \tabularnewline
50 & 112 & 115.955690292417 & -3.95569029241652 \tabularnewline
51 & 90 & 121.240818319716 & -31.2408183197158 \tabularnewline
52 & 98 & 90.7802058652143 & 7.21979413478573 \tabularnewline
53 & 125 & 82.7952557819846 & 42.2047442180154 \tabularnewline
54 & 155 & 124.409473323439 & 30.5905266765607 \tabularnewline
55 & 190 & 151.575694672860 & 38.4243053271405 \tabularnewline
56 & 236 & 132.351631649902 & 103.648368350098 \tabularnewline
57 & 189 & 137.070633005233 & 51.9293669947672 \tabularnewline
58 & 174 & 164.239352137576 & 9.76064786242446 \tabularnewline
59 & 178 & 157.634531719911 & 20.3654682800888 \tabularnewline
60 & 136 & 192.326069971329 & -56.326069971329 \tabularnewline
61 & 161 & 174.29687080369 & -13.2968708036901 \tabularnewline
62 & 171 & 185.236946979371 & -14.2369469793711 \tabularnewline
63 & 149 & 175.285000998686 & -26.2850009986861 \tabularnewline
64 & 184 & 151.636388399876 & 32.3636116001242 \tabularnewline
65 & 155 & 159.634391727341 & -4.63439172734067 \tabularnewline
66 & 276 & 200.047448093627 & 75.9525519063732 \tabularnewline
67 & 224 & 250.039308392898 & -26.0393083928978 \tabularnewline
68 & 213 & 229.784089747381 & -16.7840897473808 \tabularnewline
69 & 279 & 182.691163452238 & 96.3088365477616 \tabularnewline
70 & 268 & 204.792241682465 & 63.207758317535 \tabularnewline
71 & 287 & 211.141912861792 & 75.8580871382076 \tabularnewline
72 & 238 & 230.478008948747 & 7.52199105125348 \tabularnewline
73 & 213 & 243.992291100576 & -30.9922911005764 \tabularnewline
74 & 257 & 255.905751633004 & 1.09424836699591 \tabularnewline
75 & 293 & 239.205687846915 & 53.794312153085 \tabularnewline
76 & 212 & 252.491739446472 & -40.4917394464719 \tabularnewline
77 & 246 & 226.800650064151 & 19.1993499358493 \tabularnewline
78 & 353 & 328.91578294615 & 24.0842170538502 \tabularnewline
79 & 339 & 331.575864584611 & 7.42413541538883 \tabularnewline
80 & 308 & 316.113103317822 & -8.1131033178217 \tabularnewline
81 & 247 & 302.478464059447 & -55.4784640594471 \tabularnewline
82 & 257 & 276.864482290498 & -19.8644822904984 \tabularnewline
83 & 322 & 267.299678017872 & 54.7003219821281 \tabularnewline
84 & 298 & 256.431691255844 & 41.5683087441556 \tabularnewline
85 & 273 & 263.221976885451 & 9.77802311454889 \tabularnewline
86 & 312 & 299.571853183095 & 12.4281468169047 \tabularnewline
87 & 249 & 302.366843781185 & -53.3668437811846 \tabularnewline
88 & 286 & 257.377571209584 & 28.6224287904157 \tabularnewline
89 & 279 & 267.020914241607 & 11.9790857583935 \tabularnewline
90 & 309 & 382.363034867825 & -73.3630348678246 \tabularnewline
91 & 401 & 357.885231344662 & 43.1147686553378 \tabularnewline
92 & 309 & 342.348465368962 & -33.3484653689624 \tabularnewline
93 & 328 & 303.958862667521 & 24.0411373324789 \tabularnewline
94 & 353 & 306.884468764524 & 46.1155312354764 \tabularnewline
95 & 354 & 339.611870038297 & 14.388129961703 \tabularnewline
96 & 327 & 310.865213306325 & 16.1347866936754 \tabularnewline
97 & 324 & 299.525139483759 & 24.4748605162409 \tabularnewline
98 & 285 & 344.375760255379 & -59.3757602553791 \tabularnewline
99 & 243 & 306.569038451894 & -63.5690384518942 \tabularnewline
100 & 241 & 286.829349354318 & -45.829349354318 \tabularnewline
101 & 287 & 274.833022813212 & 12.1669771867881 \tabularnewline
102 & 355 & 360.817478409014 & -5.81747840901437 \tabularnewline
103 & 460 & 391.794319877253 & 68.2056801227468 \tabularnewline
104 & 364 & 351.619034734239 & 12.380965265761 \tabularnewline
105 & 487 & 341.247215884008 & 145.752784115992 \tabularnewline
106 & 452 & 377.665676049676 & 74.334323950324 \tabularnewline
107 & 391 & 407.361668786917 & -16.3616687869167 \tabularnewline
108 & 500 & 367.373824315778 & 132.626175684222 \tabularnewline
109 & 451 & 380.32426503703 & 70.6757349629697 \tabularnewline
110 & 375 & 407.70415901952 & -32.70415901952 \tabularnewline
111 & 372 & 364.878955872964 & 7.12104412703633 \tabularnewline
112 & 302 & 365.085961335209 & -63.085961335209 \tabularnewline
113 & 316 & 375.101472657518 & -59.1014726575185 \tabularnewline
114 & 398 & 461.649595401111 & -63.649595401111 \tabularnewline
115 & 394 & 519.019844851991 & -125.019844851991 \tabularnewline
116 & 431 & 407.677597645104 & 23.3224023548963 \tabularnewline
117 & 431 & 445.427876451213 & -14.4278764512130 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41467&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]50[/C][C]44.9818781584533[/C][C]5.01812184154671[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]54.2945300365497[/C][C]4.70546996345035[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]59.1229092170687[/C][C]3.87709078293130[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]30.1484853928934[/C][C]1.85151460710664[/C][/ROW]
[ROW][C]17[/C][C]47[/C][C]42.7937050193243[/C][C]4.20629498067568[/C][/ROW]
[ROW][C]18[/C][C]53[/C][C]47.5282918055132[/C][C]5.47170819448682[/C][/ROW]
[ROW][C]19[/C][C]60[/C][C]59.2660501556075[/C][C]0.733949844392491[/C][/ROW]
[ROW][C]20[/C][C]57[/C][C]47.1088182790875[/C][C]9.8911817209125[/C][/ROW]
[ROW][C]21[/C][C]52[/C][C]54.3911775331105[/C][C]-2.3911775331105[/C][/ROW]
[ROW][C]22[/C][C]70[/C][C]49.2965297010707[/C][C]20.7034702989293[/C][/ROW]
[ROW][C]23[/C][C]90[/C][C]45.6362081328332[/C][C]44.3637918671668[/C][/ROW]
[ROW][C]24[/C][C]74[/C][C]92.9972836592548[/C][C]-18.9972836592548[/C][/ROW]
[ROW][C]25[/C][C]62[/C][C]93.2273628458895[/C][C]-31.2273628458895[/C][/ROW]
[ROW][C]26[/C][C]55[/C][C]99.8920133561325[/C][C]-44.8920133561325[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]94.9056693010717[/C][C]-10.9056693010717[/C][/ROW]
[ROW][C]28[/C][C]94[/C][C]46.0447786844064[/C][C]47.9552213155936[/C][/ROW]
[ROW][C]29[/C][C]70[/C][C]78.7271848301798[/C][C]-8.72718483017984[/C][/ROW]
[ROW][C]30[/C][C]108[/C][C]83.1872335539068[/C][C]24.8127664460932[/C][/ROW]
[ROW][C]31[/C][C]139[/C][C]102.997140969116[/C][C]36.0028590308844[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]92.3493559172146[/C][C]27.6506440827854[/C][/ROW]
[ROW][C]33[/C][C]97[/C][C]98.968774832317[/C][C]-1.96877483231704[/C][/ROW]
[ROW][C]34[/C][C]126[/C][C]102.666597836476[/C][C]23.3334021635236[/C][/ROW]
[ROW][C]35[/C][C]149[/C][C]102.287708811369[/C][C]46.7122911886312[/C][/ROW]
[ROW][C]36[/C][C]158[/C][C]136.701114604532[/C][C]21.2988853954675[/C][/ROW]
[ROW][C]37[/C][C]124[/C][C]138.942725926159[/C][C]-14.9427259261588[/C][/ROW]
[ROW][C]38[/C][C]140[/C][C]147.113941927190[/C][C]-7.11394192719041[/C][/ROW]
[ROW][C]39[/C][C]109[/C][C]175.358308233225[/C][C]-66.3583082332254[/C][/ROW]
[ROW][C]40[/C][C]114[/C][C]107.241430811878[/C][C]6.75856918812161[/C][/ROW]
[ROW][C]41[/C][C]77[/C][C]112.530655571416[/C][C]-35.5306555714160[/C][/ROW]
[ROW][C]42[/C][C]120[/C][C]129.048900838430[/C][C]-9.04890083842955[/C][/ROW]
[ROW][C]43[/C][C]133[/C][C]149.610080578132[/C][C]-16.6100805781318[/C][/ROW]
[ROW][C]44[/C][C]110[/C][C]120.021859777717[/C][C]-10.0218597777165[/C][/ROW]
[ROW][C]45[/C][C]92[/C][C]107.427038899669[/C][C]-15.4270388996686[/C][/ROW]
[ROW][C]46[/C][C]97[/C][C]117.269087621380[/C][C]-20.2690876213804[/C][/ROW]
[ROW][C]47[/C][C]78[/C][C]114.214210369593[/C][C]-36.2142103695933[/C][/ROW]
[ROW][C]48[/C][C]99[/C][C]119.609962720668[/C][C]-20.6099627206684[/C][/ROW]
[ROW][C]49[/C][C]107[/C][C]103.914901838829[/C][C]3.08509816117078[/C][/ROW]
[ROW][C]50[/C][C]112[/C][C]115.955690292417[/C][C]-3.95569029241652[/C][/ROW]
[ROW][C]51[/C][C]90[/C][C]121.240818319716[/C][C]-31.2408183197158[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]90.7802058652143[/C][C]7.21979413478573[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]82.7952557819846[/C][C]42.2047442180154[/C][/ROW]
[ROW][C]54[/C][C]155[/C][C]124.409473323439[/C][C]30.5905266765607[/C][/ROW]
[ROW][C]55[/C][C]190[/C][C]151.575694672860[/C][C]38.4243053271405[/C][/ROW]
[ROW][C]56[/C][C]236[/C][C]132.351631649902[/C][C]103.648368350098[/C][/ROW]
[ROW][C]57[/C][C]189[/C][C]137.070633005233[/C][C]51.9293669947672[/C][/ROW]
[ROW][C]58[/C][C]174[/C][C]164.239352137576[/C][C]9.76064786242446[/C][/ROW]
[ROW][C]59[/C][C]178[/C][C]157.634531719911[/C][C]20.3654682800888[/C][/ROW]
[ROW][C]60[/C][C]136[/C][C]192.326069971329[/C][C]-56.326069971329[/C][/ROW]
[ROW][C]61[/C][C]161[/C][C]174.29687080369[/C][C]-13.2968708036901[/C][/ROW]
[ROW][C]62[/C][C]171[/C][C]185.236946979371[/C][C]-14.2369469793711[/C][/ROW]
[ROW][C]63[/C][C]149[/C][C]175.285000998686[/C][C]-26.2850009986861[/C][/ROW]
[ROW][C]64[/C][C]184[/C][C]151.636388399876[/C][C]32.3636116001242[/C][/ROW]
[ROW][C]65[/C][C]155[/C][C]159.634391727341[/C][C]-4.63439172734067[/C][/ROW]
[ROW][C]66[/C][C]276[/C][C]200.047448093627[/C][C]75.9525519063732[/C][/ROW]
[ROW][C]67[/C][C]224[/C][C]250.039308392898[/C][C]-26.0393083928978[/C][/ROW]
[ROW][C]68[/C][C]213[/C][C]229.784089747381[/C][C]-16.7840897473808[/C][/ROW]
[ROW][C]69[/C][C]279[/C][C]182.691163452238[/C][C]96.3088365477616[/C][/ROW]
[ROW][C]70[/C][C]268[/C][C]204.792241682465[/C][C]63.207758317535[/C][/ROW]
[ROW][C]71[/C][C]287[/C][C]211.141912861792[/C][C]75.8580871382076[/C][/ROW]
[ROW][C]72[/C][C]238[/C][C]230.478008948747[/C][C]7.52199105125348[/C][/ROW]
[ROW][C]73[/C][C]213[/C][C]243.992291100576[/C][C]-30.9922911005764[/C][/ROW]
[ROW][C]74[/C][C]257[/C][C]255.905751633004[/C][C]1.09424836699591[/C][/ROW]
[ROW][C]75[/C][C]293[/C][C]239.205687846915[/C][C]53.794312153085[/C][/ROW]
[ROW][C]76[/C][C]212[/C][C]252.491739446472[/C][C]-40.4917394464719[/C][/ROW]
[ROW][C]77[/C][C]246[/C][C]226.800650064151[/C][C]19.1993499358493[/C][/ROW]
[ROW][C]78[/C][C]353[/C][C]328.91578294615[/C][C]24.0842170538502[/C][/ROW]
[ROW][C]79[/C][C]339[/C][C]331.575864584611[/C][C]7.42413541538883[/C][/ROW]
[ROW][C]80[/C][C]308[/C][C]316.113103317822[/C][C]-8.1131033178217[/C][/ROW]
[ROW][C]81[/C][C]247[/C][C]302.478464059447[/C][C]-55.4784640594471[/C][/ROW]
[ROW][C]82[/C][C]257[/C][C]276.864482290498[/C][C]-19.8644822904984[/C][/ROW]
[ROW][C]83[/C][C]322[/C][C]267.299678017872[/C][C]54.7003219821281[/C][/ROW]
[ROW][C]84[/C][C]298[/C][C]256.431691255844[/C][C]41.5683087441556[/C][/ROW]
[ROW][C]85[/C][C]273[/C][C]263.221976885451[/C][C]9.77802311454889[/C][/ROW]
[ROW][C]86[/C][C]312[/C][C]299.571853183095[/C][C]12.4281468169047[/C][/ROW]
[ROW][C]87[/C][C]249[/C][C]302.366843781185[/C][C]-53.3668437811846[/C][/ROW]
[ROW][C]88[/C][C]286[/C][C]257.377571209584[/C][C]28.6224287904157[/C][/ROW]
[ROW][C]89[/C][C]279[/C][C]267.020914241607[/C][C]11.9790857583935[/C][/ROW]
[ROW][C]90[/C][C]309[/C][C]382.363034867825[/C][C]-73.3630348678246[/C][/ROW]
[ROW][C]91[/C][C]401[/C][C]357.885231344662[/C][C]43.1147686553378[/C][/ROW]
[ROW][C]92[/C][C]309[/C][C]342.348465368962[/C][C]-33.3484653689624[/C][/ROW]
[ROW][C]93[/C][C]328[/C][C]303.958862667521[/C][C]24.0411373324789[/C][/ROW]
[ROW][C]94[/C][C]353[/C][C]306.884468764524[/C][C]46.1155312354764[/C][/ROW]
[ROW][C]95[/C][C]354[/C][C]339.611870038297[/C][C]14.388129961703[/C][/ROW]
[ROW][C]96[/C][C]327[/C][C]310.865213306325[/C][C]16.1347866936754[/C][/ROW]
[ROW][C]97[/C][C]324[/C][C]299.525139483759[/C][C]24.4748605162409[/C][/ROW]
[ROW][C]98[/C][C]285[/C][C]344.375760255379[/C][C]-59.3757602553791[/C][/ROW]
[ROW][C]99[/C][C]243[/C][C]306.569038451894[/C][C]-63.5690384518942[/C][/ROW]
[ROW][C]100[/C][C]241[/C][C]286.829349354318[/C][C]-45.829349354318[/C][/ROW]
[ROW][C]101[/C][C]287[/C][C]274.833022813212[/C][C]12.1669771867881[/C][/ROW]
[ROW][C]102[/C][C]355[/C][C]360.817478409014[/C][C]-5.81747840901437[/C][/ROW]
[ROW][C]103[/C][C]460[/C][C]391.794319877253[/C][C]68.2056801227468[/C][/ROW]
[ROW][C]104[/C][C]364[/C][C]351.619034734239[/C][C]12.380965265761[/C][/ROW]
[ROW][C]105[/C][C]487[/C][C]341.247215884008[/C][C]145.752784115992[/C][/ROW]
[ROW][C]106[/C][C]452[/C][C]377.665676049676[/C][C]74.334323950324[/C][/ROW]
[ROW][C]107[/C][C]391[/C][C]407.361668786917[/C][C]-16.3616687869167[/C][/ROW]
[ROW][C]108[/C][C]500[/C][C]367.373824315778[/C][C]132.626175684222[/C][/ROW]
[ROW][C]109[/C][C]451[/C][C]380.32426503703[/C][C]70.6757349629697[/C][/ROW]
[ROW][C]110[/C][C]375[/C][C]407.70415901952[/C][C]-32.70415901952[/C][/ROW]
[ROW][C]111[/C][C]372[/C][C]364.878955872964[/C][C]7.12104412703633[/C][/ROW]
[ROW][C]112[/C][C]302[/C][C]365.085961335209[/C][C]-63.085961335209[/C][/ROW]
[ROW][C]113[/C][C]316[/C][C]375.101472657518[/C][C]-59.1014726575185[/C][/ROW]
[ROW][C]114[/C][C]398[/C][C]461.649595401111[/C][C]-63.649595401111[/C][/ROW]
[ROW][C]115[/C][C]394[/C][C]519.019844851991[/C][C]-125.019844851991[/C][/ROW]
[ROW][C]116[/C][C]431[/C][C]407.677597645104[/C][C]23.3224023548963[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]445.427876451213[/C][C]-14.4278764512130[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41467&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
135044.98187815845335.01812184154671
145954.29453003654974.70546996345035
156359.12290921706873.87709078293130
163230.14848539289341.85151460710664
174742.79370501932434.20629498067568
185347.52829180551325.47170819448682
196059.26605015560750.733949844392491
205747.10881827908759.8911817209125
215254.3911775331105-2.3911775331105
227049.296529701070720.7034702989293
239045.636208132833244.3637918671668
247492.9972836592548-18.9972836592548
256293.2273628458895-31.2273628458895
265599.8920133561325-44.8920133561325
278494.9056693010717-10.9056693010717
289446.044778684406447.9552213155936
297078.7271848301798-8.72718483017984
3010883.187233553906824.8127664460932
31139102.99714096911636.0028590308844
3212092.349355917214627.6506440827854
339798.968774832317-1.96877483231704
34126102.66659783647623.3334021635236
35149102.28770881136946.7122911886312
36158136.70111460453221.2988853954675
37124138.942725926159-14.9427259261588
38140147.113941927190-7.11394192719041
39109175.358308233225-66.3583082332254
40114107.2414308118786.75856918812161
4177112.530655571416-35.5306555714160
42120129.048900838430-9.04890083842955
43133149.610080578132-16.6100805781318
44110120.021859777717-10.0218597777165
4592107.427038899669-15.4270388996686
4697117.269087621380-20.2690876213804
4778114.214210369593-36.2142103695933
4899119.609962720668-20.6099627206684
49107103.9149018388293.08509816117078
50112115.955690292417-3.95569029241652
5190121.240818319716-31.2408183197158
529890.78020586521437.21979413478573
5312582.795255781984642.2047442180154
54155124.40947332343930.5905266765607
55190151.57569467286038.4243053271405
56236132.351631649902103.648368350098
57189137.07063300523351.9293669947672
58174164.2393521375769.76064786242446
59178157.63453171991120.3654682800888
60136192.326069971329-56.326069971329
61161174.29687080369-13.2968708036901
62171185.236946979371-14.2369469793711
63149175.285000998686-26.2850009986861
64184151.63638839987632.3636116001242
65155159.634391727341-4.63439172734067
66276200.04744809362775.9525519063732
67224250.039308392898-26.0393083928978
68213229.784089747381-16.7840897473808
69279182.69116345223896.3088365477616
70268204.79224168246563.207758317535
71287211.14191286179275.8580871382076
72238230.4780089487477.52199105125348
73213243.992291100576-30.9922911005764
74257255.9057516330041.09424836699591
75293239.20568784691553.794312153085
76212252.491739446472-40.4917394464719
77246226.80065006415119.1993499358493
78353328.9157829461524.0842170538502
79339331.5758645846117.42413541538883
80308316.113103317822-8.1131033178217
81247302.478464059447-55.4784640594471
82257276.864482290498-19.8644822904984
83322267.29967801787254.7003219821281
84298256.43169125584441.5683087441556
85273263.2219768854519.77802311454889
86312299.57185318309512.4281468169047
87249302.366843781185-53.3668437811846
88286257.37757120958428.6224287904157
89279267.02091424160711.9790857583935
90309382.363034867825-73.3630348678246
91401357.88523134466243.1147686553378
92309342.348465368962-33.3484653689624
93328303.95886266752124.0411373324789
94353306.88446876452446.1155312354764
95354339.61187003829714.388129961703
96327310.86521330632516.1347866936754
97324299.52513948375924.4748605162409
98285344.375760255379-59.3757602553791
99243306.569038451894-63.5690384518942
100241286.829349354318-45.829349354318
101287274.83302281321212.1669771867881
102355360.817478409014-5.81747840901437
103460391.79431987725368.2056801227468
104364351.61903473423912.380965265761
105487341.247215884008145.752784115992
106452377.66567604967674.334323950324
107391407.361668786917-16.3616687869167
108500367.373824315778132.626175684222
109451380.3242650370370.6757349629697
110375407.70415901952-32.70415901952
111372364.8789558729647.12104412703633
112302365.085961335209-63.085961335209
113316375.101472657518-59.1014726575185
114398461.649595401111-63.649595401111
115394519.019844851991-125.019844851991
116431407.67759764510423.3224023548963
117431445.427876451213-14.4278764512130







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
118421.252994457504374.109634423978468.396354491029
119403.781873008052353.602308462305453.961437553798
120415.312127710863361.700106392753468.924149028973
121380.095834046952324.996981426188435.194686667717
122358.948344719755302.095734876109415.800954563402
123338.45747626022280.121173973430396.79377854701
124314.335338085329255.049355209065373.621320961593
125337.195230666006273.360929072824401.029532259187
126432.526150001749356.43779404065508.614505962848
127480.543647622941396.829771857601564.257523388282
128444.109488595475363.045642774212525.173334416738
129464.870756492779386.981794380782542.759718604775

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
118 & 421.252994457504 & 374.109634423978 & 468.396354491029 \tabularnewline
119 & 403.781873008052 & 353.602308462305 & 453.961437553798 \tabularnewline
120 & 415.312127710863 & 361.700106392753 & 468.924149028973 \tabularnewline
121 & 380.095834046952 & 324.996981426188 & 435.194686667717 \tabularnewline
122 & 358.948344719755 & 302.095734876109 & 415.800954563402 \tabularnewline
123 & 338.45747626022 & 280.121173973430 & 396.79377854701 \tabularnewline
124 & 314.335338085329 & 255.049355209065 & 373.621320961593 \tabularnewline
125 & 337.195230666006 & 273.360929072824 & 401.029532259187 \tabularnewline
126 & 432.526150001749 & 356.43779404065 & 508.614505962848 \tabularnewline
127 & 480.543647622941 & 396.829771857601 & 564.257523388282 \tabularnewline
128 & 444.109488595475 & 363.045642774212 & 525.173334416738 \tabularnewline
129 & 464.870756492779 & 386.981794380782 & 542.759718604775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41467&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]118[/C][C]421.252994457504[/C][C]374.109634423978[/C][C]468.396354491029[/C][/ROW]
[ROW][C]119[/C][C]403.781873008052[/C][C]353.602308462305[/C][C]453.961437553798[/C][/ROW]
[ROW][C]120[/C][C]415.312127710863[/C][C]361.700106392753[/C][C]468.924149028973[/C][/ROW]
[ROW][C]121[/C][C]380.095834046952[/C][C]324.996981426188[/C][C]435.194686667717[/C][/ROW]
[ROW][C]122[/C][C]358.948344719755[/C][C]302.095734876109[/C][C]415.800954563402[/C][/ROW]
[ROW][C]123[/C][C]338.45747626022[/C][C]280.121173973430[/C][C]396.79377854701[/C][/ROW]
[ROW][C]124[/C][C]314.335338085329[/C][C]255.049355209065[/C][C]373.621320961593[/C][/ROW]
[ROW][C]125[/C][C]337.195230666006[/C][C]273.360929072824[/C][C]401.029532259187[/C][/ROW]
[ROW][C]126[/C][C]432.526150001749[/C][C]356.43779404065[/C][C]508.614505962848[/C][/ROW]
[ROW][C]127[/C][C]480.543647622941[/C][C]396.829771857601[/C][C]564.257523388282[/C][/ROW]
[ROW][C]128[/C][C]444.109488595475[/C][C]363.045642774212[/C][C]525.173334416738[/C][/ROW]
[ROW][C]129[/C][C]464.870756492779[/C][C]386.981794380782[/C][C]542.759718604775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41467&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41467&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
118421.252994457504374.109634423978468.396354491029
119403.781873008052353.602308462305453.961437553798
120415.312127710863361.700106392753468.924149028973
121380.095834046952324.996981426188435.194686667717
122358.948344719755302.095734876109415.800954563402
123338.45747626022280.121173973430396.79377854701
124314.335338085329255.049355209065373.621320961593
125337.195230666006273.360929072824401.029532259187
126432.526150001749356.43779404065508.614505962848
127480.543647622941396.829771857601564.257523388282
128444.109488595475363.045642774212525.173334416738
129464.870756492779386.981794380782542.759718604775



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')