Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Aug 2013 04:21:10 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/14/t1376468496ksxql3jtv7gimy6.htm/, Retrieved Sat, 04 May 2024 21:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211085, Retrieved Sat, 04 May 2024 21:00:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsalexandra de schutter
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [omzet Oregon Scie...] [2013-08-14 08:21:10] [a5e81fc5b84eaf53b9dc73271fe36a59] [Current]
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Dataseries X:
323898
323268
322574
321304
334352
333712
323898
317374
318014
318014
318646
319980
319980
314086
311490
314086
323268
321934
309526
299020
297054
293126
295784
299020
297748
295090
289900
295090
299712
298380
283312
276788
270264
265010
264380
268300
263046
261082
259118
270264
271536
265010
247340
239490
227082
221820
224416
228344
228344
225118
224416
234930
243420
239490
226380
219864
206122
197634
204158
210682
210682
202194
201562
212638
219864
217260
204158
195670
177304
170150
172744
183892
184522
168184
174078
188452
194976
191046
173384
160968
146594
135448
140008
149820
147226
132852
137412
151786
159642
155082
137412
129564
117786
105368
107332
117146
118416
106638
108604
125004
128924
122346
98150
85742
69342
53004
58258
65412
64150
51670
58888
76560
84408
80488
64782
52372
39262
24186
26854
31414




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211085&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211085&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211085&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380162943418813
beta0.0252555708743968
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380162943418813 \tabularnewline
beta & 0.0252555708743968 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211085&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]0.380162943418813[/C][/ROW]
[ROW][C]beta[/C][C]0.0252555708743968[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211085&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211085&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
alpha0.380162943418813
beta0.0252555708743968
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13319980325101.524744003-5121.52474400308
14314086317303.095120185-3217.09512018471
15311490313806.066798973-2316.06679897313
16314086316126.059114899-2040.05911489902
17323268325244.494503624-1976.49450362392
18321934323639.634729579-1705.63472957921
19309526309795.80659297-269.806592969748
20299020302605.245135898-3585.24513589783
21297054301237.780856197-4183.780856197
22293126298911.300025601-5785.30002560141
23295784296499.624274133-715.624274132773
24299020296827.7063095562192.29369044426
25297748294249.7087300023498.29126999818
26295090290971.0146778664118.98532213416
27289900290726.664396417-826.664396417211
28295090293355.2289946461734.77100535377
29299712303147.225745087-3435.22574508743
30298380301016.643123487-2636.64312348654
31283312288358.092841616-5046.09284161642
32276788277731.881283532-943.881283531664
33270264276799.389429656-6535.38942965592
34265010272449.921061792-7439.92106179229
35264380272041.923481027-7661.92348102678
36268300270950.350703561-2650.35070356115
37263046267169.739752109-4123.73975210934
38261082261325.38553325-243.385533250286
39259118256378.2967321222739.70326787824
40270264260929.6601262329334.33987376821
41271536269348.0286432142187.97135678597
42265010269499.449418514-4489.44941851427
43247340255583.38385011-8243.38385010979
44239490246527.765682528-7037.76568252846
45227082239763.723427366-12681.7234273661
46221820232211.190624576-10391.1906245761
47224416229541.255685049-5125.25568504876
48228344231184.273992935-2840.27399293522
49228344226278.4067922372065.59320776255
50225118224860.156283927257.843716073054
51224416221778.9834437152637.01655628523
52234930228641.2878100146288.71218998558
53243420230767.23378718612652.7662128136
54239490230874.731742378615.2682576298
55226380220909.5335723585470.46642764163
56219864218095.2101160721768.78988392817
57206122211604.439047947-5482.43904794726
58197634208193.652323929-10559.6523239291
59204158208306.647946311-4148.64794631131
60210682211309.905188476-627.905188476259
61210682210341.922973016340.077026984189
62202194207387.250495152-5193.25049515167
63201562203758.773938233-2196.77393823329
64212638210071.3962743672566.603725633
65219864213999.4378012555864.56219874538
66217260209481.4162789217778.58372107946
67204158198668.698515685489.30148432023
68195670194121.221143111548.77885689033
69177304184108.91955822-6804.91955822019
70170150177197.823986706-7047.82398670644
71172744181394.236990281-8650.23699028121
72183892183661.791768103230.208231897035
73184522183297.1519811291224.84801887124
74168184177731.291851936-9547.29185193649
75174078173873.099290885204.900709114678
76188452182263.7826072286188.21739277232
77194976188561.7199719266414.28002807358
78191046185769.1844635025276.81553649751
79173384174273.094862267-889.094862266997
80160968165792.458924787-4824.45892478741
81146594150230.456576953-3636.45657695338
82135448144607.63403274-9159.63403273956
83140008145423.00109766-5415.00109766028
84149820152023.319483249-2203.31948324948
85147226150752.809392039-3526.80939203911
86132852138423.277804816-5571.27780481568
87137412140412.695080655-3000.69508065539
88151786148137.5456052543648.45439474646
89159642151959.1627915837682.83720841707
90155082149410.2570783525671.74292164776
91137412137163.688231873248.311768127111
92129564128235.0164395661328.98356043405
93117786117816.82050469-30.8205046903313
94105368111071.66428108-5703.66428107968
95107332113709.515786508-6377.51578650765
96117146119180.764891169-2034.76489116877
97118416116821.3643317261594.63566827391
98106638107123.90258672-485.902586720331
99108604111057.189112601-2453.18911260071
100125004119995.2710082955008.72899170489
101128924125269.5031315363654.49686846377
102122346120732.8330702481613.16692975219
10398150106893.576456111-8743.57645611053
1048574296599.9306251865-10857.9306251865
1056934283269.4185344786-13927.4185344786
1065300470177.1215304444-17173.1215304444
1075825864970.4985050131-6712.49850501313
1086541267056.6365648604-1644.63656486035
1096415065211.9917750035-1061.99177500347
1105167056936.0838969608-5266.08389696084
1115888854695.48232162434192.5176783757
1127656061848.97920995414711.020790046
1138440866962.877310412817445.1226895872
1148048867946.147711419812541.8522885802
1156478259048.34010088535733.65989911467
1165237254952.2106085802-2580.21060858022
1173926245836.1581294742-6574.15812947418
1182418635851.8116676705-11665.8116676705
1192685435038.5667404018-8184.56674040177
1203141434940.1850986821-3526.18509868212

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 319980 & 325101.524744003 & -5121.52474400308 \tabularnewline
14 & 314086 & 317303.095120185 & -3217.09512018471 \tabularnewline
15 & 311490 & 313806.066798973 & -2316.06679897313 \tabularnewline
16 & 314086 & 316126.059114899 & -2040.05911489902 \tabularnewline
17 & 323268 & 325244.494503624 & -1976.49450362392 \tabularnewline
18 & 321934 & 323639.634729579 & -1705.63472957921 \tabularnewline
19 & 309526 & 309795.80659297 & -269.806592969748 \tabularnewline
20 & 299020 & 302605.245135898 & -3585.24513589783 \tabularnewline
21 & 297054 & 301237.780856197 & -4183.780856197 \tabularnewline
22 & 293126 & 298911.300025601 & -5785.30002560141 \tabularnewline
23 & 295784 & 296499.624274133 & -715.624274132773 \tabularnewline
24 & 299020 & 296827.706309556 & 2192.29369044426 \tabularnewline
25 & 297748 & 294249.708730002 & 3498.29126999818 \tabularnewline
26 & 295090 & 290971.014677866 & 4118.98532213416 \tabularnewline
27 & 289900 & 290726.664396417 & -826.664396417211 \tabularnewline
28 & 295090 & 293355.228994646 & 1734.77100535377 \tabularnewline
29 & 299712 & 303147.225745087 & -3435.22574508743 \tabularnewline
30 & 298380 & 301016.643123487 & -2636.64312348654 \tabularnewline
31 & 283312 & 288358.092841616 & -5046.09284161642 \tabularnewline
32 & 276788 & 277731.881283532 & -943.881283531664 \tabularnewline
33 & 270264 & 276799.389429656 & -6535.38942965592 \tabularnewline
34 & 265010 & 272449.921061792 & -7439.92106179229 \tabularnewline
35 & 264380 & 272041.923481027 & -7661.92348102678 \tabularnewline
36 & 268300 & 270950.350703561 & -2650.35070356115 \tabularnewline
37 & 263046 & 267169.739752109 & -4123.73975210934 \tabularnewline
38 & 261082 & 261325.38553325 & -243.385533250286 \tabularnewline
39 & 259118 & 256378.296732122 & 2739.70326787824 \tabularnewline
40 & 270264 & 260929.660126232 & 9334.33987376821 \tabularnewline
41 & 271536 & 269348.028643214 & 2187.97135678597 \tabularnewline
42 & 265010 & 269499.449418514 & -4489.44941851427 \tabularnewline
43 & 247340 & 255583.38385011 & -8243.38385010979 \tabularnewline
44 & 239490 & 246527.765682528 & -7037.76568252846 \tabularnewline
45 & 227082 & 239763.723427366 & -12681.7234273661 \tabularnewline
46 & 221820 & 232211.190624576 & -10391.1906245761 \tabularnewline
47 & 224416 & 229541.255685049 & -5125.25568504876 \tabularnewline
48 & 228344 & 231184.273992935 & -2840.27399293522 \tabularnewline
49 & 228344 & 226278.406792237 & 2065.59320776255 \tabularnewline
50 & 225118 & 224860.156283927 & 257.843716073054 \tabularnewline
51 & 224416 & 221778.983443715 & 2637.01655628523 \tabularnewline
52 & 234930 & 228641.287810014 & 6288.71218998558 \tabularnewline
53 & 243420 & 230767.233787186 & 12652.7662128136 \tabularnewline
54 & 239490 & 230874.73174237 & 8615.2682576298 \tabularnewline
55 & 226380 & 220909.533572358 & 5470.46642764163 \tabularnewline
56 & 219864 & 218095.210116072 & 1768.78988392817 \tabularnewline
57 & 206122 & 211604.439047947 & -5482.43904794726 \tabularnewline
58 & 197634 & 208193.652323929 & -10559.6523239291 \tabularnewline
59 & 204158 & 208306.647946311 & -4148.64794631131 \tabularnewline
60 & 210682 & 211309.905188476 & -627.905188476259 \tabularnewline
61 & 210682 & 210341.922973016 & 340.077026984189 \tabularnewline
62 & 202194 & 207387.250495152 & -5193.25049515167 \tabularnewline
63 & 201562 & 203758.773938233 & -2196.77393823329 \tabularnewline
64 & 212638 & 210071.396274367 & 2566.603725633 \tabularnewline
65 & 219864 & 213999.437801255 & 5864.56219874538 \tabularnewline
66 & 217260 & 209481.416278921 & 7778.58372107946 \tabularnewline
67 & 204158 & 198668.69851568 & 5489.30148432023 \tabularnewline
68 & 195670 & 194121.22114311 & 1548.77885689033 \tabularnewline
69 & 177304 & 184108.91955822 & -6804.91955822019 \tabularnewline
70 & 170150 & 177197.823986706 & -7047.82398670644 \tabularnewline
71 & 172744 & 181394.236990281 & -8650.23699028121 \tabularnewline
72 & 183892 & 183661.791768103 & 230.208231897035 \tabularnewline
73 & 184522 & 183297.151981129 & 1224.84801887124 \tabularnewline
74 & 168184 & 177731.291851936 & -9547.29185193649 \tabularnewline
75 & 174078 & 173873.099290885 & 204.900709114678 \tabularnewline
76 & 188452 & 182263.782607228 & 6188.21739277232 \tabularnewline
77 & 194976 & 188561.719971926 & 6414.28002807358 \tabularnewline
78 & 191046 & 185769.184463502 & 5276.81553649751 \tabularnewline
79 & 173384 & 174273.094862267 & -889.094862266997 \tabularnewline
80 & 160968 & 165792.458924787 & -4824.45892478741 \tabularnewline
81 & 146594 & 150230.456576953 & -3636.45657695338 \tabularnewline
82 & 135448 & 144607.63403274 & -9159.63403273956 \tabularnewline
83 & 140008 & 145423.00109766 & -5415.00109766028 \tabularnewline
84 & 149820 & 152023.319483249 & -2203.31948324948 \tabularnewline
85 & 147226 & 150752.809392039 & -3526.80939203911 \tabularnewline
86 & 132852 & 138423.277804816 & -5571.27780481568 \tabularnewline
87 & 137412 & 140412.695080655 & -3000.69508065539 \tabularnewline
88 & 151786 & 148137.545605254 & 3648.45439474646 \tabularnewline
89 & 159642 & 151959.162791583 & 7682.83720841707 \tabularnewline
90 & 155082 & 149410.257078352 & 5671.74292164776 \tabularnewline
91 & 137412 & 137163.688231873 & 248.311768127111 \tabularnewline
92 & 129564 & 128235.016439566 & 1328.98356043405 \tabularnewline
93 & 117786 & 117816.82050469 & -30.8205046903313 \tabularnewline
94 & 105368 & 111071.66428108 & -5703.66428107968 \tabularnewline
95 & 107332 & 113709.515786508 & -6377.51578650765 \tabularnewline
96 & 117146 & 119180.764891169 & -2034.76489116877 \tabularnewline
97 & 118416 & 116821.364331726 & 1594.63566827391 \tabularnewline
98 & 106638 & 107123.90258672 & -485.902586720331 \tabularnewline
99 & 108604 & 111057.189112601 & -2453.18911260071 \tabularnewline
100 & 125004 & 119995.271008295 & 5008.72899170489 \tabularnewline
101 & 128924 & 125269.503131536 & 3654.49686846377 \tabularnewline
102 & 122346 & 120732.833070248 & 1613.16692975219 \tabularnewline
103 & 98150 & 106893.576456111 & -8743.57645611053 \tabularnewline
104 & 85742 & 96599.9306251865 & -10857.9306251865 \tabularnewline
105 & 69342 & 83269.4185344786 & -13927.4185344786 \tabularnewline
106 & 53004 & 70177.1215304444 & -17173.1215304444 \tabularnewline
107 & 58258 & 64970.4985050131 & -6712.49850501313 \tabularnewline
108 & 65412 & 67056.6365648604 & -1644.63656486035 \tabularnewline
109 & 64150 & 65211.9917750035 & -1061.99177500347 \tabularnewline
110 & 51670 & 56936.0838969608 & -5266.08389696084 \tabularnewline
111 & 58888 & 54695.4823216243 & 4192.5176783757 \tabularnewline
112 & 76560 & 61848.979209954 & 14711.020790046 \tabularnewline
113 & 84408 & 66962.8773104128 & 17445.1226895872 \tabularnewline
114 & 80488 & 67946.1477114198 & 12541.8522885802 \tabularnewline
115 & 64782 & 59048.3401008853 & 5733.65989911467 \tabularnewline
116 & 52372 & 54952.2106085802 & -2580.21060858022 \tabularnewline
117 & 39262 & 45836.1581294742 & -6574.15812947418 \tabularnewline
118 & 24186 & 35851.8116676705 & -11665.8116676705 \tabularnewline
119 & 26854 & 35038.5667404018 & -8184.56674040177 \tabularnewline
120 & 31414 & 34940.1850986821 & -3526.18509868212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211085&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]319980[/C][C]325101.524744003[/C][C]-5121.52474400308[/C][/ROW]
[ROW][C]14[/C][C]314086[/C][C]317303.095120185[/C][C]-3217.09512018471[/C][/ROW]
[ROW][C]15[/C][C]311490[/C][C]313806.066798973[/C][C]-2316.06679897313[/C][/ROW]
[ROW][C]16[/C][C]314086[/C][C]316126.059114899[/C][C]-2040.05911489902[/C][/ROW]
[ROW][C]17[/C][C]323268[/C][C]325244.494503624[/C][C]-1976.49450362392[/C][/ROW]
[ROW][C]18[/C][C]321934[/C][C]323639.634729579[/C][C]-1705.63472957921[/C][/ROW]
[ROW][C]19[/C][C]309526[/C][C]309795.80659297[/C][C]-269.806592969748[/C][/ROW]
[ROW][C]20[/C][C]299020[/C][C]302605.245135898[/C][C]-3585.24513589783[/C][/ROW]
[ROW][C]21[/C][C]297054[/C][C]301237.780856197[/C][C]-4183.780856197[/C][/ROW]
[ROW][C]22[/C][C]293126[/C][C]298911.300025601[/C][C]-5785.30002560141[/C][/ROW]
[ROW][C]23[/C][C]295784[/C][C]296499.624274133[/C][C]-715.624274132773[/C][/ROW]
[ROW][C]24[/C][C]299020[/C][C]296827.706309556[/C][C]2192.29369044426[/C][/ROW]
[ROW][C]25[/C][C]297748[/C][C]294249.708730002[/C][C]3498.29126999818[/C][/ROW]
[ROW][C]26[/C][C]295090[/C][C]290971.014677866[/C][C]4118.98532213416[/C][/ROW]
[ROW][C]27[/C][C]289900[/C][C]290726.664396417[/C][C]-826.664396417211[/C][/ROW]
[ROW][C]28[/C][C]295090[/C][C]293355.228994646[/C][C]1734.77100535377[/C][/ROW]
[ROW][C]29[/C][C]299712[/C][C]303147.225745087[/C][C]-3435.22574508743[/C][/ROW]
[ROW][C]30[/C][C]298380[/C][C]301016.643123487[/C][C]-2636.64312348654[/C][/ROW]
[ROW][C]31[/C][C]283312[/C][C]288358.092841616[/C][C]-5046.09284161642[/C][/ROW]
[ROW][C]32[/C][C]276788[/C][C]277731.881283532[/C][C]-943.881283531664[/C][/ROW]
[ROW][C]33[/C][C]270264[/C][C]276799.389429656[/C][C]-6535.38942965592[/C][/ROW]
[ROW][C]34[/C][C]265010[/C][C]272449.921061792[/C][C]-7439.92106179229[/C][/ROW]
[ROW][C]35[/C][C]264380[/C][C]272041.923481027[/C][C]-7661.92348102678[/C][/ROW]
[ROW][C]36[/C][C]268300[/C][C]270950.350703561[/C][C]-2650.35070356115[/C][/ROW]
[ROW][C]37[/C][C]263046[/C][C]267169.739752109[/C][C]-4123.73975210934[/C][/ROW]
[ROW][C]38[/C][C]261082[/C][C]261325.38553325[/C][C]-243.385533250286[/C][/ROW]
[ROW][C]39[/C][C]259118[/C][C]256378.296732122[/C][C]2739.70326787824[/C][/ROW]
[ROW][C]40[/C][C]270264[/C][C]260929.660126232[/C][C]9334.33987376821[/C][/ROW]
[ROW][C]41[/C][C]271536[/C][C]269348.028643214[/C][C]2187.97135678597[/C][/ROW]
[ROW][C]42[/C][C]265010[/C][C]269499.449418514[/C][C]-4489.44941851427[/C][/ROW]
[ROW][C]43[/C][C]247340[/C][C]255583.38385011[/C][C]-8243.38385010979[/C][/ROW]
[ROW][C]44[/C][C]239490[/C][C]246527.765682528[/C][C]-7037.76568252846[/C][/ROW]
[ROW][C]45[/C][C]227082[/C][C]239763.723427366[/C][C]-12681.7234273661[/C][/ROW]
[ROW][C]46[/C][C]221820[/C][C]232211.190624576[/C][C]-10391.1906245761[/C][/ROW]
[ROW][C]47[/C][C]224416[/C][C]229541.255685049[/C][C]-5125.25568504876[/C][/ROW]
[ROW][C]48[/C][C]228344[/C][C]231184.273992935[/C][C]-2840.27399293522[/C][/ROW]
[ROW][C]49[/C][C]228344[/C][C]226278.406792237[/C][C]2065.59320776255[/C][/ROW]
[ROW][C]50[/C][C]225118[/C][C]224860.156283927[/C][C]257.843716073054[/C][/ROW]
[ROW][C]51[/C][C]224416[/C][C]221778.983443715[/C][C]2637.01655628523[/C][/ROW]
[ROW][C]52[/C][C]234930[/C][C]228641.287810014[/C][C]6288.71218998558[/C][/ROW]
[ROW][C]53[/C][C]243420[/C][C]230767.233787186[/C][C]12652.7662128136[/C][/ROW]
[ROW][C]54[/C][C]239490[/C][C]230874.73174237[/C][C]8615.2682576298[/C][/ROW]
[ROW][C]55[/C][C]226380[/C][C]220909.533572358[/C][C]5470.46642764163[/C][/ROW]
[ROW][C]56[/C][C]219864[/C][C]218095.210116072[/C][C]1768.78988392817[/C][/ROW]
[ROW][C]57[/C][C]206122[/C][C]211604.439047947[/C][C]-5482.43904794726[/C][/ROW]
[ROW][C]58[/C][C]197634[/C][C]208193.652323929[/C][C]-10559.6523239291[/C][/ROW]
[ROW][C]59[/C][C]204158[/C][C]208306.647946311[/C][C]-4148.64794631131[/C][/ROW]
[ROW][C]60[/C][C]210682[/C][C]211309.905188476[/C][C]-627.905188476259[/C][/ROW]
[ROW][C]61[/C][C]210682[/C][C]210341.922973016[/C][C]340.077026984189[/C][/ROW]
[ROW][C]62[/C][C]202194[/C][C]207387.250495152[/C][C]-5193.25049515167[/C][/ROW]
[ROW][C]63[/C][C]201562[/C][C]203758.773938233[/C][C]-2196.77393823329[/C][/ROW]
[ROW][C]64[/C][C]212638[/C][C]210071.396274367[/C][C]2566.603725633[/C][/ROW]
[ROW][C]65[/C][C]219864[/C][C]213999.437801255[/C][C]5864.56219874538[/C][/ROW]
[ROW][C]66[/C][C]217260[/C][C]209481.416278921[/C][C]7778.58372107946[/C][/ROW]
[ROW][C]67[/C][C]204158[/C][C]198668.69851568[/C][C]5489.30148432023[/C][/ROW]
[ROW][C]68[/C][C]195670[/C][C]194121.22114311[/C][C]1548.77885689033[/C][/ROW]
[ROW][C]69[/C][C]177304[/C][C]184108.91955822[/C][C]-6804.91955822019[/C][/ROW]
[ROW][C]70[/C][C]170150[/C][C]177197.823986706[/C][C]-7047.82398670644[/C][/ROW]
[ROW][C]71[/C][C]172744[/C][C]181394.236990281[/C][C]-8650.23699028121[/C][/ROW]
[ROW][C]72[/C][C]183892[/C][C]183661.791768103[/C][C]230.208231897035[/C][/ROW]
[ROW][C]73[/C][C]184522[/C][C]183297.151981129[/C][C]1224.84801887124[/C][/ROW]
[ROW][C]74[/C][C]168184[/C][C]177731.291851936[/C][C]-9547.29185193649[/C][/ROW]
[ROW][C]75[/C][C]174078[/C][C]173873.099290885[/C][C]204.900709114678[/C][/ROW]
[ROW][C]76[/C][C]188452[/C][C]182263.782607228[/C][C]6188.21739277232[/C][/ROW]
[ROW][C]77[/C][C]194976[/C][C]188561.719971926[/C][C]6414.28002807358[/C][/ROW]
[ROW][C]78[/C][C]191046[/C][C]185769.184463502[/C][C]5276.81553649751[/C][/ROW]
[ROW][C]79[/C][C]173384[/C][C]174273.094862267[/C][C]-889.094862266997[/C][/ROW]
[ROW][C]80[/C][C]160968[/C][C]165792.458924787[/C][C]-4824.45892478741[/C][/ROW]
[ROW][C]81[/C][C]146594[/C][C]150230.456576953[/C][C]-3636.45657695338[/C][/ROW]
[ROW][C]82[/C][C]135448[/C][C]144607.63403274[/C][C]-9159.63403273956[/C][/ROW]
[ROW][C]83[/C][C]140008[/C][C]145423.00109766[/C][C]-5415.00109766028[/C][/ROW]
[ROW][C]84[/C][C]149820[/C][C]152023.319483249[/C][C]-2203.31948324948[/C][/ROW]
[ROW][C]85[/C][C]147226[/C][C]150752.809392039[/C][C]-3526.80939203911[/C][/ROW]
[ROW][C]86[/C][C]132852[/C][C]138423.277804816[/C][C]-5571.27780481568[/C][/ROW]
[ROW][C]87[/C][C]137412[/C][C]140412.695080655[/C][C]-3000.69508065539[/C][/ROW]
[ROW][C]88[/C][C]151786[/C][C]148137.545605254[/C][C]3648.45439474646[/C][/ROW]
[ROW][C]89[/C][C]159642[/C][C]151959.162791583[/C][C]7682.83720841707[/C][/ROW]
[ROW][C]90[/C][C]155082[/C][C]149410.257078352[/C][C]5671.74292164776[/C][/ROW]
[ROW][C]91[/C][C]137412[/C][C]137163.688231873[/C][C]248.311768127111[/C][/ROW]
[ROW][C]92[/C][C]129564[/C][C]128235.016439566[/C][C]1328.98356043405[/C][/ROW]
[ROW][C]93[/C][C]117786[/C][C]117816.82050469[/C][C]-30.8205046903313[/C][/ROW]
[ROW][C]94[/C][C]105368[/C][C]111071.66428108[/C][C]-5703.66428107968[/C][/ROW]
[ROW][C]95[/C][C]107332[/C][C]113709.515786508[/C][C]-6377.51578650765[/C][/ROW]
[ROW][C]96[/C][C]117146[/C][C]119180.764891169[/C][C]-2034.76489116877[/C][/ROW]
[ROW][C]97[/C][C]118416[/C][C]116821.364331726[/C][C]1594.63566827391[/C][/ROW]
[ROW][C]98[/C][C]106638[/C][C]107123.90258672[/C][C]-485.902586720331[/C][/ROW]
[ROW][C]99[/C][C]108604[/C][C]111057.189112601[/C][C]-2453.18911260071[/C][/ROW]
[ROW][C]100[/C][C]125004[/C][C]119995.271008295[/C][C]5008.72899170489[/C][/ROW]
[ROW][C]101[/C][C]128924[/C][C]125269.503131536[/C][C]3654.49686846377[/C][/ROW]
[ROW][C]102[/C][C]122346[/C][C]120732.833070248[/C][C]1613.16692975219[/C][/ROW]
[ROW][C]103[/C][C]98150[/C][C]106893.576456111[/C][C]-8743.57645611053[/C][/ROW]
[ROW][C]104[/C][C]85742[/C][C]96599.9306251865[/C][C]-10857.9306251865[/C][/ROW]
[ROW][C]105[/C][C]69342[/C][C]83269.4185344786[/C][C]-13927.4185344786[/C][/ROW]
[ROW][C]106[/C][C]53004[/C][C]70177.1215304444[/C][C]-17173.1215304444[/C][/ROW]
[ROW][C]107[/C][C]58258[/C][C]64970.4985050131[/C][C]-6712.49850501313[/C][/ROW]
[ROW][C]108[/C][C]65412[/C][C]67056.6365648604[/C][C]-1644.63656486035[/C][/ROW]
[ROW][C]109[/C][C]64150[/C][C]65211.9917750035[/C][C]-1061.99177500347[/C][/ROW]
[ROW][C]110[/C][C]51670[/C][C]56936.0838969608[/C][C]-5266.08389696084[/C][/ROW]
[ROW][C]111[/C][C]58888[/C][C]54695.4823216243[/C][C]4192.5176783757[/C][/ROW]
[ROW][C]112[/C][C]76560[/C][C]61848.979209954[/C][C]14711.020790046[/C][/ROW]
[ROW][C]113[/C][C]84408[/C][C]66962.8773104128[/C][C]17445.1226895872[/C][/ROW]
[ROW][C]114[/C][C]80488[/C][C]67946.1477114198[/C][C]12541.8522885802[/C][/ROW]
[ROW][C]115[/C][C]64782[/C][C]59048.3401008853[/C][C]5733.65989911467[/C][/ROW]
[ROW][C]116[/C][C]52372[/C][C]54952.2106085802[/C][C]-2580.21060858022[/C][/ROW]
[ROW][C]117[/C][C]39262[/C][C]45836.1581294742[/C][C]-6574.15812947418[/C][/ROW]
[ROW][C]118[/C][C]24186[/C][C]35851.8116676705[/C][C]-11665.8116676705[/C][/ROW]
[ROW][C]119[/C][C]26854[/C][C]35038.5667404018[/C][C]-8184.56674040177[/C][/ROW]
[ROW][C]120[/C][C]31414[/C][C]34940.1850986821[/C][C]-3526.18509868212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211085&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211085&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
13319980325101.524744003-5121.52474400308
14314086317303.095120185-3217.09512018471
15311490313806.066798973-2316.06679897313
16314086316126.059114899-2040.05911489902
17323268325244.494503624-1976.49450362392
18321934323639.634729579-1705.63472957921
19309526309795.80659297-269.806592969748
20299020302605.245135898-3585.24513589783
21297054301237.780856197-4183.780856197
22293126298911.300025601-5785.30002560141
23295784296499.624274133-715.624274132773
24299020296827.7063095562192.29369044426
25297748294249.7087300023498.29126999818
26295090290971.0146778664118.98532213416
27289900290726.664396417-826.664396417211
28295090293355.2289946461734.77100535377
29299712303147.225745087-3435.22574508743
30298380301016.643123487-2636.64312348654
31283312288358.092841616-5046.09284161642
32276788277731.881283532-943.881283531664
33270264276799.389429656-6535.38942965592
34265010272449.921061792-7439.92106179229
35264380272041.923481027-7661.92348102678
36268300270950.350703561-2650.35070356115
37263046267169.739752109-4123.73975210934
38261082261325.38553325-243.385533250286
39259118256378.2967321222739.70326787824
40270264260929.6601262329334.33987376821
41271536269348.0286432142187.97135678597
42265010269499.449418514-4489.44941851427
43247340255583.38385011-8243.38385010979
44239490246527.765682528-7037.76568252846
45227082239763.723427366-12681.7234273661
46221820232211.190624576-10391.1906245761
47224416229541.255685049-5125.25568504876
48228344231184.273992935-2840.27399293522
49228344226278.4067922372065.59320776255
50225118224860.156283927257.843716073054
51224416221778.9834437152637.01655628523
52234930228641.2878100146288.71218998558
53243420230767.23378718612652.7662128136
54239490230874.731742378615.2682576298
55226380220909.5335723585470.46642764163
56219864218095.2101160721768.78988392817
57206122211604.439047947-5482.43904794726
58197634208193.652323929-10559.6523239291
59204158208306.647946311-4148.64794631131
60210682211309.905188476-627.905188476259
61210682210341.922973016340.077026984189
62202194207387.250495152-5193.25049515167
63201562203758.773938233-2196.77393823329
64212638210071.3962743672566.603725633
65219864213999.4378012555864.56219874538
66217260209481.4162789217778.58372107946
67204158198668.698515685489.30148432023
68195670194121.221143111548.77885689033
69177304184108.91955822-6804.91955822019
70170150177197.823986706-7047.82398670644
71172744181394.236990281-8650.23699028121
72183892183661.791768103230.208231897035
73184522183297.1519811291224.84801887124
74168184177731.291851936-9547.29185193649
75174078173873.099290885204.900709114678
76188452182263.7826072286188.21739277232
77194976188561.7199719266414.28002807358
78191046185769.1844635025276.81553649751
79173384174273.094862267-889.094862266997
80160968165792.458924787-4824.45892478741
81146594150230.456576953-3636.45657695338
82135448144607.63403274-9159.63403273956
83140008145423.00109766-5415.00109766028
84149820152023.319483249-2203.31948324948
85147226150752.809392039-3526.80939203911
86132852138423.277804816-5571.27780481568
87137412140412.695080655-3000.69508065539
88151786148137.5456052543648.45439474646
89159642151959.1627915837682.83720841707
90155082149410.2570783525671.74292164776
91137412137163.688231873248.311768127111
92129564128235.0164395661328.98356043405
93117786117816.82050469-30.8205046903313
94105368111071.66428108-5703.66428107968
95107332113709.515786508-6377.51578650765
96117146119180.764891169-2034.76489116877
97118416116821.3643317261594.63566827391
98106638107123.90258672-485.902586720331
99108604111057.189112601-2453.18911260071
100125004119995.2710082955008.72899170489
101128924125269.5031315363654.49686846377
102122346120732.8330702481613.16692975219
10398150106893.576456111-8743.57645611053
1048574296599.9306251865-10857.9306251865
1056934283269.4185344786-13927.4185344786
1065300470177.1215304444-17173.1215304444
1075825864970.4985050131-6712.49850501313
1086541267056.6365648604-1644.63656486035
1096415065211.9917750035-1061.99177500347
1105167056936.0838969608-5266.08389696084
1115888854695.48232162434192.5176783757
1127656061848.97920995414711.020790046
1138440866962.877310412817445.1226895872
1148048867946.147711419812541.8522885802
1156478259048.34010088535733.65989911467
1165237254952.2106085802-2580.21060858022
1173926245836.1581294742-6574.15812947418
1182418635851.8116676705-11665.8116676705
1192685435038.5667404018-8184.56674040177
1203141434940.1850986821-3526.18509868212







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12131746.34682900619851.297511094143641.3961469178
12225224.948450544512657.593182574737792.3037185144
12326452.266691573912516.152159779140388.3812233686
12429503.581685773313294.744077253245712.4192942934
12527136.08091518499637.2003089562144634.9615214136
12621605.60404530654008.8692881448839202.3388024682
12714516.7385890314-1934.9545763886230968.4317544514
1289907.86030727421-6107.6761482118525923.3967627603
1296107.01786476914-9341.2340180211621555.2697475594
1302962.80376780433-11480.36763033717405.9751659457
1311837.89251491639-15363.269719622419039.0547494552
132-222.337350121086-17988.527717022617543.8530167804

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 31746.346829006 & 19851.2975110941 & 43641.3961469178 \tabularnewline
122 & 25224.9484505445 & 12657.5931825747 & 37792.3037185144 \tabularnewline
123 & 26452.2666915739 & 12516.1521597791 & 40388.3812233686 \tabularnewline
124 & 29503.5816857733 & 13294.7440772532 & 45712.4192942934 \tabularnewline
125 & 27136.0809151849 & 9637.20030895621 & 44634.9615214136 \tabularnewline
126 & 21605.6040453065 & 4008.86928814488 & 39202.3388024682 \tabularnewline
127 & 14516.7385890314 & -1934.95457638862 & 30968.4317544514 \tabularnewline
128 & 9907.86030727421 & -6107.67614821185 & 25923.3967627603 \tabularnewline
129 & 6107.01786476914 & -9341.23401802116 & 21555.2697475594 \tabularnewline
130 & 2962.80376780433 & -11480.367630337 & 17405.9751659457 \tabularnewline
131 & 1837.89251491639 & -15363.2697196224 & 19039.0547494552 \tabularnewline
132 & -222.337350121086 & -17988.5277170226 & 17543.8530167804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211085&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]31746.346829006[/C][C]19851.2975110941[/C][C]43641.3961469178[/C][/ROW]
[ROW][C]122[/C][C]25224.9484505445[/C][C]12657.5931825747[/C][C]37792.3037185144[/C][/ROW]
[ROW][C]123[/C][C]26452.2666915739[/C][C]12516.1521597791[/C][C]40388.3812233686[/C][/ROW]
[ROW][C]124[/C][C]29503.5816857733[/C][C]13294.7440772532[/C][C]45712.4192942934[/C][/ROW]
[ROW][C]125[/C][C]27136.0809151849[/C][C]9637.20030895621[/C][C]44634.9615214136[/C][/ROW]
[ROW][C]126[/C][C]21605.6040453065[/C][C]4008.86928814488[/C][C]39202.3388024682[/C][/ROW]
[ROW][C]127[/C][C]14516.7385890314[/C][C]-1934.95457638862[/C][C]30968.4317544514[/C][/ROW]
[ROW][C]128[/C][C]9907.86030727421[/C][C]-6107.67614821185[/C][C]25923.3967627603[/C][/ROW]
[ROW][C]129[/C][C]6107.01786476914[/C][C]-9341.23401802116[/C][C]21555.2697475594[/C][/ROW]
[ROW][C]130[/C][C]2962.80376780433[/C][C]-11480.367630337[/C][C]17405.9751659457[/C][/ROW]
[ROW][C]131[/C][C]1837.89251491639[/C][C]-15363.2697196224[/C][C]19039.0547494552[/C][/ROW]
[ROW][C]132[/C][C]-222.337350121086[/C][C]-17988.5277170226[/C][C]17543.8530167804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211085&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211085&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
12131746.34682900619851.297511094143641.3961469178
12225224.948450544512657.593182574737792.3037185144
12326452.266691573912516.152159779140388.3812233686
12429503.581685773313294.744077253245712.4192942934
12527136.08091518499637.2003089562144634.9615214136
12621605.60404530654008.8692881448839202.3388024682
12714516.7385890314-1934.9545763886230968.4317544514
1289907.86030727421-6107.6761482118525923.3967627603
1296107.01786476914-9341.2340180211621555.2697475594
1302962.80376780433-11480.36763033717405.9751659457
1311837.89251491639-15363.269719622419039.0547494552
132-222.337350121086-17988.527717022617543.8530167804



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=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')