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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 20 May 2015 19:39:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/20/t1432147269z6pu4ctnecvt79b.htm/, Retrieved Mon, 29 Apr 2024 00:33:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279178, Retrieved Mon, 29 Apr 2024 00:33:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-05-15 16:45:20] [925d3f0525c27710896bdfb64818612e]
- R  D    [Exponential Smoothing] [] [2015-05-20 18:39:07] [9baff654455058ed055e965df18e01ff] [Current]
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Dataseries X:
304040
307100
304330
294710
286890
279050
271860
266710
259590
253830
250640
249140
250840
247590
237830
226380
217230
211420
207620
204310
197490
193580
192330
191970
196070
191940
185620
179410
173920
169190
166840
165170
161450
160830
163670
170830
182690
190940
197770
205090
210720
220210
229730
237070
241620
250370
258570
269860
283220
289610
281770
274700
267650
261380
260500
260730
254200
250450
253380
263740
276240
273820
265890
258400
253520
250710
252850
255260
251170
252500
257780
269900
291590
298870
295570
292100
290870
290580
297970
304010
304340
309850
322320
340170
369280
376690
379700
379520
377770
381560
394580
399320
400370
408200
419070
437730




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279178&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]2 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=279178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279178&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.353536678055785
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.353536678055785 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279178&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.353536678055785[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279178&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.353536678055785
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13250840285298.219884236-34458.2198842358
14247590235208.38473928112381.6152607195
15237830229878.0706407767951.92935922384
16226380221287.6444458115092.35555418945
17217230213846.2979255043383.70207449637
18211420209119.0359533762300.96404662388
19207620208434.45602683-814.456026830041
20204310200683.4943500113626.5056499888
21197490197573.58389947-83.5838994700462
22193580192043.9090001421536.09099985784
23192330190730.6145945491599.38540545088
24191970191335.126535566634.873464434204
25196070193510.6333336522559.36666634824
26191940194561.443117953-2621.44311795267
27185620184371.3392397721248.66076022829
28179410177068.2749412372341.72505876268
29173920173285.559824515634.440175485157
30169190170551.733104824-1361.73310482362
31166840168822.266910416-1982.26691041645
32165170162835.8377351912334.16226480942
33161450161104.081967905345.918032094865
34160830158570.0028061342259.99719386565
35163670160472.013719193197.98628080953
36170830165624.5172334995205.48276650065
37182690176944.6016634095745.39833659129
38190940187444.7230219493495.27697805112
39197770191781.9431840315988.05681596856
40205090198691.7274413766398.2725586236
41210720209494.3411662441225.65883375562
42220210218329.993062681880.00693732011
43229730233140.212516165-3410.21251616487
44237070237584.741376339-514.741376338672
45241620243360.443400733-1740.44340073343
46250370248800.0372619151569.96273808542
47258570260884.899165839-2314.8991658391
48269860270314.259527738-454.259527737799
49283220285273.411281575-2053.41128157516
50289610292518.585567199-2908.58556719875
51281770290031.851895614-8261.85189561371
52274700276855.228307702-2155.22830770211
53267650271290.847962472-3640.84796247177
54261380266800.746430662-5420.74643066182
55260500264037.444753494-3537.44475349429
56260730257360.5420081013369.45799189879
57254200257353.431087096-3153.43108709648
58250450251386.468798973-936.468798973423
59253380249992.356649083387.64335091971
60263740255927.3822293387812.61777066233
61276240272602.4582831623637.54171683808
62273820281078.978251524-7258.97825152375
63265890268696.9889478-2806.9889477996
64258400257604.874022868795.125977132062
65253520252601.857975739918.142024260858
66250710251661.638929861-951.638929861278
67252850253707.161578226-857.161578226252
68255260251175.1762550094084.82374499066
69251170253614.360418885-2444.36041888542
70252500250298.5895109552201.41048904497
71257780255140.7073330612639.29266693856
72269900263263.2448426736636.75515732722
73291590281463.0631083510126.9368916503
74298870301422.599461308-2552.59946130781
75295570299699.72942357-4129.72942356952
76292100292266.319357323-166.319357323286
77290870290991.437135338-121.437135338492
78290580293756.775814767-3176.77581476705
79297970298412.483374611-442.483374610601
80304010300564.2834108343445.7165891655
81304340306100.953895198-1760.95389519754
82309850307749.8092389032100.19076109707
83322320317394.8894982424925.11050175846
84340170334133.7024689146036.29753108631
85369280358989.04204200310290.9579579971
86376690385090.147371957-8400.14737195679
87379700379276.713860854423.286139146483
88379520378780.435927814739.564072185545
89377770381605.938444973-3835.93844497262
90381560383735.875271328-2175.87527132779
91394580394748.273035594-168.273035593913
92399320401023.796415997-1703.79641599697
93400370402900.064631184-2530.06463118427
94408200405604.2577517362595.74224826408
95419070418827.471427588242.5285724118
96437730432993.2244283094736.77557169128

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 250840 & 285298.219884236 & -34458.2198842358 \tabularnewline
14 & 247590 & 235208.384739281 & 12381.6152607195 \tabularnewline
15 & 237830 & 229878.070640776 & 7951.92935922384 \tabularnewline
16 & 226380 & 221287.644445811 & 5092.35555418945 \tabularnewline
17 & 217230 & 213846.297925504 & 3383.70207449637 \tabularnewline
18 & 211420 & 209119.035953376 & 2300.96404662388 \tabularnewline
19 & 207620 & 208434.45602683 & -814.456026830041 \tabularnewline
20 & 204310 & 200683.494350011 & 3626.5056499888 \tabularnewline
21 & 197490 & 197573.58389947 & -83.5838994700462 \tabularnewline
22 & 193580 & 192043.909000142 & 1536.09099985784 \tabularnewline
23 & 192330 & 190730.614594549 & 1599.38540545088 \tabularnewline
24 & 191970 & 191335.126535566 & 634.873464434204 \tabularnewline
25 & 196070 & 193510.633333652 & 2559.36666634824 \tabularnewline
26 & 191940 & 194561.443117953 & -2621.44311795267 \tabularnewline
27 & 185620 & 184371.339239772 & 1248.66076022829 \tabularnewline
28 & 179410 & 177068.274941237 & 2341.72505876268 \tabularnewline
29 & 173920 & 173285.559824515 & 634.440175485157 \tabularnewline
30 & 169190 & 170551.733104824 & -1361.73310482362 \tabularnewline
31 & 166840 & 168822.266910416 & -1982.26691041645 \tabularnewline
32 & 165170 & 162835.837735191 & 2334.16226480942 \tabularnewline
33 & 161450 & 161104.081967905 & 345.918032094865 \tabularnewline
34 & 160830 & 158570.002806134 & 2259.99719386565 \tabularnewline
35 & 163670 & 160472.01371919 & 3197.98628080953 \tabularnewline
36 & 170830 & 165624.517233499 & 5205.48276650065 \tabularnewline
37 & 182690 & 176944.601663409 & 5745.39833659129 \tabularnewline
38 & 190940 & 187444.723021949 & 3495.27697805112 \tabularnewline
39 & 197770 & 191781.943184031 & 5988.05681596856 \tabularnewline
40 & 205090 & 198691.727441376 & 6398.2725586236 \tabularnewline
41 & 210720 & 209494.341166244 & 1225.65883375562 \tabularnewline
42 & 220210 & 218329.99306268 & 1880.00693732011 \tabularnewline
43 & 229730 & 233140.212516165 & -3410.21251616487 \tabularnewline
44 & 237070 & 237584.741376339 & -514.741376338672 \tabularnewline
45 & 241620 & 243360.443400733 & -1740.44340073343 \tabularnewline
46 & 250370 & 248800.037261915 & 1569.96273808542 \tabularnewline
47 & 258570 & 260884.899165839 & -2314.8991658391 \tabularnewline
48 & 269860 & 270314.259527738 & -454.259527737799 \tabularnewline
49 & 283220 & 285273.411281575 & -2053.41128157516 \tabularnewline
50 & 289610 & 292518.585567199 & -2908.58556719875 \tabularnewline
51 & 281770 & 290031.851895614 & -8261.85189561371 \tabularnewline
52 & 274700 & 276855.228307702 & -2155.22830770211 \tabularnewline
53 & 267650 & 271290.847962472 & -3640.84796247177 \tabularnewline
54 & 261380 & 266800.746430662 & -5420.74643066182 \tabularnewline
55 & 260500 & 264037.444753494 & -3537.44475349429 \tabularnewline
56 & 260730 & 257360.542008101 & 3369.45799189879 \tabularnewline
57 & 254200 & 257353.431087096 & -3153.43108709648 \tabularnewline
58 & 250450 & 251386.468798973 & -936.468798973423 \tabularnewline
59 & 253380 & 249992.35664908 & 3387.64335091971 \tabularnewline
60 & 263740 & 255927.382229338 & 7812.61777066233 \tabularnewline
61 & 276240 & 272602.458283162 & 3637.54171683808 \tabularnewline
62 & 273820 & 281078.978251524 & -7258.97825152375 \tabularnewline
63 & 265890 & 268696.9889478 & -2806.9889477996 \tabularnewline
64 & 258400 & 257604.874022868 & 795.125977132062 \tabularnewline
65 & 253520 & 252601.857975739 & 918.142024260858 \tabularnewline
66 & 250710 & 251661.638929861 & -951.638929861278 \tabularnewline
67 & 252850 & 253707.161578226 & -857.161578226252 \tabularnewline
68 & 255260 & 251175.176255009 & 4084.82374499066 \tabularnewline
69 & 251170 & 253614.360418885 & -2444.36041888542 \tabularnewline
70 & 252500 & 250298.589510955 & 2201.41048904497 \tabularnewline
71 & 257780 & 255140.707333061 & 2639.29266693856 \tabularnewline
72 & 269900 & 263263.244842673 & 6636.75515732722 \tabularnewline
73 & 291590 & 281463.06310835 & 10126.9368916503 \tabularnewline
74 & 298870 & 301422.599461308 & -2552.59946130781 \tabularnewline
75 & 295570 & 299699.72942357 & -4129.72942356952 \tabularnewline
76 & 292100 & 292266.319357323 & -166.319357323286 \tabularnewline
77 & 290870 & 290991.437135338 & -121.437135338492 \tabularnewline
78 & 290580 & 293756.775814767 & -3176.77581476705 \tabularnewline
79 & 297970 & 298412.483374611 & -442.483374610601 \tabularnewline
80 & 304010 & 300564.283410834 & 3445.7165891655 \tabularnewline
81 & 304340 & 306100.953895198 & -1760.95389519754 \tabularnewline
82 & 309850 & 307749.809238903 & 2100.19076109707 \tabularnewline
83 & 322320 & 317394.889498242 & 4925.11050175846 \tabularnewline
84 & 340170 & 334133.702468914 & 6036.29753108631 \tabularnewline
85 & 369280 & 358989.042042003 & 10290.9579579971 \tabularnewline
86 & 376690 & 385090.147371957 & -8400.14737195679 \tabularnewline
87 & 379700 & 379276.713860854 & 423.286139146483 \tabularnewline
88 & 379520 & 378780.435927814 & 739.564072185545 \tabularnewline
89 & 377770 & 381605.938444973 & -3835.93844497262 \tabularnewline
90 & 381560 & 383735.875271328 & -2175.87527132779 \tabularnewline
91 & 394580 & 394748.273035594 & -168.273035593913 \tabularnewline
92 & 399320 & 401023.796415997 & -1703.79641599697 \tabularnewline
93 & 400370 & 402900.064631184 & -2530.06463118427 \tabularnewline
94 & 408200 & 405604.257751736 & 2595.74224826408 \tabularnewline
95 & 419070 & 418827.471427588 & 242.5285724118 \tabularnewline
96 & 437730 & 432993.224428309 & 4736.77557169128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279178&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]250840[/C][C]285298.219884236[/C][C]-34458.2198842358[/C][/ROW]
[ROW][C]14[/C][C]247590[/C][C]235208.384739281[/C][C]12381.6152607195[/C][/ROW]
[ROW][C]15[/C][C]237830[/C][C]229878.070640776[/C][C]7951.92935922384[/C][/ROW]
[ROW][C]16[/C][C]226380[/C][C]221287.644445811[/C][C]5092.35555418945[/C][/ROW]
[ROW][C]17[/C][C]217230[/C][C]213846.297925504[/C][C]3383.70207449637[/C][/ROW]
[ROW][C]18[/C][C]211420[/C][C]209119.035953376[/C][C]2300.96404662388[/C][/ROW]
[ROW][C]19[/C][C]207620[/C][C]208434.45602683[/C][C]-814.456026830041[/C][/ROW]
[ROW][C]20[/C][C]204310[/C][C]200683.494350011[/C][C]3626.5056499888[/C][/ROW]
[ROW][C]21[/C][C]197490[/C][C]197573.58389947[/C][C]-83.5838994700462[/C][/ROW]
[ROW][C]22[/C][C]193580[/C][C]192043.909000142[/C][C]1536.09099985784[/C][/ROW]
[ROW][C]23[/C][C]192330[/C][C]190730.614594549[/C][C]1599.38540545088[/C][/ROW]
[ROW][C]24[/C][C]191970[/C][C]191335.126535566[/C][C]634.873464434204[/C][/ROW]
[ROW][C]25[/C][C]196070[/C][C]193510.633333652[/C][C]2559.36666634824[/C][/ROW]
[ROW][C]26[/C][C]191940[/C][C]194561.443117953[/C][C]-2621.44311795267[/C][/ROW]
[ROW][C]27[/C][C]185620[/C][C]184371.339239772[/C][C]1248.66076022829[/C][/ROW]
[ROW][C]28[/C][C]179410[/C][C]177068.274941237[/C][C]2341.72505876268[/C][/ROW]
[ROW][C]29[/C][C]173920[/C][C]173285.559824515[/C][C]634.440175485157[/C][/ROW]
[ROW][C]30[/C][C]169190[/C][C]170551.733104824[/C][C]-1361.73310482362[/C][/ROW]
[ROW][C]31[/C][C]166840[/C][C]168822.266910416[/C][C]-1982.26691041645[/C][/ROW]
[ROW][C]32[/C][C]165170[/C][C]162835.837735191[/C][C]2334.16226480942[/C][/ROW]
[ROW][C]33[/C][C]161450[/C][C]161104.081967905[/C][C]345.918032094865[/C][/ROW]
[ROW][C]34[/C][C]160830[/C][C]158570.002806134[/C][C]2259.99719386565[/C][/ROW]
[ROW][C]35[/C][C]163670[/C][C]160472.01371919[/C][C]3197.98628080953[/C][/ROW]
[ROW][C]36[/C][C]170830[/C][C]165624.517233499[/C][C]5205.48276650065[/C][/ROW]
[ROW][C]37[/C][C]182690[/C][C]176944.601663409[/C][C]5745.39833659129[/C][/ROW]
[ROW][C]38[/C][C]190940[/C][C]187444.723021949[/C][C]3495.27697805112[/C][/ROW]
[ROW][C]39[/C][C]197770[/C][C]191781.943184031[/C][C]5988.05681596856[/C][/ROW]
[ROW][C]40[/C][C]205090[/C][C]198691.727441376[/C][C]6398.2725586236[/C][/ROW]
[ROW][C]41[/C][C]210720[/C][C]209494.341166244[/C][C]1225.65883375562[/C][/ROW]
[ROW][C]42[/C][C]220210[/C][C]218329.99306268[/C][C]1880.00693732011[/C][/ROW]
[ROW][C]43[/C][C]229730[/C][C]233140.212516165[/C][C]-3410.21251616487[/C][/ROW]
[ROW][C]44[/C][C]237070[/C][C]237584.741376339[/C][C]-514.741376338672[/C][/ROW]
[ROW][C]45[/C][C]241620[/C][C]243360.443400733[/C][C]-1740.44340073343[/C][/ROW]
[ROW][C]46[/C][C]250370[/C][C]248800.037261915[/C][C]1569.96273808542[/C][/ROW]
[ROW][C]47[/C][C]258570[/C][C]260884.899165839[/C][C]-2314.8991658391[/C][/ROW]
[ROW][C]48[/C][C]269860[/C][C]270314.259527738[/C][C]-454.259527737799[/C][/ROW]
[ROW][C]49[/C][C]283220[/C][C]285273.411281575[/C][C]-2053.41128157516[/C][/ROW]
[ROW][C]50[/C][C]289610[/C][C]292518.585567199[/C][C]-2908.58556719875[/C][/ROW]
[ROW][C]51[/C][C]281770[/C][C]290031.851895614[/C][C]-8261.85189561371[/C][/ROW]
[ROW][C]52[/C][C]274700[/C][C]276855.228307702[/C][C]-2155.22830770211[/C][/ROW]
[ROW][C]53[/C][C]267650[/C][C]271290.847962472[/C][C]-3640.84796247177[/C][/ROW]
[ROW][C]54[/C][C]261380[/C][C]266800.746430662[/C][C]-5420.74643066182[/C][/ROW]
[ROW][C]55[/C][C]260500[/C][C]264037.444753494[/C][C]-3537.44475349429[/C][/ROW]
[ROW][C]56[/C][C]260730[/C][C]257360.542008101[/C][C]3369.45799189879[/C][/ROW]
[ROW][C]57[/C][C]254200[/C][C]257353.431087096[/C][C]-3153.43108709648[/C][/ROW]
[ROW][C]58[/C][C]250450[/C][C]251386.468798973[/C][C]-936.468798973423[/C][/ROW]
[ROW][C]59[/C][C]253380[/C][C]249992.35664908[/C][C]3387.64335091971[/C][/ROW]
[ROW][C]60[/C][C]263740[/C][C]255927.382229338[/C][C]7812.61777066233[/C][/ROW]
[ROW][C]61[/C][C]276240[/C][C]272602.458283162[/C][C]3637.54171683808[/C][/ROW]
[ROW][C]62[/C][C]273820[/C][C]281078.978251524[/C][C]-7258.97825152375[/C][/ROW]
[ROW][C]63[/C][C]265890[/C][C]268696.9889478[/C][C]-2806.9889477996[/C][/ROW]
[ROW][C]64[/C][C]258400[/C][C]257604.874022868[/C][C]795.125977132062[/C][/ROW]
[ROW][C]65[/C][C]253520[/C][C]252601.857975739[/C][C]918.142024260858[/C][/ROW]
[ROW][C]66[/C][C]250710[/C][C]251661.638929861[/C][C]-951.638929861278[/C][/ROW]
[ROW][C]67[/C][C]252850[/C][C]253707.161578226[/C][C]-857.161578226252[/C][/ROW]
[ROW][C]68[/C][C]255260[/C][C]251175.176255009[/C][C]4084.82374499066[/C][/ROW]
[ROW][C]69[/C][C]251170[/C][C]253614.360418885[/C][C]-2444.36041888542[/C][/ROW]
[ROW][C]70[/C][C]252500[/C][C]250298.589510955[/C][C]2201.41048904497[/C][/ROW]
[ROW][C]71[/C][C]257780[/C][C]255140.707333061[/C][C]2639.29266693856[/C][/ROW]
[ROW][C]72[/C][C]269900[/C][C]263263.244842673[/C][C]6636.75515732722[/C][/ROW]
[ROW][C]73[/C][C]291590[/C][C]281463.06310835[/C][C]10126.9368916503[/C][/ROW]
[ROW][C]74[/C][C]298870[/C][C]301422.599461308[/C][C]-2552.59946130781[/C][/ROW]
[ROW][C]75[/C][C]295570[/C][C]299699.72942357[/C][C]-4129.72942356952[/C][/ROW]
[ROW][C]76[/C][C]292100[/C][C]292266.319357323[/C][C]-166.319357323286[/C][/ROW]
[ROW][C]77[/C][C]290870[/C][C]290991.437135338[/C][C]-121.437135338492[/C][/ROW]
[ROW][C]78[/C][C]290580[/C][C]293756.775814767[/C][C]-3176.77581476705[/C][/ROW]
[ROW][C]79[/C][C]297970[/C][C]298412.483374611[/C][C]-442.483374610601[/C][/ROW]
[ROW][C]80[/C][C]304010[/C][C]300564.283410834[/C][C]3445.7165891655[/C][/ROW]
[ROW][C]81[/C][C]304340[/C][C]306100.953895198[/C][C]-1760.95389519754[/C][/ROW]
[ROW][C]82[/C][C]309850[/C][C]307749.809238903[/C][C]2100.19076109707[/C][/ROW]
[ROW][C]83[/C][C]322320[/C][C]317394.889498242[/C][C]4925.11050175846[/C][/ROW]
[ROW][C]84[/C][C]340170[/C][C]334133.702468914[/C][C]6036.29753108631[/C][/ROW]
[ROW][C]85[/C][C]369280[/C][C]358989.042042003[/C][C]10290.9579579971[/C][/ROW]
[ROW][C]86[/C][C]376690[/C][C]385090.147371957[/C][C]-8400.14737195679[/C][/ROW]
[ROW][C]87[/C][C]379700[/C][C]379276.713860854[/C][C]423.286139146483[/C][/ROW]
[ROW][C]88[/C][C]379520[/C][C]378780.435927814[/C][C]739.564072185545[/C][/ROW]
[ROW][C]89[/C][C]377770[/C][C]381605.938444973[/C][C]-3835.93844497262[/C][/ROW]
[ROW][C]90[/C][C]381560[/C][C]383735.875271328[/C][C]-2175.87527132779[/C][/ROW]
[ROW][C]91[/C][C]394580[/C][C]394748.273035594[/C][C]-168.273035593913[/C][/ROW]
[ROW][C]92[/C][C]399320[/C][C]401023.796415997[/C][C]-1703.79641599697[/C][/ROW]
[ROW][C]93[/C][C]400370[/C][C]402900.064631184[/C][C]-2530.06463118427[/C][/ROW]
[ROW][C]94[/C][C]408200[/C][C]405604.257751736[/C][C]2595.74224826408[/C][/ROW]
[ROW][C]95[/C][C]419070[/C][C]418827.471427588[/C][C]242.5285724118[/C][/ROW]
[ROW][C]96[/C][C]437730[/C][C]432993.224428309[/C][C]4736.77557169128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279178&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279178&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
13250840285298.219884236-34458.2198842358
14247590235208.38473928112381.6152607195
15237830229878.0706407767951.92935922384
16226380221287.6444458115092.35555418945
17217230213846.2979255043383.70207449637
18211420209119.0359533762300.96404662388
19207620208434.45602683-814.456026830041
20204310200683.4943500113626.5056499888
21197490197573.58389947-83.5838994700462
22193580192043.9090001421536.09099985784
23192330190730.6145945491599.38540545088
24191970191335.126535566634.873464434204
25196070193510.6333336522559.36666634824
26191940194561.443117953-2621.44311795267
27185620184371.3392397721248.66076022829
28179410177068.2749412372341.72505876268
29173920173285.559824515634.440175485157
30169190170551.733104824-1361.73310482362
31166840168822.266910416-1982.26691041645
32165170162835.8377351912334.16226480942
33161450161104.081967905345.918032094865
34160830158570.0028061342259.99719386565
35163670160472.013719193197.98628080953
36170830165624.5172334995205.48276650065
37182690176944.6016634095745.39833659129
38190940187444.7230219493495.27697805112
39197770191781.9431840315988.05681596856
40205090198691.7274413766398.2725586236
41210720209494.3411662441225.65883375562
42220210218329.993062681880.00693732011
43229730233140.212516165-3410.21251616487
44237070237584.741376339-514.741376338672
45241620243360.443400733-1740.44340073343
46250370248800.0372619151569.96273808542
47258570260884.899165839-2314.8991658391
48269860270314.259527738-454.259527737799
49283220285273.411281575-2053.41128157516
50289610292518.585567199-2908.58556719875
51281770290031.851895614-8261.85189561371
52274700276855.228307702-2155.22830770211
53267650271290.847962472-3640.84796247177
54261380266800.746430662-5420.74643066182
55260500264037.444753494-3537.44475349429
56260730257360.5420081013369.45799189879
57254200257353.431087096-3153.43108709648
58250450251386.468798973-936.468798973423
59253380249992.356649083387.64335091971
60263740255927.3822293387812.61777066233
61276240272602.4582831623637.54171683808
62273820281078.978251524-7258.97825152375
63265890268696.9889478-2806.9889477996
64258400257604.874022868795.125977132062
65253520252601.857975739918.142024260858
66250710251661.638929861-951.638929861278
67252850253707.161578226-857.161578226252
68255260251175.1762550094084.82374499066
69251170253614.360418885-2444.36041888542
70252500250298.5895109552201.41048904497
71257780255140.7073330612639.29266693856
72269900263263.2448426736636.75515732722
73291590281463.0631083510126.9368916503
74298870301422.599461308-2552.59946130781
75295570299699.72942357-4129.72942356952
76292100292266.319357323-166.319357323286
77290870290991.437135338-121.437135338492
78290580293756.775814767-3176.77581476705
79297970298412.483374611-442.483374610601
80304010300564.2834108343445.7165891655
81304340306100.953895198-1760.95389519754
82309850307749.8092389032100.19076109707
83322320317394.8894982424925.11050175846
84340170334133.7024689146036.29753108631
85369280358989.04204200310290.9579579971
86376690385090.147371957-8400.14737195679
87379700379276.713860854423.286139146483
88379520378780.435927814739.564072185545
89377770381605.938444973-3835.93844497262
90381560383735.875271328-2175.87527132779
91394580394748.273035594-168.273035593913
92399320401023.796415997-1703.79641599697
93400370402900.064631184-2530.06463118427
94408200405604.2577517362595.74224826408
95419070418827.471427588242.5285724118
96437730432993.2244283094736.77557169128







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97459451.43059287448662.319275545470240.541910195
98472413.324138817454150.842416625490675.805861009
99472604.704300344447009.142140755498200.266459933
100468393.791444523435410.07214253501377.510746517
101467739.062578329426845.436487148508632.68866951
102473546.83209028423786.870330773523306.793849786
103489257.109908235428970.347043462549543.872773008
104496672.746161602426232.168819909567113.323503294
105501271.700716951420646.181264454581897.220169449
106509036.014426586417305.729040605600766.299812568
107522384.398221693417992.871636779626775.924806608
108539732.05502137421658.967505398657805.142537342

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 459451.43059287 & 448662.319275545 & 470240.541910195 \tabularnewline
98 & 472413.324138817 & 454150.842416625 & 490675.805861009 \tabularnewline
99 & 472604.704300344 & 447009.142140755 & 498200.266459933 \tabularnewline
100 & 468393.791444523 & 435410.07214253 & 501377.510746517 \tabularnewline
101 & 467739.062578329 & 426845.436487148 & 508632.68866951 \tabularnewline
102 & 473546.83209028 & 423786.870330773 & 523306.793849786 \tabularnewline
103 & 489257.109908235 & 428970.347043462 & 549543.872773008 \tabularnewline
104 & 496672.746161602 & 426232.168819909 & 567113.323503294 \tabularnewline
105 & 501271.700716951 & 420646.181264454 & 581897.220169449 \tabularnewline
106 & 509036.014426586 & 417305.729040605 & 600766.299812568 \tabularnewline
107 & 522384.398221693 & 417992.871636779 & 626775.924806608 \tabularnewline
108 & 539732.05502137 & 421658.967505398 & 657805.142537342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279178&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]97[/C][C]459451.43059287[/C][C]448662.319275545[/C][C]470240.541910195[/C][/ROW]
[ROW][C]98[/C][C]472413.324138817[/C][C]454150.842416625[/C][C]490675.805861009[/C][/ROW]
[ROW][C]99[/C][C]472604.704300344[/C][C]447009.142140755[/C][C]498200.266459933[/C][/ROW]
[ROW][C]100[/C][C]468393.791444523[/C][C]435410.07214253[/C][C]501377.510746517[/C][/ROW]
[ROW][C]101[/C][C]467739.062578329[/C][C]426845.436487148[/C][C]508632.68866951[/C][/ROW]
[ROW][C]102[/C][C]473546.83209028[/C][C]423786.870330773[/C][C]523306.793849786[/C][/ROW]
[ROW][C]103[/C][C]489257.109908235[/C][C]428970.347043462[/C][C]549543.872773008[/C][/ROW]
[ROW][C]104[/C][C]496672.746161602[/C][C]426232.168819909[/C][C]567113.323503294[/C][/ROW]
[ROW][C]105[/C][C]501271.700716951[/C][C]420646.181264454[/C][C]581897.220169449[/C][/ROW]
[ROW][C]106[/C][C]509036.014426586[/C][C]417305.729040605[/C][C]600766.299812568[/C][/ROW]
[ROW][C]107[/C][C]522384.398221693[/C][C]417992.871636779[/C][C]626775.924806608[/C][/ROW]
[ROW][C]108[/C][C]539732.05502137[/C][C]421658.967505398[/C][C]657805.142537342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279178&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279178&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
97459451.43059287448662.319275545470240.541910195
98472413.324138817454150.842416625490675.805861009
99472604.704300344447009.142140755498200.266459933
100468393.791444523435410.07214253501377.510746517
101467739.062578329426845.436487148508632.68866951
102473546.83209028423786.870330773523306.793849786
103489257.109908235428970.347043462549543.872773008
104496672.746161602426232.168819909567113.323503294
105501271.700716951420646.181264454581897.220169449
106509036.014426586417305.729040605600766.299812568
107522384.398221693417992.871636779626775.924806608
108539732.05502137421658.967505398657805.142537342



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')