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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 10:05:40 -0500
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/Jan/15/t1358262350ru08e5cjsw4n5m5.htm/, Retrieved Sat, 27 Apr 2024 22:52:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205473, Retrieved Sat, 27 Apr 2024 22:52:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2012-12-17 14:08:52] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2012-12-17 14:23:39] [b98453cac15ba1066b407e146608df68]
- R P       [Exponential Smoothing] [] [2013-01-15 15:05:40] [7338cd26db379c04f0557b08db763c32] [Current]
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Dataseries X:
164
96
73
49
39
59
169
169
210
278
298
245
200
188
90
79
78
91
167
169
289
247
275
203
223
104
107
85
75
99
135
211
335
488
326
346
261
224
141
148
145
223
272
445
560
612
467
404
518
404
300
210
196
186
247
343
464
680
711
610
513
292
273
322
189
257
324
404
677
858
895
664
628
308
324
248
272




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205473&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205473&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0710417218745324
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0710417218745324 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205473&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]0.0710417218745324[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205473&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
beta0.0710417218745324
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3732845
4498.1968774843539640.803122515646
539-12.90439843427751.904398434277
659-19.217020596644278.2170205966442
71696.33965122643716162.660348773563
8169127.89532248402341.104677515977
9210130.81546955185579.1845304481446
10278177.440874940718100.559125059282
11298252.58476833512645.4152316648742
12245275.811144591929-30.8111445919292
13200220.622267827193-20.6222678271934
14188174.15722641179213.8427735882082
1590163.140640883017-73.1406408830174
167959.94460381568119.055396184319
177850.298331971616527.7016680283835
189151.266306167149539.7336938328505
1916767.089056193470799.9109438065293
20169150.18690167559618.8130983244038
21289153.523416574357135.476583425643
22247283.147906334593-36.1479063345931
23275238.57989682642436.4201031735757
24203269.167243666723-66.1672436667233
25223192.46660874494830.5333912550525
26104214.635753434375-110.635753434375
2710787.77599900951119.224000990489
288592.141705141193-7.14170514119304
297569.63434611084255.36565388915751
309960.01553140211138.984468597889
3113586.785055177668748.2149448223313
32211126.21032787793384.7896721220673
33335208.233932182661126.766067817339
34488341.239611915669146.760388084331
35326504.665722588154-178.665722588154
36346329.97300201553416.0269979844657
37261351.11158754883-90.1115875488304
38224259.709905208514-35.7099052085138
39141220.173012054525-79.1730120545247
40148131.54842495217816.4515750478218
41145139.7171731711245.28282682887649
42223137.09247428541285.9075257145881
43272221.19549283415750.8045071658431
44445273.804732502205171.195267497795
45560458.96673908202101.03326091798
46612581.14431590423230.8556840957679
47467635.336356832012-168.336356832012
48404478.37745218858-74.3774521885802
49518410.093549916463107.906450083537
50404531.759409931766-127.759409931766
51300408.683161464539-108.683161464539
52210296.96212253533-86.96212253533
53196200.784183612556-4.78418361255612
54186186.444306970956-0.444306970956205
55247176.41274263869970.5872573613014
56343242.427382944046100.572617055954
57464345.572234833129118.427765166871
58680474.985547188336205.014452811664
59711705.5501269252425.44987307475787
60610736.93729529247-126.93729529247
61513626.919451264797-113.919451264797
62292521.826417291944-229.826417291944
63273284.49915287527-11.4991528752698
64322264.68223325491257.3177667450879
65189317.754186098486-128.754186098486
66257175.60726701949681.3927329805044
67324249.38954691850574.6104530814953
68404321.69000197525382.3099980247469
69677407.53744596242269.46255403758
70858699.680529781959158.319470218041
71895891.9278175525133.07218244748731
72664929.146070683495-265.146070683495
73628679.309637273873-51.309637273873
74308639.664512293179-331.664512293179
75324296.10249425519527.8975057448051
76248314.084381099311-66.0843810993105
77272233.38963287700338.6103671229973

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 73 & 28 & 45 \tabularnewline
4 & 49 & 8.19687748435396 & 40.803122515646 \tabularnewline
5 & 39 & -12.904398434277 & 51.904398434277 \tabularnewline
6 & 59 & -19.2170205966442 & 78.2170205966442 \tabularnewline
7 & 169 & 6.33965122643716 & 162.660348773563 \tabularnewline
8 & 169 & 127.895322484023 & 41.104677515977 \tabularnewline
9 & 210 & 130.815469551855 & 79.1845304481446 \tabularnewline
10 & 278 & 177.440874940718 & 100.559125059282 \tabularnewline
11 & 298 & 252.584768335126 & 45.4152316648742 \tabularnewline
12 & 245 & 275.811144591929 & -30.8111445919292 \tabularnewline
13 & 200 & 220.622267827193 & -20.6222678271934 \tabularnewline
14 & 188 & 174.157226411792 & 13.8427735882082 \tabularnewline
15 & 90 & 163.140640883017 & -73.1406408830174 \tabularnewline
16 & 79 & 59.944603815681 & 19.055396184319 \tabularnewline
17 & 78 & 50.2983319716165 & 27.7016680283835 \tabularnewline
18 & 91 & 51.2663061671495 & 39.7336938328505 \tabularnewline
19 & 167 & 67.0890561934707 & 99.9109438065293 \tabularnewline
20 & 169 & 150.186901675596 & 18.8130983244038 \tabularnewline
21 & 289 & 153.523416574357 & 135.476583425643 \tabularnewline
22 & 247 & 283.147906334593 & -36.1479063345931 \tabularnewline
23 & 275 & 238.579896826424 & 36.4201031735757 \tabularnewline
24 & 203 & 269.167243666723 & -66.1672436667233 \tabularnewline
25 & 223 & 192.466608744948 & 30.5333912550525 \tabularnewline
26 & 104 & 214.635753434375 & -110.635753434375 \tabularnewline
27 & 107 & 87.775999009511 & 19.224000990489 \tabularnewline
28 & 85 & 92.141705141193 & -7.14170514119304 \tabularnewline
29 & 75 & 69.6343461108425 & 5.36565388915751 \tabularnewline
30 & 99 & 60.015531402111 & 38.984468597889 \tabularnewline
31 & 135 & 86.7850551776687 & 48.2149448223313 \tabularnewline
32 & 211 & 126.210327877933 & 84.7896721220673 \tabularnewline
33 & 335 & 208.233932182661 & 126.766067817339 \tabularnewline
34 & 488 & 341.239611915669 & 146.760388084331 \tabularnewline
35 & 326 & 504.665722588154 & -178.665722588154 \tabularnewline
36 & 346 & 329.973002015534 & 16.0269979844657 \tabularnewline
37 & 261 & 351.11158754883 & -90.1115875488304 \tabularnewline
38 & 224 & 259.709905208514 & -35.7099052085138 \tabularnewline
39 & 141 & 220.173012054525 & -79.1730120545247 \tabularnewline
40 & 148 & 131.548424952178 & 16.4515750478218 \tabularnewline
41 & 145 & 139.717173171124 & 5.28282682887649 \tabularnewline
42 & 223 & 137.092474285412 & 85.9075257145881 \tabularnewline
43 & 272 & 221.195492834157 & 50.8045071658431 \tabularnewline
44 & 445 & 273.804732502205 & 171.195267497795 \tabularnewline
45 & 560 & 458.96673908202 & 101.03326091798 \tabularnewline
46 & 612 & 581.144315904232 & 30.8556840957679 \tabularnewline
47 & 467 & 635.336356832012 & -168.336356832012 \tabularnewline
48 & 404 & 478.37745218858 & -74.3774521885802 \tabularnewline
49 & 518 & 410.093549916463 & 107.906450083537 \tabularnewline
50 & 404 & 531.759409931766 & -127.759409931766 \tabularnewline
51 & 300 & 408.683161464539 & -108.683161464539 \tabularnewline
52 & 210 & 296.96212253533 & -86.96212253533 \tabularnewline
53 & 196 & 200.784183612556 & -4.78418361255612 \tabularnewline
54 & 186 & 186.444306970956 & -0.444306970956205 \tabularnewline
55 & 247 & 176.412742638699 & 70.5872573613014 \tabularnewline
56 & 343 & 242.427382944046 & 100.572617055954 \tabularnewline
57 & 464 & 345.572234833129 & 118.427765166871 \tabularnewline
58 & 680 & 474.985547188336 & 205.014452811664 \tabularnewline
59 & 711 & 705.550126925242 & 5.44987307475787 \tabularnewline
60 & 610 & 736.93729529247 & -126.93729529247 \tabularnewline
61 & 513 & 626.919451264797 & -113.919451264797 \tabularnewline
62 & 292 & 521.826417291944 & -229.826417291944 \tabularnewline
63 & 273 & 284.49915287527 & -11.4991528752698 \tabularnewline
64 & 322 & 264.682233254912 & 57.3177667450879 \tabularnewline
65 & 189 & 317.754186098486 & -128.754186098486 \tabularnewline
66 & 257 & 175.607267019496 & 81.3927329805044 \tabularnewline
67 & 324 & 249.389546918505 & 74.6104530814953 \tabularnewline
68 & 404 & 321.690001975253 & 82.3099980247469 \tabularnewline
69 & 677 & 407.53744596242 & 269.46255403758 \tabularnewline
70 & 858 & 699.680529781959 & 158.319470218041 \tabularnewline
71 & 895 & 891.927817552513 & 3.07218244748731 \tabularnewline
72 & 664 & 929.146070683495 & -265.146070683495 \tabularnewline
73 & 628 & 679.309637273873 & -51.309637273873 \tabularnewline
74 & 308 & 639.664512293179 & -331.664512293179 \tabularnewline
75 & 324 & 296.102494255195 & 27.8975057448051 \tabularnewline
76 & 248 & 314.084381099311 & -66.0843810993105 \tabularnewline
77 & 272 & 233.389632877003 & 38.6103671229973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205473&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]73[/C][C]28[/C][C]45[/C][/ROW]
[ROW][C]4[/C][C]49[/C][C]8.19687748435396[/C][C]40.803122515646[/C][/ROW]
[ROW][C]5[/C][C]39[/C][C]-12.904398434277[/C][C]51.904398434277[/C][/ROW]
[ROW][C]6[/C][C]59[/C][C]-19.2170205966442[/C][C]78.2170205966442[/C][/ROW]
[ROW][C]7[/C][C]169[/C][C]6.33965122643716[/C][C]162.660348773563[/C][/ROW]
[ROW][C]8[/C][C]169[/C][C]127.895322484023[/C][C]41.104677515977[/C][/ROW]
[ROW][C]9[/C][C]210[/C][C]130.815469551855[/C][C]79.1845304481446[/C][/ROW]
[ROW][C]10[/C][C]278[/C][C]177.440874940718[/C][C]100.559125059282[/C][/ROW]
[ROW][C]11[/C][C]298[/C][C]252.584768335126[/C][C]45.4152316648742[/C][/ROW]
[ROW][C]12[/C][C]245[/C][C]275.811144591929[/C][C]-30.8111445919292[/C][/ROW]
[ROW][C]13[/C][C]200[/C][C]220.622267827193[/C][C]-20.6222678271934[/C][/ROW]
[ROW][C]14[/C][C]188[/C][C]174.157226411792[/C][C]13.8427735882082[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]163.140640883017[/C][C]-73.1406408830174[/C][/ROW]
[ROW][C]16[/C][C]79[/C][C]59.944603815681[/C][C]19.055396184319[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]50.2983319716165[/C][C]27.7016680283835[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]51.2663061671495[/C][C]39.7336938328505[/C][/ROW]
[ROW][C]19[/C][C]167[/C][C]67.0890561934707[/C][C]99.9109438065293[/C][/ROW]
[ROW][C]20[/C][C]169[/C][C]150.186901675596[/C][C]18.8130983244038[/C][/ROW]
[ROW][C]21[/C][C]289[/C][C]153.523416574357[/C][C]135.476583425643[/C][/ROW]
[ROW][C]22[/C][C]247[/C][C]283.147906334593[/C][C]-36.1479063345931[/C][/ROW]
[ROW][C]23[/C][C]275[/C][C]238.579896826424[/C][C]36.4201031735757[/C][/ROW]
[ROW][C]24[/C][C]203[/C][C]269.167243666723[/C][C]-66.1672436667233[/C][/ROW]
[ROW][C]25[/C][C]223[/C][C]192.466608744948[/C][C]30.5333912550525[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]214.635753434375[/C][C]-110.635753434375[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]87.775999009511[/C][C]19.224000990489[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]92.141705141193[/C][C]-7.14170514119304[/C][/ROW]
[ROW][C]29[/C][C]75[/C][C]69.6343461108425[/C][C]5.36565388915751[/C][/ROW]
[ROW][C]30[/C][C]99[/C][C]60.015531402111[/C][C]38.984468597889[/C][/ROW]
[ROW][C]31[/C][C]135[/C][C]86.7850551776687[/C][C]48.2149448223313[/C][/ROW]
[ROW][C]32[/C][C]211[/C][C]126.210327877933[/C][C]84.7896721220673[/C][/ROW]
[ROW][C]33[/C][C]335[/C][C]208.233932182661[/C][C]126.766067817339[/C][/ROW]
[ROW][C]34[/C][C]488[/C][C]341.239611915669[/C][C]146.760388084331[/C][/ROW]
[ROW][C]35[/C][C]326[/C][C]504.665722588154[/C][C]-178.665722588154[/C][/ROW]
[ROW][C]36[/C][C]346[/C][C]329.973002015534[/C][C]16.0269979844657[/C][/ROW]
[ROW][C]37[/C][C]261[/C][C]351.11158754883[/C][C]-90.1115875488304[/C][/ROW]
[ROW][C]38[/C][C]224[/C][C]259.709905208514[/C][C]-35.7099052085138[/C][/ROW]
[ROW][C]39[/C][C]141[/C][C]220.173012054525[/C][C]-79.1730120545247[/C][/ROW]
[ROW][C]40[/C][C]148[/C][C]131.548424952178[/C][C]16.4515750478218[/C][/ROW]
[ROW][C]41[/C][C]145[/C][C]139.717173171124[/C][C]5.28282682887649[/C][/ROW]
[ROW][C]42[/C][C]223[/C][C]137.092474285412[/C][C]85.9075257145881[/C][/ROW]
[ROW][C]43[/C][C]272[/C][C]221.195492834157[/C][C]50.8045071658431[/C][/ROW]
[ROW][C]44[/C][C]445[/C][C]273.804732502205[/C][C]171.195267497795[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]458.96673908202[/C][C]101.03326091798[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]581.144315904232[/C][C]30.8556840957679[/C][/ROW]
[ROW][C]47[/C][C]467[/C][C]635.336356832012[/C][C]-168.336356832012[/C][/ROW]
[ROW][C]48[/C][C]404[/C][C]478.37745218858[/C][C]-74.3774521885802[/C][/ROW]
[ROW][C]49[/C][C]518[/C][C]410.093549916463[/C][C]107.906450083537[/C][/ROW]
[ROW][C]50[/C][C]404[/C][C]531.759409931766[/C][C]-127.759409931766[/C][/ROW]
[ROW][C]51[/C][C]300[/C][C]408.683161464539[/C][C]-108.683161464539[/C][/ROW]
[ROW][C]52[/C][C]210[/C][C]296.96212253533[/C][C]-86.96212253533[/C][/ROW]
[ROW][C]53[/C][C]196[/C][C]200.784183612556[/C][C]-4.78418361255612[/C][/ROW]
[ROW][C]54[/C][C]186[/C][C]186.444306970956[/C][C]-0.444306970956205[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]176.412742638699[/C][C]70.5872573613014[/C][/ROW]
[ROW][C]56[/C][C]343[/C][C]242.427382944046[/C][C]100.572617055954[/C][/ROW]
[ROW][C]57[/C][C]464[/C][C]345.572234833129[/C][C]118.427765166871[/C][/ROW]
[ROW][C]58[/C][C]680[/C][C]474.985547188336[/C][C]205.014452811664[/C][/ROW]
[ROW][C]59[/C][C]711[/C][C]705.550126925242[/C][C]5.44987307475787[/C][/ROW]
[ROW][C]60[/C][C]610[/C][C]736.93729529247[/C][C]-126.93729529247[/C][/ROW]
[ROW][C]61[/C][C]513[/C][C]626.919451264797[/C][C]-113.919451264797[/C][/ROW]
[ROW][C]62[/C][C]292[/C][C]521.826417291944[/C][C]-229.826417291944[/C][/ROW]
[ROW][C]63[/C][C]273[/C][C]284.49915287527[/C][C]-11.4991528752698[/C][/ROW]
[ROW][C]64[/C][C]322[/C][C]264.682233254912[/C][C]57.3177667450879[/C][/ROW]
[ROW][C]65[/C][C]189[/C][C]317.754186098486[/C][C]-128.754186098486[/C][/ROW]
[ROW][C]66[/C][C]257[/C][C]175.607267019496[/C][C]81.3927329805044[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]249.389546918505[/C][C]74.6104530814953[/C][/ROW]
[ROW][C]68[/C][C]404[/C][C]321.690001975253[/C][C]82.3099980247469[/C][/ROW]
[ROW][C]69[/C][C]677[/C][C]407.53744596242[/C][C]269.46255403758[/C][/ROW]
[ROW][C]70[/C][C]858[/C][C]699.680529781959[/C][C]158.319470218041[/C][/ROW]
[ROW][C]71[/C][C]895[/C][C]891.927817552513[/C][C]3.07218244748731[/C][/ROW]
[ROW][C]72[/C][C]664[/C][C]929.146070683495[/C][C]-265.146070683495[/C][/ROW]
[ROW][C]73[/C][C]628[/C][C]679.309637273873[/C][C]-51.309637273873[/C][/ROW]
[ROW][C]74[/C][C]308[/C][C]639.664512293179[/C][C]-331.664512293179[/C][/ROW]
[ROW][C]75[/C][C]324[/C][C]296.102494255195[/C][C]27.8975057448051[/C][/ROW]
[ROW][C]76[/C][C]248[/C][C]314.084381099311[/C][C]-66.0843810993105[/C][/ROW]
[ROW][C]77[/C][C]272[/C][C]233.389632877003[/C][C]38.6103671229973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205473&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205473&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
3732845
4498.1968774843539640.803122515646
539-12.90439843427751.904398434277
659-19.217020596644278.2170205966442
71696.33965122643716162.660348773563
8169127.89532248402341.104677515977
9210130.81546955185579.1845304481446
10278177.440874940718100.559125059282
11298252.58476833512645.4152316648742
12245275.811144591929-30.8111445919292
13200220.622267827193-20.6222678271934
14188174.15722641179213.8427735882082
1590163.140640883017-73.1406408830174
167959.94460381568119.055396184319
177850.298331971616527.7016680283835
189151.266306167149539.7336938328505
1916767.089056193470799.9109438065293
20169150.18690167559618.8130983244038
21289153.523416574357135.476583425643
22247283.147906334593-36.1479063345931
23275238.57989682642436.4201031735757
24203269.167243666723-66.1672436667233
25223192.46660874494830.5333912550525
26104214.635753434375-110.635753434375
2710787.77599900951119.224000990489
288592.141705141193-7.14170514119304
297569.63434611084255.36565388915751
309960.01553140211138.984468597889
3113586.785055177668748.2149448223313
32211126.21032787793384.7896721220673
33335208.233932182661126.766067817339
34488341.239611915669146.760388084331
35326504.665722588154-178.665722588154
36346329.97300201553416.0269979844657
37261351.11158754883-90.1115875488304
38224259.709905208514-35.7099052085138
39141220.173012054525-79.1730120545247
40148131.54842495217816.4515750478218
41145139.7171731711245.28282682887649
42223137.09247428541285.9075257145881
43272221.19549283415750.8045071658431
44445273.804732502205171.195267497795
45560458.96673908202101.03326091798
46612581.14431590423230.8556840957679
47467635.336356832012-168.336356832012
48404478.37745218858-74.3774521885802
49518410.093549916463107.906450083537
50404531.759409931766-127.759409931766
51300408.683161464539-108.683161464539
52210296.96212253533-86.96212253533
53196200.784183612556-4.78418361255612
54186186.444306970956-0.444306970956205
55247176.41274263869970.5872573613014
56343242.427382944046100.572617055954
57464345.572234833129118.427765166871
58680474.985547188336205.014452811664
59711705.5501269252425.44987307475787
60610736.93729529247-126.93729529247
61513626.919451264797-113.919451264797
62292521.826417291944-229.826417291944
63273284.49915287527-11.4991528752698
64322264.68223325491257.3177667450879
65189317.754186098486-128.754186098486
66257175.60726701949681.3927329805044
67324249.38954691850574.6104530814953
68404321.69000197525382.3099980247469
69677407.53744596242269.46255403758
70858699.680529781959158.319470218041
71895891.9278175525133.07218244748731
72664929.146070683495-265.146070683495
73628679.309637273873-51.309637273873
74308639.664512293179-331.664512293179
75324296.10249425519527.8975057448051
76248314.084381099311-66.0843810993105
77272233.38963287700338.6103671229973







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
78260.13257983962854.1313984054466466.13376127381
79248.265159679256-53.5902187749774550.12053813349
80236.397739518885-146.31481042695619.110289464719
81224.530319358513-232.549010236245681.609648953271
82212.662899198141-315.449655196879740.775453593161
83200.795479037769-396.566482610438798.157440685977
84188.928058877398-476.778475959169854.634593713964
85177.060638717026-556.630610819869910.751888253921
86165.193218556654-636.481677040389966.868114153697
87153.325798396282-716.5781640687141023.22976086128
88141.458378235911-797.0947605527021080.01151702452
89129.590958075539-878.1581461766691137.34006232775

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
78 & 260.132579839628 & 54.1313984054466 & 466.13376127381 \tabularnewline
79 & 248.265159679256 & -53.5902187749774 & 550.12053813349 \tabularnewline
80 & 236.397739518885 & -146.31481042695 & 619.110289464719 \tabularnewline
81 & 224.530319358513 & -232.549010236245 & 681.609648953271 \tabularnewline
82 & 212.662899198141 & -315.449655196879 & 740.775453593161 \tabularnewline
83 & 200.795479037769 & -396.566482610438 & 798.157440685977 \tabularnewline
84 & 188.928058877398 & -476.778475959169 & 854.634593713964 \tabularnewline
85 & 177.060638717026 & -556.630610819869 & 910.751888253921 \tabularnewline
86 & 165.193218556654 & -636.481677040389 & 966.868114153697 \tabularnewline
87 & 153.325798396282 & -716.578164068714 & 1023.22976086128 \tabularnewline
88 & 141.458378235911 & -797.094760552702 & 1080.01151702452 \tabularnewline
89 & 129.590958075539 & -878.158146176669 & 1137.34006232775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205473&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]78[/C][C]260.132579839628[/C][C]54.1313984054466[/C][C]466.13376127381[/C][/ROW]
[ROW][C]79[/C][C]248.265159679256[/C][C]-53.5902187749774[/C][C]550.12053813349[/C][/ROW]
[ROW][C]80[/C][C]236.397739518885[/C][C]-146.31481042695[/C][C]619.110289464719[/C][/ROW]
[ROW][C]81[/C][C]224.530319358513[/C][C]-232.549010236245[/C][C]681.609648953271[/C][/ROW]
[ROW][C]82[/C][C]212.662899198141[/C][C]-315.449655196879[/C][C]740.775453593161[/C][/ROW]
[ROW][C]83[/C][C]200.795479037769[/C][C]-396.566482610438[/C][C]798.157440685977[/C][/ROW]
[ROW][C]84[/C][C]188.928058877398[/C][C]-476.778475959169[/C][C]854.634593713964[/C][/ROW]
[ROW][C]85[/C][C]177.060638717026[/C][C]-556.630610819869[/C][C]910.751888253921[/C][/ROW]
[ROW][C]86[/C][C]165.193218556654[/C][C]-636.481677040389[/C][C]966.868114153697[/C][/ROW]
[ROW][C]87[/C][C]153.325798396282[/C][C]-716.578164068714[/C][C]1023.22976086128[/C][/ROW]
[ROW][C]88[/C][C]141.458378235911[/C][C]-797.094760552702[/C][C]1080.01151702452[/C][/ROW]
[ROW][C]89[/C][C]129.590958075539[/C][C]-878.158146176669[/C][C]1137.34006232775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205473&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205473&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
78260.13257983962854.1313984054466466.13376127381
79248.265159679256-53.5902187749774550.12053813349
80236.397739518885-146.31481042695619.110289464719
81224.530319358513-232.549010236245681.609648953271
82212.662899198141-315.449655196879740.775453593161
83200.795479037769-396.566482610438798.157440685977
84188.928058877398-476.778475959169854.634593713964
85177.060638717026-556.630610819869910.751888253921
86165.193218556654-636.481677040389966.868114153697
87153.325798396282-716.5781640687141023.22976086128
88141.458378235911-797.0947605527021080.01151702452
89129.590958075539-878.1581461766691137.34006232775



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')