Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 21:17:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417382311rpf0pr46s936020.htm/, Retrieved Sun, 19 May 2024 15:54:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261670, Retrieved Sun, 19 May 2024 15:54:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 21:17:39] [4f675b9afdd3602a3170287ae908b245] [Current]
Feedback Forum

Post a new message
Dataseries X:
239 050
238 600
236 980
236 050
234 870
233 060
231 370
230 300
228 340
226 760
223 550
221 460
220 560
220 350
219 500
218 800
218 130
217 150
216 430
215 310
213 780
213 040
211 940
212 270
212 540
213 790
214 400
215 520
216 690
217 630
218 710
219 360
219 800
221 110
221 320
225 230
227 340
228 930
230 340
231 270
231 830
232 450
233 220
233 520
234 520
234 860
236 560
238 310
239 690
240 700
241 330
241 580
241 670
241 970
241 690
241 410
242 130
242 130
243 320
242 030
242 740
243 050
243 360
243 940
244 270
244 350
244 260
244 230
245 130
246 740
247 910
249 590
251 610
253 430
255 290
256 710
257 190
257 820
257 460
257 970
259 520
261 340
263 150





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=261670&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=261670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261670&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'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999954510693059
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954510693059 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261670&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]0.999954510693059[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261670&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
alpha0.999954510693059
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2238600239050-450
3236980238600.020470188-1620.02047018812
4236050236980.073693608-930.073693608429
5234870236050.042308408-1180.04230840772
6233060234870.053679307-1810.05367930676
7231370233060.082338087-1690.08233808738
8230300231370.076880674-1070.07688067423
9228340230300.048677056-1960.04867705566
10226760228340.089161256-1580.08916125589
11223550226760.071877161-3210.07187716084
12221460223550.146023945-2090.14602394492
13220560221460.095079294-900.095079294057
14220350220560.040944701-210.040944701323
15219500220350.009554617-850.00955461699
16218800219500.038666346-700.038666345528
17218130218800.031844274-670.031844273763
18217150218130.030479284-980.030479284236
19216430217150.044580907-720.04458090727
20215310216430.032754329-1120.03275432895
21213780215310.050949514-1530.05094951377
22213040213780.069600957-740.0696009573
23211940213040.033665253-1100.03366525326
24212270211940.050039769329.949960230966
25212540212269.984990805270.01500919502
26213790212539.9877172041250.01228279562
27214400213789.943137808610.056862192403
28215520214399.9722489361120.02775106384
29216690215519.9490507141170.05094928615
30217630216689.946775193940.05322480679
31218710217629.957237631080.0427623697
32219360218709.950869603650.049130396714
33219800219359.970429716440.029570284416
34221110219799.979983361310.02001664019
35221320221109.940408097210.059591902653
36225230221319.9904445353910.00955546525
37227340225229.8221363752110.17786362482
38228930227339.9040094711590.09599052853
39230340228929.9276676351410.07233236457
40231270230339.935856787930.064143213123
41231830231269.957692027560.042307973286
42232450231829.974524064620.025475936447
43233220232449.971795471770.028204529197
44233520233219.964971951300.035028049344
45234520233519.9863516141000.0136483855
46234860234519.954510072340.045489927812
47236560234859.9845315661700.01546843367
48238310236559.9226674751750.07733252543
49239690238309.9203901951380.07960980496
50240700239689.9372211351010.06277886496
51241330240699.954052944630.045947055769
52241580241329.971339647250.028660353477
53241670241579.9886263790.0113736304629
54241970241669.995905445300.004094555014
55241690241969.986353022-279.986353021668
56241410241690.012736385-280.012736385164
57242130241410.012737585719.98726241471
58242130242129.9672482780.0327517215919215
59243320242129.999998511190.00000148985
60242030243319.945867725-1289.94586772469
61242740242030.058678744709.941321256483
62243050242739.967705261310.032294738689
63243360243049.985896846310.014103154215
64243940243359.985897673580.014102326677
65244270243939.97361556330.026384439552
66244350244269.98498732880.0150126715016
67244260244349.996360173-89.9963601725176
68244230244260.004093872-30.0040938720631
69245130244230.001364865899.998635134543
70246740245129.9590596861610.04094031415
71247910246739.9267603531170.07323964653
72249590247909.9467741791680.05322582074
73251610249589.9235755432020.07642445687
74253430251609.9081081231820.09189187651
75255290253429.9172052811860.08279471874
76256710255289.9153861231420.0846138772
77257190256709.935401335480.064598664903
78257820257189.978162194630.021837805863
79257460257819.971340743-359.971340743243
80257970257460.016374847509.983625153167
81259520257969.9768011981550.02319880167
82261340259519.9294905191820.07050948104
83263150261339.9172062541810.08279374606

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 238600 & 239050 & -450 \tabularnewline
3 & 236980 & 238600.020470188 & -1620.02047018812 \tabularnewline
4 & 236050 & 236980.073693608 & -930.073693608429 \tabularnewline
5 & 234870 & 236050.042308408 & -1180.04230840772 \tabularnewline
6 & 233060 & 234870.053679307 & -1810.05367930676 \tabularnewline
7 & 231370 & 233060.082338087 & -1690.08233808738 \tabularnewline
8 & 230300 & 231370.076880674 & -1070.07688067423 \tabularnewline
9 & 228340 & 230300.048677056 & -1960.04867705566 \tabularnewline
10 & 226760 & 228340.089161256 & -1580.08916125589 \tabularnewline
11 & 223550 & 226760.071877161 & -3210.07187716084 \tabularnewline
12 & 221460 & 223550.146023945 & -2090.14602394492 \tabularnewline
13 & 220560 & 221460.095079294 & -900.095079294057 \tabularnewline
14 & 220350 & 220560.040944701 & -210.040944701323 \tabularnewline
15 & 219500 & 220350.009554617 & -850.00955461699 \tabularnewline
16 & 218800 & 219500.038666346 & -700.038666345528 \tabularnewline
17 & 218130 & 218800.031844274 & -670.031844273763 \tabularnewline
18 & 217150 & 218130.030479284 & -980.030479284236 \tabularnewline
19 & 216430 & 217150.044580907 & -720.04458090727 \tabularnewline
20 & 215310 & 216430.032754329 & -1120.03275432895 \tabularnewline
21 & 213780 & 215310.050949514 & -1530.05094951377 \tabularnewline
22 & 213040 & 213780.069600957 & -740.0696009573 \tabularnewline
23 & 211940 & 213040.033665253 & -1100.03366525326 \tabularnewline
24 & 212270 & 211940.050039769 & 329.949960230966 \tabularnewline
25 & 212540 & 212269.984990805 & 270.01500919502 \tabularnewline
26 & 213790 & 212539.987717204 & 1250.01228279562 \tabularnewline
27 & 214400 & 213789.943137808 & 610.056862192403 \tabularnewline
28 & 215520 & 214399.972248936 & 1120.02775106384 \tabularnewline
29 & 216690 & 215519.949050714 & 1170.05094928615 \tabularnewline
30 & 217630 & 216689.946775193 & 940.05322480679 \tabularnewline
31 & 218710 & 217629.95723763 & 1080.0427623697 \tabularnewline
32 & 219360 & 218709.950869603 & 650.049130396714 \tabularnewline
33 & 219800 & 219359.970429716 & 440.029570284416 \tabularnewline
34 & 221110 & 219799.97998336 & 1310.02001664019 \tabularnewline
35 & 221320 & 221109.940408097 & 210.059591902653 \tabularnewline
36 & 225230 & 221319.990444535 & 3910.00955546525 \tabularnewline
37 & 227340 & 225229.822136375 & 2110.17786362482 \tabularnewline
38 & 228930 & 227339.904009471 & 1590.09599052853 \tabularnewline
39 & 230340 & 228929.927667635 & 1410.07233236457 \tabularnewline
40 & 231270 & 230339.935856787 & 930.064143213123 \tabularnewline
41 & 231830 & 231269.957692027 & 560.042307973286 \tabularnewline
42 & 232450 & 231829.974524064 & 620.025475936447 \tabularnewline
43 & 233220 & 232449.971795471 & 770.028204529197 \tabularnewline
44 & 233520 & 233219.964971951 & 300.035028049344 \tabularnewline
45 & 234520 & 233519.986351614 & 1000.0136483855 \tabularnewline
46 & 234860 & 234519.954510072 & 340.045489927812 \tabularnewline
47 & 236560 & 234859.984531566 & 1700.01546843367 \tabularnewline
48 & 238310 & 236559.922667475 & 1750.07733252543 \tabularnewline
49 & 239690 & 238309.920390195 & 1380.07960980496 \tabularnewline
50 & 240700 & 239689.937221135 & 1010.06277886496 \tabularnewline
51 & 241330 & 240699.954052944 & 630.045947055769 \tabularnewline
52 & 241580 & 241329.971339647 & 250.028660353477 \tabularnewline
53 & 241670 & 241579.98862637 & 90.0113736304629 \tabularnewline
54 & 241970 & 241669.995905445 & 300.004094555014 \tabularnewline
55 & 241690 & 241969.986353022 & -279.986353021668 \tabularnewline
56 & 241410 & 241690.012736385 & -280.012736385164 \tabularnewline
57 & 242130 & 241410.012737585 & 719.98726241471 \tabularnewline
58 & 242130 & 242129.967248278 & 0.0327517215919215 \tabularnewline
59 & 243320 & 242129.99999851 & 1190.00000148985 \tabularnewline
60 & 242030 & 243319.945867725 & -1289.94586772469 \tabularnewline
61 & 242740 & 242030.058678744 & 709.941321256483 \tabularnewline
62 & 243050 & 242739.967705261 & 310.032294738689 \tabularnewline
63 & 243360 & 243049.985896846 & 310.014103154215 \tabularnewline
64 & 243940 & 243359.985897673 & 580.014102326677 \tabularnewline
65 & 244270 & 243939.97361556 & 330.026384439552 \tabularnewline
66 & 244350 & 244269.984987328 & 80.0150126715016 \tabularnewline
67 & 244260 & 244349.996360173 & -89.9963601725176 \tabularnewline
68 & 244230 & 244260.004093872 & -30.0040938720631 \tabularnewline
69 & 245130 & 244230.001364865 & 899.998635134543 \tabularnewline
70 & 246740 & 245129.959059686 & 1610.04094031415 \tabularnewline
71 & 247910 & 246739.926760353 & 1170.07323964653 \tabularnewline
72 & 249590 & 247909.946774179 & 1680.05322582074 \tabularnewline
73 & 251610 & 249589.923575543 & 2020.07642445687 \tabularnewline
74 & 253430 & 251609.908108123 & 1820.09189187651 \tabularnewline
75 & 255290 & 253429.917205281 & 1860.08279471874 \tabularnewline
76 & 256710 & 255289.915386123 & 1420.0846138772 \tabularnewline
77 & 257190 & 256709.935401335 & 480.064598664903 \tabularnewline
78 & 257820 & 257189.978162194 & 630.021837805863 \tabularnewline
79 & 257460 & 257819.971340743 & -359.971340743243 \tabularnewline
80 & 257970 & 257460.016374847 & 509.983625153167 \tabularnewline
81 & 259520 & 257969.976801198 & 1550.02319880167 \tabularnewline
82 & 261340 & 259519.929490519 & 1820.07050948104 \tabularnewline
83 & 263150 & 261339.917206254 & 1810.08279374606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261670&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]2[/C][C]238600[/C][C]239050[/C][C]-450[/C][/ROW]
[ROW][C]3[/C][C]236980[/C][C]238600.020470188[/C][C]-1620.02047018812[/C][/ROW]
[ROW][C]4[/C][C]236050[/C][C]236980.073693608[/C][C]-930.073693608429[/C][/ROW]
[ROW][C]5[/C][C]234870[/C][C]236050.042308408[/C][C]-1180.04230840772[/C][/ROW]
[ROW][C]6[/C][C]233060[/C][C]234870.053679307[/C][C]-1810.05367930676[/C][/ROW]
[ROW][C]7[/C][C]231370[/C][C]233060.082338087[/C][C]-1690.08233808738[/C][/ROW]
[ROW][C]8[/C][C]230300[/C][C]231370.076880674[/C][C]-1070.07688067423[/C][/ROW]
[ROW][C]9[/C][C]228340[/C][C]230300.048677056[/C][C]-1960.04867705566[/C][/ROW]
[ROW][C]10[/C][C]226760[/C][C]228340.089161256[/C][C]-1580.08916125589[/C][/ROW]
[ROW][C]11[/C][C]223550[/C][C]226760.071877161[/C][C]-3210.07187716084[/C][/ROW]
[ROW][C]12[/C][C]221460[/C][C]223550.146023945[/C][C]-2090.14602394492[/C][/ROW]
[ROW][C]13[/C][C]220560[/C][C]221460.095079294[/C][C]-900.095079294057[/C][/ROW]
[ROW][C]14[/C][C]220350[/C][C]220560.040944701[/C][C]-210.040944701323[/C][/ROW]
[ROW][C]15[/C][C]219500[/C][C]220350.009554617[/C][C]-850.00955461699[/C][/ROW]
[ROW][C]16[/C][C]218800[/C][C]219500.038666346[/C][C]-700.038666345528[/C][/ROW]
[ROW][C]17[/C][C]218130[/C][C]218800.031844274[/C][C]-670.031844273763[/C][/ROW]
[ROW][C]18[/C][C]217150[/C][C]218130.030479284[/C][C]-980.030479284236[/C][/ROW]
[ROW][C]19[/C][C]216430[/C][C]217150.044580907[/C][C]-720.04458090727[/C][/ROW]
[ROW][C]20[/C][C]215310[/C][C]216430.032754329[/C][C]-1120.03275432895[/C][/ROW]
[ROW][C]21[/C][C]213780[/C][C]215310.050949514[/C][C]-1530.05094951377[/C][/ROW]
[ROW][C]22[/C][C]213040[/C][C]213780.069600957[/C][C]-740.0696009573[/C][/ROW]
[ROW][C]23[/C][C]211940[/C][C]213040.033665253[/C][C]-1100.03366525326[/C][/ROW]
[ROW][C]24[/C][C]212270[/C][C]211940.050039769[/C][C]329.949960230966[/C][/ROW]
[ROW][C]25[/C][C]212540[/C][C]212269.984990805[/C][C]270.01500919502[/C][/ROW]
[ROW][C]26[/C][C]213790[/C][C]212539.987717204[/C][C]1250.01228279562[/C][/ROW]
[ROW][C]27[/C][C]214400[/C][C]213789.943137808[/C][C]610.056862192403[/C][/ROW]
[ROW][C]28[/C][C]215520[/C][C]214399.972248936[/C][C]1120.02775106384[/C][/ROW]
[ROW][C]29[/C][C]216690[/C][C]215519.949050714[/C][C]1170.05094928615[/C][/ROW]
[ROW][C]30[/C][C]217630[/C][C]216689.946775193[/C][C]940.05322480679[/C][/ROW]
[ROW][C]31[/C][C]218710[/C][C]217629.95723763[/C][C]1080.0427623697[/C][/ROW]
[ROW][C]32[/C][C]219360[/C][C]218709.950869603[/C][C]650.049130396714[/C][/ROW]
[ROW][C]33[/C][C]219800[/C][C]219359.970429716[/C][C]440.029570284416[/C][/ROW]
[ROW][C]34[/C][C]221110[/C][C]219799.97998336[/C][C]1310.02001664019[/C][/ROW]
[ROW][C]35[/C][C]221320[/C][C]221109.940408097[/C][C]210.059591902653[/C][/ROW]
[ROW][C]36[/C][C]225230[/C][C]221319.990444535[/C][C]3910.00955546525[/C][/ROW]
[ROW][C]37[/C][C]227340[/C][C]225229.822136375[/C][C]2110.17786362482[/C][/ROW]
[ROW][C]38[/C][C]228930[/C][C]227339.904009471[/C][C]1590.09599052853[/C][/ROW]
[ROW][C]39[/C][C]230340[/C][C]228929.927667635[/C][C]1410.07233236457[/C][/ROW]
[ROW][C]40[/C][C]231270[/C][C]230339.935856787[/C][C]930.064143213123[/C][/ROW]
[ROW][C]41[/C][C]231830[/C][C]231269.957692027[/C][C]560.042307973286[/C][/ROW]
[ROW][C]42[/C][C]232450[/C][C]231829.974524064[/C][C]620.025475936447[/C][/ROW]
[ROW][C]43[/C][C]233220[/C][C]232449.971795471[/C][C]770.028204529197[/C][/ROW]
[ROW][C]44[/C][C]233520[/C][C]233219.964971951[/C][C]300.035028049344[/C][/ROW]
[ROW][C]45[/C][C]234520[/C][C]233519.986351614[/C][C]1000.0136483855[/C][/ROW]
[ROW][C]46[/C][C]234860[/C][C]234519.954510072[/C][C]340.045489927812[/C][/ROW]
[ROW][C]47[/C][C]236560[/C][C]234859.984531566[/C][C]1700.01546843367[/C][/ROW]
[ROW][C]48[/C][C]238310[/C][C]236559.922667475[/C][C]1750.07733252543[/C][/ROW]
[ROW][C]49[/C][C]239690[/C][C]238309.920390195[/C][C]1380.07960980496[/C][/ROW]
[ROW][C]50[/C][C]240700[/C][C]239689.937221135[/C][C]1010.06277886496[/C][/ROW]
[ROW][C]51[/C][C]241330[/C][C]240699.954052944[/C][C]630.045947055769[/C][/ROW]
[ROW][C]52[/C][C]241580[/C][C]241329.971339647[/C][C]250.028660353477[/C][/ROW]
[ROW][C]53[/C][C]241670[/C][C]241579.98862637[/C][C]90.0113736304629[/C][/ROW]
[ROW][C]54[/C][C]241970[/C][C]241669.995905445[/C][C]300.004094555014[/C][/ROW]
[ROW][C]55[/C][C]241690[/C][C]241969.986353022[/C][C]-279.986353021668[/C][/ROW]
[ROW][C]56[/C][C]241410[/C][C]241690.012736385[/C][C]-280.012736385164[/C][/ROW]
[ROW][C]57[/C][C]242130[/C][C]241410.012737585[/C][C]719.98726241471[/C][/ROW]
[ROW][C]58[/C][C]242130[/C][C]242129.967248278[/C][C]0.0327517215919215[/C][/ROW]
[ROW][C]59[/C][C]243320[/C][C]242129.99999851[/C][C]1190.00000148985[/C][/ROW]
[ROW][C]60[/C][C]242030[/C][C]243319.945867725[/C][C]-1289.94586772469[/C][/ROW]
[ROW][C]61[/C][C]242740[/C][C]242030.058678744[/C][C]709.941321256483[/C][/ROW]
[ROW][C]62[/C][C]243050[/C][C]242739.967705261[/C][C]310.032294738689[/C][/ROW]
[ROW][C]63[/C][C]243360[/C][C]243049.985896846[/C][C]310.014103154215[/C][/ROW]
[ROW][C]64[/C][C]243940[/C][C]243359.985897673[/C][C]580.014102326677[/C][/ROW]
[ROW][C]65[/C][C]244270[/C][C]243939.97361556[/C][C]330.026384439552[/C][/ROW]
[ROW][C]66[/C][C]244350[/C][C]244269.984987328[/C][C]80.0150126715016[/C][/ROW]
[ROW][C]67[/C][C]244260[/C][C]244349.996360173[/C][C]-89.9963601725176[/C][/ROW]
[ROW][C]68[/C][C]244230[/C][C]244260.004093872[/C][C]-30.0040938720631[/C][/ROW]
[ROW][C]69[/C][C]245130[/C][C]244230.001364865[/C][C]899.998635134543[/C][/ROW]
[ROW][C]70[/C][C]246740[/C][C]245129.959059686[/C][C]1610.04094031415[/C][/ROW]
[ROW][C]71[/C][C]247910[/C][C]246739.926760353[/C][C]1170.07323964653[/C][/ROW]
[ROW][C]72[/C][C]249590[/C][C]247909.946774179[/C][C]1680.05322582074[/C][/ROW]
[ROW][C]73[/C][C]251610[/C][C]249589.923575543[/C][C]2020.07642445687[/C][/ROW]
[ROW][C]74[/C][C]253430[/C][C]251609.908108123[/C][C]1820.09189187651[/C][/ROW]
[ROW][C]75[/C][C]255290[/C][C]253429.917205281[/C][C]1860.08279471874[/C][/ROW]
[ROW][C]76[/C][C]256710[/C][C]255289.915386123[/C][C]1420.0846138772[/C][/ROW]
[ROW][C]77[/C][C]257190[/C][C]256709.935401335[/C][C]480.064598664903[/C][/ROW]
[ROW][C]78[/C][C]257820[/C][C]257189.978162194[/C][C]630.021837805863[/C][/ROW]
[ROW][C]79[/C][C]257460[/C][C]257819.971340743[/C][C]-359.971340743243[/C][/ROW]
[ROW][C]80[/C][C]257970[/C][C]257460.016374847[/C][C]509.983625153167[/C][/ROW]
[ROW][C]81[/C][C]259520[/C][C]257969.976801198[/C][C]1550.02319880167[/C][/ROW]
[ROW][C]82[/C][C]261340[/C][C]259519.929490519[/C][C]1820.07050948104[/C][/ROW]
[ROW][C]83[/C][C]263150[/C][C]261339.917206254[/C][C]1810.08279374606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261670&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
2238600239050-450
3236980238600.020470188-1620.02047018812
4236050236980.073693608-930.073693608429
5234870236050.042308408-1180.04230840772
6233060234870.053679307-1810.05367930676
7231370233060.082338087-1690.08233808738
8230300231370.076880674-1070.07688067423
9228340230300.048677056-1960.04867705566
10226760228340.089161256-1580.08916125589
11223550226760.071877161-3210.07187716084
12221460223550.146023945-2090.14602394492
13220560221460.095079294-900.095079294057
14220350220560.040944701-210.040944701323
15219500220350.009554617-850.00955461699
16218800219500.038666346-700.038666345528
17218130218800.031844274-670.031844273763
18217150218130.030479284-980.030479284236
19216430217150.044580907-720.04458090727
20215310216430.032754329-1120.03275432895
21213780215310.050949514-1530.05094951377
22213040213780.069600957-740.0696009573
23211940213040.033665253-1100.03366525326
24212270211940.050039769329.949960230966
25212540212269.984990805270.01500919502
26213790212539.9877172041250.01228279562
27214400213789.943137808610.056862192403
28215520214399.9722489361120.02775106384
29216690215519.9490507141170.05094928615
30217630216689.946775193940.05322480679
31218710217629.957237631080.0427623697
32219360218709.950869603650.049130396714
33219800219359.970429716440.029570284416
34221110219799.979983361310.02001664019
35221320221109.940408097210.059591902653
36225230221319.9904445353910.00955546525
37227340225229.8221363752110.17786362482
38228930227339.9040094711590.09599052853
39230340228929.9276676351410.07233236457
40231270230339.935856787930.064143213123
41231830231269.957692027560.042307973286
42232450231829.974524064620.025475936447
43233220232449.971795471770.028204529197
44233520233219.964971951300.035028049344
45234520233519.9863516141000.0136483855
46234860234519.954510072340.045489927812
47236560234859.9845315661700.01546843367
48238310236559.9226674751750.07733252543
49239690238309.9203901951380.07960980496
50240700239689.9372211351010.06277886496
51241330240699.954052944630.045947055769
52241580241329.971339647250.028660353477
53241670241579.9886263790.0113736304629
54241970241669.995905445300.004094555014
55241690241969.986353022-279.986353021668
56241410241690.012736385-280.012736385164
57242130241410.012737585719.98726241471
58242130242129.9672482780.0327517215919215
59243320242129.999998511190.00000148985
60242030243319.945867725-1289.94586772469
61242740242030.058678744709.941321256483
62243050242739.967705261310.032294738689
63243360243049.985896846310.014103154215
64243940243359.985897673580.014102326677
65244270243939.97361556330.026384439552
66244350244269.98498732880.0150126715016
67244260244349.996360173-89.9963601725176
68244230244260.004093872-30.0040938720631
69245130244230.001364865899.998635134543
70246740245129.9590596861610.04094031415
71247910246739.9267603531170.07323964653
72249590247909.9467741791680.05322582074
73251610249589.9235755432020.07642445687
74253430251609.9081081231820.09189187651
75255290253429.9172052811860.08279471874
76256710255289.9153861231420.0846138772
77257190256709.935401335480.064598664903
78257820257189.978162194630.021837805863
79257460257819.971340743-359.971340743243
80257970257460.016374847509.983625153167
81259520257969.9768011981550.02319880167
82261340259519.9294905191820.07050948104
83263150261339.9172062541810.08279374606







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
84263149.917660588260791.874470804265507.960850372
85263149.917660588259815.216848411266484.618472766
86263149.917660588259065.790908321267234.044412856
87263149.917660588258433.99217873267865.843142446
88263149.917660588257877.364676285268422.470644891
89263149.917660588257374.134008638268925.701312538
90263149.917660588256911.365054736269388.47026644
91263149.917660588256480.629809713269819.205511463
92263149.917660588256076.074132514270223.761188663
93263149.917660588255693.435642805270606.399678372
94263149.917660588255329.496578359270970.338742818
95263149.917660588254981.757052151271318.078269025

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
84 & 263149.917660588 & 260791.874470804 & 265507.960850372 \tabularnewline
85 & 263149.917660588 & 259815.216848411 & 266484.618472766 \tabularnewline
86 & 263149.917660588 & 259065.790908321 & 267234.044412856 \tabularnewline
87 & 263149.917660588 & 258433.99217873 & 267865.843142446 \tabularnewline
88 & 263149.917660588 & 257877.364676285 & 268422.470644891 \tabularnewline
89 & 263149.917660588 & 257374.134008638 & 268925.701312538 \tabularnewline
90 & 263149.917660588 & 256911.365054736 & 269388.47026644 \tabularnewline
91 & 263149.917660588 & 256480.629809713 & 269819.205511463 \tabularnewline
92 & 263149.917660588 & 256076.074132514 & 270223.761188663 \tabularnewline
93 & 263149.917660588 & 255693.435642805 & 270606.399678372 \tabularnewline
94 & 263149.917660588 & 255329.496578359 & 270970.338742818 \tabularnewline
95 & 263149.917660588 & 254981.757052151 & 271318.078269025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261670&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]84[/C][C]263149.917660588[/C][C]260791.874470804[/C][C]265507.960850372[/C][/ROW]
[ROW][C]85[/C][C]263149.917660588[/C][C]259815.216848411[/C][C]266484.618472766[/C][/ROW]
[ROW][C]86[/C][C]263149.917660588[/C][C]259065.790908321[/C][C]267234.044412856[/C][/ROW]
[ROW][C]87[/C][C]263149.917660588[/C][C]258433.99217873[/C][C]267865.843142446[/C][/ROW]
[ROW][C]88[/C][C]263149.917660588[/C][C]257877.364676285[/C][C]268422.470644891[/C][/ROW]
[ROW][C]89[/C][C]263149.917660588[/C][C]257374.134008638[/C][C]268925.701312538[/C][/ROW]
[ROW][C]90[/C][C]263149.917660588[/C][C]256911.365054736[/C][C]269388.47026644[/C][/ROW]
[ROW][C]91[/C][C]263149.917660588[/C][C]256480.629809713[/C][C]269819.205511463[/C][/ROW]
[ROW][C]92[/C][C]263149.917660588[/C][C]256076.074132514[/C][C]270223.761188663[/C][/ROW]
[ROW][C]93[/C][C]263149.917660588[/C][C]255693.435642805[/C][C]270606.399678372[/C][/ROW]
[ROW][C]94[/C][C]263149.917660588[/C][C]255329.496578359[/C][C]270970.338742818[/C][/ROW]
[ROW][C]95[/C][C]263149.917660588[/C][C]254981.757052151[/C][C]271318.078269025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261670&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261670&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
84263149.917660588260791.874470804265507.960850372
85263149.917660588259815.216848411266484.618472766
86263149.917660588259065.790908321267234.044412856
87263149.917660588258433.99217873267865.843142446
88263149.917660588257877.364676285268422.470644891
89263149.917660588257374.134008638268925.701312538
90263149.917660588256911.365054736269388.47026644
91263149.917660588256480.629809713269819.205511463
92263149.917660588256076.074132514270223.761188663
93263149.917660588255693.435642805270606.399678372
94263149.917660588255329.496578359270970.338742818
95263149.917660588254981.757052151271318.078269025



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')