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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 computationSat, 16 Jan 2010 10:09:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/16/t1263661803uldper14cwcef0s.htm/, Retrieved Fri, 03 May 2024 04:07:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72241, Retrieved Fri, 03 May 2024 04:07:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oefening 2] [2010-01-16 17:09:08] [99dd5e7f67b5ad84b7cfa9edf27cffe4] [Current]
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Dataseries X:
10
15
12
13
12
15
13
13
16
14
12
15
14
19
16
16
11
13
12
11
6
9
6
15
17
13
12
13
10
14
13
10
11
12
7
11
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72241&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72241&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.635345371205515
beta0.281122102631007
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.635345371205515 \tabularnewline
beta & 0.281122102631007 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72241&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]0.635345371205515[/C][/ROW]
[ROW][C]beta[/C][C]0.281122102631007[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72241&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
alpha0.635345371205515
beta0.281122102631007
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31220-8
41318.4883600171545-5.4883600171545
51217.5922049379589-5.5922049379589
61515.6312508328869-0.631250832886929
71316.7094684796509-3.70946847965089
81315.1694080127592-2.16940801275921
91614.22034067967291.77965932032705
101416.0981592840101-2.09815928401006
111215.1374723413373-3.13747234133733
121512.95607989494682.04392010505323
131414.431724962636-0.431724962636004
141914.25737016142914.74262983857086
151618.2175970769512-2.21759707695120
161617.3595918531815-1.35959185318151
171116.8038800835107-5.80388008351069
181312.38788150355890.612118496441143
191212.1575881791556-0.157588179155598
201111.4101185153825-0.410118515382502
21610.4289537564839-4.42895375648388
2296.103386852617432.89661314738257
2366.94944796538283-0.94944796538283
24155.182351406158419.8176485938416
251712.00960635708874.99039364291132
261316.6612195647143-3.66121956471428
271215.1621413078765-3.16214130787654
281313.4153612329751-0.415361232975057
291013.3395476496351-3.33954764963514
301410.80939040304643.19060959695359
311312.99801192522030.00198807477968899
321013.1611126120489-3.1611126120489
331110.74994677540680.250053224593248
341210.55071127657691.44928872342315
35711.3722614187128-4.37226141871278
36117.71418864518863.28581135481140
3799.50851450000374-0.508514500003741
38138.801307401124814.19869259887519
391211.83472946132830.165270538671715
40512.3350543946717-7.3350543946717
41136.759971272187056.24002872781295
421110.92428357666410.0757164233358534
43811.1856522739298-3.18565227392982
4488.80593730230932-0.805937302309315
4587.794215062027450.205784937972554
4687.462041034995840.537958965004157
4707.43699688836597-7.43699688836597
4831.016782217099521.98321778290048
4900.935879120754331-0.935879120754331
50-1-1.166815701775920.166815701775916
51-1-2.53912358274571.5391235827457
52-4-2.7646397151898-1.2353602848102
531-4.973558569618315.97355856961831
54-1-1.535389132597050.535389132597048
550-1.456709822132831.45670982213283
56-1-0.532491278707392-0.467508721292608
576-0.9143176382008976.9143176382009
5804.62882890275241-4.62882890275241
59-32.01133731761596-5.01133731761596
60-3-1.74425230566867-1.25574769433133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 12 & 20 & -8 \tabularnewline
4 & 13 & 18.4883600171545 & -5.4883600171545 \tabularnewline
5 & 12 & 17.5922049379589 & -5.5922049379589 \tabularnewline
6 & 15 & 15.6312508328869 & -0.631250832886929 \tabularnewline
7 & 13 & 16.7094684796509 & -3.70946847965089 \tabularnewline
8 & 13 & 15.1694080127592 & -2.16940801275921 \tabularnewline
9 & 16 & 14.2203406796729 & 1.77965932032705 \tabularnewline
10 & 14 & 16.0981592840101 & -2.09815928401006 \tabularnewline
11 & 12 & 15.1374723413373 & -3.13747234133733 \tabularnewline
12 & 15 & 12.9560798949468 & 2.04392010505323 \tabularnewline
13 & 14 & 14.431724962636 & -0.431724962636004 \tabularnewline
14 & 19 & 14.2573701614291 & 4.74262983857086 \tabularnewline
15 & 16 & 18.2175970769512 & -2.21759707695120 \tabularnewline
16 & 16 & 17.3595918531815 & -1.35959185318151 \tabularnewline
17 & 11 & 16.8038800835107 & -5.80388008351069 \tabularnewline
18 & 13 & 12.3878815035589 & 0.612118496441143 \tabularnewline
19 & 12 & 12.1575881791556 & -0.157588179155598 \tabularnewline
20 & 11 & 11.4101185153825 & -0.410118515382502 \tabularnewline
21 & 6 & 10.4289537564839 & -4.42895375648388 \tabularnewline
22 & 9 & 6.10338685261743 & 2.89661314738257 \tabularnewline
23 & 6 & 6.94944796538283 & -0.94944796538283 \tabularnewline
24 & 15 & 5.18235140615841 & 9.8176485938416 \tabularnewline
25 & 17 & 12.0096063570887 & 4.99039364291132 \tabularnewline
26 & 13 & 16.6612195647143 & -3.66121956471428 \tabularnewline
27 & 12 & 15.1621413078765 & -3.16214130787654 \tabularnewline
28 & 13 & 13.4153612329751 & -0.415361232975057 \tabularnewline
29 & 10 & 13.3395476496351 & -3.33954764963514 \tabularnewline
30 & 14 & 10.8093904030464 & 3.19060959695359 \tabularnewline
31 & 13 & 12.9980119252203 & 0.00198807477968899 \tabularnewline
32 & 10 & 13.1611126120489 & -3.1611126120489 \tabularnewline
33 & 11 & 10.7499467754068 & 0.250053224593248 \tabularnewline
34 & 12 & 10.5507112765769 & 1.44928872342315 \tabularnewline
35 & 7 & 11.3722614187128 & -4.37226141871278 \tabularnewline
36 & 11 & 7.7141886451886 & 3.28581135481140 \tabularnewline
37 & 9 & 9.50851450000374 & -0.508514500003741 \tabularnewline
38 & 13 & 8.80130740112481 & 4.19869259887519 \tabularnewline
39 & 12 & 11.8347294613283 & 0.165270538671715 \tabularnewline
40 & 5 & 12.3350543946717 & -7.3350543946717 \tabularnewline
41 & 13 & 6.75997127218705 & 6.24002872781295 \tabularnewline
42 & 11 & 10.9242835766641 & 0.0757164233358534 \tabularnewline
43 & 8 & 11.1856522739298 & -3.18565227392982 \tabularnewline
44 & 8 & 8.80593730230932 & -0.805937302309315 \tabularnewline
45 & 8 & 7.79421506202745 & 0.205784937972554 \tabularnewline
46 & 8 & 7.46204103499584 & 0.537958965004157 \tabularnewline
47 & 0 & 7.43699688836597 & -7.43699688836597 \tabularnewline
48 & 3 & 1.01678221709952 & 1.98321778290048 \tabularnewline
49 & 0 & 0.935879120754331 & -0.935879120754331 \tabularnewline
50 & -1 & -1.16681570177592 & 0.166815701775916 \tabularnewline
51 & -1 & -2.5391235827457 & 1.5391235827457 \tabularnewline
52 & -4 & -2.7646397151898 & -1.2353602848102 \tabularnewline
53 & 1 & -4.97355856961831 & 5.97355856961831 \tabularnewline
54 & -1 & -1.53538913259705 & 0.535389132597048 \tabularnewline
55 & 0 & -1.45670982213283 & 1.45670982213283 \tabularnewline
56 & -1 & -0.532491278707392 & -0.467508721292608 \tabularnewline
57 & 6 & -0.914317638200897 & 6.9143176382009 \tabularnewline
58 & 0 & 4.62882890275241 & -4.62882890275241 \tabularnewline
59 & -3 & 2.01133731761596 & -5.01133731761596 \tabularnewline
60 & -3 & -1.74425230566867 & -1.25574769433133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72241&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]12[/C][C]20[/C][C]-8[/C][/ROW]
[ROW][C]4[/C][C]13[/C][C]18.4883600171545[/C][C]-5.4883600171545[/C][/ROW]
[ROW][C]5[/C][C]12[/C][C]17.5922049379589[/C][C]-5.5922049379589[/C][/ROW]
[ROW][C]6[/C][C]15[/C][C]15.6312508328869[/C][C]-0.631250832886929[/C][/ROW]
[ROW][C]7[/C][C]13[/C][C]16.7094684796509[/C][C]-3.70946847965089[/C][/ROW]
[ROW][C]8[/C][C]13[/C][C]15.1694080127592[/C][C]-2.16940801275921[/C][/ROW]
[ROW][C]9[/C][C]16[/C][C]14.2203406796729[/C][C]1.77965932032705[/C][/ROW]
[ROW][C]10[/C][C]14[/C][C]16.0981592840101[/C][C]-2.09815928401006[/C][/ROW]
[ROW][C]11[/C][C]12[/C][C]15.1374723413373[/C][C]-3.13747234133733[/C][/ROW]
[ROW][C]12[/C][C]15[/C][C]12.9560798949468[/C][C]2.04392010505323[/C][/ROW]
[ROW][C]13[/C][C]14[/C][C]14.431724962636[/C][C]-0.431724962636004[/C][/ROW]
[ROW][C]14[/C][C]19[/C][C]14.2573701614291[/C][C]4.74262983857086[/C][/ROW]
[ROW][C]15[/C][C]16[/C][C]18.2175970769512[/C][C]-2.21759707695120[/C][/ROW]
[ROW][C]16[/C][C]16[/C][C]17.3595918531815[/C][C]-1.35959185318151[/C][/ROW]
[ROW][C]17[/C][C]11[/C][C]16.8038800835107[/C][C]-5.80388008351069[/C][/ROW]
[ROW][C]18[/C][C]13[/C][C]12.3878815035589[/C][C]0.612118496441143[/C][/ROW]
[ROW][C]19[/C][C]12[/C][C]12.1575881791556[/C][C]-0.157588179155598[/C][/ROW]
[ROW][C]20[/C][C]11[/C][C]11.4101185153825[/C][C]-0.410118515382502[/C][/ROW]
[ROW][C]21[/C][C]6[/C][C]10.4289537564839[/C][C]-4.42895375648388[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]6.10338685261743[/C][C]2.89661314738257[/C][/ROW]
[ROW][C]23[/C][C]6[/C][C]6.94944796538283[/C][C]-0.94944796538283[/C][/ROW]
[ROW][C]24[/C][C]15[/C][C]5.18235140615841[/C][C]9.8176485938416[/C][/ROW]
[ROW][C]25[/C][C]17[/C][C]12.0096063570887[/C][C]4.99039364291132[/C][/ROW]
[ROW][C]26[/C][C]13[/C][C]16.6612195647143[/C][C]-3.66121956471428[/C][/ROW]
[ROW][C]27[/C][C]12[/C][C]15.1621413078765[/C][C]-3.16214130787654[/C][/ROW]
[ROW][C]28[/C][C]13[/C][C]13.4153612329751[/C][C]-0.415361232975057[/C][/ROW]
[ROW][C]29[/C][C]10[/C][C]13.3395476496351[/C][C]-3.33954764963514[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]10.8093904030464[/C][C]3.19060959695359[/C][/ROW]
[ROW][C]31[/C][C]13[/C][C]12.9980119252203[/C][C]0.00198807477968899[/C][/ROW]
[ROW][C]32[/C][C]10[/C][C]13.1611126120489[/C][C]-3.1611126120489[/C][/ROW]
[ROW][C]33[/C][C]11[/C][C]10.7499467754068[/C][C]0.250053224593248[/C][/ROW]
[ROW][C]34[/C][C]12[/C][C]10.5507112765769[/C][C]1.44928872342315[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]11.3722614187128[/C][C]-4.37226141871278[/C][/ROW]
[ROW][C]36[/C][C]11[/C][C]7.7141886451886[/C][C]3.28581135481140[/C][/ROW]
[ROW][C]37[/C][C]9[/C][C]9.50851450000374[/C][C]-0.508514500003741[/C][/ROW]
[ROW][C]38[/C][C]13[/C][C]8.80130740112481[/C][C]4.19869259887519[/C][/ROW]
[ROW][C]39[/C][C]12[/C][C]11.8347294613283[/C][C]0.165270538671715[/C][/ROW]
[ROW][C]40[/C][C]5[/C][C]12.3350543946717[/C][C]-7.3350543946717[/C][/ROW]
[ROW][C]41[/C][C]13[/C][C]6.75997127218705[/C][C]6.24002872781295[/C][/ROW]
[ROW][C]42[/C][C]11[/C][C]10.9242835766641[/C][C]0.0757164233358534[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]11.1856522739298[/C][C]-3.18565227392982[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]8.80593730230932[/C][C]-0.805937302309315[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]7.79421506202745[/C][C]0.205784937972554[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]7.46204103499584[/C][C]0.537958965004157[/C][/ROW]
[ROW][C]47[/C][C]0[/C][C]7.43699688836597[/C][C]-7.43699688836597[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]1.01678221709952[/C][C]1.98321778290048[/C][/ROW]
[ROW][C]49[/C][C]0[/C][C]0.935879120754331[/C][C]-0.935879120754331[/C][/ROW]
[ROW][C]50[/C][C]-1[/C][C]-1.16681570177592[/C][C]0.166815701775916[/C][/ROW]
[ROW][C]51[/C][C]-1[/C][C]-2.5391235827457[/C][C]1.5391235827457[/C][/ROW]
[ROW][C]52[/C][C]-4[/C][C]-2.7646397151898[/C][C]-1.2353602848102[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]-4.97355856961831[/C][C]5.97355856961831[/C][/ROW]
[ROW][C]54[/C][C]-1[/C][C]-1.53538913259705[/C][C]0.535389132597048[/C][/ROW]
[ROW][C]55[/C][C]0[/C][C]-1.45670982213283[/C][C]1.45670982213283[/C][/ROW]
[ROW][C]56[/C][C]-1[/C][C]-0.532491278707392[/C][C]-0.467508721292608[/C][/ROW]
[ROW][C]57[/C][C]6[/C][C]-0.914317638200897[/C][C]6.9143176382009[/C][/ROW]
[ROW][C]58[/C][C]0[/C][C]4.62882890275241[/C][C]-4.62882890275241[/C][/ROW]
[ROW][C]59[/C][C]-3[/C][C]2.01133731761596[/C][C]-5.01133731761596[/C][/ROW]
[ROW][C]60[/C][C]-3[/C][C]-1.74425230566867[/C][C]-1.25574769433133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72241&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72241&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
31220-8
41318.4883600171545-5.4883600171545
51217.5922049379589-5.5922049379589
61515.6312508328869-0.631250832886929
71316.7094684796509-3.70946847965089
81315.1694080127592-2.16940801275921
91614.22034067967291.77965932032705
101416.0981592840101-2.09815928401006
111215.1374723413373-3.13747234133733
121512.95607989494682.04392010505323
131414.431724962636-0.431724962636004
141914.25737016142914.74262983857086
151618.2175970769512-2.21759707695120
161617.3595918531815-1.35959185318151
171116.8038800835107-5.80388008351069
181312.38788150355890.612118496441143
191212.1575881791556-0.157588179155598
201111.4101185153825-0.410118515382502
21610.4289537564839-4.42895375648388
2296.103386852617432.89661314738257
2366.94944796538283-0.94944796538283
24155.182351406158419.8176485938416
251712.00960635708874.99039364291132
261316.6612195647143-3.66121956471428
271215.1621413078765-3.16214130787654
281313.4153612329751-0.415361232975057
291013.3395476496351-3.33954764963514
301410.80939040304643.19060959695359
311312.99801192522030.00198807477968899
321013.1611126120489-3.1611126120489
331110.74994677540680.250053224593248
341210.55071127657691.44928872342315
35711.3722614187128-4.37226141871278
36117.71418864518863.28581135481140
3799.50851450000374-0.508514500003741
38138.801307401124814.19869259887519
391211.83472946132830.165270538671715
40512.3350543946717-7.3350543946717
41136.759971272187056.24002872781295
421110.92428357666410.0757164233358534
43811.1856522739298-3.18565227392982
4488.80593730230932-0.805937302309315
4587.794215062027450.205784937972554
4687.462041034995840.537958965004157
4707.43699688836597-7.43699688836597
4831.016782217099521.98321778290048
4900.935879120754331-0.935879120754331
50-1-1.166815701775920.166815701775916
51-1-2.53912358274571.5391235827457
52-4-2.7646397151898-1.2353602848102
531-4.973558569618315.97355856961831
54-1-1.535389132597050.535389132597048
550-1.456709822132831.45670982213283
56-1-0.532491278707392-0.467508721292608
576-0.9143176382008976.9143176382009
5804.62882890275241-4.62882890275241
59-32.01133731761596-5.01133731761596
60-3-1.74425230566867-1.25574769433133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61-3.33803407250328-10.53535347559143.85928533058483
62-4.13398235434248-13.41412332008475.14615861139974
63-4.92993063618169-16.6412482796726.78138700730863
64-5.72587891802089-20.15530423752478.70354640148296
65-6.52182719986009-23.916830887997310.8731764882772
66-7.3177754816993-27.899163927993813.2636129645952
67-8.1137237635385-32.083195616398315.8557480893213
68-8.9096720453777-36.454495870311718.6351517795563
69-9.7056203272169-41.001687827066421.5904471726326
70-10.5015686090561-45.715489432837224.712352214725
71-11.2975168908953-50.588120483673627.9930867018830
72-12.0934651727345-55.612918849361831.4259885038928

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & -3.33803407250328 & -10.5353534755914 & 3.85928533058483 \tabularnewline
62 & -4.13398235434248 & -13.4141233200847 & 5.14615861139974 \tabularnewline
63 & -4.92993063618169 & -16.641248279672 & 6.78138700730863 \tabularnewline
64 & -5.72587891802089 & -20.1553042375247 & 8.70354640148296 \tabularnewline
65 & -6.52182719986009 & -23.9168308879973 & 10.8731764882772 \tabularnewline
66 & -7.3177754816993 & -27.8991639279938 & 13.2636129645952 \tabularnewline
67 & -8.1137237635385 & -32.0831956163983 & 15.8557480893213 \tabularnewline
68 & -8.9096720453777 & -36.4544958703117 & 18.6351517795563 \tabularnewline
69 & -9.7056203272169 & -41.0016878270664 & 21.5904471726326 \tabularnewline
70 & -10.5015686090561 & -45.7154894328372 & 24.712352214725 \tabularnewline
71 & -11.2975168908953 & -50.5881204836736 & 27.9930867018830 \tabularnewline
72 & -12.0934651727345 & -55.6129188493618 & 31.4259885038928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72241&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]61[/C][C]-3.33803407250328[/C][C]-10.5353534755914[/C][C]3.85928533058483[/C][/ROW]
[ROW][C]62[/C][C]-4.13398235434248[/C][C]-13.4141233200847[/C][C]5.14615861139974[/C][/ROW]
[ROW][C]63[/C][C]-4.92993063618169[/C][C]-16.641248279672[/C][C]6.78138700730863[/C][/ROW]
[ROW][C]64[/C][C]-5.72587891802089[/C][C]-20.1553042375247[/C][C]8.70354640148296[/C][/ROW]
[ROW][C]65[/C][C]-6.52182719986009[/C][C]-23.9168308879973[/C][C]10.8731764882772[/C][/ROW]
[ROW][C]66[/C][C]-7.3177754816993[/C][C]-27.8991639279938[/C][C]13.2636129645952[/C][/ROW]
[ROW][C]67[/C][C]-8.1137237635385[/C][C]-32.0831956163983[/C][C]15.8557480893213[/C][/ROW]
[ROW][C]68[/C][C]-8.9096720453777[/C][C]-36.4544958703117[/C][C]18.6351517795563[/C][/ROW]
[ROW][C]69[/C][C]-9.7056203272169[/C][C]-41.0016878270664[/C][C]21.5904471726326[/C][/ROW]
[ROW][C]70[/C][C]-10.5015686090561[/C][C]-45.7154894328372[/C][C]24.712352214725[/C][/ROW]
[ROW][C]71[/C][C]-11.2975168908953[/C][C]-50.5881204836736[/C][C]27.9930867018830[/C][/ROW]
[ROW][C]72[/C][C]-12.0934651727345[/C][C]-55.6129188493618[/C][C]31.4259885038928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72241&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72241&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
61-3.33803407250328-10.53535347559143.85928533058483
62-4.13398235434248-13.41412332008475.14615861139974
63-4.92993063618169-16.6412482796726.78138700730863
64-5.72587891802089-20.15530423752478.70354640148296
65-6.52182719986009-23.916830887997310.8731764882772
66-7.3177754816993-27.899163927993813.2636129645952
67-8.1137237635385-32.083195616398315.8557480893213
68-8.9096720453777-36.454495870311718.6351517795563
69-9.7056203272169-41.001687827066421.5904471726326
70-10.5015686090561-45.715489432837224.712352214725
71-11.2975168908953-50.588120483673627.9930867018830
72-12.0934651727345-55.612918849361831.4259885038928



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