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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 22 Apr 2016 16:44:35 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/22/t146133991542bx7fslldobez6.htm/, Retrieved Mon, 06 May 2024 06:11:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294594, Retrieved Mon, 06 May 2024 06:11:21 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

166

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2016-04-22 15:44:35] [bfab382a4ab6d7836f6b75894769f754] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294594&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294594&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.110839319883062
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.110839319883062 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294594&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]0.110839319883062[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294594&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
Parameter	Value
alpha	1
beta	0.110839319883062
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.3	98	1.3
4	99.5	98.444091115848	1.05590888415202
5	100.7	98.7611273384259	1.93887266157412
6	102.9	100.176030665575	2.72396933442539
7	101.2	102.677953573985	-1.47795357398464
8	99.5	100.814138205025	-1.31413820502544
9	99.5	98.9684800201481	0.531519979851922
10	99.5	99.0273933332191	0.472606666780877
11	99.4	99.0797767347373	0.320223265262698
12	99.5	99.0152700636698	0.484729936330226
13	99.7	99.1689972001396	0.531002799860431
14	99.8	99.4278531893321	0.3721468106679
15	99.8	99.5691016887232	0.230898311276817
16	100.1	99.5946943005072	0.505305699492752
17	100	99.9507020405721	0.0492979594279461
18	100	99.8561661928667	0.143833807133319
19	100.1	99.8721086342255	0.227891365774468
20	100.1	99.9973679582152	0.102632041784815
21	100	100.008743623925	-0.00874362392481487
22	99.9	99.9077744865957	-0.00777448659567881
23	99.9	99.806912767789	0.093087232211019
24	99.8	99.817230493297	-0.0172304932970491
25	100.4	99.7153206771387	0.684679322861257
26	102.2	100.391210067623	1.80878993237731
27	103.1	102.391695113539	0.708304886461278
28	103	103.370203145424	-0.370203145423929
29	102.9	103.229170080567	-0.32917008056657
30	102.8	103.092685092711	-0.292685092710741
31	103	102.960244076095	0.039755923905247
32	103.5	103.164650595662	0.33534940433826
33	103.6	103.701820495562	-0.101820495561782
34	103.2	103.790534781084	-0.590534781083548
35	103	103.325080307581	-0.325080307580961
36	103	103.089048627381	-0.0890486273813167
37	106.1	103.079178538086	3.02082146191415
38	104.8	106.514004334413	-1.71400433441256
39	105.3	105.02402525971	0.275974740290337
40	106.3	105.554614112228	0.745385887771661
41	107.9	106.637232177079	1.26276782292062
42	106.1	108.377196503742	-2.27719650374213
43	106.8	106.324793592027	0.475206407972749
44	108.7	107.077465147091	1.62253485290897
45	110.8	109.157305806674	1.64269419332597
46	111.8	111.439380913838	0.360619086161876
47	111.3	112.479351688085	-1.17935168808516
48	111.7	111.848633149075	-0.148633149074854
49	110.8	112.232158751919	-1.43215875191933
50	110.3	111.173419249892	-0.873419249892009
51	110.5	110.576610054261	-0.0766100542612094
52	110.5	110.768118647951	-0.268118647950686
53	112.5	110.738400559364	1.76159944063613
54	113	112.93365504327	0.0663449567296368
55	113.5	113.441008673152	0.0589913268480586
56	112.8	113.947547231699	-1.14754723169878
57	109.5	113.120353877004	-3.62035387700359
58	111.5	109.419076315541	2.08092368445948
59	111.5	111.649724481455	-0.149724481454555
60	111.2	111.63312912176	-0.433129121760288

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.3 & 98 & 1.3 \tabularnewline
4 & 99.5 & 98.444091115848 & 1.05590888415202 \tabularnewline
5 & 100.7 & 98.7611273384259 & 1.93887266157412 \tabularnewline
6 & 102.9 & 100.176030665575 & 2.72396933442539 \tabularnewline
7 & 101.2 & 102.677953573985 & -1.47795357398464 \tabularnewline
8 & 99.5 & 100.814138205025 & -1.31413820502544 \tabularnewline
9 & 99.5 & 98.9684800201481 & 0.531519979851922 \tabularnewline
10 & 99.5 & 99.0273933332191 & 0.472606666780877 \tabularnewline
11 & 99.4 & 99.0797767347373 & 0.320223265262698 \tabularnewline
12 & 99.5 & 99.0152700636698 & 0.484729936330226 \tabularnewline
13 & 99.7 & 99.1689972001396 & 0.531002799860431 \tabularnewline
14 & 99.8 & 99.4278531893321 & 0.3721468106679 \tabularnewline
15 & 99.8 & 99.5691016887232 & 0.230898311276817 \tabularnewline
16 & 100.1 & 99.5946943005072 & 0.505305699492752 \tabularnewline
17 & 100 & 99.9507020405721 & 0.0492979594279461 \tabularnewline
18 & 100 & 99.8561661928667 & 0.143833807133319 \tabularnewline
19 & 100.1 & 99.8721086342255 & 0.227891365774468 \tabularnewline
20 & 100.1 & 99.9973679582152 & 0.102632041784815 \tabularnewline
21 & 100 & 100.008743623925 & -0.00874362392481487 \tabularnewline
22 & 99.9 & 99.9077744865957 & -0.00777448659567881 \tabularnewline
23 & 99.9 & 99.806912767789 & 0.093087232211019 \tabularnewline
24 & 99.8 & 99.817230493297 & -0.0172304932970491 \tabularnewline
25 & 100.4 & 99.7153206771387 & 0.684679322861257 \tabularnewline
26 & 102.2 & 100.391210067623 & 1.80878993237731 \tabularnewline
27 & 103.1 & 102.391695113539 & 0.708304886461278 \tabularnewline
28 & 103 & 103.370203145424 & -0.370203145423929 \tabularnewline
29 & 102.9 & 103.229170080567 & -0.32917008056657 \tabularnewline
30 & 102.8 & 103.092685092711 & -0.292685092710741 \tabularnewline
31 & 103 & 102.960244076095 & 0.039755923905247 \tabularnewline
32 & 103.5 & 103.164650595662 & 0.33534940433826 \tabularnewline
33 & 103.6 & 103.701820495562 & -0.101820495561782 \tabularnewline
34 & 103.2 & 103.790534781084 & -0.590534781083548 \tabularnewline
35 & 103 & 103.325080307581 & -0.325080307580961 \tabularnewline
36 & 103 & 103.089048627381 & -0.0890486273813167 \tabularnewline
37 & 106.1 & 103.079178538086 & 3.02082146191415 \tabularnewline
38 & 104.8 & 106.514004334413 & -1.71400433441256 \tabularnewline
39 & 105.3 & 105.02402525971 & 0.275974740290337 \tabularnewline
40 & 106.3 & 105.554614112228 & 0.745385887771661 \tabularnewline
41 & 107.9 & 106.637232177079 & 1.26276782292062 \tabularnewline
42 & 106.1 & 108.377196503742 & -2.27719650374213 \tabularnewline
43 & 106.8 & 106.324793592027 & 0.475206407972749 \tabularnewline
44 & 108.7 & 107.077465147091 & 1.62253485290897 \tabularnewline
45 & 110.8 & 109.157305806674 & 1.64269419332597 \tabularnewline
46 & 111.8 & 111.439380913838 & 0.360619086161876 \tabularnewline
47 & 111.3 & 112.479351688085 & -1.17935168808516 \tabularnewline
48 & 111.7 & 111.848633149075 & -0.148633149074854 \tabularnewline
49 & 110.8 & 112.232158751919 & -1.43215875191933 \tabularnewline
50 & 110.3 & 111.173419249892 & -0.873419249892009 \tabularnewline
51 & 110.5 & 110.576610054261 & -0.0766100542612094 \tabularnewline
52 & 110.5 & 110.768118647951 & -0.268118647950686 \tabularnewline
53 & 112.5 & 110.738400559364 & 1.76159944063613 \tabularnewline
54 & 113 & 112.93365504327 & 0.0663449567296368 \tabularnewline
55 & 113.5 & 113.441008673152 & 0.0589913268480586 \tabularnewline
56 & 112.8 & 113.947547231699 & -1.14754723169878 \tabularnewline
57 & 109.5 & 113.120353877004 & -3.62035387700359 \tabularnewline
58 & 111.5 & 109.419076315541 & 2.08092368445948 \tabularnewline
59 & 111.5 & 111.649724481455 & -0.149724481454555 \tabularnewline
60 & 111.2 & 111.63312912176 & -0.433129121760288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294594&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]99.3[/C][C]98[/C][C]1.3[/C][/ROW]
[ROW][C]4[/C][C]99.5[/C][C]98.444091115848[/C][C]1.05590888415202[/C][/ROW]
[ROW][C]5[/C][C]100.7[/C][C]98.7611273384259[/C][C]1.93887266157412[/C][/ROW]
[ROW][C]6[/C][C]102.9[/C][C]100.176030665575[/C][C]2.72396933442539[/C][/ROW]
[ROW][C]7[/C][C]101.2[/C][C]102.677953573985[/C][C]-1.47795357398464[/C][/ROW]
[ROW][C]8[/C][C]99.5[/C][C]100.814138205025[/C][C]-1.31413820502544[/C][/ROW]
[ROW][C]9[/C][C]99.5[/C][C]98.9684800201481[/C][C]0.531519979851922[/C][/ROW]
[ROW][C]10[/C][C]99.5[/C][C]99.0273933332191[/C][C]0.472606666780877[/C][/ROW]
[ROW][C]11[/C][C]99.4[/C][C]99.0797767347373[/C][C]0.320223265262698[/C][/ROW]
[ROW][C]12[/C][C]99.5[/C][C]99.0152700636698[/C][C]0.484729936330226[/C][/ROW]
[ROW][C]13[/C][C]99.7[/C][C]99.1689972001396[/C][C]0.531002799860431[/C][/ROW]
[ROW][C]14[/C][C]99.8[/C][C]99.4278531893321[/C][C]0.3721468106679[/C][/ROW]
[ROW][C]15[/C][C]99.8[/C][C]99.5691016887232[/C][C]0.230898311276817[/C][/ROW]
[ROW][C]16[/C][C]100.1[/C][C]99.5946943005072[/C][C]0.505305699492752[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]99.9507020405721[/C][C]0.0492979594279461[/C][/ROW]
[ROW][C]18[/C][C]100[/C][C]99.8561661928667[/C][C]0.143833807133319[/C][/ROW]
[ROW][C]19[/C][C]100.1[/C][C]99.8721086342255[/C][C]0.227891365774468[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]99.9973679582152[/C][C]0.102632041784815[/C][/ROW]
[ROW][C]21[/C][C]100[/C][C]100.008743623925[/C][C]-0.00874362392481487[/C][/ROW]
[ROW][C]22[/C][C]99.9[/C][C]99.9077744865957[/C][C]-0.00777448659567881[/C][/ROW]
[ROW][C]23[/C][C]99.9[/C][C]99.806912767789[/C][C]0.093087232211019[/C][/ROW]
[ROW][C]24[/C][C]99.8[/C][C]99.817230493297[/C][C]-0.0172304932970491[/C][/ROW]
[ROW][C]25[/C][C]100.4[/C][C]99.7153206771387[/C][C]0.684679322861257[/C][/ROW]
[ROW][C]26[/C][C]102.2[/C][C]100.391210067623[/C][C]1.80878993237731[/C][/ROW]
[ROW][C]27[/C][C]103.1[/C][C]102.391695113539[/C][C]0.708304886461278[/C][/ROW]
[ROW][C]28[/C][C]103[/C][C]103.370203145424[/C][C]-0.370203145423929[/C][/ROW]
[ROW][C]29[/C][C]102.9[/C][C]103.229170080567[/C][C]-0.32917008056657[/C][/ROW]
[ROW][C]30[/C][C]102.8[/C][C]103.092685092711[/C][C]-0.292685092710741[/C][/ROW]
[ROW][C]31[/C][C]103[/C][C]102.960244076095[/C][C]0.039755923905247[/C][/ROW]
[ROW][C]32[/C][C]103.5[/C][C]103.164650595662[/C][C]0.33534940433826[/C][/ROW]
[ROW][C]33[/C][C]103.6[/C][C]103.701820495562[/C][C]-0.101820495561782[/C][/ROW]
[ROW][C]34[/C][C]103.2[/C][C]103.790534781084[/C][C]-0.590534781083548[/C][/ROW]
[ROW][C]35[/C][C]103[/C][C]103.325080307581[/C][C]-0.325080307580961[/C][/ROW]
[ROW][C]36[/C][C]103[/C][C]103.089048627381[/C][C]-0.0890486273813167[/C][/ROW]
[ROW][C]37[/C][C]106.1[/C][C]103.079178538086[/C][C]3.02082146191415[/C][/ROW]
[ROW][C]38[/C][C]104.8[/C][C]106.514004334413[/C][C]-1.71400433441256[/C][/ROW]
[ROW][C]39[/C][C]105.3[/C][C]105.02402525971[/C][C]0.275974740290337[/C][/ROW]
[ROW][C]40[/C][C]106.3[/C][C]105.554614112228[/C][C]0.745385887771661[/C][/ROW]
[ROW][C]41[/C][C]107.9[/C][C]106.637232177079[/C][C]1.26276782292062[/C][/ROW]
[ROW][C]42[/C][C]106.1[/C][C]108.377196503742[/C][C]-2.27719650374213[/C][/ROW]
[ROW][C]43[/C][C]106.8[/C][C]106.324793592027[/C][C]0.475206407972749[/C][/ROW]
[ROW][C]44[/C][C]108.7[/C][C]107.077465147091[/C][C]1.62253485290897[/C][/ROW]
[ROW][C]45[/C][C]110.8[/C][C]109.157305806674[/C][C]1.64269419332597[/C][/ROW]
[ROW][C]46[/C][C]111.8[/C][C]111.439380913838[/C][C]0.360619086161876[/C][/ROW]
[ROW][C]47[/C][C]111.3[/C][C]112.479351688085[/C][C]-1.17935168808516[/C][/ROW]
[ROW][C]48[/C][C]111.7[/C][C]111.848633149075[/C][C]-0.148633149074854[/C][/ROW]
[ROW][C]49[/C][C]110.8[/C][C]112.232158751919[/C][C]-1.43215875191933[/C][/ROW]
[ROW][C]50[/C][C]110.3[/C][C]111.173419249892[/C][C]-0.873419249892009[/C][/ROW]
[ROW][C]51[/C][C]110.5[/C][C]110.576610054261[/C][C]-0.0766100542612094[/C][/ROW]
[ROW][C]52[/C][C]110.5[/C][C]110.768118647951[/C][C]-0.268118647950686[/C][/ROW]
[ROW][C]53[/C][C]112.5[/C][C]110.738400559364[/C][C]1.76159944063613[/C][/ROW]
[ROW][C]54[/C][C]113[/C][C]112.93365504327[/C][C]0.0663449567296368[/C][/ROW]
[ROW][C]55[/C][C]113.5[/C][C]113.441008673152[/C][C]0.0589913268480586[/C][/ROW]
[ROW][C]56[/C][C]112.8[/C][C]113.947547231699[/C][C]-1.14754723169878[/C][/ROW]
[ROW][C]57[/C][C]109.5[/C][C]113.120353877004[/C][C]-3.62035387700359[/C][/ROW]
[ROW][C]58[/C][C]111.5[/C][C]109.419076315541[/C][C]2.08092368445948[/C][/ROW]
[ROW][C]59[/C][C]111.5[/C][C]111.649724481455[/C][C]-0.149724481454555[/C][/ROW]
[ROW][C]60[/C][C]111.2[/C][C]111.63312912176[/C][C]-0.433129121760288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294594&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294594&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
t	Observed	Fitted	Residuals
3	99.3	98	1.3
4	99.5	98.444091115848	1.05590888415202
5	100.7	98.7611273384259	1.93887266157412
6	102.9	100.176030665575	2.72396933442539
7	101.2	102.677953573985	-1.47795357398464
8	99.5	100.814138205025	-1.31413820502544
9	99.5	98.9684800201481	0.531519979851922
10	99.5	99.0273933332191	0.472606666780877
11	99.4	99.0797767347373	0.320223265262698
12	99.5	99.0152700636698	0.484729936330226
13	99.7	99.1689972001396	0.531002799860431
14	99.8	99.4278531893321	0.3721468106679
15	99.8	99.5691016887232	0.230898311276817
16	100.1	99.5946943005072	0.505305699492752
17	100	99.9507020405721	0.0492979594279461
18	100	99.8561661928667	0.143833807133319
19	100.1	99.8721086342255	0.227891365774468
20	100.1	99.9973679582152	0.102632041784815
21	100	100.008743623925	-0.00874362392481487
22	99.9	99.9077744865957	-0.00777448659567881
23	99.9	99.806912767789	0.093087232211019
24	99.8	99.817230493297	-0.0172304932970491
25	100.4	99.7153206771387	0.684679322861257
26	102.2	100.391210067623	1.80878993237731
27	103.1	102.391695113539	0.708304886461278
28	103	103.370203145424	-0.370203145423929
29	102.9	103.229170080567	-0.32917008056657
30	102.8	103.092685092711	-0.292685092710741
31	103	102.960244076095	0.039755923905247
32	103.5	103.164650595662	0.33534940433826
33	103.6	103.701820495562	-0.101820495561782
34	103.2	103.790534781084	-0.590534781083548
35	103	103.325080307581	-0.325080307580961
36	103	103.089048627381	-0.0890486273813167
37	106.1	103.079178538086	3.02082146191415
38	104.8	106.514004334413	-1.71400433441256
39	105.3	105.02402525971	0.275974740290337
40	106.3	105.554614112228	0.745385887771661
41	107.9	106.637232177079	1.26276782292062
42	106.1	108.377196503742	-2.27719650374213
43	106.8	106.324793592027	0.475206407972749
44	108.7	107.077465147091	1.62253485290897
45	110.8	109.157305806674	1.64269419332597
46	111.8	111.439380913838	0.360619086161876
47	111.3	112.479351688085	-1.17935168808516
48	111.7	111.848633149075	-0.148633149074854
49	110.8	112.232158751919	-1.43215875191933
50	110.3	111.173419249892	-0.873419249892009
51	110.5	110.576610054261	-0.0766100542612094
52	110.5	110.768118647951	-0.268118647950686
53	112.5	110.738400559364	1.76159944063613
54	113	112.93365504327	0.0663449567296368
55	113.5	113.441008673152	0.0589913268480586
56	112.8	113.947547231699	-1.14754723169878
57	109.5	113.120353877004	-3.62035387700359
58	111.5	109.419076315541	2.08092368445948
59	111.5	111.649724481455	-0.149724481454555
60	111.2	111.63312912176	-0.433129121760288

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	111.285121384483	109.042709902245	113.527532866721
62	111.370242768966	108.018633420118	114.721852117813
63	111.455364153448	107.126602263634	115.784126043263
64	111.540485537931	106.280576446144	116.800394629719
65	111.625606922414	105.44966737635	117.801546468478
66	111.710728306897	104.619290656398	118.802165957396
67	111.79584969138	103.781551764512	119.810147618248
68	111.880971075863	102.931824145033	120.830118006693
69	111.966092460346	102.067263331516	121.864921589175
70	112.051213844828	101.186073033913	122.916354655744
71	112.136335229311	100.287108143494	123.985562315129
72	112.221456613794	99.3696449603193	125.073268267269

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 111.285121384483 & 109.042709902245 & 113.527532866721 \tabularnewline
62 & 111.370242768966 & 108.018633420118 & 114.721852117813 \tabularnewline
63 & 111.455364153448 & 107.126602263634 & 115.784126043263 \tabularnewline
64 & 111.540485537931 & 106.280576446144 & 116.800394629719 \tabularnewline
65 & 111.625606922414 & 105.44966737635 & 117.801546468478 \tabularnewline
66 & 111.710728306897 & 104.619290656398 & 118.802165957396 \tabularnewline
67 & 111.79584969138 & 103.781551764512 & 119.810147618248 \tabularnewline
68 & 111.880971075863 & 102.931824145033 & 120.830118006693 \tabularnewline
69 & 111.966092460346 & 102.067263331516 & 121.864921589175 \tabularnewline
70 & 112.051213844828 & 101.186073033913 & 122.916354655744 \tabularnewline
71 & 112.136335229311 & 100.287108143494 & 123.985562315129 \tabularnewline
72 & 112.221456613794 & 99.3696449603193 & 125.073268267269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294594&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]111.285121384483[/C][C]109.042709902245[/C][C]113.527532866721[/C][/ROW]
[ROW][C]62[/C][C]111.370242768966[/C][C]108.018633420118[/C][C]114.721852117813[/C][/ROW]
[ROW][C]63[/C][C]111.455364153448[/C][C]107.126602263634[/C][C]115.784126043263[/C][/ROW]
[ROW][C]64[/C][C]111.540485537931[/C][C]106.280576446144[/C][C]116.800394629719[/C][/ROW]
[ROW][C]65[/C][C]111.625606922414[/C][C]105.44966737635[/C][C]117.801546468478[/C][/ROW]
[ROW][C]66[/C][C]111.710728306897[/C][C]104.619290656398[/C][C]118.802165957396[/C][/ROW]
[ROW][C]67[/C][C]111.79584969138[/C][C]103.781551764512[/C][C]119.810147618248[/C][/ROW]
[ROW][C]68[/C][C]111.880971075863[/C][C]102.931824145033[/C][C]120.830118006693[/C][/ROW]
[ROW][C]69[/C][C]111.966092460346[/C][C]102.067263331516[/C][C]121.864921589175[/C][/ROW]
[ROW][C]70[/C][C]112.051213844828[/C][C]101.186073033913[/C][C]122.916354655744[/C][/ROW]
[ROW][C]71[/C][C]112.136335229311[/C][C]100.287108143494[/C][C]123.985562315129[/C][/ROW]
[ROW][C]72[/C][C]112.221456613794[/C][C]99.3696449603193[/C][C]125.073268267269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294594&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294594&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
t	Forecast	95% Lower Bound	95% Upper Bound
61	111.285121384483	109.042709902245	113.527532866721
62	111.370242768966	108.018633420118	114.721852117813
63	111.455364153448	107.126602263634	115.784126043263
64	111.540485537931	106.280576446144	116.800394629719
65	111.625606922414	105.44966737635	117.801546468478
66	111.710728306897	104.619290656398	118.802165957396
67	111.79584969138	103.781551764512	119.810147618248
68	111.880971075863	102.931824145033	120.830118006693
69	111.966092460346	102.067263331516	121.864921589175
70	112.051213844828	101.186073033913	122.916354655744
71	112.136335229311	100.287108143494	123.985562315129
72	112.221456613794	99.3696449603193	125.073268267269

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code