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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 11 Jan 2014 09:44:38 -0500

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/2014/Jan/11/t1389451544waprrc1ih2pkhf1.htm/, Retrieved Sun, 19 May 2024 10:50:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232910, Retrieved Sun, 19 May 2024 10:50:10 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

137

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

-       [Exponential Smoothing] [exponential smoot...] [2014-01-11 14:44:38] [45baafc513cf820e9f0a314ccf5f72d1] [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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232910&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232910&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.760510282023055
beta	0.240924803373457
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.760510282023055 \tabularnewline
beta & 0.240924803373457 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232910&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]0.760510282023055[/C][/ROW]
[ROW][C]beta[/C][C]0.240924803373457[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232910&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	0.760510282023055
beta	0.240924803373457
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	31.3	31.08	0.220000000000002
4	31.06	31.0776219358802	-0.0176219358802499
5	31.09	30.8913011531635	0.198698846836461
6	31.11	30.9059013031336	0.204098696866367
7	31.13	30.9620042395768	0.167995760423199
8	31.1	31.0214316775908	0.0785683224092359
9	31.03	31.0272443724551	0.00275562754489656
10	30.74	30.9759056354015	-0.235905635401537
11	30.83	30.699838557507	0.130161442493023
12	30.82	30.7260181894105	0.0939818105895007
13	30.8	30.7419027307575	0.0580972692424986
14	30.74	30.7411416275075	-0.001141627507522
15	30.71	30.6951195585813	0.0148804414186898
16	30.58	30.6640089184496	-0.0840089184496371
17	30.71	30.542299302892	0.167700697107993
18	30.7	30.642744530788	0.0572554692119951
19	30.7	30.6696857058561	0.0303142941439383
20	30.72	30.6816922007727	0.0383077992272618
21	30.68	30.7067968152774	-0.0267968152773861
22	30.78	30.6774788333911	0.102521166608867
23	30.84	30.7652930281399	0.0747069718601274
24	30.8	30.8456424857455	-0.0456424857455282
25	30.8	30.8261020628906	-0.0261020628905975
26	30.88	30.816639761434	0.063360238566009
27	30.87	30.8868236898646	-0.0168236898645517
28	30.92	30.8929443824018	0.0270556175981653
29	30.82	30.9373930263453	-0.117393026345255
30	30.75	30.850477561334	-0.100477561334046
31	30.75	30.7580164008203	-0.00801640082029209
32	30.75	30.7344040921905	0.0155959078095051
33	30.63	30.7316067595876	-0.101606759587618
34	30.52	30.6210586145377	-0.101058614537671
35	30.58	30.4924107949331	0.0875892050668803
36	30.6	30.5232801831269	0.0767198168730836
37	30.6	30.5599403389075	0.0400596610924744
38	30.63	30.5760600323336	0.053939967666377
39	30.56	30.6126190348237	-0.0526190348236746
40	30.61	30.5584976560449	0.0515023439550966
41	30.53	30.5929982140721	-0.06299821407206
42	30.6	30.5288770228702	0.071122977129825
43	30.6	30.5797879402976	0.020212059702363
44	30.63	30.595683952164	0.0343160478359827
45	30.66	30.6285937770035	0.0314062229965479
46	30.34	30.6650450801581	-0.325045080158095
47	30.32	30.3708548605736	-0.0508548605735584
48	30.3	30.2758712002012	0.024128799798838
49	30.3	30.2423344029344	0.0576655970655509
50	30.08	30.2448685094026	-0.164868509402574
51	29.96	30.0479549768931	-0.0879549768931014
52	29.91	29.8934193565441	0.016580643455935
53	29.83	29.8214221518067	0.0085778481932941
54	29.89	29.7449104220003	0.145089577999737
55	29.85	29.7988014189013	0.0511985810986531
56	30.06	29.7906682477466	0.269331752253372
57	29.83	29.9977761192271	-0.167776119227138
58	29.95	29.8417180480782	0.108281951921846
59	30.02	29.9154450246744	0.104554975325637
60	30.03	30.0054947652175	0.0245052347825165
61	30.03	30.0391558460104	-0.00915584601036201
62	29.96	30.0455397416364	-0.0855397416364205
63	29.85	29.9781598125065	-0.128159812506475
64	30.12	29.8548846983461	0.265115301653939
65	29.91	30.0792753127975	-0.169275312797456
66	29.9	29.9422917956024	-0.0422917956023774
67	29.92	29.8941316012151	0.025868398784926
68	29.89	29.9025476932916	-0.0125476932915518
69	29.96	29.8794488913307	0.080551108669308
70	29.72	29.9419117260393	-0.221911726039284
71	29.6	29.7336885136729	-0.133688513672855
72	29.54	29.5680647778712	-0.0280647778711902
73	29.54	29.4776267880713	0.0623732119287332
74	29.54	29.4673962004401	0.0726037995598681
75	29.48	29.4782489684366	0.00175103156341905
76	29.55	29.4355383120037	0.114461687996261
77	29.58	29.4995176019078	0.0804823980922045
78	29.6	29.5524017434484	0.0475982565516233
79	29.6	29.5889983853988	0.0110016146012484
80	29.56	29.5997786843867	-0.0397786843867003
81	29.7	29.5646515629918	0.135348437008165
82	29.76	29.6875097423966	0.072490257603409
83	29.24	29.7758457147831	-0.535845714783061
84	29.28	29.3033551707502	-0.0233551707502002

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 31.3 & 31.08 & 0.220000000000002 \tabularnewline
4 & 31.06 & 31.0776219358802 & -0.0176219358802499 \tabularnewline
5 & 31.09 & 30.8913011531635 & 0.198698846836461 \tabularnewline
6 & 31.11 & 30.9059013031336 & 0.204098696866367 \tabularnewline
7 & 31.13 & 30.9620042395768 & 0.167995760423199 \tabularnewline
8 & 31.1 & 31.0214316775908 & 0.0785683224092359 \tabularnewline
9 & 31.03 & 31.0272443724551 & 0.00275562754489656 \tabularnewline
10 & 30.74 & 30.9759056354015 & -0.235905635401537 \tabularnewline
11 & 30.83 & 30.699838557507 & 0.130161442493023 \tabularnewline
12 & 30.82 & 30.7260181894105 & 0.0939818105895007 \tabularnewline
13 & 30.8 & 30.7419027307575 & 0.0580972692424986 \tabularnewline
14 & 30.74 & 30.7411416275075 & -0.001141627507522 \tabularnewline
15 & 30.71 & 30.6951195585813 & 0.0148804414186898 \tabularnewline
16 & 30.58 & 30.6640089184496 & -0.0840089184496371 \tabularnewline
17 & 30.71 & 30.542299302892 & 0.167700697107993 \tabularnewline
18 & 30.7 & 30.642744530788 & 0.0572554692119951 \tabularnewline
19 & 30.7 & 30.6696857058561 & 0.0303142941439383 \tabularnewline
20 & 30.72 & 30.6816922007727 & 0.0383077992272618 \tabularnewline
21 & 30.68 & 30.7067968152774 & -0.0267968152773861 \tabularnewline
22 & 30.78 & 30.6774788333911 & 0.102521166608867 \tabularnewline
23 & 30.84 & 30.7652930281399 & 0.0747069718601274 \tabularnewline
24 & 30.8 & 30.8456424857455 & -0.0456424857455282 \tabularnewline
25 & 30.8 & 30.8261020628906 & -0.0261020628905975 \tabularnewline
26 & 30.88 & 30.816639761434 & 0.063360238566009 \tabularnewline
27 & 30.87 & 30.8868236898646 & -0.0168236898645517 \tabularnewline
28 & 30.92 & 30.8929443824018 & 0.0270556175981653 \tabularnewline
29 & 30.82 & 30.9373930263453 & -0.117393026345255 \tabularnewline
30 & 30.75 & 30.850477561334 & -0.100477561334046 \tabularnewline
31 & 30.75 & 30.7580164008203 & -0.00801640082029209 \tabularnewline
32 & 30.75 & 30.7344040921905 & 0.0155959078095051 \tabularnewline
33 & 30.63 & 30.7316067595876 & -0.101606759587618 \tabularnewline
34 & 30.52 & 30.6210586145377 & -0.101058614537671 \tabularnewline
35 & 30.58 & 30.4924107949331 & 0.0875892050668803 \tabularnewline
36 & 30.6 & 30.5232801831269 & 0.0767198168730836 \tabularnewline
37 & 30.6 & 30.5599403389075 & 0.0400596610924744 \tabularnewline
38 & 30.63 & 30.5760600323336 & 0.053939967666377 \tabularnewline
39 & 30.56 & 30.6126190348237 & -0.0526190348236746 \tabularnewline
40 & 30.61 & 30.5584976560449 & 0.0515023439550966 \tabularnewline
41 & 30.53 & 30.5929982140721 & -0.06299821407206 \tabularnewline
42 & 30.6 & 30.5288770228702 & 0.071122977129825 \tabularnewline
43 & 30.6 & 30.5797879402976 & 0.020212059702363 \tabularnewline
44 & 30.63 & 30.595683952164 & 0.0343160478359827 \tabularnewline
45 & 30.66 & 30.6285937770035 & 0.0314062229965479 \tabularnewline
46 & 30.34 & 30.6650450801581 & -0.325045080158095 \tabularnewline
47 & 30.32 & 30.3708548605736 & -0.0508548605735584 \tabularnewline
48 & 30.3 & 30.2758712002012 & 0.024128799798838 \tabularnewline
49 & 30.3 & 30.2423344029344 & 0.0576655970655509 \tabularnewline
50 & 30.08 & 30.2448685094026 & -0.164868509402574 \tabularnewline
51 & 29.96 & 30.0479549768931 & -0.0879549768931014 \tabularnewline
52 & 29.91 & 29.8934193565441 & 0.016580643455935 \tabularnewline
53 & 29.83 & 29.8214221518067 & 0.0085778481932941 \tabularnewline
54 & 29.89 & 29.7449104220003 & 0.145089577999737 \tabularnewline
55 & 29.85 & 29.7988014189013 & 0.0511985810986531 \tabularnewline
56 & 30.06 & 29.7906682477466 & 0.269331752253372 \tabularnewline
57 & 29.83 & 29.9977761192271 & -0.167776119227138 \tabularnewline
58 & 29.95 & 29.8417180480782 & 0.108281951921846 \tabularnewline
59 & 30.02 & 29.9154450246744 & 0.104554975325637 \tabularnewline
60 & 30.03 & 30.0054947652175 & 0.0245052347825165 \tabularnewline
61 & 30.03 & 30.0391558460104 & -0.00915584601036201 \tabularnewline
62 & 29.96 & 30.0455397416364 & -0.0855397416364205 \tabularnewline
63 & 29.85 & 29.9781598125065 & -0.128159812506475 \tabularnewline
64 & 30.12 & 29.8548846983461 & 0.265115301653939 \tabularnewline
65 & 29.91 & 30.0792753127975 & -0.169275312797456 \tabularnewline
66 & 29.9 & 29.9422917956024 & -0.0422917956023774 \tabularnewline
67 & 29.92 & 29.8941316012151 & 0.025868398784926 \tabularnewline
68 & 29.89 & 29.9025476932916 & -0.0125476932915518 \tabularnewline
69 & 29.96 & 29.8794488913307 & 0.080551108669308 \tabularnewline
70 & 29.72 & 29.9419117260393 & -0.221911726039284 \tabularnewline
71 & 29.6 & 29.7336885136729 & -0.133688513672855 \tabularnewline
72 & 29.54 & 29.5680647778712 & -0.0280647778711902 \tabularnewline
73 & 29.54 & 29.4776267880713 & 0.0623732119287332 \tabularnewline
74 & 29.54 & 29.4673962004401 & 0.0726037995598681 \tabularnewline
75 & 29.48 & 29.4782489684366 & 0.00175103156341905 \tabularnewline
76 & 29.55 & 29.4355383120037 & 0.114461687996261 \tabularnewline
77 & 29.58 & 29.4995176019078 & 0.0804823980922045 \tabularnewline
78 & 29.6 & 29.5524017434484 & 0.0475982565516233 \tabularnewline
79 & 29.6 & 29.5889983853988 & 0.0110016146012484 \tabularnewline
80 & 29.56 & 29.5997786843867 & -0.0397786843867003 \tabularnewline
81 & 29.7 & 29.5646515629918 & 0.135348437008165 \tabularnewline
82 & 29.76 & 29.6875097423966 & 0.072490257603409 \tabularnewline
83 & 29.24 & 29.7758457147831 & -0.535845714783061 \tabularnewline
84 & 29.28 & 29.3033551707502 & -0.0233551707502002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232910&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]31.3[/C][C]31.08[/C][C]0.220000000000002[/C][/ROW]
[ROW][C]4[/C][C]31.06[/C][C]31.0776219358802[/C][C]-0.0176219358802499[/C][/ROW]
[ROW][C]5[/C][C]31.09[/C][C]30.8913011531635[/C][C]0.198698846836461[/C][/ROW]
[ROW][C]6[/C][C]31.11[/C][C]30.9059013031336[/C][C]0.204098696866367[/C][/ROW]
[ROW][C]7[/C][C]31.13[/C][C]30.9620042395768[/C][C]0.167995760423199[/C][/ROW]
[ROW][C]8[/C][C]31.1[/C][C]31.0214316775908[/C][C]0.0785683224092359[/C][/ROW]
[ROW][C]9[/C][C]31.03[/C][C]31.0272443724551[/C][C]0.00275562754489656[/C][/ROW]
[ROW][C]10[/C][C]30.74[/C][C]30.9759056354015[/C][C]-0.235905635401537[/C][/ROW]
[ROW][C]11[/C][C]30.83[/C][C]30.699838557507[/C][C]0.130161442493023[/C][/ROW]
[ROW][C]12[/C][C]30.82[/C][C]30.7260181894105[/C][C]0.0939818105895007[/C][/ROW]
[ROW][C]13[/C][C]30.8[/C][C]30.7419027307575[/C][C]0.0580972692424986[/C][/ROW]
[ROW][C]14[/C][C]30.74[/C][C]30.7411416275075[/C][C]-0.001141627507522[/C][/ROW]
[ROW][C]15[/C][C]30.71[/C][C]30.6951195585813[/C][C]0.0148804414186898[/C][/ROW]
[ROW][C]16[/C][C]30.58[/C][C]30.6640089184496[/C][C]-0.0840089184496371[/C][/ROW]
[ROW][C]17[/C][C]30.71[/C][C]30.542299302892[/C][C]0.167700697107993[/C][/ROW]
[ROW][C]18[/C][C]30.7[/C][C]30.642744530788[/C][C]0.0572554692119951[/C][/ROW]
[ROW][C]19[/C][C]30.7[/C][C]30.6696857058561[/C][C]0.0303142941439383[/C][/ROW]
[ROW][C]20[/C][C]30.72[/C][C]30.6816922007727[/C][C]0.0383077992272618[/C][/ROW]
[ROW][C]21[/C][C]30.68[/C][C]30.7067968152774[/C][C]-0.0267968152773861[/C][/ROW]
[ROW][C]22[/C][C]30.78[/C][C]30.6774788333911[/C][C]0.102521166608867[/C][/ROW]
[ROW][C]23[/C][C]30.84[/C][C]30.7652930281399[/C][C]0.0747069718601274[/C][/ROW]
[ROW][C]24[/C][C]30.8[/C][C]30.8456424857455[/C][C]-0.0456424857455282[/C][/ROW]
[ROW][C]25[/C][C]30.8[/C][C]30.8261020628906[/C][C]-0.0261020628905975[/C][/ROW]
[ROW][C]26[/C][C]30.88[/C][C]30.816639761434[/C][C]0.063360238566009[/C][/ROW]
[ROW][C]27[/C][C]30.87[/C][C]30.8868236898646[/C][C]-0.0168236898645517[/C][/ROW]
[ROW][C]28[/C][C]30.92[/C][C]30.8929443824018[/C][C]0.0270556175981653[/C][/ROW]
[ROW][C]29[/C][C]30.82[/C][C]30.9373930263453[/C][C]-0.117393026345255[/C][/ROW]
[ROW][C]30[/C][C]30.75[/C][C]30.850477561334[/C][C]-0.100477561334046[/C][/ROW]
[ROW][C]31[/C][C]30.75[/C][C]30.7580164008203[/C][C]-0.00801640082029209[/C][/ROW]
[ROW][C]32[/C][C]30.75[/C][C]30.7344040921905[/C][C]0.0155959078095051[/C][/ROW]
[ROW][C]33[/C][C]30.63[/C][C]30.7316067595876[/C][C]-0.101606759587618[/C][/ROW]
[ROW][C]34[/C][C]30.52[/C][C]30.6210586145377[/C][C]-0.101058614537671[/C][/ROW]
[ROW][C]35[/C][C]30.58[/C][C]30.4924107949331[/C][C]0.0875892050668803[/C][/ROW]
[ROW][C]36[/C][C]30.6[/C][C]30.5232801831269[/C][C]0.0767198168730836[/C][/ROW]
[ROW][C]37[/C][C]30.6[/C][C]30.5599403389075[/C][C]0.0400596610924744[/C][/ROW]
[ROW][C]38[/C][C]30.63[/C][C]30.5760600323336[/C][C]0.053939967666377[/C][/ROW]
[ROW][C]39[/C][C]30.56[/C][C]30.6126190348237[/C][C]-0.0526190348236746[/C][/ROW]
[ROW][C]40[/C][C]30.61[/C][C]30.5584976560449[/C][C]0.0515023439550966[/C][/ROW]
[ROW][C]41[/C][C]30.53[/C][C]30.5929982140721[/C][C]-0.06299821407206[/C][/ROW]
[ROW][C]42[/C][C]30.6[/C][C]30.5288770228702[/C][C]0.071122977129825[/C][/ROW]
[ROW][C]43[/C][C]30.6[/C][C]30.5797879402976[/C][C]0.020212059702363[/C][/ROW]
[ROW][C]44[/C][C]30.63[/C][C]30.595683952164[/C][C]0.0343160478359827[/C][/ROW]
[ROW][C]45[/C][C]30.66[/C][C]30.6285937770035[/C][C]0.0314062229965479[/C][/ROW]
[ROW][C]46[/C][C]30.34[/C][C]30.6650450801581[/C][C]-0.325045080158095[/C][/ROW]
[ROW][C]47[/C][C]30.32[/C][C]30.3708548605736[/C][C]-0.0508548605735584[/C][/ROW]
[ROW][C]48[/C][C]30.3[/C][C]30.2758712002012[/C][C]0.024128799798838[/C][/ROW]
[ROW][C]49[/C][C]30.3[/C][C]30.2423344029344[/C][C]0.0576655970655509[/C][/ROW]
[ROW][C]50[/C][C]30.08[/C][C]30.2448685094026[/C][C]-0.164868509402574[/C][/ROW]
[ROW][C]51[/C][C]29.96[/C][C]30.0479549768931[/C][C]-0.0879549768931014[/C][/ROW]
[ROW][C]52[/C][C]29.91[/C][C]29.8934193565441[/C][C]0.016580643455935[/C][/ROW]
[ROW][C]53[/C][C]29.83[/C][C]29.8214221518067[/C][C]0.0085778481932941[/C][/ROW]
[ROW][C]54[/C][C]29.89[/C][C]29.7449104220003[/C][C]0.145089577999737[/C][/ROW]
[ROW][C]55[/C][C]29.85[/C][C]29.7988014189013[/C][C]0.0511985810986531[/C][/ROW]
[ROW][C]56[/C][C]30.06[/C][C]29.7906682477466[/C][C]0.269331752253372[/C][/ROW]
[ROW][C]57[/C][C]29.83[/C][C]29.9977761192271[/C][C]-0.167776119227138[/C][/ROW]
[ROW][C]58[/C][C]29.95[/C][C]29.8417180480782[/C][C]0.108281951921846[/C][/ROW]
[ROW][C]59[/C][C]30.02[/C][C]29.9154450246744[/C][C]0.104554975325637[/C][/ROW]
[ROW][C]60[/C][C]30.03[/C][C]30.0054947652175[/C][C]0.0245052347825165[/C][/ROW]
[ROW][C]61[/C][C]30.03[/C][C]30.0391558460104[/C][C]-0.00915584601036201[/C][/ROW]
[ROW][C]62[/C][C]29.96[/C][C]30.0455397416364[/C][C]-0.0855397416364205[/C][/ROW]
[ROW][C]63[/C][C]29.85[/C][C]29.9781598125065[/C][C]-0.128159812506475[/C][/ROW]
[ROW][C]64[/C][C]30.12[/C][C]29.8548846983461[/C][C]0.265115301653939[/C][/ROW]
[ROW][C]65[/C][C]29.91[/C][C]30.0792753127975[/C][C]-0.169275312797456[/C][/ROW]
[ROW][C]66[/C][C]29.9[/C][C]29.9422917956024[/C][C]-0.0422917956023774[/C][/ROW]
[ROW][C]67[/C][C]29.92[/C][C]29.8941316012151[/C][C]0.025868398784926[/C][/ROW]
[ROW][C]68[/C][C]29.89[/C][C]29.9025476932916[/C][C]-0.0125476932915518[/C][/ROW]
[ROW][C]69[/C][C]29.96[/C][C]29.8794488913307[/C][C]0.080551108669308[/C][/ROW]
[ROW][C]70[/C][C]29.72[/C][C]29.9419117260393[/C][C]-0.221911726039284[/C][/ROW]
[ROW][C]71[/C][C]29.6[/C][C]29.7336885136729[/C][C]-0.133688513672855[/C][/ROW]
[ROW][C]72[/C][C]29.54[/C][C]29.5680647778712[/C][C]-0.0280647778711902[/C][/ROW]
[ROW][C]73[/C][C]29.54[/C][C]29.4776267880713[/C][C]0.0623732119287332[/C][/ROW]
[ROW][C]74[/C][C]29.54[/C][C]29.4673962004401[/C][C]0.0726037995598681[/C][/ROW]
[ROW][C]75[/C][C]29.48[/C][C]29.4782489684366[/C][C]0.00175103156341905[/C][/ROW]
[ROW][C]76[/C][C]29.55[/C][C]29.4355383120037[/C][C]0.114461687996261[/C][/ROW]
[ROW][C]77[/C][C]29.58[/C][C]29.4995176019078[/C][C]0.0804823980922045[/C][/ROW]
[ROW][C]78[/C][C]29.6[/C][C]29.5524017434484[/C][C]0.0475982565516233[/C][/ROW]
[ROW][C]79[/C][C]29.6[/C][C]29.5889983853988[/C][C]0.0110016146012484[/C][/ROW]
[ROW][C]80[/C][C]29.56[/C][C]29.5997786843867[/C][C]-0.0397786843867003[/C][/ROW]
[ROW][C]81[/C][C]29.7[/C][C]29.5646515629918[/C][C]0.135348437008165[/C][/ROW]
[ROW][C]82[/C][C]29.76[/C][C]29.6875097423966[/C][C]0.072490257603409[/C][/ROW]
[ROW][C]83[/C][C]29.24[/C][C]29.7758457147831[/C][C]-0.535845714783061[/C][/ROW]
[ROW][C]84[/C][C]29.28[/C][C]29.3033551707502[/C][C]-0.0233551707502002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232910&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232910&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	31.3	31.08	0.220000000000002
4	31.06	31.0776219358802	-0.0176219358802499
5	31.09	30.8913011531635	0.198698846836461
6	31.11	30.9059013031336	0.204098696866367
7	31.13	30.9620042395768	0.167995760423199
8	31.1	31.0214316775908	0.0785683224092359
9	31.03	31.0272443724551	0.00275562754489656
10	30.74	30.9759056354015	-0.235905635401537
11	30.83	30.699838557507	0.130161442493023
12	30.82	30.7260181894105	0.0939818105895007
13	30.8	30.7419027307575	0.0580972692424986
14	30.74	30.7411416275075	-0.001141627507522
15	30.71	30.6951195585813	0.0148804414186898
16	30.58	30.6640089184496	-0.0840089184496371
17	30.71	30.542299302892	0.167700697107993
18	30.7	30.642744530788	0.0572554692119951
19	30.7	30.6696857058561	0.0303142941439383
20	30.72	30.6816922007727	0.0383077992272618
21	30.68	30.7067968152774	-0.0267968152773861
22	30.78	30.6774788333911	0.102521166608867
23	30.84	30.7652930281399	0.0747069718601274
24	30.8	30.8456424857455	-0.0456424857455282
25	30.8	30.8261020628906	-0.0261020628905975
26	30.88	30.816639761434	0.063360238566009
27	30.87	30.8868236898646	-0.0168236898645517
28	30.92	30.8929443824018	0.0270556175981653
29	30.82	30.9373930263453	-0.117393026345255
30	30.75	30.850477561334	-0.100477561334046
31	30.75	30.7580164008203	-0.00801640082029209
32	30.75	30.7344040921905	0.0155959078095051
33	30.63	30.7316067595876	-0.101606759587618
34	30.52	30.6210586145377	-0.101058614537671
35	30.58	30.4924107949331	0.0875892050668803
36	30.6	30.5232801831269	0.0767198168730836
37	30.6	30.5599403389075	0.0400596610924744
38	30.63	30.5760600323336	0.053939967666377
39	30.56	30.6126190348237	-0.0526190348236746
40	30.61	30.5584976560449	0.0515023439550966
41	30.53	30.5929982140721	-0.06299821407206
42	30.6	30.5288770228702	0.071122977129825
43	30.6	30.5797879402976	0.020212059702363
44	30.63	30.595683952164	0.0343160478359827
45	30.66	30.6285937770035	0.0314062229965479
46	30.34	30.6650450801581	-0.325045080158095
47	30.32	30.3708548605736	-0.0508548605735584
48	30.3	30.2758712002012	0.024128799798838
49	30.3	30.2423344029344	0.0576655970655509
50	30.08	30.2448685094026	-0.164868509402574
51	29.96	30.0479549768931	-0.0879549768931014
52	29.91	29.8934193565441	0.016580643455935
53	29.83	29.8214221518067	0.0085778481932941
54	29.89	29.7449104220003	0.145089577999737
55	29.85	29.7988014189013	0.0511985810986531
56	30.06	29.7906682477466	0.269331752253372
57	29.83	29.9977761192271	-0.167776119227138
58	29.95	29.8417180480782	0.108281951921846
59	30.02	29.9154450246744	0.104554975325637
60	30.03	30.0054947652175	0.0245052347825165
61	30.03	30.0391558460104	-0.00915584601036201
62	29.96	30.0455397416364	-0.0855397416364205
63	29.85	29.9781598125065	-0.128159812506475
64	30.12	29.8548846983461	0.265115301653939
65	29.91	30.0792753127975	-0.169275312797456
66	29.9	29.9422917956024	-0.0422917956023774
67	29.92	29.8941316012151	0.025868398784926
68	29.89	29.9025476932916	-0.0125476932915518
69	29.96	29.8794488913307	0.080551108669308
70	29.72	29.9419117260393	-0.221911726039284
71	29.6	29.7336885136729	-0.133688513672855
72	29.54	29.5680647778712	-0.0280647778711902
73	29.54	29.4776267880713	0.0623732119287332
74	29.54	29.4673962004401	0.0726037995598681
75	29.48	29.4782489684366	0.00175103156341905
76	29.55	29.4355383120037	0.114461687996261
77	29.58	29.4995176019078	0.0804823980922045
78	29.6	29.5524017434484	0.0475982565516233
79	29.6	29.5889983853988	0.0110016146012484
80	29.56	29.5997786843867	-0.0397786843867003
81	29.7	29.5646515629918	0.135348437008165
82	29.76	29.6875097423966	0.072490257603409
83	29.24	29.7758457147831	-0.535845714783061
84	29.28	29.3033551707502	-0.0233551707502002

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	29.2163396852789	28.9751988218451	29.4574805487127
86	29.1470860473015	28.815516239966	29.4786558546371
87	29.0778324093242	28.6491248596352	29.5065399590131
88	29.0085787713468	28.476030079794	29.5411274628995
89	28.9393251333694	28.2964435820204	29.5822066847185
90	28.8700714953921	28.1106241841734	29.6295188066107
91	28.8008178574147	27.9188297554445	29.6828059593849
92	28.7315642194373	27.7213021819689	29.7418262569058
93	28.6623105814599	27.5182635324704	29.8063576304494
94	28.5930569434826	27.3099162167274	29.8761976702377
95	28.5238033055052	27.0964445131184	29.9511620978921
96	28.4545496675278	26.8780164589572	30.0310828760985

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 29.2163396852789 & 28.9751988218451 & 29.4574805487127 \tabularnewline
86 & 29.1470860473015 & 28.815516239966 & 29.4786558546371 \tabularnewline
87 & 29.0778324093242 & 28.6491248596352 & 29.5065399590131 \tabularnewline
88 & 29.0085787713468 & 28.476030079794 & 29.5411274628995 \tabularnewline
89 & 28.9393251333694 & 28.2964435820204 & 29.5822066847185 \tabularnewline
90 & 28.8700714953921 & 28.1106241841734 & 29.6295188066107 \tabularnewline
91 & 28.8008178574147 & 27.9188297554445 & 29.6828059593849 \tabularnewline
92 & 28.7315642194373 & 27.7213021819689 & 29.7418262569058 \tabularnewline
93 & 28.6623105814599 & 27.5182635324704 & 29.8063576304494 \tabularnewline
94 & 28.5930569434826 & 27.3099162167274 & 29.8761976702377 \tabularnewline
95 & 28.5238033055052 & 27.0964445131184 & 29.9511620978921 \tabularnewline
96 & 28.4545496675278 & 26.8780164589572 & 30.0310828760985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232910&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]85[/C][C]29.2163396852789[/C][C]28.9751988218451[/C][C]29.4574805487127[/C][/ROW]
[ROW][C]86[/C][C]29.1470860473015[/C][C]28.815516239966[/C][C]29.4786558546371[/C][/ROW]
[ROW][C]87[/C][C]29.0778324093242[/C][C]28.6491248596352[/C][C]29.5065399590131[/C][/ROW]
[ROW][C]88[/C][C]29.0085787713468[/C][C]28.476030079794[/C][C]29.5411274628995[/C][/ROW]
[ROW][C]89[/C][C]28.9393251333694[/C][C]28.2964435820204[/C][C]29.5822066847185[/C][/ROW]
[ROW][C]90[/C][C]28.8700714953921[/C][C]28.1106241841734[/C][C]29.6295188066107[/C][/ROW]
[ROW][C]91[/C][C]28.8008178574147[/C][C]27.9188297554445[/C][C]29.6828059593849[/C][/ROW]
[ROW][C]92[/C][C]28.7315642194373[/C][C]27.7213021819689[/C][C]29.7418262569058[/C][/ROW]
[ROW][C]93[/C][C]28.6623105814599[/C][C]27.5182635324704[/C][C]29.8063576304494[/C][/ROW]
[ROW][C]94[/C][C]28.5930569434826[/C][C]27.3099162167274[/C][C]29.8761976702377[/C][/ROW]
[ROW][C]95[/C][C]28.5238033055052[/C][C]27.0964445131184[/C][C]29.9511620978921[/C][/ROW]
[ROW][C]96[/C][C]28.4545496675278[/C][C]26.8780164589572[/C][C]30.0310828760985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232910&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232910&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
85	29.2163396852789	28.9751988218451	29.4574805487127
86	29.1470860473015	28.815516239966	29.4786558546371
87	29.0778324093242	28.6491248596352	29.5065399590131
88	29.0085787713468	28.476030079794	29.5411274628995
89	28.9393251333694	28.2964435820204	29.5822066847185
90	28.8700714953921	28.1106241841734	29.6295188066107
91	28.8008178574147	27.9188297554445	29.6828059593849
92	28.7315642194373	27.7213021819689	29.7418262569058
93	28.6623105814599	27.5182635324704	29.8063576304494
94	28.5930569434826	27.3099162167274	29.8761976702377
95	28.5238033055052	27.0964445131184	29.9511620978921
96	28.4545496675278	26.8780164589572	30.0310828760985

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code