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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 15 Jan 2011 22:13:23 +0000

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/2011/Jan/15/t1295129625gigk6vfsjz5afum.htm/, Retrieved Thu, 16 May 2024 15:07:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117365, Retrieved Thu, 16 May 2024 15:07:18 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

156

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

-     [] [Maximumprijs 2005] [1970-01-01 00:00:00] [44f4e89d2978fa9cb7cef84cf6986739]
- RMPD    [Exponential Smoothing] [opgave10_deel2] [2011-01-15 22:13:23] [ba6a6eaac02e80e5d4f1379a58894c63] [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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117365&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117365&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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.335559903587047
beta	0
gamma	0.746828588388269

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.335559903587047 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.746828588388269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117365&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]0.335559903587047[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.746828588388269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117365&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	0.335559903587047
beta	0
gamma	0.746828588388269

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	22.3	22.4976495726496	-0.197649572649578
14	28.9	29.0394556717366	-0.139455671736624
15	31.7	31.8091226439367	-0.109122643936725
16	34.2	34.2098014973542	-0.00980149735418223
17	38.6	38.468808545143	0.131191454856967
18	37.2	37.0751271743823	0.124872825617686
19	38.8	39.1709921916699	-0.370992191669927
20	43.4	43.0379647915643	0.362035208435678
21	38.8	39.4717453284981	-0.671745328498147
22	36.3	34.0419639014616	2.25803609853838
23	33	32.5286329809459	0.471367019054071
24	29.2	30.2324342230432	-1.0324342230432
25	22.64	22.521041829254	0.118958170745962
26	28.44	29.1979659360931	-0.757965936093058
27	30.14	31.7751376054034	-1.63513760540337
28	34.39	33.7130324488221	0.676967551177874
29	36.82	38.2724555782065	-1.45245557820648
30	36.74	36.3442303134473	0.395769686552718
31	38.9	38.2849378985805	0.615062101419461
32	42.8	42.8465357344012	-0.0465357344012034
33	39.09	38.6302307112505	0.459769288749513
34	37.49	35.0339647368529	2.4560352631471
35	33.17	32.7004883577279	0.469511642272117
36	30.98	29.6574464576398	1.32255354236019
37	21.2	23.3076407571489	-2.10764075714892
38	27.8	28.8022577547557	-1.00225775475574
39	29	30.8621822511304	-1.86218225113037
40	35.4	33.8712094468568	1.5287905531432
41	37.5	37.6598017867894	-0.159801786789444
42	34.7	37.0824709291083	-2.38247092910833
43	38.4	38.1997302702307	0.200269729769268
44	39.9	42.2938404480323	-2.39384044803229
45	35.9	37.5411142077381	-1.64111420773806
46	34.7	34.2304687794958	0.469531220504237
47	30.4	30.244642864183	0.155357135817006
48	29	27.5194821989385	1.48051780106151
49	21.5	19.5205421467045	1.97945785329555
50	28	26.9351418740217	1.0648581259783
51	29.3	29.2619933836891	0.0380066163109127
52	34.3	34.5913259932237	-0.29132599322373
53	36.6	36.931242081273	-0.331242081273025
54	36.2	35.1934434978855	1.00655650211451
55	37.5	38.7295395115909	-1.22953951159086
56	41.6	41.0566062685168	0.543393731483228
57	39.4	37.6630180135217	1.73698198647829
58	37.3	36.5332767278316	0.766723272168427
59	32.7	32.4912761861092	0.208723813890799
60	30.7	30.4415982525172	0.258401747482829
61	22.9	22.2801505144973	0.61984948550268
62	29.1	28.7846748972225	0.3153251027775
63	29.5	30.3504659857137	-0.850465985713733
64	37.1	35.2182404454182	1.88175955458176
65	37.7	38.2675496350328	-0.567549635032755
66	38.4	37.1143019498682	1.28569805013181
67	39.4	39.6344647169843	-0.23446471698432
68	40.6	43.1752086792281	-2.57520867922806
69	39.7	39.3274282766563	0.372571723343725
70	36.6	37.2583810611665	-0.658381061166487
71	32.8	32.4612805600897	0.338719439910342
72	31.6	30.4798752724813	1.12012472751873
73	24.1	22.7869458445988	1.31305415540115
74	30.3	29.3729699596071	0.927030040392875
75	31.8	30.5655325107426	1.2344674892574
76	38.7	37.488719816077	1.21128018392299
77	37.8	39.0976398034029	-1.29763980340287
78	38.4	38.619026997003	-0.219026997002956
79	40.7	39.8799248575193	0.820075142480661
80	43.8	42.6129994515641	1.18700054843593
81	41.5	41.4904216345736	0.0095783654264352
82	39.3	38.7879860643936	0.512013935606447
83	35.9	34.8784072572191	1.02159274278085
84	33.4	33.513898035352	-0.113898035351966

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22.3 & 22.4976495726496 & -0.197649572649578 \tabularnewline
14 & 28.9 & 29.0394556717366 & -0.139455671736624 \tabularnewline
15 & 31.7 & 31.8091226439367 & -0.109122643936725 \tabularnewline
16 & 34.2 & 34.2098014973542 & -0.00980149735418223 \tabularnewline
17 & 38.6 & 38.468808545143 & 0.131191454856967 \tabularnewline
18 & 37.2 & 37.0751271743823 & 0.124872825617686 \tabularnewline
19 & 38.8 & 39.1709921916699 & -0.370992191669927 \tabularnewline
20 & 43.4 & 43.0379647915643 & 0.362035208435678 \tabularnewline
21 & 38.8 & 39.4717453284981 & -0.671745328498147 \tabularnewline
22 & 36.3 & 34.0419639014616 & 2.25803609853838 \tabularnewline
23 & 33 & 32.5286329809459 & 0.471367019054071 \tabularnewline
24 & 29.2 & 30.2324342230432 & -1.0324342230432 \tabularnewline
25 & 22.64 & 22.521041829254 & 0.118958170745962 \tabularnewline
26 & 28.44 & 29.1979659360931 & -0.757965936093058 \tabularnewline
27 & 30.14 & 31.7751376054034 & -1.63513760540337 \tabularnewline
28 & 34.39 & 33.7130324488221 & 0.676967551177874 \tabularnewline
29 & 36.82 & 38.2724555782065 & -1.45245557820648 \tabularnewline
30 & 36.74 & 36.3442303134473 & 0.395769686552718 \tabularnewline
31 & 38.9 & 38.2849378985805 & 0.615062101419461 \tabularnewline
32 & 42.8 & 42.8465357344012 & -0.0465357344012034 \tabularnewline
33 & 39.09 & 38.6302307112505 & 0.459769288749513 \tabularnewline
34 & 37.49 & 35.0339647368529 & 2.4560352631471 \tabularnewline
35 & 33.17 & 32.7004883577279 & 0.469511642272117 \tabularnewline
36 & 30.98 & 29.6574464576398 & 1.32255354236019 \tabularnewline
37 & 21.2 & 23.3076407571489 & -2.10764075714892 \tabularnewline
38 & 27.8 & 28.8022577547557 & -1.00225775475574 \tabularnewline
39 & 29 & 30.8621822511304 & -1.86218225113037 \tabularnewline
40 & 35.4 & 33.8712094468568 & 1.5287905531432 \tabularnewline
41 & 37.5 & 37.6598017867894 & -0.159801786789444 \tabularnewline
42 & 34.7 & 37.0824709291083 & -2.38247092910833 \tabularnewline
43 & 38.4 & 38.1997302702307 & 0.200269729769268 \tabularnewline
44 & 39.9 & 42.2938404480323 & -2.39384044803229 \tabularnewline
45 & 35.9 & 37.5411142077381 & -1.64111420773806 \tabularnewline
46 & 34.7 & 34.2304687794958 & 0.469531220504237 \tabularnewline
47 & 30.4 & 30.244642864183 & 0.155357135817006 \tabularnewline
48 & 29 & 27.5194821989385 & 1.48051780106151 \tabularnewline
49 & 21.5 & 19.5205421467045 & 1.97945785329555 \tabularnewline
50 & 28 & 26.9351418740217 & 1.0648581259783 \tabularnewline
51 & 29.3 & 29.2619933836891 & 0.0380066163109127 \tabularnewline
52 & 34.3 & 34.5913259932237 & -0.29132599322373 \tabularnewline
53 & 36.6 & 36.931242081273 & -0.331242081273025 \tabularnewline
54 & 36.2 & 35.1934434978855 & 1.00655650211451 \tabularnewline
55 & 37.5 & 38.7295395115909 & -1.22953951159086 \tabularnewline
56 & 41.6 & 41.0566062685168 & 0.543393731483228 \tabularnewline
57 & 39.4 & 37.6630180135217 & 1.73698198647829 \tabularnewline
58 & 37.3 & 36.5332767278316 & 0.766723272168427 \tabularnewline
59 & 32.7 & 32.4912761861092 & 0.208723813890799 \tabularnewline
60 & 30.7 & 30.4415982525172 & 0.258401747482829 \tabularnewline
61 & 22.9 & 22.2801505144973 & 0.61984948550268 \tabularnewline
62 & 29.1 & 28.7846748972225 & 0.3153251027775 \tabularnewline
63 & 29.5 & 30.3504659857137 & -0.850465985713733 \tabularnewline
64 & 37.1 & 35.2182404454182 & 1.88175955458176 \tabularnewline
65 & 37.7 & 38.2675496350328 & -0.567549635032755 \tabularnewline
66 & 38.4 & 37.1143019498682 & 1.28569805013181 \tabularnewline
67 & 39.4 & 39.6344647169843 & -0.23446471698432 \tabularnewline
68 & 40.6 & 43.1752086792281 & -2.57520867922806 \tabularnewline
69 & 39.7 & 39.3274282766563 & 0.372571723343725 \tabularnewline
70 & 36.6 & 37.2583810611665 & -0.658381061166487 \tabularnewline
71 & 32.8 & 32.4612805600897 & 0.338719439910342 \tabularnewline
72 & 31.6 & 30.4798752724813 & 1.12012472751873 \tabularnewline
73 & 24.1 & 22.7869458445988 & 1.31305415540115 \tabularnewline
74 & 30.3 & 29.3729699596071 & 0.927030040392875 \tabularnewline
75 & 31.8 & 30.5655325107426 & 1.2344674892574 \tabularnewline
76 & 38.7 & 37.488719816077 & 1.21128018392299 \tabularnewline
77 & 37.8 & 39.0976398034029 & -1.29763980340287 \tabularnewline
78 & 38.4 & 38.619026997003 & -0.219026997002956 \tabularnewline
79 & 40.7 & 39.8799248575193 & 0.820075142480661 \tabularnewline
80 & 43.8 & 42.6129994515641 & 1.18700054843593 \tabularnewline
81 & 41.5 & 41.4904216345736 & 0.0095783654264352 \tabularnewline
82 & 39.3 & 38.7879860643936 & 0.512013935606447 \tabularnewline
83 & 35.9 & 34.8784072572191 & 1.02159274278085 \tabularnewline
84 & 33.4 & 33.513898035352 & -0.113898035351966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117365&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]13[/C][C]22.3[/C][C]22.4976495726496[/C][C]-0.197649572649578[/C][/ROW]
[ROW][C]14[/C][C]28.9[/C][C]29.0394556717366[/C][C]-0.139455671736624[/C][/ROW]
[ROW][C]15[/C][C]31.7[/C][C]31.8091226439367[/C][C]-0.109122643936725[/C][/ROW]
[ROW][C]16[/C][C]34.2[/C][C]34.2098014973542[/C][C]-0.00980149735418223[/C][/ROW]
[ROW][C]17[/C][C]38.6[/C][C]38.468808545143[/C][C]0.131191454856967[/C][/ROW]
[ROW][C]18[/C][C]37.2[/C][C]37.0751271743823[/C][C]0.124872825617686[/C][/ROW]
[ROW][C]19[/C][C]38.8[/C][C]39.1709921916699[/C][C]-0.370992191669927[/C][/ROW]
[ROW][C]20[/C][C]43.4[/C][C]43.0379647915643[/C][C]0.362035208435678[/C][/ROW]
[ROW][C]21[/C][C]38.8[/C][C]39.4717453284981[/C][C]-0.671745328498147[/C][/ROW]
[ROW][C]22[/C][C]36.3[/C][C]34.0419639014616[/C][C]2.25803609853838[/C][/ROW]
[ROW][C]23[/C][C]33[/C][C]32.5286329809459[/C][C]0.471367019054071[/C][/ROW]
[ROW][C]24[/C][C]29.2[/C][C]30.2324342230432[/C][C]-1.0324342230432[/C][/ROW]
[ROW][C]25[/C][C]22.64[/C][C]22.521041829254[/C][C]0.118958170745962[/C][/ROW]
[ROW][C]26[/C][C]28.44[/C][C]29.1979659360931[/C][C]-0.757965936093058[/C][/ROW]
[ROW][C]27[/C][C]30.14[/C][C]31.7751376054034[/C][C]-1.63513760540337[/C][/ROW]
[ROW][C]28[/C][C]34.39[/C][C]33.7130324488221[/C][C]0.676967551177874[/C][/ROW]
[ROW][C]29[/C][C]36.82[/C][C]38.2724555782065[/C][C]-1.45245557820648[/C][/ROW]
[ROW][C]30[/C][C]36.74[/C][C]36.3442303134473[/C][C]0.395769686552718[/C][/ROW]
[ROW][C]31[/C][C]38.9[/C][C]38.2849378985805[/C][C]0.615062101419461[/C][/ROW]
[ROW][C]32[/C][C]42.8[/C][C]42.8465357344012[/C][C]-0.0465357344012034[/C][/ROW]
[ROW][C]33[/C][C]39.09[/C][C]38.6302307112505[/C][C]0.459769288749513[/C][/ROW]
[ROW][C]34[/C][C]37.49[/C][C]35.0339647368529[/C][C]2.4560352631471[/C][/ROW]
[ROW][C]35[/C][C]33.17[/C][C]32.7004883577279[/C][C]0.469511642272117[/C][/ROW]
[ROW][C]36[/C][C]30.98[/C][C]29.6574464576398[/C][C]1.32255354236019[/C][/ROW]
[ROW][C]37[/C][C]21.2[/C][C]23.3076407571489[/C][C]-2.10764075714892[/C][/ROW]
[ROW][C]38[/C][C]27.8[/C][C]28.8022577547557[/C][C]-1.00225775475574[/C][/ROW]
[ROW][C]39[/C][C]29[/C][C]30.8621822511304[/C][C]-1.86218225113037[/C][/ROW]
[ROW][C]40[/C][C]35.4[/C][C]33.8712094468568[/C][C]1.5287905531432[/C][/ROW]
[ROW][C]41[/C][C]37.5[/C][C]37.6598017867894[/C][C]-0.159801786789444[/C][/ROW]
[ROW][C]42[/C][C]34.7[/C][C]37.0824709291083[/C][C]-2.38247092910833[/C][/ROW]
[ROW][C]43[/C][C]38.4[/C][C]38.1997302702307[/C][C]0.200269729769268[/C][/ROW]
[ROW][C]44[/C][C]39.9[/C][C]42.2938404480323[/C][C]-2.39384044803229[/C][/ROW]
[ROW][C]45[/C][C]35.9[/C][C]37.5411142077381[/C][C]-1.64111420773806[/C][/ROW]
[ROW][C]46[/C][C]34.7[/C][C]34.2304687794958[/C][C]0.469531220504237[/C][/ROW]
[ROW][C]47[/C][C]30.4[/C][C]30.244642864183[/C][C]0.155357135817006[/C][/ROW]
[ROW][C]48[/C][C]29[/C][C]27.5194821989385[/C][C]1.48051780106151[/C][/ROW]
[ROW][C]49[/C][C]21.5[/C][C]19.5205421467045[/C][C]1.97945785329555[/C][/ROW]
[ROW][C]50[/C][C]28[/C][C]26.9351418740217[/C][C]1.0648581259783[/C][/ROW]
[ROW][C]51[/C][C]29.3[/C][C]29.2619933836891[/C][C]0.0380066163109127[/C][/ROW]
[ROW][C]52[/C][C]34.3[/C][C]34.5913259932237[/C][C]-0.29132599322373[/C][/ROW]
[ROW][C]53[/C][C]36.6[/C][C]36.931242081273[/C][C]-0.331242081273025[/C][/ROW]
[ROW][C]54[/C][C]36.2[/C][C]35.1934434978855[/C][C]1.00655650211451[/C][/ROW]
[ROW][C]55[/C][C]37.5[/C][C]38.7295395115909[/C][C]-1.22953951159086[/C][/ROW]
[ROW][C]56[/C][C]41.6[/C][C]41.0566062685168[/C][C]0.543393731483228[/C][/ROW]
[ROW][C]57[/C][C]39.4[/C][C]37.6630180135217[/C][C]1.73698198647829[/C][/ROW]
[ROW][C]58[/C][C]37.3[/C][C]36.5332767278316[/C][C]0.766723272168427[/C][/ROW]
[ROW][C]59[/C][C]32.7[/C][C]32.4912761861092[/C][C]0.208723813890799[/C][/ROW]
[ROW][C]60[/C][C]30.7[/C][C]30.4415982525172[/C][C]0.258401747482829[/C][/ROW]
[ROW][C]61[/C][C]22.9[/C][C]22.2801505144973[/C][C]0.61984948550268[/C][/ROW]
[ROW][C]62[/C][C]29.1[/C][C]28.7846748972225[/C][C]0.3153251027775[/C][/ROW]
[ROW][C]63[/C][C]29.5[/C][C]30.3504659857137[/C][C]-0.850465985713733[/C][/ROW]
[ROW][C]64[/C][C]37.1[/C][C]35.2182404454182[/C][C]1.88175955458176[/C][/ROW]
[ROW][C]65[/C][C]37.7[/C][C]38.2675496350328[/C][C]-0.567549635032755[/C][/ROW]
[ROW][C]66[/C][C]38.4[/C][C]37.1143019498682[/C][C]1.28569805013181[/C][/ROW]
[ROW][C]67[/C][C]39.4[/C][C]39.6344647169843[/C][C]-0.23446471698432[/C][/ROW]
[ROW][C]68[/C][C]40.6[/C][C]43.1752086792281[/C][C]-2.57520867922806[/C][/ROW]
[ROW][C]69[/C][C]39.7[/C][C]39.3274282766563[/C][C]0.372571723343725[/C][/ROW]
[ROW][C]70[/C][C]36.6[/C][C]37.2583810611665[/C][C]-0.658381061166487[/C][/ROW]
[ROW][C]71[/C][C]32.8[/C][C]32.4612805600897[/C][C]0.338719439910342[/C][/ROW]
[ROW][C]72[/C][C]31.6[/C][C]30.4798752724813[/C][C]1.12012472751873[/C][/ROW]
[ROW][C]73[/C][C]24.1[/C][C]22.7869458445988[/C][C]1.31305415540115[/C][/ROW]
[ROW][C]74[/C][C]30.3[/C][C]29.3729699596071[/C][C]0.927030040392875[/C][/ROW]
[ROW][C]75[/C][C]31.8[/C][C]30.5655325107426[/C][C]1.2344674892574[/C][/ROW]
[ROW][C]76[/C][C]38.7[/C][C]37.488719816077[/C][C]1.21128018392299[/C][/ROW]
[ROW][C]77[/C][C]37.8[/C][C]39.0976398034029[/C][C]-1.29763980340287[/C][/ROW]
[ROW][C]78[/C][C]38.4[/C][C]38.619026997003[/C][C]-0.219026997002956[/C][/ROW]
[ROW][C]79[/C][C]40.7[/C][C]39.8799248575193[/C][C]0.820075142480661[/C][/ROW]
[ROW][C]80[/C][C]43.8[/C][C]42.6129994515641[/C][C]1.18700054843593[/C][/ROW]
[ROW][C]81[/C][C]41.5[/C][C]41.4904216345736[/C][C]0.0095783654264352[/C][/ROW]
[ROW][C]82[/C][C]39.3[/C][C]38.7879860643936[/C][C]0.512013935606447[/C][/ROW]
[ROW][C]83[/C][C]35.9[/C][C]34.8784072572191[/C][C]1.02159274278085[/C][/ROW]
[ROW][C]84[/C][C]33.4[/C][C]33.513898035352[/C][C]-0.113898035351966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117365&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
13	22.3	22.4976495726496	-0.197649572649578
14	28.9	29.0394556717366	-0.139455671736624
15	31.7	31.8091226439367	-0.109122643936725
16	34.2	34.2098014973542	-0.00980149735418223
17	38.6	38.468808545143	0.131191454856967
18	37.2	37.0751271743823	0.124872825617686
19	38.8	39.1709921916699	-0.370992191669927
20	43.4	43.0379647915643	0.362035208435678
21	38.8	39.4717453284981	-0.671745328498147
22	36.3	34.0419639014616	2.25803609853838
23	33	32.5286329809459	0.471367019054071
24	29.2	30.2324342230432	-1.0324342230432
25	22.64	22.521041829254	0.118958170745962
26	28.44	29.1979659360931	-0.757965936093058
27	30.14	31.7751376054034	-1.63513760540337
28	34.39	33.7130324488221	0.676967551177874
29	36.82	38.2724555782065	-1.45245557820648
30	36.74	36.3442303134473	0.395769686552718
31	38.9	38.2849378985805	0.615062101419461
32	42.8	42.8465357344012	-0.0465357344012034
33	39.09	38.6302307112505	0.459769288749513
34	37.49	35.0339647368529	2.4560352631471
35	33.17	32.7004883577279	0.469511642272117
36	30.98	29.6574464576398	1.32255354236019
37	21.2	23.3076407571489	-2.10764075714892
38	27.8	28.8022577547557	-1.00225775475574
39	29	30.8621822511304	-1.86218225113037
40	35.4	33.8712094468568	1.5287905531432
41	37.5	37.6598017867894	-0.159801786789444
42	34.7	37.0824709291083	-2.38247092910833
43	38.4	38.1997302702307	0.200269729769268
44	39.9	42.2938404480323	-2.39384044803229
45	35.9	37.5411142077381	-1.64111420773806
46	34.7	34.2304687794958	0.469531220504237
47	30.4	30.244642864183	0.155357135817006
48	29	27.5194821989385	1.48051780106151
49	21.5	19.5205421467045	1.97945785329555
50	28	26.9351418740217	1.0648581259783
51	29.3	29.2619933836891	0.0380066163109127
52	34.3	34.5913259932237	-0.29132599322373
53	36.6	36.931242081273	-0.331242081273025
54	36.2	35.1934434978855	1.00655650211451
55	37.5	38.7295395115909	-1.22953951159086
56	41.6	41.0566062685168	0.543393731483228
57	39.4	37.6630180135217	1.73698198647829
58	37.3	36.5332767278316	0.766723272168427
59	32.7	32.4912761861092	0.208723813890799
60	30.7	30.4415982525172	0.258401747482829
61	22.9	22.2801505144973	0.61984948550268
62	29.1	28.7846748972225	0.3153251027775
63	29.5	30.3504659857137	-0.850465985713733
64	37.1	35.2182404454182	1.88175955458176
65	37.7	38.2675496350328	-0.567549635032755
66	38.4	37.1143019498682	1.28569805013181
67	39.4	39.6344647169843	-0.23446471698432
68	40.6	43.1752086792281	-2.57520867922806
69	39.7	39.3274282766563	0.372571723343725
70	36.6	37.2583810611665	-0.658381061166487
71	32.8	32.4612805600897	0.338719439910342
72	31.6	30.4798752724813	1.12012472751873
73	24.1	22.7869458445988	1.31305415540115
74	30.3	29.3729699596071	0.927030040392875
75	31.8	30.5655325107426	1.2344674892574
76	38.7	37.488719816077	1.21128018392299
77	37.8	39.0976398034029	-1.29763980340287
78	38.4	38.619026997003	-0.219026997002956
79	40.7	39.8799248575193	0.820075142480661
80	43.8	42.6129994515641	1.18700054843593
81	41.5	41.4904216345736	0.0095783654264352
82	39.3	38.7879860643936	0.512013935606447
83	35.9	34.8784072572191	1.02159274278085
84	33.4	33.513898035352	-0.113898035351966

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	25.5026160404781	23.3414066422652	27.6638254386909
86	31.4564778395978	29.176836820858	33.7361188583375
87	32.4905237696798	30.0983071645794	34.8827403747802
88	38.9879672123858	36.4882397478178	41.4876946769537
89	38.9454466881804	36.342645407154	41.5482479692068
90	39.4375020999409	36.7355562048664	42.1394479950154
91	41.2875228731855	38.4899437891724	44.0851019571985
92	43.9274899055682	41.0374404522362	46.8175393589001
93	41.8223384967627	38.8426870147766	44.8019899787488
94	39.3660088264387	36.2993722217039	42.4326454311735
95	35.5374833251178	32.386261787857	38.6887048623786
96	33.266712060375	30.0331174215414	36.5003066992087

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 25.5026160404781 & 23.3414066422652 & 27.6638254386909 \tabularnewline
86 & 31.4564778395978 & 29.176836820858 & 33.7361188583375 \tabularnewline
87 & 32.4905237696798 & 30.0983071645794 & 34.8827403747802 \tabularnewline
88 & 38.9879672123858 & 36.4882397478178 & 41.4876946769537 \tabularnewline
89 & 38.9454466881804 & 36.342645407154 & 41.5482479692068 \tabularnewline
90 & 39.4375020999409 & 36.7355562048664 & 42.1394479950154 \tabularnewline
91 & 41.2875228731855 & 38.4899437891724 & 44.0851019571985 \tabularnewline
92 & 43.9274899055682 & 41.0374404522362 & 46.8175393589001 \tabularnewline
93 & 41.8223384967627 & 38.8426870147766 & 44.8019899787488 \tabularnewline
94 & 39.3660088264387 & 36.2993722217039 & 42.4326454311735 \tabularnewline
95 & 35.5374833251178 & 32.386261787857 & 38.6887048623786 \tabularnewline
96 & 33.266712060375 & 30.0331174215414 & 36.5003066992087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117365&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]25.5026160404781[/C][C]23.3414066422652[/C][C]27.6638254386909[/C][/ROW]
[ROW][C]86[/C][C]31.4564778395978[/C][C]29.176836820858[/C][C]33.7361188583375[/C][/ROW]
[ROW][C]87[/C][C]32.4905237696798[/C][C]30.0983071645794[/C][C]34.8827403747802[/C][/ROW]
[ROW][C]88[/C][C]38.9879672123858[/C][C]36.4882397478178[/C][C]41.4876946769537[/C][/ROW]
[ROW][C]89[/C][C]38.9454466881804[/C][C]36.342645407154[/C][C]41.5482479692068[/C][/ROW]
[ROW][C]90[/C][C]39.4375020999409[/C][C]36.7355562048664[/C][C]42.1394479950154[/C][/ROW]
[ROW][C]91[/C][C]41.2875228731855[/C][C]38.4899437891724[/C][C]44.0851019571985[/C][/ROW]
[ROW][C]92[/C][C]43.9274899055682[/C][C]41.0374404522362[/C][C]46.8175393589001[/C][/ROW]
[ROW][C]93[/C][C]41.8223384967627[/C][C]38.8426870147766[/C][C]44.8019899787488[/C][/ROW]
[ROW][C]94[/C][C]39.3660088264387[/C][C]36.2993722217039[/C][C]42.4326454311735[/C][/ROW]
[ROW][C]95[/C][C]35.5374833251178[/C][C]32.386261787857[/C][C]38.6887048623786[/C][/ROW]
[ROW][C]96[/C][C]33.266712060375[/C][C]30.0331174215414[/C][C]36.5003066992087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117365&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117365&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	25.5026160404781	23.3414066422652	27.6638254386909
86	31.4564778395978	29.176836820858	33.7361188583375
87	32.4905237696798	30.0983071645794	34.8827403747802
88	38.9879672123858	36.4882397478178	41.4876946769537
89	38.9454466881804	36.342645407154	41.5482479692068
90	39.4375020999409	36.7355562048664	42.1394479950154
91	41.2875228731855	38.4899437891724	44.0851019571985
92	43.9274899055682	41.0374404522362	46.8175393589001
93	41.8223384967627	38.8426870147766	44.8019899787488
94	39.3660088264387	36.2993722217039	42.4326454311735
95	35.5374833251178	32.386261787857	38.6887048623786
96	33.266712060375	30.0331174215414	36.5003066992087

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 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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