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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

Tue, 06 May 2008 02:51:54 -0600

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/2008/May/06/t1210064137kwoy0o2gauqmcrn.htm/, Retrieved Mon, 07 Apr 2025 21:13:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11644, Retrieved Mon, 07 Apr 2025 21:13:36 +0000

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Original text written by user:

Dit is duidelijk een veel betere voorspeller dan de vorige. Houdt namelijk rekening met seizoenseffecten

IsPrivate?

No (this computation is public)

User-defined keywords

Triple Exponential Smoothing Model

Estimated Impact

281

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

-       [Exponential Smoothing] [Holt Winters Model] [2008-05-06 08:51:54] [d7c31bd3c757fc6c80d739cd1483597b] [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	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11644&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11644&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0512572023235812
beta	0.000425534174427011
gamma	0.368605978860725

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0512572023235812 \tabularnewline
beta & 0.000425534174427011 \tabularnewline
gamma & 0.368605978860725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11644&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]0.0512572023235812[/C][/ROW]
[ROW][C]beta[/C][C]0.000425534174427011[/C][/ROW]
[ROW][C]gamma[/C][C]0.368605978860725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11644&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	0.0512572023235812
beta	0.000425534174427011
gamma	0.368605978860725

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	50556	50513.9134722223	42.0865277777484
14	43901	43931.2207583048	-30.2207583047712
15	48572	48571.4461160293	0.553883970744209
16	43899	43787.7905745671	111.209425432899
17	37532	37307.3093522476	224.690647752446
18	40357	39878.9830941167	478.016905883254
19	35489	35015.15205761	473.847942389999
20	29027	28634.6593337897	392.340666210319
21	34485	33503.7889993035	981.211000696465
22	42598	40907.1239125659	1690.87608743407
23	30306	28398.0378202951	1907.96217970492
24	26451	24599.1622363261	1851.83776367391
25	47460	53185.4184385885	-5725.41843858849
26	50104	46281.8642188605	3822.13578113946
27	61465	51130.4482996314	10334.5517003686
28	53726	46915.5430119018	6810.45698809817
29	39477	40818.6392113434	-1341.63921134340
30	43895	43399.0913610316	495.908638968445
31	31481	38535.1926514119	-7054.1926514119
32	29896	31740.6385184782	-1844.63851847820
33	33842	36701.3022621234	-2859.30226212342
34	39120	44156.1382214790	-5036.13822147904
35	33702	31378.1915624761	2323.80843752393
36	25094	27581.0424649262	-2487.04246492615
37	51442	53294.9844857177	-1852.98448571766
38	45594	49928.8458265101	-4334.84582651011
39	52518	56636.6482653951	-4118.64826539515
40	48564	50448.0286568089	-1884.02865680889
41	41745	41053.9275843764	691.072415623552
42	49585	44380.5739934001	5204.42600659989
43	32747	37117.1504914156	-4370.15049141558
44	33379	32281.5692064946	1097.43079350543
45	35645	37037.8103717865	-1392.81037178655
46	37034	43806.1958880855	-6772.19588808546
47	35681	33512.7370643893	2168.26293561075
48	20972	28024.8078272207	-7052.80782722075
49	58552	53725.9660216681	4826.03397833186
50	54955	49833.8901653443	5121.10983465568
51	65540	57101.8439860219	8438.15601397814
52	51570	52338.4574206093	-768.457420609338
53	51145	43902.2386717266	7242.7613282734
54	46641	49143.3811748015	-2502.3811748015
55	35704	38136.7130716886	-2432.71307168862
56	33253	35312.6935494417	-2059.69354944170
57	35193	39036.3464977491	-3843.34649774914
58	41668	43797.9388594381	-2129.93885943813
59	34865	36869.170106545	-2004.17010654498
60	21210	27942.7138847439	-6732.71388474385
61	56126	57814.5247119143	-1688.52471191430
62	49231	53691.6491642265	-4460.6491642265
63	59723	61628.1982867343	-1905.19828673426
64	48103	53114.4667700878	-5011.46677008781
65	47472	47261.784274631	210.215725368987
66	50497	48733.7084571041	1763.29154289586
67	40059	37969.3898106767	2089.61018932334
68	34149	35507.0592861316	-1358.05928613158
69	36860	38642.3638867991	-1782.36388679905
70	46356	44108.2942354146	2247.7057645854
71	36577	37447.4877720121	-870.487772012071

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50556 & 50513.9134722223 & 42.0865277777484 \tabularnewline
14 & 43901 & 43931.2207583048 & -30.2207583047712 \tabularnewline
15 & 48572 & 48571.4461160293 & 0.553883970744209 \tabularnewline
16 & 43899 & 43787.7905745671 & 111.209425432899 \tabularnewline
17 & 37532 & 37307.3093522476 & 224.690647752446 \tabularnewline
18 & 40357 & 39878.9830941167 & 478.016905883254 \tabularnewline
19 & 35489 & 35015.15205761 & 473.847942389999 \tabularnewline
20 & 29027 & 28634.6593337897 & 392.340666210319 \tabularnewline
21 & 34485 & 33503.7889993035 & 981.211000696465 \tabularnewline
22 & 42598 & 40907.1239125659 & 1690.87608743407 \tabularnewline
23 & 30306 & 28398.0378202951 & 1907.96217970492 \tabularnewline
24 & 26451 & 24599.1622363261 & 1851.83776367391 \tabularnewline
25 & 47460 & 53185.4184385885 & -5725.41843858849 \tabularnewline
26 & 50104 & 46281.8642188605 & 3822.13578113946 \tabularnewline
27 & 61465 & 51130.4482996314 & 10334.5517003686 \tabularnewline
28 & 53726 & 46915.5430119018 & 6810.45698809817 \tabularnewline
29 & 39477 & 40818.6392113434 & -1341.63921134340 \tabularnewline
30 & 43895 & 43399.0913610316 & 495.908638968445 \tabularnewline
31 & 31481 & 38535.1926514119 & -7054.1926514119 \tabularnewline
32 & 29896 & 31740.6385184782 & -1844.63851847820 \tabularnewline
33 & 33842 & 36701.3022621234 & -2859.30226212342 \tabularnewline
34 & 39120 & 44156.1382214790 & -5036.13822147904 \tabularnewline
35 & 33702 & 31378.1915624761 & 2323.80843752393 \tabularnewline
36 & 25094 & 27581.0424649262 & -2487.04246492615 \tabularnewline
37 & 51442 & 53294.9844857177 & -1852.98448571766 \tabularnewline
38 & 45594 & 49928.8458265101 & -4334.84582651011 \tabularnewline
39 & 52518 & 56636.6482653951 & -4118.64826539515 \tabularnewline
40 & 48564 & 50448.0286568089 & -1884.02865680889 \tabularnewline
41 & 41745 & 41053.9275843764 & 691.072415623552 \tabularnewline
42 & 49585 & 44380.5739934001 & 5204.42600659989 \tabularnewline
43 & 32747 & 37117.1504914156 & -4370.15049141558 \tabularnewline
44 & 33379 & 32281.5692064946 & 1097.43079350543 \tabularnewline
45 & 35645 & 37037.8103717865 & -1392.81037178655 \tabularnewline
46 & 37034 & 43806.1958880855 & -6772.19588808546 \tabularnewline
47 & 35681 & 33512.7370643893 & 2168.26293561075 \tabularnewline
48 & 20972 & 28024.8078272207 & -7052.80782722075 \tabularnewline
49 & 58552 & 53725.9660216681 & 4826.03397833186 \tabularnewline
50 & 54955 & 49833.8901653443 & 5121.10983465568 \tabularnewline
51 & 65540 & 57101.8439860219 & 8438.15601397814 \tabularnewline
52 & 51570 & 52338.4574206093 & -768.457420609338 \tabularnewline
53 & 51145 & 43902.2386717266 & 7242.7613282734 \tabularnewline
54 & 46641 & 49143.3811748015 & -2502.3811748015 \tabularnewline
55 & 35704 & 38136.7130716886 & -2432.71307168862 \tabularnewline
56 & 33253 & 35312.6935494417 & -2059.69354944170 \tabularnewline
57 & 35193 & 39036.3464977491 & -3843.34649774914 \tabularnewline
58 & 41668 & 43797.9388594381 & -2129.93885943813 \tabularnewline
59 & 34865 & 36869.170106545 & -2004.17010654498 \tabularnewline
60 & 21210 & 27942.7138847439 & -6732.71388474385 \tabularnewline
61 & 56126 & 57814.5247119143 & -1688.52471191430 \tabularnewline
62 & 49231 & 53691.6491642265 & -4460.6491642265 \tabularnewline
63 & 59723 & 61628.1982867343 & -1905.19828673426 \tabularnewline
64 & 48103 & 53114.4667700878 & -5011.46677008781 \tabularnewline
65 & 47472 & 47261.784274631 & 210.215725368987 \tabularnewline
66 & 50497 & 48733.7084571041 & 1763.29154289586 \tabularnewline
67 & 40059 & 37969.3898106767 & 2089.61018932334 \tabularnewline
68 & 34149 & 35507.0592861316 & -1358.05928613158 \tabularnewline
69 & 36860 & 38642.3638867991 & -1782.36388679905 \tabularnewline
70 & 46356 & 44108.2942354146 & 2247.7057645854 \tabularnewline
71 & 36577 & 37447.4877720121 & -870.487772012071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11644&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]50556[/C][C]50513.9134722223[/C][C]42.0865277777484[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]43931.2207583048[/C][C]-30.2207583047712[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]48571.4461160293[/C][C]0.553883970744209[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]43787.7905745671[/C][C]111.209425432899[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]37307.3093522476[/C][C]224.690647752446[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]39878.9830941167[/C][C]478.016905883254[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]35015.15205761[/C][C]473.847942389999[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]28634.6593337897[/C][C]392.340666210319[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]33503.7889993035[/C][C]981.211000696465[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]40907.1239125659[/C][C]1690.87608743407[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]28398.0378202951[/C][C]1907.96217970492[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]24599.1622363261[/C][C]1851.83776367391[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]53185.4184385885[/C][C]-5725.41843858849[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]46281.8642188605[/C][C]3822.13578113946[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]51130.4482996314[/C][C]10334.5517003686[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]46915.5430119018[/C][C]6810.45698809817[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]40818.6392113434[/C][C]-1341.63921134340[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]43399.0913610316[/C][C]495.908638968445[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]38535.1926514119[/C][C]-7054.1926514119[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]31740.6385184782[/C][C]-1844.63851847820[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]36701.3022621234[/C][C]-2859.30226212342[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]44156.1382214790[/C][C]-5036.13822147904[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]31378.1915624761[/C][C]2323.80843752393[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]27581.0424649262[/C][C]-2487.04246492615[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]53294.9844857177[/C][C]-1852.98448571766[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]49928.8458265101[/C][C]-4334.84582651011[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]56636.6482653951[/C][C]-4118.64826539515[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]50448.0286568089[/C][C]-1884.02865680889[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]41053.9275843764[/C][C]691.072415623552[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44380.5739934001[/C][C]5204.42600659989[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]37117.1504914156[/C][C]-4370.15049141558[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]32281.5692064946[/C][C]1097.43079350543[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]37037.8103717865[/C][C]-1392.81037178655[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]43806.1958880855[/C][C]-6772.19588808546[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]33512.7370643893[/C][C]2168.26293561075[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]28024.8078272207[/C][C]-7052.80782722075[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]53725.9660216681[/C][C]4826.03397833186[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]49833.8901653443[/C][C]5121.10983465568[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]57101.8439860219[/C][C]8438.15601397814[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]52338.4574206093[/C][C]-768.457420609338[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]43902.2386717266[/C][C]7242.7613282734[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]49143.3811748015[/C][C]-2502.3811748015[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]38136.7130716886[/C][C]-2432.71307168862[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]35312.6935494417[/C][C]-2059.69354944170[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]39036.3464977491[/C][C]-3843.34649774914[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]43797.9388594381[/C][C]-2129.93885943813[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]36869.170106545[/C][C]-2004.17010654498[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]27942.7138847439[/C][C]-6732.71388474385[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]57814.5247119143[/C][C]-1688.52471191430[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]53691.6491642265[/C][C]-4460.6491642265[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]61628.1982867343[/C][C]-1905.19828673426[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]53114.4667700878[/C][C]-5011.46677008781[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]47261.784274631[/C][C]210.215725368987[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48733.7084571041[/C][C]1763.29154289586[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]37969.3898106767[/C][C]2089.61018932334[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]35507.0592861316[/C][C]-1358.05928613158[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38642.3638867991[/C][C]-1782.36388679905[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]44108.2942354146[/C][C]2247.7057645854[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]37447.4877720121[/C][C]-870.487772012071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11644&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	50556	50513.9134722223	42.0865277777484
14	43901	43931.2207583048	-30.2207583047712
15	48572	48571.4461160293	0.553883970744209
16	43899	43787.7905745671	111.209425432899
17	37532	37307.3093522476	224.690647752446
18	40357	39878.9830941167	478.016905883254
19	35489	35015.15205761	473.847942389999
20	29027	28634.6593337897	392.340666210319
21	34485	33503.7889993035	981.211000696465
22	42598	40907.1239125659	1690.87608743407
23	30306	28398.0378202951	1907.96217970492
24	26451	24599.1622363261	1851.83776367391
25	47460	53185.4184385885	-5725.41843858849
26	50104	46281.8642188605	3822.13578113946
27	61465	51130.4482996314	10334.5517003686
28	53726	46915.5430119018	6810.45698809817
29	39477	40818.6392113434	-1341.63921134340
30	43895	43399.0913610316	495.908638968445
31	31481	38535.1926514119	-7054.1926514119
32	29896	31740.6385184782	-1844.63851847820
33	33842	36701.3022621234	-2859.30226212342
34	39120	44156.1382214790	-5036.13822147904
35	33702	31378.1915624761	2323.80843752393
36	25094	27581.0424649262	-2487.04246492615
37	51442	53294.9844857177	-1852.98448571766
38	45594	49928.8458265101	-4334.84582651011
39	52518	56636.6482653951	-4118.64826539515
40	48564	50448.0286568089	-1884.02865680889
41	41745	41053.9275843764	691.072415623552
42	49585	44380.5739934001	5204.42600659989
43	32747	37117.1504914156	-4370.15049141558
44	33379	32281.5692064946	1097.43079350543
45	35645	37037.8103717865	-1392.81037178655
46	37034	43806.1958880855	-6772.19588808546
47	35681	33512.7370643893	2168.26293561075
48	20972	28024.8078272207	-7052.80782722075
49	58552	53725.9660216681	4826.03397833186
50	54955	49833.8901653443	5121.10983465568
51	65540	57101.8439860219	8438.15601397814
52	51570	52338.4574206093	-768.457420609338
53	51145	43902.2386717266	7242.7613282734
54	46641	49143.3811748015	-2502.3811748015
55	35704	38136.7130716886	-2432.71307168862
56	33253	35312.6935494417	-2059.69354944170
57	35193	39036.3464977491	-3843.34649774914
58	41668	43797.9388594381	-2129.93885943813
59	34865	36869.170106545	-2004.17010654498
60	21210	27942.7138847439	-6732.71388474385
61	56126	57814.5247119143	-1688.52471191430
62	49231	53691.6491642265	-4460.6491642265
63	59723	61628.1982867343	-1905.19828673426
64	48103	53114.4667700878	-5011.46677008781
65	47472	47261.784274631	210.215725368987
66	50497	48733.7084571041	1763.29154289586
67	40059	37969.3898106767	2089.61018932334
68	34149	35507.0592861316	-1358.05928613158
69	36860	38642.3638867991	-1782.36388679905
70	46356	44108.2942354146	2247.7057645854
71	36577	37447.4877720121	-870.487772012071

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
72	26925.1294928216	19538.9820340103	34311.2769516328
73	58905.8204086582	51509.9682503327	66301.6725669837
74	53899.849991913	46494.2976103394	61305.4023734865
75	62958.6113331107	55543.3631834882	70373.8594827331
76	53456.1756117601	46031.2361283391	60881.1150951812
77	49686.5034737539	42251.8770699529	57121.129877555
78	51690.8278320165	44246.5189005386	59135.1367634944
79	40950.252547475	33496.2654604233	48404.2396345266
80	37175.0836819099	29711.4227909023	44638.7445729175
81	40231.6052411939	32758.2748774764	47704.9356049115
82	47198.2894120937	39715.2938866533	54681.2849375341
83	39331.7823201656	31839.1259238426	46824.4387164886

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 26925.1294928216 & 19538.9820340103 & 34311.2769516328 \tabularnewline
73 & 58905.8204086582 & 51509.9682503327 & 66301.6725669837 \tabularnewline
74 & 53899.849991913 & 46494.2976103394 & 61305.4023734865 \tabularnewline
75 & 62958.6113331107 & 55543.3631834882 & 70373.8594827331 \tabularnewline
76 & 53456.1756117601 & 46031.2361283391 & 60881.1150951812 \tabularnewline
77 & 49686.5034737539 & 42251.8770699529 & 57121.129877555 \tabularnewline
78 & 51690.8278320165 & 44246.5189005386 & 59135.1367634944 \tabularnewline
79 & 40950.252547475 & 33496.2654604233 & 48404.2396345266 \tabularnewline
80 & 37175.0836819099 & 29711.4227909023 & 44638.7445729175 \tabularnewline
81 & 40231.6052411939 & 32758.2748774764 & 47704.9356049115 \tabularnewline
82 & 47198.2894120937 & 39715.2938866533 & 54681.2849375341 \tabularnewline
83 & 39331.7823201656 & 31839.1259238426 & 46824.4387164886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11644&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]72[/C][C]26925.1294928216[/C][C]19538.9820340103[/C][C]34311.2769516328[/C][/ROW]
[ROW][C]73[/C][C]58905.8204086582[/C][C]51509.9682503327[/C][C]66301.6725669837[/C][/ROW]
[ROW][C]74[/C][C]53899.849991913[/C][C]46494.2976103394[/C][C]61305.4023734865[/C][/ROW]
[ROW][C]75[/C][C]62958.6113331107[/C][C]55543.3631834882[/C][C]70373.8594827331[/C][/ROW]
[ROW][C]76[/C][C]53456.1756117601[/C][C]46031.2361283391[/C][C]60881.1150951812[/C][/ROW]
[ROW][C]77[/C][C]49686.5034737539[/C][C]42251.8770699529[/C][C]57121.129877555[/C][/ROW]
[ROW][C]78[/C][C]51690.8278320165[/C][C]44246.5189005386[/C][C]59135.1367634944[/C][/ROW]
[ROW][C]79[/C][C]40950.252547475[/C][C]33496.2654604233[/C][C]48404.2396345266[/C][/ROW]
[ROW][C]80[/C][C]37175.0836819099[/C][C]29711.4227909023[/C][C]44638.7445729175[/C][/ROW]
[ROW][C]81[/C][C]40231.6052411939[/C][C]32758.2748774764[/C][C]47704.9356049115[/C][/ROW]
[ROW][C]82[/C][C]47198.2894120937[/C][C]39715.2938866533[/C][C]54681.2849375341[/C][/ROW]
[ROW][C]83[/C][C]39331.7823201656[/C][C]31839.1259238426[/C][C]46824.4387164886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11644&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
72	26925.1294928216	19538.9820340103	34311.2769516328
73	58905.8204086582	51509.9682503327	66301.6725669837
74	53899.849991913	46494.2976103394	61305.4023734865
75	62958.6113331107	55543.3631834882	70373.8594827331
76	53456.1756117601	46031.2361283391	60881.1150951812
77	49686.5034737539	42251.8770699529	57121.129877555
78	51690.8278320165	44246.5189005386	59135.1367634944
79	40950.252547475	33496.2654604233	48404.2396345266
80	37175.0836819099	29711.4227909023	44638.7445729175
81	40231.6052411939	32758.2748774764	47704.9356049115
82	47198.2894120937	39715.2938866533	54681.2849375341
83	39331.7823201656	31839.1259238426	46824.4387164886

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 = Triple ; par3 = additive ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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