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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 20 Dec 2010 10:32:55 +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/2010/Dec/20/t12928412632r5c0bolbv9bk3z.htm/, Retrieved Fri, 03 May 2024 23:45:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112838, Retrieved Fri, 03 May 2024 23:45:58 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102 - Evi Van Dingenen

Estimated Impact

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

-       [Exponential Smoothing] [opdracht 10] [2010-12-20 10:32:55] [89ec97ab3733ab465a33f3d446b0a375] [Current]

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Dataseries X:

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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=112838&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=112838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112838&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	0.0545658791491502
beta	0.25774916210425
gamma	0.484979752162203

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0545658791491502 \tabularnewline
beta & 0.25774916210425 \tabularnewline
gamma & 0.484979752162203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112838&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]0.0545658791491502[/C][/ROW]
[ROW][C]beta[/C][C]0.25774916210425[/C][/ROW]
[ROW][C]gamma[/C][C]0.484979752162203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112838&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	0.0545658791491502
beta	0.25774916210425
gamma	0.484979752162203

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	87.6	87.4374732905983	0.162526709401661
14	85.4	85.4574707694395	-0.0574707694395045
15	86.1	86.3438222724077	-0.243822272407698
16	86.7	86.9249094831851	-0.224909483185087
17	89.1	89.1038654903233	-0.00386549032332084
18	103.7	103.728161925143	-0.0281619251432375
19	86.9	89.263236525602	-2.36323652560203
20	85.2	87.7751584373825	-2.57515843738254
21	80.8	82.160132151459	-1.36013215145903
22	91.2	89.1006088566335	2.09939114336653
23	102.8	99.0552173122356	3.74478268776444
24	182.5	185.839775787221	-3.33977578722073
25	80.9	86.181975289146	-5.28197528914602
26	83.1	83.668516015986	-0.568516015986035
27	88.3	84.2988489052085	4.00115109479145
28	86.6	85.0372535044138	1.56274649558621
29	93	87.357263836485	5.64273616351507
30	105.3	102.300104302552	2.99989569744844
31	93.8	86.993897618399	6.80610238160105
32	86.4	86.1021034188466	0.297896581153410
33	87	81.434485449809	5.56551455019095
34	96.7	90.6700468404298	6.0299531595702
35	100.5	101.979782024187	-1.47978202418733
36	196.7	185.543604488798	11.1563955112018
37	86.8	86.3028818725309	0.497118127469122
38	88.2	86.8638531606971	1.3361468393029
39	93.8	90.3180616041513	3.48193839584873
40	85	90.5274626381015	-5.52746263810151
41	90.4	94.8489890207248	-4.44898902072482
42	115.9	108.405104118965	7.49489588103494
43	94.9	95.5283225539246	-0.628322553924605
44	87.7	91.5811265114215	-3.8811265114215
45	91.7	89.376373876203	2.323626123797
46	95.9	98.8780047194497	-2.97800471944967
47	106.8	106.356198492784	0.443801507216449
48	204.5	195.949254076707	8.55074592329348
49	90.2	91.7726280734287	-1.57262807342873
50	90.5	92.6699904442213	-2.16999044422133
51	93.2	96.9320728302648	-3.73207283026477
52	97.8	92.5307255072453	5.26927449275469
53	99.4	98.0015805305656	1.3984194694344
54	120	117.501168892219	2.49883110778102
55	108.2	100.704814643964	7.49518535603633
56	98.5	95.9013434063614	2.59865659363864
57	104.3	97.178202817712	7.12179718228789
58	102.9	104.86130443706	-1.96130443705988
59	111.1	114.328767906606	-3.22876790660592
60	188.1	207.751779632248	-19.6517796322481
61	93.8	97.3110620246897	-3.51106202468972
62	94.5	97.7180259149318	-3.21802591493179
63	112.4	101.081215347127	11.3187846528730
64	102.5	101.714611058633	0.785388941367344
65	115.8	105.189099981901	10.6109000180992
66	136.5	125.848651000864	10.6513489991358
67	122.1	112.055434753528	10.0445652464716
68	110.6	105.449167474752	5.15083252524811
69	116.4	109.278350938839	7.12164906116134
70	112.6	113.135819450739	-0.535819450739439
71	121.5	122.459087510953	-0.959087510953069
72	199.3	208.866822068269	-9.56682206826866
73	102.1	106.910116854964	-4.81011685496409
74	100.6	107.895222227845	-7.2952222278455
75	119	118.158622725819	0.841377274181042
76	106.8	113.700537986824	-6.90053798682369
77	121.3	121.462661551200	-0.162661551199690
78	145.5	141.603233506010	3.89676649398976
79	129.7	127.118571954011	2.58142804598928
80	117.7	117.711596156171	-0.0115961561713505
81	121.3	121.940513740341	-0.640513740340609
82	124.3	121.531963481098	2.76803651890198
83	135.2	130.55650585504	4.64349414495996
84	210.1	213.11703099708	-3.01703099708001
85	106.8	113.584734859316	-6.78473485931625
86	110.5	113.180846833161	-2.68084683316064
87	111.5	127.349912094680	-15.8499120946802
88	122.1	118.119618813076	3.98038118692401
89	126.3	129.406290293180	-3.10629029318035
90	143.2	151.047548918185	-7.84754891818466
91	137.3	134.95376252927	2.34623747073013
92	121.5	123.976519736902	-2.47651973690213
93	121.9	127.379410643105	-5.47941064310531
94	123.9	127.798485263545	-3.89848526354541
95	131.6	136.754218408707	-5.15421840870664
96	220.9	214.564875538885	6.33512446111544

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 87.6 & 87.4374732905983 & 0.162526709401661 \tabularnewline
14 & 85.4 & 85.4574707694395 & -0.0574707694395045 \tabularnewline
15 & 86.1 & 86.3438222724077 & -0.243822272407698 \tabularnewline
16 & 86.7 & 86.9249094831851 & -0.224909483185087 \tabularnewline
17 & 89.1 & 89.1038654903233 & -0.00386549032332084 \tabularnewline
18 & 103.7 & 103.728161925143 & -0.0281619251432375 \tabularnewline
19 & 86.9 & 89.263236525602 & -2.36323652560203 \tabularnewline
20 & 85.2 & 87.7751584373825 & -2.57515843738254 \tabularnewline
21 & 80.8 & 82.160132151459 & -1.36013215145903 \tabularnewline
22 & 91.2 & 89.1006088566335 & 2.09939114336653 \tabularnewline
23 & 102.8 & 99.0552173122356 & 3.74478268776444 \tabularnewline
24 & 182.5 & 185.839775787221 & -3.33977578722073 \tabularnewline
25 & 80.9 & 86.181975289146 & -5.28197528914602 \tabularnewline
26 & 83.1 & 83.668516015986 & -0.568516015986035 \tabularnewline
27 & 88.3 & 84.2988489052085 & 4.00115109479145 \tabularnewline
28 & 86.6 & 85.0372535044138 & 1.56274649558621 \tabularnewline
29 & 93 & 87.357263836485 & 5.64273616351507 \tabularnewline
30 & 105.3 & 102.300104302552 & 2.99989569744844 \tabularnewline
31 & 93.8 & 86.993897618399 & 6.80610238160105 \tabularnewline
32 & 86.4 & 86.1021034188466 & 0.297896581153410 \tabularnewline
33 & 87 & 81.434485449809 & 5.56551455019095 \tabularnewline
34 & 96.7 & 90.6700468404298 & 6.0299531595702 \tabularnewline
35 & 100.5 & 101.979782024187 & -1.47978202418733 \tabularnewline
36 & 196.7 & 185.543604488798 & 11.1563955112018 \tabularnewline
37 & 86.8 & 86.3028818725309 & 0.497118127469122 \tabularnewline
38 & 88.2 & 86.8638531606971 & 1.3361468393029 \tabularnewline
39 & 93.8 & 90.3180616041513 & 3.48193839584873 \tabularnewline
40 & 85 & 90.5274626381015 & -5.52746263810151 \tabularnewline
41 & 90.4 & 94.8489890207248 & -4.44898902072482 \tabularnewline
42 & 115.9 & 108.405104118965 & 7.49489588103494 \tabularnewline
43 & 94.9 & 95.5283225539246 & -0.628322553924605 \tabularnewline
44 & 87.7 & 91.5811265114215 & -3.8811265114215 \tabularnewline
45 & 91.7 & 89.376373876203 & 2.323626123797 \tabularnewline
46 & 95.9 & 98.8780047194497 & -2.97800471944967 \tabularnewline
47 & 106.8 & 106.356198492784 & 0.443801507216449 \tabularnewline
48 & 204.5 & 195.949254076707 & 8.55074592329348 \tabularnewline
49 & 90.2 & 91.7726280734287 & -1.57262807342873 \tabularnewline
50 & 90.5 & 92.6699904442213 & -2.16999044422133 \tabularnewline
51 & 93.2 & 96.9320728302648 & -3.73207283026477 \tabularnewline
52 & 97.8 & 92.5307255072453 & 5.26927449275469 \tabularnewline
53 & 99.4 & 98.0015805305656 & 1.3984194694344 \tabularnewline
54 & 120 & 117.501168892219 & 2.49883110778102 \tabularnewline
55 & 108.2 & 100.704814643964 & 7.49518535603633 \tabularnewline
56 & 98.5 & 95.9013434063614 & 2.59865659363864 \tabularnewline
57 & 104.3 & 97.178202817712 & 7.12179718228789 \tabularnewline
58 & 102.9 & 104.86130443706 & -1.96130443705988 \tabularnewline
59 & 111.1 & 114.328767906606 & -3.22876790660592 \tabularnewline
60 & 188.1 & 207.751779632248 & -19.6517796322481 \tabularnewline
61 & 93.8 & 97.3110620246897 & -3.51106202468972 \tabularnewline
62 & 94.5 & 97.7180259149318 & -3.21802591493179 \tabularnewline
63 & 112.4 & 101.081215347127 & 11.3187846528730 \tabularnewline
64 & 102.5 & 101.714611058633 & 0.785388941367344 \tabularnewline
65 & 115.8 & 105.189099981901 & 10.6109000180992 \tabularnewline
66 & 136.5 & 125.848651000864 & 10.6513489991358 \tabularnewline
67 & 122.1 & 112.055434753528 & 10.0445652464716 \tabularnewline
68 & 110.6 & 105.449167474752 & 5.15083252524811 \tabularnewline
69 & 116.4 & 109.278350938839 & 7.12164906116134 \tabularnewline
70 & 112.6 & 113.135819450739 & -0.535819450739439 \tabularnewline
71 & 121.5 & 122.459087510953 & -0.959087510953069 \tabularnewline
72 & 199.3 & 208.866822068269 & -9.56682206826866 \tabularnewline
73 & 102.1 & 106.910116854964 & -4.81011685496409 \tabularnewline
74 & 100.6 & 107.895222227845 & -7.2952222278455 \tabularnewline
75 & 119 & 118.158622725819 & 0.841377274181042 \tabularnewline
76 & 106.8 & 113.700537986824 & -6.90053798682369 \tabularnewline
77 & 121.3 & 121.462661551200 & -0.162661551199690 \tabularnewline
78 & 145.5 & 141.603233506010 & 3.89676649398976 \tabularnewline
79 & 129.7 & 127.118571954011 & 2.58142804598928 \tabularnewline
80 & 117.7 & 117.711596156171 & -0.0115961561713505 \tabularnewline
81 & 121.3 & 121.940513740341 & -0.640513740340609 \tabularnewline
82 & 124.3 & 121.531963481098 & 2.76803651890198 \tabularnewline
83 & 135.2 & 130.55650585504 & 4.64349414495996 \tabularnewline
84 & 210.1 & 213.11703099708 & -3.01703099708001 \tabularnewline
85 & 106.8 & 113.584734859316 & -6.78473485931625 \tabularnewline
86 & 110.5 & 113.180846833161 & -2.68084683316064 \tabularnewline
87 & 111.5 & 127.349912094680 & -15.8499120946802 \tabularnewline
88 & 122.1 & 118.119618813076 & 3.98038118692401 \tabularnewline
89 & 126.3 & 129.406290293180 & -3.10629029318035 \tabularnewline
90 & 143.2 & 151.047548918185 & -7.84754891818466 \tabularnewline
91 & 137.3 & 134.95376252927 & 2.34623747073013 \tabularnewline
92 & 121.5 & 123.976519736902 & -2.47651973690213 \tabularnewline
93 & 121.9 & 127.379410643105 & -5.47941064310531 \tabularnewline
94 & 123.9 & 127.798485263545 & -3.89848526354541 \tabularnewline
95 & 131.6 & 136.754218408707 & -5.15421840870664 \tabularnewline
96 & 220.9 & 214.564875538885 & 6.33512446111544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112838&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]87.6[/C][C]87.4374732905983[/C][C]0.162526709401661[/C][/ROW]
[ROW][C]14[/C][C]85.4[/C][C]85.4574707694395[/C][C]-0.0574707694395045[/C][/ROW]
[ROW][C]15[/C][C]86.1[/C][C]86.3438222724077[/C][C]-0.243822272407698[/C][/ROW]
[ROW][C]16[/C][C]86.7[/C][C]86.9249094831851[/C][C]-0.224909483185087[/C][/ROW]
[ROW][C]17[/C][C]89.1[/C][C]89.1038654903233[/C][C]-0.00386549032332084[/C][/ROW]
[ROW][C]18[/C][C]103.7[/C][C]103.728161925143[/C][C]-0.0281619251432375[/C][/ROW]
[ROW][C]19[/C][C]86.9[/C][C]89.263236525602[/C][C]-2.36323652560203[/C][/ROW]
[ROW][C]20[/C][C]85.2[/C][C]87.7751584373825[/C][C]-2.57515843738254[/C][/ROW]
[ROW][C]21[/C][C]80.8[/C][C]82.160132151459[/C][C]-1.36013215145903[/C][/ROW]
[ROW][C]22[/C][C]91.2[/C][C]89.1006088566335[/C][C]2.09939114336653[/C][/ROW]
[ROW][C]23[/C][C]102.8[/C][C]99.0552173122356[/C][C]3.74478268776444[/C][/ROW]
[ROW][C]24[/C][C]182.5[/C][C]185.839775787221[/C][C]-3.33977578722073[/C][/ROW]
[ROW][C]25[/C][C]80.9[/C][C]86.181975289146[/C][C]-5.28197528914602[/C][/ROW]
[ROW][C]26[/C][C]83.1[/C][C]83.668516015986[/C][C]-0.568516015986035[/C][/ROW]
[ROW][C]27[/C][C]88.3[/C][C]84.2988489052085[/C][C]4.00115109479145[/C][/ROW]
[ROW][C]28[/C][C]86.6[/C][C]85.0372535044138[/C][C]1.56274649558621[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]87.357263836485[/C][C]5.64273616351507[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]102.300104302552[/C][C]2.99989569744844[/C][/ROW]
[ROW][C]31[/C][C]93.8[/C][C]86.993897618399[/C][C]6.80610238160105[/C][/ROW]
[ROW][C]32[/C][C]86.4[/C][C]86.1021034188466[/C][C]0.297896581153410[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]81.434485449809[/C][C]5.56551455019095[/C][/ROW]
[ROW][C]34[/C][C]96.7[/C][C]90.6700468404298[/C][C]6.0299531595702[/C][/ROW]
[ROW][C]35[/C][C]100.5[/C][C]101.979782024187[/C][C]-1.47978202418733[/C][/ROW]
[ROW][C]36[/C][C]196.7[/C][C]185.543604488798[/C][C]11.1563955112018[/C][/ROW]
[ROW][C]37[/C][C]86.8[/C][C]86.3028818725309[/C][C]0.497118127469122[/C][/ROW]
[ROW][C]38[/C][C]88.2[/C][C]86.8638531606971[/C][C]1.3361468393029[/C][/ROW]
[ROW][C]39[/C][C]93.8[/C][C]90.3180616041513[/C][C]3.48193839584873[/C][/ROW]
[ROW][C]40[/C][C]85[/C][C]90.5274626381015[/C][C]-5.52746263810151[/C][/ROW]
[ROW][C]41[/C][C]90.4[/C][C]94.8489890207248[/C][C]-4.44898902072482[/C][/ROW]
[ROW][C]42[/C][C]115.9[/C][C]108.405104118965[/C][C]7.49489588103494[/C][/ROW]
[ROW][C]43[/C][C]94.9[/C][C]95.5283225539246[/C][C]-0.628322553924605[/C][/ROW]
[ROW][C]44[/C][C]87.7[/C][C]91.5811265114215[/C][C]-3.8811265114215[/C][/ROW]
[ROW][C]45[/C][C]91.7[/C][C]89.376373876203[/C][C]2.323626123797[/C][/ROW]
[ROW][C]46[/C][C]95.9[/C][C]98.8780047194497[/C][C]-2.97800471944967[/C][/ROW]
[ROW][C]47[/C][C]106.8[/C][C]106.356198492784[/C][C]0.443801507216449[/C][/ROW]
[ROW][C]48[/C][C]204.5[/C][C]195.949254076707[/C][C]8.55074592329348[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]91.7726280734287[/C][C]-1.57262807342873[/C][/ROW]
[ROW][C]50[/C][C]90.5[/C][C]92.6699904442213[/C][C]-2.16999044422133[/C][/ROW]
[ROW][C]51[/C][C]93.2[/C][C]96.9320728302648[/C][C]-3.73207283026477[/C][/ROW]
[ROW][C]52[/C][C]97.8[/C][C]92.5307255072453[/C][C]5.26927449275469[/C][/ROW]
[ROW][C]53[/C][C]99.4[/C][C]98.0015805305656[/C][C]1.3984194694344[/C][/ROW]
[ROW][C]54[/C][C]120[/C][C]117.501168892219[/C][C]2.49883110778102[/C][/ROW]
[ROW][C]55[/C][C]108.2[/C][C]100.704814643964[/C][C]7.49518535603633[/C][/ROW]
[ROW][C]56[/C][C]98.5[/C][C]95.9013434063614[/C][C]2.59865659363864[/C][/ROW]
[ROW][C]57[/C][C]104.3[/C][C]97.178202817712[/C][C]7.12179718228789[/C][/ROW]
[ROW][C]58[/C][C]102.9[/C][C]104.86130443706[/C][C]-1.96130443705988[/C][/ROW]
[ROW][C]59[/C][C]111.1[/C][C]114.328767906606[/C][C]-3.22876790660592[/C][/ROW]
[ROW][C]60[/C][C]188.1[/C][C]207.751779632248[/C][C]-19.6517796322481[/C][/ROW]
[ROW][C]61[/C][C]93.8[/C][C]97.3110620246897[/C][C]-3.51106202468972[/C][/ROW]
[ROW][C]62[/C][C]94.5[/C][C]97.7180259149318[/C][C]-3.21802591493179[/C][/ROW]
[ROW][C]63[/C][C]112.4[/C][C]101.081215347127[/C][C]11.3187846528730[/C][/ROW]
[ROW][C]64[/C][C]102.5[/C][C]101.714611058633[/C][C]0.785388941367344[/C][/ROW]
[ROW][C]65[/C][C]115.8[/C][C]105.189099981901[/C][C]10.6109000180992[/C][/ROW]
[ROW][C]66[/C][C]136.5[/C][C]125.848651000864[/C][C]10.6513489991358[/C][/ROW]
[ROW][C]67[/C][C]122.1[/C][C]112.055434753528[/C][C]10.0445652464716[/C][/ROW]
[ROW][C]68[/C][C]110.6[/C][C]105.449167474752[/C][C]5.15083252524811[/C][/ROW]
[ROW][C]69[/C][C]116.4[/C][C]109.278350938839[/C][C]7.12164906116134[/C][/ROW]
[ROW][C]70[/C][C]112.6[/C][C]113.135819450739[/C][C]-0.535819450739439[/C][/ROW]
[ROW][C]71[/C][C]121.5[/C][C]122.459087510953[/C][C]-0.959087510953069[/C][/ROW]
[ROW][C]72[/C][C]199.3[/C][C]208.866822068269[/C][C]-9.56682206826866[/C][/ROW]
[ROW][C]73[/C][C]102.1[/C][C]106.910116854964[/C][C]-4.81011685496409[/C][/ROW]
[ROW][C]74[/C][C]100.6[/C][C]107.895222227845[/C][C]-7.2952222278455[/C][/ROW]
[ROW][C]75[/C][C]119[/C][C]118.158622725819[/C][C]0.841377274181042[/C][/ROW]
[ROW][C]76[/C][C]106.8[/C][C]113.700537986824[/C][C]-6.90053798682369[/C][/ROW]
[ROW][C]77[/C][C]121.3[/C][C]121.462661551200[/C][C]-0.162661551199690[/C][/ROW]
[ROW][C]78[/C][C]145.5[/C][C]141.603233506010[/C][C]3.89676649398976[/C][/ROW]
[ROW][C]79[/C][C]129.7[/C][C]127.118571954011[/C][C]2.58142804598928[/C][/ROW]
[ROW][C]80[/C][C]117.7[/C][C]117.711596156171[/C][C]-0.0115961561713505[/C][/ROW]
[ROW][C]81[/C][C]121.3[/C][C]121.940513740341[/C][C]-0.640513740340609[/C][/ROW]
[ROW][C]82[/C][C]124.3[/C][C]121.531963481098[/C][C]2.76803651890198[/C][/ROW]
[ROW][C]83[/C][C]135.2[/C][C]130.55650585504[/C][C]4.64349414495996[/C][/ROW]
[ROW][C]84[/C][C]210.1[/C][C]213.11703099708[/C][C]-3.01703099708001[/C][/ROW]
[ROW][C]85[/C][C]106.8[/C][C]113.584734859316[/C][C]-6.78473485931625[/C][/ROW]
[ROW][C]86[/C][C]110.5[/C][C]113.180846833161[/C][C]-2.68084683316064[/C][/ROW]
[ROW][C]87[/C][C]111.5[/C][C]127.349912094680[/C][C]-15.8499120946802[/C][/ROW]
[ROW][C]88[/C][C]122.1[/C][C]118.119618813076[/C][C]3.98038118692401[/C][/ROW]
[ROW][C]89[/C][C]126.3[/C][C]129.406290293180[/C][C]-3.10629029318035[/C][/ROW]
[ROW][C]90[/C][C]143.2[/C][C]151.047548918185[/C][C]-7.84754891818466[/C][/ROW]
[ROW][C]91[/C][C]137.3[/C][C]134.95376252927[/C][C]2.34623747073013[/C][/ROW]
[ROW][C]92[/C][C]121.5[/C][C]123.976519736902[/C][C]-2.47651973690213[/C][/ROW]
[ROW][C]93[/C][C]121.9[/C][C]127.379410643105[/C][C]-5.47941064310531[/C][/ROW]
[ROW][C]94[/C][C]123.9[/C][C]127.798485263545[/C][C]-3.89848526354541[/C][/ROW]
[ROW][C]95[/C][C]131.6[/C][C]136.754218408707[/C][C]-5.15421840870664[/C][/ROW]
[ROW][C]96[/C][C]220.9[/C][C]214.564875538885[/C][C]6.33512446111544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112838&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	87.6	87.4374732905983	0.162526709401661
14	85.4	85.4574707694395	-0.0574707694395045
15	86.1	86.3438222724077	-0.243822272407698
16	86.7	86.9249094831851	-0.224909483185087
17	89.1	89.1038654903233	-0.00386549032332084
18	103.7	103.728161925143	-0.0281619251432375
19	86.9	89.263236525602	-2.36323652560203
20	85.2	87.7751584373825	-2.57515843738254
21	80.8	82.160132151459	-1.36013215145903
22	91.2	89.1006088566335	2.09939114336653
23	102.8	99.0552173122356	3.74478268776444
24	182.5	185.839775787221	-3.33977578722073
25	80.9	86.181975289146	-5.28197528914602
26	83.1	83.668516015986	-0.568516015986035
27	88.3	84.2988489052085	4.00115109479145
28	86.6	85.0372535044138	1.56274649558621
29	93	87.357263836485	5.64273616351507
30	105.3	102.300104302552	2.99989569744844
31	93.8	86.993897618399	6.80610238160105
32	86.4	86.1021034188466	0.297896581153410
33	87	81.434485449809	5.56551455019095
34	96.7	90.6700468404298	6.0299531595702
35	100.5	101.979782024187	-1.47978202418733
36	196.7	185.543604488798	11.1563955112018
37	86.8	86.3028818725309	0.497118127469122
38	88.2	86.8638531606971	1.3361468393029
39	93.8	90.3180616041513	3.48193839584873
40	85	90.5274626381015	-5.52746263810151
41	90.4	94.8489890207248	-4.44898902072482
42	115.9	108.405104118965	7.49489588103494
43	94.9	95.5283225539246	-0.628322553924605
44	87.7	91.5811265114215	-3.8811265114215
45	91.7	89.376373876203	2.323626123797
46	95.9	98.8780047194497	-2.97800471944967
47	106.8	106.356198492784	0.443801507216449
48	204.5	195.949254076707	8.55074592329348
49	90.2	91.7726280734287	-1.57262807342873
50	90.5	92.6699904442213	-2.16999044422133
51	93.2	96.9320728302648	-3.73207283026477
52	97.8	92.5307255072453	5.26927449275469
53	99.4	98.0015805305656	1.3984194694344
54	120	117.501168892219	2.49883110778102
55	108.2	100.704814643964	7.49518535603633
56	98.5	95.9013434063614	2.59865659363864
57	104.3	97.178202817712	7.12179718228789
58	102.9	104.86130443706	-1.96130443705988
59	111.1	114.328767906606	-3.22876790660592
60	188.1	207.751779632248	-19.6517796322481
61	93.8	97.3110620246897	-3.51106202468972
62	94.5	97.7180259149318	-3.21802591493179
63	112.4	101.081215347127	11.3187846528730
64	102.5	101.714611058633	0.785388941367344
65	115.8	105.189099981901	10.6109000180992
66	136.5	125.848651000864	10.6513489991358
67	122.1	112.055434753528	10.0445652464716
68	110.6	105.449167474752	5.15083252524811
69	116.4	109.278350938839	7.12164906116134
70	112.6	113.135819450739	-0.535819450739439
71	121.5	122.459087510953	-0.959087510953069
72	199.3	208.866822068269	-9.56682206826866
73	102.1	106.910116854964	-4.81011685496409
74	100.6	107.895222227845	-7.2952222278455
75	119	118.158622725819	0.841377274181042
76	106.8	113.700537986824	-6.90053798682369
77	121.3	121.462661551200	-0.162661551199690
78	145.5	141.603233506010	3.89676649398976
79	129.7	127.118571954011	2.58142804598928
80	117.7	117.711596156171	-0.0115961561713505
81	121.3	121.940513740341	-0.640513740340609
82	124.3	121.531963481098	2.76803651890198
83	135.2	130.55650585504	4.64349414495996
84	210.1	213.11703099708	-3.01703099708001
85	106.8	113.584734859316	-6.78473485931625
86	110.5	113.180846833161	-2.68084683316064
87	111.5	127.349912094680	-15.8499120946802
88	122.1	118.119618813076	3.98038118692401
89	126.3	129.406290293180	-3.10629029318035
90	143.2	151.047548918185	-7.84754891818466
91	137.3	134.95376252927	2.34623747073013
92	121.5	123.976519736902	-2.47651973690213
93	121.9	127.379410643105	-5.47941064310531
94	123.9	127.798485263545	-3.89848526354541
95	131.6	136.754218408707	-5.15421840870664
96	220.9	214.564875538885	6.33512446111544

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	113.244094803911	102.467369407242	124.020820200579
98	114.616305249382	103.814229925541	125.418380573224
99	122.455308528548	111.616534345608	133.294082711489
100	122.967200226293	112.078383074296	133.85601737829
101	130.516148052962	119.562029371918	141.470266734005
102	149.925471584574	138.888982000064	160.961961169083
103	138.816794562731	127.679180679348	149.954408446115
104	125.350098416348	114.091071668384	136.609125164312
105	127.395963051111	115.993868135220	138.798057967002
106	128.800685877624	117.232685024923	140.368686730326
107	137.409977678774	125.652245996318	149.167709361230
108	220.859030615277	208.886957049244	232.831104181309

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 113.244094803911 & 102.467369407242 & 124.020820200579 \tabularnewline
98 & 114.616305249382 & 103.814229925541 & 125.418380573224 \tabularnewline
99 & 122.455308528548 & 111.616534345608 & 133.294082711489 \tabularnewline
100 & 122.967200226293 & 112.078383074296 & 133.85601737829 \tabularnewline
101 & 130.516148052962 & 119.562029371918 & 141.470266734005 \tabularnewline
102 & 149.925471584574 & 138.888982000064 & 160.961961169083 \tabularnewline
103 & 138.816794562731 & 127.679180679348 & 149.954408446115 \tabularnewline
104 & 125.350098416348 & 114.091071668384 & 136.609125164312 \tabularnewline
105 & 127.395963051111 & 115.993868135220 & 138.798057967002 \tabularnewline
106 & 128.800685877624 & 117.232685024923 & 140.368686730326 \tabularnewline
107 & 137.409977678774 & 125.652245996318 & 149.167709361230 \tabularnewline
108 & 220.859030615277 & 208.886957049244 & 232.831104181309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112838&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]97[/C][C]113.244094803911[/C][C]102.467369407242[/C][C]124.020820200579[/C][/ROW]
[ROW][C]98[/C][C]114.616305249382[/C][C]103.814229925541[/C][C]125.418380573224[/C][/ROW]
[ROW][C]99[/C][C]122.455308528548[/C][C]111.616534345608[/C][C]133.294082711489[/C][/ROW]
[ROW][C]100[/C][C]122.967200226293[/C][C]112.078383074296[/C][C]133.85601737829[/C][/ROW]
[ROW][C]101[/C][C]130.516148052962[/C][C]119.562029371918[/C][C]141.470266734005[/C][/ROW]
[ROW][C]102[/C][C]149.925471584574[/C][C]138.888982000064[/C][C]160.961961169083[/C][/ROW]
[ROW][C]103[/C][C]138.816794562731[/C][C]127.679180679348[/C][C]149.954408446115[/C][/ROW]
[ROW][C]104[/C][C]125.350098416348[/C][C]114.091071668384[/C][C]136.609125164312[/C][/ROW]
[ROW][C]105[/C][C]127.395963051111[/C][C]115.993868135220[/C][C]138.798057967002[/C][/ROW]
[ROW][C]106[/C][C]128.800685877624[/C][C]117.232685024923[/C][C]140.368686730326[/C][/ROW]
[ROW][C]107[/C][C]137.409977678774[/C][C]125.652245996318[/C][C]149.167709361230[/C][/ROW]
[ROW][C]108[/C][C]220.859030615277[/C][C]208.886957049244[/C][C]232.831104181309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112838&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112838&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
97	113.244094803911	102.467369407242	124.020820200579
98	114.616305249382	103.814229925541	125.418380573224
99	122.455308528548	111.616534345608	133.294082711489
100	122.967200226293	112.078383074296	133.85601737829
101	130.516148052962	119.562029371918	141.470266734005
102	149.925471584574	138.888982000064	160.961961169083
103	138.816794562731	127.679180679348	149.954408446115
104	125.350098416348	114.091071668384	136.609125164312
105	127.395963051111	115.993868135220	138.798057967002
106	128.800685877624	117.232685024923	140.368686730326
107	137.409977678774	125.652245996318	149.167709361230
108	220.859030615277	208.886957049244	232.831104181309

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=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