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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 15 Aug 2016 20:23:48 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/15/t1471289132viimd36pcepwocd.htm/, Retrieved Sun, 28 Apr 2024 10:43:23 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 10:43:23 +0200

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Estimated Impact

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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.791744303433318
beta	0.0130842068064546
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.791744303433318 \tabularnewline
beta & 0.0130842068064546 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.791744303433318[/C][/ROW]
[ROW][C]beta[/C][C]0.0130842068064546[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.791744303433318
beta	0.0130842068064546
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	21051	21137.6057692308	-86.6057692307731
14	21643	21681.5136742758	-38.5136742758368
15	21864	21876.6825783896	-12.6825783895729
16	21643	21647.4633889691	-4.46338896906309
17	22455	22479.0387914928	-24.0387914928397
18	21935	21978.0331210843	-43.0331210842669
19	20759	21255.7930034246	-496.793003424602
20	20467	20102.9362997479	364.063700252111
21	20467	20413.3461158575	53.6538841425281
22	20610	20391.3382141602	218.661785839802
23	20026	20603.8229051276	-577.822905127639
24	20467	20305.0428450643	161.957154935688
25	20097	20368.2877254567	-271.287725456681
26	20467	20769.0463405366	-302.046340536563
27	21051	20751.2703482002	299.729651799778
28	21272	20764.6759597875	507.324040212545
29	21792	21996.2437424226	-204.243742422565
30	21571	21345.6036334268	225.396366573154
31	20246	20741.1711892185	-495.171189218487
32	19726	19768.6718971996	-42.6718971996415
33	19506	19687.9880307114	-181.988030711404
34	19726	19506.9162467724	219.083753227573
35	19363	19547.0073511866	-184.007351186552
36	19506	19711.3163932312	-205.316393231231
37	19064	19386.9685748307	-322.968574830706
38	19805	19733.2878903225	71.7121096774936
39	20168	20133.512568756	34.4874312439715
40	20246	19974.1554096515	271.844590348501
41	21643	20862.6647544101	780.33524558994
42	21643	21082.8031645832	560.196835416762
43	19805	20598.6218140378	-793.621814037833
44	19363	19486.2067697941	-123.206769794142
45	19363	19314.057484224	48.9425157760124
46	19584	19403.0524041227	180.947595877271
47	18622	19332.3116142435	-710.311614243543
48	18180	19073.3405664496	-893.340566449595
49	17668	18170.480352344	-502.480352343966
50	17817	18445.7356779097	-628.735677909721
51	18480	18265.2453146481	214.754685351858
52	17960	18281.5249137942	-321.52491379423
53	19363	18783.4666955121	579.533304487868
54	19584	18774.0293440118	809.970655988163
55	18180	18183.5051499276	-3.50514992760873
56	17668	17822.3039203778	-154.303920377832
57	17375	17647.0882610202	-272.088261020206
58	17668	17491.7775817719	176.222418228055
59	16855	17214.0147817313	-359.014781731308
60	16563	17181.0323134181	-618.032313418098
61	15388	16566.3648554516	-1178.36485545161
62	15680	16262.017512535	-582.017512535012
63	15751	16276.4800607761	-525.480060776099
64	15830	15569.633784042	260.366215957976
65	17226	16700.5971205659	525.402879434077
66	17076	16676.3935094361	399.606490563921
67	15388	15567.4050548811	-179.405054881123
68	14647	15009.559367054	-362.559367053986
69	14355	14616.799986381	-261.799986381009
70	14725	14534.975424709	190.02457529097
71	13322	14128.7943712689	-806.794371268896
72	12367	13654.8245467469	-1287.82454674688
73	10601	12353.7033095642	-1752.70330956421
74	10750	11673.4125776276	-923.41257762758
75	10750	11380.4082235595	-630.408223559456
76	10601	10704.1120975626	-103.112097562622
77	11854	11548.6930093507	305.306990649326
78	11926	11267.9559324144	658.044067585593
79	10451	10189.6027638129	261.39723618714
80	10159	9893.7845328295	265.215467170505
81	9568	9976.71703565696	-408.717035656964
82	10380	9828.81583104047	551.184168959529
83	8905	9460.87803679673	-555.87803679673
84	8022	9047.88227799039	-1025.88227799039
85	6333	7822.54200152473	-1489.54200152473
86	6697	7491.24174641587	-794.241746415873
87	6255	7330.79510461057	-1075.79510461057
88	6404	6376.33257446613	27.6674255338676
89	7509	7375.52152046658	133.478479533424
90	7730	6996.42816340307	733.571836596927
91	6996	5860.28059086458	1135.71940913542
92	6917	6231.56541147607	685.434588523935
93	6917	6485.27520581774	431.724794182258
94	7879	7189.82183302986	689.178166970141
95	6184	6689.14542409978	-505.145424099777
96	5079	6207.51885273741	-1128.51885273741
97	3163	4792.37661736828	-1629.37661736828
98	4709	4481.73448866733	227.265511332673
99	4488	5068.5786036757	-580.5786036757
100	4566	4738.28668944919	-172.286689449188
101	6333	5601.41087930296	731.589120697037
102	6112	5827.24913106807	284.750868931935
103	5300	4421.25820095752	878.741799042482
104	5671	4494.40452766508	1176.59547233492
105	5671	5088.33619349111	582.663806508887
106	6996	5971.7522344506	1024.2477655494
107	5450	5496.85986112768	-46.8598611276757
108	4566	5262.22402586184	-696.224025861836
109	3163	4103.48738606461	-940.487386064614
110	5008	4750.50723541932	257.492764580677
111	4859	5218.94015537483	-359.940155374828
112	4930	5176.54695104849	-246.546951048488
113	6476	6196.52435884203	279.475641157973
114	6333	5994.07519782536	338.924802174639
115	5813	4777.96684271114	1035.03315728886
116	5892	5061.79343953372	830.206560466281
117	6255	5279.10339551756	975.896604482444
118	7067	6591.21466455324	475.785335446762
119	5813	5478.72733483937	334.272665160626
120	4787	5434.27681663424	-647.276816634238

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21051 & 21137.6057692308 & -86.6057692307731 \tabularnewline
14 & 21643 & 21681.5136742758 & -38.5136742758368 \tabularnewline
15 & 21864 & 21876.6825783896 & -12.6825783895729 \tabularnewline
16 & 21643 & 21647.4633889691 & -4.46338896906309 \tabularnewline
17 & 22455 & 22479.0387914928 & -24.0387914928397 \tabularnewline
18 & 21935 & 21978.0331210843 & -43.0331210842669 \tabularnewline
19 & 20759 & 21255.7930034246 & -496.793003424602 \tabularnewline
20 & 20467 & 20102.9362997479 & 364.063700252111 \tabularnewline
21 & 20467 & 20413.3461158575 & 53.6538841425281 \tabularnewline
22 & 20610 & 20391.3382141602 & 218.661785839802 \tabularnewline
23 & 20026 & 20603.8229051276 & -577.822905127639 \tabularnewline
24 & 20467 & 20305.0428450643 & 161.957154935688 \tabularnewline
25 & 20097 & 20368.2877254567 & -271.287725456681 \tabularnewline
26 & 20467 & 20769.0463405366 & -302.046340536563 \tabularnewline
27 & 21051 & 20751.2703482002 & 299.729651799778 \tabularnewline
28 & 21272 & 20764.6759597875 & 507.324040212545 \tabularnewline
29 & 21792 & 21996.2437424226 & -204.243742422565 \tabularnewline
30 & 21571 & 21345.6036334268 & 225.396366573154 \tabularnewline
31 & 20246 & 20741.1711892185 & -495.171189218487 \tabularnewline
32 & 19726 & 19768.6718971996 & -42.6718971996415 \tabularnewline
33 & 19506 & 19687.9880307114 & -181.988030711404 \tabularnewline
34 & 19726 & 19506.9162467724 & 219.083753227573 \tabularnewline
35 & 19363 & 19547.0073511866 & -184.007351186552 \tabularnewline
36 & 19506 & 19711.3163932312 & -205.316393231231 \tabularnewline
37 & 19064 & 19386.9685748307 & -322.968574830706 \tabularnewline
38 & 19805 & 19733.2878903225 & 71.7121096774936 \tabularnewline
39 & 20168 & 20133.512568756 & 34.4874312439715 \tabularnewline
40 & 20246 & 19974.1554096515 & 271.844590348501 \tabularnewline
41 & 21643 & 20862.6647544101 & 780.33524558994 \tabularnewline
42 & 21643 & 21082.8031645832 & 560.196835416762 \tabularnewline
43 & 19805 & 20598.6218140378 & -793.621814037833 \tabularnewline
44 & 19363 & 19486.2067697941 & -123.206769794142 \tabularnewline
45 & 19363 & 19314.057484224 & 48.9425157760124 \tabularnewline
46 & 19584 & 19403.0524041227 & 180.947595877271 \tabularnewline
47 & 18622 & 19332.3116142435 & -710.311614243543 \tabularnewline
48 & 18180 & 19073.3405664496 & -893.340566449595 \tabularnewline
49 & 17668 & 18170.480352344 & -502.480352343966 \tabularnewline
50 & 17817 & 18445.7356779097 & -628.735677909721 \tabularnewline
51 & 18480 & 18265.2453146481 & 214.754685351858 \tabularnewline
52 & 17960 & 18281.5249137942 & -321.52491379423 \tabularnewline
53 & 19363 & 18783.4666955121 & 579.533304487868 \tabularnewline
54 & 19584 & 18774.0293440118 & 809.970655988163 \tabularnewline
55 & 18180 & 18183.5051499276 & -3.50514992760873 \tabularnewline
56 & 17668 & 17822.3039203778 & -154.303920377832 \tabularnewline
57 & 17375 & 17647.0882610202 & -272.088261020206 \tabularnewline
58 & 17668 & 17491.7775817719 & 176.222418228055 \tabularnewline
59 & 16855 & 17214.0147817313 & -359.014781731308 \tabularnewline
60 & 16563 & 17181.0323134181 & -618.032313418098 \tabularnewline
61 & 15388 & 16566.3648554516 & -1178.36485545161 \tabularnewline
62 & 15680 & 16262.017512535 & -582.017512535012 \tabularnewline
63 & 15751 & 16276.4800607761 & -525.480060776099 \tabularnewline
64 & 15830 & 15569.633784042 & 260.366215957976 \tabularnewline
65 & 17226 & 16700.5971205659 & 525.402879434077 \tabularnewline
66 & 17076 & 16676.3935094361 & 399.606490563921 \tabularnewline
67 & 15388 & 15567.4050548811 & -179.405054881123 \tabularnewline
68 & 14647 & 15009.559367054 & -362.559367053986 \tabularnewline
69 & 14355 & 14616.799986381 & -261.799986381009 \tabularnewline
70 & 14725 & 14534.975424709 & 190.02457529097 \tabularnewline
71 & 13322 & 14128.7943712689 & -806.794371268896 \tabularnewline
72 & 12367 & 13654.8245467469 & -1287.82454674688 \tabularnewline
73 & 10601 & 12353.7033095642 & -1752.70330956421 \tabularnewline
74 & 10750 & 11673.4125776276 & -923.41257762758 \tabularnewline
75 & 10750 & 11380.4082235595 & -630.408223559456 \tabularnewline
76 & 10601 & 10704.1120975626 & -103.112097562622 \tabularnewline
77 & 11854 & 11548.6930093507 & 305.306990649326 \tabularnewline
78 & 11926 & 11267.9559324144 & 658.044067585593 \tabularnewline
79 & 10451 & 10189.6027638129 & 261.39723618714 \tabularnewline
80 & 10159 & 9893.7845328295 & 265.215467170505 \tabularnewline
81 & 9568 & 9976.71703565696 & -408.717035656964 \tabularnewline
82 & 10380 & 9828.81583104047 & 551.184168959529 \tabularnewline
83 & 8905 & 9460.87803679673 & -555.87803679673 \tabularnewline
84 & 8022 & 9047.88227799039 & -1025.88227799039 \tabularnewline
85 & 6333 & 7822.54200152473 & -1489.54200152473 \tabularnewline
86 & 6697 & 7491.24174641587 & -794.241746415873 \tabularnewline
87 & 6255 & 7330.79510461057 & -1075.79510461057 \tabularnewline
88 & 6404 & 6376.33257446613 & 27.6674255338676 \tabularnewline
89 & 7509 & 7375.52152046658 & 133.478479533424 \tabularnewline
90 & 7730 & 6996.42816340307 & 733.571836596927 \tabularnewline
91 & 6996 & 5860.28059086458 & 1135.71940913542 \tabularnewline
92 & 6917 & 6231.56541147607 & 685.434588523935 \tabularnewline
93 & 6917 & 6485.27520581774 & 431.724794182258 \tabularnewline
94 & 7879 & 7189.82183302986 & 689.178166970141 \tabularnewline
95 & 6184 & 6689.14542409978 & -505.145424099777 \tabularnewline
96 & 5079 & 6207.51885273741 & -1128.51885273741 \tabularnewline
97 & 3163 & 4792.37661736828 & -1629.37661736828 \tabularnewline
98 & 4709 & 4481.73448866733 & 227.265511332673 \tabularnewline
99 & 4488 & 5068.5786036757 & -580.5786036757 \tabularnewline
100 & 4566 & 4738.28668944919 & -172.286689449188 \tabularnewline
101 & 6333 & 5601.41087930296 & 731.589120697037 \tabularnewline
102 & 6112 & 5827.24913106807 & 284.750868931935 \tabularnewline
103 & 5300 & 4421.25820095752 & 878.741799042482 \tabularnewline
104 & 5671 & 4494.40452766508 & 1176.59547233492 \tabularnewline
105 & 5671 & 5088.33619349111 & 582.663806508887 \tabularnewline
106 & 6996 & 5971.7522344506 & 1024.2477655494 \tabularnewline
107 & 5450 & 5496.85986112768 & -46.8598611276757 \tabularnewline
108 & 4566 & 5262.22402586184 & -696.224025861836 \tabularnewline
109 & 3163 & 4103.48738606461 & -940.487386064614 \tabularnewline
110 & 5008 & 4750.50723541932 & 257.492764580677 \tabularnewline
111 & 4859 & 5218.94015537483 & -359.940155374828 \tabularnewline
112 & 4930 & 5176.54695104849 & -246.546951048488 \tabularnewline
113 & 6476 & 6196.52435884203 & 279.475641157973 \tabularnewline
114 & 6333 & 5994.07519782536 & 338.924802174639 \tabularnewline
115 & 5813 & 4777.96684271114 & 1035.03315728886 \tabularnewline
116 & 5892 & 5061.79343953372 & 830.206560466281 \tabularnewline
117 & 6255 & 5279.10339551756 & 975.896604482444 \tabularnewline
118 & 7067 & 6591.21466455324 & 475.785335446762 \tabularnewline
119 & 5813 & 5478.72733483937 & 334.272665160626 \tabularnewline
120 & 4787 & 5434.27681663424 & -647.276816634238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]21051[/C][C]21137.6057692308[/C][C]-86.6057692307731[/C][/ROW]
[ROW][C]14[/C][C]21643[/C][C]21681.5136742758[/C][C]-38.5136742758368[/C][/ROW]
[ROW][C]15[/C][C]21864[/C][C]21876.6825783896[/C][C]-12.6825783895729[/C][/ROW]
[ROW][C]16[/C][C]21643[/C][C]21647.4633889691[/C][C]-4.46338896906309[/C][/ROW]
[ROW][C]17[/C][C]22455[/C][C]22479.0387914928[/C][C]-24.0387914928397[/C][/ROW]
[ROW][C]18[/C][C]21935[/C][C]21978.0331210843[/C][C]-43.0331210842669[/C][/ROW]
[ROW][C]19[/C][C]20759[/C][C]21255.7930034246[/C][C]-496.793003424602[/C][/ROW]
[ROW][C]20[/C][C]20467[/C][C]20102.9362997479[/C][C]364.063700252111[/C][/ROW]
[ROW][C]21[/C][C]20467[/C][C]20413.3461158575[/C][C]53.6538841425281[/C][/ROW]
[ROW][C]22[/C][C]20610[/C][C]20391.3382141602[/C][C]218.661785839802[/C][/ROW]
[ROW][C]23[/C][C]20026[/C][C]20603.8229051276[/C][C]-577.822905127639[/C][/ROW]
[ROW][C]24[/C][C]20467[/C][C]20305.0428450643[/C][C]161.957154935688[/C][/ROW]
[ROW][C]25[/C][C]20097[/C][C]20368.2877254567[/C][C]-271.287725456681[/C][/ROW]
[ROW][C]26[/C][C]20467[/C][C]20769.0463405366[/C][C]-302.046340536563[/C][/ROW]
[ROW][C]27[/C][C]21051[/C][C]20751.2703482002[/C][C]299.729651799778[/C][/ROW]
[ROW][C]28[/C][C]21272[/C][C]20764.6759597875[/C][C]507.324040212545[/C][/ROW]
[ROW][C]29[/C][C]21792[/C][C]21996.2437424226[/C][C]-204.243742422565[/C][/ROW]
[ROW][C]30[/C][C]21571[/C][C]21345.6036334268[/C][C]225.396366573154[/C][/ROW]
[ROW][C]31[/C][C]20246[/C][C]20741.1711892185[/C][C]-495.171189218487[/C][/ROW]
[ROW][C]32[/C][C]19726[/C][C]19768.6718971996[/C][C]-42.6718971996415[/C][/ROW]
[ROW][C]33[/C][C]19506[/C][C]19687.9880307114[/C][C]-181.988030711404[/C][/ROW]
[ROW][C]34[/C][C]19726[/C][C]19506.9162467724[/C][C]219.083753227573[/C][/ROW]
[ROW][C]35[/C][C]19363[/C][C]19547.0073511866[/C][C]-184.007351186552[/C][/ROW]
[ROW][C]36[/C][C]19506[/C][C]19711.3163932312[/C][C]-205.316393231231[/C][/ROW]
[ROW][C]37[/C][C]19064[/C][C]19386.9685748307[/C][C]-322.968574830706[/C][/ROW]
[ROW][C]38[/C][C]19805[/C][C]19733.2878903225[/C][C]71.7121096774936[/C][/ROW]
[ROW][C]39[/C][C]20168[/C][C]20133.512568756[/C][C]34.4874312439715[/C][/ROW]
[ROW][C]40[/C][C]20246[/C][C]19974.1554096515[/C][C]271.844590348501[/C][/ROW]
[ROW][C]41[/C][C]21643[/C][C]20862.6647544101[/C][C]780.33524558994[/C][/ROW]
[ROW][C]42[/C][C]21643[/C][C]21082.8031645832[/C][C]560.196835416762[/C][/ROW]
[ROW][C]43[/C][C]19805[/C][C]20598.6218140378[/C][C]-793.621814037833[/C][/ROW]
[ROW][C]44[/C][C]19363[/C][C]19486.2067697941[/C][C]-123.206769794142[/C][/ROW]
[ROW][C]45[/C][C]19363[/C][C]19314.057484224[/C][C]48.9425157760124[/C][/ROW]
[ROW][C]46[/C][C]19584[/C][C]19403.0524041227[/C][C]180.947595877271[/C][/ROW]
[ROW][C]47[/C][C]18622[/C][C]19332.3116142435[/C][C]-710.311614243543[/C][/ROW]
[ROW][C]48[/C][C]18180[/C][C]19073.3405664496[/C][C]-893.340566449595[/C][/ROW]
[ROW][C]49[/C][C]17668[/C][C]18170.480352344[/C][C]-502.480352343966[/C][/ROW]
[ROW][C]50[/C][C]17817[/C][C]18445.7356779097[/C][C]-628.735677909721[/C][/ROW]
[ROW][C]51[/C][C]18480[/C][C]18265.2453146481[/C][C]214.754685351858[/C][/ROW]
[ROW][C]52[/C][C]17960[/C][C]18281.5249137942[/C][C]-321.52491379423[/C][/ROW]
[ROW][C]53[/C][C]19363[/C][C]18783.4666955121[/C][C]579.533304487868[/C][/ROW]
[ROW][C]54[/C][C]19584[/C][C]18774.0293440118[/C][C]809.970655988163[/C][/ROW]
[ROW][C]55[/C][C]18180[/C][C]18183.5051499276[/C][C]-3.50514992760873[/C][/ROW]
[ROW][C]56[/C][C]17668[/C][C]17822.3039203778[/C][C]-154.303920377832[/C][/ROW]
[ROW][C]57[/C][C]17375[/C][C]17647.0882610202[/C][C]-272.088261020206[/C][/ROW]
[ROW][C]58[/C][C]17668[/C][C]17491.7775817719[/C][C]176.222418228055[/C][/ROW]
[ROW][C]59[/C][C]16855[/C][C]17214.0147817313[/C][C]-359.014781731308[/C][/ROW]
[ROW][C]60[/C][C]16563[/C][C]17181.0323134181[/C][C]-618.032313418098[/C][/ROW]
[ROW][C]61[/C][C]15388[/C][C]16566.3648554516[/C][C]-1178.36485545161[/C][/ROW]
[ROW][C]62[/C][C]15680[/C][C]16262.017512535[/C][C]-582.017512535012[/C][/ROW]
[ROW][C]63[/C][C]15751[/C][C]16276.4800607761[/C][C]-525.480060776099[/C][/ROW]
[ROW][C]64[/C][C]15830[/C][C]15569.633784042[/C][C]260.366215957976[/C][/ROW]
[ROW][C]65[/C][C]17226[/C][C]16700.5971205659[/C][C]525.402879434077[/C][/ROW]
[ROW][C]66[/C][C]17076[/C][C]16676.3935094361[/C][C]399.606490563921[/C][/ROW]
[ROW][C]67[/C][C]15388[/C][C]15567.4050548811[/C][C]-179.405054881123[/C][/ROW]
[ROW][C]68[/C][C]14647[/C][C]15009.559367054[/C][C]-362.559367053986[/C][/ROW]
[ROW][C]69[/C][C]14355[/C][C]14616.799986381[/C][C]-261.799986381009[/C][/ROW]
[ROW][C]70[/C][C]14725[/C][C]14534.975424709[/C][C]190.02457529097[/C][/ROW]
[ROW][C]71[/C][C]13322[/C][C]14128.7943712689[/C][C]-806.794371268896[/C][/ROW]
[ROW][C]72[/C][C]12367[/C][C]13654.8245467469[/C][C]-1287.82454674688[/C][/ROW]
[ROW][C]73[/C][C]10601[/C][C]12353.7033095642[/C][C]-1752.70330956421[/C][/ROW]
[ROW][C]74[/C][C]10750[/C][C]11673.4125776276[/C][C]-923.41257762758[/C][/ROW]
[ROW][C]75[/C][C]10750[/C][C]11380.4082235595[/C][C]-630.408223559456[/C][/ROW]
[ROW][C]76[/C][C]10601[/C][C]10704.1120975626[/C][C]-103.112097562622[/C][/ROW]
[ROW][C]77[/C][C]11854[/C][C]11548.6930093507[/C][C]305.306990649326[/C][/ROW]
[ROW][C]78[/C][C]11926[/C][C]11267.9559324144[/C][C]658.044067585593[/C][/ROW]
[ROW][C]79[/C][C]10451[/C][C]10189.6027638129[/C][C]261.39723618714[/C][/ROW]
[ROW][C]80[/C][C]10159[/C][C]9893.7845328295[/C][C]265.215467170505[/C][/ROW]
[ROW][C]81[/C][C]9568[/C][C]9976.71703565696[/C][C]-408.717035656964[/C][/ROW]
[ROW][C]82[/C][C]10380[/C][C]9828.81583104047[/C][C]551.184168959529[/C][/ROW]
[ROW][C]83[/C][C]8905[/C][C]9460.87803679673[/C][C]-555.87803679673[/C][/ROW]
[ROW][C]84[/C][C]8022[/C][C]9047.88227799039[/C][C]-1025.88227799039[/C][/ROW]
[ROW][C]85[/C][C]6333[/C][C]7822.54200152473[/C][C]-1489.54200152473[/C][/ROW]
[ROW][C]86[/C][C]6697[/C][C]7491.24174641587[/C][C]-794.241746415873[/C][/ROW]
[ROW][C]87[/C][C]6255[/C][C]7330.79510461057[/C][C]-1075.79510461057[/C][/ROW]
[ROW][C]88[/C][C]6404[/C][C]6376.33257446613[/C][C]27.6674255338676[/C][/ROW]
[ROW][C]89[/C][C]7509[/C][C]7375.52152046658[/C][C]133.478479533424[/C][/ROW]
[ROW][C]90[/C][C]7730[/C][C]6996.42816340307[/C][C]733.571836596927[/C][/ROW]
[ROW][C]91[/C][C]6996[/C][C]5860.28059086458[/C][C]1135.71940913542[/C][/ROW]
[ROW][C]92[/C][C]6917[/C][C]6231.56541147607[/C][C]685.434588523935[/C][/ROW]
[ROW][C]93[/C][C]6917[/C][C]6485.27520581774[/C][C]431.724794182258[/C][/ROW]
[ROW][C]94[/C][C]7879[/C][C]7189.82183302986[/C][C]689.178166970141[/C][/ROW]
[ROW][C]95[/C][C]6184[/C][C]6689.14542409978[/C][C]-505.145424099777[/C][/ROW]
[ROW][C]96[/C][C]5079[/C][C]6207.51885273741[/C][C]-1128.51885273741[/C][/ROW]
[ROW][C]97[/C][C]3163[/C][C]4792.37661736828[/C][C]-1629.37661736828[/C][/ROW]
[ROW][C]98[/C][C]4709[/C][C]4481.73448866733[/C][C]227.265511332673[/C][/ROW]
[ROW][C]99[/C][C]4488[/C][C]5068.5786036757[/C][C]-580.5786036757[/C][/ROW]
[ROW][C]100[/C][C]4566[/C][C]4738.28668944919[/C][C]-172.286689449188[/C][/ROW]
[ROW][C]101[/C][C]6333[/C][C]5601.41087930296[/C][C]731.589120697037[/C][/ROW]
[ROW][C]102[/C][C]6112[/C][C]5827.24913106807[/C][C]284.750868931935[/C][/ROW]
[ROW][C]103[/C][C]5300[/C][C]4421.25820095752[/C][C]878.741799042482[/C][/ROW]
[ROW][C]104[/C][C]5671[/C][C]4494.40452766508[/C][C]1176.59547233492[/C][/ROW]
[ROW][C]105[/C][C]5671[/C][C]5088.33619349111[/C][C]582.663806508887[/C][/ROW]
[ROW][C]106[/C][C]6996[/C][C]5971.7522344506[/C][C]1024.2477655494[/C][/ROW]
[ROW][C]107[/C][C]5450[/C][C]5496.85986112768[/C][C]-46.8598611276757[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]5262.22402586184[/C][C]-696.224025861836[/C][/ROW]
[ROW][C]109[/C][C]3163[/C][C]4103.48738606461[/C][C]-940.487386064614[/C][/ROW]
[ROW][C]110[/C][C]5008[/C][C]4750.50723541932[/C][C]257.492764580677[/C][/ROW]
[ROW][C]111[/C][C]4859[/C][C]5218.94015537483[/C][C]-359.940155374828[/C][/ROW]
[ROW][C]112[/C][C]4930[/C][C]5176.54695104849[/C][C]-246.546951048488[/C][/ROW]
[ROW][C]113[/C][C]6476[/C][C]6196.52435884203[/C][C]279.475641157973[/C][/ROW]
[ROW][C]114[/C][C]6333[/C][C]5994.07519782536[/C][C]338.924802174639[/C][/ROW]
[ROW][C]115[/C][C]5813[/C][C]4777.96684271114[/C][C]1035.03315728886[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5061.79343953372[/C][C]830.206560466281[/C][/ROW]
[ROW][C]117[/C][C]6255[/C][C]5279.10339551756[/C][C]975.896604482444[/C][/ROW]
[ROW][C]118[/C][C]7067[/C][C]6591.21466455324[/C][C]475.785335446762[/C][/ROW]
[ROW][C]119[/C][C]5813[/C][C]5478.72733483937[/C][C]334.272665160626[/C][/ROW]
[ROW][C]120[/C][C]4787[/C][C]5434.27681663424[/C][C]-647.276816634238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	21051	21137.6057692308	-86.6057692307731
14	21643	21681.5136742758	-38.5136742758368
15	21864	21876.6825783896	-12.6825783895729
16	21643	21647.4633889691	-4.46338896906309
17	22455	22479.0387914928	-24.0387914928397
18	21935	21978.0331210843	-43.0331210842669
19	20759	21255.7930034246	-496.793003424602
20	20467	20102.9362997479	364.063700252111
21	20467	20413.3461158575	53.6538841425281
22	20610	20391.3382141602	218.661785839802
23	20026	20603.8229051276	-577.822905127639
24	20467	20305.0428450643	161.957154935688
25	20097	20368.2877254567	-271.287725456681
26	20467	20769.0463405366	-302.046340536563
27	21051	20751.2703482002	299.729651799778
28	21272	20764.6759597875	507.324040212545
29	21792	21996.2437424226	-204.243742422565
30	21571	21345.6036334268	225.396366573154
31	20246	20741.1711892185	-495.171189218487
32	19726	19768.6718971996	-42.6718971996415
33	19506	19687.9880307114	-181.988030711404
34	19726	19506.9162467724	219.083753227573
35	19363	19547.0073511866	-184.007351186552
36	19506	19711.3163932312	-205.316393231231
37	19064	19386.9685748307	-322.968574830706
38	19805	19733.2878903225	71.7121096774936
39	20168	20133.512568756	34.4874312439715
40	20246	19974.1554096515	271.844590348501
41	21643	20862.6647544101	780.33524558994
42	21643	21082.8031645832	560.196835416762
43	19805	20598.6218140378	-793.621814037833
44	19363	19486.2067697941	-123.206769794142
45	19363	19314.057484224	48.9425157760124
46	19584	19403.0524041227	180.947595877271
47	18622	19332.3116142435	-710.311614243543
48	18180	19073.3405664496	-893.340566449595
49	17668	18170.480352344	-502.480352343966
50	17817	18445.7356779097	-628.735677909721
51	18480	18265.2453146481	214.754685351858
52	17960	18281.5249137942	-321.52491379423
53	19363	18783.4666955121	579.533304487868
54	19584	18774.0293440118	809.970655988163
55	18180	18183.5051499276	-3.50514992760873
56	17668	17822.3039203778	-154.303920377832
57	17375	17647.0882610202	-272.088261020206
58	17668	17491.7775817719	176.222418228055
59	16855	17214.0147817313	-359.014781731308
60	16563	17181.0323134181	-618.032313418098
61	15388	16566.3648554516	-1178.36485545161
62	15680	16262.017512535	-582.017512535012
63	15751	16276.4800607761	-525.480060776099
64	15830	15569.633784042	260.366215957976
65	17226	16700.5971205659	525.402879434077
66	17076	16676.3935094361	399.606490563921
67	15388	15567.4050548811	-179.405054881123
68	14647	15009.559367054	-362.559367053986
69	14355	14616.799986381	-261.799986381009
70	14725	14534.975424709	190.02457529097
71	13322	14128.7943712689	-806.794371268896
72	12367	13654.8245467469	-1287.82454674688
73	10601	12353.7033095642	-1752.70330956421
74	10750	11673.4125776276	-923.41257762758
75	10750	11380.4082235595	-630.408223559456
76	10601	10704.1120975626	-103.112097562622
77	11854	11548.6930093507	305.306990649326
78	11926	11267.9559324144	658.044067585593
79	10451	10189.6027638129	261.39723618714
80	10159	9893.7845328295	265.215467170505
81	9568	9976.71703565696	-408.717035656964
82	10380	9828.81583104047	551.184168959529
83	8905	9460.87803679673	-555.87803679673
84	8022	9047.88227799039	-1025.88227799039
85	6333	7822.54200152473	-1489.54200152473
86	6697	7491.24174641587	-794.241746415873
87	6255	7330.79510461057	-1075.79510461057
88	6404	6376.33257446613	27.6674255338676
89	7509	7375.52152046658	133.478479533424
90	7730	6996.42816340307	733.571836596927
91	6996	5860.28059086458	1135.71940913542
92	6917	6231.56541147607	685.434588523935
93	6917	6485.27520581774	431.724794182258
94	7879	7189.82183302986	689.178166970141
95	6184	6689.14542409978	-505.145424099777
96	5079	6207.51885273741	-1128.51885273741
97	3163	4792.37661736828	-1629.37661736828
98	4709	4481.73448866733	227.265511332673
99	4488	5068.5786036757	-580.5786036757
100	4566	4738.28668944919	-172.286689449188
101	6333	5601.41087930296	731.589120697037
102	6112	5827.24913106807	284.750868931935
103	5300	4421.25820095752	878.741799042482
104	5671	4494.40452766508	1176.59547233492
105	5671	5088.33619349111	582.663806508887
106	6996	5971.7522344506	1024.2477655494
107	5450	5496.85986112768	-46.8598611276757
108	4566	5262.22402586184	-696.224025861836
109	3163	4103.48738606461	-940.487386064614
110	5008	4750.50723541932	257.492764580677
111	4859	5218.94015537483	-359.940155374828
112	4930	5176.54695104849	-246.546951048488
113	6476	6196.52435884203	279.475641157973
114	6333	5994.07519782536	338.924802174639
115	5813	4777.96684271114	1035.03315728886
116	5892	5061.79343953372	830.206560466281
117	6255	5279.10339551756	975.896604482444
118	7067	6591.21466455324	475.785335446762
119	5813	5478.72733483937	334.272665160626
120	4787	5434.27681663424	-647.276816634238

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	4287.59127274423	3092.4007942745	5482.78175121396
122	5962.63233570193	4430.46980657455	7494.79486482931
123	6129.85493909329	4315.89344410076	7943.81643408583
124	6431.02786359346	4367.63508796435	8494.42063922258
125	7793.27946245838	5502.15988089927	10084.3990440175
126	7416.56734182213	4913.43321147591	9919.70147216836
127	6108.20435708903	3405.0116231625	8811.39709101556
128	5550.28939677292	2656.46027578396	8444.11851776187
129	5152.42477685939	2075.57977809381	8229.26977562496
130	5589.41075450257	2335.83701946576	8842.98448953938
131	4067.50975769978	642.476285178002	7492.54323022156
132	3547.28212538108	-44.7393750948686	7139.30362585704

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4287.59127274423 & 3092.4007942745 & 5482.78175121396 \tabularnewline
122 & 5962.63233570193 & 4430.46980657455 & 7494.79486482931 \tabularnewline
123 & 6129.85493909329 & 4315.89344410076 & 7943.81643408583 \tabularnewline
124 & 6431.02786359346 & 4367.63508796435 & 8494.42063922258 \tabularnewline
125 & 7793.27946245838 & 5502.15988089927 & 10084.3990440175 \tabularnewline
126 & 7416.56734182213 & 4913.43321147591 & 9919.70147216836 \tabularnewline
127 & 6108.20435708903 & 3405.0116231625 & 8811.39709101556 \tabularnewline
128 & 5550.28939677292 & 2656.46027578396 & 8444.11851776187 \tabularnewline
129 & 5152.42477685939 & 2075.57977809381 & 8229.26977562496 \tabularnewline
130 & 5589.41075450257 & 2335.83701946576 & 8842.98448953938 \tabularnewline
131 & 4067.50975769978 & 642.476285178002 & 7492.54323022156 \tabularnewline
132 & 3547.28212538108 & -44.7393750948686 & 7139.30362585704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121[/C][C]4287.59127274423[/C][C]3092.4007942745[/C][C]5482.78175121396[/C][/ROW]
[ROW][C]122[/C][C]5962.63233570193[/C][C]4430.46980657455[/C][C]7494.79486482931[/C][/ROW]
[ROW][C]123[/C][C]6129.85493909329[/C][C]4315.89344410076[/C][C]7943.81643408583[/C][/ROW]
[ROW][C]124[/C][C]6431.02786359346[/C][C]4367.63508796435[/C][C]8494.42063922258[/C][/ROW]
[ROW][C]125[/C][C]7793.27946245838[/C][C]5502.15988089927[/C][C]10084.3990440175[/C][/ROW]
[ROW][C]126[/C][C]7416.56734182213[/C][C]4913.43321147591[/C][C]9919.70147216836[/C][/ROW]
[ROW][C]127[/C][C]6108.20435708903[/C][C]3405.0116231625[/C][C]8811.39709101556[/C][/ROW]
[ROW][C]128[/C][C]5550.28939677292[/C][C]2656.46027578396[/C][C]8444.11851776187[/C][/ROW]
[ROW][C]129[/C][C]5152.42477685939[/C][C]2075.57977809381[/C][C]8229.26977562496[/C][/ROW]
[ROW][C]130[/C][C]5589.41075450257[/C][C]2335.83701946576[/C][C]8842.98448953938[/C][/ROW]
[ROW][C]131[/C][C]4067.50975769978[/C][C]642.476285178002[/C][C]7492.54323022156[/C][/ROW]
[ROW][C]132[/C][C]3547.28212538108[/C][C]-44.7393750948686[/C][C]7139.30362585704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
121	4287.59127274423	3092.4007942745	5482.78175121396
122	5962.63233570193	4430.46980657455	7494.79486482931
123	6129.85493909329	4315.89344410076	7943.81643408583
124	6431.02786359346	4367.63508796435	8494.42063922258
125	7793.27946245838	5502.15988089927	10084.3990440175
126	7416.56734182213	4913.43321147591	9919.70147216836
127	6108.20435708903	3405.0116231625	8811.39709101556
128	5550.28939677292	2656.46027578396	8444.11851776187
129	5152.42477685939	2075.57977809381	8229.26977562496
130	5589.41075450257	2335.83701946576	8842.98448953938
131	4067.50975769978	642.476285178002	7492.54323022156
132	3547.28212538108	-44.7393750948686	7139.30362585704

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