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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 29 Dec 2010 14:15:21 +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/29/t1293631995nuc7pvnv4xaxiht.htm/, Retrieved Fri, 03 May 2024 11:13:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116858, Retrieved Fri, 03 May 2024 11:13:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

116

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

-       [Exponential Smoothing] [exponential smoot...] [2010-12-29 14:15:21] [923770d86edf74ed976a539eae527e37] [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	9 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116858&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116858&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116858&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	9 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.611306563466685
beta	0.0042163536530995
gamma	0.543456035858712

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.611306563466685 \tabularnewline
beta & 0.0042163536530995 \tabularnewline
gamma & 0.543456035858712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116858&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]0.611306563466685[/C][/ROW]
[ROW][C]beta[/C][C]0.0042163536530995[/C][/ROW]
[ROW][C]gamma[/C][C]0.543456035858712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116858&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116858&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	0.611306563466685
beta	0.0042163536530995
gamma	0.543456035858712

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	100.2	100.073758953843	0.126241046156537
14	101.2	101.175925243110	0.0240747568902009
15	99.5	99.5283757246126	-0.0283757246126015
16	100.8	101.046690931865	-0.246690931865302
17	100.7	100.930184121145	-0.23018412114466
18	99.5	99.8294268455624	-0.329426845562381
19	99.4	102.179676415538	-2.77967641553784
20	101.1	97.4995918015234	3.60040819847657
21	97.2	100.148989056564	-2.94898905656382
22	98.1	98.9982205173613	-0.898220517361324
23	97.8	95.7014682991133	2.09853170088667
24	95.5	99.657109506434	-4.15710950643403
25	96.3	95.8502735802102	0.449726419789755
26	93.6	97.071631778231	-3.47163177823107
27	96.7	93.3529540730192	3.34704592698077
28	95.1	96.8104298262166	-1.71042982621664
29	97.7	95.7796133846752	1.92038661532484
30	96.5	95.9947752709451	0.505224729054873
31	98.1	98.2492440286075	-0.149244028607541
32	97.3	96.5321834603746	0.767816539625358
33	97	96.0749007227674	0.925099277232562
34	93.7	97.7110975407261	-4.01109754072614
35	95.6	93.1926032628681	2.40739673713188
36	94.6	95.9451895832956	-1.34518958329562
37	95.1	94.8319869396478	0.268013060352189
38	94.5	95.0941185939793	-0.594118593979275
39	93.6	94.565470387543	-0.965470387542936
40	92.1	94.3001392730265	-2.20013927302651
41	95.9	93.7035862743688	2.19641372563119
42	98.1	93.8106660278394	4.28933397216062
43	98.2	98.244842798676	-0.0448427986759441
44	96.2	96.787783873408	-0.587783873407929
45	94.1	95.5410816366926	-1.44108163669259
46	95	94.659380119631	0.340619880368934
47	93.4	94.1519502448447	-0.751950244844693
48	95.4	94.1670748098099	1.23292519019013
49	93.5	94.975099943669	-1.47509994366891
50	94.5	93.9890248477688	0.510975152231239
51	94.3	94.0594990043168	0.240500995683206
52	95.7	94.2703971101342	1.42960288986579
53	98.4	96.8809770139362	1.51902298606376
54	99.4	96.9874252484805	2.41257475151946
55	99.2	99.378768702455	-0.178768702455059
56	99	97.7170917134642	1.28290828653577
57	99.4	97.4211498433922	1.97885015660785
58	99.3	99.0487723450886	0.251227654911446
59	98.6	98.2375426912802	0.362457308719769
60	98.7	99.4269186556882	-0.726918655688209
61	96	98.4635609572362	-2.46356095723618
62	98.7	97.3235301984307	1.3764698015693
63	100.1	97.8762691605635	2.22373083943647
64	100	99.5929602011838	0.4070397988162
65	101.5	101.700645751741	-0.200645751740836
66	101.5	100.934562447550	0.565437552450476
67	103.8	101.672297241971	2.12770275802882
68	104.1	101.701265645488	2.39873435451166
69	101	102.211569308638	-1.21156930863759
70	104.9	101.539538425765	3.3604615742352
71	104.4	102.634456100791	1.76554389920912
72	105.6	104.51703514563	1.08296485436995
73	103.4	104.260427157478	-0.860427157478412
74	101.7	105.036388879648	-3.33638887964821
75	103.5	102.899508026172	0.600491973828412
76	101.2	103.258139899006	-2.05813989900570
77	105.4	103.778483104434	1.62151689556634
78	105.4	104.289785394418	1.11021460558186
79	108.6	105.729192817119	2.87080718288090
80	110.6	106.23525534015	4.36474465984992
81	110.2	107.121708331375	3.07829166862504
82	106.2	110.140696798502	-3.94069679850176
83	108.6	106.405879818506	2.19412018149447
84	107.5	108.446111311381	-0.946111311380974
85	106.9	106.518970080770	0.381029919229732
86	108.4	107.556435461298	0.843564538702381
87	109.9	108.875543191652	1.02445680834801
88	108.6	108.921457356521	-0.321457356521464
89	106.5	111.492630245337	-4.99263024533687
90	105.7	107.848689090801	-2.14868909080069
91	105.6	107.679225310936	-2.07922531093588
92	104.2	105.460587537077	-1.2605875370773
93	105.1	102.700653613581	2.39934638641905
94	102.7	103.798984124562	-1.09898412456202
95	108.3	103.077215641222	5.22278435877813
96	104.2	106.296582556833	-2.09658255683333
97	105.4	103.962345117945	1.43765488205467
98	104.6	105.718258520970	-1.11825852097039
99	106.4	105.837304203483	0.562695796516635
100	111	105.330555983880	5.66944401612011
101	111.7	110.551843996194	1.14815600380638
102	113.8	111.275653415863	2.52434658413654
103	115.9	114.077512089127	1.82248791087328
104	117.3	114.390282912053	2.90971708794734
105	113.6	114.862338528902	-1.26233852890235
106	113.6	112.924948115477	0.675051884523157
107	114.6	114.765763632705	-0.165763632704582
108	113.2	113.068171268960	0.131828731039647
109	112.8	112.853419018552	-0.0534190185519066
110	109.6	113.215172458439	-3.61517245843929
111	111.1	112.259090562465	-1.15909056246477
112	109.7	111.773061443891	-2.07306144389112
113	113	111.310450763333	1.68954923666658
114	111	112.654376695229	-1.65437669522946
115	113.3	112.725584660595	0.574415339404823
116	111.8	112.497641376262	-0.697641376262212
117	107.2	109.950594114005	-2.75059411400534
118	106.4	107.526184557959	-1.12618455795938
119	110	107.987379206616	2.01262079338409
120	108.2	107.734788514316	0.465211485684023

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.2 & 100.073758953843 & 0.126241046156537 \tabularnewline
14 & 101.2 & 101.175925243110 & 0.0240747568902009 \tabularnewline
15 & 99.5 & 99.5283757246126 & -0.0283757246126015 \tabularnewline
16 & 100.8 & 101.046690931865 & -0.246690931865302 \tabularnewline
17 & 100.7 & 100.930184121145 & -0.23018412114466 \tabularnewline
18 & 99.5 & 99.8294268455624 & -0.329426845562381 \tabularnewline
19 & 99.4 & 102.179676415538 & -2.77967641553784 \tabularnewline
20 & 101.1 & 97.4995918015234 & 3.60040819847657 \tabularnewline
21 & 97.2 & 100.148989056564 & -2.94898905656382 \tabularnewline
22 & 98.1 & 98.9982205173613 & -0.898220517361324 \tabularnewline
23 & 97.8 & 95.7014682991133 & 2.09853170088667 \tabularnewline
24 & 95.5 & 99.657109506434 & -4.15710950643403 \tabularnewline
25 & 96.3 & 95.8502735802102 & 0.449726419789755 \tabularnewline
26 & 93.6 & 97.071631778231 & -3.47163177823107 \tabularnewline
27 & 96.7 & 93.3529540730192 & 3.34704592698077 \tabularnewline
28 & 95.1 & 96.8104298262166 & -1.71042982621664 \tabularnewline
29 & 97.7 & 95.7796133846752 & 1.92038661532484 \tabularnewline
30 & 96.5 & 95.9947752709451 & 0.505224729054873 \tabularnewline
31 & 98.1 & 98.2492440286075 & -0.149244028607541 \tabularnewline
32 & 97.3 & 96.5321834603746 & 0.767816539625358 \tabularnewline
33 & 97 & 96.0749007227674 & 0.925099277232562 \tabularnewline
34 & 93.7 & 97.7110975407261 & -4.01109754072614 \tabularnewline
35 & 95.6 & 93.1926032628681 & 2.40739673713188 \tabularnewline
36 & 94.6 & 95.9451895832956 & -1.34518958329562 \tabularnewline
37 & 95.1 & 94.8319869396478 & 0.268013060352189 \tabularnewline
38 & 94.5 & 95.0941185939793 & -0.594118593979275 \tabularnewline
39 & 93.6 & 94.565470387543 & -0.965470387542936 \tabularnewline
40 & 92.1 & 94.3001392730265 & -2.20013927302651 \tabularnewline
41 & 95.9 & 93.7035862743688 & 2.19641372563119 \tabularnewline
42 & 98.1 & 93.8106660278394 & 4.28933397216062 \tabularnewline
43 & 98.2 & 98.244842798676 & -0.0448427986759441 \tabularnewline
44 & 96.2 & 96.787783873408 & -0.587783873407929 \tabularnewline
45 & 94.1 & 95.5410816366926 & -1.44108163669259 \tabularnewline
46 & 95 & 94.659380119631 & 0.340619880368934 \tabularnewline
47 & 93.4 & 94.1519502448447 & -0.751950244844693 \tabularnewline
48 & 95.4 & 94.1670748098099 & 1.23292519019013 \tabularnewline
49 & 93.5 & 94.975099943669 & -1.47509994366891 \tabularnewline
50 & 94.5 & 93.9890248477688 & 0.510975152231239 \tabularnewline
51 & 94.3 & 94.0594990043168 & 0.240500995683206 \tabularnewline
52 & 95.7 & 94.2703971101342 & 1.42960288986579 \tabularnewline
53 & 98.4 & 96.8809770139362 & 1.51902298606376 \tabularnewline
54 & 99.4 & 96.9874252484805 & 2.41257475151946 \tabularnewline
55 & 99.2 & 99.378768702455 & -0.178768702455059 \tabularnewline
56 & 99 & 97.7170917134642 & 1.28290828653577 \tabularnewline
57 & 99.4 & 97.4211498433922 & 1.97885015660785 \tabularnewline
58 & 99.3 & 99.0487723450886 & 0.251227654911446 \tabularnewline
59 & 98.6 & 98.2375426912802 & 0.362457308719769 \tabularnewline
60 & 98.7 & 99.4269186556882 & -0.726918655688209 \tabularnewline
61 & 96 & 98.4635609572362 & -2.46356095723618 \tabularnewline
62 & 98.7 & 97.3235301984307 & 1.3764698015693 \tabularnewline
63 & 100.1 & 97.8762691605635 & 2.22373083943647 \tabularnewline
64 & 100 & 99.5929602011838 & 0.4070397988162 \tabularnewline
65 & 101.5 & 101.700645751741 & -0.200645751740836 \tabularnewline
66 & 101.5 & 100.934562447550 & 0.565437552450476 \tabularnewline
67 & 103.8 & 101.672297241971 & 2.12770275802882 \tabularnewline
68 & 104.1 & 101.701265645488 & 2.39873435451166 \tabularnewline
69 & 101 & 102.211569308638 & -1.21156930863759 \tabularnewline
70 & 104.9 & 101.539538425765 & 3.3604615742352 \tabularnewline
71 & 104.4 & 102.634456100791 & 1.76554389920912 \tabularnewline
72 & 105.6 & 104.51703514563 & 1.08296485436995 \tabularnewline
73 & 103.4 & 104.260427157478 & -0.860427157478412 \tabularnewline
74 & 101.7 & 105.036388879648 & -3.33638887964821 \tabularnewline
75 & 103.5 & 102.899508026172 & 0.600491973828412 \tabularnewline
76 & 101.2 & 103.258139899006 & -2.05813989900570 \tabularnewline
77 & 105.4 & 103.778483104434 & 1.62151689556634 \tabularnewline
78 & 105.4 & 104.289785394418 & 1.11021460558186 \tabularnewline
79 & 108.6 & 105.729192817119 & 2.87080718288090 \tabularnewline
80 & 110.6 & 106.23525534015 & 4.36474465984992 \tabularnewline
81 & 110.2 & 107.121708331375 & 3.07829166862504 \tabularnewline
82 & 106.2 & 110.140696798502 & -3.94069679850176 \tabularnewline
83 & 108.6 & 106.405879818506 & 2.19412018149447 \tabularnewline
84 & 107.5 & 108.446111311381 & -0.946111311380974 \tabularnewline
85 & 106.9 & 106.518970080770 & 0.381029919229732 \tabularnewline
86 & 108.4 & 107.556435461298 & 0.843564538702381 \tabularnewline
87 & 109.9 & 108.875543191652 & 1.02445680834801 \tabularnewline
88 & 108.6 & 108.921457356521 & -0.321457356521464 \tabularnewline
89 & 106.5 & 111.492630245337 & -4.99263024533687 \tabularnewline
90 & 105.7 & 107.848689090801 & -2.14868909080069 \tabularnewline
91 & 105.6 & 107.679225310936 & -2.07922531093588 \tabularnewline
92 & 104.2 & 105.460587537077 & -1.2605875370773 \tabularnewline
93 & 105.1 & 102.700653613581 & 2.39934638641905 \tabularnewline
94 & 102.7 & 103.798984124562 & -1.09898412456202 \tabularnewline
95 & 108.3 & 103.077215641222 & 5.22278435877813 \tabularnewline
96 & 104.2 & 106.296582556833 & -2.09658255683333 \tabularnewline
97 & 105.4 & 103.962345117945 & 1.43765488205467 \tabularnewline
98 & 104.6 & 105.718258520970 & -1.11825852097039 \tabularnewline
99 & 106.4 & 105.837304203483 & 0.562695796516635 \tabularnewline
100 & 111 & 105.330555983880 & 5.66944401612011 \tabularnewline
101 & 111.7 & 110.551843996194 & 1.14815600380638 \tabularnewline
102 & 113.8 & 111.275653415863 & 2.52434658413654 \tabularnewline
103 & 115.9 & 114.077512089127 & 1.82248791087328 \tabularnewline
104 & 117.3 & 114.390282912053 & 2.90971708794734 \tabularnewline
105 & 113.6 & 114.862338528902 & -1.26233852890235 \tabularnewline
106 & 113.6 & 112.924948115477 & 0.675051884523157 \tabularnewline
107 & 114.6 & 114.765763632705 & -0.165763632704582 \tabularnewline
108 & 113.2 & 113.068171268960 & 0.131828731039647 \tabularnewline
109 & 112.8 & 112.853419018552 & -0.0534190185519066 \tabularnewline
110 & 109.6 & 113.215172458439 & -3.61517245843929 \tabularnewline
111 & 111.1 & 112.259090562465 & -1.15909056246477 \tabularnewline
112 & 109.7 & 111.773061443891 & -2.07306144389112 \tabularnewline
113 & 113 & 111.310450763333 & 1.68954923666658 \tabularnewline
114 & 111 & 112.654376695229 & -1.65437669522946 \tabularnewline
115 & 113.3 & 112.725584660595 & 0.574415339404823 \tabularnewline
116 & 111.8 & 112.497641376262 & -0.697641376262212 \tabularnewline
117 & 107.2 & 109.950594114005 & -2.75059411400534 \tabularnewline
118 & 106.4 & 107.526184557959 & -1.12618455795938 \tabularnewline
119 & 110 & 107.987379206616 & 2.01262079338409 \tabularnewline
120 & 108.2 & 107.734788514316 & 0.465211485684023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116858&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]100.2[/C][C]100.073758953843[/C][C]0.126241046156537[/C][/ROW]
[ROW][C]14[/C][C]101.2[/C][C]101.175925243110[/C][C]0.0240747568902009[/C][/ROW]
[ROW][C]15[/C][C]99.5[/C][C]99.5283757246126[/C][C]-0.0283757246126015[/C][/ROW]
[ROW][C]16[/C][C]100.8[/C][C]101.046690931865[/C][C]-0.246690931865302[/C][/ROW]
[ROW][C]17[/C][C]100.7[/C][C]100.930184121145[/C][C]-0.23018412114466[/C][/ROW]
[ROW][C]18[/C][C]99.5[/C][C]99.8294268455624[/C][C]-0.329426845562381[/C][/ROW]
[ROW][C]19[/C][C]99.4[/C][C]102.179676415538[/C][C]-2.77967641553784[/C][/ROW]
[ROW][C]20[/C][C]101.1[/C][C]97.4995918015234[/C][C]3.60040819847657[/C][/ROW]
[ROW][C]21[/C][C]97.2[/C][C]100.148989056564[/C][C]-2.94898905656382[/C][/ROW]
[ROW][C]22[/C][C]98.1[/C][C]98.9982205173613[/C][C]-0.898220517361324[/C][/ROW]
[ROW][C]23[/C][C]97.8[/C][C]95.7014682991133[/C][C]2.09853170088667[/C][/ROW]
[ROW][C]24[/C][C]95.5[/C][C]99.657109506434[/C][C]-4.15710950643403[/C][/ROW]
[ROW][C]25[/C][C]96.3[/C][C]95.8502735802102[/C][C]0.449726419789755[/C][/ROW]
[ROW][C]26[/C][C]93.6[/C][C]97.071631778231[/C][C]-3.47163177823107[/C][/ROW]
[ROW][C]27[/C][C]96.7[/C][C]93.3529540730192[/C][C]3.34704592698077[/C][/ROW]
[ROW][C]28[/C][C]95.1[/C][C]96.8104298262166[/C][C]-1.71042982621664[/C][/ROW]
[ROW][C]29[/C][C]97.7[/C][C]95.7796133846752[/C][C]1.92038661532484[/C][/ROW]
[ROW][C]30[/C][C]96.5[/C][C]95.9947752709451[/C][C]0.505224729054873[/C][/ROW]
[ROW][C]31[/C][C]98.1[/C][C]98.2492440286075[/C][C]-0.149244028607541[/C][/ROW]
[ROW][C]32[/C][C]97.3[/C][C]96.5321834603746[/C][C]0.767816539625358[/C][/ROW]
[ROW][C]33[/C][C]97[/C][C]96.0749007227674[/C][C]0.925099277232562[/C][/ROW]
[ROW][C]34[/C][C]93.7[/C][C]97.7110975407261[/C][C]-4.01109754072614[/C][/ROW]
[ROW][C]35[/C][C]95.6[/C][C]93.1926032628681[/C][C]2.40739673713188[/C][/ROW]
[ROW][C]36[/C][C]94.6[/C][C]95.9451895832956[/C][C]-1.34518958329562[/C][/ROW]
[ROW][C]37[/C][C]95.1[/C][C]94.8319869396478[/C][C]0.268013060352189[/C][/ROW]
[ROW][C]38[/C][C]94.5[/C][C]95.0941185939793[/C][C]-0.594118593979275[/C][/ROW]
[ROW][C]39[/C][C]93.6[/C][C]94.565470387543[/C][C]-0.965470387542936[/C][/ROW]
[ROW][C]40[/C][C]92.1[/C][C]94.3001392730265[/C][C]-2.20013927302651[/C][/ROW]
[ROW][C]41[/C][C]95.9[/C][C]93.7035862743688[/C][C]2.19641372563119[/C][/ROW]
[ROW][C]42[/C][C]98.1[/C][C]93.8106660278394[/C][C]4.28933397216062[/C][/ROW]
[ROW][C]43[/C][C]98.2[/C][C]98.244842798676[/C][C]-0.0448427986759441[/C][/ROW]
[ROW][C]44[/C][C]96.2[/C][C]96.787783873408[/C][C]-0.587783873407929[/C][/ROW]
[ROW][C]45[/C][C]94.1[/C][C]95.5410816366926[/C][C]-1.44108163669259[/C][/ROW]
[ROW][C]46[/C][C]95[/C][C]94.659380119631[/C][C]0.340619880368934[/C][/ROW]
[ROW][C]47[/C][C]93.4[/C][C]94.1519502448447[/C][C]-0.751950244844693[/C][/ROW]
[ROW][C]48[/C][C]95.4[/C][C]94.1670748098099[/C][C]1.23292519019013[/C][/ROW]
[ROW][C]49[/C][C]93.5[/C][C]94.975099943669[/C][C]-1.47509994366891[/C][/ROW]
[ROW][C]50[/C][C]94.5[/C][C]93.9890248477688[/C][C]0.510975152231239[/C][/ROW]
[ROW][C]51[/C][C]94.3[/C][C]94.0594990043168[/C][C]0.240500995683206[/C][/ROW]
[ROW][C]52[/C][C]95.7[/C][C]94.2703971101342[/C][C]1.42960288986579[/C][/ROW]
[ROW][C]53[/C][C]98.4[/C][C]96.8809770139362[/C][C]1.51902298606376[/C][/ROW]
[ROW][C]54[/C][C]99.4[/C][C]96.9874252484805[/C][C]2.41257475151946[/C][/ROW]
[ROW][C]55[/C][C]99.2[/C][C]99.378768702455[/C][C]-0.178768702455059[/C][/ROW]
[ROW][C]56[/C][C]99[/C][C]97.7170917134642[/C][C]1.28290828653577[/C][/ROW]
[ROW][C]57[/C][C]99.4[/C][C]97.4211498433922[/C][C]1.97885015660785[/C][/ROW]
[ROW][C]58[/C][C]99.3[/C][C]99.0487723450886[/C][C]0.251227654911446[/C][/ROW]
[ROW][C]59[/C][C]98.6[/C][C]98.2375426912802[/C][C]0.362457308719769[/C][/ROW]
[ROW][C]60[/C][C]98.7[/C][C]99.4269186556882[/C][C]-0.726918655688209[/C][/ROW]
[ROW][C]61[/C][C]96[/C][C]98.4635609572362[/C][C]-2.46356095723618[/C][/ROW]
[ROW][C]62[/C][C]98.7[/C][C]97.3235301984307[/C][C]1.3764698015693[/C][/ROW]
[ROW][C]63[/C][C]100.1[/C][C]97.8762691605635[/C][C]2.22373083943647[/C][/ROW]
[ROW][C]64[/C][C]100[/C][C]99.5929602011838[/C][C]0.4070397988162[/C][/ROW]
[ROW][C]65[/C][C]101.5[/C][C]101.700645751741[/C][C]-0.200645751740836[/C][/ROW]
[ROW][C]66[/C][C]101.5[/C][C]100.934562447550[/C][C]0.565437552450476[/C][/ROW]
[ROW][C]67[/C][C]103.8[/C][C]101.672297241971[/C][C]2.12770275802882[/C][/ROW]
[ROW][C]68[/C][C]104.1[/C][C]101.701265645488[/C][C]2.39873435451166[/C][/ROW]
[ROW][C]69[/C][C]101[/C][C]102.211569308638[/C][C]-1.21156930863759[/C][/ROW]
[ROW][C]70[/C][C]104.9[/C][C]101.539538425765[/C][C]3.3604615742352[/C][/ROW]
[ROW][C]71[/C][C]104.4[/C][C]102.634456100791[/C][C]1.76554389920912[/C][/ROW]
[ROW][C]72[/C][C]105.6[/C][C]104.51703514563[/C][C]1.08296485436995[/C][/ROW]
[ROW][C]73[/C][C]103.4[/C][C]104.260427157478[/C][C]-0.860427157478412[/C][/ROW]
[ROW][C]74[/C][C]101.7[/C][C]105.036388879648[/C][C]-3.33638887964821[/C][/ROW]
[ROW][C]75[/C][C]103.5[/C][C]102.899508026172[/C][C]0.600491973828412[/C][/ROW]
[ROW][C]76[/C][C]101.2[/C][C]103.258139899006[/C][C]-2.05813989900570[/C][/ROW]
[ROW][C]77[/C][C]105.4[/C][C]103.778483104434[/C][C]1.62151689556634[/C][/ROW]
[ROW][C]78[/C][C]105.4[/C][C]104.289785394418[/C][C]1.11021460558186[/C][/ROW]
[ROW][C]79[/C][C]108.6[/C][C]105.729192817119[/C][C]2.87080718288090[/C][/ROW]
[ROW][C]80[/C][C]110.6[/C][C]106.23525534015[/C][C]4.36474465984992[/C][/ROW]
[ROW][C]81[/C][C]110.2[/C][C]107.121708331375[/C][C]3.07829166862504[/C][/ROW]
[ROW][C]82[/C][C]106.2[/C][C]110.140696798502[/C][C]-3.94069679850176[/C][/ROW]
[ROW][C]83[/C][C]108.6[/C][C]106.405879818506[/C][C]2.19412018149447[/C][/ROW]
[ROW][C]84[/C][C]107.5[/C][C]108.446111311381[/C][C]-0.946111311380974[/C][/ROW]
[ROW][C]85[/C][C]106.9[/C][C]106.518970080770[/C][C]0.381029919229732[/C][/ROW]
[ROW][C]86[/C][C]108.4[/C][C]107.556435461298[/C][C]0.843564538702381[/C][/ROW]
[ROW][C]87[/C][C]109.9[/C][C]108.875543191652[/C][C]1.02445680834801[/C][/ROW]
[ROW][C]88[/C][C]108.6[/C][C]108.921457356521[/C][C]-0.321457356521464[/C][/ROW]
[ROW][C]89[/C][C]106.5[/C][C]111.492630245337[/C][C]-4.99263024533687[/C][/ROW]
[ROW][C]90[/C][C]105.7[/C][C]107.848689090801[/C][C]-2.14868909080069[/C][/ROW]
[ROW][C]91[/C][C]105.6[/C][C]107.679225310936[/C][C]-2.07922531093588[/C][/ROW]
[ROW][C]92[/C][C]104.2[/C][C]105.460587537077[/C][C]-1.2605875370773[/C][/ROW]
[ROW][C]93[/C][C]105.1[/C][C]102.700653613581[/C][C]2.39934638641905[/C][/ROW]
[ROW][C]94[/C][C]102.7[/C][C]103.798984124562[/C][C]-1.09898412456202[/C][/ROW]
[ROW][C]95[/C][C]108.3[/C][C]103.077215641222[/C][C]5.22278435877813[/C][/ROW]
[ROW][C]96[/C][C]104.2[/C][C]106.296582556833[/C][C]-2.09658255683333[/C][/ROW]
[ROW][C]97[/C][C]105.4[/C][C]103.962345117945[/C][C]1.43765488205467[/C][/ROW]
[ROW][C]98[/C][C]104.6[/C][C]105.718258520970[/C][C]-1.11825852097039[/C][/ROW]
[ROW][C]99[/C][C]106.4[/C][C]105.837304203483[/C][C]0.562695796516635[/C][/ROW]
[ROW][C]100[/C][C]111[/C][C]105.330555983880[/C][C]5.66944401612011[/C][/ROW]
[ROW][C]101[/C][C]111.7[/C][C]110.551843996194[/C][C]1.14815600380638[/C][/ROW]
[ROW][C]102[/C][C]113.8[/C][C]111.275653415863[/C][C]2.52434658413654[/C][/ROW]
[ROW][C]103[/C][C]115.9[/C][C]114.077512089127[/C][C]1.82248791087328[/C][/ROW]
[ROW][C]104[/C][C]117.3[/C][C]114.390282912053[/C][C]2.90971708794734[/C][/ROW]
[ROW][C]105[/C][C]113.6[/C][C]114.862338528902[/C][C]-1.26233852890235[/C][/ROW]
[ROW][C]106[/C][C]113.6[/C][C]112.924948115477[/C][C]0.675051884523157[/C][/ROW]
[ROW][C]107[/C][C]114.6[/C][C]114.765763632705[/C][C]-0.165763632704582[/C][/ROW]
[ROW][C]108[/C][C]113.2[/C][C]113.068171268960[/C][C]0.131828731039647[/C][/ROW]
[ROW][C]109[/C][C]112.8[/C][C]112.853419018552[/C][C]-0.0534190185519066[/C][/ROW]
[ROW][C]110[/C][C]109.6[/C][C]113.215172458439[/C][C]-3.61517245843929[/C][/ROW]
[ROW][C]111[/C][C]111.1[/C][C]112.259090562465[/C][C]-1.15909056246477[/C][/ROW]
[ROW][C]112[/C][C]109.7[/C][C]111.773061443891[/C][C]-2.07306144389112[/C][/ROW]
[ROW][C]113[/C][C]113[/C][C]111.310450763333[/C][C]1.68954923666658[/C][/ROW]
[ROW][C]114[/C][C]111[/C][C]112.654376695229[/C][C]-1.65437669522946[/C][/ROW]
[ROW][C]115[/C][C]113.3[/C][C]112.725584660595[/C][C]0.574415339404823[/C][/ROW]
[ROW][C]116[/C][C]111.8[/C][C]112.497641376262[/C][C]-0.697641376262212[/C][/ROW]
[ROW][C]117[/C][C]107.2[/C][C]109.950594114005[/C][C]-2.75059411400534[/C][/ROW]
[ROW][C]118[/C][C]106.4[/C][C]107.526184557959[/C][C]-1.12618455795938[/C][/ROW]
[ROW][C]119[/C][C]110[/C][C]107.987379206616[/C][C]2.01262079338409[/C][/ROW]
[ROW][C]120[/C][C]108.2[/C][C]107.734788514316[/C][C]0.465211485684023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116858&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116858&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	100.2	100.073758953843	0.126241046156537
14	101.2	101.175925243110	0.0240747568902009
15	99.5	99.5283757246126	-0.0283757246126015
16	100.8	101.046690931865	-0.246690931865302
17	100.7	100.930184121145	-0.23018412114466
18	99.5	99.8294268455624	-0.329426845562381
19	99.4	102.179676415538	-2.77967641553784
20	101.1	97.4995918015234	3.60040819847657
21	97.2	100.148989056564	-2.94898905656382
22	98.1	98.9982205173613	-0.898220517361324
23	97.8	95.7014682991133	2.09853170088667
24	95.5	99.657109506434	-4.15710950643403
25	96.3	95.8502735802102	0.449726419789755
26	93.6	97.071631778231	-3.47163177823107
27	96.7	93.3529540730192	3.34704592698077
28	95.1	96.8104298262166	-1.71042982621664
29	97.7	95.7796133846752	1.92038661532484
30	96.5	95.9947752709451	0.505224729054873
31	98.1	98.2492440286075	-0.149244028607541
32	97.3	96.5321834603746	0.767816539625358
33	97	96.0749007227674	0.925099277232562
34	93.7	97.7110975407261	-4.01109754072614
35	95.6	93.1926032628681	2.40739673713188
36	94.6	95.9451895832956	-1.34518958329562
37	95.1	94.8319869396478	0.268013060352189
38	94.5	95.0941185939793	-0.594118593979275
39	93.6	94.565470387543	-0.965470387542936
40	92.1	94.3001392730265	-2.20013927302651
41	95.9	93.7035862743688	2.19641372563119
42	98.1	93.8106660278394	4.28933397216062
43	98.2	98.244842798676	-0.0448427986759441
44	96.2	96.787783873408	-0.587783873407929
45	94.1	95.5410816366926	-1.44108163669259
46	95	94.659380119631	0.340619880368934
47	93.4	94.1519502448447	-0.751950244844693
48	95.4	94.1670748098099	1.23292519019013
49	93.5	94.975099943669	-1.47509994366891
50	94.5	93.9890248477688	0.510975152231239
51	94.3	94.0594990043168	0.240500995683206
52	95.7	94.2703971101342	1.42960288986579
53	98.4	96.8809770139362	1.51902298606376
54	99.4	96.9874252484805	2.41257475151946
55	99.2	99.378768702455	-0.178768702455059
56	99	97.7170917134642	1.28290828653577
57	99.4	97.4211498433922	1.97885015660785
58	99.3	99.0487723450886	0.251227654911446
59	98.6	98.2375426912802	0.362457308719769
60	98.7	99.4269186556882	-0.726918655688209
61	96	98.4635609572362	-2.46356095723618
62	98.7	97.3235301984307	1.3764698015693
63	100.1	97.8762691605635	2.22373083943647
64	100	99.5929602011838	0.4070397988162
65	101.5	101.700645751741	-0.200645751740836
66	101.5	100.934562447550	0.565437552450476
67	103.8	101.672297241971	2.12770275802882
68	104.1	101.701265645488	2.39873435451166
69	101	102.211569308638	-1.21156930863759
70	104.9	101.539538425765	3.3604615742352
71	104.4	102.634456100791	1.76554389920912
72	105.6	104.51703514563	1.08296485436995
73	103.4	104.260427157478	-0.860427157478412
74	101.7	105.036388879648	-3.33638887964821
75	103.5	102.899508026172	0.600491973828412
76	101.2	103.258139899006	-2.05813989900570
77	105.4	103.778483104434	1.62151689556634
78	105.4	104.289785394418	1.11021460558186
79	108.6	105.729192817119	2.87080718288090
80	110.6	106.23525534015	4.36474465984992
81	110.2	107.121708331375	3.07829166862504
82	106.2	110.140696798502	-3.94069679850176
83	108.6	106.405879818506	2.19412018149447
84	107.5	108.446111311381	-0.946111311380974
85	106.9	106.518970080770	0.381029919229732
86	108.4	107.556435461298	0.843564538702381
87	109.9	108.875543191652	1.02445680834801
88	108.6	108.921457356521	-0.321457356521464
89	106.5	111.492630245337	-4.99263024533687
90	105.7	107.848689090801	-2.14868909080069
91	105.6	107.679225310936	-2.07922531093588
92	104.2	105.460587537077	-1.2605875370773
93	105.1	102.700653613581	2.39934638641905
94	102.7	103.798984124562	-1.09898412456202
95	108.3	103.077215641222	5.22278435877813
96	104.2	106.296582556833	-2.09658255683333
97	105.4	103.962345117945	1.43765488205467
98	104.6	105.718258520970	-1.11825852097039
99	106.4	105.837304203483	0.562695796516635
100	111	105.330555983880	5.66944401612011
101	111.7	110.551843996194	1.14815600380638
102	113.8	111.275653415863	2.52434658413654
103	115.9	114.077512089127	1.82248791087328
104	117.3	114.390282912053	2.90971708794734
105	113.6	114.862338528902	-1.26233852890235
106	113.6	112.924948115477	0.675051884523157
107	114.6	114.765763632705	-0.165763632704582
108	113.2	113.068171268960	0.131828731039647
109	112.8	112.853419018552	-0.0534190185519066
110	109.6	113.215172458439	-3.61517245843929
111	111.1	112.259090562465	-1.15909056246477
112	109.7	111.773061443891	-2.07306144389112
113	113	111.310450763333	1.68954923666658
114	111	112.654376695229	-1.65437669522946
115	113.3	112.725584660595	0.574415339404823
116	111.8	112.497641376262	-0.697641376262212
117	107.2	109.950594114005	-2.75059411400534
118	106.4	107.526184557959	-1.12618455795938
119	110	107.987379206616	2.01262079338409
120	108.2	107.734788514316	0.465211485684023

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	107.678970249798	104.382891224621	110.975049274975
122	107.301999061144	103.194149464670	111.409848657618
123	109.013790636026	104.179692190779	113.847889081273
124	109.028504522773	103.594000894275	114.463008151271
125	110.605636955157	104.566435622978	116.644838287335
126	110.206291469366	103.685986693286	116.726596245445
127	111.739955480428	104.675813666229	118.804097294628
128	110.896951325895	103.440055521015	118.353847130775
129	108.353520173819	100.625732315036	116.081308032602
130	107.953206177576	99.8427946084802	116.063617746673
131	109.790700220231	101.164772523165	118.416627917297
132	107.979427658106	-174.529727147312	390.488582463524

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 107.678970249798 & 104.382891224621 & 110.975049274975 \tabularnewline
122 & 107.301999061144 & 103.194149464670 & 111.409848657618 \tabularnewline
123 & 109.013790636026 & 104.179692190779 & 113.847889081273 \tabularnewline
124 & 109.028504522773 & 103.594000894275 & 114.463008151271 \tabularnewline
125 & 110.605636955157 & 104.566435622978 & 116.644838287335 \tabularnewline
126 & 110.206291469366 & 103.685986693286 & 116.726596245445 \tabularnewline
127 & 111.739955480428 & 104.675813666229 & 118.804097294628 \tabularnewline
128 & 110.896951325895 & 103.440055521015 & 118.353847130775 \tabularnewline
129 & 108.353520173819 & 100.625732315036 & 116.081308032602 \tabularnewline
130 & 107.953206177576 & 99.8427946084802 & 116.063617746673 \tabularnewline
131 & 109.790700220231 & 101.164772523165 & 118.416627917297 \tabularnewline
132 & 107.979427658106 & -174.529727147312 & 390.488582463524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116858&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]107.678970249798[/C][C]104.382891224621[/C][C]110.975049274975[/C][/ROW]
[ROW][C]122[/C][C]107.301999061144[/C][C]103.194149464670[/C][C]111.409848657618[/C][/ROW]
[ROW][C]123[/C][C]109.013790636026[/C][C]104.179692190779[/C][C]113.847889081273[/C][/ROW]
[ROW][C]124[/C][C]109.028504522773[/C][C]103.594000894275[/C][C]114.463008151271[/C][/ROW]
[ROW][C]125[/C][C]110.605636955157[/C][C]104.566435622978[/C][C]116.644838287335[/C][/ROW]
[ROW][C]126[/C][C]110.206291469366[/C][C]103.685986693286[/C][C]116.726596245445[/C][/ROW]
[ROW][C]127[/C][C]111.739955480428[/C][C]104.675813666229[/C][C]118.804097294628[/C][/ROW]
[ROW][C]128[/C][C]110.896951325895[/C][C]103.440055521015[/C][C]118.353847130775[/C][/ROW]
[ROW][C]129[/C][C]108.353520173819[/C][C]100.625732315036[/C][C]116.081308032602[/C][/ROW]
[ROW][C]130[/C][C]107.953206177576[/C][C]99.8427946084802[/C][C]116.063617746673[/C][/ROW]
[ROW][C]131[/C][C]109.790700220231[/C][C]101.164772523165[/C][C]118.416627917297[/C][/ROW]
[ROW][C]132[/C][C]107.979427658106[/C][C]-174.529727147312[/C][C]390.488582463524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116858&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116858&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	107.678970249798	104.382891224621	110.975049274975
122	107.301999061144	103.194149464670	111.409848657618
123	109.013790636026	104.179692190779	113.847889081273
124	109.028504522773	103.594000894275	114.463008151271
125	110.605636955157	104.566435622978	116.644838287335
126	110.206291469366	103.685986693286	116.726596245445
127	111.739955480428	104.675813666229	118.804097294628
128	110.896951325895	103.440055521015	118.353847130775
129	108.353520173819	100.625732315036	116.081308032602
130	107.953206177576	99.8427946084802	116.063617746673
131	109.790700220231	101.164772523165	118.416627917297
132	107.979427658106	-174.529727147312	390.488582463524

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 = 4 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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