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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 May 2012 15:30:19 -0400

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/2012/May/28/t13382337833lokag0jdyja42h.htm/, Retrieved Wed, 01 May 2024 23:35:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167864, Retrieved Wed, 01 May 2024 23:35:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

102

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

-     [(Partial) Autocorrelation Function] [KDGP2W12] [2012-04-07 16:19:00] [6285f4e2f27456c551d88825e9bb3ea0]
- RMP     [Exponential Smoothing] [KDGP2W102] [2012-05-28 19:30:19] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

3,9
5,9
5,7
3,6
4,9
5,3
8,7
6,8
8,9
9,6
11,2
9,9
9,3
9,2
9,4
12,7
13,6
16,1
14,8
14,1
13,2
8,7
4,9
-1,3
-3,9
-6
-6,6
-8,7
-11,6
-14,6
-12,9
-13,8
-14,1
-13,2
-10,4
-3,3
1
3,1
4,5
1,9
3,9
7
5,6
8,1
6,1
8
6,5
5,6
4,8
5,1
7,8
10,3
8,6
6,8
4,9
5,4
5,5
4,7
4,2
5
5
6
2,9
3,6
5,1
2,9
4,7
3
5
2,6
3,2
2,4
3,2
2,6
2,4
2,1
2,7
4,4
4,3
4,2
5,5
8,8
10,1
7
5,7
5,2
5,5
7,3
5,9
7,1
6,9
6,7
4,7
6,7
8,5
2,1
-0,9
-4,7
4,8
2,6
1,7
-1,8
0,2
1,9
3,2
3,1
4,2
16,2
18,3
21,6
12,6
9,8
10,6
13
9,7
7,9
3,3
3,4
0,4
0,7
1,4
3,8
4
8
6
5,8
3,9
6,4
11

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167864&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167864&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999932001538549
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999932001538549 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167864&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]0.999932001538549[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167864&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	0.999932001538549
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	5.9	3.9	2
3	5.7	5.8998640030771	-0.199864003077098
4	3.6	5.70001359044471	-2.10001359044471
5	4.9	3.60014279769318	1.29985720230682
6	5.3	4.89991161171014	0.400088388289863
7	8.7	5.29997279460515	3.40002720539485
8	6.8	8.69976880338114	-1.89976880338114
9	8.9	6.80012918135574	2.09987081864426
10	9.6	8.89985721201509	0.700142787984914
11	11.2	9.59995239136762	1.60004760863238
12	9.9	11.1998911992244	-1.29989119922436
13	9.3	9.9000883906016	-0.6000883906016
14	9.2	9.3000408050873	-0.100040805087296
15	9.4	9.20000680262083	0.199993197379174
16	12.7	9.39998640077028	3.30001359922972
17	13.6	12.6997756041525	0.900224395847516
18	16.1	13.5999387861261	2.50006121387388
19	14.8	16.0998299996839	-1.29982999968392
20	14.1	14.8000883864401	-0.700088386440127
21	13.2	14.1000476049332	-0.900047604933158
22	8.7	13.2000612018524	-4.50006120185237
23	4.9	8.70030599723816	-3.80030599723816
24	-1.3	4.90025841496086	-6.20025841496086
25	-3.9	-1.29957839196718	-2.60042160803282
26	-6	-3.89982317533153	-2.10017682466847
27	-6.6	-5.99985719120715	-0.600142808792853
28	-8.7	-6.59995919121235	-2.10004080878765
29	-11.6	-8.69985720045602	-2.90014279954398
30	-14.6	-11.5998027947516	-3.00019720524836
31	-12.9	-14.599795991206	1.69979599120599
32	-13.8	-12.9001155835122	-0.899884416487817
33	-14.1	-13.7999388092442	-0.300061190755804
34	-13.2	-14.0999795963007	0.899979596300687
35	-10.4	-13.2000611972279	2.80006119722789
36	-3.3	-10.4001903998534	7.10019039985338
37	1	-3.3004828020232	4.3004828020232
38	3.1	0.999707573785965	2.10029242621404
39	4.5	3.09985718334642	1.40014281665358
40	1.9	4.49990479244266	-2.59990479244266
41	3.9	1.90017678952581	1.99982321047419
42	7	3.89986401509851	3.10013598490149
43	5.6	6.99978919552274	-1.39978919552274
44	8.1	5.60009518351165	2.49990481648835
45	6.1	8.0998300103187	-1.9998300103187
46	8	6.10013598536387	1.89986401463613
47	6.5	7.99987081217004	-1.49987081217004
48	5.6	6.5001019889076	-0.900101988907604
49	4.8	5.60006120555039	-0.800061205550395
50	5.1	4.80005440293104	0.299945597068955
51	7.8	5.09997960416088	2.70002039583912
52	10.3	7.7998164027672	2.50018359723281
53	8.6	10.299829991362	-1.69982999136204
54	6.8	8.60011558582414	-1.80011558582414
55	4.9	6.80012240509027	-1.90012240509027
56	5.4	4.90012920540012	0.499870794599885
57	5.5	5.39996600955504	0.100033990444957
58	4.7	5.49999319784256	-0.799993197842556
59	4.2	4.70005439830662	-0.500054398306625
60	5	4.20003400292973	0.799965997070273
61	5	4.99994560354299	5.43964570143274e-05
62	6	4.99999999630113	1.00000000369887
63	2.9	5.9999320015383	-3.0999320015383
64	3.6	2.90021079060671	0.699789209393292
65	5.1	3.59995241541042	1.50004758458958
66	2.9	5.09989799907214	-2.19989799907214
67	4.7	2.90014958967929	1.79985041032071
68	3	4.69987761294126	-1.69987761294126
69	5	3.00011558906234	1.99988441093766
70	2.6	4.99986401093698	-2.39986401093698
71	3.2	2.60016318706044	0.599836812939564
72	2.4	3.1999592120196	-0.799959212019599
73	3.2	2.40005439599564	0.799945604004359
74	2.6	3.19994560492968	-0.599945604929683
75	2.4	2.60004079537809	-0.20004079537809
76	2.1	2.40001360246631	-0.300013602466313
77	2.7	2.10002040046338	0.599979599536618
78	4.4	2.69995920231033	1.70004079768967
79	4.3	4.39988439984135	-0.0998843998413532
80	4.2	4.30000679198551	-0.100006791985511
81	5.5	4.20000680030799	1.29999319969201
82	8.8	5.49991160246252	3.30008839753748
83	10.1	8.79977559906632	1.30022440093368
84	7	10.0999115867412	-3.09991158674119
85	5.7	7.00021078921853	-1.30021078921853
86	5.2	5.70008841233323	-0.50008841233323
87	5.5	5.20003400524263	0.299965994757372
88	7.3	5.49997960277387	1.80002039722613
89	5.9	7.29987760138241	-1.39987760138241
90	7.1	5.90009518952311	1.19990481047688
91	6.9	7.099918408319	-0.199918408318998
92	6.7	6.90001359414418	-0.200013594144182
93	4.7	6.70001360061667	-2.00001360061667
94	6.7	4.70013599784772	1.99986400215228
95	8.5	6.69986401232474	1.80013598767526
96	2.1	8.49987759352243	-6.39987759352243
97	-0.9	2.10043518182984	-3.00043518182984
98	-4.7	-0.899795975023951	-3.80020402497605
99	4.8	-4.6997415919731	9.4997415919731
100	2.6	4.79935403218756	-2.19935403218756
101	1.7	2.60014955269038	-0.900149552690376
102	-1.8	1.70006120878466	-3.50006120878466
103	0.2	-1.79976200122282	1.99976200122282
104	1.9	0.199864019260648	1.70013598073935
105	3.2	1.89988439336905	1.30011560663095
106	3.1	3.19991159413904	-0.0999115941390403
107	4.2	3.10000679383468	1.09999320616532
108	16.2	4.19992520215437	12.0000747978456
109	18.3	16.1991840133764	2.10081598662356
110	21.6	18.2998571477451	3.30014285225488
111	12.6	21.5997755953635	-8.99977559536348
112	9.8	12.6006119708939	-2.80061197089389
113	10.6	9.80019043730514	0.799809562694856
114	13	10.5999456141803	2.40005438581972
115	9.7	12.9998367999944	-3.29983679999436
116	7.9	9.70022438382544	-1.80022438382544
117	3.3	7.90012241248837	-4.60012241248837
118	3.4	3.30031280124654	0.0996871987534629
119	0.4	3.39999322142386	-2.99999322142386
120	0.7	0.400203994923421	0.299796005076579
121	1.4	0.699979614332905	0.700020385667094
122	3.8	1.39995239969079	2.40004760030921
123	4	3.79983680045577	0.200163199544231
124	8	3.99998638921039	4.00001361078961
125	6	7.99972800522868	-1.99972800522868
126	5.8	6.00013597842768	-0.200135978427677
127	3.9	5.80001360893861	-1.90001360893861
128	6.4	3.90012919800214	2.49987080199786
129	11	6.39983001263164	4.60016998736836

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5.9 & 3.9 & 2 \tabularnewline
3 & 5.7 & 5.8998640030771 & -0.199864003077098 \tabularnewline
4 & 3.6 & 5.70001359044471 & -2.10001359044471 \tabularnewline
5 & 4.9 & 3.60014279769318 & 1.29985720230682 \tabularnewline
6 & 5.3 & 4.89991161171014 & 0.400088388289863 \tabularnewline
7 & 8.7 & 5.29997279460515 & 3.40002720539485 \tabularnewline
8 & 6.8 & 8.69976880338114 & -1.89976880338114 \tabularnewline
9 & 8.9 & 6.80012918135574 & 2.09987081864426 \tabularnewline
10 & 9.6 & 8.89985721201509 & 0.700142787984914 \tabularnewline
11 & 11.2 & 9.59995239136762 & 1.60004760863238 \tabularnewline
12 & 9.9 & 11.1998911992244 & -1.29989119922436 \tabularnewline
13 & 9.3 & 9.9000883906016 & -0.6000883906016 \tabularnewline
14 & 9.2 & 9.3000408050873 & -0.100040805087296 \tabularnewline
15 & 9.4 & 9.20000680262083 & 0.199993197379174 \tabularnewline
16 & 12.7 & 9.39998640077028 & 3.30001359922972 \tabularnewline
17 & 13.6 & 12.6997756041525 & 0.900224395847516 \tabularnewline
18 & 16.1 & 13.5999387861261 & 2.50006121387388 \tabularnewline
19 & 14.8 & 16.0998299996839 & -1.29982999968392 \tabularnewline
20 & 14.1 & 14.8000883864401 & -0.700088386440127 \tabularnewline
21 & 13.2 & 14.1000476049332 & -0.900047604933158 \tabularnewline
22 & 8.7 & 13.2000612018524 & -4.50006120185237 \tabularnewline
23 & 4.9 & 8.70030599723816 & -3.80030599723816 \tabularnewline
24 & -1.3 & 4.90025841496086 & -6.20025841496086 \tabularnewline
25 & -3.9 & -1.29957839196718 & -2.60042160803282 \tabularnewline
26 & -6 & -3.89982317533153 & -2.10017682466847 \tabularnewline
27 & -6.6 & -5.99985719120715 & -0.600142808792853 \tabularnewline
28 & -8.7 & -6.59995919121235 & -2.10004080878765 \tabularnewline
29 & -11.6 & -8.69985720045602 & -2.90014279954398 \tabularnewline
30 & -14.6 & -11.5998027947516 & -3.00019720524836 \tabularnewline
31 & -12.9 & -14.599795991206 & 1.69979599120599 \tabularnewline
32 & -13.8 & -12.9001155835122 & -0.899884416487817 \tabularnewline
33 & -14.1 & -13.7999388092442 & -0.300061190755804 \tabularnewline
34 & -13.2 & -14.0999795963007 & 0.899979596300687 \tabularnewline
35 & -10.4 & -13.2000611972279 & 2.80006119722789 \tabularnewline
36 & -3.3 & -10.4001903998534 & 7.10019039985338 \tabularnewline
37 & 1 & -3.3004828020232 & 4.3004828020232 \tabularnewline
38 & 3.1 & 0.999707573785965 & 2.10029242621404 \tabularnewline
39 & 4.5 & 3.09985718334642 & 1.40014281665358 \tabularnewline
40 & 1.9 & 4.49990479244266 & -2.59990479244266 \tabularnewline
41 & 3.9 & 1.90017678952581 & 1.99982321047419 \tabularnewline
42 & 7 & 3.89986401509851 & 3.10013598490149 \tabularnewline
43 & 5.6 & 6.99978919552274 & -1.39978919552274 \tabularnewline
44 & 8.1 & 5.60009518351165 & 2.49990481648835 \tabularnewline
45 & 6.1 & 8.0998300103187 & -1.9998300103187 \tabularnewline
46 & 8 & 6.10013598536387 & 1.89986401463613 \tabularnewline
47 & 6.5 & 7.99987081217004 & -1.49987081217004 \tabularnewline
48 & 5.6 & 6.5001019889076 & -0.900101988907604 \tabularnewline
49 & 4.8 & 5.60006120555039 & -0.800061205550395 \tabularnewline
50 & 5.1 & 4.80005440293104 & 0.299945597068955 \tabularnewline
51 & 7.8 & 5.09997960416088 & 2.70002039583912 \tabularnewline
52 & 10.3 & 7.7998164027672 & 2.50018359723281 \tabularnewline
53 & 8.6 & 10.299829991362 & -1.69982999136204 \tabularnewline
54 & 6.8 & 8.60011558582414 & -1.80011558582414 \tabularnewline
55 & 4.9 & 6.80012240509027 & -1.90012240509027 \tabularnewline
56 & 5.4 & 4.90012920540012 & 0.499870794599885 \tabularnewline
57 & 5.5 & 5.39996600955504 & 0.100033990444957 \tabularnewline
58 & 4.7 & 5.49999319784256 & -0.799993197842556 \tabularnewline
59 & 4.2 & 4.70005439830662 & -0.500054398306625 \tabularnewline
60 & 5 & 4.20003400292973 & 0.799965997070273 \tabularnewline
61 & 5 & 4.99994560354299 & 5.43964570143274e-05 \tabularnewline
62 & 6 & 4.99999999630113 & 1.00000000369887 \tabularnewline
63 & 2.9 & 5.9999320015383 & -3.0999320015383 \tabularnewline
64 & 3.6 & 2.90021079060671 & 0.699789209393292 \tabularnewline
65 & 5.1 & 3.59995241541042 & 1.50004758458958 \tabularnewline
66 & 2.9 & 5.09989799907214 & -2.19989799907214 \tabularnewline
67 & 4.7 & 2.90014958967929 & 1.79985041032071 \tabularnewline
68 & 3 & 4.69987761294126 & -1.69987761294126 \tabularnewline
69 & 5 & 3.00011558906234 & 1.99988441093766 \tabularnewline
70 & 2.6 & 4.99986401093698 & -2.39986401093698 \tabularnewline
71 & 3.2 & 2.60016318706044 & 0.599836812939564 \tabularnewline
72 & 2.4 & 3.1999592120196 & -0.799959212019599 \tabularnewline
73 & 3.2 & 2.40005439599564 & 0.799945604004359 \tabularnewline
74 & 2.6 & 3.19994560492968 & -0.599945604929683 \tabularnewline
75 & 2.4 & 2.60004079537809 & -0.20004079537809 \tabularnewline
76 & 2.1 & 2.40001360246631 & -0.300013602466313 \tabularnewline
77 & 2.7 & 2.10002040046338 & 0.599979599536618 \tabularnewline
78 & 4.4 & 2.69995920231033 & 1.70004079768967 \tabularnewline
79 & 4.3 & 4.39988439984135 & -0.0998843998413532 \tabularnewline
80 & 4.2 & 4.30000679198551 & -0.100006791985511 \tabularnewline
81 & 5.5 & 4.20000680030799 & 1.29999319969201 \tabularnewline
82 & 8.8 & 5.49991160246252 & 3.30008839753748 \tabularnewline
83 & 10.1 & 8.79977559906632 & 1.30022440093368 \tabularnewline
84 & 7 & 10.0999115867412 & -3.09991158674119 \tabularnewline
85 & 5.7 & 7.00021078921853 & -1.30021078921853 \tabularnewline
86 & 5.2 & 5.70008841233323 & -0.50008841233323 \tabularnewline
87 & 5.5 & 5.20003400524263 & 0.299965994757372 \tabularnewline
88 & 7.3 & 5.49997960277387 & 1.80002039722613 \tabularnewline
89 & 5.9 & 7.29987760138241 & -1.39987760138241 \tabularnewline
90 & 7.1 & 5.90009518952311 & 1.19990481047688 \tabularnewline
91 & 6.9 & 7.099918408319 & -0.199918408318998 \tabularnewline
92 & 6.7 & 6.90001359414418 & -0.200013594144182 \tabularnewline
93 & 4.7 & 6.70001360061667 & -2.00001360061667 \tabularnewline
94 & 6.7 & 4.70013599784772 & 1.99986400215228 \tabularnewline
95 & 8.5 & 6.69986401232474 & 1.80013598767526 \tabularnewline
96 & 2.1 & 8.49987759352243 & -6.39987759352243 \tabularnewline
97 & -0.9 & 2.10043518182984 & -3.00043518182984 \tabularnewline
98 & -4.7 & -0.899795975023951 & -3.80020402497605 \tabularnewline
99 & 4.8 & -4.6997415919731 & 9.4997415919731 \tabularnewline
100 & 2.6 & 4.79935403218756 & -2.19935403218756 \tabularnewline
101 & 1.7 & 2.60014955269038 & -0.900149552690376 \tabularnewline
102 & -1.8 & 1.70006120878466 & -3.50006120878466 \tabularnewline
103 & 0.2 & -1.79976200122282 & 1.99976200122282 \tabularnewline
104 & 1.9 & 0.199864019260648 & 1.70013598073935 \tabularnewline
105 & 3.2 & 1.89988439336905 & 1.30011560663095 \tabularnewline
106 & 3.1 & 3.19991159413904 & -0.0999115941390403 \tabularnewline
107 & 4.2 & 3.10000679383468 & 1.09999320616532 \tabularnewline
108 & 16.2 & 4.19992520215437 & 12.0000747978456 \tabularnewline
109 & 18.3 & 16.1991840133764 & 2.10081598662356 \tabularnewline
110 & 21.6 & 18.2998571477451 & 3.30014285225488 \tabularnewline
111 & 12.6 & 21.5997755953635 & -8.99977559536348 \tabularnewline
112 & 9.8 & 12.6006119708939 & -2.80061197089389 \tabularnewline
113 & 10.6 & 9.80019043730514 & 0.799809562694856 \tabularnewline
114 & 13 & 10.5999456141803 & 2.40005438581972 \tabularnewline
115 & 9.7 & 12.9998367999944 & -3.29983679999436 \tabularnewline
116 & 7.9 & 9.70022438382544 & -1.80022438382544 \tabularnewline
117 & 3.3 & 7.90012241248837 & -4.60012241248837 \tabularnewline
118 & 3.4 & 3.30031280124654 & 0.0996871987534629 \tabularnewline
119 & 0.4 & 3.39999322142386 & -2.99999322142386 \tabularnewline
120 & 0.7 & 0.400203994923421 & 0.299796005076579 \tabularnewline
121 & 1.4 & 0.699979614332905 & 0.700020385667094 \tabularnewline
122 & 3.8 & 1.39995239969079 & 2.40004760030921 \tabularnewline
123 & 4 & 3.79983680045577 & 0.200163199544231 \tabularnewline
124 & 8 & 3.99998638921039 & 4.00001361078961 \tabularnewline
125 & 6 & 7.99972800522868 & -1.99972800522868 \tabularnewline
126 & 5.8 & 6.00013597842768 & -0.200135978427677 \tabularnewline
127 & 3.9 & 5.80001360893861 & -1.90001360893861 \tabularnewline
128 & 6.4 & 3.90012919800214 & 2.49987080199786 \tabularnewline
129 & 11 & 6.39983001263164 & 4.60016998736836 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167864&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]2[/C][C]5.9[/C][C]3.9[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]5.7[/C][C]5.8998640030771[/C][C]-0.199864003077098[/C][/ROW]
[ROW][C]4[/C][C]3.6[/C][C]5.70001359044471[/C][C]-2.10001359044471[/C][/ROW]
[ROW][C]5[/C][C]4.9[/C][C]3.60014279769318[/C][C]1.29985720230682[/C][/ROW]
[ROW][C]6[/C][C]5.3[/C][C]4.89991161171014[/C][C]0.400088388289863[/C][/ROW]
[ROW][C]7[/C][C]8.7[/C][C]5.29997279460515[/C][C]3.40002720539485[/C][/ROW]
[ROW][C]8[/C][C]6.8[/C][C]8.69976880338114[/C][C]-1.89976880338114[/C][/ROW]
[ROW][C]9[/C][C]8.9[/C][C]6.80012918135574[/C][C]2.09987081864426[/C][/ROW]
[ROW][C]10[/C][C]9.6[/C][C]8.89985721201509[/C][C]0.700142787984914[/C][/ROW]
[ROW][C]11[/C][C]11.2[/C][C]9.59995239136762[/C][C]1.60004760863238[/C][/ROW]
[ROW][C]12[/C][C]9.9[/C][C]11.1998911992244[/C][C]-1.29989119922436[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]9.9000883906016[/C][C]-0.6000883906016[/C][/ROW]
[ROW][C]14[/C][C]9.2[/C][C]9.3000408050873[/C][C]-0.100040805087296[/C][/ROW]
[ROW][C]15[/C][C]9.4[/C][C]9.20000680262083[/C][C]0.199993197379174[/C][/ROW]
[ROW][C]16[/C][C]12.7[/C][C]9.39998640077028[/C][C]3.30001359922972[/C][/ROW]
[ROW][C]17[/C][C]13.6[/C][C]12.6997756041525[/C][C]0.900224395847516[/C][/ROW]
[ROW][C]18[/C][C]16.1[/C][C]13.5999387861261[/C][C]2.50006121387388[/C][/ROW]
[ROW][C]19[/C][C]14.8[/C][C]16.0998299996839[/C][C]-1.29982999968392[/C][/ROW]
[ROW][C]20[/C][C]14.1[/C][C]14.8000883864401[/C][C]-0.700088386440127[/C][/ROW]
[ROW][C]21[/C][C]13.2[/C][C]14.1000476049332[/C][C]-0.900047604933158[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]13.2000612018524[/C][C]-4.50006120185237[/C][/ROW]
[ROW][C]23[/C][C]4.9[/C][C]8.70030599723816[/C][C]-3.80030599723816[/C][/ROW]
[ROW][C]24[/C][C]-1.3[/C][C]4.90025841496086[/C][C]-6.20025841496086[/C][/ROW]
[ROW][C]25[/C][C]-3.9[/C][C]-1.29957839196718[/C][C]-2.60042160803282[/C][/ROW]
[ROW][C]26[/C][C]-6[/C][C]-3.89982317533153[/C][C]-2.10017682466847[/C][/ROW]
[ROW][C]27[/C][C]-6.6[/C][C]-5.99985719120715[/C][C]-0.600142808792853[/C][/ROW]
[ROW][C]28[/C][C]-8.7[/C][C]-6.59995919121235[/C][C]-2.10004080878765[/C][/ROW]
[ROW][C]29[/C][C]-11.6[/C][C]-8.69985720045602[/C][C]-2.90014279954398[/C][/ROW]
[ROW][C]30[/C][C]-14.6[/C][C]-11.5998027947516[/C][C]-3.00019720524836[/C][/ROW]
[ROW][C]31[/C][C]-12.9[/C][C]-14.599795991206[/C][C]1.69979599120599[/C][/ROW]
[ROW][C]32[/C][C]-13.8[/C][C]-12.9001155835122[/C][C]-0.899884416487817[/C][/ROW]
[ROW][C]33[/C][C]-14.1[/C][C]-13.7999388092442[/C][C]-0.300061190755804[/C][/ROW]
[ROW][C]34[/C][C]-13.2[/C][C]-14.0999795963007[/C][C]0.899979596300687[/C][/ROW]
[ROW][C]35[/C][C]-10.4[/C][C]-13.2000611972279[/C][C]2.80006119722789[/C][/ROW]
[ROW][C]36[/C][C]-3.3[/C][C]-10.4001903998534[/C][C]7.10019039985338[/C][/ROW]
[ROW][C]37[/C][C]1[/C][C]-3.3004828020232[/C][C]4.3004828020232[/C][/ROW]
[ROW][C]38[/C][C]3.1[/C][C]0.999707573785965[/C][C]2.10029242621404[/C][/ROW]
[ROW][C]39[/C][C]4.5[/C][C]3.09985718334642[/C][C]1.40014281665358[/C][/ROW]
[ROW][C]40[/C][C]1.9[/C][C]4.49990479244266[/C][C]-2.59990479244266[/C][/ROW]
[ROW][C]41[/C][C]3.9[/C][C]1.90017678952581[/C][C]1.99982321047419[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]3.89986401509851[/C][C]3.10013598490149[/C][/ROW]
[ROW][C]43[/C][C]5.6[/C][C]6.99978919552274[/C][C]-1.39978919552274[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]5.60009518351165[/C][C]2.49990481648835[/C][/ROW]
[ROW][C]45[/C][C]6.1[/C][C]8.0998300103187[/C][C]-1.9998300103187[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]6.10013598536387[/C][C]1.89986401463613[/C][/ROW]
[ROW][C]47[/C][C]6.5[/C][C]7.99987081217004[/C][C]-1.49987081217004[/C][/ROW]
[ROW][C]48[/C][C]5.6[/C][C]6.5001019889076[/C][C]-0.900101988907604[/C][/ROW]
[ROW][C]49[/C][C]4.8[/C][C]5.60006120555039[/C][C]-0.800061205550395[/C][/ROW]
[ROW][C]50[/C][C]5.1[/C][C]4.80005440293104[/C][C]0.299945597068955[/C][/ROW]
[ROW][C]51[/C][C]7.8[/C][C]5.09997960416088[/C][C]2.70002039583912[/C][/ROW]
[ROW][C]52[/C][C]10.3[/C][C]7.7998164027672[/C][C]2.50018359723281[/C][/ROW]
[ROW][C]53[/C][C]8.6[/C][C]10.299829991362[/C][C]-1.69982999136204[/C][/ROW]
[ROW][C]54[/C][C]6.8[/C][C]8.60011558582414[/C][C]-1.80011558582414[/C][/ROW]
[ROW][C]55[/C][C]4.9[/C][C]6.80012240509027[/C][C]-1.90012240509027[/C][/ROW]
[ROW][C]56[/C][C]5.4[/C][C]4.90012920540012[/C][C]0.499870794599885[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]5.39996600955504[/C][C]0.100033990444957[/C][/ROW]
[ROW][C]58[/C][C]4.7[/C][C]5.49999319784256[/C][C]-0.799993197842556[/C][/ROW]
[ROW][C]59[/C][C]4.2[/C][C]4.70005439830662[/C][C]-0.500054398306625[/C][/ROW]
[ROW][C]60[/C][C]5[/C][C]4.20003400292973[/C][C]0.799965997070273[/C][/ROW]
[ROW][C]61[/C][C]5[/C][C]4.99994560354299[/C][C]5.43964570143274e-05[/C][/ROW]
[ROW][C]62[/C][C]6[/C][C]4.99999999630113[/C][C]1.00000000369887[/C][/ROW]
[ROW][C]63[/C][C]2.9[/C][C]5.9999320015383[/C][C]-3.0999320015383[/C][/ROW]
[ROW][C]64[/C][C]3.6[/C][C]2.90021079060671[/C][C]0.699789209393292[/C][/ROW]
[ROW][C]65[/C][C]5.1[/C][C]3.59995241541042[/C][C]1.50004758458958[/C][/ROW]
[ROW][C]66[/C][C]2.9[/C][C]5.09989799907214[/C][C]-2.19989799907214[/C][/ROW]
[ROW][C]67[/C][C]4.7[/C][C]2.90014958967929[/C][C]1.79985041032071[/C][/ROW]
[ROW][C]68[/C][C]3[/C][C]4.69987761294126[/C][C]-1.69987761294126[/C][/ROW]
[ROW][C]69[/C][C]5[/C][C]3.00011558906234[/C][C]1.99988441093766[/C][/ROW]
[ROW][C]70[/C][C]2.6[/C][C]4.99986401093698[/C][C]-2.39986401093698[/C][/ROW]
[ROW][C]71[/C][C]3.2[/C][C]2.60016318706044[/C][C]0.599836812939564[/C][/ROW]
[ROW][C]72[/C][C]2.4[/C][C]3.1999592120196[/C][C]-0.799959212019599[/C][/ROW]
[ROW][C]73[/C][C]3.2[/C][C]2.40005439599564[/C][C]0.799945604004359[/C][/ROW]
[ROW][C]74[/C][C]2.6[/C][C]3.19994560492968[/C][C]-0.599945604929683[/C][/ROW]
[ROW][C]75[/C][C]2.4[/C][C]2.60004079537809[/C][C]-0.20004079537809[/C][/ROW]
[ROW][C]76[/C][C]2.1[/C][C]2.40001360246631[/C][C]-0.300013602466313[/C][/ROW]
[ROW][C]77[/C][C]2.7[/C][C]2.10002040046338[/C][C]0.599979599536618[/C][/ROW]
[ROW][C]78[/C][C]4.4[/C][C]2.69995920231033[/C][C]1.70004079768967[/C][/ROW]
[ROW][C]79[/C][C]4.3[/C][C]4.39988439984135[/C][C]-0.0998843998413532[/C][/ROW]
[ROW][C]80[/C][C]4.2[/C][C]4.30000679198551[/C][C]-0.100006791985511[/C][/ROW]
[ROW][C]81[/C][C]5.5[/C][C]4.20000680030799[/C][C]1.29999319969201[/C][/ROW]
[ROW][C]82[/C][C]8.8[/C][C]5.49991160246252[/C][C]3.30008839753748[/C][/ROW]
[ROW][C]83[/C][C]10.1[/C][C]8.79977559906632[/C][C]1.30022440093368[/C][/ROW]
[ROW][C]84[/C][C]7[/C][C]10.0999115867412[/C][C]-3.09991158674119[/C][/ROW]
[ROW][C]85[/C][C]5.7[/C][C]7.00021078921853[/C][C]-1.30021078921853[/C][/ROW]
[ROW][C]86[/C][C]5.2[/C][C]5.70008841233323[/C][C]-0.50008841233323[/C][/ROW]
[ROW][C]87[/C][C]5.5[/C][C]5.20003400524263[/C][C]0.299965994757372[/C][/ROW]
[ROW][C]88[/C][C]7.3[/C][C]5.49997960277387[/C][C]1.80002039722613[/C][/ROW]
[ROW][C]89[/C][C]5.9[/C][C]7.29987760138241[/C][C]-1.39987760138241[/C][/ROW]
[ROW][C]90[/C][C]7.1[/C][C]5.90009518952311[/C][C]1.19990481047688[/C][/ROW]
[ROW][C]91[/C][C]6.9[/C][C]7.099918408319[/C][C]-0.199918408318998[/C][/ROW]
[ROW][C]92[/C][C]6.7[/C][C]6.90001359414418[/C][C]-0.200013594144182[/C][/ROW]
[ROW][C]93[/C][C]4.7[/C][C]6.70001360061667[/C][C]-2.00001360061667[/C][/ROW]
[ROW][C]94[/C][C]6.7[/C][C]4.70013599784772[/C][C]1.99986400215228[/C][/ROW]
[ROW][C]95[/C][C]8.5[/C][C]6.69986401232474[/C][C]1.80013598767526[/C][/ROW]
[ROW][C]96[/C][C]2.1[/C][C]8.49987759352243[/C][C]-6.39987759352243[/C][/ROW]
[ROW][C]97[/C][C]-0.9[/C][C]2.10043518182984[/C][C]-3.00043518182984[/C][/ROW]
[ROW][C]98[/C][C]-4.7[/C][C]-0.899795975023951[/C][C]-3.80020402497605[/C][/ROW]
[ROW][C]99[/C][C]4.8[/C][C]-4.6997415919731[/C][C]9.4997415919731[/C][/ROW]
[ROW][C]100[/C][C]2.6[/C][C]4.79935403218756[/C][C]-2.19935403218756[/C][/ROW]
[ROW][C]101[/C][C]1.7[/C][C]2.60014955269038[/C][C]-0.900149552690376[/C][/ROW]
[ROW][C]102[/C][C]-1.8[/C][C]1.70006120878466[/C][C]-3.50006120878466[/C][/ROW]
[ROW][C]103[/C][C]0.2[/C][C]-1.79976200122282[/C][C]1.99976200122282[/C][/ROW]
[ROW][C]104[/C][C]1.9[/C][C]0.199864019260648[/C][C]1.70013598073935[/C][/ROW]
[ROW][C]105[/C][C]3.2[/C][C]1.89988439336905[/C][C]1.30011560663095[/C][/ROW]
[ROW][C]106[/C][C]3.1[/C][C]3.19991159413904[/C][C]-0.0999115941390403[/C][/ROW]
[ROW][C]107[/C][C]4.2[/C][C]3.10000679383468[/C][C]1.09999320616532[/C][/ROW]
[ROW][C]108[/C][C]16.2[/C][C]4.19992520215437[/C][C]12.0000747978456[/C][/ROW]
[ROW][C]109[/C][C]18.3[/C][C]16.1991840133764[/C][C]2.10081598662356[/C][/ROW]
[ROW][C]110[/C][C]21.6[/C][C]18.2998571477451[/C][C]3.30014285225488[/C][/ROW]
[ROW][C]111[/C][C]12.6[/C][C]21.5997755953635[/C][C]-8.99977559536348[/C][/ROW]
[ROW][C]112[/C][C]9.8[/C][C]12.6006119708939[/C][C]-2.80061197089389[/C][/ROW]
[ROW][C]113[/C][C]10.6[/C][C]9.80019043730514[/C][C]0.799809562694856[/C][/ROW]
[ROW][C]114[/C][C]13[/C][C]10.5999456141803[/C][C]2.40005438581972[/C][/ROW]
[ROW][C]115[/C][C]9.7[/C][C]12.9998367999944[/C][C]-3.29983679999436[/C][/ROW]
[ROW][C]116[/C][C]7.9[/C][C]9.70022438382544[/C][C]-1.80022438382544[/C][/ROW]
[ROW][C]117[/C][C]3.3[/C][C]7.90012241248837[/C][C]-4.60012241248837[/C][/ROW]
[ROW][C]118[/C][C]3.4[/C][C]3.30031280124654[/C][C]0.0996871987534629[/C][/ROW]
[ROW][C]119[/C][C]0.4[/C][C]3.39999322142386[/C][C]-2.99999322142386[/C][/ROW]
[ROW][C]120[/C][C]0.7[/C][C]0.400203994923421[/C][C]0.299796005076579[/C][/ROW]
[ROW][C]121[/C][C]1.4[/C][C]0.699979614332905[/C][C]0.700020385667094[/C][/ROW]
[ROW][C]122[/C][C]3.8[/C][C]1.39995239969079[/C][C]2.40004760030921[/C][/ROW]
[ROW][C]123[/C][C]4[/C][C]3.79983680045577[/C][C]0.200163199544231[/C][/ROW]
[ROW][C]124[/C][C]8[/C][C]3.99998638921039[/C][C]4.00001361078961[/C][/ROW]
[ROW][C]125[/C][C]6[/C][C]7.99972800522868[/C][C]-1.99972800522868[/C][/ROW]
[ROW][C]126[/C][C]5.8[/C][C]6.00013597842768[/C][C]-0.200135978427677[/C][/ROW]
[ROW][C]127[/C][C]3.9[/C][C]5.80001360893861[/C][C]-1.90001360893861[/C][/ROW]
[ROW][C]128[/C][C]6.4[/C][C]3.90012919800214[/C][C]2.49987080199786[/C][/ROW]
[ROW][C]129[/C][C]11[/C][C]6.39983001263164[/C][C]4.60016998736836[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167864&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167864&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
2	5.9	3.9	2
3	5.7	5.8998640030771	-0.199864003077098
4	3.6	5.70001359044471	-2.10001359044471
5	4.9	3.60014279769318	1.29985720230682
6	5.3	4.89991161171014	0.400088388289863
7	8.7	5.29997279460515	3.40002720539485
8	6.8	8.69976880338114	-1.89976880338114
9	8.9	6.80012918135574	2.09987081864426
10	9.6	8.89985721201509	0.700142787984914
11	11.2	9.59995239136762	1.60004760863238
12	9.9	11.1998911992244	-1.29989119922436
13	9.3	9.9000883906016	-0.6000883906016
14	9.2	9.3000408050873	-0.100040805087296
15	9.4	9.20000680262083	0.199993197379174
16	12.7	9.39998640077028	3.30001359922972
17	13.6	12.6997756041525	0.900224395847516
18	16.1	13.5999387861261	2.50006121387388
19	14.8	16.0998299996839	-1.29982999968392
20	14.1	14.8000883864401	-0.700088386440127
21	13.2	14.1000476049332	-0.900047604933158
22	8.7	13.2000612018524	-4.50006120185237
23	4.9	8.70030599723816	-3.80030599723816
24	-1.3	4.90025841496086	-6.20025841496086
25	-3.9	-1.29957839196718	-2.60042160803282
26	-6	-3.89982317533153	-2.10017682466847
27	-6.6	-5.99985719120715	-0.600142808792853
28	-8.7	-6.59995919121235	-2.10004080878765
29	-11.6	-8.69985720045602	-2.90014279954398
30	-14.6	-11.5998027947516	-3.00019720524836
31	-12.9	-14.599795991206	1.69979599120599
32	-13.8	-12.9001155835122	-0.899884416487817
33	-14.1	-13.7999388092442	-0.300061190755804
34	-13.2	-14.0999795963007	0.899979596300687
35	-10.4	-13.2000611972279	2.80006119722789
36	-3.3	-10.4001903998534	7.10019039985338
37	1	-3.3004828020232	4.3004828020232
38	3.1	0.999707573785965	2.10029242621404
39	4.5	3.09985718334642	1.40014281665358
40	1.9	4.49990479244266	-2.59990479244266
41	3.9	1.90017678952581	1.99982321047419
42	7	3.89986401509851	3.10013598490149
43	5.6	6.99978919552274	-1.39978919552274
44	8.1	5.60009518351165	2.49990481648835
45	6.1	8.0998300103187	-1.9998300103187
46	8	6.10013598536387	1.89986401463613
47	6.5	7.99987081217004	-1.49987081217004
48	5.6	6.5001019889076	-0.900101988907604
49	4.8	5.60006120555039	-0.800061205550395
50	5.1	4.80005440293104	0.299945597068955
51	7.8	5.09997960416088	2.70002039583912
52	10.3	7.7998164027672	2.50018359723281
53	8.6	10.299829991362	-1.69982999136204
54	6.8	8.60011558582414	-1.80011558582414
55	4.9	6.80012240509027	-1.90012240509027
56	5.4	4.90012920540012	0.499870794599885
57	5.5	5.39996600955504	0.100033990444957
58	4.7	5.49999319784256	-0.799993197842556
59	4.2	4.70005439830662	-0.500054398306625
60	5	4.20003400292973	0.799965997070273
61	5	4.99994560354299	5.43964570143274e-05
62	6	4.99999999630113	1.00000000369887
63	2.9	5.9999320015383	-3.0999320015383
64	3.6	2.90021079060671	0.699789209393292
65	5.1	3.59995241541042	1.50004758458958
66	2.9	5.09989799907214	-2.19989799907214
67	4.7	2.90014958967929	1.79985041032071
68	3	4.69987761294126	-1.69987761294126
69	5	3.00011558906234	1.99988441093766
70	2.6	4.99986401093698	-2.39986401093698
71	3.2	2.60016318706044	0.599836812939564
72	2.4	3.1999592120196	-0.799959212019599
73	3.2	2.40005439599564	0.799945604004359
74	2.6	3.19994560492968	-0.599945604929683
75	2.4	2.60004079537809	-0.20004079537809
76	2.1	2.40001360246631	-0.300013602466313
77	2.7	2.10002040046338	0.599979599536618
78	4.4	2.69995920231033	1.70004079768967
79	4.3	4.39988439984135	-0.0998843998413532
80	4.2	4.30000679198551	-0.100006791985511
81	5.5	4.20000680030799	1.29999319969201
82	8.8	5.49991160246252	3.30008839753748
83	10.1	8.79977559906632	1.30022440093368
84	7	10.0999115867412	-3.09991158674119
85	5.7	7.00021078921853	-1.30021078921853
86	5.2	5.70008841233323	-0.50008841233323
87	5.5	5.20003400524263	0.299965994757372
88	7.3	5.49997960277387	1.80002039722613
89	5.9	7.29987760138241	-1.39987760138241
90	7.1	5.90009518952311	1.19990481047688
91	6.9	7.099918408319	-0.199918408318998
92	6.7	6.90001359414418	-0.200013594144182
93	4.7	6.70001360061667	-2.00001360061667
94	6.7	4.70013599784772	1.99986400215228
95	8.5	6.69986401232474	1.80013598767526
96	2.1	8.49987759352243	-6.39987759352243
97	-0.9	2.10043518182984	-3.00043518182984
98	-4.7	-0.899795975023951	-3.80020402497605
99	4.8	-4.6997415919731	9.4997415919731
100	2.6	4.79935403218756	-2.19935403218756
101	1.7	2.60014955269038	-0.900149552690376
102	-1.8	1.70006120878466	-3.50006120878466
103	0.2	-1.79976200122282	1.99976200122282
104	1.9	0.199864019260648	1.70013598073935
105	3.2	1.89988439336905	1.30011560663095
106	3.1	3.19991159413904	-0.0999115941390403
107	4.2	3.10000679383468	1.09999320616532
108	16.2	4.19992520215437	12.0000747978456
109	18.3	16.1991840133764	2.10081598662356
110	21.6	18.2998571477451	3.30014285225488
111	12.6	21.5997755953635	-8.99977559536348
112	9.8	12.6006119708939	-2.80061197089389
113	10.6	9.80019043730514	0.799809562694856
114	13	10.5999456141803	2.40005438581972
115	9.7	12.9998367999944	-3.29983679999436
116	7.9	9.70022438382544	-1.80022438382544
117	3.3	7.90012241248837	-4.60012241248837
118	3.4	3.30031280124654	0.0996871987534629
119	0.4	3.39999322142386	-2.99999322142386
120	0.7	0.400203994923421	0.299796005076579
121	1.4	0.699979614332905	0.700020385667094
122	3.8	1.39995239969079	2.40004760030921
123	4	3.79983680045577	0.200163199544231
124	8	3.99998638921039	4.00001361078961
125	6	7.99972800522868	-1.99972800522868
126	5.8	6.00013597842768	-0.200135978427677
127	3.9	5.80001360893861	-1.90001360893861
128	6.4	3.90012919800214	2.49987080199786
129	11	6.39983001263164	4.60016998736836

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
130	10.9996871955184	5.67649058289287	16.322883808144
131	10.9996871955184	3.47180629727515	18.5275680937617
132	10.9996871955184	1.78005816504198	20.2193162259949
133	10.9996871955184	0.353836919421553	21.6455374716153
134	10.9996871955184	-0.902694782158973	22.9020691731959
135	10.9996871955184	-2.03868944361912	24.038063834656
136	10.9996871955184	-3.08334635643605	25.0827207474729
137	10.9996871955184	-4.05569066978086	26.0550650608177
138	10.9996871955184	-4.96893739485915	26.968311785896
139	10.9996871955184	-5.83270835442869	27.8320827454656
140	10.9996871955184	-6.65426727908435	28.6536416701212
141	10.9996871955184	-7.43925738471217	29.4386317757491

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
130 & 10.9996871955184 & 5.67649058289287 & 16.322883808144 \tabularnewline
131 & 10.9996871955184 & 3.47180629727515 & 18.5275680937617 \tabularnewline
132 & 10.9996871955184 & 1.78005816504198 & 20.2193162259949 \tabularnewline
133 & 10.9996871955184 & 0.353836919421553 & 21.6455374716153 \tabularnewline
134 & 10.9996871955184 & -0.902694782158973 & 22.9020691731959 \tabularnewline
135 & 10.9996871955184 & -2.03868944361912 & 24.038063834656 \tabularnewline
136 & 10.9996871955184 & -3.08334635643605 & 25.0827207474729 \tabularnewline
137 & 10.9996871955184 & -4.05569066978086 & 26.0550650608177 \tabularnewline
138 & 10.9996871955184 & -4.96893739485915 & 26.968311785896 \tabularnewline
139 & 10.9996871955184 & -5.83270835442869 & 27.8320827454656 \tabularnewline
140 & 10.9996871955184 & -6.65426727908435 & 28.6536416701212 \tabularnewline
141 & 10.9996871955184 & -7.43925738471217 & 29.4386317757491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167864&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]130[/C][C]10.9996871955184[/C][C]5.67649058289287[/C][C]16.322883808144[/C][/ROW]
[ROW][C]131[/C][C]10.9996871955184[/C][C]3.47180629727515[/C][C]18.5275680937617[/C][/ROW]
[ROW][C]132[/C][C]10.9996871955184[/C][C]1.78005816504198[/C][C]20.2193162259949[/C][/ROW]
[ROW][C]133[/C][C]10.9996871955184[/C][C]0.353836919421553[/C][C]21.6455374716153[/C][/ROW]
[ROW][C]134[/C][C]10.9996871955184[/C][C]-0.902694782158973[/C][C]22.9020691731959[/C][/ROW]
[ROW][C]135[/C][C]10.9996871955184[/C][C]-2.03868944361912[/C][C]24.038063834656[/C][/ROW]
[ROW][C]136[/C][C]10.9996871955184[/C][C]-3.08334635643605[/C][C]25.0827207474729[/C][/ROW]
[ROW][C]137[/C][C]10.9996871955184[/C][C]-4.05569066978086[/C][C]26.0550650608177[/C][/ROW]
[ROW][C]138[/C][C]10.9996871955184[/C][C]-4.96893739485915[/C][C]26.968311785896[/C][/ROW]
[ROW][C]139[/C][C]10.9996871955184[/C][C]-5.83270835442869[/C][C]27.8320827454656[/C][/ROW]
[ROW][C]140[/C][C]10.9996871955184[/C][C]-6.65426727908435[/C][C]28.6536416701212[/C][/ROW]
[ROW][C]141[/C][C]10.9996871955184[/C][C]-7.43925738471217[/C][C]29.4386317757491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167864&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167864&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
130	10.9996871955184	5.67649058289287	16.322883808144
131	10.9996871955184	3.47180629727515	18.5275680937617
132	10.9996871955184	1.78005816504198	20.2193162259949
133	10.9996871955184	0.353836919421553	21.6455374716153
134	10.9996871955184	-0.902694782158973	22.9020691731959
135	10.9996871955184	-2.03868944361912	24.038063834656
136	10.9996871955184	-3.08334635643605	25.0827207474729
137	10.9996871955184	-4.05569066978086	26.0550650608177
138	10.9996871955184	-4.96893739485915	26.968311785896
139	10.9996871955184	-5.83270835442869	27.8320827454656
140	10.9996871955184	-6.65426727908435	28.6536416701212
141	10.9996871955184	-7.43925738471217	29.4386317757491

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 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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