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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 21 May 2014 05:03:58 -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/2014/May/21/t1400663047bu228f9f4p3xstp.htm/, Retrieved Tue, 14 May 2024 16:55:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235005, Retrieved Tue, 14 May 2024 16:55:36 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

110

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

-       [Exponential Smoothing] [] [2014-05-21 09:03:58] [b3e3d38149b35cb70244b37a39776b3a] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235005&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235005&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999947828280081
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999947828280081 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235005&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]0.999947828280081[/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=235005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235005&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	0.999947828280081
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	83.6	83.5	0.0999999999999943
3	83.9	83.599994782828	0.300005217172
4	83.9	83.8999843482118	1.56517881606533e-05
5	84.2	83.8999999991834	0.300000000816581
6	84.4	84.199984348484	0.200015651516026
7	84.6	84.3999895648395	0.200010435160536
8	84.8	84.5999895651116	0.200010434888412
9	84.8	84.7999895651116	1.04348883951388e-05
10	84.9	84.7999999994556	0.100000000544412
11	85	84.899994782828	0.100005217172011
12	85.1	84.9999947825558	0.100005217444178
13	85.3	85.0999947825558	0.2000052174442
14	85.5	85.2999895653838	0.200010434616189
15	86.1	85.4999895651116	0.600010434888375
16	86.2	86.0999686964236	0.100031303576372
17	86.3	86.1999947811948	0.100005218805151
18	86.5	86.2999947825557	0.200005217444271
19	86.5	86.4999895653838	1.04346161862168e-05
20	86.6	86.4999999994556	0.100000000544384
21	86.8	86.599994782828	0.20000521717202
22	87.3	86.7999895653838	0.500010434616172
23	87.7	87.2999739135957	0.400026086404353
24	87.8	87.6999791299511	0.100020870048937
25	88.1	87.7999947817392	0.300005218260821
26	88.8	88.0999843482118	0.70001565178822
27	89.3	88.7999634789795	0.500036521020519
28	89.2	89.2999739122347	-0.0999739122346739
29	89.3	89.2000052158109	0.0999947841890503
30	89.6	89.2999947831001	0.300005216899876
31	89.6	89.5999843482118	1.56517881464424e-05
32	89.9	89.5999999991834	0.300000000816596
33	90.2	89.899984348484	0.30001565151602
34	90.2	90.1999843476675	1.56523325358648e-05
35	90.4	90.1999999991834	0.200000000816615
36	90.5	90.399989565656	0.100010434344014
37	91.5	90.4999947822836	1.00000521771636
38	91.5	91.4999478280079	5.21719921380281e-05
39	91.8	91.4999999972781	0.300000002721902
40	92.2	91.7999843484839	0.400015651516128
41	92.4	92.1999791304955	0.200020869504542
42	92.7	92.3999895645672	0.300010435432782
43	93.1	92.6999843479396	0.400015652060404
44	93.1	93.0999791304954	2.08695045671448e-05
45	93.5	93.0999999989112	0.400000001088799
46	93.9	93.499979131312	0.400020868688031
47	94.3	93.8999791302233	0.400020869776711
48	94.7	94.2999791302232	0.400020869776782
49	95.3	94.6999791302232	0.60002086977677
50	95.9	95.2999686958792	0.600031304120776
51	96.2	95.8999686953349	0.30003130466514
52	96.7	96.1999843468508	0.500015653149191
53	96.7	96.6999739133234	2.60866766126355e-05
54	96.9	96.699999998639	0.200000001360991
55	97.3	96.899989565656	0.40001043434404
56	97.4	97.2999791307677	0.100020869232353
57	97.9	97.3999947817392	0.500005218260782
58	98.4	97.8999739138678	0.500026086132209
59	98.4	98.3999739127791	2.60872209167928e-05
60	98.8	98.399999998639	0.400000001361008
61	98.9	98.799979131312	0.100020868688048
62	98.9	98.8999947817393	5.21826075328136e-06
63	99.3	98.8999999997278	0.400000000272243
64	99.4	99.299979131312	0.100020868687992
65	99.7	99.3999947817393	0.30000521826075
66	99.8	99.6999843482118	0.100015651788212
67	99.7	99.7999947820114	-0.0999947820114215
68	99.9	99.7000052168998	0.199994783100237
69	100.4	99.8999895659282	0.500010434071811
70	101.1	100.399973913596	0.700026086404307
71	101.3	101.099963478435	0.200036521564925
72	101.4	101.299989563751	0.100010436249391
73	101.8	101.399994782284	0.400005217716455
74	102.2	101.79997913104	0.400020868960198
75	102.4	102.199979130223	0.200020869776736
76	102.5	102.399989564567	0.100010435432793
77	102.8	102.499994782284	0.300005217716418
78	103	102.799984348212	0.200015651788192
79	103.2	102.999989564839	0.200010435160564
80	103.2	103.199989565112	1.04348884093497e-05
81	103.6	103.199999999456	0.400000000544395
82	103.7	103.599979131312	0.100020868688006
83	103.7	103.699994781739	5.21826075328136e-06
84	103.8	103.699999999728	0.100000000272246
85	104.2	103.799994782828	0.400005217172009
86	104.5	104.19997913104	0.300020868960161
87	104.5	104.499984347395	1.56526047447869e-05
88	104.8	104.499999999183	0.300000000816624
89	105.2	104.799984348484	0.400015651516028
90	105.3	105.199979130495	0.100020869504533
91	105.5	105.299994781739	0.200005218260799
92	105.4	105.499989565384	-0.0999895653837655
93	105.7	105.400005216628	0.299994783372398
94	106.8	105.699984348756	1.10001565124381
95	106.8	106.799942610292	5.73897084592545e-05
96	107	106.799999997006	0.200000002994116

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 83.6 & 83.5 & 0.0999999999999943 \tabularnewline
3 & 83.9 & 83.599994782828 & 0.300005217172 \tabularnewline
4 & 83.9 & 83.8999843482118 & 1.56517881606533e-05 \tabularnewline
5 & 84.2 & 83.8999999991834 & 0.300000000816581 \tabularnewline
6 & 84.4 & 84.199984348484 & 0.200015651516026 \tabularnewline
7 & 84.6 & 84.3999895648395 & 0.200010435160536 \tabularnewline
8 & 84.8 & 84.5999895651116 & 0.200010434888412 \tabularnewline
9 & 84.8 & 84.7999895651116 & 1.04348883951388e-05 \tabularnewline
10 & 84.9 & 84.7999999994556 & 0.100000000544412 \tabularnewline
11 & 85 & 84.899994782828 & 0.100005217172011 \tabularnewline
12 & 85.1 & 84.9999947825558 & 0.100005217444178 \tabularnewline
13 & 85.3 & 85.0999947825558 & 0.2000052174442 \tabularnewline
14 & 85.5 & 85.2999895653838 & 0.200010434616189 \tabularnewline
15 & 86.1 & 85.4999895651116 & 0.600010434888375 \tabularnewline
16 & 86.2 & 86.0999686964236 & 0.100031303576372 \tabularnewline
17 & 86.3 & 86.1999947811948 & 0.100005218805151 \tabularnewline
18 & 86.5 & 86.2999947825557 & 0.200005217444271 \tabularnewline
19 & 86.5 & 86.4999895653838 & 1.04346161862168e-05 \tabularnewline
20 & 86.6 & 86.4999999994556 & 0.100000000544384 \tabularnewline
21 & 86.8 & 86.599994782828 & 0.20000521717202 \tabularnewline
22 & 87.3 & 86.7999895653838 & 0.500010434616172 \tabularnewline
23 & 87.7 & 87.2999739135957 & 0.400026086404353 \tabularnewline
24 & 87.8 & 87.6999791299511 & 0.100020870048937 \tabularnewline
25 & 88.1 & 87.7999947817392 & 0.300005218260821 \tabularnewline
26 & 88.8 & 88.0999843482118 & 0.70001565178822 \tabularnewline
27 & 89.3 & 88.7999634789795 & 0.500036521020519 \tabularnewline
28 & 89.2 & 89.2999739122347 & -0.0999739122346739 \tabularnewline
29 & 89.3 & 89.2000052158109 & 0.0999947841890503 \tabularnewline
30 & 89.6 & 89.2999947831001 & 0.300005216899876 \tabularnewline
31 & 89.6 & 89.5999843482118 & 1.56517881464424e-05 \tabularnewline
32 & 89.9 & 89.5999999991834 & 0.300000000816596 \tabularnewline
33 & 90.2 & 89.899984348484 & 0.30001565151602 \tabularnewline
34 & 90.2 & 90.1999843476675 & 1.56523325358648e-05 \tabularnewline
35 & 90.4 & 90.1999999991834 & 0.200000000816615 \tabularnewline
36 & 90.5 & 90.399989565656 & 0.100010434344014 \tabularnewline
37 & 91.5 & 90.4999947822836 & 1.00000521771636 \tabularnewline
38 & 91.5 & 91.4999478280079 & 5.21719921380281e-05 \tabularnewline
39 & 91.8 & 91.4999999972781 & 0.300000002721902 \tabularnewline
40 & 92.2 & 91.7999843484839 & 0.400015651516128 \tabularnewline
41 & 92.4 & 92.1999791304955 & 0.200020869504542 \tabularnewline
42 & 92.7 & 92.3999895645672 & 0.300010435432782 \tabularnewline
43 & 93.1 & 92.6999843479396 & 0.400015652060404 \tabularnewline
44 & 93.1 & 93.0999791304954 & 2.08695045671448e-05 \tabularnewline
45 & 93.5 & 93.0999999989112 & 0.400000001088799 \tabularnewline
46 & 93.9 & 93.499979131312 & 0.400020868688031 \tabularnewline
47 & 94.3 & 93.8999791302233 & 0.400020869776711 \tabularnewline
48 & 94.7 & 94.2999791302232 & 0.400020869776782 \tabularnewline
49 & 95.3 & 94.6999791302232 & 0.60002086977677 \tabularnewline
50 & 95.9 & 95.2999686958792 & 0.600031304120776 \tabularnewline
51 & 96.2 & 95.8999686953349 & 0.30003130466514 \tabularnewline
52 & 96.7 & 96.1999843468508 & 0.500015653149191 \tabularnewline
53 & 96.7 & 96.6999739133234 & 2.60866766126355e-05 \tabularnewline
54 & 96.9 & 96.699999998639 & 0.200000001360991 \tabularnewline
55 & 97.3 & 96.899989565656 & 0.40001043434404 \tabularnewline
56 & 97.4 & 97.2999791307677 & 0.100020869232353 \tabularnewline
57 & 97.9 & 97.3999947817392 & 0.500005218260782 \tabularnewline
58 & 98.4 & 97.8999739138678 & 0.500026086132209 \tabularnewline
59 & 98.4 & 98.3999739127791 & 2.60872209167928e-05 \tabularnewline
60 & 98.8 & 98.399999998639 & 0.400000001361008 \tabularnewline
61 & 98.9 & 98.799979131312 & 0.100020868688048 \tabularnewline
62 & 98.9 & 98.8999947817393 & 5.21826075328136e-06 \tabularnewline
63 & 99.3 & 98.8999999997278 & 0.400000000272243 \tabularnewline
64 & 99.4 & 99.299979131312 & 0.100020868687992 \tabularnewline
65 & 99.7 & 99.3999947817393 & 0.30000521826075 \tabularnewline
66 & 99.8 & 99.6999843482118 & 0.100015651788212 \tabularnewline
67 & 99.7 & 99.7999947820114 & -0.0999947820114215 \tabularnewline
68 & 99.9 & 99.7000052168998 & 0.199994783100237 \tabularnewline
69 & 100.4 & 99.8999895659282 & 0.500010434071811 \tabularnewline
70 & 101.1 & 100.399973913596 & 0.700026086404307 \tabularnewline
71 & 101.3 & 101.099963478435 & 0.200036521564925 \tabularnewline
72 & 101.4 & 101.299989563751 & 0.100010436249391 \tabularnewline
73 & 101.8 & 101.399994782284 & 0.400005217716455 \tabularnewline
74 & 102.2 & 101.79997913104 & 0.400020868960198 \tabularnewline
75 & 102.4 & 102.199979130223 & 0.200020869776736 \tabularnewline
76 & 102.5 & 102.399989564567 & 0.100010435432793 \tabularnewline
77 & 102.8 & 102.499994782284 & 0.300005217716418 \tabularnewline
78 & 103 & 102.799984348212 & 0.200015651788192 \tabularnewline
79 & 103.2 & 102.999989564839 & 0.200010435160564 \tabularnewline
80 & 103.2 & 103.199989565112 & 1.04348884093497e-05 \tabularnewline
81 & 103.6 & 103.199999999456 & 0.400000000544395 \tabularnewline
82 & 103.7 & 103.599979131312 & 0.100020868688006 \tabularnewline
83 & 103.7 & 103.699994781739 & 5.21826075328136e-06 \tabularnewline
84 & 103.8 & 103.699999999728 & 0.100000000272246 \tabularnewline
85 & 104.2 & 103.799994782828 & 0.400005217172009 \tabularnewline
86 & 104.5 & 104.19997913104 & 0.300020868960161 \tabularnewline
87 & 104.5 & 104.499984347395 & 1.56526047447869e-05 \tabularnewline
88 & 104.8 & 104.499999999183 & 0.300000000816624 \tabularnewline
89 & 105.2 & 104.799984348484 & 0.400015651516028 \tabularnewline
90 & 105.3 & 105.199979130495 & 0.100020869504533 \tabularnewline
91 & 105.5 & 105.299994781739 & 0.200005218260799 \tabularnewline
92 & 105.4 & 105.499989565384 & -0.0999895653837655 \tabularnewline
93 & 105.7 & 105.400005216628 & 0.299994783372398 \tabularnewline
94 & 106.8 & 105.699984348756 & 1.10001565124381 \tabularnewline
95 & 106.8 & 106.799942610292 & 5.73897084592545e-05 \tabularnewline
96 & 107 & 106.799999997006 & 0.200000002994116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235005&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]83.6[/C][C]83.5[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]3[/C][C]83.9[/C][C]83.599994782828[/C][C]0.300005217172[/C][/ROW]
[ROW][C]4[/C][C]83.9[/C][C]83.8999843482118[/C][C]1.56517881606533e-05[/C][/ROW]
[ROW][C]5[/C][C]84.2[/C][C]83.8999999991834[/C][C]0.300000000816581[/C][/ROW]
[ROW][C]6[/C][C]84.4[/C][C]84.199984348484[/C][C]0.200015651516026[/C][/ROW]
[ROW][C]7[/C][C]84.6[/C][C]84.3999895648395[/C][C]0.200010435160536[/C][/ROW]
[ROW][C]8[/C][C]84.8[/C][C]84.5999895651116[/C][C]0.200010434888412[/C][/ROW]
[ROW][C]9[/C][C]84.8[/C][C]84.7999895651116[/C][C]1.04348883951388e-05[/C][/ROW]
[ROW][C]10[/C][C]84.9[/C][C]84.7999999994556[/C][C]0.100000000544412[/C][/ROW]
[ROW][C]11[/C][C]85[/C][C]84.899994782828[/C][C]0.100005217172011[/C][/ROW]
[ROW][C]12[/C][C]85.1[/C][C]84.9999947825558[/C][C]0.100005217444178[/C][/ROW]
[ROW][C]13[/C][C]85.3[/C][C]85.0999947825558[/C][C]0.2000052174442[/C][/ROW]
[ROW][C]14[/C][C]85.5[/C][C]85.2999895653838[/C][C]0.200010434616189[/C][/ROW]
[ROW][C]15[/C][C]86.1[/C][C]85.4999895651116[/C][C]0.600010434888375[/C][/ROW]
[ROW][C]16[/C][C]86.2[/C][C]86.0999686964236[/C][C]0.100031303576372[/C][/ROW]
[ROW][C]17[/C][C]86.3[/C][C]86.1999947811948[/C][C]0.100005218805151[/C][/ROW]
[ROW][C]18[/C][C]86.5[/C][C]86.2999947825557[/C][C]0.200005217444271[/C][/ROW]
[ROW][C]19[/C][C]86.5[/C][C]86.4999895653838[/C][C]1.04346161862168e-05[/C][/ROW]
[ROW][C]20[/C][C]86.6[/C][C]86.4999999994556[/C][C]0.100000000544384[/C][/ROW]
[ROW][C]21[/C][C]86.8[/C][C]86.599994782828[/C][C]0.20000521717202[/C][/ROW]
[ROW][C]22[/C][C]87.3[/C][C]86.7999895653838[/C][C]0.500010434616172[/C][/ROW]
[ROW][C]23[/C][C]87.7[/C][C]87.2999739135957[/C][C]0.400026086404353[/C][/ROW]
[ROW][C]24[/C][C]87.8[/C][C]87.6999791299511[/C][C]0.100020870048937[/C][/ROW]
[ROW][C]25[/C][C]88.1[/C][C]87.7999947817392[/C][C]0.300005218260821[/C][/ROW]
[ROW][C]26[/C][C]88.8[/C][C]88.0999843482118[/C][C]0.70001565178822[/C][/ROW]
[ROW][C]27[/C][C]89.3[/C][C]88.7999634789795[/C][C]0.500036521020519[/C][/ROW]
[ROW][C]28[/C][C]89.2[/C][C]89.2999739122347[/C][C]-0.0999739122346739[/C][/ROW]
[ROW][C]29[/C][C]89.3[/C][C]89.2000052158109[/C][C]0.0999947841890503[/C][/ROW]
[ROW][C]30[/C][C]89.6[/C][C]89.2999947831001[/C][C]0.300005216899876[/C][/ROW]
[ROW][C]31[/C][C]89.6[/C][C]89.5999843482118[/C][C]1.56517881464424e-05[/C][/ROW]
[ROW][C]32[/C][C]89.9[/C][C]89.5999999991834[/C][C]0.300000000816596[/C][/ROW]
[ROW][C]33[/C][C]90.2[/C][C]89.899984348484[/C][C]0.30001565151602[/C][/ROW]
[ROW][C]34[/C][C]90.2[/C][C]90.1999843476675[/C][C]1.56523325358648e-05[/C][/ROW]
[ROW][C]35[/C][C]90.4[/C][C]90.1999999991834[/C][C]0.200000000816615[/C][/ROW]
[ROW][C]36[/C][C]90.5[/C][C]90.399989565656[/C][C]0.100010434344014[/C][/ROW]
[ROW][C]37[/C][C]91.5[/C][C]90.4999947822836[/C][C]1.00000521771636[/C][/ROW]
[ROW][C]38[/C][C]91.5[/C][C]91.4999478280079[/C][C]5.21719921380281e-05[/C][/ROW]
[ROW][C]39[/C][C]91.8[/C][C]91.4999999972781[/C][C]0.300000002721902[/C][/ROW]
[ROW][C]40[/C][C]92.2[/C][C]91.7999843484839[/C][C]0.400015651516128[/C][/ROW]
[ROW][C]41[/C][C]92.4[/C][C]92.1999791304955[/C][C]0.200020869504542[/C][/ROW]
[ROW][C]42[/C][C]92.7[/C][C]92.3999895645672[/C][C]0.300010435432782[/C][/ROW]
[ROW][C]43[/C][C]93.1[/C][C]92.6999843479396[/C][C]0.400015652060404[/C][/ROW]
[ROW][C]44[/C][C]93.1[/C][C]93.0999791304954[/C][C]2.08695045671448e-05[/C][/ROW]
[ROW][C]45[/C][C]93.5[/C][C]93.0999999989112[/C][C]0.400000001088799[/C][/ROW]
[ROW][C]46[/C][C]93.9[/C][C]93.499979131312[/C][C]0.400020868688031[/C][/ROW]
[ROW][C]47[/C][C]94.3[/C][C]93.8999791302233[/C][C]0.400020869776711[/C][/ROW]
[ROW][C]48[/C][C]94.7[/C][C]94.2999791302232[/C][C]0.400020869776782[/C][/ROW]
[ROW][C]49[/C][C]95.3[/C][C]94.6999791302232[/C][C]0.60002086977677[/C][/ROW]
[ROW][C]50[/C][C]95.9[/C][C]95.2999686958792[/C][C]0.600031304120776[/C][/ROW]
[ROW][C]51[/C][C]96.2[/C][C]95.8999686953349[/C][C]0.30003130466514[/C][/ROW]
[ROW][C]52[/C][C]96.7[/C][C]96.1999843468508[/C][C]0.500015653149191[/C][/ROW]
[ROW][C]53[/C][C]96.7[/C][C]96.6999739133234[/C][C]2.60866766126355e-05[/C][/ROW]
[ROW][C]54[/C][C]96.9[/C][C]96.699999998639[/C][C]0.200000001360991[/C][/ROW]
[ROW][C]55[/C][C]97.3[/C][C]96.899989565656[/C][C]0.40001043434404[/C][/ROW]
[ROW][C]56[/C][C]97.4[/C][C]97.2999791307677[/C][C]0.100020869232353[/C][/ROW]
[ROW][C]57[/C][C]97.9[/C][C]97.3999947817392[/C][C]0.500005218260782[/C][/ROW]
[ROW][C]58[/C][C]98.4[/C][C]97.8999739138678[/C][C]0.500026086132209[/C][/ROW]
[ROW][C]59[/C][C]98.4[/C][C]98.3999739127791[/C][C]2.60872209167928e-05[/C][/ROW]
[ROW][C]60[/C][C]98.8[/C][C]98.399999998639[/C][C]0.400000001361008[/C][/ROW]
[ROW][C]61[/C][C]98.9[/C][C]98.799979131312[/C][C]0.100020868688048[/C][/ROW]
[ROW][C]62[/C][C]98.9[/C][C]98.8999947817393[/C][C]5.21826075328136e-06[/C][/ROW]
[ROW][C]63[/C][C]99.3[/C][C]98.8999999997278[/C][C]0.400000000272243[/C][/ROW]
[ROW][C]64[/C][C]99.4[/C][C]99.299979131312[/C][C]0.100020868687992[/C][/ROW]
[ROW][C]65[/C][C]99.7[/C][C]99.3999947817393[/C][C]0.30000521826075[/C][/ROW]
[ROW][C]66[/C][C]99.8[/C][C]99.6999843482118[/C][C]0.100015651788212[/C][/ROW]
[ROW][C]67[/C][C]99.7[/C][C]99.7999947820114[/C][C]-0.0999947820114215[/C][/ROW]
[ROW][C]68[/C][C]99.9[/C][C]99.7000052168998[/C][C]0.199994783100237[/C][/ROW]
[ROW][C]69[/C][C]100.4[/C][C]99.8999895659282[/C][C]0.500010434071811[/C][/ROW]
[ROW][C]70[/C][C]101.1[/C][C]100.399973913596[/C][C]0.700026086404307[/C][/ROW]
[ROW][C]71[/C][C]101.3[/C][C]101.099963478435[/C][C]0.200036521564925[/C][/ROW]
[ROW][C]72[/C][C]101.4[/C][C]101.299989563751[/C][C]0.100010436249391[/C][/ROW]
[ROW][C]73[/C][C]101.8[/C][C]101.399994782284[/C][C]0.400005217716455[/C][/ROW]
[ROW][C]74[/C][C]102.2[/C][C]101.79997913104[/C][C]0.400020868960198[/C][/ROW]
[ROW][C]75[/C][C]102.4[/C][C]102.199979130223[/C][C]0.200020869776736[/C][/ROW]
[ROW][C]76[/C][C]102.5[/C][C]102.399989564567[/C][C]0.100010435432793[/C][/ROW]
[ROW][C]77[/C][C]102.8[/C][C]102.499994782284[/C][C]0.300005217716418[/C][/ROW]
[ROW][C]78[/C][C]103[/C][C]102.799984348212[/C][C]0.200015651788192[/C][/ROW]
[ROW][C]79[/C][C]103.2[/C][C]102.999989564839[/C][C]0.200010435160564[/C][/ROW]
[ROW][C]80[/C][C]103.2[/C][C]103.199989565112[/C][C]1.04348884093497e-05[/C][/ROW]
[ROW][C]81[/C][C]103.6[/C][C]103.199999999456[/C][C]0.400000000544395[/C][/ROW]
[ROW][C]82[/C][C]103.7[/C][C]103.599979131312[/C][C]0.100020868688006[/C][/ROW]
[ROW][C]83[/C][C]103.7[/C][C]103.699994781739[/C][C]5.21826075328136e-06[/C][/ROW]
[ROW][C]84[/C][C]103.8[/C][C]103.699999999728[/C][C]0.100000000272246[/C][/ROW]
[ROW][C]85[/C][C]104.2[/C][C]103.799994782828[/C][C]0.400005217172009[/C][/ROW]
[ROW][C]86[/C][C]104.5[/C][C]104.19997913104[/C][C]0.300020868960161[/C][/ROW]
[ROW][C]87[/C][C]104.5[/C][C]104.499984347395[/C][C]1.56526047447869e-05[/C][/ROW]
[ROW][C]88[/C][C]104.8[/C][C]104.499999999183[/C][C]0.300000000816624[/C][/ROW]
[ROW][C]89[/C][C]105.2[/C][C]104.799984348484[/C][C]0.400015651516028[/C][/ROW]
[ROW][C]90[/C][C]105.3[/C][C]105.199979130495[/C][C]0.100020869504533[/C][/ROW]
[ROW][C]91[/C][C]105.5[/C][C]105.299994781739[/C][C]0.200005218260799[/C][/ROW]
[ROW][C]92[/C][C]105.4[/C][C]105.499989565384[/C][C]-0.0999895653837655[/C][/ROW]
[ROW][C]93[/C][C]105.7[/C][C]105.400005216628[/C][C]0.299994783372398[/C][/ROW]
[ROW][C]94[/C][C]106.8[/C][C]105.699984348756[/C][C]1.10001565124381[/C][/ROW]
[ROW][C]95[/C][C]106.8[/C][C]106.799942610292[/C][C]5.73897084592545e-05[/C][/ROW]
[ROW][C]96[/C][C]107[/C][C]106.799999997006[/C][C]0.200000002994116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235005&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	83.6	83.5	0.0999999999999943
3	83.9	83.599994782828	0.300005217172
4	83.9	83.8999843482118	1.56517881606533e-05
5	84.2	83.8999999991834	0.300000000816581
6	84.4	84.199984348484	0.200015651516026
7	84.6	84.3999895648395	0.200010435160536
8	84.8	84.5999895651116	0.200010434888412
9	84.8	84.7999895651116	1.04348883951388e-05
10	84.9	84.7999999994556	0.100000000544412
11	85	84.899994782828	0.100005217172011
12	85.1	84.9999947825558	0.100005217444178
13	85.3	85.0999947825558	0.2000052174442
14	85.5	85.2999895653838	0.200010434616189
15	86.1	85.4999895651116	0.600010434888375
16	86.2	86.0999686964236	0.100031303576372
17	86.3	86.1999947811948	0.100005218805151
18	86.5	86.2999947825557	0.200005217444271
19	86.5	86.4999895653838	1.04346161862168e-05
20	86.6	86.4999999994556	0.100000000544384
21	86.8	86.599994782828	0.20000521717202
22	87.3	86.7999895653838	0.500010434616172
23	87.7	87.2999739135957	0.400026086404353
24	87.8	87.6999791299511	0.100020870048937
25	88.1	87.7999947817392	0.300005218260821
26	88.8	88.0999843482118	0.70001565178822
27	89.3	88.7999634789795	0.500036521020519
28	89.2	89.2999739122347	-0.0999739122346739
29	89.3	89.2000052158109	0.0999947841890503
30	89.6	89.2999947831001	0.300005216899876
31	89.6	89.5999843482118	1.56517881464424e-05
32	89.9	89.5999999991834	0.300000000816596
33	90.2	89.899984348484	0.30001565151602
34	90.2	90.1999843476675	1.56523325358648e-05
35	90.4	90.1999999991834	0.200000000816615
36	90.5	90.399989565656	0.100010434344014
37	91.5	90.4999947822836	1.00000521771636
38	91.5	91.4999478280079	5.21719921380281e-05
39	91.8	91.4999999972781	0.300000002721902
40	92.2	91.7999843484839	0.400015651516128
41	92.4	92.1999791304955	0.200020869504542
42	92.7	92.3999895645672	0.300010435432782
43	93.1	92.6999843479396	0.400015652060404
44	93.1	93.0999791304954	2.08695045671448e-05
45	93.5	93.0999999989112	0.400000001088799
46	93.9	93.499979131312	0.400020868688031
47	94.3	93.8999791302233	0.400020869776711
48	94.7	94.2999791302232	0.400020869776782
49	95.3	94.6999791302232	0.60002086977677
50	95.9	95.2999686958792	0.600031304120776
51	96.2	95.8999686953349	0.30003130466514
52	96.7	96.1999843468508	0.500015653149191
53	96.7	96.6999739133234	2.60866766126355e-05
54	96.9	96.699999998639	0.200000001360991
55	97.3	96.899989565656	0.40001043434404
56	97.4	97.2999791307677	0.100020869232353
57	97.9	97.3999947817392	0.500005218260782
58	98.4	97.8999739138678	0.500026086132209
59	98.4	98.3999739127791	2.60872209167928e-05
60	98.8	98.399999998639	0.400000001361008
61	98.9	98.799979131312	0.100020868688048
62	98.9	98.8999947817393	5.21826075328136e-06
63	99.3	98.8999999997278	0.400000000272243
64	99.4	99.299979131312	0.100020868687992
65	99.7	99.3999947817393	0.30000521826075
66	99.8	99.6999843482118	0.100015651788212
67	99.7	99.7999947820114	-0.0999947820114215
68	99.9	99.7000052168998	0.199994783100237
69	100.4	99.8999895659282	0.500010434071811
70	101.1	100.399973913596	0.700026086404307
71	101.3	101.099963478435	0.200036521564925
72	101.4	101.299989563751	0.100010436249391
73	101.8	101.399994782284	0.400005217716455
74	102.2	101.79997913104	0.400020868960198
75	102.4	102.199979130223	0.200020869776736
76	102.5	102.399989564567	0.100010435432793
77	102.8	102.499994782284	0.300005217716418
78	103	102.799984348212	0.200015651788192
79	103.2	102.999989564839	0.200010435160564
80	103.2	103.199989565112	1.04348884093497e-05
81	103.6	103.199999999456	0.400000000544395
82	103.7	103.599979131312	0.100020868688006
83	103.7	103.699994781739	5.21826075328136e-06
84	103.8	103.699999999728	0.100000000272246
85	104.2	103.799994782828	0.400005217172009
86	104.5	104.19997913104	0.300020868960161
87	104.5	104.499984347395	1.56526047447869e-05
88	104.8	104.499999999183	0.300000000816624
89	105.2	104.799984348484	0.400015651516028
90	105.3	105.199979130495	0.100020869504533
91	105.5	105.299994781739	0.200005218260799
92	105.4	105.499989565384	-0.0999895653837655
93	105.7	105.400005216628	0.299994783372398
94	106.8	105.699984348756	1.10001565124381
95	106.8	106.799942610292	5.73897084592545e-05
96	107	106.799999997006	0.200000002994116

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	106.999989565656	106.57035338383	107.429625747482
98	106.999989565656	106.392408099924	107.607571031388
99	106.999989565656	106.255863752188	107.744115379124
100	106.999989565656	106.140750824073	107.859228307239
101	106.999989565656	106.039333954209	107.960645177103
102	106.999989565656	105.947645899085	108.052333232227
103	106.999989565656	105.863329906242	108.13664922507
104	106.999989565656	105.784850408972	108.21512872234
105	106.999989565656	105.711140792962	108.28883833835
106	106.999989565656	105.641424459508	108.358554671804
107	106.999989565656	105.57511513736	108.424863993951
108	106.999989565656	105.511757350853	108.488221780459

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 106.999989565656 & 106.57035338383 & 107.429625747482 \tabularnewline
98 & 106.999989565656 & 106.392408099924 & 107.607571031388 \tabularnewline
99 & 106.999989565656 & 106.255863752188 & 107.744115379124 \tabularnewline
100 & 106.999989565656 & 106.140750824073 & 107.859228307239 \tabularnewline
101 & 106.999989565656 & 106.039333954209 & 107.960645177103 \tabularnewline
102 & 106.999989565656 & 105.947645899085 & 108.052333232227 \tabularnewline
103 & 106.999989565656 & 105.863329906242 & 108.13664922507 \tabularnewline
104 & 106.999989565656 & 105.784850408972 & 108.21512872234 \tabularnewline
105 & 106.999989565656 & 105.711140792962 & 108.28883833835 \tabularnewline
106 & 106.999989565656 & 105.641424459508 & 108.358554671804 \tabularnewline
107 & 106.999989565656 & 105.57511513736 & 108.424863993951 \tabularnewline
108 & 106.999989565656 & 105.511757350853 & 108.488221780459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235005&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]97[/C][C]106.999989565656[/C][C]106.57035338383[/C][C]107.429625747482[/C][/ROW]
[ROW][C]98[/C][C]106.999989565656[/C][C]106.392408099924[/C][C]107.607571031388[/C][/ROW]
[ROW][C]99[/C][C]106.999989565656[/C][C]106.255863752188[/C][C]107.744115379124[/C][/ROW]
[ROW][C]100[/C][C]106.999989565656[/C][C]106.140750824073[/C][C]107.859228307239[/C][/ROW]
[ROW][C]101[/C][C]106.999989565656[/C][C]106.039333954209[/C][C]107.960645177103[/C][/ROW]
[ROW][C]102[/C][C]106.999989565656[/C][C]105.947645899085[/C][C]108.052333232227[/C][/ROW]
[ROW][C]103[/C][C]106.999989565656[/C][C]105.863329906242[/C][C]108.13664922507[/C][/ROW]
[ROW][C]104[/C][C]106.999989565656[/C][C]105.784850408972[/C][C]108.21512872234[/C][/ROW]
[ROW][C]105[/C][C]106.999989565656[/C][C]105.711140792962[/C][C]108.28883833835[/C][/ROW]
[ROW][C]106[/C][C]106.999989565656[/C][C]105.641424459508[/C][C]108.358554671804[/C][/ROW]
[ROW][C]107[/C][C]106.999989565656[/C][C]105.57511513736[/C][C]108.424863993951[/C][/ROW]
[ROW][C]108[/C][C]106.999989565656[/C][C]105.511757350853[/C][C]108.488221780459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235005&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235005&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	106.999989565656	106.57035338383	107.429625747482
98	106.999989565656	106.392408099924	107.607571031388
99	106.999989565656	106.255863752188	107.744115379124
100	106.999989565656	106.140750824073	107.859228307239
101	106.999989565656	106.039333954209	107.960645177103
102	106.999989565656	105.947645899085	108.052333232227
103	106.999989565656	105.863329906242	108.13664922507
104	106.999989565656	105.784850408972	108.21512872234
105	106.999989565656	105.711140792962	108.28883833835
106	106.999989565656	105.641424459508	108.358554671804
107	106.999989565656	105.57511513736	108.424863993951
108	106.999989565656	105.511757350853	108.488221780459

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 = Single ; par3 = additive ;

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