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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 14 Dec 2013 12:13:57 -0500

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/2013/Dec/14/t1387041261e9h058yx0wq7nv2.htm/, Retrieved Thu, 27 Aug 2026 11:16:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232328, Retrieved Thu, 27 Aug 2026 11:16:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

579

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

-       [Exponential Smoothing] [] [2013-12-14 17:13:57] [cbeaf4c3f774367e9472b81246022ded] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.238639444547544
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.238639444547544 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]0.238639444547544[/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=232328&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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	0.238639444547544
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	86.6	86.5	0.0999999999999943
3	98.8	86.5238639444548	12.2761360555452
4	84.4	89.4534342339402	-5.05343423394015
5	91.4	88.2474854952951	3.15251450470487
6	95.7	88.999799805626	6.70020019437402
7	78.5	90.5987318583688	-12.0987318583688
8	81.7	87.711497207958	-6.01149720795796
9	94.3	86.2769168533518	8.02308314664823
10	98.5	88.1915409590267	10.3084590409733
11	95.4	90.6515458987056	4.74845410129436
12	91.7	91.784714347898	-0.0847143478980428
13	92.8	91.7644981629705	1.03550183702954
14	90.6	92.0116097461871	-1.41160974618715
15	102.2	91.6747439804391	10.5252560195609
16	91.8	94.1864852306678	-2.38648523066784
17	95	93.6169757208004	1.38302427919965
18	102	93.9470198665843	8.05298013341567
19	88.9	95.8687785725751	-6.96877857257505
20	89.6	94.2057531248409	-4.60575312484092
21	97.9	93.1066387574058	4.79336124259424
22	108.6	94.2505238218542	14.3494761781458
23	100.8	97.6748748465551	3.12512515344488
24	95.1	98.4206529773148	-3.32065297731477
25	101	97.6282141952732	3.37178580472678
26	100.9	98.4328552868465	2.4671447131535
27	102.5	99.0216133308119	3.47838666918814
28	105.4	99.8516935934685	5.54830640653151
29	98.4	101.175738352503	-2.77573835250276
30	105.3	100.513337693852	4.7866623061478
31	96.5	101.655624127828	-5.15562412782798
32	88.1	100.425288849667	-12.3252888496672
33	107.9	97.4839887646946	10.4160112353054
34	107.1	99.9696599002888	7.13034009971115
35	92.5	101.671240301119	-9.171240301119
36	95.7	99.4826206098479	-3.78262060984791
37	85.2	98.5799381285797	-13.3799381285797
38	85.5	95.3869571254949	-9.88695712549494
39	94.7	93.0275391688015	1.67246083119855
40	86.2	93.4266542925862	-7.22665429258619
41	88.8	91.7020895262663	-2.90208952626629
42	93.4	91.0095364936909	2.39046350630915
43	83.4	91.5799953770477	-8.17999537704765
44	82.9	89.6279258238675	-6.72792582386752
45	96.7	88.0223773423027	8.6776226576973
46	96.2	90.0932003933288	6.10679960667123
47	92.8	91.550523659428	1.24947634057204
48	92.8	91.8486979993174	0.951302000682631
49	90.2	92.0757161803572	-1.87571618035723
50	95.9	91.6280963129479	4.27190368705206
51	107.5	92.6475410359866	14.8524589640134
52	98	96.191923593324	1.80807640667601
53	95	96.6234019427127	-1.62340194271268
54	108.5	96.2359942048263	12.2640057951737
55	91.8	99.1626697357144	-7.36266973571443
56	91.7	97.4056463195965	-5.70564631959653
57	108.3	96.0440540511033	12.2559459488967
58	105.1	98.9688061847527	6.13119381524729
59	104.8	100.431950871237	4.36804912876333
60	103.2	101.474339689081	1.72566031091887
61	98.6	101.886150307157	-3.28615030715656
62	102.4	101.101945223157	1.29805477684303
63	121.2	101.411712294095	19.7882877059049
64	102.6	106.133978280779	-3.53397828077924
65	108.9	105.290631666811	3.60936833318901
66	105.5	106.151969321011	-0.651969321010711
67	90.8	105.996383724383	-15.1963837243827
68	99.6	102.369927153265	-2.76992715326466
69	111.6	101.708913275972	9.89108672402757
70	104.7	104.069316717766	0.63068328223406
71	103.1	104.219822625924	-1.1198226259237
72	101.7	103.952588776481	-2.25258877648149
73	98.8	103.415032242068	-4.61503224206793
74	101.4	102.313703511252	-0.913703511251825
75	114.2	102.095657812846	12.1043421871544
76	96.9	104.984231309002	-8.0842313090015
77	98.3	103.055014839828	-4.75501483982752
78	104.8	101.920280739636	2.87971926036424
79	94.4	102.607495344382	-8.20749534438194
80	94.5	100.648863214272	-6.14886321427208
81	102.4	99.1815019122194	3.21849808778065
82	105.5	99.9495625081647	5.55043749183534
83	101.2	101.274115828212	-0.0741158282121148
84	99.5	101.256428868135	-1.7564288681354

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.6 & 86.5 & 0.0999999999999943 \tabularnewline
3 & 98.8 & 86.5238639444548 & 12.2761360555452 \tabularnewline
4 & 84.4 & 89.4534342339402 & -5.05343423394015 \tabularnewline
5 & 91.4 & 88.2474854952951 & 3.15251450470487 \tabularnewline
6 & 95.7 & 88.999799805626 & 6.70020019437402 \tabularnewline
7 & 78.5 & 90.5987318583688 & -12.0987318583688 \tabularnewline
8 & 81.7 & 87.711497207958 & -6.01149720795796 \tabularnewline
9 & 94.3 & 86.2769168533518 & 8.02308314664823 \tabularnewline
10 & 98.5 & 88.1915409590267 & 10.3084590409733 \tabularnewline
11 & 95.4 & 90.6515458987056 & 4.74845410129436 \tabularnewline
12 & 91.7 & 91.784714347898 & -0.0847143478980428 \tabularnewline
13 & 92.8 & 91.7644981629705 & 1.03550183702954 \tabularnewline
14 & 90.6 & 92.0116097461871 & -1.41160974618715 \tabularnewline
15 & 102.2 & 91.6747439804391 & 10.5252560195609 \tabularnewline
16 & 91.8 & 94.1864852306678 & -2.38648523066784 \tabularnewline
17 & 95 & 93.6169757208004 & 1.38302427919965 \tabularnewline
18 & 102 & 93.9470198665843 & 8.05298013341567 \tabularnewline
19 & 88.9 & 95.8687785725751 & -6.96877857257505 \tabularnewline
20 & 89.6 & 94.2057531248409 & -4.60575312484092 \tabularnewline
21 & 97.9 & 93.1066387574058 & 4.79336124259424 \tabularnewline
22 & 108.6 & 94.2505238218542 & 14.3494761781458 \tabularnewline
23 & 100.8 & 97.6748748465551 & 3.12512515344488 \tabularnewline
24 & 95.1 & 98.4206529773148 & -3.32065297731477 \tabularnewline
25 & 101 & 97.6282141952732 & 3.37178580472678 \tabularnewline
26 & 100.9 & 98.4328552868465 & 2.4671447131535 \tabularnewline
27 & 102.5 & 99.0216133308119 & 3.47838666918814 \tabularnewline
28 & 105.4 & 99.8516935934685 & 5.54830640653151 \tabularnewline
29 & 98.4 & 101.175738352503 & -2.77573835250276 \tabularnewline
30 & 105.3 & 100.513337693852 & 4.7866623061478 \tabularnewline
31 & 96.5 & 101.655624127828 & -5.15562412782798 \tabularnewline
32 & 88.1 & 100.425288849667 & -12.3252888496672 \tabularnewline
33 & 107.9 & 97.4839887646946 & 10.4160112353054 \tabularnewline
34 & 107.1 & 99.9696599002888 & 7.13034009971115 \tabularnewline
35 & 92.5 & 101.671240301119 & -9.171240301119 \tabularnewline
36 & 95.7 & 99.4826206098479 & -3.78262060984791 \tabularnewline
37 & 85.2 & 98.5799381285797 & -13.3799381285797 \tabularnewline
38 & 85.5 & 95.3869571254949 & -9.88695712549494 \tabularnewline
39 & 94.7 & 93.0275391688015 & 1.67246083119855 \tabularnewline
40 & 86.2 & 93.4266542925862 & -7.22665429258619 \tabularnewline
41 & 88.8 & 91.7020895262663 & -2.90208952626629 \tabularnewline
42 & 93.4 & 91.0095364936909 & 2.39046350630915 \tabularnewline
43 & 83.4 & 91.5799953770477 & -8.17999537704765 \tabularnewline
44 & 82.9 & 89.6279258238675 & -6.72792582386752 \tabularnewline
45 & 96.7 & 88.0223773423027 & 8.6776226576973 \tabularnewline
46 & 96.2 & 90.0932003933288 & 6.10679960667123 \tabularnewline
47 & 92.8 & 91.550523659428 & 1.24947634057204 \tabularnewline
48 & 92.8 & 91.8486979993174 & 0.951302000682631 \tabularnewline
49 & 90.2 & 92.0757161803572 & -1.87571618035723 \tabularnewline
50 & 95.9 & 91.6280963129479 & 4.27190368705206 \tabularnewline
51 & 107.5 & 92.6475410359866 & 14.8524589640134 \tabularnewline
52 & 98 & 96.191923593324 & 1.80807640667601 \tabularnewline
53 & 95 & 96.6234019427127 & -1.62340194271268 \tabularnewline
54 & 108.5 & 96.2359942048263 & 12.2640057951737 \tabularnewline
55 & 91.8 & 99.1626697357144 & -7.36266973571443 \tabularnewline
56 & 91.7 & 97.4056463195965 & -5.70564631959653 \tabularnewline
57 & 108.3 & 96.0440540511033 & 12.2559459488967 \tabularnewline
58 & 105.1 & 98.9688061847527 & 6.13119381524729 \tabularnewline
59 & 104.8 & 100.431950871237 & 4.36804912876333 \tabularnewline
60 & 103.2 & 101.474339689081 & 1.72566031091887 \tabularnewline
61 & 98.6 & 101.886150307157 & -3.28615030715656 \tabularnewline
62 & 102.4 & 101.101945223157 & 1.29805477684303 \tabularnewline
63 & 121.2 & 101.411712294095 & 19.7882877059049 \tabularnewline
64 & 102.6 & 106.133978280779 & -3.53397828077924 \tabularnewline
65 & 108.9 & 105.290631666811 & 3.60936833318901 \tabularnewline
66 & 105.5 & 106.151969321011 & -0.651969321010711 \tabularnewline
67 & 90.8 & 105.996383724383 & -15.1963837243827 \tabularnewline
68 & 99.6 & 102.369927153265 & -2.76992715326466 \tabularnewline
69 & 111.6 & 101.708913275972 & 9.89108672402757 \tabularnewline
70 & 104.7 & 104.069316717766 & 0.63068328223406 \tabularnewline
71 & 103.1 & 104.219822625924 & -1.1198226259237 \tabularnewline
72 & 101.7 & 103.952588776481 & -2.25258877648149 \tabularnewline
73 & 98.8 & 103.415032242068 & -4.61503224206793 \tabularnewline
74 & 101.4 & 102.313703511252 & -0.913703511251825 \tabularnewline
75 & 114.2 & 102.095657812846 & 12.1043421871544 \tabularnewline
76 & 96.9 & 104.984231309002 & -8.0842313090015 \tabularnewline
77 & 98.3 & 103.055014839828 & -4.75501483982752 \tabularnewline
78 & 104.8 & 101.920280739636 & 2.87971926036424 \tabularnewline
79 & 94.4 & 102.607495344382 & -8.20749534438194 \tabularnewline
80 & 94.5 & 100.648863214272 & -6.14886321427208 \tabularnewline
81 & 102.4 & 99.1815019122194 & 3.21849808778065 \tabularnewline
82 & 105.5 & 99.9495625081647 & 5.55043749183534 \tabularnewline
83 & 101.2 & 101.274115828212 & -0.0741158282121148 \tabularnewline
84 & 99.5 & 101.256428868135 & -1.7564288681354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]86.6[/C][C]86.5[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]3[/C][C]98.8[/C][C]86.5238639444548[/C][C]12.2761360555452[/C][/ROW]
[ROW][C]4[/C][C]84.4[/C][C]89.4534342339402[/C][C]-5.05343423394015[/C][/ROW]
[ROW][C]5[/C][C]91.4[/C][C]88.2474854952951[/C][C]3.15251450470487[/C][/ROW]
[ROW][C]6[/C][C]95.7[/C][C]88.999799805626[/C][C]6.70020019437402[/C][/ROW]
[ROW][C]7[/C][C]78.5[/C][C]90.5987318583688[/C][C]-12.0987318583688[/C][/ROW]
[ROW][C]8[/C][C]81.7[/C][C]87.711497207958[/C][C]-6.01149720795796[/C][/ROW]
[ROW][C]9[/C][C]94.3[/C][C]86.2769168533518[/C][C]8.02308314664823[/C][/ROW]
[ROW][C]10[/C][C]98.5[/C][C]88.1915409590267[/C][C]10.3084590409733[/C][/ROW]
[ROW][C]11[/C][C]95.4[/C][C]90.6515458987056[/C][C]4.74845410129436[/C][/ROW]
[ROW][C]12[/C][C]91.7[/C][C]91.784714347898[/C][C]-0.0847143478980428[/C][/ROW]
[ROW][C]13[/C][C]92.8[/C][C]91.7644981629705[/C][C]1.03550183702954[/C][/ROW]
[ROW][C]14[/C][C]90.6[/C][C]92.0116097461871[/C][C]-1.41160974618715[/C][/ROW]
[ROW][C]15[/C][C]102.2[/C][C]91.6747439804391[/C][C]10.5252560195609[/C][/ROW]
[ROW][C]16[/C][C]91.8[/C][C]94.1864852306678[/C][C]-2.38648523066784[/C][/ROW]
[ROW][C]17[/C][C]95[/C][C]93.6169757208004[/C][C]1.38302427919965[/C][/ROW]
[ROW][C]18[/C][C]102[/C][C]93.9470198665843[/C][C]8.05298013341567[/C][/ROW]
[ROW][C]19[/C][C]88.9[/C][C]95.8687785725751[/C][C]-6.96877857257505[/C][/ROW]
[ROW][C]20[/C][C]89.6[/C][C]94.2057531248409[/C][C]-4.60575312484092[/C][/ROW]
[ROW][C]21[/C][C]97.9[/C][C]93.1066387574058[/C][C]4.79336124259424[/C][/ROW]
[ROW][C]22[/C][C]108.6[/C][C]94.2505238218542[/C][C]14.3494761781458[/C][/ROW]
[ROW][C]23[/C][C]100.8[/C][C]97.6748748465551[/C][C]3.12512515344488[/C][/ROW]
[ROW][C]24[/C][C]95.1[/C][C]98.4206529773148[/C][C]-3.32065297731477[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]97.6282141952732[/C][C]3.37178580472678[/C][/ROW]
[ROW][C]26[/C][C]100.9[/C][C]98.4328552868465[/C][C]2.4671447131535[/C][/ROW]
[ROW][C]27[/C][C]102.5[/C][C]99.0216133308119[/C][C]3.47838666918814[/C][/ROW]
[ROW][C]28[/C][C]105.4[/C][C]99.8516935934685[/C][C]5.54830640653151[/C][/ROW]
[ROW][C]29[/C][C]98.4[/C][C]101.175738352503[/C][C]-2.77573835250276[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]100.513337693852[/C][C]4.7866623061478[/C][/ROW]
[ROW][C]31[/C][C]96.5[/C][C]101.655624127828[/C][C]-5.15562412782798[/C][/ROW]
[ROW][C]32[/C][C]88.1[/C][C]100.425288849667[/C][C]-12.3252888496672[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]97.4839887646946[/C][C]10.4160112353054[/C][/ROW]
[ROW][C]34[/C][C]107.1[/C][C]99.9696599002888[/C][C]7.13034009971115[/C][/ROW]
[ROW][C]35[/C][C]92.5[/C][C]101.671240301119[/C][C]-9.171240301119[/C][/ROW]
[ROW][C]36[/C][C]95.7[/C][C]99.4826206098479[/C][C]-3.78262060984791[/C][/ROW]
[ROW][C]37[/C][C]85.2[/C][C]98.5799381285797[/C][C]-13.3799381285797[/C][/ROW]
[ROW][C]38[/C][C]85.5[/C][C]95.3869571254949[/C][C]-9.88695712549494[/C][/ROW]
[ROW][C]39[/C][C]94.7[/C][C]93.0275391688015[/C][C]1.67246083119855[/C][/ROW]
[ROW][C]40[/C][C]86.2[/C][C]93.4266542925862[/C][C]-7.22665429258619[/C][/ROW]
[ROW][C]41[/C][C]88.8[/C][C]91.7020895262663[/C][C]-2.90208952626629[/C][/ROW]
[ROW][C]42[/C][C]93.4[/C][C]91.0095364936909[/C][C]2.39046350630915[/C][/ROW]
[ROW][C]43[/C][C]83.4[/C][C]91.5799953770477[/C][C]-8.17999537704765[/C][/ROW]
[ROW][C]44[/C][C]82.9[/C][C]89.6279258238675[/C][C]-6.72792582386752[/C][/ROW]
[ROW][C]45[/C][C]96.7[/C][C]88.0223773423027[/C][C]8.6776226576973[/C][/ROW]
[ROW][C]46[/C][C]96.2[/C][C]90.0932003933288[/C][C]6.10679960667123[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]91.550523659428[/C][C]1.24947634057204[/C][/ROW]
[ROW][C]48[/C][C]92.8[/C][C]91.8486979993174[/C][C]0.951302000682631[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]92.0757161803572[/C][C]-1.87571618035723[/C][/ROW]
[ROW][C]50[/C][C]95.9[/C][C]91.6280963129479[/C][C]4.27190368705206[/C][/ROW]
[ROW][C]51[/C][C]107.5[/C][C]92.6475410359866[/C][C]14.8524589640134[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]96.191923593324[/C][C]1.80807640667601[/C][/ROW]
[ROW][C]53[/C][C]95[/C][C]96.6234019427127[/C][C]-1.62340194271268[/C][/ROW]
[ROW][C]54[/C][C]108.5[/C][C]96.2359942048263[/C][C]12.2640057951737[/C][/ROW]
[ROW][C]55[/C][C]91.8[/C][C]99.1626697357144[/C][C]-7.36266973571443[/C][/ROW]
[ROW][C]56[/C][C]91.7[/C][C]97.4056463195965[/C][C]-5.70564631959653[/C][/ROW]
[ROW][C]57[/C][C]108.3[/C][C]96.0440540511033[/C][C]12.2559459488967[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]98.9688061847527[/C][C]6.13119381524729[/C][/ROW]
[ROW][C]59[/C][C]104.8[/C][C]100.431950871237[/C][C]4.36804912876333[/C][/ROW]
[ROW][C]60[/C][C]103.2[/C][C]101.474339689081[/C][C]1.72566031091887[/C][/ROW]
[ROW][C]61[/C][C]98.6[/C][C]101.886150307157[/C][C]-3.28615030715656[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]101.101945223157[/C][C]1.29805477684303[/C][/ROW]
[ROW][C]63[/C][C]121.2[/C][C]101.411712294095[/C][C]19.7882877059049[/C][/ROW]
[ROW][C]64[/C][C]102.6[/C][C]106.133978280779[/C][C]-3.53397828077924[/C][/ROW]
[ROW][C]65[/C][C]108.9[/C][C]105.290631666811[/C][C]3.60936833318901[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]106.151969321011[/C][C]-0.651969321010711[/C][/ROW]
[ROW][C]67[/C][C]90.8[/C][C]105.996383724383[/C][C]-15.1963837243827[/C][/ROW]
[ROW][C]68[/C][C]99.6[/C][C]102.369927153265[/C][C]-2.76992715326466[/C][/ROW]
[ROW][C]69[/C][C]111.6[/C][C]101.708913275972[/C][C]9.89108672402757[/C][/ROW]
[ROW][C]70[/C][C]104.7[/C][C]104.069316717766[/C][C]0.63068328223406[/C][/ROW]
[ROW][C]71[/C][C]103.1[/C][C]104.219822625924[/C][C]-1.1198226259237[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]103.952588776481[/C][C]-2.25258877648149[/C][/ROW]
[ROW][C]73[/C][C]98.8[/C][C]103.415032242068[/C][C]-4.61503224206793[/C][/ROW]
[ROW][C]74[/C][C]101.4[/C][C]102.313703511252[/C][C]-0.913703511251825[/C][/ROW]
[ROW][C]75[/C][C]114.2[/C][C]102.095657812846[/C][C]12.1043421871544[/C][/ROW]
[ROW][C]76[/C][C]96.9[/C][C]104.984231309002[/C][C]-8.0842313090015[/C][/ROW]
[ROW][C]77[/C][C]98.3[/C][C]103.055014839828[/C][C]-4.75501483982752[/C][/ROW]
[ROW][C]78[/C][C]104.8[/C][C]101.920280739636[/C][C]2.87971926036424[/C][/ROW]
[ROW][C]79[/C][C]94.4[/C][C]102.607495344382[/C][C]-8.20749534438194[/C][/ROW]
[ROW][C]80[/C][C]94.5[/C][C]100.648863214272[/C][C]-6.14886321427208[/C][/ROW]
[ROW][C]81[/C][C]102.4[/C][C]99.1815019122194[/C][C]3.21849808778065[/C][/ROW]
[ROW][C]82[/C][C]105.5[/C][C]99.9495625081647[/C][C]5.55043749183534[/C][/ROW]
[ROW][C]83[/C][C]101.2[/C][C]101.274115828212[/C][C]-0.0741158282121148[/C][/ROW]
[ROW][C]84[/C][C]99.5[/C][C]101.256428868135[/C][C]-1.7564288681354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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	86.6	86.5	0.0999999999999943
3	98.8	86.5238639444548	12.2761360555452
4	84.4	89.4534342339402	-5.05343423394015
5	91.4	88.2474854952951	3.15251450470487
6	95.7	88.999799805626	6.70020019437402
7	78.5	90.5987318583688	-12.0987318583688
8	81.7	87.711497207958	-6.01149720795796
9	94.3	86.2769168533518	8.02308314664823
10	98.5	88.1915409590267	10.3084590409733
11	95.4	90.6515458987056	4.74845410129436
12	91.7	91.784714347898	-0.0847143478980428
13	92.8	91.7644981629705	1.03550183702954
14	90.6	92.0116097461871	-1.41160974618715
15	102.2	91.6747439804391	10.5252560195609
16	91.8	94.1864852306678	-2.38648523066784
17	95	93.6169757208004	1.38302427919965
18	102	93.9470198665843	8.05298013341567
19	88.9	95.8687785725751	-6.96877857257505
20	89.6	94.2057531248409	-4.60575312484092
21	97.9	93.1066387574058	4.79336124259424
22	108.6	94.2505238218542	14.3494761781458
23	100.8	97.6748748465551	3.12512515344488
24	95.1	98.4206529773148	-3.32065297731477
25	101	97.6282141952732	3.37178580472678
26	100.9	98.4328552868465	2.4671447131535
27	102.5	99.0216133308119	3.47838666918814
28	105.4	99.8516935934685	5.54830640653151
29	98.4	101.175738352503	-2.77573835250276
30	105.3	100.513337693852	4.7866623061478
31	96.5	101.655624127828	-5.15562412782798
32	88.1	100.425288849667	-12.3252888496672
33	107.9	97.4839887646946	10.4160112353054
34	107.1	99.9696599002888	7.13034009971115
35	92.5	101.671240301119	-9.171240301119
36	95.7	99.4826206098479	-3.78262060984791
37	85.2	98.5799381285797	-13.3799381285797
38	85.5	95.3869571254949	-9.88695712549494
39	94.7	93.0275391688015	1.67246083119855
40	86.2	93.4266542925862	-7.22665429258619
41	88.8	91.7020895262663	-2.90208952626629
42	93.4	91.0095364936909	2.39046350630915
43	83.4	91.5799953770477	-8.17999537704765
44	82.9	89.6279258238675	-6.72792582386752
45	96.7	88.0223773423027	8.6776226576973
46	96.2	90.0932003933288	6.10679960667123
47	92.8	91.550523659428	1.24947634057204
48	92.8	91.8486979993174	0.951302000682631
49	90.2	92.0757161803572	-1.87571618035723
50	95.9	91.6280963129479	4.27190368705206
51	107.5	92.6475410359866	14.8524589640134
52	98	96.191923593324	1.80807640667601
53	95	96.6234019427127	-1.62340194271268
54	108.5	96.2359942048263	12.2640057951737
55	91.8	99.1626697357144	-7.36266973571443
56	91.7	97.4056463195965	-5.70564631959653
57	108.3	96.0440540511033	12.2559459488967
58	105.1	98.9688061847527	6.13119381524729
59	104.8	100.431950871237	4.36804912876333
60	103.2	101.474339689081	1.72566031091887
61	98.6	101.886150307157	-3.28615030715656
62	102.4	101.101945223157	1.29805477684303
63	121.2	101.411712294095	19.7882877059049
64	102.6	106.133978280779	-3.53397828077924
65	108.9	105.290631666811	3.60936833318901
66	105.5	106.151969321011	-0.651969321010711
67	90.8	105.996383724383	-15.1963837243827
68	99.6	102.369927153265	-2.76992715326466
69	111.6	101.708913275972	9.89108672402757
70	104.7	104.069316717766	0.63068328223406
71	103.1	104.219822625924	-1.1198226259237
72	101.7	103.952588776481	-2.25258877648149
73	98.8	103.415032242068	-4.61503224206793
74	101.4	102.313703511252	-0.913703511251825
75	114.2	102.095657812846	12.1043421871544
76	96.9	104.984231309002	-8.0842313090015
77	98.3	103.055014839828	-4.75501483982752
78	104.8	101.920280739636	2.87971926036424
79	94.4	102.607495344382	-8.20749534438194
80	94.5	100.648863214272	-6.14886321427208
81	102.4	99.1815019122194	3.21849808778065
82	105.5	99.9495625081647	5.55043749183534
83	101.2	101.274115828212	-0.0741158282121148
84	99.5	101.256428868135	-1.7564288681354

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	100.837275658656	87.0592202442631	114.615331073049
86	100.837275658656	86.672330450739	115.002220866574
87	100.837275658656	86.295730538398	115.378820778915
88	100.837275658656	85.9286407035131	115.745910613799
89	100.837275658656	85.5703749264537	116.104176390859
90	100.837275658656	85.2203259018012	116.454225415511
91	100.837275658656	84.8779529459173	116.796598371395
92	100.837275658656	84.542772193053	117.13177912426
93	100.837275658656	84.2143485718955	117.460202745417
94	100.837275658656	83.8922891826223	117.78226213469
95	100.837275658656	83.5762377867847	118.098313530528
96	100.837275658656	83.2658701896736	118.408681127639

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.837275658656 & 87.0592202442631 & 114.615331073049 \tabularnewline
86 & 100.837275658656 & 86.672330450739 & 115.002220866574 \tabularnewline
87 & 100.837275658656 & 86.295730538398 & 115.378820778915 \tabularnewline
88 & 100.837275658656 & 85.9286407035131 & 115.745910613799 \tabularnewline
89 & 100.837275658656 & 85.5703749264537 & 116.104176390859 \tabularnewline
90 & 100.837275658656 & 85.2203259018012 & 116.454225415511 \tabularnewline
91 & 100.837275658656 & 84.8779529459173 & 116.796598371395 \tabularnewline
92 & 100.837275658656 & 84.542772193053 & 117.13177912426 \tabularnewline
93 & 100.837275658656 & 84.2143485718955 & 117.460202745417 \tabularnewline
94 & 100.837275658656 & 83.8922891826223 & 117.78226213469 \tabularnewline
95 & 100.837275658656 & 83.5762377867847 & 118.098313530528 \tabularnewline
96 & 100.837275658656 & 83.2658701896736 & 118.408681127639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]85[/C][C]100.837275658656[/C][C]87.0592202442631[/C][C]114.615331073049[/C][/ROW]
[ROW][C]86[/C][C]100.837275658656[/C][C]86.672330450739[/C][C]115.002220866574[/C][/ROW]
[ROW][C]87[/C][C]100.837275658656[/C][C]86.295730538398[/C][C]115.378820778915[/C][/ROW]
[ROW][C]88[/C][C]100.837275658656[/C][C]85.9286407035131[/C][C]115.745910613799[/C][/ROW]
[ROW][C]89[/C][C]100.837275658656[/C][C]85.5703749264537[/C][C]116.104176390859[/C][/ROW]
[ROW][C]90[/C][C]100.837275658656[/C][C]85.2203259018012[/C][C]116.454225415511[/C][/ROW]
[ROW][C]91[/C][C]100.837275658656[/C][C]84.8779529459173[/C][C]116.796598371395[/C][/ROW]
[ROW][C]92[/C][C]100.837275658656[/C][C]84.542772193053[/C][C]117.13177912426[/C][/ROW]
[ROW][C]93[/C][C]100.837275658656[/C][C]84.2143485718955[/C][C]117.460202745417[/C][/ROW]
[ROW][C]94[/C][C]100.837275658656[/C][C]83.8922891826223[/C][C]117.78226213469[/C][/ROW]
[ROW][C]95[/C][C]100.837275658656[/C][C]83.5762377867847[/C][C]118.098313530528[/C][/ROW]
[ROW][C]96[/C][C]100.837275658656[/C][C]83.2658701896736[/C][C]118.408681127639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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
85	100.837275658656	87.0592202442631	114.615331073049
86	100.837275658656	86.672330450739	115.002220866574
87	100.837275658656	86.295730538398	115.378820778915
88	100.837275658656	85.9286407035131	115.745910613799
89	100.837275658656	85.5703749264537	116.104176390859
90	100.837275658656	85.2203259018012	116.454225415511
91	100.837275658656	84.8779529459173	116.796598371395
92	100.837275658656	84.542772193053	117.13177912426
93	100.837275658656	84.2143485718955	117.460202745417
94	100.837275658656	83.8922891826223	117.78226213469
95	100.837275658656	83.5762377867847	118.098313530528
96	100.837275658656	83.2658701896736	118.408681127639

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