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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

Tue, 24 Nov 2015 20:18:28 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/24/t14483964164xbgt6h559j9gap.htm/, Retrieved Tue, 10 Feb 2026 23:10:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284059, Retrieved Tue, 10 Feb 2026 23:10:42 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

299

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

-       [Exponential Smoothing] [] [2015-11-24 20:18:28] [c1ddba2a8e5acbd364f51ad7d8f1d5c9] [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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284059&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284059&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284059&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.998338859722899
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.998338859722899 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284059&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]0.998338859722899[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284059&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284059&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	0.998338859722899
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	89.24	88.2028205128205	1.03717948717946
14	89.24	89.2341279152301	0.00587208476991918
15	89.24	89.2358410614943	0.00415893850571081
16	89.24	89.2491772406039	-0.0091772406038757
17	89.24	89.2625327272015	-0.0225327272014653
18	89.24	89.2625549125382	-0.0225549125381974
19	89.24	89.1692216160578	0.0707783839421836
20	89.24	89.2357332430265	0.0042667569734931
21	89.24	89.235843728169	0.00415627183103595
22	91	91.3158439117003	-0.31584391170027
23	91	90.9963754768938	0.00362452310618266
24	91	90.9958447950095	0.00415520499049649
25	91	90.9958439134725	0.00415608652754429
26	91	90.9958439120081	0.00415608799191602
27	91	90.9958439120057	0.00415608799434608
28	91	91.009177245339	-0.00917724533897513
29	91	91.0225327272093	-0.0225327272093381
30	91	91.0225549125382	-0.0225549125381974
31	91	90.9292216160578	0.0707783839421836
32	91	90.9957332430265	0.0042667569734931
33	91	90.9958437281689	0.00415627183105016
34	92.51	93.0758439117003	-0.56584391170027
35	92.51	92.5067907619631	0.00320923803690221
36	92.51	92.5058454848563	0.0041545151437532
37	92.51	92.5058439146184	0.0041560853816236
38	92.51	92.50584391201	0.00415608799001177
39	92.51	92.5058439120057	0.00415608799433187
40	92.51	92.519177245339	-0.00917724533896092
41	92.51	92.5325327272093	-0.0225327272093381
42	92.51	92.5325549125382	-0.0225549125382116
43	92.51	92.4392216160578	0.0707783839421836
44	92.51	92.5057332430265	0.0042667569734931
45	92.51	92.505843728169	0.00415627183105016
46	96.67	94.5858439117003	2.08415608829972
47	96.67	96.6623887402288	0.0076112597712239
48	96.67	96.6658381724807	0.00416182751934002
49	96.67	96.6658439024715	0.00415609752850798
50	96.67	96.6658439119898	0.00415608801017697
51	96.67	96.6658439120056	0.0041560879943745
52	96.67	96.679177245339	-0.00917724533897513
53	96.67	96.6925327272093	-0.0225327272093381
54	96.67	96.6925549125382	-0.0225549125381974
55	96.67	96.5992216160578	0.0707783839421836
56	96.67	96.6657332430265	0.00426675697350731
57	96.67	96.665843728169	0.00415627183105016
58	96.19	98.7458439117003	-2.55584391170026
59	96.19	96.1900964311145	-9.64311145139618e-05
60	96.19	96.1858509760364	0.00414902396357775
61	96.19	96.18584392374	0.00415607625998859
62	96.19	96.1858439120251	0.004156087974863
63	96.19	96.1858439120057	0.00415608799430345
64	96.19	96.199177245339	-0.00917724533897513
65	96.19	96.2125327272093	-0.0225327272093381
66	96.19	96.2125549125382	-0.0225549125381974
67	96.19	96.1192216160578	0.0707783839421836
68	96.19	96.1857332430265	0.00426675697350731
69	96.19	96.1858437281689	0.00415627183105016
70	99.13	98.2658439117003	0.864156088299723
71	99.13	99.1244153313668	0.00558466863316198
72	99.13	99.1258415389328	0.00415846106717765
73	99.13	99.1258439080636	0.00415609193635191
74	99.13	99.1258439119991	0.00415608800089728
75	99.13	99.1258439120056	0.00415608799436029
76	99.13	99.139177245339	-0.00917724533897513
77	99.13	99.1525327272093	-0.0225327272093381
78	99.13	99.1525549125382	-0.0225549125382116
79	99.13	99.0592216160578	0.0707783839421836
80	99.13	99.1257332430265	0.00426675697350731
81	99.13	99.125843728169	0.00415627183103595
82	99.58	101.2058439117	-1.62584391170027
83	99.58	99.5785515706568	0.0014484293431849
84	99.58	99.5758484098065	0.00415159019351563
85	99.58	99.5758439194771	0.00415608052287553
86	99.58	99.5758439120181	0.00415608798192579
87	99.58	99.5758439120057	0.00415608799433187
88	99.58	99.589177245339	-0.00917724533897513
89	99.58	99.6025327272093	-0.0225327272093381
90	99.58	99.6025549125382	-0.0225549125382116
91	99.58	99.5092216160578	0.0707783839421836
92	99.58	99.5757332430265	0.0042667569734931
93	99.58	99.575843728169	0.00415627183103595
94	101.27	101.6558439117	-0.385843911700277
95	101.27	101.266491756713	0.0035082432867739
96	101.27	101.265844988167	0.0041550118334186
97	101.25	101.265843913793	-0.0158439137933044
98	101.25	101.245877134814	0.00412286518583471
99	101.25	101.245843967193	0.00415603280660548
100	101.25	101.259177245431	-0.00917724543063514
101	101.25	101.272532727209	-0.0225327272094944
102	101.25	101.272554912538	-0.0225549125382116
103	101.25	101.179221616058	0.0707783839421836
104	101.25	101.245733243027	0.0042667569734931
105	101.25	101.245843728169	0.00415627183105016
106	102.55	103.3258439117	-0.775843911700278
107	102.55	102.547139601421	0.00286039857871856
108	102.55	102.545846064328	0.0041539356724769

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 89.24 & 88.2028205128205 & 1.03717948717946 \tabularnewline
14 & 89.24 & 89.2341279152301 & 0.00587208476991918 \tabularnewline
15 & 89.24 & 89.2358410614943 & 0.00415893850571081 \tabularnewline
16 & 89.24 & 89.2491772406039 & -0.0091772406038757 \tabularnewline
17 & 89.24 & 89.2625327272015 & -0.0225327272014653 \tabularnewline
18 & 89.24 & 89.2625549125382 & -0.0225549125381974 \tabularnewline
19 & 89.24 & 89.1692216160578 & 0.0707783839421836 \tabularnewline
20 & 89.24 & 89.2357332430265 & 0.0042667569734931 \tabularnewline
21 & 89.24 & 89.235843728169 & 0.00415627183103595 \tabularnewline
22 & 91 & 91.3158439117003 & -0.31584391170027 \tabularnewline
23 & 91 & 90.9963754768938 & 0.00362452310618266 \tabularnewline
24 & 91 & 90.9958447950095 & 0.00415520499049649 \tabularnewline
25 & 91 & 90.9958439134725 & 0.00415608652754429 \tabularnewline
26 & 91 & 90.9958439120081 & 0.00415608799191602 \tabularnewline
27 & 91 & 90.9958439120057 & 0.00415608799434608 \tabularnewline
28 & 91 & 91.009177245339 & -0.00917724533897513 \tabularnewline
29 & 91 & 91.0225327272093 & -0.0225327272093381 \tabularnewline
30 & 91 & 91.0225549125382 & -0.0225549125381974 \tabularnewline
31 & 91 & 90.9292216160578 & 0.0707783839421836 \tabularnewline
32 & 91 & 90.9957332430265 & 0.0042667569734931 \tabularnewline
33 & 91 & 90.9958437281689 & 0.00415627183105016 \tabularnewline
34 & 92.51 & 93.0758439117003 & -0.56584391170027 \tabularnewline
35 & 92.51 & 92.5067907619631 & 0.00320923803690221 \tabularnewline
36 & 92.51 & 92.5058454848563 & 0.0041545151437532 \tabularnewline
37 & 92.51 & 92.5058439146184 & 0.0041560853816236 \tabularnewline
38 & 92.51 & 92.50584391201 & 0.00415608799001177 \tabularnewline
39 & 92.51 & 92.5058439120057 & 0.00415608799433187 \tabularnewline
40 & 92.51 & 92.519177245339 & -0.00917724533896092 \tabularnewline
41 & 92.51 & 92.5325327272093 & -0.0225327272093381 \tabularnewline
42 & 92.51 & 92.5325549125382 & -0.0225549125382116 \tabularnewline
43 & 92.51 & 92.4392216160578 & 0.0707783839421836 \tabularnewline
44 & 92.51 & 92.5057332430265 & 0.0042667569734931 \tabularnewline
45 & 92.51 & 92.505843728169 & 0.00415627183105016 \tabularnewline
46 & 96.67 & 94.5858439117003 & 2.08415608829972 \tabularnewline
47 & 96.67 & 96.6623887402288 & 0.0076112597712239 \tabularnewline
48 & 96.67 & 96.6658381724807 & 0.00416182751934002 \tabularnewline
49 & 96.67 & 96.6658439024715 & 0.00415609752850798 \tabularnewline
50 & 96.67 & 96.6658439119898 & 0.00415608801017697 \tabularnewline
51 & 96.67 & 96.6658439120056 & 0.0041560879943745 \tabularnewline
52 & 96.67 & 96.679177245339 & -0.00917724533897513 \tabularnewline
53 & 96.67 & 96.6925327272093 & -0.0225327272093381 \tabularnewline
54 & 96.67 & 96.6925549125382 & -0.0225549125381974 \tabularnewline
55 & 96.67 & 96.5992216160578 & 0.0707783839421836 \tabularnewline
56 & 96.67 & 96.6657332430265 & 0.00426675697350731 \tabularnewline
57 & 96.67 & 96.665843728169 & 0.00415627183105016 \tabularnewline
58 & 96.19 & 98.7458439117003 & -2.55584391170026 \tabularnewline
59 & 96.19 & 96.1900964311145 & -9.64311145139618e-05 \tabularnewline
60 & 96.19 & 96.1858509760364 & 0.00414902396357775 \tabularnewline
61 & 96.19 & 96.18584392374 & 0.00415607625998859 \tabularnewline
62 & 96.19 & 96.1858439120251 & 0.004156087974863 \tabularnewline
63 & 96.19 & 96.1858439120057 & 0.00415608799430345 \tabularnewline
64 & 96.19 & 96.199177245339 & -0.00917724533897513 \tabularnewline
65 & 96.19 & 96.2125327272093 & -0.0225327272093381 \tabularnewline
66 & 96.19 & 96.2125549125382 & -0.0225549125381974 \tabularnewline
67 & 96.19 & 96.1192216160578 & 0.0707783839421836 \tabularnewline
68 & 96.19 & 96.1857332430265 & 0.00426675697350731 \tabularnewline
69 & 96.19 & 96.1858437281689 & 0.00415627183105016 \tabularnewline
70 & 99.13 & 98.2658439117003 & 0.864156088299723 \tabularnewline
71 & 99.13 & 99.1244153313668 & 0.00558466863316198 \tabularnewline
72 & 99.13 & 99.1258415389328 & 0.00415846106717765 \tabularnewline
73 & 99.13 & 99.1258439080636 & 0.00415609193635191 \tabularnewline
74 & 99.13 & 99.1258439119991 & 0.00415608800089728 \tabularnewline
75 & 99.13 & 99.1258439120056 & 0.00415608799436029 \tabularnewline
76 & 99.13 & 99.139177245339 & -0.00917724533897513 \tabularnewline
77 & 99.13 & 99.1525327272093 & -0.0225327272093381 \tabularnewline
78 & 99.13 & 99.1525549125382 & -0.0225549125382116 \tabularnewline
79 & 99.13 & 99.0592216160578 & 0.0707783839421836 \tabularnewline
80 & 99.13 & 99.1257332430265 & 0.00426675697350731 \tabularnewline
81 & 99.13 & 99.125843728169 & 0.00415627183103595 \tabularnewline
82 & 99.58 & 101.2058439117 & -1.62584391170027 \tabularnewline
83 & 99.58 & 99.5785515706568 & 0.0014484293431849 \tabularnewline
84 & 99.58 & 99.5758484098065 & 0.00415159019351563 \tabularnewline
85 & 99.58 & 99.5758439194771 & 0.00415608052287553 \tabularnewline
86 & 99.58 & 99.5758439120181 & 0.00415608798192579 \tabularnewline
87 & 99.58 & 99.5758439120057 & 0.00415608799433187 \tabularnewline
88 & 99.58 & 99.589177245339 & -0.00917724533897513 \tabularnewline
89 & 99.58 & 99.6025327272093 & -0.0225327272093381 \tabularnewline
90 & 99.58 & 99.6025549125382 & -0.0225549125382116 \tabularnewline
91 & 99.58 & 99.5092216160578 & 0.0707783839421836 \tabularnewline
92 & 99.58 & 99.5757332430265 & 0.0042667569734931 \tabularnewline
93 & 99.58 & 99.575843728169 & 0.00415627183103595 \tabularnewline
94 & 101.27 & 101.6558439117 & -0.385843911700277 \tabularnewline
95 & 101.27 & 101.266491756713 & 0.0035082432867739 \tabularnewline
96 & 101.27 & 101.265844988167 & 0.0041550118334186 \tabularnewline
97 & 101.25 & 101.265843913793 & -0.0158439137933044 \tabularnewline
98 & 101.25 & 101.245877134814 & 0.00412286518583471 \tabularnewline
99 & 101.25 & 101.245843967193 & 0.00415603280660548 \tabularnewline
100 & 101.25 & 101.259177245431 & -0.00917724543063514 \tabularnewline
101 & 101.25 & 101.272532727209 & -0.0225327272094944 \tabularnewline
102 & 101.25 & 101.272554912538 & -0.0225549125382116 \tabularnewline
103 & 101.25 & 101.179221616058 & 0.0707783839421836 \tabularnewline
104 & 101.25 & 101.245733243027 & 0.0042667569734931 \tabularnewline
105 & 101.25 & 101.245843728169 & 0.00415627183105016 \tabularnewline
106 & 102.55 & 103.3258439117 & -0.775843911700278 \tabularnewline
107 & 102.55 & 102.547139601421 & 0.00286039857871856 \tabularnewline
108 & 102.55 & 102.545846064328 & 0.0041539356724769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284059&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]89.24[/C][C]88.2028205128205[/C][C]1.03717948717946[/C][/ROW]
[ROW][C]14[/C][C]89.24[/C][C]89.2341279152301[/C][C]0.00587208476991918[/C][/ROW]
[ROW][C]15[/C][C]89.24[/C][C]89.2358410614943[/C][C]0.00415893850571081[/C][/ROW]
[ROW][C]16[/C][C]89.24[/C][C]89.2491772406039[/C][C]-0.0091772406038757[/C][/ROW]
[ROW][C]17[/C][C]89.24[/C][C]89.2625327272015[/C][C]-0.0225327272014653[/C][/ROW]
[ROW][C]18[/C][C]89.24[/C][C]89.2625549125382[/C][C]-0.0225549125381974[/C][/ROW]
[ROW][C]19[/C][C]89.24[/C][C]89.1692216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]20[/C][C]89.24[/C][C]89.2357332430265[/C][C]0.0042667569734931[/C][/ROW]
[ROW][C]21[/C][C]89.24[/C][C]89.235843728169[/C][C]0.00415627183103595[/C][/ROW]
[ROW][C]22[/C][C]91[/C][C]91.3158439117003[/C][C]-0.31584391170027[/C][/ROW]
[ROW][C]23[/C][C]91[/C][C]90.9963754768938[/C][C]0.00362452310618266[/C][/ROW]
[ROW][C]24[/C][C]91[/C][C]90.9958447950095[/C][C]0.00415520499049649[/C][/ROW]
[ROW][C]25[/C][C]91[/C][C]90.9958439134725[/C][C]0.00415608652754429[/C][/ROW]
[ROW][C]26[/C][C]91[/C][C]90.9958439120081[/C][C]0.00415608799191602[/C][/ROW]
[ROW][C]27[/C][C]91[/C][C]90.9958439120057[/C][C]0.00415608799434608[/C][/ROW]
[ROW][C]28[/C][C]91[/C][C]91.009177245339[/C][C]-0.00917724533897513[/C][/ROW]
[ROW][C]29[/C][C]91[/C][C]91.0225327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]30[/C][C]91[/C][C]91.0225549125382[/C][C]-0.0225549125381974[/C][/ROW]
[ROW][C]31[/C][C]91[/C][C]90.9292216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]32[/C][C]91[/C][C]90.9957332430265[/C][C]0.0042667569734931[/C][/ROW]
[ROW][C]33[/C][C]91[/C][C]90.9958437281689[/C][C]0.00415627183105016[/C][/ROW]
[ROW][C]34[/C][C]92.51[/C][C]93.0758439117003[/C][C]-0.56584391170027[/C][/ROW]
[ROW][C]35[/C][C]92.51[/C][C]92.5067907619631[/C][C]0.00320923803690221[/C][/ROW]
[ROW][C]36[/C][C]92.51[/C][C]92.5058454848563[/C][C]0.0041545151437532[/C][/ROW]
[ROW][C]37[/C][C]92.51[/C][C]92.5058439146184[/C][C]0.0041560853816236[/C][/ROW]
[ROW][C]38[/C][C]92.51[/C][C]92.50584391201[/C][C]0.00415608799001177[/C][/ROW]
[ROW][C]39[/C][C]92.51[/C][C]92.5058439120057[/C][C]0.00415608799433187[/C][/ROW]
[ROW][C]40[/C][C]92.51[/C][C]92.519177245339[/C][C]-0.00917724533896092[/C][/ROW]
[ROW][C]41[/C][C]92.51[/C][C]92.5325327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]42[/C][C]92.51[/C][C]92.5325549125382[/C][C]-0.0225549125382116[/C][/ROW]
[ROW][C]43[/C][C]92.51[/C][C]92.4392216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]44[/C][C]92.51[/C][C]92.5057332430265[/C][C]0.0042667569734931[/C][/ROW]
[ROW][C]45[/C][C]92.51[/C][C]92.505843728169[/C][C]0.00415627183105016[/C][/ROW]
[ROW][C]46[/C][C]96.67[/C][C]94.5858439117003[/C][C]2.08415608829972[/C][/ROW]
[ROW][C]47[/C][C]96.67[/C][C]96.6623887402288[/C][C]0.0076112597712239[/C][/ROW]
[ROW][C]48[/C][C]96.67[/C][C]96.6658381724807[/C][C]0.00416182751934002[/C][/ROW]
[ROW][C]49[/C][C]96.67[/C][C]96.6658439024715[/C][C]0.00415609752850798[/C][/ROW]
[ROW][C]50[/C][C]96.67[/C][C]96.6658439119898[/C][C]0.00415608801017697[/C][/ROW]
[ROW][C]51[/C][C]96.67[/C][C]96.6658439120056[/C][C]0.0041560879943745[/C][/ROW]
[ROW][C]52[/C][C]96.67[/C][C]96.679177245339[/C][C]-0.00917724533897513[/C][/ROW]
[ROW][C]53[/C][C]96.67[/C][C]96.6925327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]54[/C][C]96.67[/C][C]96.6925549125382[/C][C]-0.0225549125381974[/C][/ROW]
[ROW][C]55[/C][C]96.67[/C][C]96.5992216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]56[/C][C]96.67[/C][C]96.6657332430265[/C][C]0.00426675697350731[/C][/ROW]
[ROW][C]57[/C][C]96.67[/C][C]96.665843728169[/C][C]0.00415627183105016[/C][/ROW]
[ROW][C]58[/C][C]96.19[/C][C]98.7458439117003[/C][C]-2.55584391170026[/C][/ROW]
[ROW][C]59[/C][C]96.19[/C][C]96.1900964311145[/C][C]-9.64311145139618e-05[/C][/ROW]
[ROW][C]60[/C][C]96.19[/C][C]96.1858509760364[/C][C]0.00414902396357775[/C][/ROW]
[ROW][C]61[/C][C]96.19[/C][C]96.18584392374[/C][C]0.00415607625998859[/C][/ROW]
[ROW][C]62[/C][C]96.19[/C][C]96.1858439120251[/C][C]0.004156087974863[/C][/ROW]
[ROW][C]63[/C][C]96.19[/C][C]96.1858439120057[/C][C]0.00415608799430345[/C][/ROW]
[ROW][C]64[/C][C]96.19[/C][C]96.199177245339[/C][C]-0.00917724533897513[/C][/ROW]
[ROW][C]65[/C][C]96.19[/C][C]96.2125327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]66[/C][C]96.19[/C][C]96.2125549125382[/C][C]-0.0225549125381974[/C][/ROW]
[ROW][C]67[/C][C]96.19[/C][C]96.1192216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]68[/C][C]96.19[/C][C]96.1857332430265[/C][C]0.00426675697350731[/C][/ROW]
[ROW][C]69[/C][C]96.19[/C][C]96.1858437281689[/C][C]0.00415627183105016[/C][/ROW]
[ROW][C]70[/C][C]99.13[/C][C]98.2658439117003[/C][C]0.864156088299723[/C][/ROW]
[ROW][C]71[/C][C]99.13[/C][C]99.1244153313668[/C][C]0.00558466863316198[/C][/ROW]
[ROW][C]72[/C][C]99.13[/C][C]99.1258415389328[/C][C]0.00415846106717765[/C][/ROW]
[ROW][C]73[/C][C]99.13[/C][C]99.1258439080636[/C][C]0.00415609193635191[/C][/ROW]
[ROW][C]74[/C][C]99.13[/C][C]99.1258439119991[/C][C]0.00415608800089728[/C][/ROW]
[ROW][C]75[/C][C]99.13[/C][C]99.1258439120056[/C][C]0.00415608799436029[/C][/ROW]
[ROW][C]76[/C][C]99.13[/C][C]99.139177245339[/C][C]-0.00917724533897513[/C][/ROW]
[ROW][C]77[/C][C]99.13[/C][C]99.1525327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]78[/C][C]99.13[/C][C]99.1525549125382[/C][C]-0.0225549125382116[/C][/ROW]
[ROW][C]79[/C][C]99.13[/C][C]99.0592216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]80[/C][C]99.13[/C][C]99.1257332430265[/C][C]0.00426675697350731[/C][/ROW]
[ROW][C]81[/C][C]99.13[/C][C]99.125843728169[/C][C]0.00415627183103595[/C][/ROW]
[ROW][C]82[/C][C]99.58[/C][C]101.2058439117[/C][C]-1.62584391170027[/C][/ROW]
[ROW][C]83[/C][C]99.58[/C][C]99.5785515706568[/C][C]0.0014484293431849[/C][/ROW]
[ROW][C]84[/C][C]99.58[/C][C]99.5758484098065[/C][C]0.00415159019351563[/C][/ROW]
[ROW][C]85[/C][C]99.58[/C][C]99.5758439194771[/C][C]0.00415608052287553[/C][/ROW]
[ROW][C]86[/C][C]99.58[/C][C]99.5758439120181[/C][C]0.00415608798192579[/C][/ROW]
[ROW][C]87[/C][C]99.58[/C][C]99.5758439120057[/C][C]0.00415608799433187[/C][/ROW]
[ROW][C]88[/C][C]99.58[/C][C]99.589177245339[/C][C]-0.00917724533897513[/C][/ROW]
[ROW][C]89[/C][C]99.58[/C][C]99.6025327272093[/C][C]-0.0225327272093381[/C][/ROW]
[ROW][C]90[/C][C]99.58[/C][C]99.6025549125382[/C][C]-0.0225549125382116[/C][/ROW]
[ROW][C]91[/C][C]99.58[/C][C]99.5092216160578[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]92[/C][C]99.58[/C][C]99.5757332430265[/C][C]0.0042667569734931[/C][/ROW]
[ROW][C]93[/C][C]99.58[/C][C]99.575843728169[/C][C]0.00415627183103595[/C][/ROW]
[ROW][C]94[/C][C]101.27[/C][C]101.6558439117[/C][C]-0.385843911700277[/C][/ROW]
[ROW][C]95[/C][C]101.27[/C][C]101.266491756713[/C][C]0.0035082432867739[/C][/ROW]
[ROW][C]96[/C][C]101.27[/C][C]101.265844988167[/C][C]0.0041550118334186[/C][/ROW]
[ROW][C]97[/C][C]101.25[/C][C]101.265843913793[/C][C]-0.0158439137933044[/C][/ROW]
[ROW][C]98[/C][C]101.25[/C][C]101.245877134814[/C][C]0.00412286518583471[/C][/ROW]
[ROW][C]99[/C][C]101.25[/C][C]101.245843967193[/C][C]0.00415603280660548[/C][/ROW]
[ROW][C]100[/C][C]101.25[/C][C]101.259177245431[/C][C]-0.00917724543063514[/C][/ROW]
[ROW][C]101[/C][C]101.25[/C][C]101.272532727209[/C][C]-0.0225327272094944[/C][/ROW]
[ROW][C]102[/C][C]101.25[/C][C]101.272554912538[/C][C]-0.0225549125382116[/C][/ROW]
[ROW][C]103[/C][C]101.25[/C][C]101.179221616058[/C][C]0.0707783839421836[/C][/ROW]
[ROW][C]104[/C][C]101.25[/C][C]101.245733243027[/C][C]0.0042667569734931[/C][/ROW]
[ROW][C]105[/C][C]101.25[/C][C]101.245843728169[/C][C]0.00415627183105016[/C][/ROW]
[ROW][C]106[/C][C]102.55[/C][C]103.3258439117[/C][C]-0.775843911700278[/C][/ROW]
[ROW][C]107[/C][C]102.55[/C][C]102.547139601421[/C][C]0.00286039857871856[/C][/ROW]
[ROW][C]108[/C][C]102.55[/C][C]102.545846064328[/C][C]0.0041539356724769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284059&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284059&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	89.24	88.2028205128205	1.03717948717946
14	89.24	89.2341279152301	0.00587208476991918
15	89.24	89.2358410614943	0.00415893850571081
16	89.24	89.2491772406039	-0.0091772406038757
17	89.24	89.2625327272015	-0.0225327272014653
18	89.24	89.2625549125382	-0.0225549125381974
19	89.24	89.1692216160578	0.0707783839421836
20	89.24	89.2357332430265	0.0042667569734931
21	89.24	89.235843728169	0.00415627183103595
22	91	91.3158439117003	-0.31584391170027
23	91	90.9963754768938	0.00362452310618266
24	91	90.9958447950095	0.00415520499049649
25	91	90.9958439134725	0.00415608652754429
26	91	90.9958439120081	0.00415608799191602
27	91	90.9958439120057	0.00415608799434608
28	91	91.009177245339	-0.00917724533897513
29	91	91.0225327272093	-0.0225327272093381
30	91	91.0225549125382	-0.0225549125381974
31	91	90.9292216160578	0.0707783839421836
32	91	90.9957332430265	0.0042667569734931
33	91	90.9958437281689	0.00415627183105016
34	92.51	93.0758439117003	-0.56584391170027
35	92.51	92.5067907619631	0.00320923803690221
36	92.51	92.5058454848563	0.0041545151437532
37	92.51	92.5058439146184	0.0041560853816236
38	92.51	92.50584391201	0.00415608799001177
39	92.51	92.5058439120057	0.00415608799433187
40	92.51	92.519177245339	-0.00917724533896092
41	92.51	92.5325327272093	-0.0225327272093381
42	92.51	92.5325549125382	-0.0225549125382116
43	92.51	92.4392216160578	0.0707783839421836
44	92.51	92.5057332430265	0.0042667569734931
45	92.51	92.505843728169	0.00415627183105016
46	96.67	94.5858439117003	2.08415608829972
47	96.67	96.6623887402288	0.0076112597712239
48	96.67	96.6658381724807	0.00416182751934002
49	96.67	96.6658439024715	0.00415609752850798
50	96.67	96.6658439119898	0.00415608801017697
51	96.67	96.6658439120056	0.0041560879943745
52	96.67	96.679177245339	-0.00917724533897513
53	96.67	96.6925327272093	-0.0225327272093381
54	96.67	96.6925549125382	-0.0225549125381974
55	96.67	96.5992216160578	0.0707783839421836
56	96.67	96.6657332430265	0.00426675697350731
57	96.67	96.665843728169	0.00415627183105016
58	96.19	98.7458439117003	-2.55584391170026
59	96.19	96.1900964311145	-9.64311145139618e-05
60	96.19	96.1858509760364	0.00414902396357775
61	96.19	96.18584392374	0.00415607625998859
62	96.19	96.1858439120251	0.004156087974863
63	96.19	96.1858439120057	0.00415608799430345
64	96.19	96.199177245339	-0.00917724533897513
65	96.19	96.2125327272093	-0.0225327272093381
66	96.19	96.2125549125382	-0.0225549125381974
67	96.19	96.1192216160578	0.0707783839421836
68	96.19	96.1857332430265	0.00426675697350731
69	96.19	96.1858437281689	0.00415627183105016
70	99.13	98.2658439117003	0.864156088299723
71	99.13	99.1244153313668	0.00558466863316198
72	99.13	99.1258415389328	0.00415846106717765
73	99.13	99.1258439080636	0.00415609193635191
74	99.13	99.1258439119991	0.00415608800089728
75	99.13	99.1258439120056	0.00415608799436029
76	99.13	99.139177245339	-0.00917724533897513
77	99.13	99.1525327272093	-0.0225327272093381
78	99.13	99.1525549125382	-0.0225549125382116
79	99.13	99.0592216160578	0.0707783839421836
80	99.13	99.1257332430265	0.00426675697350731
81	99.13	99.125843728169	0.00415627183103595
82	99.58	101.2058439117	-1.62584391170027
83	99.58	99.5785515706568	0.0014484293431849
84	99.58	99.5758484098065	0.00415159019351563
85	99.58	99.5758439194771	0.00415608052287553
86	99.58	99.5758439120181	0.00415608798192579
87	99.58	99.5758439120057	0.00415608799433187
88	99.58	99.589177245339	-0.00917724533897513
89	99.58	99.6025327272093	-0.0225327272093381
90	99.58	99.6025549125382	-0.0225549125382116
91	99.58	99.5092216160578	0.0707783839421836
92	99.58	99.5757332430265	0.0042667569734931
93	99.58	99.575843728169	0.00415627183103595
94	101.27	101.6558439117	-0.385843911700277
95	101.27	101.266491756713	0.0035082432867739
96	101.27	101.265844988167	0.0041550118334186
97	101.25	101.265843913793	-0.0158439137933044
98	101.25	101.245877134814	0.00412286518583471
99	101.25	101.245843967193	0.00415603280660548
100	101.25	101.259177245431	-0.00917724543063514
101	101.25	101.272532727209	-0.0225327272094944
102	101.25	101.272554912538	-0.0225549125382116
103	101.25	101.179221616058	0.0707783839421836
104	101.25	101.245733243027	0.0042667569734931
105	101.25	101.245843728169	0.00415627183105016
106	102.55	103.3258439117	-0.775843911700278
107	102.55	102.547139601421	0.00286039857871856
108	102.55	102.545846064328	0.0041539356724769

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	102.545843915581	101.728399864657	103.363287966505
110	102.541694731432	101.386614041744	103.696775421119
111	102.537545547283	101.12325843959	103.951832654975
112	102.546729696467	100.913878005013	104.17958138792
113	102.569247178984	100.743815375388	104.39467898258
114	102.591764661502	100.592215239037	104.591314083966
115	102.520948810686	100.36127417867	104.680623442702
116	102.516799626537	100.208078954937	104.825520298136
117	102.512650442387	100.063938992917	104.961361891858
118	104.588501258238	102.007380496618	107.169622019858
119	104.584352074089	101.877290750557	107.291413397621
120	104.58020288994	101.752805211392	107.407600568488

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.545843915581 & 101.728399864657 & 103.363287966505 \tabularnewline
110 & 102.541694731432 & 101.386614041744 & 103.696775421119 \tabularnewline
111 & 102.537545547283 & 101.12325843959 & 103.951832654975 \tabularnewline
112 & 102.546729696467 & 100.913878005013 & 104.17958138792 \tabularnewline
113 & 102.569247178984 & 100.743815375388 & 104.39467898258 \tabularnewline
114 & 102.591764661502 & 100.592215239037 & 104.591314083966 \tabularnewline
115 & 102.520948810686 & 100.36127417867 & 104.680623442702 \tabularnewline
116 & 102.516799626537 & 100.208078954937 & 104.825520298136 \tabularnewline
117 & 102.512650442387 & 100.063938992917 & 104.961361891858 \tabularnewline
118 & 104.588501258238 & 102.007380496618 & 107.169622019858 \tabularnewline
119 & 104.584352074089 & 101.877290750557 & 107.291413397621 \tabularnewline
120 & 104.58020288994 & 101.752805211392 & 107.407600568488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284059&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]109[/C][C]102.545843915581[/C][C]101.728399864657[/C][C]103.363287966505[/C][/ROW]
[ROW][C]110[/C][C]102.541694731432[/C][C]101.386614041744[/C][C]103.696775421119[/C][/ROW]
[ROW][C]111[/C][C]102.537545547283[/C][C]101.12325843959[/C][C]103.951832654975[/C][/ROW]
[ROW][C]112[/C][C]102.546729696467[/C][C]100.913878005013[/C][C]104.17958138792[/C][/ROW]
[ROW][C]113[/C][C]102.569247178984[/C][C]100.743815375388[/C][C]104.39467898258[/C][/ROW]
[ROW][C]114[/C][C]102.591764661502[/C][C]100.592215239037[/C][C]104.591314083966[/C][/ROW]
[ROW][C]115[/C][C]102.520948810686[/C][C]100.36127417867[/C][C]104.680623442702[/C][/ROW]
[ROW][C]116[/C][C]102.516799626537[/C][C]100.208078954937[/C][C]104.825520298136[/C][/ROW]
[ROW][C]117[/C][C]102.512650442387[/C][C]100.063938992917[/C][C]104.961361891858[/C][/ROW]
[ROW][C]118[/C][C]104.588501258238[/C][C]102.007380496618[/C][C]107.169622019858[/C][/ROW]
[ROW][C]119[/C][C]104.584352074089[/C][C]101.877290750557[/C][C]107.291413397621[/C][/ROW]
[ROW][C]120[/C][C]104.58020288994[/C][C]101.752805211392[/C][C]107.407600568488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284059&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284059&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
109	102.545843915581	101.728399864657	103.363287966505
110	102.541694731432	101.386614041744	103.696775421119
111	102.537545547283	101.12325843959	103.951832654975
112	102.546729696467	100.913878005013	104.17958138792
113	102.569247178984	100.743815375388	104.39467898258
114	102.591764661502	100.592215239037	104.591314083966
115	102.520948810686	100.36127417867	104.680623442702
116	102.516799626537	100.208078954937	104.825520298136
117	102.512650442387	100.063938992917	104.961361891858
118	104.588501258238	102.007380496618	107.169622019858
119	104.584352074089	101.877290750557	107.291413397621
120	104.58020288994	101.752805211392	107.407600568488

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code