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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 13 May 2013 05:17:26 -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/2013/May/13/t1368436731d4826qqv3gagogl.htm/, Retrieved Tue, 07 May 2024 05:45:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208898, Retrieved Tue, 07 May 2024 05:45:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Prijzen eau de toilette

Estimated Impact

110

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

-       [Exponential Smoothing] [Exponential smoot...] [2013-05-13 09:17:26] [d21ef05d1ac55c15fda1e2aa772f6a37] [Current]

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Dataseries X:

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208898&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208898&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208898&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]1[/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=208898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208898&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	1
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	54.4	53.3946340811966	1.00536591880343
14	54.73	54.7202432983683	0.0097567016316944
15	54.96	54.9689932983683	-0.00899329836830276
16	55.27	55.3027432983683	-0.0327432983682954
17	55.27	55.3127432983683	-0.0427432983683005
18	55.26	55.3077432983683	-0.0477432983682959
19	55.37	55.1777432983683	0.192256701631699
20	55.53	55.591909965035	-0.0619099650349568
21	55.55	55.8939932983683	-0.343993298368289
22	55.54	55.740659965035	-0.200659965034966
23	55.6	55.615659965035	-0.0156599650349634
24	55.56	55.6377432983683	-0.07774329836829
25	55.64	55.6277432983683	0.0122567016317134
26	56.13	55.9602432983683	0.169756701631705
27	56.69	56.3689932983683	0.321006701631688
28	56.8	57.0327432983683	-0.232743298368291
29	56.93	56.8427432983683	0.0872567016317092
30	57	56.9677432983683	0.0322567016317095
31	57.01	56.9177432983683	0.0922567016316904
32	57.21	57.231909965035	-0.0219099650349577
33	57.17	57.5739932983683	-0.403993298368292
34	57.36	57.360659965035	-0.0006599650349699
35	57.29	57.435659965035	-0.145659965034973
36	57.26	57.3277432983683	-0.067743298368292
37	57.29	57.3277432983683	-0.0377432983682908
38	57.68	57.6102432983683	0.0697567016316967
39	58.19	57.9189932983683	0.271006701631691
40	58.34	58.5327432983683	-0.192743298368285
41	58.46	58.3827432983683	0.0772567016317041
42	58.67	58.4977432983683	0.17225670163171
43	58.72	58.5877432983683	0.13225670163169
44	58.74	58.941909965035	-0.20190996503495
45	58.77	59.1039932983683	-0.333993298368291
46	58.84	58.960659965035	-0.120659965034974
47	59.13	58.915659965035	0.214340034965026
48	59.12	59.1677432983683	-0.0477432983682959
49	59.12	59.1877432983683	-0.067743298368292
50	59.33	59.4402432983683	-0.110243298368303
51	59.49	59.5689932983683	-0.0789932983682959
52	59.67	59.8327432983683	-0.162743298368298
53	59.7	59.7127432983683	-0.0127432983682922
54	59.73	59.7377432983683	-0.00774329836828969
55	59.74	59.6477432983683	0.0922567016317046
56	59.62	59.961909965035	-0.341909965034965
57	59.6	59.9839932983683	-0.383993298368289
58	59.98	59.790659965035	0.189340034965021
59	60.05	60.055659965035	-0.00565996503496535
60	60.06	60.0877432983683	-0.0277432983682786
61	60.1	60.1277432983683	-0.0277432983682857
62	60.18	60.4202432983683	-0.240243298368306
63	60.38	60.4189932983683	-0.0389932983683039
64	60.52	60.7227432983683	-0.202743298368297
65	60.78	60.5627432983683	0.217256701631698
66	60.72	60.8177432983683	-0.097743298368286
67	60.72	60.6377432983683	0.0822567016316924
68	60.86	60.941909965035	-0.0819099650349528
69	60.99	61.2239932983683	-0.233993298368283
70	61.11	61.180659965035	-0.0706599650349773
71	61.17	61.185659965035	-0.0156599650349705
72	61.19	61.2077432983683	-0.0177432983682877

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 54.4 & 53.3946340811966 & 1.00536591880343 \tabularnewline
14 & 54.73 & 54.7202432983683 & 0.0097567016316944 \tabularnewline
15 & 54.96 & 54.9689932983683 & -0.00899329836830276 \tabularnewline
16 & 55.27 & 55.3027432983683 & -0.0327432983682954 \tabularnewline
17 & 55.27 & 55.3127432983683 & -0.0427432983683005 \tabularnewline
18 & 55.26 & 55.3077432983683 & -0.0477432983682959 \tabularnewline
19 & 55.37 & 55.1777432983683 & 0.192256701631699 \tabularnewline
20 & 55.53 & 55.591909965035 & -0.0619099650349568 \tabularnewline
21 & 55.55 & 55.8939932983683 & -0.343993298368289 \tabularnewline
22 & 55.54 & 55.740659965035 & -0.200659965034966 \tabularnewline
23 & 55.6 & 55.615659965035 & -0.0156599650349634 \tabularnewline
24 & 55.56 & 55.6377432983683 & -0.07774329836829 \tabularnewline
25 & 55.64 & 55.6277432983683 & 0.0122567016317134 \tabularnewline
26 & 56.13 & 55.9602432983683 & 0.169756701631705 \tabularnewline
27 & 56.69 & 56.3689932983683 & 0.321006701631688 \tabularnewline
28 & 56.8 & 57.0327432983683 & -0.232743298368291 \tabularnewline
29 & 56.93 & 56.8427432983683 & 0.0872567016317092 \tabularnewline
30 & 57 & 56.9677432983683 & 0.0322567016317095 \tabularnewline
31 & 57.01 & 56.9177432983683 & 0.0922567016316904 \tabularnewline
32 & 57.21 & 57.231909965035 & -0.0219099650349577 \tabularnewline
33 & 57.17 & 57.5739932983683 & -0.403993298368292 \tabularnewline
34 & 57.36 & 57.360659965035 & -0.0006599650349699 \tabularnewline
35 & 57.29 & 57.435659965035 & -0.145659965034973 \tabularnewline
36 & 57.26 & 57.3277432983683 & -0.067743298368292 \tabularnewline
37 & 57.29 & 57.3277432983683 & -0.0377432983682908 \tabularnewline
38 & 57.68 & 57.6102432983683 & 0.0697567016316967 \tabularnewline
39 & 58.19 & 57.9189932983683 & 0.271006701631691 \tabularnewline
40 & 58.34 & 58.5327432983683 & -0.192743298368285 \tabularnewline
41 & 58.46 & 58.3827432983683 & 0.0772567016317041 \tabularnewline
42 & 58.67 & 58.4977432983683 & 0.17225670163171 \tabularnewline
43 & 58.72 & 58.5877432983683 & 0.13225670163169 \tabularnewline
44 & 58.74 & 58.941909965035 & -0.20190996503495 \tabularnewline
45 & 58.77 & 59.1039932983683 & -0.333993298368291 \tabularnewline
46 & 58.84 & 58.960659965035 & -0.120659965034974 \tabularnewline
47 & 59.13 & 58.915659965035 & 0.214340034965026 \tabularnewline
48 & 59.12 & 59.1677432983683 & -0.0477432983682959 \tabularnewline
49 & 59.12 & 59.1877432983683 & -0.067743298368292 \tabularnewline
50 & 59.33 & 59.4402432983683 & -0.110243298368303 \tabularnewline
51 & 59.49 & 59.5689932983683 & -0.0789932983682959 \tabularnewline
52 & 59.67 & 59.8327432983683 & -0.162743298368298 \tabularnewline
53 & 59.7 & 59.7127432983683 & -0.0127432983682922 \tabularnewline
54 & 59.73 & 59.7377432983683 & -0.00774329836828969 \tabularnewline
55 & 59.74 & 59.6477432983683 & 0.0922567016317046 \tabularnewline
56 & 59.62 & 59.961909965035 & -0.341909965034965 \tabularnewline
57 & 59.6 & 59.9839932983683 & -0.383993298368289 \tabularnewline
58 & 59.98 & 59.790659965035 & 0.189340034965021 \tabularnewline
59 & 60.05 & 60.055659965035 & -0.00565996503496535 \tabularnewline
60 & 60.06 & 60.0877432983683 & -0.0277432983682786 \tabularnewline
61 & 60.1 & 60.1277432983683 & -0.0277432983682857 \tabularnewline
62 & 60.18 & 60.4202432983683 & -0.240243298368306 \tabularnewline
63 & 60.38 & 60.4189932983683 & -0.0389932983683039 \tabularnewline
64 & 60.52 & 60.7227432983683 & -0.202743298368297 \tabularnewline
65 & 60.78 & 60.5627432983683 & 0.217256701631698 \tabularnewline
66 & 60.72 & 60.8177432983683 & -0.097743298368286 \tabularnewline
67 & 60.72 & 60.6377432983683 & 0.0822567016316924 \tabularnewline
68 & 60.86 & 60.941909965035 & -0.0819099650349528 \tabularnewline
69 & 60.99 & 61.2239932983683 & -0.233993298368283 \tabularnewline
70 & 61.11 & 61.180659965035 & -0.0706599650349773 \tabularnewline
71 & 61.17 & 61.185659965035 & -0.0156599650349705 \tabularnewline
72 & 61.19 & 61.2077432983683 & -0.0177432983682877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208898&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]54.4[/C][C]53.3946340811966[/C][C]1.00536591880343[/C][/ROW]
[ROW][C]14[/C][C]54.73[/C][C]54.7202432983683[/C][C]0.0097567016316944[/C][/ROW]
[ROW][C]15[/C][C]54.96[/C][C]54.9689932983683[/C][C]-0.00899329836830276[/C][/ROW]
[ROW][C]16[/C][C]55.27[/C][C]55.3027432983683[/C][C]-0.0327432983682954[/C][/ROW]
[ROW][C]17[/C][C]55.27[/C][C]55.3127432983683[/C][C]-0.0427432983683005[/C][/ROW]
[ROW][C]18[/C][C]55.26[/C][C]55.3077432983683[/C][C]-0.0477432983682959[/C][/ROW]
[ROW][C]19[/C][C]55.37[/C][C]55.1777432983683[/C][C]0.192256701631699[/C][/ROW]
[ROW][C]20[/C][C]55.53[/C][C]55.591909965035[/C][C]-0.0619099650349568[/C][/ROW]
[ROW][C]21[/C][C]55.55[/C][C]55.8939932983683[/C][C]-0.343993298368289[/C][/ROW]
[ROW][C]22[/C][C]55.54[/C][C]55.740659965035[/C][C]-0.200659965034966[/C][/ROW]
[ROW][C]23[/C][C]55.6[/C][C]55.615659965035[/C][C]-0.0156599650349634[/C][/ROW]
[ROW][C]24[/C][C]55.56[/C][C]55.6377432983683[/C][C]-0.07774329836829[/C][/ROW]
[ROW][C]25[/C][C]55.64[/C][C]55.6277432983683[/C][C]0.0122567016317134[/C][/ROW]
[ROW][C]26[/C][C]56.13[/C][C]55.9602432983683[/C][C]0.169756701631705[/C][/ROW]
[ROW][C]27[/C][C]56.69[/C][C]56.3689932983683[/C][C]0.321006701631688[/C][/ROW]
[ROW][C]28[/C][C]56.8[/C][C]57.0327432983683[/C][C]-0.232743298368291[/C][/ROW]
[ROW][C]29[/C][C]56.93[/C][C]56.8427432983683[/C][C]0.0872567016317092[/C][/ROW]
[ROW][C]30[/C][C]57[/C][C]56.9677432983683[/C][C]0.0322567016317095[/C][/ROW]
[ROW][C]31[/C][C]57.01[/C][C]56.9177432983683[/C][C]0.0922567016316904[/C][/ROW]
[ROW][C]32[/C][C]57.21[/C][C]57.231909965035[/C][C]-0.0219099650349577[/C][/ROW]
[ROW][C]33[/C][C]57.17[/C][C]57.5739932983683[/C][C]-0.403993298368292[/C][/ROW]
[ROW][C]34[/C][C]57.36[/C][C]57.360659965035[/C][C]-0.0006599650349699[/C][/ROW]
[ROW][C]35[/C][C]57.29[/C][C]57.435659965035[/C][C]-0.145659965034973[/C][/ROW]
[ROW][C]36[/C][C]57.26[/C][C]57.3277432983683[/C][C]-0.067743298368292[/C][/ROW]
[ROW][C]37[/C][C]57.29[/C][C]57.3277432983683[/C][C]-0.0377432983682908[/C][/ROW]
[ROW][C]38[/C][C]57.68[/C][C]57.6102432983683[/C][C]0.0697567016316967[/C][/ROW]
[ROW][C]39[/C][C]58.19[/C][C]57.9189932983683[/C][C]0.271006701631691[/C][/ROW]
[ROW][C]40[/C][C]58.34[/C][C]58.5327432983683[/C][C]-0.192743298368285[/C][/ROW]
[ROW][C]41[/C][C]58.46[/C][C]58.3827432983683[/C][C]0.0772567016317041[/C][/ROW]
[ROW][C]42[/C][C]58.67[/C][C]58.4977432983683[/C][C]0.17225670163171[/C][/ROW]
[ROW][C]43[/C][C]58.72[/C][C]58.5877432983683[/C][C]0.13225670163169[/C][/ROW]
[ROW][C]44[/C][C]58.74[/C][C]58.941909965035[/C][C]-0.20190996503495[/C][/ROW]
[ROW][C]45[/C][C]58.77[/C][C]59.1039932983683[/C][C]-0.333993298368291[/C][/ROW]
[ROW][C]46[/C][C]58.84[/C][C]58.960659965035[/C][C]-0.120659965034974[/C][/ROW]
[ROW][C]47[/C][C]59.13[/C][C]58.915659965035[/C][C]0.214340034965026[/C][/ROW]
[ROW][C]48[/C][C]59.12[/C][C]59.1677432983683[/C][C]-0.0477432983682959[/C][/ROW]
[ROW][C]49[/C][C]59.12[/C][C]59.1877432983683[/C][C]-0.067743298368292[/C][/ROW]
[ROW][C]50[/C][C]59.33[/C][C]59.4402432983683[/C][C]-0.110243298368303[/C][/ROW]
[ROW][C]51[/C][C]59.49[/C][C]59.5689932983683[/C][C]-0.0789932983682959[/C][/ROW]
[ROW][C]52[/C][C]59.67[/C][C]59.8327432983683[/C][C]-0.162743298368298[/C][/ROW]
[ROW][C]53[/C][C]59.7[/C][C]59.7127432983683[/C][C]-0.0127432983682922[/C][/ROW]
[ROW][C]54[/C][C]59.73[/C][C]59.7377432983683[/C][C]-0.00774329836828969[/C][/ROW]
[ROW][C]55[/C][C]59.74[/C][C]59.6477432983683[/C][C]0.0922567016317046[/C][/ROW]
[ROW][C]56[/C][C]59.62[/C][C]59.961909965035[/C][C]-0.341909965034965[/C][/ROW]
[ROW][C]57[/C][C]59.6[/C][C]59.9839932983683[/C][C]-0.383993298368289[/C][/ROW]
[ROW][C]58[/C][C]59.98[/C][C]59.790659965035[/C][C]0.189340034965021[/C][/ROW]
[ROW][C]59[/C][C]60.05[/C][C]60.055659965035[/C][C]-0.00565996503496535[/C][/ROW]
[ROW][C]60[/C][C]60.06[/C][C]60.0877432983683[/C][C]-0.0277432983682786[/C][/ROW]
[ROW][C]61[/C][C]60.1[/C][C]60.1277432983683[/C][C]-0.0277432983682857[/C][/ROW]
[ROW][C]62[/C][C]60.18[/C][C]60.4202432983683[/C][C]-0.240243298368306[/C][/ROW]
[ROW][C]63[/C][C]60.38[/C][C]60.4189932983683[/C][C]-0.0389932983683039[/C][/ROW]
[ROW][C]64[/C][C]60.52[/C][C]60.7227432983683[/C][C]-0.202743298368297[/C][/ROW]
[ROW][C]65[/C][C]60.78[/C][C]60.5627432983683[/C][C]0.217256701631698[/C][/ROW]
[ROW][C]66[/C][C]60.72[/C][C]60.8177432983683[/C][C]-0.097743298368286[/C][/ROW]
[ROW][C]67[/C][C]60.72[/C][C]60.6377432983683[/C][C]0.0822567016316924[/C][/ROW]
[ROW][C]68[/C][C]60.86[/C][C]60.941909965035[/C][C]-0.0819099650349528[/C][/ROW]
[ROW][C]69[/C][C]60.99[/C][C]61.2239932983683[/C][C]-0.233993298368283[/C][/ROW]
[ROW][C]70[/C][C]61.11[/C][C]61.180659965035[/C][C]-0.0706599650349773[/C][/ROW]
[ROW][C]71[/C][C]61.17[/C][C]61.185659965035[/C][C]-0.0156599650349705[/C][/ROW]
[ROW][C]72[/C][C]61.19[/C][C]61.2077432983683[/C][C]-0.0177432983682877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208898&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208898&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	54.4	53.3946340811966	1.00536591880343
14	54.73	54.7202432983683	0.0097567016316944
15	54.96	54.9689932983683	-0.00899329836830276
16	55.27	55.3027432983683	-0.0327432983682954
17	55.27	55.3127432983683	-0.0427432983683005
18	55.26	55.3077432983683	-0.0477432983682959
19	55.37	55.1777432983683	0.192256701631699
20	55.53	55.591909965035	-0.0619099650349568
21	55.55	55.8939932983683	-0.343993298368289
22	55.54	55.740659965035	-0.200659965034966
23	55.6	55.615659965035	-0.0156599650349634
24	55.56	55.6377432983683	-0.07774329836829
25	55.64	55.6277432983683	0.0122567016317134
26	56.13	55.9602432983683	0.169756701631705
27	56.69	56.3689932983683	0.321006701631688
28	56.8	57.0327432983683	-0.232743298368291
29	56.93	56.8427432983683	0.0872567016317092
30	57	56.9677432983683	0.0322567016317095
31	57.01	56.9177432983683	0.0922567016316904
32	57.21	57.231909965035	-0.0219099650349577
33	57.17	57.5739932983683	-0.403993298368292
34	57.36	57.360659965035	-0.0006599650349699
35	57.29	57.435659965035	-0.145659965034973
36	57.26	57.3277432983683	-0.067743298368292
37	57.29	57.3277432983683	-0.0377432983682908
38	57.68	57.6102432983683	0.0697567016316967
39	58.19	57.9189932983683	0.271006701631691
40	58.34	58.5327432983683	-0.192743298368285
41	58.46	58.3827432983683	0.0772567016317041
42	58.67	58.4977432983683	0.17225670163171
43	58.72	58.5877432983683	0.13225670163169
44	58.74	58.941909965035	-0.20190996503495
45	58.77	59.1039932983683	-0.333993298368291
46	58.84	58.960659965035	-0.120659965034974
47	59.13	58.915659965035	0.214340034965026
48	59.12	59.1677432983683	-0.0477432983682959
49	59.12	59.1877432983683	-0.067743298368292
50	59.33	59.4402432983683	-0.110243298368303
51	59.49	59.5689932983683	-0.0789932983682959
52	59.67	59.8327432983683	-0.162743298368298
53	59.7	59.7127432983683	-0.0127432983682922
54	59.73	59.7377432983683	-0.00774329836828969
55	59.74	59.6477432983683	0.0922567016317046
56	59.62	59.961909965035	-0.341909965034965
57	59.6	59.9839932983683	-0.383993298368289
58	59.98	59.790659965035	0.189340034965021
59	60.05	60.055659965035	-0.00565996503496535
60	60.06	60.0877432983683	-0.0277432983682786
61	60.1	60.1277432983683	-0.0277432983682857
62	60.18	60.4202432983683	-0.240243298368306
63	60.38	60.4189932983683	-0.0389932983683039
64	60.52	60.7227432983683	-0.202743298368297
65	60.78	60.5627432983683	0.217256701631698
66	60.72	60.8177432983683	-0.097743298368286
67	60.72	60.6377432983683	0.0822567016316924
68	60.86	60.941909965035	-0.0819099650349528
69	60.99	61.2239932983683	-0.233993298368283
70	61.11	61.180659965035	-0.0706599650349773
71	61.17	61.185659965035	-0.0156599650349705
72	61.19	61.2077432983683	-0.0177432983682877

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	61.2577432983683	60.8497418549524	61.6657447417841
74	61.5779865967366	61.0009854219901	62.1549877714831
75	61.8169798951049	61.1103006655472	62.5236591246626
76	62.1597231934732	61.3437203066415	62.9757260803049
77	62.2024664918415	61.2901475294456	63.1147854542374
78	62.2402097902098	61.2408144395219	63.2396051408976
79	62.1579530885781	61.0784827347444	63.2374234424118
80	62.3798630536131	61.2258607041201	63.533865403106
81	62.7438563519813	61.5198520217338	63.9678606822289
82	62.9345163170163	61.6443024671859	64.2247301668467
83	63.0101762820513	61.6569885803175	64.3633639837851
84	63.0479195804196	61.6345611213042	64.4612780395349

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 61.2577432983683 & 60.8497418549524 & 61.6657447417841 \tabularnewline
74 & 61.5779865967366 & 61.0009854219901 & 62.1549877714831 \tabularnewline
75 & 61.8169798951049 & 61.1103006655472 & 62.5236591246626 \tabularnewline
76 & 62.1597231934732 & 61.3437203066415 & 62.9757260803049 \tabularnewline
77 & 62.2024664918415 & 61.2901475294456 & 63.1147854542374 \tabularnewline
78 & 62.2402097902098 & 61.2408144395219 & 63.2396051408976 \tabularnewline
79 & 62.1579530885781 & 61.0784827347444 & 63.2374234424118 \tabularnewline
80 & 62.3798630536131 & 61.2258607041201 & 63.533865403106 \tabularnewline
81 & 62.7438563519813 & 61.5198520217338 & 63.9678606822289 \tabularnewline
82 & 62.9345163170163 & 61.6443024671859 & 64.2247301668467 \tabularnewline
83 & 63.0101762820513 & 61.6569885803175 & 64.3633639837851 \tabularnewline
84 & 63.0479195804196 & 61.6345611213042 & 64.4612780395349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208898&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]73[/C][C]61.2577432983683[/C][C]60.8497418549524[/C][C]61.6657447417841[/C][/ROW]
[ROW][C]74[/C][C]61.5779865967366[/C][C]61.0009854219901[/C][C]62.1549877714831[/C][/ROW]
[ROW][C]75[/C][C]61.8169798951049[/C][C]61.1103006655472[/C][C]62.5236591246626[/C][/ROW]
[ROW][C]76[/C][C]62.1597231934732[/C][C]61.3437203066415[/C][C]62.9757260803049[/C][/ROW]
[ROW][C]77[/C][C]62.2024664918415[/C][C]61.2901475294456[/C][C]63.1147854542374[/C][/ROW]
[ROW][C]78[/C][C]62.2402097902098[/C][C]61.2408144395219[/C][C]63.2396051408976[/C][/ROW]
[ROW][C]79[/C][C]62.1579530885781[/C][C]61.0784827347444[/C][C]63.2374234424118[/C][/ROW]
[ROW][C]80[/C][C]62.3798630536131[/C][C]61.2258607041201[/C][C]63.533865403106[/C][/ROW]
[ROW][C]81[/C][C]62.7438563519813[/C][C]61.5198520217338[/C][C]63.9678606822289[/C][/ROW]
[ROW][C]82[/C][C]62.9345163170163[/C][C]61.6443024671859[/C][C]64.2247301668467[/C][/ROW]
[ROW][C]83[/C][C]63.0101762820513[/C][C]61.6569885803175[/C][C]64.3633639837851[/C][/ROW]
[ROW][C]84[/C][C]63.0479195804196[/C][C]61.6345611213042[/C][C]64.4612780395349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208898&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208898&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
73	61.2577432983683	60.8497418549524	61.6657447417841
74	61.5779865967366	61.0009854219901	62.1549877714831
75	61.8169798951049	61.1103006655472	62.5236591246626
76	62.1597231934732	61.3437203066415	62.9757260803049
77	62.2024664918415	61.2901475294456	63.1147854542374
78	62.2402097902098	61.2408144395219	63.2396051408976
79	62.1579530885781	61.0784827347444	63.2374234424118
80	62.3798630536131	61.2258607041201	63.533865403106
81	62.7438563519813	61.5198520217338	63.9678606822289
82	62.9345163170163	61.6443024671859	64.2247301668467
83	63.0101762820513	61.6569885803175	64.3633639837851
84	63.0479195804196	61.6345611213042	64.4612780395349

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