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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

Sat, 22 Dec 2012 07:59:08 -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/2012/Dec/22/t1356181165wprnu4ou2bdf908.htm/, Retrieved Wed, 24 Apr 2024 19:05:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204498, Retrieved Wed, 24 Apr 2024 19:05:02 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-       [Exponential Smoothing] [] [2012-12-22 12:59:08] [0b7e70096319a28f23e2583f3bf72e62] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	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=204498&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=204498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204498&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	0.999954119796388
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954119796388 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204498&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]0.999954119796388[/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=204498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204498&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	0.999954119796388
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	39.36	39.28	0.0799999999999983
3	39.55	39.3599963295837	0.190003670416289
4	39.64	39.5499912825929	0.0900087174070876
5	39.8	39.6399958703817	0.160004129618279
6	39.79	39.7999926589779	-0.00999265897794999
7	39.79	39.7900004584652	-4.58465230224192e-07
8	39.86	39.790000000021	0.0699999999789682
9	39.91	39.8599967883858	0.0500032116142464
10	40	39.9099977058425	0.0900022941575358
11	40.01	39.9999958706764	0.0100041293235762
12	40.01	40.0099995410085	4.58991493701433e-07
13	40.01	40.0099999999789	2.10604866879294e-11
14	39.96	40.01	-0.0499999999999972
15	40	39.9600022940102	0.0399977059898191
16	39.76	39.9999981648971	-0.239998164897109
17	39.68	39.7600110111647	-0.0800110111646717
18	39.7	39.6800036709215	0.0199963290785163
19	39.7	39.6999990825644	9.17435649228082e-07
20	39.73	39.6999999999579	0.0300000000420866
21	39.64	39.7299986235939	-0.0899986235938854
22	39.56	39.6400041291552	-0.0800041291551707
23	39.67	39.5600036706057	0.109996329394264
24	39.66	39.669994953346	-0.00999495334601619
25	39.66	39.6600004585705	-4.58570497130495e-07
26	40.05	39.660000000021	0.389999999978961
27	39.99	40.0499821067206	-0.0599821067205895
28	40.06	39.9900027519913	0.0699972480087325
29	40.08	40.059996788512	0.0200032114879889
30	40.1	40.0799990822486	0.0200009177514175
31	40.1	40.0999990823538	9.17646175935261e-07
32	40.12	40.0999999999579	0.0200000000420957
33	40.07	40.1199990823959	-0.0499990823959209
34	40.24	40.0700022939681	0.169997706031921
35	40.58	40.2399922004706	0.34000779952936
36	40.72	40.5799844003729	0.14001559962707
37	40.72	40.7199935760558	6.42394422101233e-06
38	40.89	40.7199999997053	0.170000000294735
39	40.9	40.8899922003654	0.0100077996346286
40	41.04	40.8999995408401	0.140000459159886
41	41.27	41.0399935767504	0.230006423249577
42	41.29	41.2699894472585	0.0200105527415246
43	41.29	41.2899990819118	9.18088232992886e-07
44	41.33	41.2899999999579	0.0400000000421201
45	41.34	41.3299981647919	0.0100018352081506
46	41.37	41.3399995411138	0.0300004588862279
47	41.33	41.3699986235728	-0.0399986235728349
48	41.37	41.330001835145	0.0399981648550067
49	41.37	41.3699981648761	1.83512394613672e-06
50	41.42	41.3699999999158	0.0500000000842036
51	41.61	41.4199977059898	0.190002294010185
52	41.58	41.6099912826561	-0.0299912826560629
53	41.75	41.5800013760062	0.169998623993848
54	41.75	41.7499922004285	7.79957148466792e-06
55	41.75	41.7499999996422	3.57843532583502e-10
56	41.85	41.75	0.100000000000016
57	41.84	41.8499954119796	-0.00999541197963794
58	41.97	41.8400004585915	0.129999541408459
59	42.01	41.9699940355946	0.0400059644054309
60	42.04	42.0099981645182	0.0300018354817908
61	42.04	42.0399986235097	1.37649031728415e-06
62	42.06	42.0399999999368	0.0200000000631562
63	41.93	42.0599990823959	-0.129999082395926
64	41.93	41.9300059643844	-5.96438437128199e-06
65	41.99	41.9300000002736	0.0599999997263581
66	42.03	41.9899972471878	0.0400027528122067
67	42.03	42.0299981646656	1.83533444442219e-06
68	42.12	42.0299999999158	0.0900000000842027
69	42.22	42.1199958707817	0.100004129218327
70	42.21	42.2199954117902	-0.00999541179018593
71	42.23	42.2100004585915	0.0199995414084668
72	42.22	42.229999082417	-0.00999908241696801

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 39.36 & 39.28 & 0.0799999999999983 \tabularnewline
3 & 39.55 & 39.3599963295837 & 0.190003670416289 \tabularnewline
4 & 39.64 & 39.5499912825929 & 0.0900087174070876 \tabularnewline
5 & 39.8 & 39.6399958703817 & 0.160004129618279 \tabularnewline
6 & 39.79 & 39.7999926589779 & -0.00999265897794999 \tabularnewline
7 & 39.79 & 39.7900004584652 & -4.58465230224192e-07 \tabularnewline
8 & 39.86 & 39.790000000021 & 0.0699999999789682 \tabularnewline
9 & 39.91 & 39.8599967883858 & 0.0500032116142464 \tabularnewline
10 & 40 & 39.9099977058425 & 0.0900022941575358 \tabularnewline
11 & 40.01 & 39.9999958706764 & 0.0100041293235762 \tabularnewline
12 & 40.01 & 40.0099995410085 & 4.58991493701433e-07 \tabularnewline
13 & 40.01 & 40.0099999999789 & 2.10604866879294e-11 \tabularnewline
14 & 39.96 & 40.01 & -0.0499999999999972 \tabularnewline
15 & 40 & 39.9600022940102 & 0.0399977059898191 \tabularnewline
16 & 39.76 & 39.9999981648971 & -0.239998164897109 \tabularnewline
17 & 39.68 & 39.7600110111647 & -0.0800110111646717 \tabularnewline
18 & 39.7 & 39.6800036709215 & 0.0199963290785163 \tabularnewline
19 & 39.7 & 39.6999990825644 & 9.17435649228082e-07 \tabularnewline
20 & 39.73 & 39.6999999999579 & 0.0300000000420866 \tabularnewline
21 & 39.64 & 39.7299986235939 & -0.0899986235938854 \tabularnewline
22 & 39.56 & 39.6400041291552 & -0.0800041291551707 \tabularnewline
23 & 39.67 & 39.5600036706057 & 0.109996329394264 \tabularnewline
24 & 39.66 & 39.669994953346 & -0.00999495334601619 \tabularnewline
25 & 39.66 & 39.6600004585705 & -4.58570497130495e-07 \tabularnewline
26 & 40.05 & 39.660000000021 & 0.389999999978961 \tabularnewline
27 & 39.99 & 40.0499821067206 & -0.0599821067205895 \tabularnewline
28 & 40.06 & 39.9900027519913 & 0.0699972480087325 \tabularnewline
29 & 40.08 & 40.059996788512 & 0.0200032114879889 \tabularnewline
30 & 40.1 & 40.0799990822486 & 0.0200009177514175 \tabularnewline
31 & 40.1 & 40.0999990823538 & 9.17646175935261e-07 \tabularnewline
32 & 40.12 & 40.0999999999579 & 0.0200000000420957 \tabularnewline
33 & 40.07 & 40.1199990823959 & -0.0499990823959209 \tabularnewline
34 & 40.24 & 40.0700022939681 & 0.169997706031921 \tabularnewline
35 & 40.58 & 40.2399922004706 & 0.34000779952936 \tabularnewline
36 & 40.72 & 40.5799844003729 & 0.14001559962707 \tabularnewline
37 & 40.72 & 40.7199935760558 & 6.42394422101233e-06 \tabularnewline
38 & 40.89 & 40.7199999997053 & 0.170000000294735 \tabularnewline
39 & 40.9 & 40.8899922003654 & 0.0100077996346286 \tabularnewline
40 & 41.04 & 40.8999995408401 & 0.140000459159886 \tabularnewline
41 & 41.27 & 41.0399935767504 & 0.230006423249577 \tabularnewline
42 & 41.29 & 41.2699894472585 & 0.0200105527415246 \tabularnewline
43 & 41.29 & 41.2899990819118 & 9.18088232992886e-07 \tabularnewline
44 & 41.33 & 41.2899999999579 & 0.0400000000421201 \tabularnewline
45 & 41.34 & 41.3299981647919 & 0.0100018352081506 \tabularnewline
46 & 41.37 & 41.3399995411138 & 0.0300004588862279 \tabularnewline
47 & 41.33 & 41.3699986235728 & -0.0399986235728349 \tabularnewline
48 & 41.37 & 41.330001835145 & 0.0399981648550067 \tabularnewline
49 & 41.37 & 41.3699981648761 & 1.83512394613672e-06 \tabularnewline
50 & 41.42 & 41.3699999999158 & 0.0500000000842036 \tabularnewline
51 & 41.61 & 41.4199977059898 & 0.190002294010185 \tabularnewline
52 & 41.58 & 41.6099912826561 & -0.0299912826560629 \tabularnewline
53 & 41.75 & 41.5800013760062 & 0.169998623993848 \tabularnewline
54 & 41.75 & 41.7499922004285 & 7.79957148466792e-06 \tabularnewline
55 & 41.75 & 41.7499999996422 & 3.57843532583502e-10 \tabularnewline
56 & 41.85 & 41.75 & 0.100000000000016 \tabularnewline
57 & 41.84 & 41.8499954119796 & -0.00999541197963794 \tabularnewline
58 & 41.97 & 41.8400004585915 & 0.129999541408459 \tabularnewline
59 & 42.01 & 41.9699940355946 & 0.0400059644054309 \tabularnewline
60 & 42.04 & 42.0099981645182 & 0.0300018354817908 \tabularnewline
61 & 42.04 & 42.0399986235097 & 1.37649031728415e-06 \tabularnewline
62 & 42.06 & 42.0399999999368 & 0.0200000000631562 \tabularnewline
63 & 41.93 & 42.0599990823959 & -0.129999082395926 \tabularnewline
64 & 41.93 & 41.9300059643844 & -5.96438437128199e-06 \tabularnewline
65 & 41.99 & 41.9300000002736 & 0.0599999997263581 \tabularnewline
66 & 42.03 & 41.9899972471878 & 0.0400027528122067 \tabularnewline
67 & 42.03 & 42.0299981646656 & 1.83533444442219e-06 \tabularnewline
68 & 42.12 & 42.0299999999158 & 0.0900000000842027 \tabularnewline
69 & 42.22 & 42.1199958707817 & 0.100004129218327 \tabularnewline
70 & 42.21 & 42.2199954117902 & -0.00999541179018593 \tabularnewline
71 & 42.23 & 42.2100004585915 & 0.0199995414084668 \tabularnewline
72 & 42.22 & 42.229999082417 & -0.00999908241696801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204498&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]39.36[/C][C]39.28[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]3[/C][C]39.55[/C][C]39.3599963295837[/C][C]0.190003670416289[/C][/ROW]
[ROW][C]4[/C][C]39.64[/C][C]39.5499912825929[/C][C]0.0900087174070876[/C][/ROW]
[ROW][C]5[/C][C]39.8[/C][C]39.6399958703817[/C][C]0.160004129618279[/C][/ROW]
[ROW][C]6[/C][C]39.79[/C][C]39.7999926589779[/C][C]-0.00999265897794999[/C][/ROW]
[ROW][C]7[/C][C]39.79[/C][C]39.7900004584652[/C][C]-4.58465230224192e-07[/C][/ROW]
[ROW][C]8[/C][C]39.86[/C][C]39.790000000021[/C][C]0.0699999999789682[/C][/ROW]
[ROW][C]9[/C][C]39.91[/C][C]39.8599967883858[/C][C]0.0500032116142464[/C][/ROW]
[ROW][C]10[/C][C]40[/C][C]39.9099977058425[/C][C]0.0900022941575358[/C][/ROW]
[ROW][C]11[/C][C]40.01[/C][C]39.9999958706764[/C][C]0.0100041293235762[/C][/ROW]
[ROW][C]12[/C][C]40.01[/C][C]40.0099995410085[/C][C]4.58991493701433e-07[/C][/ROW]
[ROW][C]13[/C][C]40.01[/C][C]40.0099999999789[/C][C]2.10604866879294e-11[/C][/ROW]
[ROW][C]14[/C][C]39.96[/C][C]40.01[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]15[/C][C]40[/C][C]39.9600022940102[/C][C]0.0399977059898191[/C][/ROW]
[ROW][C]16[/C][C]39.76[/C][C]39.9999981648971[/C][C]-0.239998164897109[/C][/ROW]
[ROW][C]17[/C][C]39.68[/C][C]39.7600110111647[/C][C]-0.0800110111646717[/C][/ROW]
[ROW][C]18[/C][C]39.7[/C][C]39.6800036709215[/C][C]0.0199963290785163[/C][/ROW]
[ROW][C]19[/C][C]39.7[/C][C]39.6999990825644[/C][C]9.17435649228082e-07[/C][/ROW]
[ROW][C]20[/C][C]39.73[/C][C]39.6999999999579[/C][C]0.0300000000420866[/C][/ROW]
[ROW][C]21[/C][C]39.64[/C][C]39.7299986235939[/C][C]-0.0899986235938854[/C][/ROW]
[ROW][C]22[/C][C]39.56[/C][C]39.6400041291552[/C][C]-0.0800041291551707[/C][/ROW]
[ROW][C]23[/C][C]39.67[/C][C]39.5600036706057[/C][C]0.109996329394264[/C][/ROW]
[ROW][C]24[/C][C]39.66[/C][C]39.669994953346[/C][C]-0.00999495334601619[/C][/ROW]
[ROW][C]25[/C][C]39.66[/C][C]39.6600004585705[/C][C]-4.58570497130495e-07[/C][/ROW]
[ROW][C]26[/C][C]40.05[/C][C]39.660000000021[/C][C]0.389999999978961[/C][/ROW]
[ROW][C]27[/C][C]39.99[/C][C]40.0499821067206[/C][C]-0.0599821067205895[/C][/ROW]
[ROW][C]28[/C][C]40.06[/C][C]39.9900027519913[/C][C]0.0699972480087325[/C][/ROW]
[ROW][C]29[/C][C]40.08[/C][C]40.059996788512[/C][C]0.0200032114879889[/C][/ROW]
[ROW][C]30[/C][C]40.1[/C][C]40.0799990822486[/C][C]0.0200009177514175[/C][/ROW]
[ROW][C]31[/C][C]40.1[/C][C]40.0999990823538[/C][C]9.17646175935261e-07[/C][/ROW]
[ROW][C]32[/C][C]40.12[/C][C]40.0999999999579[/C][C]0.0200000000420957[/C][/ROW]
[ROW][C]33[/C][C]40.07[/C][C]40.1199990823959[/C][C]-0.0499990823959209[/C][/ROW]
[ROW][C]34[/C][C]40.24[/C][C]40.0700022939681[/C][C]0.169997706031921[/C][/ROW]
[ROW][C]35[/C][C]40.58[/C][C]40.2399922004706[/C][C]0.34000779952936[/C][/ROW]
[ROW][C]36[/C][C]40.72[/C][C]40.5799844003729[/C][C]0.14001559962707[/C][/ROW]
[ROW][C]37[/C][C]40.72[/C][C]40.7199935760558[/C][C]6.42394422101233e-06[/C][/ROW]
[ROW][C]38[/C][C]40.89[/C][C]40.7199999997053[/C][C]0.170000000294735[/C][/ROW]
[ROW][C]39[/C][C]40.9[/C][C]40.8899922003654[/C][C]0.0100077996346286[/C][/ROW]
[ROW][C]40[/C][C]41.04[/C][C]40.8999995408401[/C][C]0.140000459159886[/C][/ROW]
[ROW][C]41[/C][C]41.27[/C][C]41.0399935767504[/C][C]0.230006423249577[/C][/ROW]
[ROW][C]42[/C][C]41.29[/C][C]41.2699894472585[/C][C]0.0200105527415246[/C][/ROW]
[ROW][C]43[/C][C]41.29[/C][C]41.2899990819118[/C][C]9.18088232992886e-07[/C][/ROW]
[ROW][C]44[/C][C]41.33[/C][C]41.2899999999579[/C][C]0.0400000000421201[/C][/ROW]
[ROW][C]45[/C][C]41.34[/C][C]41.3299981647919[/C][C]0.0100018352081506[/C][/ROW]
[ROW][C]46[/C][C]41.37[/C][C]41.3399995411138[/C][C]0.0300004588862279[/C][/ROW]
[ROW][C]47[/C][C]41.33[/C][C]41.3699986235728[/C][C]-0.0399986235728349[/C][/ROW]
[ROW][C]48[/C][C]41.37[/C][C]41.330001835145[/C][C]0.0399981648550067[/C][/ROW]
[ROW][C]49[/C][C]41.37[/C][C]41.3699981648761[/C][C]1.83512394613672e-06[/C][/ROW]
[ROW][C]50[/C][C]41.42[/C][C]41.3699999999158[/C][C]0.0500000000842036[/C][/ROW]
[ROW][C]51[/C][C]41.61[/C][C]41.4199977059898[/C][C]0.190002294010185[/C][/ROW]
[ROW][C]52[/C][C]41.58[/C][C]41.6099912826561[/C][C]-0.0299912826560629[/C][/ROW]
[ROW][C]53[/C][C]41.75[/C][C]41.5800013760062[/C][C]0.169998623993848[/C][/ROW]
[ROW][C]54[/C][C]41.75[/C][C]41.7499922004285[/C][C]7.79957148466792e-06[/C][/ROW]
[ROW][C]55[/C][C]41.75[/C][C]41.7499999996422[/C][C]3.57843532583502e-10[/C][/ROW]
[ROW][C]56[/C][C]41.85[/C][C]41.75[/C][C]0.100000000000016[/C][/ROW]
[ROW][C]57[/C][C]41.84[/C][C]41.8499954119796[/C][C]-0.00999541197963794[/C][/ROW]
[ROW][C]58[/C][C]41.97[/C][C]41.8400004585915[/C][C]0.129999541408459[/C][/ROW]
[ROW][C]59[/C][C]42.01[/C][C]41.9699940355946[/C][C]0.0400059644054309[/C][/ROW]
[ROW][C]60[/C][C]42.04[/C][C]42.0099981645182[/C][C]0.0300018354817908[/C][/ROW]
[ROW][C]61[/C][C]42.04[/C][C]42.0399986235097[/C][C]1.37649031728415e-06[/C][/ROW]
[ROW][C]62[/C][C]42.06[/C][C]42.0399999999368[/C][C]0.0200000000631562[/C][/ROW]
[ROW][C]63[/C][C]41.93[/C][C]42.0599990823959[/C][C]-0.129999082395926[/C][/ROW]
[ROW][C]64[/C][C]41.93[/C][C]41.9300059643844[/C][C]-5.96438437128199e-06[/C][/ROW]
[ROW][C]65[/C][C]41.99[/C][C]41.9300000002736[/C][C]0.0599999997263581[/C][/ROW]
[ROW][C]66[/C][C]42.03[/C][C]41.9899972471878[/C][C]0.0400027528122067[/C][/ROW]
[ROW][C]67[/C][C]42.03[/C][C]42.0299981646656[/C][C]1.83533444442219e-06[/C][/ROW]
[ROW][C]68[/C][C]42.12[/C][C]42.0299999999158[/C][C]0.0900000000842027[/C][/ROW]
[ROW][C]69[/C][C]42.22[/C][C]42.1199958707817[/C][C]0.100004129218327[/C][/ROW]
[ROW][C]70[/C][C]42.21[/C][C]42.2199954117902[/C][C]-0.00999541179018593[/C][/ROW]
[ROW][C]71[/C][C]42.23[/C][C]42.2100004585915[/C][C]0.0199995414084668[/C][/ROW]
[ROW][C]72[/C][C]42.22[/C][C]42.229999082417[/C][C]-0.00999908241696801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204498&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	39.36	39.28	0.0799999999999983
3	39.55	39.3599963295837	0.190003670416289
4	39.64	39.5499912825929	0.0900087174070876
5	39.8	39.6399958703817	0.160004129618279
6	39.79	39.7999926589779	-0.00999265897794999
7	39.79	39.7900004584652	-4.58465230224192e-07
8	39.86	39.790000000021	0.0699999999789682
9	39.91	39.8599967883858	0.0500032116142464
10	40	39.9099977058425	0.0900022941575358
11	40.01	39.9999958706764	0.0100041293235762
12	40.01	40.0099995410085	4.58991493701433e-07
13	40.01	40.0099999999789	2.10604866879294e-11
14	39.96	40.01	-0.0499999999999972
15	40	39.9600022940102	0.0399977059898191
16	39.76	39.9999981648971	-0.239998164897109
17	39.68	39.7600110111647	-0.0800110111646717
18	39.7	39.6800036709215	0.0199963290785163
19	39.7	39.6999990825644	9.17435649228082e-07
20	39.73	39.6999999999579	0.0300000000420866
21	39.64	39.7299986235939	-0.0899986235938854
22	39.56	39.6400041291552	-0.0800041291551707
23	39.67	39.5600036706057	0.109996329394264
24	39.66	39.669994953346	-0.00999495334601619
25	39.66	39.6600004585705	-4.58570497130495e-07
26	40.05	39.660000000021	0.389999999978961
27	39.99	40.0499821067206	-0.0599821067205895
28	40.06	39.9900027519913	0.0699972480087325
29	40.08	40.059996788512	0.0200032114879889
30	40.1	40.0799990822486	0.0200009177514175
31	40.1	40.0999990823538	9.17646175935261e-07
32	40.12	40.0999999999579	0.0200000000420957
33	40.07	40.1199990823959	-0.0499990823959209
34	40.24	40.0700022939681	0.169997706031921
35	40.58	40.2399922004706	0.34000779952936
36	40.72	40.5799844003729	0.14001559962707
37	40.72	40.7199935760558	6.42394422101233e-06
38	40.89	40.7199999997053	0.170000000294735
39	40.9	40.8899922003654	0.0100077996346286
40	41.04	40.8999995408401	0.140000459159886
41	41.27	41.0399935767504	0.230006423249577
42	41.29	41.2699894472585	0.0200105527415246
43	41.29	41.2899990819118	9.18088232992886e-07
44	41.33	41.2899999999579	0.0400000000421201
45	41.34	41.3299981647919	0.0100018352081506
46	41.37	41.3399995411138	0.0300004588862279
47	41.33	41.3699986235728	-0.0399986235728349
48	41.37	41.330001835145	0.0399981648550067
49	41.37	41.3699981648761	1.83512394613672e-06
50	41.42	41.3699999999158	0.0500000000842036
51	41.61	41.4199977059898	0.190002294010185
52	41.58	41.6099912826561	-0.0299912826560629
53	41.75	41.5800013760062	0.169998623993848
54	41.75	41.7499922004285	7.79957148466792e-06
55	41.75	41.7499999996422	3.57843532583502e-10
56	41.85	41.75	0.100000000000016
57	41.84	41.8499954119796	-0.00999541197963794
58	41.97	41.8400004585915	0.129999541408459
59	42.01	41.9699940355946	0.0400059644054309
60	42.04	42.0099981645182	0.0300018354817908
61	42.04	42.0399986235097	1.37649031728415e-06
62	42.06	42.0399999999368	0.0200000000631562
63	41.93	42.0599990823959	-0.129999082395926
64	41.93	41.9300059643844	-5.96438437128199e-06
65	41.99	41.9300000002736	0.0599999997263581
66	42.03	41.9899972471878	0.0400027528122067
67	42.03	42.0299981646656	1.83533444442219e-06
68	42.12	42.0299999999158	0.0900000000842027
69	42.22	42.1199958707817	0.100004129218327
70	42.21	42.2199954117902	-0.00999541179018593
71	42.23	42.2100004585915	0.0199995414084668
72	42.22	42.229999082417	-0.00999908241696801

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	42.2200004587599	42.0323778606825	42.4076230568373
74	42.2200004587599	41.9546681227718	42.485332794748
75	42.2200004587599	41.8950385260163	42.5449623915036
76	42.2200004587599	41.8447681747756	42.5952327427443
77	42.2200004587599	41.8004789740232	42.6395219434966
78	42.2200004587599	41.760438400527	42.6795625169929
79	42.2200004587599	41.7236172453261	42.7163836721937
80	42.2200004587599	41.6893449171979	42.750656000322
81	42.2200004587599	41.6571556195706	42.7828452979493
82	42.2200004587599	41.6267102075223	42.8132907099976
83	42.2200004587599	41.5977526532795	42.8422482642404
84	42.2200004587599	41.5700840482602	42.8699168692597

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 42.2200004587599 & 42.0323778606825 & 42.4076230568373 \tabularnewline
74 & 42.2200004587599 & 41.9546681227718 & 42.485332794748 \tabularnewline
75 & 42.2200004587599 & 41.8950385260163 & 42.5449623915036 \tabularnewline
76 & 42.2200004587599 & 41.8447681747756 & 42.5952327427443 \tabularnewline
77 & 42.2200004587599 & 41.8004789740232 & 42.6395219434966 \tabularnewline
78 & 42.2200004587599 & 41.760438400527 & 42.6795625169929 \tabularnewline
79 & 42.2200004587599 & 41.7236172453261 & 42.7163836721937 \tabularnewline
80 & 42.2200004587599 & 41.6893449171979 & 42.750656000322 \tabularnewline
81 & 42.2200004587599 & 41.6571556195706 & 42.7828452979493 \tabularnewline
82 & 42.2200004587599 & 41.6267102075223 & 42.8132907099976 \tabularnewline
83 & 42.2200004587599 & 41.5977526532795 & 42.8422482642404 \tabularnewline
84 & 42.2200004587599 & 41.5700840482602 & 42.8699168692597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204498&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]42.2200004587599[/C][C]42.0323778606825[/C][C]42.4076230568373[/C][/ROW]
[ROW][C]74[/C][C]42.2200004587599[/C][C]41.9546681227718[/C][C]42.485332794748[/C][/ROW]
[ROW][C]75[/C][C]42.2200004587599[/C][C]41.8950385260163[/C][C]42.5449623915036[/C][/ROW]
[ROW][C]76[/C][C]42.2200004587599[/C][C]41.8447681747756[/C][C]42.5952327427443[/C][/ROW]
[ROW][C]77[/C][C]42.2200004587599[/C][C]41.8004789740232[/C][C]42.6395219434966[/C][/ROW]
[ROW][C]78[/C][C]42.2200004587599[/C][C]41.760438400527[/C][C]42.6795625169929[/C][/ROW]
[ROW][C]79[/C][C]42.2200004587599[/C][C]41.7236172453261[/C][C]42.7163836721937[/C][/ROW]
[ROW][C]80[/C][C]42.2200004587599[/C][C]41.6893449171979[/C][C]42.750656000322[/C][/ROW]
[ROW][C]81[/C][C]42.2200004587599[/C][C]41.6571556195706[/C][C]42.7828452979493[/C][/ROW]
[ROW][C]82[/C][C]42.2200004587599[/C][C]41.6267102075223[/C][C]42.8132907099976[/C][/ROW]
[ROW][C]83[/C][C]42.2200004587599[/C][C]41.5977526532795[/C][C]42.8422482642404[/C][/ROW]
[ROW][C]84[/C][C]42.2200004587599[/C][C]41.5700840482602[/C][C]42.8699168692597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204498&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	42.2200004587599	42.0323778606825	42.4076230568373
74	42.2200004587599	41.9546681227718	42.485332794748
75	42.2200004587599	41.8950385260163	42.5449623915036
76	42.2200004587599	41.8447681747756	42.5952327427443
77	42.2200004587599	41.8004789740232	42.6395219434966
78	42.2200004587599	41.760438400527	42.6795625169929
79	42.2200004587599	41.7236172453261	42.7163836721937
80	42.2200004587599	41.6893449171979	42.750656000322
81	42.2200004587599	41.6571556195706	42.7828452979493
82	42.2200004587599	41.6267102075223	42.8132907099976
83	42.2200004587599	41.5977526532795	42.8422482642404
84	42.2200004587599	41.5700840482602	42.8699168692597

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