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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 14 May 2014 13:23:54 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/14/t1400088279ply0t6e5uhyclnr.htm/, Retrieved Thu, 16 May 2024 03:01:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234867, Retrieved Thu, 16 May 2024 03:01:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

167

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

-       [Exponential Smoothing] [Prijs scheerappar...] [2014-05-14 17:23:54] [7314f5de623f4497f735e8af2050bf2f] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234867&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234867&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.887773288244519
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.887773288244519 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234867&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]0.887773288244519[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234867&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	0.887773288244519
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	74.46	74.86	-0.400000000000006
4	74.03	74.5648906847022	-0.534890684702191
5	74.45	74.1500290226928	0.29997097730724
6	74.74	74.4763352435947	0.263664756405262
7	74.74	74.7704097713828	-0.0304097713828355
8	74.78	74.8034127886475	-0.0234127886475335
9	74.25	74.8426275402829	-0.592627540282948
10	74.14	74.3765086401417	-0.236508640141693
11	74.41	74.2265425869849	0.183457413015134
12	74.51	74.4494111777901	0.0605888222098656
13	74.51	74.5632003157143	-0.0532003157142498
14	74.64	74.575970496497	0.0640295035030363
15	74.52	74.6928141793665	-0.172814179366526
16	74.51	74.599394367095	-0.089394367095025
17	74.39	74.5800324358685	-0.190032435868545
18	74.11	74.4713267154044	-0.361326715404417
19	74.11	74.2105505091393	-0.100550509139254
20	74.2	74.181284453006	0.0187155469939597
21	73.84	74.2578996157022	-0.417899615702169
22	73.89	73.9468994997141	-0.0568994997141345
23	74.31	73.9563856437534	0.353614356246553
24	73.56	74.3303150235689	-0.770315023568926
25	73.56	73.706449922111	-0.146449922110989
26	73.99	73.6364355931954	0.353564406804622
27	73.63	74.0103206292305	-0.380320629230539
28	73.51	73.7326821336313	-0.222682133631309
29	73.6	73.5949908836241	0.00500911637584522
30	73.03	73.6594378433403	-0.629437843340327
31	73.03	73.1606397394125	-0.130639739412544
32	72.61	73.1046612683789	-0.494661268378863
33	72.3	72.725514207583	-0.425514207582964
34	72.56	72.4077540603223	0.152245939677726
35	72.76	72.6029139388119	0.157086061188153
36	72.92	72.8023707478902	0.117629252109765
37	72.92	72.9667988558295	-0.046798855829465
38	72.93	72.9852520817037	-0.0552520817036566
39	73.13	72.9962007594473	0.133799240552733
40	73.31	73.1749841511974	0.135015848802624
41	73.34	73.354847615254	-0.0148476152540127
42	74.31	73.4016662990374	0.908333700962629
43	74.31	74.2680606955643	0.041939304435715
44	74.65	74.3652932897699	0.284706710230139
45	74.78	74.6780483020962	0.101951697903843
46	74.73	74.8285582961864	-0.0985582961863685
47	74.71	74.8010608734972	-0.0910608734972271
48	74.63	74.7802194624022	-0.150219462402177
49	74.63	74.7068586363071	-0.0768586363070796
50	74.95	74.6986255920228	0.251374407977252
51	75.17	74.9817890767732	0.188210923226762
52	75.49	75.2088777069698	0.281122293030194
53	74.54	75.5184505694521	-0.97845056945205
54	75.59	74.7098082900249	0.880191709975108
55	75.59	75.5512189786751	0.0387810213249367
56	76.06	75.6456477334982	0.414352266501808
57	76.06	76.0734986076221	-0.0134986076220684
58	76.39	76.1215149043467	0.26848509565329
59	76.39	76.4198688005595	-0.029868800559484
60	76.93	76.4533520772709	0.476647922729128
61	76.93	76.936507370967	-0.00650737096702869
62	77.39	76.9907303008458	0.399269699154189
63	77.65	77.4051912745603	0.244808725439682
64	78.04	77.6825259217349	0.357474078265142
65	77.66	78.0598818596585	-0.399881859658493
66	77.31	77.7648774262001	-0.454877426200142
67	77.31	77.4210493977942	-0.111049397794247
68	77.33	77.3824627087569	-0.0524627087568774
69	78.01	77.3958877172936	0.614112282706429
70	78.31	78.0010801978632	0.308919802136785
71	78.61	78.33533094641	0.27466905358996
72	78.94	78.6391747952946	0.30082520470539
73	78.94	78.9662393764627	-0.0262393764627404
74	79.84	79.0029447589389	0.83705524106108
75	78.76	79.806060042738	-1.04606004273802
76	78.62	78.9373958788953	-0.317395878895283
77	78.36	78.7156202958132	-0.355620295813168
78	78.53	78.4599100964326	0.0700899035673785
79	78.53	78.5821340405954	-0.0521340405953765
80	78.76	78.5958508319465	0.164149168053456
81	78.76	78.801578078632	-0.0415780786319715
82	79.37	78.824666171046	0.545333828954014
83	79.83	79.3687989775675	0.461201022432533
84	79.89	79.8382409257941	0.0517590742058758

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 74.46 & 74.86 & -0.400000000000006 \tabularnewline
4 & 74.03 & 74.5648906847022 & -0.534890684702191 \tabularnewline
5 & 74.45 & 74.1500290226928 & 0.29997097730724 \tabularnewline
6 & 74.74 & 74.4763352435947 & 0.263664756405262 \tabularnewline
7 & 74.74 & 74.7704097713828 & -0.0304097713828355 \tabularnewline
8 & 74.78 & 74.8034127886475 & -0.0234127886475335 \tabularnewline
9 & 74.25 & 74.8426275402829 & -0.592627540282948 \tabularnewline
10 & 74.14 & 74.3765086401417 & -0.236508640141693 \tabularnewline
11 & 74.41 & 74.2265425869849 & 0.183457413015134 \tabularnewline
12 & 74.51 & 74.4494111777901 & 0.0605888222098656 \tabularnewline
13 & 74.51 & 74.5632003157143 & -0.0532003157142498 \tabularnewline
14 & 74.64 & 74.575970496497 & 0.0640295035030363 \tabularnewline
15 & 74.52 & 74.6928141793665 & -0.172814179366526 \tabularnewline
16 & 74.51 & 74.599394367095 & -0.089394367095025 \tabularnewline
17 & 74.39 & 74.5800324358685 & -0.190032435868545 \tabularnewline
18 & 74.11 & 74.4713267154044 & -0.361326715404417 \tabularnewline
19 & 74.11 & 74.2105505091393 & -0.100550509139254 \tabularnewline
20 & 74.2 & 74.181284453006 & 0.0187155469939597 \tabularnewline
21 & 73.84 & 74.2578996157022 & -0.417899615702169 \tabularnewline
22 & 73.89 & 73.9468994997141 & -0.0568994997141345 \tabularnewline
23 & 74.31 & 73.9563856437534 & 0.353614356246553 \tabularnewline
24 & 73.56 & 74.3303150235689 & -0.770315023568926 \tabularnewline
25 & 73.56 & 73.706449922111 & -0.146449922110989 \tabularnewline
26 & 73.99 & 73.6364355931954 & 0.353564406804622 \tabularnewline
27 & 73.63 & 74.0103206292305 & -0.380320629230539 \tabularnewline
28 & 73.51 & 73.7326821336313 & -0.222682133631309 \tabularnewline
29 & 73.6 & 73.5949908836241 & 0.00500911637584522 \tabularnewline
30 & 73.03 & 73.6594378433403 & -0.629437843340327 \tabularnewline
31 & 73.03 & 73.1606397394125 & -0.130639739412544 \tabularnewline
32 & 72.61 & 73.1046612683789 & -0.494661268378863 \tabularnewline
33 & 72.3 & 72.725514207583 & -0.425514207582964 \tabularnewline
34 & 72.56 & 72.4077540603223 & 0.152245939677726 \tabularnewline
35 & 72.76 & 72.6029139388119 & 0.157086061188153 \tabularnewline
36 & 72.92 & 72.8023707478902 & 0.117629252109765 \tabularnewline
37 & 72.92 & 72.9667988558295 & -0.046798855829465 \tabularnewline
38 & 72.93 & 72.9852520817037 & -0.0552520817036566 \tabularnewline
39 & 73.13 & 72.9962007594473 & 0.133799240552733 \tabularnewline
40 & 73.31 & 73.1749841511974 & 0.135015848802624 \tabularnewline
41 & 73.34 & 73.354847615254 & -0.0148476152540127 \tabularnewline
42 & 74.31 & 73.4016662990374 & 0.908333700962629 \tabularnewline
43 & 74.31 & 74.2680606955643 & 0.041939304435715 \tabularnewline
44 & 74.65 & 74.3652932897699 & 0.284706710230139 \tabularnewline
45 & 74.78 & 74.6780483020962 & 0.101951697903843 \tabularnewline
46 & 74.73 & 74.8285582961864 & -0.0985582961863685 \tabularnewline
47 & 74.71 & 74.8010608734972 & -0.0910608734972271 \tabularnewline
48 & 74.63 & 74.7802194624022 & -0.150219462402177 \tabularnewline
49 & 74.63 & 74.7068586363071 & -0.0768586363070796 \tabularnewline
50 & 74.95 & 74.6986255920228 & 0.251374407977252 \tabularnewline
51 & 75.17 & 74.9817890767732 & 0.188210923226762 \tabularnewline
52 & 75.49 & 75.2088777069698 & 0.281122293030194 \tabularnewline
53 & 74.54 & 75.5184505694521 & -0.97845056945205 \tabularnewline
54 & 75.59 & 74.7098082900249 & 0.880191709975108 \tabularnewline
55 & 75.59 & 75.5512189786751 & 0.0387810213249367 \tabularnewline
56 & 76.06 & 75.6456477334982 & 0.414352266501808 \tabularnewline
57 & 76.06 & 76.0734986076221 & -0.0134986076220684 \tabularnewline
58 & 76.39 & 76.1215149043467 & 0.26848509565329 \tabularnewline
59 & 76.39 & 76.4198688005595 & -0.029868800559484 \tabularnewline
60 & 76.93 & 76.4533520772709 & 0.476647922729128 \tabularnewline
61 & 76.93 & 76.936507370967 & -0.00650737096702869 \tabularnewline
62 & 77.39 & 76.9907303008458 & 0.399269699154189 \tabularnewline
63 & 77.65 & 77.4051912745603 & 0.244808725439682 \tabularnewline
64 & 78.04 & 77.6825259217349 & 0.357474078265142 \tabularnewline
65 & 77.66 & 78.0598818596585 & -0.399881859658493 \tabularnewline
66 & 77.31 & 77.7648774262001 & -0.454877426200142 \tabularnewline
67 & 77.31 & 77.4210493977942 & -0.111049397794247 \tabularnewline
68 & 77.33 & 77.3824627087569 & -0.0524627087568774 \tabularnewline
69 & 78.01 & 77.3958877172936 & 0.614112282706429 \tabularnewline
70 & 78.31 & 78.0010801978632 & 0.308919802136785 \tabularnewline
71 & 78.61 & 78.33533094641 & 0.27466905358996 \tabularnewline
72 & 78.94 & 78.6391747952946 & 0.30082520470539 \tabularnewline
73 & 78.94 & 78.9662393764627 & -0.0262393764627404 \tabularnewline
74 & 79.84 & 79.0029447589389 & 0.83705524106108 \tabularnewline
75 & 78.76 & 79.806060042738 & -1.04606004273802 \tabularnewline
76 & 78.62 & 78.9373958788953 & -0.317395878895283 \tabularnewline
77 & 78.36 & 78.7156202958132 & -0.355620295813168 \tabularnewline
78 & 78.53 & 78.4599100964326 & 0.0700899035673785 \tabularnewline
79 & 78.53 & 78.5821340405954 & -0.0521340405953765 \tabularnewline
80 & 78.76 & 78.5958508319465 & 0.164149168053456 \tabularnewline
81 & 78.76 & 78.801578078632 & -0.0415780786319715 \tabularnewline
82 & 79.37 & 78.824666171046 & 0.545333828954014 \tabularnewline
83 & 79.83 & 79.3687989775675 & 0.461201022432533 \tabularnewline
84 & 79.89 & 79.8382409257941 & 0.0517590742058758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234867&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]3[/C][C]74.46[/C][C]74.86[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]4[/C][C]74.03[/C][C]74.5648906847022[/C][C]-0.534890684702191[/C][/ROW]
[ROW][C]5[/C][C]74.45[/C][C]74.1500290226928[/C][C]0.29997097730724[/C][/ROW]
[ROW][C]6[/C][C]74.74[/C][C]74.4763352435947[/C][C]0.263664756405262[/C][/ROW]
[ROW][C]7[/C][C]74.74[/C][C]74.7704097713828[/C][C]-0.0304097713828355[/C][/ROW]
[ROW][C]8[/C][C]74.78[/C][C]74.8034127886475[/C][C]-0.0234127886475335[/C][/ROW]
[ROW][C]9[/C][C]74.25[/C][C]74.8426275402829[/C][C]-0.592627540282948[/C][/ROW]
[ROW][C]10[/C][C]74.14[/C][C]74.3765086401417[/C][C]-0.236508640141693[/C][/ROW]
[ROW][C]11[/C][C]74.41[/C][C]74.2265425869849[/C][C]0.183457413015134[/C][/ROW]
[ROW][C]12[/C][C]74.51[/C][C]74.4494111777901[/C][C]0.0605888222098656[/C][/ROW]
[ROW][C]13[/C][C]74.51[/C][C]74.5632003157143[/C][C]-0.0532003157142498[/C][/ROW]
[ROW][C]14[/C][C]74.64[/C][C]74.575970496497[/C][C]0.0640295035030363[/C][/ROW]
[ROW][C]15[/C][C]74.52[/C][C]74.6928141793665[/C][C]-0.172814179366526[/C][/ROW]
[ROW][C]16[/C][C]74.51[/C][C]74.599394367095[/C][C]-0.089394367095025[/C][/ROW]
[ROW][C]17[/C][C]74.39[/C][C]74.5800324358685[/C][C]-0.190032435868545[/C][/ROW]
[ROW][C]18[/C][C]74.11[/C][C]74.4713267154044[/C][C]-0.361326715404417[/C][/ROW]
[ROW][C]19[/C][C]74.11[/C][C]74.2105505091393[/C][C]-0.100550509139254[/C][/ROW]
[ROW][C]20[/C][C]74.2[/C][C]74.181284453006[/C][C]0.0187155469939597[/C][/ROW]
[ROW][C]21[/C][C]73.84[/C][C]74.2578996157022[/C][C]-0.417899615702169[/C][/ROW]
[ROW][C]22[/C][C]73.89[/C][C]73.9468994997141[/C][C]-0.0568994997141345[/C][/ROW]
[ROW][C]23[/C][C]74.31[/C][C]73.9563856437534[/C][C]0.353614356246553[/C][/ROW]
[ROW][C]24[/C][C]73.56[/C][C]74.3303150235689[/C][C]-0.770315023568926[/C][/ROW]
[ROW][C]25[/C][C]73.56[/C][C]73.706449922111[/C][C]-0.146449922110989[/C][/ROW]
[ROW][C]26[/C][C]73.99[/C][C]73.6364355931954[/C][C]0.353564406804622[/C][/ROW]
[ROW][C]27[/C][C]73.63[/C][C]74.0103206292305[/C][C]-0.380320629230539[/C][/ROW]
[ROW][C]28[/C][C]73.51[/C][C]73.7326821336313[/C][C]-0.222682133631309[/C][/ROW]
[ROW][C]29[/C][C]73.6[/C][C]73.5949908836241[/C][C]0.00500911637584522[/C][/ROW]
[ROW][C]30[/C][C]73.03[/C][C]73.6594378433403[/C][C]-0.629437843340327[/C][/ROW]
[ROW][C]31[/C][C]73.03[/C][C]73.1606397394125[/C][C]-0.130639739412544[/C][/ROW]
[ROW][C]32[/C][C]72.61[/C][C]73.1046612683789[/C][C]-0.494661268378863[/C][/ROW]
[ROW][C]33[/C][C]72.3[/C][C]72.725514207583[/C][C]-0.425514207582964[/C][/ROW]
[ROW][C]34[/C][C]72.56[/C][C]72.4077540603223[/C][C]0.152245939677726[/C][/ROW]
[ROW][C]35[/C][C]72.76[/C][C]72.6029139388119[/C][C]0.157086061188153[/C][/ROW]
[ROW][C]36[/C][C]72.92[/C][C]72.8023707478902[/C][C]0.117629252109765[/C][/ROW]
[ROW][C]37[/C][C]72.92[/C][C]72.9667988558295[/C][C]-0.046798855829465[/C][/ROW]
[ROW][C]38[/C][C]72.93[/C][C]72.9852520817037[/C][C]-0.0552520817036566[/C][/ROW]
[ROW][C]39[/C][C]73.13[/C][C]72.9962007594473[/C][C]0.133799240552733[/C][/ROW]
[ROW][C]40[/C][C]73.31[/C][C]73.1749841511974[/C][C]0.135015848802624[/C][/ROW]
[ROW][C]41[/C][C]73.34[/C][C]73.354847615254[/C][C]-0.0148476152540127[/C][/ROW]
[ROW][C]42[/C][C]74.31[/C][C]73.4016662990374[/C][C]0.908333700962629[/C][/ROW]
[ROW][C]43[/C][C]74.31[/C][C]74.2680606955643[/C][C]0.041939304435715[/C][/ROW]
[ROW][C]44[/C][C]74.65[/C][C]74.3652932897699[/C][C]0.284706710230139[/C][/ROW]
[ROW][C]45[/C][C]74.78[/C][C]74.6780483020962[/C][C]0.101951697903843[/C][/ROW]
[ROW][C]46[/C][C]74.73[/C][C]74.8285582961864[/C][C]-0.0985582961863685[/C][/ROW]
[ROW][C]47[/C][C]74.71[/C][C]74.8010608734972[/C][C]-0.0910608734972271[/C][/ROW]
[ROW][C]48[/C][C]74.63[/C][C]74.7802194624022[/C][C]-0.150219462402177[/C][/ROW]
[ROW][C]49[/C][C]74.63[/C][C]74.7068586363071[/C][C]-0.0768586363070796[/C][/ROW]
[ROW][C]50[/C][C]74.95[/C][C]74.6986255920228[/C][C]0.251374407977252[/C][/ROW]
[ROW][C]51[/C][C]75.17[/C][C]74.9817890767732[/C][C]0.188210923226762[/C][/ROW]
[ROW][C]52[/C][C]75.49[/C][C]75.2088777069698[/C][C]0.281122293030194[/C][/ROW]
[ROW][C]53[/C][C]74.54[/C][C]75.5184505694521[/C][C]-0.97845056945205[/C][/ROW]
[ROW][C]54[/C][C]75.59[/C][C]74.7098082900249[/C][C]0.880191709975108[/C][/ROW]
[ROW][C]55[/C][C]75.59[/C][C]75.5512189786751[/C][C]0.0387810213249367[/C][/ROW]
[ROW][C]56[/C][C]76.06[/C][C]75.6456477334982[/C][C]0.414352266501808[/C][/ROW]
[ROW][C]57[/C][C]76.06[/C][C]76.0734986076221[/C][C]-0.0134986076220684[/C][/ROW]
[ROW][C]58[/C][C]76.39[/C][C]76.1215149043467[/C][C]0.26848509565329[/C][/ROW]
[ROW][C]59[/C][C]76.39[/C][C]76.4198688005595[/C][C]-0.029868800559484[/C][/ROW]
[ROW][C]60[/C][C]76.93[/C][C]76.4533520772709[/C][C]0.476647922729128[/C][/ROW]
[ROW][C]61[/C][C]76.93[/C][C]76.936507370967[/C][C]-0.00650737096702869[/C][/ROW]
[ROW][C]62[/C][C]77.39[/C][C]76.9907303008458[/C][C]0.399269699154189[/C][/ROW]
[ROW][C]63[/C][C]77.65[/C][C]77.4051912745603[/C][C]0.244808725439682[/C][/ROW]
[ROW][C]64[/C][C]78.04[/C][C]77.6825259217349[/C][C]0.357474078265142[/C][/ROW]
[ROW][C]65[/C][C]77.66[/C][C]78.0598818596585[/C][C]-0.399881859658493[/C][/ROW]
[ROW][C]66[/C][C]77.31[/C][C]77.7648774262001[/C][C]-0.454877426200142[/C][/ROW]
[ROW][C]67[/C][C]77.31[/C][C]77.4210493977942[/C][C]-0.111049397794247[/C][/ROW]
[ROW][C]68[/C][C]77.33[/C][C]77.3824627087569[/C][C]-0.0524627087568774[/C][/ROW]
[ROW][C]69[/C][C]78.01[/C][C]77.3958877172936[/C][C]0.614112282706429[/C][/ROW]
[ROW][C]70[/C][C]78.31[/C][C]78.0010801978632[/C][C]0.308919802136785[/C][/ROW]
[ROW][C]71[/C][C]78.61[/C][C]78.33533094641[/C][C]0.27466905358996[/C][/ROW]
[ROW][C]72[/C][C]78.94[/C][C]78.6391747952946[/C][C]0.30082520470539[/C][/ROW]
[ROW][C]73[/C][C]78.94[/C][C]78.9662393764627[/C][C]-0.0262393764627404[/C][/ROW]
[ROW][C]74[/C][C]79.84[/C][C]79.0029447589389[/C][C]0.83705524106108[/C][/ROW]
[ROW][C]75[/C][C]78.76[/C][C]79.806060042738[/C][C]-1.04606004273802[/C][/ROW]
[ROW][C]76[/C][C]78.62[/C][C]78.9373958788953[/C][C]-0.317395878895283[/C][/ROW]
[ROW][C]77[/C][C]78.36[/C][C]78.7156202958132[/C][C]-0.355620295813168[/C][/ROW]
[ROW][C]78[/C][C]78.53[/C][C]78.4599100964326[/C][C]0.0700899035673785[/C][/ROW]
[ROW][C]79[/C][C]78.53[/C][C]78.5821340405954[/C][C]-0.0521340405953765[/C][/ROW]
[ROW][C]80[/C][C]78.76[/C][C]78.5958508319465[/C][C]0.164149168053456[/C][/ROW]
[ROW][C]81[/C][C]78.76[/C][C]78.801578078632[/C][C]-0.0415780786319715[/C][/ROW]
[ROW][C]82[/C][C]79.37[/C][C]78.824666171046[/C][C]0.545333828954014[/C][/ROW]
[ROW][C]83[/C][C]79.83[/C][C]79.3687989775675[/C][C]0.461201022432533[/C][/ROW]
[ROW][C]84[/C][C]79.89[/C][C]79.8382409257941[/C][C]0.0517590742058758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234867&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
3	74.46	74.86	-0.400000000000006
4	74.03	74.5648906847022	-0.534890684702191
5	74.45	74.1500290226928	0.29997097730724
6	74.74	74.4763352435947	0.263664756405262
7	74.74	74.7704097713828	-0.0304097713828355
8	74.78	74.8034127886475	-0.0234127886475335
9	74.25	74.8426275402829	-0.592627540282948
10	74.14	74.3765086401417	-0.236508640141693
11	74.41	74.2265425869849	0.183457413015134
12	74.51	74.4494111777901	0.0605888222098656
13	74.51	74.5632003157143	-0.0532003157142498
14	74.64	74.575970496497	0.0640295035030363
15	74.52	74.6928141793665	-0.172814179366526
16	74.51	74.599394367095	-0.089394367095025
17	74.39	74.5800324358685	-0.190032435868545
18	74.11	74.4713267154044	-0.361326715404417
19	74.11	74.2105505091393	-0.100550509139254
20	74.2	74.181284453006	0.0187155469939597
21	73.84	74.2578996157022	-0.417899615702169
22	73.89	73.9468994997141	-0.0568994997141345
23	74.31	73.9563856437534	0.353614356246553
24	73.56	74.3303150235689	-0.770315023568926
25	73.56	73.706449922111	-0.146449922110989
26	73.99	73.6364355931954	0.353564406804622
27	73.63	74.0103206292305	-0.380320629230539
28	73.51	73.7326821336313	-0.222682133631309
29	73.6	73.5949908836241	0.00500911637584522
30	73.03	73.6594378433403	-0.629437843340327
31	73.03	73.1606397394125	-0.130639739412544
32	72.61	73.1046612683789	-0.494661268378863
33	72.3	72.725514207583	-0.425514207582964
34	72.56	72.4077540603223	0.152245939677726
35	72.76	72.6029139388119	0.157086061188153
36	72.92	72.8023707478902	0.117629252109765
37	72.92	72.9667988558295	-0.046798855829465
38	72.93	72.9852520817037	-0.0552520817036566
39	73.13	72.9962007594473	0.133799240552733
40	73.31	73.1749841511974	0.135015848802624
41	73.34	73.354847615254	-0.0148476152540127
42	74.31	73.4016662990374	0.908333700962629
43	74.31	74.2680606955643	0.041939304435715
44	74.65	74.3652932897699	0.284706710230139
45	74.78	74.6780483020962	0.101951697903843
46	74.73	74.8285582961864	-0.0985582961863685
47	74.71	74.8010608734972	-0.0910608734972271
48	74.63	74.7802194624022	-0.150219462402177
49	74.63	74.7068586363071	-0.0768586363070796
50	74.95	74.6986255920228	0.251374407977252
51	75.17	74.9817890767732	0.188210923226762
52	75.49	75.2088777069698	0.281122293030194
53	74.54	75.5184505694521	-0.97845056945205
54	75.59	74.7098082900249	0.880191709975108
55	75.59	75.5512189786751	0.0387810213249367
56	76.06	75.6456477334982	0.414352266501808
57	76.06	76.0734986076221	-0.0134986076220684
58	76.39	76.1215149043467	0.26848509565329
59	76.39	76.4198688005595	-0.029868800559484
60	76.93	76.4533520772709	0.476647922729128
61	76.93	76.936507370967	-0.00650737096702869
62	77.39	76.9907303008458	0.399269699154189
63	77.65	77.4051912745603	0.244808725439682
64	78.04	77.6825259217349	0.357474078265142
65	77.66	78.0598818596585	-0.399881859658493
66	77.31	77.7648774262001	-0.454877426200142
67	77.31	77.4210493977942	-0.111049397794247
68	77.33	77.3824627087569	-0.0524627087568774
69	78.01	77.3958877172936	0.614112282706429
70	78.31	78.0010801978632	0.308919802136785
71	78.61	78.33533094641	0.27466905358996
72	78.94	78.6391747952946	0.30082520470539
73	78.94	78.9662393764627	-0.0262393764627404
74	79.84	79.0029447589389	0.83705524106108
75	78.76	79.806060042738	-1.04606004273802
76	78.62	78.9373958788953	-0.317395878895283
77	78.36	78.7156202958132	-0.355620295813168
78	78.53	78.4599100964326	0.0700899035673785
79	78.53	78.5821340405954	-0.0521340405953765
80	78.76	78.5958508319465	0.164149168053456
81	78.76	78.801578078632	-0.0415780786319715
82	79.37	78.824666171046	0.545333828954014
83	79.83	79.3687989775675	0.461201022432533
84	79.89	79.8382409257941	0.0517590742058758

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	79.9441912492984	79.2305084094366	80.6578740891602
86	80.0041912492984	79.0498445297112	80.9585379688855
87	80.0641912492984	78.9186729707623	81.2097095278345
88	80.1241912492984	78.8151279995912	81.4332544990055
89	80.1841912492984	78.7298594243673	81.6385230742295
90	80.2441912492984	78.6578383496317	81.8305441489651
91	80.3041912492984	78.5959904450735	82.0123920535232
92	80.3641912492984	78.5422734539992	82.1861090445976
93	80.4241912492984	78.4952488141538	82.353133684443
94	80.4841912492984	78.4538579310043	82.5145245675925
95	80.5441912492984	78.417294954542	82.6710875440548
96	80.6041912492984	78.3849295896642	82.8234529089326

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 79.9441912492984 & 79.2305084094366 & 80.6578740891602 \tabularnewline
86 & 80.0041912492984 & 79.0498445297112 & 80.9585379688855 \tabularnewline
87 & 80.0641912492984 & 78.9186729707623 & 81.2097095278345 \tabularnewline
88 & 80.1241912492984 & 78.8151279995912 & 81.4332544990055 \tabularnewline
89 & 80.1841912492984 & 78.7298594243673 & 81.6385230742295 \tabularnewline
90 & 80.2441912492984 & 78.6578383496317 & 81.8305441489651 \tabularnewline
91 & 80.3041912492984 & 78.5959904450735 & 82.0123920535232 \tabularnewline
92 & 80.3641912492984 & 78.5422734539992 & 82.1861090445976 \tabularnewline
93 & 80.4241912492984 & 78.4952488141538 & 82.353133684443 \tabularnewline
94 & 80.4841912492984 & 78.4538579310043 & 82.5145245675925 \tabularnewline
95 & 80.5441912492984 & 78.417294954542 & 82.6710875440548 \tabularnewline
96 & 80.6041912492984 & 78.3849295896642 & 82.8234529089326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234867&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]79.9441912492984[/C][C]79.2305084094366[/C][C]80.6578740891602[/C][/ROW]
[ROW][C]86[/C][C]80.0041912492984[/C][C]79.0498445297112[/C][C]80.9585379688855[/C][/ROW]
[ROW][C]87[/C][C]80.0641912492984[/C][C]78.9186729707623[/C][C]81.2097095278345[/C][/ROW]
[ROW][C]88[/C][C]80.1241912492984[/C][C]78.8151279995912[/C][C]81.4332544990055[/C][/ROW]
[ROW][C]89[/C][C]80.1841912492984[/C][C]78.7298594243673[/C][C]81.6385230742295[/C][/ROW]
[ROW][C]90[/C][C]80.2441912492984[/C][C]78.6578383496317[/C][C]81.8305441489651[/C][/ROW]
[ROW][C]91[/C][C]80.3041912492984[/C][C]78.5959904450735[/C][C]82.0123920535232[/C][/ROW]
[ROW][C]92[/C][C]80.3641912492984[/C][C]78.5422734539992[/C][C]82.1861090445976[/C][/ROW]
[ROW][C]93[/C][C]80.4241912492984[/C][C]78.4952488141538[/C][C]82.353133684443[/C][/ROW]
[ROW][C]94[/C][C]80.4841912492984[/C][C]78.4538579310043[/C][C]82.5145245675925[/C][/ROW]
[ROW][C]95[/C][C]80.5441912492984[/C][C]78.417294954542[/C][C]82.6710875440548[/C][/ROW]
[ROW][C]96[/C][C]80.6041912492984[/C][C]78.3849295896642[/C][C]82.8234529089326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234867&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234867&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	79.9441912492984	79.2305084094366	80.6578740891602
86	80.0041912492984	79.0498445297112	80.9585379688855
87	80.0641912492984	78.9186729707623	81.2097095278345
88	80.1241912492984	78.8151279995912	81.4332544990055
89	80.1841912492984	78.7298594243673	81.6385230742295
90	80.2441912492984	78.6578383496317	81.8305441489651
91	80.3041912492984	78.5959904450735	82.0123920535232
92	80.3641912492984	78.5422734539992	82.1861090445976
93	80.4241912492984	78.4952488141538	82.353133684443
94	80.4841912492984	78.4538579310043	82.5145245675925
95	80.5441912492984	78.417294954542	82.6710875440548
96	80.6041912492984	78.3849295896642	82.8234529089326

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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