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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

Sun, 24 May 2015 21:31:45 +0100

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/May/24/t1432500325ji5re8bu08h6qr4.htm/, Retrieved Thu, 02 May 2024 22:53:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279316, Retrieved Thu, 02 May 2024 22:53:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

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

-       [Exponential Smoothing] [] [2015-05-24 20:31:45] [63f2940fabeba4f82aed7f8ad2e0a56b] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279316&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279316&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.953217434578408
beta	0.0178271804673795
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.953217434578408 \tabularnewline
beta & 0.0178271804673795 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279316&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]0.953217434578408[/C][/ROW]
[ROW][C]beta[/C][C]0.0178271804673795[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279316&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	0.953217434578408
beta	0.0178271804673795
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	599	599	0
4	599	599	0
5	599	599	0
6	599	599	0
7	599	599	0
8	599	599	0
9	599	599	0
10	617.06	599	18.0599999999999
11	617.06	616.522003685396	0.537996314604356
12	617.06	617.350870236925	-0.290870236924775
13	617.06	617.384703930528	-0.324703930528472
14	617.06	617.380769005424	-0.320769005424495
15	617.06	617.375134034332	-0.315134034332459
16	617.06	617.369515286802	-0.30951528680157
17	617.06	617.363992778634	-0.30399277863421
18	617.06	617.358568617762	-0.298568617762385
19	617.06	617.353241231567	-0.293241231567208
20	617.06	617.348008901968	-0.288008901968169
21	617.06	617.342869933275	-0.282869933275151
22	628.18	617.337822659661	10.8421773403392
23	628.18	628.121607470562	0.0583925294378105
24	628.18	628.627092863689	-0.447092863688908
25	628.18	628.643143237997	-0.463143237997087
26	628.18	628.63602383963	-0.456023839630348
27	628.18	628.62794148107	-0.447941481070075
28	628.18	628.619951417729	-0.439951417729162
29	628.18	628.612101448774	-0.432101448773892
30	628.18	628.604391429723	-0.424391429722732
31	628.18	628.596818975623	-0.416818975622732
32	628.18	628.589381637234	-0.409381637233764
33	628.18	628.582077003929	-0.402077003928753
34	641.08	628.574902707851	12.5050972921492
35	641.08	641.083573341522	-0.00357334152170097
36	641.08	641.668700321346	-0.588700321345755
37	641.08	641.686070172485	-0.606070172485374
38	641.08	641.676583719615	-0.596583719615069
39	641.08	641.666002064939	-0.586002064939407
40	641.08	641.655548989868	-0.575548989868139
41	641.08	641.645279561059	-0.565279561058787
42	641.08	641.635193233937	-0.555193233936961
43	641.08	641.625286871547	-0.545286871546523
44	641.08	641.615557268959	-0.535557268959451
45	641.08	641.60600127253	-0.526001272530152
46	668.21	641.596615784602	26.6133842153979
47	668.21	667.909211715424	0.300788284576015
48	668.21	669.1452938052	-0.93529380519999
49	668.21	669.187227281166	-0.977227281166051
50	668.21	669.172582838411	-0.96258283841064
51	668.21	669.155540391112	-0.945540391111649
52	668.21	669.13867536437	-0.928675364369838
53	668.21	669.122105228239	-0.912105228238943
54	668.21	669.10583046714	-0.895830467140399
55	668.21	669.089846084376	-0.879846084376027
56	668.21	669.074146911736	-0.86414691173627
57	668.21	669.058727860812	-0.848727860812119
58	665.27	669.043583933397	-3.77358393339659
59	665.27	666.176291015838	-0.906291015837951
60	665.27	666.026750931672	-0.756750931671945
61	665.27	666.006895458686	-0.736895458686149
62	665.27	665.993444372118	-0.723444372118365
63	665.27	665.980521475902	-0.710521475902055
64	665.27	665.967842890877	-0.697842890876927
65	665.27	665.955391184824	-0.685391184823857
66	665.27	665.943161686824	-0.673161686823846
67	665.27	665.931150402338	-0.66115040233808
68	665.27	665.91935343635	-0.649353436350339
69	665.27	665.907766964689	-0.637766964689035
70	674.3	665.896387231482	8.40361276851786
71	674.3	674.646212390574	-0.346212390574351
72	674.3	675.049668409302	-0.749668409302103
73	674.3	675.05580386725	-0.755803867249938
74	674.3	675.043247389133	-0.743247389133217
75	674.3	675.030029828778	-0.730029828777901
76	674.3	675.017005949671	-0.717005949671488
77	674.3	675.004212448583	-0.70421244858278
78	674.3	674.991647127426	-0.691647127425767
79	674.3	674.979306005866	-0.679306005865783
80	674.3	674.967185087829	-0.667185087828784
81	674.3	674.95528044441	-0.655280444410096
82	685.34	674.943588216612	10.396411783388
83	685.34	685.643229790739	-0.303229790739124
84	685.34	686.138633634486	-0.798633634486123
85	685.34	686.148238572726	-0.808238572725713
86	685.34	686.13495337345	-0.79495337344963
87	685.34	686.12082307259	-0.780823072590124
88	685.34	686.106893354446	-0.766893354445529
89	685.34	686.093209730272	-0.753209730272147
90	685.34	686.079770147284	-0.739770147284048
91	685.34	686.066570362411	-0.72657036241128
92	685.34	686.05360610222	-0.713606102219501
93	685.34	686.040873164474	-0.700873164473705
94	694.3	686.028367421679	8.27163257832137
95	694.3	694.709171919706	-0.409171919706068
96	694.3	695.108329092279	-0.808329092279337

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 599 & 599 & 0 \tabularnewline
4 & 599 & 599 & 0 \tabularnewline
5 & 599 & 599 & 0 \tabularnewline
6 & 599 & 599 & 0 \tabularnewline
7 & 599 & 599 & 0 \tabularnewline
8 & 599 & 599 & 0 \tabularnewline
9 & 599 & 599 & 0 \tabularnewline
10 & 617.06 & 599 & 18.0599999999999 \tabularnewline
11 & 617.06 & 616.522003685396 & 0.537996314604356 \tabularnewline
12 & 617.06 & 617.350870236925 & -0.290870236924775 \tabularnewline
13 & 617.06 & 617.384703930528 & -0.324703930528472 \tabularnewline
14 & 617.06 & 617.380769005424 & -0.320769005424495 \tabularnewline
15 & 617.06 & 617.375134034332 & -0.315134034332459 \tabularnewline
16 & 617.06 & 617.369515286802 & -0.30951528680157 \tabularnewline
17 & 617.06 & 617.363992778634 & -0.30399277863421 \tabularnewline
18 & 617.06 & 617.358568617762 & -0.298568617762385 \tabularnewline
19 & 617.06 & 617.353241231567 & -0.293241231567208 \tabularnewline
20 & 617.06 & 617.348008901968 & -0.288008901968169 \tabularnewline
21 & 617.06 & 617.342869933275 & -0.282869933275151 \tabularnewline
22 & 628.18 & 617.337822659661 & 10.8421773403392 \tabularnewline
23 & 628.18 & 628.121607470562 & 0.0583925294378105 \tabularnewline
24 & 628.18 & 628.627092863689 & -0.447092863688908 \tabularnewline
25 & 628.18 & 628.643143237997 & -0.463143237997087 \tabularnewline
26 & 628.18 & 628.63602383963 & -0.456023839630348 \tabularnewline
27 & 628.18 & 628.62794148107 & -0.447941481070075 \tabularnewline
28 & 628.18 & 628.619951417729 & -0.439951417729162 \tabularnewline
29 & 628.18 & 628.612101448774 & -0.432101448773892 \tabularnewline
30 & 628.18 & 628.604391429723 & -0.424391429722732 \tabularnewline
31 & 628.18 & 628.596818975623 & -0.416818975622732 \tabularnewline
32 & 628.18 & 628.589381637234 & -0.409381637233764 \tabularnewline
33 & 628.18 & 628.582077003929 & -0.402077003928753 \tabularnewline
34 & 641.08 & 628.574902707851 & 12.5050972921492 \tabularnewline
35 & 641.08 & 641.083573341522 & -0.00357334152170097 \tabularnewline
36 & 641.08 & 641.668700321346 & -0.588700321345755 \tabularnewline
37 & 641.08 & 641.686070172485 & -0.606070172485374 \tabularnewline
38 & 641.08 & 641.676583719615 & -0.596583719615069 \tabularnewline
39 & 641.08 & 641.666002064939 & -0.586002064939407 \tabularnewline
40 & 641.08 & 641.655548989868 & -0.575548989868139 \tabularnewline
41 & 641.08 & 641.645279561059 & -0.565279561058787 \tabularnewline
42 & 641.08 & 641.635193233937 & -0.555193233936961 \tabularnewline
43 & 641.08 & 641.625286871547 & -0.545286871546523 \tabularnewline
44 & 641.08 & 641.615557268959 & -0.535557268959451 \tabularnewline
45 & 641.08 & 641.60600127253 & -0.526001272530152 \tabularnewline
46 & 668.21 & 641.596615784602 & 26.6133842153979 \tabularnewline
47 & 668.21 & 667.909211715424 & 0.300788284576015 \tabularnewline
48 & 668.21 & 669.1452938052 & -0.93529380519999 \tabularnewline
49 & 668.21 & 669.187227281166 & -0.977227281166051 \tabularnewline
50 & 668.21 & 669.172582838411 & -0.96258283841064 \tabularnewline
51 & 668.21 & 669.155540391112 & -0.945540391111649 \tabularnewline
52 & 668.21 & 669.13867536437 & -0.928675364369838 \tabularnewline
53 & 668.21 & 669.122105228239 & -0.912105228238943 \tabularnewline
54 & 668.21 & 669.10583046714 & -0.895830467140399 \tabularnewline
55 & 668.21 & 669.089846084376 & -0.879846084376027 \tabularnewline
56 & 668.21 & 669.074146911736 & -0.86414691173627 \tabularnewline
57 & 668.21 & 669.058727860812 & -0.848727860812119 \tabularnewline
58 & 665.27 & 669.043583933397 & -3.77358393339659 \tabularnewline
59 & 665.27 & 666.176291015838 & -0.906291015837951 \tabularnewline
60 & 665.27 & 666.026750931672 & -0.756750931671945 \tabularnewline
61 & 665.27 & 666.006895458686 & -0.736895458686149 \tabularnewline
62 & 665.27 & 665.993444372118 & -0.723444372118365 \tabularnewline
63 & 665.27 & 665.980521475902 & -0.710521475902055 \tabularnewline
64 & 665.27 & 665.967842890877 & -0.697842890876927 \tabularnewline
65 & 665.27 & 665.955391184824 & -0.685391184823857 \tabularnewline
66 & 665.27 & 665.943161686824 & -0.673161686823846 \tabularnewline
67 & 665.27 & 665.931150402338 & -0.66115040233808 \tabularnewline
68 & 665.27 & 665.91935343635 & -0.649353436350339 \tabularnewline
69 & 665.27 & 665.907766964689 & -0.637766964689035 \tabularnewline
70 & 674.3 & 665.896387231482 & 8.40361276851786 \tabularnewline
71 & 674.3 & 674.646212390574 & -0.346212390574351 \tabularnewline
72 & 674.3 & 675.049668409302 & -0.749668409302103 \tabularnewline
73 & 674.3 & 675.05580386725 & -0.755803867249938 \tabularnewline
74 & 674.3 & 675.043247389133 & -0.743247389133217 \tabularnewline
75 & 674.3 & 675.030029828778 & -0.730029828777901 \tabularnewline
76 & 674.3 & 675.017005949671 & -0.717005949671488 \tabularnewline
77 & 674.3 & 675.004212448583 & -0.70421244858278 \tabularnewline
78 & 674.3 & 674.991647127426 & -0.691647127425767 \tabularnewline
79 & 674.3 & 674.979306005866 & -0.679306005865783 \tabularnewline
80 & 674.3 & 674.967185087829 & -0.667185087828784 \tabularnewline
81 & 674.3 & 674.95528044441 & -0.655280444410096 \tabularnewline
82 & 685.34 & 674.943588216612 & 10.396411783388 \tabularnewline
83 & 685.34 & 685.643229790739 & -0.303229790739124 \tabularnewline
84 & 685.34 & 686.138633634486 & -0.798633634486123 \tabularnewline
85 & 685.34 & 686.148238572726 & -0.808238572725713 \tabularnewline
86 & 685.34 & 686.13495337345 & -0.79495337344963 \tabularnewline
87 & 685.34 & 686.12082307259 & -0.780823072590124 \tabularnewline
88 & 685.34 & 686.106893354446 & -0.766893354445529 \tabularnewline
89 & 685.34 & 686.093209730272 & -0.753209730272147 \tabularnewline
90 & 685.34 & 686.079770147284 & -0.739770147284048 \tabularnewline
91 & 685.34 & 686.066570362411 & -0.72657036241128 \tabularnewline
92 & 685.34 & 686.05360610222 & -0.713606102219501 \tabularnewline
93 & 685.34 & 686.040873164474 & -0.700873164473705 \tabularnewline
94 & 694.3 & 686.028367421679 & 8.27163257832137 \tabularnewline
95 & 694.3 & 694.709171919706 & -0.409171919706068 \tabularnewline
96 & 694.3 & 695.108329092279 & -0.808329092279337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279316&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]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]599[/C][C]599[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]617.06[/C][C]599[/C][C]18.0599999999999[/C][/ROW]
[ROW][C]11[/C][C]617.06[/C][C]616.522003685396[/C][C]0.537996314604356[/C][/ROW]
[ROW][C]12[/C][C]617.06[/C][C]617.350870236925[/C][C]-0.290870236924775[/C][/ROW]
[ROW][C]13[/C][C]617.06[/C][C]617.384703930528[/C][C]-0.324703930528472[/C][/ROW]
[ROW][C]14[/C][C]617.06[/C][C]617.380769005424[/C][C]-0.320769005424495[/C][/ROW]
[ROW][C]15[/C][C]617.06[/C][C]617.375134034332[/C][C]-0.315134034332459[/C][/ROW]
[ROW][C]16[/C][C]617.06[/C][C]617.369515286802[/C][C]-0.30951528680157[/C][/ROW]
[ROW][C]17[/C][C]617.06[/C][C]617.363992778634[/C][C]-0.30399277863421[/C][/ROW]
[ROW][C]18[/C][C]617.06[/C][C]617.358568617762[/C][C]-0.298568617762385[/C][/ROW]
[ROW][C]19[/C][C]617.06[/C][C]617.353241231567[/C][C]-0.293241231567208[/C][/ROW]
[ROW][C]20[/C][C]617.06[/C][C]617.348008901968[/C][C]-0.288008901968169[/C][/ROW]
[ROW][C]21[/C][C]617.06[/C][C]617.342869933275[/C][C]-0.282869933275151[/C][/ROW]
[ROW][C]22[/C][C]628.18[/C][C]617.337822659661[/C][C]10.8421773403392[/C][/ROW]
[ROW][C]23[/C][C]628.18[/C][C]628.121607470562[/C][C]0.0583925294378105[/C][/ROW]
[ROW][C]24[/C][C]628.18[/C][C]628.627092863689[/C][C]-0.447092863688908[/C][/ROW]
[ROW][C]25[/C][C]628.18[/C][C]628.643143237997[/C][C]-0.463143237997087[/C][/ROW]
[ROW][C]26[/C][C]628.18[/C][C]628.63602383963[/C][C]-0.456023839630348[/C][/ROW]
[ROW][C]27[/C][C]628.18[/C][C]628.62794148107[/C][C]-0.447941481070075[/C][/ROW]
[ROW][C]28[/C][C]628.18[/C][C]628.619951417729[/C][C]-0.439951417729162[/C][/ROW]
[ROW][C]29[/C][C]628.18[/C][C]628.612101448774[/C][C]-0.432101448773892[/C][/ROW]
[ROW][C]30[/C][C]628.18[/C][C]628.604391429723[/C][C]-0.424391429722732[/C][/ROW]
[ROW][C]31[/C][C]628.18[/C][C]628.596818975623[/C][C]-0.416818975622732[/C][/ROW]
[ROW][C]32[/C][C]628.18[/C][C]628.589381637234[/C][C]-0.409381637233764[/C][/ROW]
[ROW][C]33[/C][C]628.18[/C][C]628.582077003929[/C][C]-0.402077003928753[/C][/ROW]
[ROW][C]34[/C][C]641.08[/C][C]628.574902707851[/C][C]12.5050972921492[/C][/ROW]
[ROW][C]35[/C][C]641.08[/C][C]641.083573341522[/C][C]-0.00357334152170097[/C][/ROW]
[ROW][C]36[/C][C]641.08[/C][C]641.668700321346[/C][C]-0.588700321345755[/C][/ROW]
[ROW][C]37[/C][C]641.08[/C][C]641.686070172485[/C][C]-0.606070172485374[/C][/ROW]
[ROW][C]38[/C][C]641.08[/C][C]641.676583719615[/C][C]-0.596583719615069[/C][/ROW]
[ROW][C]39[/C][C]641.08[/C][C]641.666002064939[/C][C]-0.586002064939407[/C][/ROW]
[ROW][C]40[/C][C]641.08[/C][C]641.655548989868[/C][C]-0.575548989868139[/C][/ROW]
[ROW][C]41[/C][C]641.08[/C][C]641.645279561059[/C][C]-0.565279561058787[/C][/ROW]
[ROW][C]42[/C][C]641.08[/C][C]641.635193233937[/C][C]-0.555193233936961[/C][/ROW]
[ROW][C]43[/C][C]641.08[/C][C]641.625286871547[/C][C]-0.545286871546523[/C][/ROW]
[ROW][C]44[/C][C]641.08[/C][C]641.615557268959[/C][C]-0.535557268959451[/C][/ROW]
[ROW][C]45[/C][C]641.08[/C][C]641.60600127253[/C][C]-0.526001272530152[/C][/ROW]
[ROW][C]46[/C][C]668.21[/C][C]641.596615784602[/C][C]26.6133842153979[/C][/ROW]
[ROW][C]47[/C][C]668.21[/C][C]667.909211715424[/C][C]0.300788284576015[/C][/ROW]
[ROW][C]48[/C][C]668.21[/C][C]669.1452938052[/C][C]-0.93529380519999[/C][/ROW]
[ROW][C]49[/C][C]668.21[/C][C]669.187227281166[/C][C]-0.977227281166051[/C][/ROW]
[ROW][C]50[/C][C]668.21[/C][C]669.172582838411[/C][C]-0.96258283841064[/C][/ROW]
[ROW][C]51[/C][C]668.21[/C][C]669.155540391112[/C][C]-0.945540391111649[/C][/ROW]
[ROW][C]52[/C][C]668.21[/C][C]669.13867536437[/C][C]-0.928675364369838[/C][/ROW]
[ROW][C]53[/C][C]668.21[/C][C]669.122105228239[/C][C]-0.912105228238943[/C][/ROW]
[ROW][C]54[/C][C]668.21[/C][C]669.10583046714[/C][C]-0.895830467140399[/C][/ROW]
[ROW][C]55[/C][C]668.21[/C][C]669.089846084376[/C][C]-0.879846084376027[/C][/ROW]
[ROW][C]56[/C][C]668.21[/C][C]669.074146911736[/C][C]-0.86414691173627[/C][/ROW]
[ROW][C]57[/C][C]668.21[/C][C]669.058727860812[/C][C]-0.848727860812119[/C][/ROW]
[ROW][C]58[/C][C]665.27[/C][C]669.043583933397[/C][C]-3.77358393339659[/C][/ROW]
[ROW][C]59[/C][C]665.27[/C][C]666.176291015838[/C][C]-0.906291015837951[/C][/ROW]
[ROW][C]60[/C][C]665.27[/C][C]666.026750931672[/C][C]-0.756750931671945[/C][/ROW]
[ROW][C]61[/C][C]665.27[/C][C]666.006895458686[/C][C]-0.736895458686149[/C][/ROW]
[ROW][C]62[/C][C]665.27[/C][C]665.993444372118[/C][C]-0.723444372118365[/C][/ROW]
[ROW][C]63[/C][C]665.27[/C][C]665.980521475902[/C][C]-0.710521475902055[/C][/ROW]
[ROW][C]64[/C][C]665.27[/C][C]665.967842890877[/C][C]-0.697842890876927[/C][/ROW]
[ROW][C]65[/C][C]665.27[/C][C]665.955391184824[/C][C]-0.685391184823857[/C][/ROW]
[ROW][C]66[/C][C]665.27[/C][C]665.943161686824[/C][C]-0.673161686823846[/C][/ROW]
[ROW][C]67[/C][C]665.27[/C][C]665.931150402338[/C][C]-0.66115040233808[/C][/ROW]
[ROW][C]68[/C][C]665.27[/C][C]665.91935343635[/C][C]-0.649353436350339[/C][/ROW]
[ROW][C]69[/C][C]665.27[/C][C]665.907766964689[/C][C]-0.637766964689035[/C][/ROW]
[ROW][C]70[/C][C]674.3[/C][C]665.896387231482[/C][C]8.40361276851786[/C][/ROW]
[ROW][C]71[/C][C]674.3[/C][C]674.646212390574[/C][C]-0.346212390574351[/C][/ROW]
[ROW][C]72[/C][C]674.3[/C][C]675.049668409302[/C][C]-0.749668409302103[/C][/ROW]
[ROW][C]73[/C][C]674.3[/C][C]675.05580386725[/C][C]-0.755803867249938[/C][/ROW]
[ROW][C]74[/C][C]674.3[/C][C]675.043247389133[/C][C]-0.743247389133217[/C][/ROW]
[ROW][C]75[/C][C]674.3[/C][C]675.030029828778[/C][C]-0.730029828777901[/C][/ROW]
[ROW][C]76[/C][C]674.3[/C][C]675.017005949671[/C][C]-0.717005949671488[/C][/ROW]
[ROW][C]77[/C][C]674.3[/C][C]675.004212448583[/C][C]-0.70421244858278[/C][/ROW]
[ROW][C]78[/C][C]674.3[/C][C]674.991647127426[/C][C]-0.691647127425767[/C][/ROW]
[ROW][C]79[/C][C]674.3[/C][C]674.979306005866[/C][C]-0.679306005865783[/C][/ROW]
[ROW][C]80[/C][C]674.3[/C][C]674.967185087829[/C][C]-0.667185087828784[/C][/ROW]
[ROW][C]81[/C][C]674.3[/C][C]674.95528044441[/C][C]-0.655280444410096[/C][/ROW]
[ROW][C]82[/C][C]685.34[/C][C]674.943588216612[/C][C]10.396411783388[/C][/ROW]
[ROW][C]83[/C][C]685.34[/C][C]685.643229790739[/C][C]-0.303229790739124[/C][/ROW]
[ROW][C]84[/C][C]685.34[/C][C]686.138633634486[/C][C]-0.798633634486123[/C][/ROW]
[ROW][C]85[/C][C]685.34[/C][C]686.148238572726[/C][C]-0.808238572725713[/C][/ROW]
[ROW][C]86[/C][C]685.34[/C][C]686.13495337345[/C][C]-0.79495337344963[/C][/ROW]
[ROW][C]87[/C][C]685.34[/C][C]686.12082307259[/C][C]-0.780823072590124[/C][/ROW]
[ROW][C]88[/C][C]685.34[/C][C]686.106893354446[/C][C]-0.766893354445529[/C][/ROW]
[ROW][C]89[/C][C]685.34[/C][C]686.093209730272[/C][C]-0.753209730272147[/C][/ROW]
[ROW][C]90[/C][C]685.34[/C][C]686.079770147284[/C][C]-0.739770147284048[/C][/ROW]
[ROW][C]91[/C][C]685.34[/C][C]686.066570362411[/C][C]-0.72657036241128[/C][/ROW]
[ROW][C]92[/C][C]685.34[/C][C]686.05360610222[/C][C]-0.713606102219501[/C][/ROW]
[ROW][C]93[/C][C]685.34[/C][C]686.040873164474[/C][C]-0.700873164473705[/C][/ROW]
[ROW][C]94[/C][C]694.3[/C][C]686.028367421679[/C][C]8.27163257832137[/C][/ROW]
[ROW][C]95[/C][C]694.3[/C][C]694.709171919706[/C][C]-0.409171919706068[/C][/ROW]
[ROW][C]96[/C][C]694.3[/C][C]695.108329092279[/C][C]-0.808329092279337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279316&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	599	599	0
4	599	599	0
5	599	599	0
6	599	599	0
7	599	599	0
8	599	599	0
9	599	599	0
10	617.06	599	18.0599999999999
11	617.06	616.522003685396	0.537996314604356
12	617.06	617.350870236925	-0.290870236924775
13	617.06	617.384703930528	-0.324703930528472
14	617.06	617.380769005424	-0.320769005424495
15	617.06	617.375134034332	-0.315134034332459
16	617.06	617.369515286802	-0.30951528680157
17	617.06	617.363992778634	-0.30399277863421
18	617.06	617.358568617762	-0.298568617762385
19	617.06	617.353241231567	-0.293241231567208
20	617.06	617.348008901968	-0.288008901968169
21	617.06	617.342869933275	-0.282869933275151
22	628.18	617.337822659661	10.8421773403392
23	628.18	628.121607470562	0.0583925294378105
24	628.18	628.627092863689	-0.447092863688908
25	628.18	628.643143237997	-0.463143237997087
26	628.18	628.63602383963	-0.456023839630348
27	628.18	628.62794148107	-0.447941481070075
28	628.18	628.619951417729	-0.439951417729162
29	628.18	628.612101448774	-0.432101448773892
30	628.18	628.604391429723	-0.424391429722732
31	628.18	628.596818975623	-0.416818975622732
32	628.18	628.589381637234	-0.409381637233764
33	628.18	628.582077003929	-0.402077003928753
34	641.08	628.574902707851	12.5050972921492
35	641.08	641.083573341522	-0.00357334152170097
36	641.08	641.668700321346	-0.588700321345755
37	641.08	641.686070172485	-0.606070172485374
38	641.08	641.676583719615	-0.596583719615069
39	641.08	641.666002064939	-0.586002064939407
40	641.08	641.655548989868	-0.575548989868139
41	641.08	641.645279561059	-0.565279561058787
42	641.08	641.635193233937	-0.555193233936961
43	641.08	641.625286871547	-0.545286871546523
44	641.08	641.615557268959	-0.535557268959451
45	641.08	641.60600127253	-0.526001272530152
46	668.21	641.596615784602	26.6133842153979
47	668.21	667.909211715424	0.300788284576015
48	668.21	669.1452938052	-0.93529380519999
49	668.21	669.187227281166	-0.977227281166051
50	668.21	669.172582838411	-0.96258283841064
51	668.21	669.155540391112	-0.945540391111649
52	668.21	669.13867536437	-0.928675364369838
53	668.21	669.122105228239	-0.912105228238943
54	668.21	669.10583046714	-0.895830467140399
55	668.21	669.089846084376	-0.879846084376027
56	668.21	669.074146911736	-0.86414691173627
57	668.21	669.058727860812	-0.848727860812119
58	665.27	669.043583933397	-3.77358393339659
59	665.27	666.176291015838	-0.906291015837951
60	665.27	666.026750931672	-0.756750931671945
61	665.27	666.006895458686	-0.736895458686149
62	665.27	665.993444372118	-0.723444372118365
63	665.27	665.980521475902	-0.710521475902055
64	665.27	665.967842890877	-0.697842890876927
65	665.27	665.955391184824	-0.685391184823857
66	665.27	665.943161686824	-0.673161686823846
67	665.27	665.931150402338	-0.66115040233808
68	665.27	665.91935343635	-0.649353436350339
69	665.27	665.907766964689	-0.637766964689035
70	674.3	665.896387231482	8.40361276851786
71	674.3	674.646212390574	-0.346212390574351
72	674.3	675.049668409302	-0.749668409302103
73	674.3	675.05580386725	-0.755803867249938
74	674.3	675.043247389133	-0.743247389133217
75	674.3	675.030029828778	-0.730029828777901
76	674.3	675.017005949671	-0.717005949671488
77	674.3	675.004212448583	-0.70421244858278
78	674.3	674.991647127426	-0.691647127425767
79	674.3	674.979306005866	-0.679306005865783
80	674.3	674.967185087829	-0.667185087828784
81	674.3	674.95528044441	-0.655280444410096
82	685.34	674.943588216612	10.396411783388
83	685.34	685.643229790739	-0.303229790739124
84	685.34	686.138633634486	-0.798633634486123
85	685.34	686.148238572726	-0.808238572725713
86	685.34	686.13495337345	-0.79495337344963
87	685.34	686.12082307259	-0.780823072590124
88	685.34	686.106893354446	-0.766893354445529
89	685.34	686.093209730272	-0.753209730272147
90	685.34	686.079770147284	-0.739770147284048
91	685.34	686.066570362411	-0.72657036241128
92	685.34	686.05360610222	-0.713606102219501
93	685.34	686.040873164474	-0.700873164473705
94	694.3	686.028367421679	8.27163257832137
95	694.3	694.709171919706	-0.409171919706068
96	694.3	695.108329092279	-0.808329092279337

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	695.113266607676	687.035019279749	703.191513935603
98	695.88871750671	684.633226668639	707.144208344781
99	696.664168405745	682.869795362618	710.458541448872
100	697.439619304779	681.43675300711	713.442485602448
101	698.215070203813	680.211049286835	716.219091120792
102	698.990521102848	679.128961877161	718.852080328535
103	699.765972001882	678.15255682197	721.379387181794
104	700.541422900916	677.257157813112	723.82568798872
105	701.31687379995	676.425689043018	726.208058556883
106	702.092324698985	675.6457816655	728.53886773247
107	702.867775598019	674.908155267219	730.827395928819
108	703.643226497053	674.205649161714	733.080803832393

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 695.113266607676 & 687.035019279749 & 703.191513935603 \tabularnewline
98 & 695.88871750671 & 684.633226668639 & 707.144208344781 \tabularnewline
99 & 696.664168405745 & 682.869795362618 & 710.458541448872 \tabularnewline
100 & 697.439619304779 & 681.43675300711 & 713.442485602448 \tabularnewline
101 & 698.215070203813 & 680.211049286835 & 716.219091120792 \tabularnewline
102 & 698.990521102848 & 679.128961877161 & 718.852080328535 \tabularnewline
103 & 699.765972001882 & 678.15255682197 & 721.379387181794 \tabularnewline
104 & 700.541422900916 & 677.257157813112 & 723.82568798872 \tabularnewline
105 & 701.31687379995 & 676.425689043018 & 726.208058556883 \tabularnewline
106 & 702.092324698985 & 675.6457816655 & 728.53886773247 \tabularnewline
107 & 702.867775598019 & 674.908155267219 & 730.827395928819 \tabularnewline
108 & 703.643226497053 & 674.205649161714 & 733.080803832393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279316&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]97[/C][C]695.113266607676[/C][C]687.035019279749[/C][C]703.191513935603[/C][/ROW]
[ROW][C]98[/C][C]695.88871750671[/C][C]684.633226668639[/C][C]707.144208344781[/C][/ROW]
[ROW][C]99[/C][C]696.664168405745[/C][C]682.869795362618[/C][C]710.458541448872[/C][/ROW]
[ROW][C]100[/C][C]697.439619304779[/C][C]681.43675300711[/C][C]713.442485602448[/C][/ROW]
[ROW][C]101[/C][C]698.215070203813[/C][C]680.211049286835[/C][C]716.219091120792[/C][/ROW]
[ROW][C]102[/C][C]698.990521102848[/C][C]679.128961877161[/C][C]718.852080328535[/C][/ROW]
[ROW][C]103[/C][C]699.765972001882[/C][C]678.15255682197[/C][C]721.379387181794[/C][/ROW]
[ROW][C]104[/C][C]700.541422900916[/C][C]677.257157813112[/C][C]723.82568798872[/C][/ROW]
[ROW][C]105[/C][C]701.31687379995[/C][C]676.425689043018[/C][C]726.208058556883[/C][/ROW]
[ROW][C]106[/C][C]702.092324698985[/C][C]675.6457816655[/C][C]728.53886773247[/C][/ROW]
[ROW][C]107[/C][C]702.867775598019[/C][C]674.908155267219[/C][C]730.827395928819[/C][/ROW]
[ROW][C]108[/C][C]703.643226497053[/C][C]674.205649161714[/C][C]733.080803832393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279316&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279316&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
97	695.113266607676	687.035019279749	703.191513935603
98	695.88871750671	684.633226668639	707.144208344781
99	696.664168405745	682.869795362618	710.458541448872
100	697.439619304779	681.43675300711	713.442485602448
101	698.215070203813	680.211049286835	716.219091120792
102	698.990521102848	679.128961877161	718.852080328535
103	699.765972001882	678.15255682197	721.379387181794
104	700.541422900916	677.257157813112	723.82568798872
105	701.31687379995	676.425689043018	726.208058556883
106	702.092324698985	675.6457816655	728.53886773247
107	702.867775598019	674.908155267219	730.827395928819
108	703.643226497053	674.205649161714	733.080803832393

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