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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 31 Mar 2015 17:31:14 +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/Mar/31/t14278195204ee1c930h964fef.htm/, Retrieved Fri, 17 May 2024 06:16:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278490, Retrieved Fri, 17 May 2024 06:16:30 +0000

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No (this computation is public)

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Estimated Impact

182

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

-       [Exponential Smoothing] [] [2015-03-31 16:31:14] [3b0947f879d0db9a6034293524e1b6d0] [Current]

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Dataseries X:

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6
6,7
-0,6
5,8
16,4
1,5
5,1
14,7
4,3
1,5
9,1
4,3
5,7
13
14,5
9,7
-4,7
7,3
5,2
-2,5
11,5
4,9
-2,4
-0,3
4,4
7,9
-9,7
-4,1
16,4
-4,9
3,5
3,8
-0,2
3,1
0,7
-2,8
5,9
-5,3
-2,9
6,6
-8,1
1,3
6,9
-7,2
-1,9
4
-5,7
3,9
-7,6
-0,9
7,3
-3,7
-2,5
9,3
1,3
9,5
11,3
-1,7
8
-4,8
1,6
1,9
-0,9
5,5
1,7
-5,4
1,9
0,2
-13,3
-8,2
0,2
5,7
-1,2
-2,8
5,5
-17,3
1,4
-2,2
-8,6
-5
4,1
0,7
-4,2
-2,3
-3,4
-4,2
-14,2
1,6
-4,9
-1,8
-0,5
-2,3
-5,3
-0,2
5,1
-1,5

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=278490&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=278490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278490&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	0.174547793268507
beta	0.0460753131100587
gamma	0.0548325626631011

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.174547793268507 \tabularnewline
beta & 0.0460753131100587 \tabularnewline
gamma & 0.0548325626631011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278490&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]0.174547793268507[/C][/ROW]
[ROW][C]beta[/C][C]0.0460753131100587[/C][/ROW]
[ROW][C]gamma[/C][C]0.0548325626631011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278490&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	0.174547793268507
beta	0.0460753131100587
gamma	0.0548325626631011

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.7	5.38995517771609	0.310044822283911
14	13	13.5905890799449	-0.590589079944934
15	14.5	15.831789897595	-1.33178989759502
16	9.7	9.53493925000786	0.165060749992138
17	-4.7	-4.80456564965315	0.104565649653154
18	7.3	8.20887007147707	-0.908870071477069
19	5.2	4.73789991337966	0.462100086620341
20	-2.5	13.0883597733986	-15.5883597733986
21	11.5	2.56531185650992	8.93468814349008
22	4.9	1.29031603510105	3.60968396489895
23	-2.4	12.9069028791896	-15.3069028791896
24	-0.3	5.29541644570581	-5.59541644570581
25	4.4	5.48885744301816	-1.08885744301816
26	7.9	13.2337451851955	-5.33374518519549
27	-9.7	14.4314990407101	-24.1314990407101
28	-4.1	6.12633961046321	-10.2263396104632
29	16.4	-2.04022283604379	18.4402228360438
30	-4.9	-2.61821445486674	-2.28178554513326
31	3.5	-2.18453655841707	5.68453655841707
32	3.8	-3.86076716573836	7.66076716573836
33	-0.2	-0.986582648283826	0.786582648283826
34	3.1	-0.331519873267917	3.43151987326792
35	0.7	1.30219766659315	-0.602197666593153
36	-2.8	0.504123368058854	-3.30412336805885
37	5.9	-0.296623288361682	6.19662328836168
38	-5.3	1.5901370463491	-6.8901370463491
39	-2.9	-0.0432137997009828	-2.85678620029902
40	6.6	-0.643539604430957	7.24353960443096
41	-8.1	-0.365765366248854	-7.73423463375115
42	1.3	1.62028807773682	-0.320288077736815
43	6.9	0.631832712086666	6.26816728791333
44	-7.2	4.77613361241113	-11.9761336124111
45	-1.9	0.835754362992934	-2.73575436299293
46	4	0.137835870221443	3.86216412977856
47	-5.7	2.81541025253599	-8.51541025253599
48	3.9	1.97272287496302	1.92727712503698
49	-7.6	1.27285020597758	-8.87285020597758
50	-0.9	-0.164256268092913	-0.735743731907087
51	7.3	-2.50598828910644	9.80598828910644
52	-3.7	-0.929922812944683	-2.77007718705532
53	-2.5	1.34866230893113	-3.84866230893113
54	9.3	-0.786471143552499	10.0864711435525
55	1.3	0.462547035001524	0.837452964998476
56	9.5	1.06920641294517	8.43079358705483
57	11.3	0.688882794729514	10.6111172052705
58	-1.7	2.49358712663606	-4.19358712663606
59	8	3.71099668063212	4.28900331936788
60	-4.8	10.9120721449173	-15.7120721449173
61	1.6	11.7666352899931	-10.1666352899931
62	1.9	1.64654648224521	0.253453517754787
63	-0.9	4.66994493532066	-5.56994493532066
64	5.5	7.05909053403752	-1.55909053403752
65	1.7	-3.56566165233685	5.26566165233685
66	-5.4	4.47124426517675	-9.87124426517675
67	1.9	1.0169490555051	0.883050944494897
68	0.2	2.35263492463449	-2.15263492463449
69	-13.3	0.528580174629818	-13.8285801746298
70	-8.2	-1.45396421117906	-6.74603578882094
71	0.2	-6.73610704225134	6.93610704225134
72	5.7	-12.2300281485966	17.9300281485966
73	-1.2	-14.2741959084173	13.0741959084173
74	-2.8	-2.18266518014752	-0.617334819852483
75	5.5	-6.1019940026112	11.6019940026112
76	-17.3	-8.69261838285188	-8.60738161714812
77	1.4	5.17076946271416	-3.77076946271416
78	-2.2	-7.46873425971128	5.26873425971127
79	-8.6	-3.30851575302753	-5.29148424697247
80	-5	-8.53295408965046	3.53295408965046
81	4.1	-3.29700108123967	7.39700108123967
82	0.7	-1.24790955795959	1.94790955795959
83	-4.2	-1.91218672352559	-2.28781327647441
84	-2.3	-4.82205987687573	2.52205987687573
85	-3.4	-6.98398534173906	3.58398534173906
86	-4.2	-1.19834874354066	-3.00165125645934
87	-14.2	-3.87117414812606	-10.3288258518739
88	1.6	-14.1772687081831	15.7772687081831
89	-4.9	5.27851055918268	-10.1785105591827
90	-1.8	-5.67203836648913	3.87203836648913
91	-0.5	-2.70080200710793	2.20080200710793
92	-2.3	-4.21443523625637	1.91443523625637
93	-5.3	-1.33601155387895	-3.96398844612105
94	-0.2	-1.35040655426849	1.15040655426849
95	5.1	-2.76868020586673	7.86868020586673
96	-1.5	-2.60816503308965	1.10816503308965

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.7 & 5.38995517771609 & 0.310044822283911 \tabularnewline
14 & 13 & 13.5905890799449 & -0.590589079944934 \tabularnewline
15 & 14.5 & 15.831789897595 & -1.33178989759502 \tabularnewline
16 & 9.7 & 9.53493925000786 & 0.165060749992138 \tabularnewline
17 & -4.7 & -4.80456564965315 & 0.104565649653154 \tabularnewline
18 & 7.3 & 8.20887007147707 & -0.908870071477069 \tabularnewline
19 & 5.2 & 4.73789991337966 & 0.462100086620341 \tabularnewline
20 & -2.5 & 13.0883597733986 & -15.5883597733986 \tabularnewline
21 & 11.5 & 2.56531185650992 & 8.93468814349008 \tabularnewline
22 & 4.9 & 1.29031603510105 & 3.60968396489895 \tabularnewline
23 & -2.4 & 12.9069028791896 & -15.3069028791896 \tabularnewline
24 & -0.3 & 5.29541644570581 & -5.59541644570581 \tabularnewline
25 & 4.4 & 5.48885744301816 & -1.08885744301816 \tabularnewline
26 & 7.9 & 13.2337451851955 & -5.33374518519549 \tabularnewline
27 & -9.7 & 14.4314990407101 & -24.1314990407101 \tabularnewline
28 & -4.1 & 6.12633961046321 & -10.2263396104632 \tabularnewline
29 & 16.4 & -2.04022283604379 & 18.4402228360438 \tabularnewline
30 & -4.9 & -2.61821445486674 & -2.28178554513326 \tabularnewline
31 & 3.5 & -2.18453655841707 & 5.68453655841707 \tabularnewline
32 & 3.8 & -3.86076716573836 & 7.66076716573836 \tabularnewline
33 & -0.2 & -0.986582648283826 & 0.786582648283826 \tabularnewline
34 & 3.1 & -0.331519873267917 & 3.43151987326792 \tabularnewline
35 & 0.7 & 1.30219766659315 & -0.602197666593153 \tabularnewline
36 & -2.8 & 0.504123368058854 & -3.30412336805885 \tabularnewline
37 & 5.9 & -0.296623288361682 & 6.19662328836168 \tabularnewline
38 & -5.3 & 1.5901370463491 & -6.8901370463491 \tabularnewline
39 & -2.9 & -0.0432137997009828 & -2.85678620029902 \tabularnewline
40 & 6.6 & -0.643539604430957 & 7.24353960443096 \tabularnewline
41 & -8.1 & -0.365765366248854 & -7.73423463375115 \tabularnewline
42 & 1.3 & 1.62028807773682 & -0.320288077736815 \tabularnewline
43 & 6.9 & 0.631832712086666 & 6.26816728791333 \tabularnewline
44 & -7.2 & 4.77613361241113 & -11.9761336124111 \tabularnewline
45 & -1.9 & 0.835754362992934 & -2.73575436299293 \tabularnewline
46 & 4 & 0.137835870221443 & 3.86216412977856 \tabularnewline
47 & -5.7 & 2.81541025253599 & -8.51541025253599 \tabularnewline
48 & 3.9 & 1.97272287496302 & 1.92727712503698 \tabularnewline
49 & -7.6 & 1.27285020597758 & -8.87285020597758 \tabularnewline
50 & -0.9 & -0.164256268092913 & -0.735743731907087 \tabularnewline
51 & 7.3 & -2.50598828910644 & 9.80598828910644 \tabularnewline
52 & -3.7 & -0.929922812944683 & -2.77007718705532 \tabularnewline
53 & -2.5 & 1.34866230893113 & -3.84866230893113 \tabularnewline
54 & 9.3 & -0.786471143552499 & 10.0864711435525 \tabularnewline
55 & 1.3 & 0.462547035001524 & 0.837452964998476 \tabularnewline
56 & 9.5 & 1.06920641294517 & 8.43079358705483 \tabularnewline
57 & 11.3 & 0.688882794729514 & 10.6111172052705 \tabularnewline
58 & -1.7 & 2.49358712663606 & -4.19358712663606 \tabularnewline
59 & 8 & 3.71099668063212 & 4.28900331936788 \tabularnewline
60 & -4.8 & 10.9120721449173 & -15.7120721449173 \tabularnewline
61 & 1.6 & 11.7666352899931 & -10.1666352899931 \tabularnewline
62 & 1.9 & 1.64654648224521 & 0.253453517754787 \tabularnewline
63 & -0.9 & 4.66994493532066 & -5.56994493532066 \tabularnewline
64 & 5.5 & 7.05909053403752 & -1.55909053403752 \tabularnewline
65 & 1.7 & -3.56566165233685 & 5.26566165233685 \tabularnewline
66 & -5.4 & 4.47124426517675 & -9.87124426517675 \tabularnewline
67 & 1.9 & 1.0169490555051 & 0.883050944494897 \tabularnewline
68 & 0.2 & 2.35263492463449 & -2.15263492463449 \tabularnewline
69 & -13.3 & 0.528580174629818 & -13.8285801746298 \tabularnewline
70 & -8.2 & -1.45396421117906 & -6.74603578882094 \tabularnewline
71 & 0.2 & -6.73610704225134 & 6.93610704225134 \tabularnewline
72 & 5.7 & -12.2300281485966 & 17.9300281485966 \tabularnewline
73 & -1.2 & -14.2741959084173 & 13.0741959084173 \tabularnewline
74 & -2.8 & -2.18266518014752 & -0.617334819852483 \tabularnewline
75 & 5.5 & -6.1019940026112 & 11.6019940026112 \tabularnewline
76 & -17.3 & -8.69261838285188 & -8.60738161714812 \tabularnewline
77 & 1.4 & 5.17076946271416 & -3.77076946271416 \tabularnewline
78 & -2.2 & -7.46873425971128 & 5.26873425971127 \tabularnewline
79 & -8.6 & -3.30851575302753 & -5.29148424697247 \tabularnewline
80 & -5 & -8.53295408965046 & 3.53295408965046 \tabularnewline
81 & 4.1 & -3.29700108123967 & 7.39700108123967 \tabularnewline
82 & 0.7 & -1.24790955795959 & 1.94790955795959 \tabularnewline
83 & -4.2 & -1.91218672352559 & -2.28781327647441 \tabularnewline
84 & -2.3 & -4.82205987687573 & 2.52205987687573 \tabularnewline
85 & -3.4 & -6.98398534173906 & 3.58398534173906 \tabularnewline
86 & -4.2 & -1.19834874354066 & -3.00165125645934 \tabularnewline
87 & -14.2 & -3.87117414812606 & -10.3288258518739 \tabularnewline
88 & 1.6 & -14.1772687081831 & 15.7772687081831 \tabularnewline
89 & -4.9 & 5.27851055918268 & -10.1785105591827 \tabularnewline
90 & -1.8 & -5.67203836648913 & 3.87203836648913 \tabularnewline
91 & -0.5 & -2.70080200710793 & 2.20080200710793 \tabularnewline
92 & -2.3 & -4.21443523625637 & 1.91443523625637 \tabularnewline
93 & -5.3 & -1.33601155387895 & -3.96398844612105 \tabularnewline
94 & -0.2 & -1.35040655426849 & 1.15040655426849 \tabularnewline
95 & 5.1 & -2.76868020586673 & 7.86868020586673 \tabularnewline
96 & -1.5 & -2.60816503308965 & 1.10816503308965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278490&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]5.7[/C][C]5.38995517771609[/C][C]0.310044822283911[/C][/ROW]
[ROW][C]14[/C][C]13[/C][C]13.5905890799449[/C][C]-0.590589079944934[/C][/ROW]
[ROW][C]15[/C][C]14.5[/C][C]15.831789897595[/C][C]-1.33178989759502[/C][/ROW]
[ROW][C]16[/C][C]9.7[/C][C]9.53493925000786[/C][C]0.165060749992138[/C][/ROW]
[ROW][C]17[/C][C]-4.7[/C][C]-4.80456564965315[/C][C]0.104565649653154[/C][/ROW]
[ROW][C]18[/C][C]7.3[/C][C]8.20887007147707[/C][C]-0.908870071477069[/C][/ROW]
[ROW][C]19[/C][C]5.2[/C][C]4.73789991337966[/C][C]0.462100086620341[/C][/ROW]
[ROW][C]20[/C][C]-2.5[/C][C]13.0883597733986[/C][C]-15.5883597733986[/C][/ROW]
[ROW][C]21[/C][C]11.5[/C][C]2.56531185650992[/C][C]8.93468814349008[/C][/ROW]
[ROW][C]22[/C][C]4.9[/C][C]1.29031603510105[/C][C]3.60968396489895[/C][/ROW]
[ROW][C]23[/C][C]-2.4[/C][C]12.9069028791896[/C][C]-15.3069028791896[/C][/ROW]
[ROW][C]24[/C][C]-0.3[/C][C]5.29541644570581[/C][C]-5.59541644570581[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]5.48885744301816[/C][C]-1.08885744301816[/C][/ROW]
[ROW][C]26[/C][C]7.9[/C][C]13.2337451851955[/C][C]-5.33374518519549[/C][/ROW]
[ROW][C]27[/C][C]-9.7[/C][C]14.4314990407101[/C][C]-24.1314990407101[/C][/ROW]
[ROW][C]28[/C][C]-4.1[/C][C]6.12633961046321[/C][C]-10.2263396104632[/C][/ROW]
[ROW][C]29[/C][C]16.4[/C][C]-2.04022283604379[/C][C]18.4402228360438[/C][/ROW]
[ROW][C]30[/C][C]-4.9[/C][C]-2.61821445486674[/C][C]-2.28178554513326[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]-2.18453655841707[/C][C]5.68453655841707[/C][/ROW]
[ROW][C]32[/C][C]3.8[/C][C]-3.86076716573836[/C][C]7.66076716573836[/C][/ROW]
[ROW][C]33[/C][C]-0.2[/C][C]-0.986582648283826[/C][C]0.786582648283826[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]-0.331519873267917[/C][C]3.43151987326792[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]1.30219766659315[/C][C]-0.602197666593153[/C][/ROW]
[ROW][C]36[/C][C]-2.8[/C][C]0.504123368058854[/C][C]-3.30412336805885[/C][/ROW]
[ROW][C]37[/C][C]5.9[/C][C]-0.296623288361682[/C][C]6.19662328836168[/C][/ROW]
[ROW][C]38[/C][C]-5.3[/C][C]1.5901370463491[/C][C]-6.8901370463491[/C][/ROW]
[ROW][C]39[/C][C]-2.9[/C][C]-0.0432137997009828[/C][C]-2.85678620029902[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]-0.643539604430957[/C][C]7.24353960443096[/C][/ROW]
[ROW][C]41[/C][C]-8.1[/C][C]-0.365765366248854[/C][C]-7.73423463375115[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]1.62028807773682[/C][C]-0.320288077736815[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]0.631832712086666[/C][C]6.26816728791333[/C][/ROW]
[ROW][C]44[/C][C]-7.2[/C][C]4.77613361241113[/C][C]-11.9761336124111[/C][/ROW]
[ROW][C]45[/C][C]-1.9[/C][C]0.835754362992934[/C][C]-2.73575436299293[/C][/ROW]
[ROW][C]46[/C][C]4[/C][C]0.137835870221443[/C][C]3.86216412977856[/C][/ROW]
[ROW][C]47[/C][C]-5.7[/C][C]2.81541025253599[/C][C]-8.51541025253599[/C][/ROW]
[ROW][C]48[/C][C]3.9[/C][C]1.97272287496302[/C][C]1.92727712503698[/C][/ROW]
[ROW][C]49[/C][C]-7.6[/C][C]1.27285020597758[/C][C]-8.87285020597758[/C][/ROW]
[ROW][C]50[/C][C]-0.9[/C][C]-0.164256268092913[/C][C]-0.735743731907087[/C][/ROW]
[ROW][C]51[/C][C]7.3[/C][C]-2.50598828910644[/C][C]9.80598828910644[/C][/ROW]
[ROW][C]52[/C][C]-3.7[/C][C]-0.929922812944683[/C][C]-2.77007718705532[/C][/ROW]
[ROW][C]53[/C][C]-2.5[/C][C]1.34866230893113[/C][C]-3.84866230893113[/C][/ROW]
[ROW][C]54[/C][C]9.3[/C][C]-0.786471143552499[/C][C]10.0864711435525[/C][/ROW]
[ROW][C]55[/C][C]1.3[/C][C]0.462547035001524[/C][C]0.837452964998476[/C][/ROW]
[ROW][C]56[/C][C]9.5[/C][C]1.06920641294517[/C][C]8.43079358705483[/C][/ROW]
[ROW][C]57[/C][C]11.3[/C][C]0.688882794729514[/C][C]10.6111172052705[/C][/ROW]
[ROW][C]58[/C][C]-1.7[/C][C]2.49358712663606[/C][C]-4.19358712663606[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]3.71099668063212[/C][C]4.28900331936788[/C][/ROW]
[ROW][C]60[/C][C]-4.8[/C][C]10.9120721449173[/C][C]-15.7120721449173[/C][/ROW]
[ROW][C]61[/C][C]1.6[/C][C]11.7666352899931[/C][C]-10.1666352899931[/C][/ROW]
[ROW][C]62[/C][C]1.9[/C][C]1.64654648224521[/C][C]0.253453517754787[/C][/ROW]
[ROW][C]63[/C][C]-0.9[/C][C]4.66994493532066[/C][C]-5.56994493532066[/C][/ROW]
[ROW][C]64[/C][C]5.5[/C][C]7.05909053403752[/C][C]-1.55909053403752[/C][/ROW]
[ROW][C]65[/C][C]1.7[/C][C]-3.56566165233685[/C][C]5.26566165233685[/C][/ROW]
[ROW][C]66[/C][C]-5.4[/C][C]4.47124426517675[/C][C]-9.87124426517675[/C][/ROW]
[ROW][C]67[/C][C]1.9[/C][C]1.0169490555051[/C][C]0.883050944494897[/C][/ROW]
[ROW][C]68[/C][C]0.2[/C][C]2.35263492463449[/C][C]-2.15263492463449[/C][/ROW]
[ROW][C]69[/C][C]-13.3[/C][C]0.528580174629818[/C][C]-13.8285801746298[/C][/ROW]
[ROW][C]70[/C][C]-8.2[/C][C]-1.45396421117906[/C][C]-6.74603578882094[/C][/ROW]
[ROW][C]71[/C][C]0.2[/C][C]-6.73610704225134[/C][C]6.93610704225134[/C][/ROW]
[ROW][C]72[/C][C]5.7[/C][C]-12.2300281485966[/C][C]17.9300281485966[/C][/ROW]
[ROW][C]73[/C][C]-1.2[/C][C]-14.2741959084173[/C][C]13.0741959084173[/C][/ROW]
[ROW][C]74[/C][C]-2.8[/C][C]-2.18266518014752[/C][C]-0.617334819852483[/C][/ROW]
[ROW][C]75[/C][C]5.5[/C][C]-6.1019940026112[/C][C]11.6019940026112[/C][/ROW]
[ROW][C]76[/C][C]-17.3[/C][C]-8.69261838285188[/C][C]-8.60738161714812[/C][/ROW]
[ROW][C]77[/C][C]1.4[/C][C]5.17076946271416[/C][C]-3.77076946271416[/C][/ROW]
[ROW][C]78[/C][C]-2.2[/C][C]-7.46873425971128[/C][C]5.26873425971127[/C][/ROW]
[ROW][C]79[/C][C]-8.6[/C][C]-3.30851575302753[/C][C]-5.29148424697247[/C][/ROW]
[ROW][C]80[/C][C]-5[/C][C]-8.53295408965046[/C][C]3.53295408965046[/C][/ROW]
[ROW][C]81[/C][C]4.1[/C][C]-3.29700108123967[/C][C]7.39700108123967[/C][/ROW]
[ROW][C]82[/C][C]0.7[/C][C]-1.24790955795959[/C][C]1.94790955795959[/C][/ROW]
[ROW][C]83[/C][C]-4.2[/C][C]-1.91218672352559[/C][C]-2.28781327647441[/C][/ROW]
[ROW][C]84[/C][C]-2.3[/C][C]-4.82205987687573[/C][C]2.52205987687573[/C][/ROW]
[ROW][C]85[/C][C]-3.4[/C][C]-6.98398534173906[/C][C]3.58398534173906[/C][/ROW]
[ROW][C]86[/C][C]-4.2[/C][C]-1.19834874354066[/C][C]-3.00165125645934[/C][/ROW]
[ROW][C]87[/C][C]-14.2[/C][C]-3.87117414812606[/C][C]-10.3288258518739[/C][/ROW]
[ROW][C]88[/C][C]1.6[/C][C]-14.1772687081831[/C][C]15.7772687081831[/C][/ROW]
[ROW][C]89[/C][C]-4.9[/C][C]5.27851055918268[/C][C]-10.1785105591827[/C][/ROW]
[ROW][C]90[/C][C]-1.8[/C][C]-5.67203836648913[/C][C]3.87203836648913[/C][/ROW]
[ROW][C]91[/C][C]-0.5[/C][C]-2.70080200710793[/C][C]2.20080200710793[/C][/ROW]
[ROW][C]92[/C][C]-2.3[/C][C]-4.21443523625637[/C][C]1.91443523625637[/C][/ROW]
[ROW][C]93[/C][C]-5.3[/C][C]-1.33601155387895[/C][C]-3.96398844612105[/C][/ROW]
[ROW][C]94[/C][C]-0.2[/C][C]-1.35040655426849[/C][C]1.15040655426849[/C][/ROW]
[ROW][C]95[/C][C]5.1[/C][C]-2.76868020586673[/C][C]7.86868020586673[/C][/ROW]
[ROW][C]96[/C][C]-1.5[/C][C]-2.60816503308965[/C][C]1.10816503308965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278490&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278490&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.7	5.38995517771609	0.310044822283911
14	13	13.5905890799449	-0.590589079944934
15	14.5	15.831789897595	-1.33178989759502
16	9.7	9.53493925000786	0.165060749992138
17	-4.7	-4.80456564965315	0.104565649653154
18	7.3	8.20887007147707	-0.908870071477069
19	5.2	4.73789991337966	0.462100086620341
20	-2.5	13.0883597733986	-15.5883597733986
21	11.5	2.56531185650992	8.93468814349008
22	4.9	1.29031603510105	3.60968396489895
23	-2.4	12.9069028791896	-15.3069028791896
24	-0.3	5.29541644570581	-5.59541644570581
25	4.4	5.48885744301816	-1.08885744301816
26	7.9	13.2337451851955	-5.33374518519549
27	-9.7	14.4314990407101	-24.1314990407101
28	-4.1	6.12633961046321	-10.2263396104632
29	16.4	-2.04022283604379	18.4402228360438
30	-4.9	-2.61821445486674	-2.28178554513326
31	3.5	-2.18453655841707	5.68453655841707
32	3.8	-3.86076716573836	7.66076716573836
33	-0.2	-0.986582648283826	0.786582648283826
34	3.1	-0.331519873267917	3.43151987326792
35	0.7	1.30219766659315	-0.602197666593153
36	-2.8	0.504123368058854	-3.30412336805885
37	5.9	-0.296623288361682	6.19662328836168
38	-5.3	1.5901370463491	-6.8901370463491
39	-2.9	-0.0432137997009828	-2.85678620029902
40	6.6	-0.643539604430957	7.24353960443096
41	-8.1	-0.365765366248854	-7.73423463375115
42	1.3	1.62028807773682	-0.320288077736815
43	6.9	0.631832712086666	6.26816728791333
44	-7.2	4.77613361241113	-11.9761336124111
45	-1.9	0.835754362992934	-2.73575436299293
46	4	0.137835870221443	3.86216412977856
47	-5.7	2.81541025253599	-8.51541025253599
48	3.9	1.97272287496302	1.92727712503698
49	-7.6	1.27285020597758	-8.87285020597758
50	-0.9	-0.164256268092913	-0.735743731907087
51	7.3	-2.50598828910644	9.80598828910644
52	-3.7	-0.929922812944683	-2.77007718705532
53	-2.5	1.34866230893113	-3.84866230893113
54	9.3	-0.786471143552499	10.0864711435525
55	1.3	0.462547035001524	0.837452964998476
56	9.5	1.06920641294517	8.43079358705483
57	11.3	0.688882794729514	10.6111172052705
58	-1.7	2.49358712663606	-4.19358712663606
59	8	3.71099668063212	4.28900331936788
60	-4.8	10.9120721449173	-15.7120721449173
61	1.6	11.7666352899931	-10.1666352899931
62	1.9	1.64654648224521	0.253453517754787
63	-0.9	4.66994493532066	-5.56994493532066
64	5.5	7.05909053403752	-1.55909053403752
65	1.7	-3.56566165233685	5.26566165233685
66	-5.4	4.47124426517675	-9.87124426517675
67	1.9	1.0169490555051	0.883050944494897
68	0.2	2.35263492463449	-2.15263492463449
69	-13.3	0.528580174629818	-13.8285801746298
70	-8.2	-1.45396421117906	-6.74603578882094
71	0.2	-6.73610704225134	6.93610704225134
72	5.7	-12.2300281485966	17.9300281485966
73	-1.2	-14.2741959084173	13.0741959084173
74	-2.8	-2.18266518014752	-0.617334819852483
75	5.5	-6.1019940026112	11.6019940026112
76	-17.3	-8.69261838285188	-8.60738161714812
77	1.4	5.17076946271416	-3.77076946271416
78	-2.2	-7.46873425971128	5.26873425971127
79	-8.6	-3.30851575302753	-5.29148424697247
80	-5	-8.53295408965046	3.53295408965046
81	4.1	-3.29700108123967	7.39700108123967
82	0.7	-1.24790955795959	1.94790955795959
83	-4.2	-1.91218672352559	-2.28781327647441
84	-2.3	-4.82205987687573	2.52205987687573
85	-3.4	-6.98398534173906	3.58398534173906
86	-4.2	-1.19834874354066	-3.00165125645934
87	-14.2	-3.87117414812606	-10.3288258518739
88	1.6	-14.1772687081831	15.7772687081831
89	-4.9	5.27851055918268	-10.1785105591827
90	-1.8	-5.67203836648913	3.87203836648913
91	-0.5	-2.70080200710793	2.20080200710793
92	-2.3	-4.21443523625637	1.91443523625637
93	-5.3	-1.33601155387895	-3.96398844612105
94	-0.2	-1.35040655426849	1.15040655426849
95	5.1	-2.76868020586673	7.86868020586673
96	-1.5	-2.60816503308965	1.10816503308965

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	-3.69479487528448	-7.04445824912708	-0.345131501441873
98	-0.741412292025396	-4.13826657104231	2.65544198699152
99	-1.60045021411038	-8.65198169874347	5.45108127052272
100	-3.30487537424673	-18.3970907576855	11.787340009192
101	1.35471313587954	-5.92248739966039	8.63191367141947
102	-2.35322045320458	-15.5650308173244	10.8585899109152
103	-1.22186713894261	-9.09859479160077	6.65486051371555
104	-2.20898202698563	-17.0533217763981	12.6353577224268
105	-0.825915944303806	-7.50071168192815	5.84887979332054
106	-0.465432843128997	-5.50344497829907	4.57257929204108
107	-0.84722251432162	-10.2881942843238	8.59374925568053
108	-2.07080117045007	-259.698255951621	255.556653610721

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & -3.69479487528448 & -7.04445824912708 & -0.345131501441873 \tabularnewline
98 & -0.741412292025396 & -4.13826657104231 & 2.65544198699152 \tabularnewline
99 & -1.60045021411038 & -8.65198169874347 & 5.45108127052272 \tabularnewline
100 & -3.30487537424673 & -18.3970907576855 & 11.787340009192 \tabularnewline
101 & 1.35471313587954 & -5.92248739966039 & 8.63191367141947 \tabularnewline
102 & -2.35322045320458 & -15.5650308173244 & 10.8585899109152 \tabularnewline
103 & -1.22186713894261 & -9.09859479160077 & 6.65486051371555 \tabularnewline
104 & -2.20898202698563 & -17.0533217763981 & 12.6353577224268 \tabularnewline
105 & -0.825915944303806 & -7.50071168192815 & 5.84887979332054 \tabularnewline
106 & -0.465432843128997 & -5.50344497829907 & 4.57257929204108 \tabularnewline
107 & -0.84722251432162 & -10.2881942843238 & 8.59374925568053 \tabularnewline
108 & -2.07080117045007 & -259.698255951621 & 255.556653610721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278490&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]-3.69479487528448[/C][C]-7.04445824912708[/C][C]-0.345131501441873[/C][/ROW]
[ROW][C]98[/C][C]-0.741412292025396[/C][C]-4.13826657104231[/C][C]2.65544198699152[/C][/ROW]
[ROW][C]99[/C][C]-1.60045021411038[/C][C]-8.65198169874347[/C][C]5.45108127052272[/C][/ROW]
[ROW][C]100[/C][C]-3.30487537424673[/C][C]-18.3970907576855[/C][C]11.787340009192[/C][/ROW]
[ROW][C]101[/C][C]1.35471313587954[/C][C]-5.92248739966039[/C][C]8.63191367141947[/C][/ROW]
[ROW][C]102[/C][C]-2.35322045320458[/C][C]-15.5650308173244[/C][C]10.8585899109152[/C][/ROW]
[ROW][C]103[/C][C]-1.22186713894261[/C][C]-9.09859479160077[/C][C]6.65486051371555[/C][/ROW]
[ROW][C]104[/C][C]-2.20898202698563[/C][C]-17.0533217763981[/C][C]12.6353577224268[/C][/ROW]
[ROW][C]105[/C][C]-0.825915944303806[/C][C]-7.50071168192815[/C][C]5.84887979332054[/C][/ROW]
[ROW][C]106[/C][C]-0.465432843128997[/C][C]-5.50344497829907[/C][C]4.57257929204108[/C][/ROW]
[ROW][C]107[/C][C]-0.84722251432162[/C][C]-10.2881942843238[/C][C]8.59374925568053[/C][/ROW]
[ROW][C]108[/C][C]-2.07080117045007[/C][C]-259.698255951621[/C][C]255.556653610721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278490&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278490&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	-3.69479487528448	-7.04445824912708	-0.345131501441873
98	-0.741412292025396	-4.13826657104231	2.65544198699152
99	-1.60045021411038	-8.65198169874347	5.45108127052272
100	-3.30487537424673	-18.3970907576855	11.787340009192
101	1.35471313587954	-5.92248739966039	8.63191367141947
102	-2.35322045320458	-15.5650308173244	10.8585899109152
103	-1.22186713894261	-9.09859479160077	6.65486051371555
104	-2.20898202698563	-17.0533217763981	12.6353577224268
105	-0.825915944303806	-7.50071168192815	5.84887979332054
106	-0.465432843128997	-5.50344497829907	4.57257929204108
107	-0.84722251432162	-10.2881942843238	8.59374925568053
108	-2.07080117045007	-259.698255951621	255.556653610721

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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