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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 25 Nov 2015 18:56:13 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/25/t1448477819eyzh6zmpe93iy4s.htm/, Retrieved Wed, 15 May 2024 12:41:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284154, Retrieved Wed, 15 May 2024 12:41:09 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-11-25 18:56:13] [6e9c8a19a65400226bf8d1f1815bc708] [Current]

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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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284154&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284154&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	'Herman Ole Andreas Wold' @ wold.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284154&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284154&T=1

As an alternative you can also use a QR Code:

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

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	76.54	74.4407158119658	2.09928418803418
14	77.41	77.5197814685315	-0.109781468531494
15	76.87	76.9606148018648	-0.0906148018648025
16	76.51	76.5985314685315	-0.0885314685314569
17	75.66	75.7731148018648	-0.11311480186481
18	75.09	75.2310314685315	-0.141031468531466
19	75.16	76.5297814685315	-1.36978146853149
20	75	74.8847814685315	0.115218531468528
21	75.05	74.3160314685314	0.733968531468548
22	74.78	75.1006148018648	-0.320614801864807
23	75.43	75.4431148018648	-0.013114801864802
24	75.61	76.1347814685315	-0.524781468531486
25	77.12	77.7501981351981	-0.630198135198114
26	83.09	78.0997814685315	4.99021853146851
27	86.09	82.6406148018648	3.44938519813519
28	87.64	85.8185314685315	1.82146853146854
29	88.29	86.9031148018648	1.3868851981352
30	89.3	87.8610314685315	1.43896853146852
31	89.99	90.7397814685315	-0.749781468531481
32	90.43	89.7147814685315	0.715218531468537
33	91.03	89.7460314685315	1.28396853146855
34	91.4	91.0806148018648	0.319385198135194
35	92.19	92.0631148018648	0.126885198135184
36	92.45	92.8947814685315	-0.444781468531474
37	92.42	94.5901981351981	-2.17019813519812
38	90.2	93.3997814685315	-3.19978146853148
39	88.23	89.7506148018648	-1.52061480186481
40	84.91	87.9585314685315	-3.04853146853146
41	82.92	84.1731148018648	-1.2531148018648
42	81.8	82.4910314685315	-0.691031468531477
43	81.7	83.2397814685315	-1.53978146853147
44	83.22	81.4247814685315	1.79521853146852
45	82.7	82.5360314685314	0.163968531468555
46	82.83	82.7506148018648	0.079385198135185
47	83.66	83.4931148018648	0.166885198135191
48	84.28	84.3647814685315	-0.0847814685314745
49	84.37	86.4201981351981	-2.05019813519812
50	86.49	85.3497814685315	1.14021853146851
51	87.62	86.0406148018648	1.5793851981352
52	88.59	87.3485314685315	1.24146853146854
53	89.74	87.8531148018648	1.88688519813519
54	89.73	89.3110314685315	0.418968531468536
55	89.14	91.1697814685315	-2.02978146853148
56	88.37	88.8647814685315	-0.494781468531471
57	88.65	87.6860314685315	0.963968531468552
58	89.16	88.7006148018648	0.45938519813518
59	89.56	89.8231148018648	-0.263114801864802
60	89.37	90.2647814685315	-0.894781468531477
61	89.67	91.5101981351981	-1.84019813519812
62	93.04	90.6497814685315	2.39021853146852
63	94.4	92.5906148018648	1.80938519813519
64	95.5	94.1285314685315	1.37146853146854
65	101.66	94.7631148018648	6.89688519813519
66	102.86	101.231031468531	1.62896853146853
67	102.48	104.299781468531	-1.81978146853147
68	102.02	102.204781468531	-0.184781468531483
69	101.83	101.336031468531	0.493968531468553
70	101.3	101.880614801865	-0.580614801864812
71	101.29	101.963114801865	-0.673114801864799
72	100.53	101.994781468531	-1.46478146853148
73	100.45	102.670198135198	-2.22019813519812
74	101.88	101.429781468531	0.450218531468508
75	101.95	101.430614801865	0.519385198135197
76	102.18	101.678531468531	0.501468531468547
77	100.95	101.443114801865	-0.493114801864806
78	100.52	100.521031468531	-0.00103146853147962
79	100.39	101.959781468531	-1.56978146853147
80	99.61	100.114781468531	-0.504781468531476
81	99.43	98.9260314685314	0.503968531468558
82	99.34	99.4806148018648	-0.140614801864814
83	100.73	100.003114801865	0.726885198135193
84	102.14	101.434781468531	0.705218531468518
85	102.22	104.280198135198	-2.06019813519812
86	101.14	103.199781468531	-2.05978146853148
87	100.91	100.690614801865	0.219385198135186
88	101.62	100.638531468531	0.981468531468551
89	100	100.883114801865	-0.883114801864807
90	99.92	99.5710314685315	0.348968531468529
91	100.07	101.359781468531	-1.28978146853149
92	98.48	99.7947814685315	-1.31478146853146
93	98.3	97.7960314685315	0.503968531468544
94	98.86	98.3506148018648	0.509385198135192
95	98.96	99.5231148018648	-0.563114801864813
96	99.52	99.6647814685315	-0.144781468531477
97	99.06	101.660198135198	-2.60019813519811
98	100.47	100.039781468531	0.430218531468512
99	100.24	100.020614801865	0.219385198135186
100	86.43	99.9685314685315	-13.5385314685314
101	85.14	85.6931148018648	-0.553114801864808
102	85.41	84.7110314685315	0.698968531468523
103	86.13	86.8497814685315	-0.71978146853148
104	86.19	85.8547814685315	0.335218531468527
105	86.29	85.5060314685314	0.78396853146856
106	87.55	86.3406148018648	1.20938519813518
107	87.87	88.2131148018648	-0.3431148018648
108	88.37	88.5747814685315	-0.204781468531479

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 76.54 & 74.4407158119658 & 2.09928418803418 \tabularnewline
14 & 77.41 & 77.5197814685315 & -0.109781468531494 \tabularnewline
15 & 76.87 & 76.9606148018648 & -0.0906148018648025 \tabularnewline
16 & 76.51 & 76.5985314685315 & -0.0885314685314569 \tabularnewline
17 & 75.66 & 75.7731148018648 & -0.11311480186481 \tabularnewline
18 & 75.09 & 75.2310314685315 & -0.141031468531466 \tabularnewline
19 & 75.16 & 76.5297814685315 & -1.36978146853149 \tabularnewline
20 & 75 & 74.8847814685315 & 0.115218531468528 \tabularnewline
21 & 75.05 & 74.3160314685314 & 0.733968531468548 \tabularnewline
22 & 74.78 & 75.1006148018648 & -0.320614801864807 \tabularnewline
23 & 75.43 & 75.4431148018648 & -0.013114801864802 \tabularnewline
24 & 75.61 & 76.1347814685315 & -0.524781468531486 \tabularnewline
25 & 77.12 & 77.7501981351981 & -0.630198135198114 \tabularnewline
26 & 83.09 & 78.0997814685315 & 4.99021853146851 \tabularnewline
27 & 86.09 & 82.6406148018648 & 3.44938519813519 \tabularnewline
28 & 87.64 & 85.8185314685315 & 1.82146853146854 \tabularnewline
29 & 88.29 & 86.9031148018648 & 1.3868851981352 \tabularnewline
30 & 89.3 & 87.8610314685315 & 1.43896853146852 \tabularnewline
31 & 89.99 & 90.7397814685315 & -0.749781468531481 \tabularnewline
32 & 90.43 & 89.7147814685315 & 0.715218531468537 \tabularnewline
33 & 91.03 & 89.7460314685315 & 1.28396853146855 \tabularnewline
34 & 91.4 & 91.0806148018648 & 0.319385198135194 \tabularnewline
35 & 92.19 & 92.0631148018648 & 0.126885198135184 \tabularnewline
36 & 92.45 & 92.8947814685315 & -0.444781468531474 \tabularnewline
37 & 92.42 & 94.5901981351981 & -2.17019813519812 \tabularnewline
38 & 90.2 & 93.3997814685315 & -3.19978146853148 \tabularnewline
39 & 88.23 & 89.7506148018648 & -1.52061480186481 \tabularnewline
40 & 84.91 & 87.9585314685315 & -3.04853146853146 \tabularnewline
41 & 82.92 & 84.1731148018648 & -1.2531148018648 \tabularnewline
42 & 81.8 & 82.4910314685315 & -0.691031468531477 \tabularnewline
43 & 81.7 & 83.2397814685315 & -1.53978146853147 \tabularnewline
44 & 83.22 & 81.4247814685315 & 1.79521853146852 \tabularnewline
45 & 82.7 & 82.5360314685314 & 0.163968531468555 \tabularnewline
46 & 82.83 & 82.7506148018648 & 0.079385198135185 \tabularnewline
47 & 83.66 & 83.4931148018648 & 0.166885198135191 \tabularnewline
48 & 84.28 & 84.3647814685315 & -0.0847814685314745 \tabularnewline
49 & 84.37 & 86.4201981351981 & -2.05019813519812 \tabularnewline
50 & 86.49 & 85.3497814685315 & 1.14021853146851 \tabularnewline
51 & 87.62 & 86.0406148018648 & 1.5793851981352 \tabularnewline
52 & 88.59 & 87.3485314685315 & 1.24146853146854 \tabularnewline
53 & 89.74 & 87.8531148018648 & 1.88688519813519 \tabularnewline
54 & 89.73 & 89.3110314685315 & 0.418968531468536 \tabularnewline
55 & 89.14 & 91.1697814685315 & -2.02978146853148 \tabularnewline
56 & 88.37 & 88.8647814685315 & -0.494781468531471 \tabularnewline
57 & 88.65 & 87.6860314685315 & 0.963968531468552 \tabularnewline
58 & 89.16 & 88.7006148018648 & 0.45938519813518 \tabularnewline
59 & 89.56 & 89.8231148018648 & -0.263114801864802 \tabularnewline
60 & 89.37 & 90.2647814685315 & -0.894781468531477 \tabularnewline
61 & 89.67 & 91.5101981351981 & -1.84019813519812 \tabularnewline
62 & 93.04 & 90.6497814685315 & 2.39021853146852 \tabularnewline
63 & 94.4 & 92.5906148018648 & 1.80938519813519 \tabularnewline
64 & 95.5 & 94.1285314685315 & 1.37146853146854 \tabularnewline
65 & 101.66 & 94.7631148018648 & 6.89688519813519 \tabularnewline
66 & 102.86 & 101.231031468531 & 1.62896853146853 \tabularnewline
67 & 102.48 & 104.299781468531 & -1.81978146853147 \tabularnewline
68 & 102.02 & 102.204781468531 & -0.184781468531483 \tabularnewline
69 & 101.83 & 101.336031468531 & 0.493968531468553 \tabularnewline
70 & 101.3 & 101.880614801865 & -0.580614801864812 \tabularnewline
71 & 101.29 & 101.963114801865 & -0.673114801864799 \tabularnewline
72 & 100.53 & 101.994781468531 & -1.46478146853148 \tabularnewline
73 & 100.45 & 102.670198135198 & -2.22019813519812 \tabularnewline
74 & 101.88 & 101.429781468531 & 0.450218531468508 \tabularnewline
75 & 101.95 & 101.430614801865 & 0.519385198135197 \tabularnewline
76 & 102.18 & 101.678531468531 & 0.501468531468547 \tabularnewline
77 & 100.95 & 101.443114801865 & -0.493114801864806 \tabularnewline
78 & 100.52 & 100.521031468531 & -0.00103146853147962 \tabularnewline
79 & 100.39 & 101.959781468531 & -1.56978146853147 \tabularnewline
80 & 99.61 & 100.114781468531 & -0.504781468531476 \tabularnewline
81 & 99.43 & 98.9260314685314 & 0.503968531468558 \tabularnewline
82 & 99.34 & 99.4806148018648 & -0.140614801864814 \tabularnewline
83 & 100.73 & 100.003114801865 & 0.726885198135193 \tabularnewline
84 & 102.14 & 101.434781468531 & 0.705218531468518 \tabularnewline
85 & 102.22 & 104.280198135198 & -2.06019813519812 \tabularnewline
86 & 101.14 & 103.199781468531 & -2.05978146853148 \tabularnewline
87 & 100.91 & 100.690614801865 & 0.219385198135186 \tabularnewline
88 & 101.62 & 100.638531468531 & 0.981468531468551 \tabularnewline
89 & 100 & 100.883114801865 & -0.883114801864807 \tabularnewline
90 & 99.92 & 99.5710314685315 & 0.348968531468529 \tabularnewline
91 & 100.07 & 101.359781468531 & -1.28978146853149 \tabularnewline
92 & 98.48 & 99.7947814685315 & -1.31478146853146 \tabularnewline
93 & 98.3 & 97.7960314685315 & 0.503968531468544 \tabularnewline
94 & 98.86 & 98.3506148018648 & 0.509385198135192 \tabularnewline
95 & 98.96 & 99.5231148018648 & -0.563114801864813 \tabularnewline
96 & 99.52 & 99.6647814685315 & -0.144781468531477 \tabularnewline
97 & 99.06 & 101.660198135198 & -2.60019813519811 \tabularnewline
98 & 100.47 & 100.039781468531 & 0.430218531468512 \tabularnewline
99 & 100.24 & 100.020614801865 & 0.219385198135186 \tabularnewline
100 & 86.43 & 99.9685314685315 & -13.5385314685314 \tabularnewline
101 & 85.14 & 85.6931148018648 & -0.553114801864808 \tabularnewline
102 & 85.41 & 84.7110314685315 & 0.698968531468523 \tabularnewline
103 & 86.13 & 86.8497814685315 & -0.71978146853148 \tabularnewline
104 & 86.19 & 85.8547814685315 & 0.335218531468527 \tabularnewline
105 & 86.29 & 85.5060314685314 & 0.78396853146856 \tabularnewline
106 & 87.55 & 86.3406148018648 & 1.20938519813518 \tabularnewline
107 & 87.87 & 88.2131148018648 & -0.3431148018648 \tabularnewline
108 & 88.37 & 88.5747814685315 & -0.204781468531479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284154&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]76.54[/C][C]74.4407158119658[/C][C]2.09928418803418[/C][/ROW]
[ROW][C]14[/C][C]77.41[/C][C]77.5197814685315[/C][C]-0.109781468531494[/C][/ROW]
[ROW][C]15[/C][C]76.87[/C][C]76.9606148018648[/C][C]-0.0906148018648025[/C][/ROW]
[ROW][C]16[/C][C]76.51[/C][C]76.5985314685315[/C][C]-0.0885314685314569[/C][/ROW]
[ROW][C]17[/C][C]75.66[/C][C]75.7731148018648[/C][C]-0.11311480186481[/C][/ROW]
[ROW][C]18[/C][C]75.09[/C][C]75.2310314685315[/C][C]-0.141031468531466[/C][/ROW]
[ROW][C]19[/C][C]75.16[/C][C]76.5297814685315[/C][C]-1.36978146853149[/C][/ROW]
[ROW][C]20[/C][C]75[/C][C]74.8847814685315[/C][C]0.115218531468528[/C][/ROW]
[ROW][C]21[/C][C]75.05[/C][C]74.3160314685314[/C][C]0.733968531468548[/C][/ROW]
[ROW][C]22[/C][C]74.78[/C][C]75.1006148018648[/C][C]-0.320614801864807[/C][/ROW]
[ROW][C]23[/C][C]75.43[/C][C]75.4431148018648[/C][C]-0.013114801864802[/C][/ROW]
[ROW][C]24[/C][C]75.61[/C][C]76.1347814685315[/C][C]-0.524781468531486[/C][/ROW]
[ROW][C]25[/C][C]77.12[/C][C]77.7501981351981[/C][C]-0.630198135198114[/C][/ROW]
[ROW][C]26[/C][C]83.09[/C][C]78.0997814685315[/C][C]4.99021853146851[/C][/ROW]
[ROW][C]27[/C][C]86.09[/C][C]82.6406148018648[/C][C]3.44938519813519[/C][/ROW]
[ROW][C]28[/C][C]87.64[/C][C]85.8185314685315[/C][C]1.82146853146854[/C][/ROW]
[ROW][C]29[/C][C]88.29[/C][C]86.9031148018648[/C][C]1.3868851981352[/C][/ROW]
[ROW][C]30[/C][C]89.3[/C][C]87.8610314685315[/C][C]1.43896853146852[/C][/ROW]
[ROW][C]31[/C][C]89.99[/C][C]90.7397814685315[/C][C]-0.749781468531481[/C][/ROW]
[ROW][C]32[/C][C]90.43[/C][C]89.7147814685315[/C][C]0.715218531468537[/C][/ROW]
[ROW][C]33[/C][C]91.03[/C][C]89.7460314685315[/C][C]1.28396853146855[/C][/ROW]
[ROW][C]34[/C][C]91.4[/C][C]91.0806148018648[/C][C]0.319385198135194[/C][/ROW]
[ROW][C]35[/C][C]92.19[/C][C]92.0631148018648[/C][C]0.126885198135184[/C][/ROW]
[ROW][C]36[/C][C]92.45[/C][C]92.8947814685315[/C][C]-0.444781468531474[/C][/ROW]
[ROW][C]37[/C][C]92.42[/C][C]94.5901981351981[/C][C]-2.17019813519812[/C][/ROW]
[ROW][C]38[/C][C]90.2[/C][C]93.3997814685315[/C][C]-3.19978146853148[/C][/ROW]
[ROW][C]39[/C][C]88.23[/C][C]89.7506148018648[/C][C]-1.52061480186481[/C][/ROW]
[ROW][C]40[/C][C]84.91[/C][C]87.9585314685315[/C][C]-3.04853146853146[/C][/ROW]
[ROW][C]41[/C][C]82.92[/C][C]84.1731148018648[/C][C]-1.2531148018648[/C][/ROW]
[ROW][C]42[/C][C]81.8[/C][C]82.4910314685315[/C][C]-0.691031468531477[/C][/ROW]
[ROW][C]43[/C][C]81.7[/C][C]83.2397814685315[/C][C]-1.53978146853147[/C][/ROW]
[ROW][C]44[/C][C]83.22[/C][C]81.4247814685315[/C][C]1.79521853146852[/C][/ROW]
[ROW][C]45[/C][C]82.7[/C][C]82.5360314685314[/C][C]0.163968531468555[/C][/ROW]
[ROW][C]46[/C][C]82.83[/C][C]82.7506148018648[/C][C]0.079385198135185[/C][/ROW]
[ROW][C]47[/C][C]83.66[/C][C]83.4931148018648[/C][C]0.166885198135191[/C][/ROW]
[ROW][C]48[/C][C]84.28[/C][C]84.3647814685315[/C][C]-0.0847814685314745[/C][/ROW]
[ROW][C]49[/C][C]84.37[/C][C]86.4201981351981[/C][C]-2.05019813519812[/C][/ROW]
[ROW][C]50[/C][C]86.49[/C][C]85.3497814685315[/C][C]1.14021853146851[/C][/ROW]
[ROW][C]51[/C][C]87.62[/C][C]86.0406148018648[/C][C]1.5793851981352[/C][/ROW]
[ROW][C]52[/C][C]88.59[/C][C]87.3485314685315[/C][C]1.24146853146854[/C][/ROW]
[ROW][C]53[/C][C]89.74[/C][C]87.8531148018648[/C][C]1.88688519813519[/C][/ROW]
[ROW][C]54[/C][C]89.73[/C][C]89.3110314685315[/C][C]0.418968531468536[/C][/ROW]
[ROW][C]55[/C][C]89.14[/C][C]91.1697814685315[/C][C]-2.02978146853148[/C][/ROW]
[ROW][C]56[/C][C]88.37[/C][C]88.8647814685315[/C][C]-0.494781468531471[/C][/ROW]
[ROW][C]57[/C][C]88.65[/C][C]87.6860314685315[/C][C]0.963968531468552[/C][/ROW]
[ROW][C]58[/C][C]89.16[/C][C]88.7006148018648[/C][C]0.45938519813518[/C][/ROW]
[ROW][C]59[/C][C]89.56[/C][C]89.8231148018648[/C][C]-0.263114801864802[/C][/ROW]
[ROW][C]60[/C][C]89.37[/C][C]90.2647814685315[/C][C]-0.894781468531477[/C][/ROW]
[ROW][C]61[/C][C]89.67[/C][C]91.5101981351981[/C][C]-1.84019813519812[/C][/ROW]
[ROW][C]62[/C][C]93.04[/C][C]90.6497814685315[/C][C]2.39021853146852[/C][/ROW]
[ROW][C]63[/C][C]94.4[/C][C]92.5906148018648[/C][C]1.80938519813519[/C][/ROW]
[ROW][C]64[/C][C]95.5[/C][C]94.1285314685315[/C][C]1.37146853146854[/C][/ROW]
[ROW][C]65[/C][C]101.66[/C][C]94.7631148018648[/C][C]6.89688519813519[/C][/ROW]
[ROW][C]66[/C][C]102.86[/C][C]101.231031468531[/C][C]1.62896853146853[/C][/ROW]
[ROW][C]67[/C][C]102.48[/C][C]104.299781468531[/C][C]-1.81978146853147[/C][/ROW]
[ROW][C]68[/C][C]102.02[/C][C]102.204781468531[/C][C]-0.184781468531483[/C][/ROW]
[ROW][C]69[/C][C]101.83[/C][C]101.336031468531[/C][C]0.493968531468553[/C][/ROW]
[ROW][C]70[/C][C]101.3[/C][C]101.880614801865[/C][C]-0.580614801864812[/C][/ROW]
[ROW][C]71[/C][C]101.29[/C][C]101.963114801865[/C][C]-0.673114801864799[/C][/ROW]
[ROW][C]72[/C][C]100.53[/C][C]101.994781468531[/C][C]-1.46478146853148[/C][/ROW]
[ROW][C]73[/C][C]100.45[/C][C]102.670198135198[/C][C]-2.22019813519812[/C][/ROW]
[ROW][C]74[/C][C]101.88[/C][C]101.429781468531[/C][C]0.450218531468508[/C][/ROW]
[ROW][C]75[/C][C]101.95[/C][C]101.430614801865[/C][C]0.519385198135197[/C][/ROW]
[ROW][C]76[/C][C]102.18[/C][C]101.678531468531[/C][C]0.501468531468547[/C][/ROW]
[ROW][C]77[/C][C]100.95[/C][C]101.443114801865[/C][C]-0.493114801864806[/C][/ROW]
[ROW][C]78[/C][C]100.52[/C][C]100.521031468531[/C][C]-0.00103146853147962[/C][/ROW]
[ROW][C]79[/C][C]100.39[/C][C]101.959781468531[/C][C]-1.56978146853147[/C][/ROW]
[ROW][C]80[/C][C]99.61[/C][C]100.114781468531[/C][C]-0.504781468531476[/C][/ROW]
[ROW][C]81[/C][C]99.43[/C][C]98.9260314685314[/C][C]0.503968531468558[/C][/ROW]
[ROW][C]82[/C][C]99.34[/C][C]99.4806148018648[/C][C]-0.140614801864814[/C][/ROW]
[ROW][C]83[/C][C]100.73[/C][C]100.003114801865[/C][C]0.726885198135193[/C][/ROW]
[ROW][C]84[/C][C]102.14[/C][C]101.434781468531[/C][C]0.705218531468518[/C][/ROW]
[ROW][C]85[/C][C]102.22[/C][C]104.280198135198[/C][C]-2.06019813519812[/C][/ROW]
[ROW][C]86[/C][C]101.14[/C][C]103.199781468531[/C][C]-2.05978146853148[/C][/ROW]
[ROW][C]87[/C][C]100.91[/C][C]100.690614801865[/C][C]0.219385198135186[/C][/ROW]
[ROW][C]88[/C][C]101.62[/C][C]100.638531468531[/C][C]0.981468531468551[/C][/ROW]
[ROW][C]89[/C][C]100[/C][C]100.883114801865[/C][C]-0.883114801864807[/C][/ROW]
[ROW][C]90[/C][C]99.92[/C][C]99.5710314685315[/C][C]0.348968531468529[/C][/ROW]
[ROW][C]91[/C][C]100.07[/C][C]101.359781468531[/C][C]-1.28978146853149[/C][/ROW]
[ROW][C]92[/C][C]98.48[/C][C]99.7947814685315[/C][C]-1.31478146853146[/C][/ROW]
[ROW][C]93[/C][C]98.3[/C][C]97.7960314685315[/C][C]0.503968531468544[/C][/ROW]
[ROW][C]94[/C][C]98.86[/C][C]98.3506148018648[/C][C]0.509385198135192[/C][/ROW]
[ROW][C]95[/C][C]98.96[/C][C]99.5231148018648[/C][C]-0.563114801864813[/C][/ROW]
[ROW][C]96[/C][C]99.52[/C][C]99.6647814685315[/C][C]-0.144781468531477[/C][/ROW]
[ROW][C]97[/C][C]99.06[/C][C]101.660198135198[/C][C]-2.60019813519811[/C][/ROW]
[ROW][C]98[/C][C]100.47[/C][C]100.039781468531[/C][C]0.430218531468512[/C][/ROW]
[ROW][C]99[/C][C]100.24[/C][C]100.020614801865[/C][C]0.219385198135186[/C][/ROW]
[ROW][C]100[/C][C]86.43[/C][C]99.9685314685315[/C][C]-13.5385314685314[/C][/ROW]
[ROW][C]101[/C][C]85.14[/C][C]85.6931148018648[/C][C]-0.553114801864808[/C][/ROW]
[ROW][C]102[/C][C]85.41[/C][C]84.7110314685315[/C][C]0.698968531468523[/C][/ROW]
[ROW][C]103[/C][C]86.13[/C][C]86.8497814685315[/C][C]-0.71978146853148[/C][/ROW]
[ROW][C]104[/C][C]86.19[/C][C]85.8547814685315[/C][C]0.335218531468527[/C][/ROW]
[ROW][C]105[/C][C]86.29[/C][C]85.5060314685314[/C][C]0.78396853146856[/C][/ROW]
[ROW][C]106[/C][C]87.55[/C][C]86.3406148018648[/C][C]1.20938519813518[/C][/ROW]
[ROW][C]107[/C][C]87.87[/C][C]88.2131148018648[/C][C]-0.3431148018648[/C][/ROW]
[ROW][C]108[/C][C]88.37[/C][C]88.5747814685315[/C][C]-0.204781468531479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284154&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	76.54	74.4407158119658	2.09928418803418
14	77.41	77.5197814685315	-0.109781468531494
15	76.87	76.9606148018648	-0.0906148018648025
16	76.51	76.5985314685315	-0.0885314685314569
17	75.66	75.7731148018648	-0.11311480186481
18	75.09	75.2310314685315	-0.141031468531466
19	75.16	76.5297814685315	-1.36978146853149
20	75	74.8847814685315	0.115218531468528
21	75.05	74.3160314685314	0.733968531468548
22	74.78	75.1006148018648	-0.320614801864807
23	75.43	75.4431148018648	-0.013114801864802
24	75.61	76.1347814685315	-0.524781468531486
25	77.12	77.7501981351981	-0.630198135198114
26	83.09	78.0997814685315	4.99021853146851
27	86.09	82.6406148018648	3.44938519813519
28	87.64	85.8185314685315	1.82146853146854
29	88.29	86.9031148018648	1.3868851981352
30	89.3	87.8610314685315	1.43896853146852
31	89.99	90.7397814685315	-0.749781468531481
32	90.43	89.7147814685315	0.715218531468537
33	91.03	89.7460314685315	1.28396853146855
34	91.4	91.0806148018648	0.319385198135194
35	92.19	92.0631148018648	0.126885198135184
36	92.45	92.8947814685315	-0.444781468531474
37	92.42	94.5901981351981	-2.17019813519812
38	90.2	93.3997814685315	-3.19978146853148
39	88.23	89.7506148018648	-1.52061480186481
40	84.91	87.9585314685315	-3.04853146853146
41	82.92	84.1731148018648	-1.2531148018648
42	81.8	82.4910314685315	-0.691031468531477
43	81.7	83.2397814685315	-1.53978146853147
44	83.22	81.4247814685315	1.79521853146852
45	82.7	82.5360314685314	0.163968531468555
46	82.83	82.7506148018648	0.079385198135185
47	83.66	83.4931148018648	0.166885198135191
48	84.28	84.3647814685315	-0.0847814685314745
49	84.37	86.4201981351981	-2.05019813519812
50	86.49	85.3497814685315	1.14021853146851
51	87.62	86.0406148018648	1.5793851981352
52	88.59	87.3485314685315	1.24146853146854
53	89.74	87.8531148018648	1.88688519813519
54	89.73	89.3110314685315	0.418968531468536
55	89.14	91.1697814685315	-2.02978146853148
56	88.37	88.8647814685315	-0.494781468531471
57	88.65	87.6860314685315	0.963968531468552
58	89.16	88.7006148018648	0.45938519813518
59	89.56	89.8231148018648	-0.263114801864802
60	89.37	90.2647814685315	-0.894781468531477
61	89.67	91.5101981351981	-1.84019813519812
62	93.04	90.6497814685315	2.39021853146852
63	94.4	92.5906148018648	1.80938519813519
64	95.5	94.1285314685315	1.37146853146854
65	101.66	94.7631148018648	6.89688519813519
66	102.86	101.231031468531	1.62896853146853
67	102.48	104.299781468531	-1.81978146853147
68	102.02	102.204781468531	-0.184781468531483
69	101.83	101.336031468531	0.493968531468553
70	101.3	101.880614801865	-0.580614801864812
71	101.29	101.963114801865	-0.673114801864799
72	100.53	101.994781468531	-1.46478146853148
73	100.45	102.670198135198	-2.22019813519812
74	101.88	101.429781468531	0.450218531468508
75	101.95	101.430614801865	0.519385198135197
76	102.18	101.678531468531	0.501468531468547
77	100.95	101.443114801865	-0.493114801864806
78	100.52	100.521031468531	-0.00103146853147962
79	100.39	101.959781468531	-1.56978146853147
80	99.61	100.114781468531	-0.504781468531476
81	99.43	98.9260314685314	0.503968531468558
82	99.34	99.4806148018648	-0.140614801864814
83	100.73	100.003114801865	0.726885198135193
84	102.14	101.434781468531	0.705218531468518
85	102.22	104.280198135198	-2.06019813519812
86	101.14	103.199781468531	-2.05978146853148
87	100.91	100.690614801865	0.219385198135186
88	101.62	100.638531468531	0.981468531468551
89	100	100.883114801865	-0.883114801864807
90	99.92	99.5710314685315	0.348968531468529
91	100.07	101.359781468531	-1.28978146853149
92	98.48	99.7947814685315	-1.31478146853146
93	98.3	97.7960314685315	0.503968531468544
94	98.86	98.3506148018648	0.509385198135192
95	98.96	99.5231148018648	-0.563114801864813
96	99.52	99.6647814685315	-0.144781468531477
97	99.06	101.660198135198	-2.60019813519811
98	100.47	100.039781468531	0.430218531468512
99	100.24	100.020614801865	0.219385198135186
100	86.43	99.9685314685315	-13.5385314685314
101	85.14	85.6931148018648	-0.553114801864808
102	85.41	84.7110314685315	0.698968531468523
103	86.13	86.8497814685315	-0.71978146853148
104	86.19	85.8547814685315	0.335218531468527
105	86.29	85.5060314685314	0.78396853146856
106	87.55	86.3406148018648	1.20938519813518
107	87.87	88.2131148018648	-0.3431148018648
108	88.37	88.5747814685315	-0.204781468531479

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	90.5101981351981	86.501522343397	94.5188739269992
110	91.4899796037296	85.8208559318078	97.1591032756514
111	91.0405944055944	84.0973642631235	97.9838245480653
112	90.7691258741259	82.7517742905237	98.7864774577281
113	90.0322406759907	81.0685691057656	98.9959122462157
114	89.6032721445221	79.7840619103621	99.4224823786822
115	91.0430536130536	80.437094381263	101.649012844844
116	90.7678350815851	79.4295877377414	102.106082425429
117	90.0838665501165	78.0578391747132	102.10989392552
118	90.1344813519813	77.4579354487109	102.811027255252
119	90.7975961538461	77.5023226462611	104.092869661431
120	91.5023776223776	77.6159173374358	105.388837907319

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 90.5101981351981 & 86.501522343397 & 94.5188739269992 \tabularnewline
110 & 91.4899796037296 & 85.8208559318078 & 97.1591032756514 \tabularnewline
111 & 91.0405944055944 & 84.0973642631235 & 97.9838245480653 \tabularnewline
112 & 90.7691258741259 & 82.7517742905237 & 98.7864774577281 \tabularnewline
113 & 90.0322406759907 & 81.0685691057656 & 98.9959122462157 \tabularnewline
114 & 89.6032721445221 & 79.7840619103621 & 99.4224823786822 \tabularnewline
115 & 91.0430536130536 & 80.437094381263 & 101.649012844844 \tabularnewline
116 & 90.7678350815851 & 79.4295877377414 & 102.106082425429 \tabularnewline
117 & 90.0838665501165 & 78.0578391747132 & 102.10989392552 \tabularnewline
118 & 90.1344813519813 & 77.4579354487109 & 102.811027255252 \tabularnewline
119 & 90.7975961538461 & 77.5023226462611 & 104.092869661431 \tabularnewline
120 & 91.5023776223776 & 77.6159173374358 & 105.388837907319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284154&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]109[/C][C]90.5101981351981[/C][C]86.501522343397[/C][C]94.5188739269992[/C][/ROW]
[ROW][C]110[/C][C]91.4899796037296[/C][C]85.8208559318078[/C][C]97.1591032756514[/C][/ROW]
[ROW][C]111[/C][C]91.0405944055944[/C][C]84.0973642631235[/C][C]97.9838245480653[/C][/ROW]
[ROW][C]112[/C][C]90.7691258741259[/C][C]82.7517742905237[/C][C]98.7864774577281[/C][/ROW]
[ROW][C]113[/C][C]90.0322406759907[/C][C]81.0685691057656[/C][C]98.9959122462157[/C][/ROW]
[ROW][C]114[/C][C]89.6032721445221[/C][C]79.7840619103621[/C][C]99.4224823786822[/C][/ROW]
[ROW][C]115[/C][C]91.0430536130536[/C][C]80.437094381263[/C][C]101.649012844844[/C][/ROW]
[ROW][C]116[/C][C]90.7678350815851[/C][C]79.4295877377414[/C][C]102.106082425429[/C][/ROW]
[ROW][C]117[/C][C]90.0838665501165[/C][C]78.0578391747132[/C][C]102.10989392552[/C][/ROW]
[ROW][C]118[/C][C]90.1344813519813[/C][C]77.4579354487109[/C][C]102.811027255252[/C][/ROW]
[ROW][C]119[/C][C]90.7975961538461[/C][C]77.5023226462611[/C][C]104.092869661431[/C][/ROW]
[ROW][C]120[/C][C]91.5023776223776[/C][C]77.6159173374358[/C][C]105.388837907319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284154&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284154&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
109	90.5101981351981	86.501522343397	94.5188739269992
110	91.4899796037296	85.8208559318078	97.1591032756514
111	91.0405944055944	84.0973642631235	97.9838245480653
112	90.7691258741259	82.7517742905237	98.7864774577281
113	90.0322406759907	81.0685691057656	98.9959122462157
114	89.6032721445221	79.7840619103621	99.4224823786822
115	91.0430536130536	80.437094381263	101.649012844844
116	90.7678350815851	79.4295877377414	102.106082425429
117	90.0838665501165	78.0578391747132	102.10989392552
118	90.1344813519813	77.4579354487109	102.811027255252
119	90.7975961538461	77.5023226462611	104.092869661431
120	91.5023776223776	77.6159173374358	105.388837907319

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code