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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 19 Dec 2012 10:07:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/19/t1355929698exp00gkg51c7dag.htm/, Retrieved Fri, 03 May 2024 22:13:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202045, Retrieved Fri, 03 May 2024 22:13:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2012-12-14 15:11:56] [bbed103f50d9b60ea97669d7e6947a11]
- R PD    [Exponential Smoothing] [] [2012-12-19 15:07:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
59.8
60.7
59.7
60.2
61.3
59.8
61.2
59.3
59.4
63.1
68
69.4
70.2
72.6
72.1
69.7
71.5
75.7
76
76.4
83.8
86.2
88.5
95.9
103.1
113.5
115.7
113.1
112.7
121.9
120.3
108.7
102.8
83.4
79.4
77.8
85.7
83.2
82
86.9
95.7
97.9
89.3
91.5
86.8
91
93.8
96.8
95.7
91.4
88.7
88.2
87.7
89.5
95.6
100.5
106.3
112
117.7
125
132.4
138.1
134.7
136.7
134.3
131.6
129.8
131.9
129.8
119.4
116.7
112.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202045&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202045&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202045&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202045&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202045&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202045&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
ParameterValue
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
359.761.6-1.90000000000001
460.260.6-0.400000000000006
561.361.10.199999999999989
659.862.2-2.40000000000001
761.260.70.5
859.362.1-2.80000000000001
959.460.2-0.800000000000004
1063.160.32.8
1168644
1269.468.90.5
1370.270.3-0.100000000000009
1472.671.11.49999999999999
1572.173.5-1.40000000000001
1669.773-3.3
1771.570.60.899999999999991
1875.772.43.3
197676.6-0.600000000000009
2076.476.9-0.5
2183.877.36.49999999999999
2286.284.71.5
2388.587.11.39999999999999
2495.989.46.5
25103.196.86.29999999999998
26113.51049.5
27115.7114.41.3
28113.1116.6-3.50000000000001
29112.7114-1.3
30121.9113.68.3
31120.3122.8-2.50000000000001
32108.7121.2-12.5
33102.8109.6-6.80000000000001
3483.4103.7-20.3
3579.484.3-4.90000000000001
3677.880.3-2.50000000000001
3785.778.77
3883.286.6-3.40000000000001
398284.1-2.10000000000001
4086.982.94
4195.787.87.89999999999999
4297.996.61.3
4389.398.8-9.50000000000001
4491.590.21.3
4586.892.4-5.60000000000001
469187.73.3
4793.891.91.89999999999999
4896.894.72.09999999999999
4995.797.7-2
5091.496.6-5.2
5188.792.3-3.60000000000001
5288.289.6-1.40000000000001
5387.789.1-1.40000000000001
5489.588.60.899999999999991
5595.690.45.19999999999999
56100.596.54
57106.3101.44.89999999999999
58112107.24.8
59117.7112.94.8
60125118.66.39999999999999
61132.4125.96.5
62138.1133.34.79999999999998
63134.7139-4.30000000000001
64136.7135.61.09999999999999
65134.3137.6-3.29999999999998
66131.6135.2-3.60000000000002
67129.8132.5-2.69999999999999
68131.9130.71.19999999999999
69129.8132.8-3
70119.4130.7-11.3
71116.7120.3-3.60000000000001
72112.8117.6-4.80000000000001

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 59.7 & 61.6 & -1.90000000000001 \tabularnewline
4 & 60.2 & 60.6 & -0.400000000000006 \tabularnewline
5 & 61.3 & 61.1 & 0.199999999999989 \tabularnewline
6 & 59.8 & 62.2 & -2.40000000000001 \tabularnewline
7 & 61.2 & 60.7 & 0.5 \tabularnewline
8 & 59.3 & 62.1 & -2.80000000000001 \tabularnewline
9 & 59.4 & 60.2 & -0.800000000000004 \tabularnewline
10 & 63.1 & 60.3 & 2.8 \tabularnewline
11 & 68 & 64 & 4 \tabularnewline
12 & 69.4 & 68.9 & 0.5 \tabularnewline
13 & 70.2 & 70.3 & -0.100000000000009 \tabularnewline
14 & 72.6 & 71.1 & 1.49999999999999 \tabularnewline
15 & 72.1 & 73.5 & -1.40000000000001 \tabularnewline
16 & 69.7 & 73 & -3.3 \tabularnewline
17 & 71.5 & 70.6 & 0.899999999999991 \tabularnewline
18 & 75.7 & 72.4 & 3.3 \tabularnewline
19 & 76 & 76.6 & -0.600000000000009 \tabularnewline
20 & 76.4 & 76.9 & -0.5 \tabularnewline
21 & 83.8 & 77.3 & 6.49999999999999 \tabularnewline
22 & 86.2 & 84.7 & 1.5 \tabularnewline
23 & 88.5 & 87.1 & 1.39999999999999 \tabularnewline
24 & 95.9 & 89.4 & 6.5 \tabularnewline
25 & 103.1 & 96.8 & 6.29999999999998 \tabularnewline
26 & 113.5 & 104 & 9.5 \tabularnewline
27 & 115.7 & 114.4 & 1.3 \tabularnewline
28 & 113.1 & 116.6 & -3.50000000000001 \tabularnewline
29 & 112.7 & 114 & -1.3 \tabularnewline
30 & 121.9 & 113.6 & 8.3 \tabularnewline
31 & 120.3 & 122.8 & -2.50000000000001 \tabularnewline
32 & 108.7 & 121.2 & -12.5 \tabularnewline
33 & 102.8 & 109.6 & -6.80000000000001 \tabularnewline
34 & 83.4 & 103.7 & -20.3 \tabularnewline
35 & 79.4 & 84.3 & -4.90000000000001 \tabularnewline
36 & 77.8 & 80.3 & -2.50000000000001 \tabularnewline
37 & 85.7 & 78.7 & 7 \tabularnewline
38 & 83.2 & 86.6 & -3.40000000000001 \tabularnewline
39 & 82 & 84.1 & -2.10000000000001 \tabularnewline
40 & 86.9 & 82.9 & 4 \tabularnewline
41 & 95.7 & 87.8 & 7.89999999999999 \tabularnewline
42 & 97.9 & 96.6 & 1.3 \tabularnewline
43 & 89.3 & 98.8 & -9.50000000000001 \tabularnewline
44 & 91.5 & 90.2 & 1.3 \tabularnewline
45 & 86.8 & 92.4 & -5.60000000000001 \tabularnewline
46 & 91 & 87.7 & 3.3 \tabularnewline
47 & 93.8 & 91.9 & 1.89999999999999 \tabularnewline
48 & 96.8 & 94.7 & 2.09999999999999 \tabularnewline
49 & 95.7 & 97.7 & -2 \tabularnewline
50 & 91.4 & 96.6 & -5.2 \tabularnewline
51 & 88.7 & 92.3 & -3.60000000000001 \tabularnewline
52 & 88.2 & 89.6 & -1.40000000000001 \tabularnewline
53 & 87.7 & 89.1 & -1.40000000000001 \tabularnewline
54 & 89.5 & 88.6 & 0.899999999999991 \tabularnewline
55 & 95.6 & 90.4 & 5.19999999999999 \tabularnewline
56 & 100.5 & 96.5 & 4 \tabularnewline
57 & 106.3 & 101.4 & 4.89999999999999 \tabularnewline
58 & 112 & 107.2 & 4.8 \tabularnewline
59 & 117.7 & 112.9 & 4.8 \tabularnewline
60 & 125 & 118.6 & 6.39999999999999 \tabularnewline
61 & 132.4 & 125.9 & 6.5 \tabularnewline
62 & 138.1 & 133.3 & 4.79999999999998 \tabularnewline
63 & 134.7 & 139 & -4.30000000000001 \tabularnewline
64 & 136.7 & 135.6 & 1.09999999999999 \tabularnewline
65 & 134.3 & 137.6 & -3.29999999999998 \tabularnewline
66 & 131.6 & 135.2 & -3.60000000000002 \tabularnewline
67 & 129.8 & 132.5 & -2.69999999999999 \tabularnewline
68 & 131.9 & 130.7 & 1.19999999999999 \tabularnewline
69 & 129.8 & 132.8 & -3 \tabularnewline
70 & 119.4 & 130.7 & -11.3 \tabularnewline
71 & 116.7 & 120.3 & -3.60000000000001 \tabularnewline
72 & 112.8 & 117.6 & -4.80000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202045&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]59.7[/C][C]61.6[/C][C]-1.90000000000001[/C][/ROW]
[ROW][C]4[/C][C]60.2[/C][C]60.6[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]5[/C][C]61.3[/C][C]61.1[/C][C]0.199999999999989[/C][/ROW]
[ROW][C]6[/C][C]59.8[/C][C]62.2[/C][C]-2.40000000000001[/C][/ROW]
[ROW][C]7[/C][C]61.2[/C][C]60.7[/C][C]0.5[/C][/ROW]
[ROW][C]8[/C][C]59.3[/C][C]62.1[/C][C]-2.80000000000001[/C][/ROW]
[ROW][C]9[/C][C]59.4[/C][C]60.2[/C][C]-0.800000000000004[/C][/ROW]
[ROW][C]10[/C][C]63.1[/C][C]60.3[/C][C]2.8[/C][/ROW]
[ROW][C]11[/C][C]68[/C][C]64[/C][C]4[/C][/ROW]
[ROW][C]12[/C][C]69.4[/C][C]68.9[/C][C]0.5[/C][/ROW]
[ROW][C]13[/C][C]70.2[/C][C]70.3[/C][C]-0.100000000000009[/C][/ROW]
[ROW][C]14[/C][C]72.6[/C][C]71.1[/C][C]1.49999999999999[/C][/ROW]
[ROW][C]15[/C][C]72.1[/C][C]73.5[/C][C]-1.40000000000001[/C][/ROW]
[ROW][C]16[/C][C]69.7[/C][C]73[/C][C]-3.3[/C][/ROW]
[ROW][C]17[/C][C]71.5[/C][C]70.6[/C][C]0.899999999999991[/C][/ROW]
[ROW][C]18[/C][C]75.7[/C][C]72.4[/C][C]3.3[/C][/ROW]
[ROW][C]19[/C][C]76[/C][C]76.6[/C][C]-0.600000000000009[/C][/ROW]
[ROW][C]20[/C][C]76.4[/C][C]76.9[/C][C]-0.5[/C][/ROW]
[ROW][C]21[/C][C]83.8[/C][C]77.3[/C][C]6.49999999999999[/C][/ROW]
[ROW][C]22[/C][C]86.2[/C][C]84.7[/C][C]1.5[/C][/ROW]
[ROW][C]23[/C][C]88.5[/C][C]87.1[/C][C]1.39999999999999[/C][/ROW]
[ROW][C]24[/C][C]95.9[/C][C]89.4[/C][C]6.5[/C][/ROW]
[ROW][C]25[/C][C]103.1[/C][C]96.8[/C][C]6.29999999999998[/C][/ROW]
[ROW][C]26[/C][C]113.5[/C][C]104[/C][C]9.5[/C][/ROW]
[ROW][C]27[/C][C]115.7[/C][C]114.4[/C][C]1.3[/C][/ROW]
[ROW][C]28[/C][C]113.1[/C][C]116.6[/C][C]-3.50000000000001[/C][/ROW]
[ROW][C]29[/C][C]112.7[/C][C]114[/C][C]-1.3[/C][/ROW]
[ROW][C]30[/C][C]121.9[/C][C]113.6[/C][C]8.3[/C][/ROW]
[ROW][C]31[/C][C]120.3[/C][C]122.8[/C][C]-2.50000000000001[/C][/ROW]
[ROW][C]32[/C][C]108.7[/C][C]121.2[/C][C]-12.5[/C][/ROW]
[ROW][C]33[/C][C]102.8[/C][C]109.6[/C][C]-6.80000000000001[/C][/ROW]
[ROW][C]34[/C][C]83.4[/C][C]103.7[/C][C]-20.3[/C][/ROW]
[ROW][C]35[/C][C]79.4[/C][C]84.3[/C][C]-4.90000000000001[/C][/ROW]
[ROW][C]36[/C][C]77.8[/C][C]80.3[/C][C]-2.50000000000001[/C][/ROW]
[ROW][C]37[/C][C]85.7[/C][C]78.7[/C][C]7[/C][/ROW]
[ROW][C]38[/C][C]83.2[/C][C]86.6[/C][C]-3.40000000000001[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]84.1[/C][C]-2.10000000000001[/C][/ROW]
[ROW][C]40[/C][C]86.9[/C][C]82.9[/C][C]4[/C][/ROW]
[ROW][C]41[/C][C]95.7[/C][C]87.8[/C][C]7.89999999999999[/C][/ROW]
[ROW][C]42[/C][C]97.9[/C][C]96.6[/C][C]1.3[/C][/ROW]
[ROW][C]43[/C][C]89.3[/C][C]98.8[/C][C]-9.50000000000001[/C][/ROW]
[ROW][C]44[/C][C]91.5[/C][C]90.2[/C][C]1.3[/C][/ROW]
[ROW][C]45[/C][C]86.8[/C][C]92.4[/C][C]-5.60000000000001[/C][/ROW]
[ROW][C]46[/C][C]91[/C][C]87.7[/C][C]3.3[/C][/ROW]
[ROW][C]47[/C][C]93.8[/C][C]91.9[/C][C]1.89999999999999[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]94.7[/C][C]2.09999999999999[/C][/ROW]
[ROW][C]49[/C][C]95.7[/C][C]97.7[/C][C]-2[/C][/ROW]
[ROW][C]50[/C][C]91.4[/C][C]96.6[/C][C]-5.2[/C][/ROW]
[ROW][C]51[/C][C]88.7[/C][C]92.3[/C][C]-3.60000000000001[/C][/ROW]
[ROW][C]52[/C][C]88.2[/C][C]89.6[/C][C]-1.40000000000001[/C][/ROW]
[ROW][C]53[/C][C]87.7[/C][C]89.1[/C][C]-1.40000000000001[/C][/ROW]
[ROW][C]54[/C][C]89.5[/C][C]88.6[/C][C]0.899999999999991[/C][/ROW]
[ROW][C]55[/C][C]95.6[/C][C]90.4[/C][C]5.19999999999999[/C][/ROW]
[ROW][C]56[/C][C]100.5[/C][C]96.5[/C][C]4[/C][/ROW]
[ROW][C]57[/C][C]106.3[/C][C]101.4[/C][C]4.89999999999999[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]107.2[/C][C]4.8[/C][/ROW]
[ROW][C]59[/C][C]117.7[/C][C]112.9[/C][C]4.8[/C][/ROW]
[ROW][C]60[/C][C]125[/C][C]118.6[/C][C]6.39999999999999[/C][/ROW]
[ROW][C]61[/C][C]132.4[/C][C]125.9[/C][C]6.5[/C][/ROW]
[ROW][C]62[/C][C]138.1[/C][C]133.3[/C][C]4.79999999999998[/C][/ROW]
[ROW][C]63[/C][C]134.7[/C][C]139[/C][C]-4.30000000000001[/C][/ROW]
[ROW][C]64[/C][C]136.7[/C][C]135.6[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]65[/C][C]134.3[/C][C]137.6[/C][C]-3.29999999999998[/C][/ROW]
[ROW][C]66[/C][C]131.6[/C][C]135.2[/C][C]-3.60000000000002[/C][/ROW]
[ROW][C]67[/C][C]129.8[/C][C]132.5[/C][C]-2.69999999999999[/C][/ROW]
[ROW][C]68[/C][C]131.9[/C][C]130.7[/C][C]1.19999999999999[/C][/ROW]
[ROW][C]69[/C][C]129.8[/C][C]132.8[/C][C]-3[/C][/ROW]
[ROW][C]70[/C][C]119.4[/C][C]130.7[/C][C]-11.3[/C][/ROW]
[ROW][C]71[/C][C]116.7[/C][C]120.3[/C][C]-3.60000000000001[/C][/ROW]
[ROW][C]72[/C][C]112.8[/C][C]117.6[/C][C]-4.80000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202045&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202045&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
tObservedFittedResiduals
359.761.6-1.90000000000001
460.260.6-0.400000000000006
561.361.10.199999999999989
659.862.2-2.40000000000001
761.260.70.5
859.362.1-2.80000000000001
959.460.2-0.800000000000004
1063.160.32.8
1168644
1269.468.90.5
1370.270.3-0.100000000000009
1472.671.11.49999999999999
1572.173.5-1.40000000000001
1669.773-3.3
1771.570.60.899999999999991
1875.772.43.3
197676.6-0.600000000000009
2076.476.9-0.5
2183.877.36.49999999999999
2286.284.71.5
2388.587.11.39999999999999
2495.989.46.5
25103.196.86.29999999999998
26113.51049.5
27115.7114.41.3
28113.1116.6-3.50000000000001
29112.7114-1.3
30121.9113.68.3
31120.3122.8-2.50000000000001
32108.7121.2-12.5
33102.8109.6-6.80000000000001
3483.4103.7-20.3
3579.484.3-4.90000000000001
3677.880.3-2.50000000000001
3785.778.77
3883.286.6-3.40000000000001
398284.1-2.10000000000001
4086.982.94
4195.787.87.89999999999999
4297.996.61.3
4389.398.8-9.50000000000001
4491.590.21.3
4586.892.4-5.60000000000001
469187.73.3
4793.891.91.89999999999999
4896.894.72.09999999999999
4995.797.7-2
5091.496.6-5.2
5188.792.3-3.60000000000001
5288.289.6-1.40000000000001
5387.789.1-1.40000000000001
5489.588.60.899999999999991
5595.690.45.19999999999999
56100.596.54
57106.3101.44.89999999999999
58112107.24.8
59117.7112.94.8
60125118.66.39999999999999
61132.4125.96.5
62138.1133.34.79999999999998
63134.7139-4.30000000000001
64136.7135.61.09999999999999
65134.3137.6-3.29999999999998
66131.6135.2-3.60000000000002
67129.8132.5-2.69999999999999
68131.9130.71.19999999999999
69129.8132.8-3
70119.4130.7-11.3
71116.7120.3-3.60000000000001
72112.8117.6-4.80000000000001







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73113.7103.681811116668123.718188883332
74114.6100.432141410776128.767858589224
75115.598.1479878542465132.852012145754
76116.496.3636222333351136.436377766665
77117.394.8986486454359139.701351354564
78118.293.6605490890127142.739450910987
79119.192.5943636274304145.60563637257
8012091.6642828215517148.335717178448
81120.990.8454333500026150.954566649997
82121.890.1197050988906153.48029490111
83122.789.4734263950767155.926573604923
84123.688.895975708493158.304024291507

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 113.7 & 103.681811116668 & 123.718188883332 \tabularnewline
74 & 114.6 & 100.432141410776 & 128.767858589224 \tabularnewline
75 & 115.5 & 98.1479878542465 & 132.852012145754 \tabularnewline
76 & 116.4 & 96.3636222333351 & 136.436377766665 \tabularnewline
77 & 117.3 & 94.8986486454359 & 139.701351354564 \tabularnewline
78 & 118.2 & 93.6605490890127 & 142.739450910987 \tabularnewline
79 & 119.1 & 92.5943636274304 & 145.60563637257 \tabularnewline
80 & 120 & 91.6642828215517 & 148.335717178448 \tabularnewline
81 & 120.9 & 90.8454333500026 & 150.954566649997 \tabularnewline
82 & 121.8 & 90.1197050988906 & 153.48029490111 \tabularnewline
83 & 122.7 & 89.4734263950767 & 155.926573604923 \tabularnewline
84 & 123.6 & 88.895975708493 & 158.304024291507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202045&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]113.7[/C][C]103.681811116668[/C][C]123.718188883332[/C][/ROW]
[ROW][C]74[/C][C]114.6[/C][C]100.432141410776[/C][C]128.767858589224[/C][/ROW]
[ROW][C]75[/C][C]115.5[/C][C]98.1479878542465[/C][C]132.852012145754[/C][/ROW]
[ROW][C]76[/C][C]116.4[/C][C]96.3636222333351[/C][C]136.436377766665[/C][/ROW]
[ROW][C]77[/C][C]117.3[/C][C]94.8986486454359[/C][C]139.701351354564[/C][/ROW]
[ROW][C]78[/C][C]118.2[/C][C]93.6605490890127[/C][C]142.739450910987[/C][/ROW]
[ROW][C]79[/C][C]119.1[/C][C]92.5943636274304[/C][C]145.60563637257[/C][/ROW]
[ROW][C]80[/C][C]120[/C][C]91.6642828215517[/C][C]148.335717178448[/C][/ROW]
[ROW][C]81[/C][C]120.9[/C][C]90.8454333500026[/C][C]150.954566649997[/C][/ROW]
[ROW][C]82[/C][C]121.8[/C][C]90.1197050988906[/C][C]153.48029490111[/C][/ROW]
[ROW][C]83[/C][C]122.7[/C][C]89.4734263950767[/C][C]155.926573604923[/C][/ROW]
[ROW][C]84[/C][C]123.6[/C][C]88.895975708493[/C][C]158.304024291507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202045&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202045&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
tForecast95% Lower Bound95% Upper Bound
73113.7103.681811116668123.718188883332
74114.6100.432141410776128.767858589224
75115.598.1479878542465132.852012145754
76116.496.3636222333351136.436377766665
77117.394.8986486454359139.701351354564
78118.293.6605490890127142.739450910987
79119.192.5943636274304145.60563637257
8012091.6642828215517148.335717178448
81120.990.8454333500026150.954566649997
82121.890.1197050988906153.48029490111
83122.789.4734263950767155.926573604923
84123.688.895975708493158.304024291507



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')