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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Dec 2012 17:02:56 -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/18/t1355868203ezzkagpge5rv9o8.htm/, Retrieved Tue, 23 Apr 2024 07:05:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201693, Retrieved Tue, 23 Apr 2024 07:05:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-18 22:02:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
65
65.3
62.9
63.5
62.1
59.3
61.6
61.5
60.1
59.5
62.7
65.5
63.8
63.8
62.7
62.3
62.4
64.8
66.4
65.1
67.4
68.8
68.6
71.5
75
84.3
84
79.1
78.8
82.7
85.3
84.5
80.8
70.1
68.2
68.1
72.3
73.1
71.5
74.1
80.3
80.6
81.4
87.4
89.3
93.2
92.8
96.8
100.3
95.6
89
87.4
86.7
92.8
98.6
100.8
105.5
107.8
113.7
120.3
126.5
134.8
134.5
133.1
128.8
127.1
129.1
128.4
126.5
117.1
114.2
109.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201693&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]4 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=201693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201693&T=0

As an alternative you can also use a QR Code:  
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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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=201693&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=201693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201693&T=1

As an alternative you can also use a QR Code:  
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
362.965.6-2.7
463.563.20.300000000000004
562.163.8-1.7
659.362.4-3.1
761.659.62.00000000000001
861.561.9-0.399999999999999
960.161.8-1.7
1059.560.4-0.899999999999999
1162.759.82.90000000000001
1265.5632.5
1363.865.8-2
1463.864.1-0.299999999999997
1562.764.1-1.39999999999999
1662.363-0.700000000000003
1762.462.6-0.199999999999996
1864.862.72.1
1966.465.11.30000000000001
2065.166.7-1.60000000000001
2167.465.42.00000000000001
2268.867.71.09999999999999
2368.669.1-0.5
2471.568.92.60000000000001
257571.83.2
2684.375.39
278484.6-0.599999999999994
2879.184.3-5.2
2978.879.4-0.599999999999994
3082.779.13.60000000000001
3185.3832.3
3284.585.6-1.09999999999999
3380.884.8-4
3470.181.1-11
3568.270.4-2.19999999999999
3668.168.5-0.400000000000006
3772.368.43.90000000000001
3873.172.60.5
3971.573.4-1.89999999999999
4074.171.82.3
4180.374.45.90000000000001
4280.680.60
4381.480.90.500000000000014
4487.481.75.7
4589.387.71.59999999999999
4693.289.63.60000000000001
4792.893.5-0.700000000000003
4896.893.13.7
49100.397.13.2
5095.6100.6-5
518995.9-6.89999999999999
5287.489.3-1.89999999999999
5386.787.7-1
5492.8875.8
5598.693.15.5
56100.898.91.90000000000001
57105.5101.14.40000000000001
58107.8105.82
59113.7108.15.60000000000001
60120.31146.3
61126.5120.65.90000000000001
62134.8126.88.00000000000001
63134.5135.1-0.600000000000023
64133.1134.8-1.70000000000002
65128.8133.4-4.59999999999997
66127.1129.1-2.00000000000003
67129.1127.41.7
68128.4129.4-0.999999999999972
69126.5128.7-2.19999999999999
70117.1126.8-9.7
71114.2117.4-3.19999999999999
72109.1114.5-5.40000000000001

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 62.9 & 65.6 & -2.7 \tabularnewline
4 & 63.5 & 63.2 & 0.300000000000004 \tabularnewline
5 & 62.1 & 63.8 & -1.7 \tabularnewline
6 & 59.3 & 62.4 & -3.1 \tabularnewline
7 & 61.6 & 59.6 & 2.00000000000001 \tabularnewline
8 & 61.5 & 61.9 & -0.399999999999999 \tabularnewline
9 & 60.1 & 61.8 & -1.7 \tabularnewline
10 & 59.5 & 60.4 & -0.899999999999999 \tabularnewline
11 & 62.7 & 59.8 & 2.90000000000001 \tabularnewline
12 & 65.5 & 63 & 2.5 \tabularnewline
13 & 63.8 & 65.8 & -2 \tabularnewline
14 & 63.8 & 64.1 & -0.299999999999997 \tabularnewline
15 & 62.7 & 64.1 & -1.39999999999999 \tabularnewline
16 & 62.3 & 63 & -0.700000000000003 \tabularnewline
17 & 62.4 & 62.6 & -0.199999999999996 \tabularnewline
18 & 64.8 & 62.7 & 2.1 \tabularnewline
19 & 66.4 & 65.1 & 1.30000000000001 \tabularnewline
20 & 65.1 & 66.7 & -1.60000000000001 \tabularnewline
21 & 67.4 & 65.4 & 2.00000000000001 \tabularnewline
22 & 68.8 & 67.7 & 1.09999999999999 \tabularnewline
23 & 68.6 & 69.1 & -0.5 \tabularnewline
24 & 71.5 & 68.9 & 2.60000000000001 \tabularnewline
25 & 75 & 71.8 & 3.2 \tabularnewline
26 & 84.3 & 75.3 & 9 \tabularnewline
27 & 84 & 84.6 & -0.599999999999994 \tabularnewline
28 & 79.1 & 84.3 & -5.2 \tabularnewline
29 & 78.8 & 79.4 & -0.599999999999994 \tabularnewline
30 & 82.7 & 79.1 & 3.60000000000001 \tabularnewline
31 & 85.3 & 83 & 2.3 \tabularnewline
32 & 84.5 & 85.6 & -1.09999999999999 \tabularnewline
33 & 80.8 & 84.8 & -4 \tabularnewline
34 & 70.1 & 81.1 & -11 \tabularnewline
35 & 68.2 & 70.4 & -2.19999999999999 \tabularnewline
36 & 68.1 & 68.5 & -0.400000000000006 \tabularnewline
37 & 72.3 & 68.4 & 3.90000000000001 \tabularnewline
38 & 73.1 & 72.6 & 0.5 \tabularnewline
39 & 71.5 & 73.4 & -1.89999999999999 \tabularnewline
40 & 74.1 & 71.8 & 2.3 \tabularnewline
41 & 80.3 & 74.4 & 5.90000000000001 \tabularnewline
42 & 80.6 & 80.6 & 0 \tabularnewline
43 & 81.4 & 80.9 & 0.500000000000014 \tabularnewline
44 & 87.4 & 81.7 & 5.7 \tabularnewline
45 & 89.3 & 87.7 & 1.59999999999999 \tabularnewline
46 & 93.2 & 89.6 & 3.60000000000001 \tabularnewline
47 & 92.8 & 93.5 & -0.700000000000003 \tabularnewline
48 & 96.8 & 93.1 & 3.7 \tabularnewline
49 & 100.3 & 97.1 & 3.2 \tabularnewline
50 & 95.6 & 100.6 & -5 \tabularnewline
51 & 89 & 95.9 & -6.89999999999999 \tabularnewline
52 & 87.4 & 89.3 & -1.89999999999999 \tabularnewline
53 & 86.7 & 87.7 & -1 \tabularnewline
54 & 92.8 & 87 & 5.8 \tabularnewline
55 & 98.6 & 93.1 & 5.5 \tabularnewline
56 & 100.8 & 98.9 & 1.90000000000001 \tabularnewline
57 & 105.5 & 101.1 & 4.40000000000001 \tabularnewline
58 & 107.8 & 105.8 & 2 \tabularnewline
59 & 113.7 & 108.1 & 5.60000000000001 \tabularnewline
60 & 120.3 & 114 & 6.3 \tabularnewline
61 & 126.5 & 120.6 & 5.90000000000001 \tabularnewline
62 & 134.8 & 126.8 & 8.00000000000001 \tabularnewline
63 & 134.5 & 135.1 & -0.600000000000023 \tabularnewline
64 & 133.1 & 134.8 & -1.70000000000002 \tabularnewline
65 & 128.8 & 133.4 & -4.59999999999997 \tabularnewline
66 & 127.1 & 129.1 & -2.00000000000003 \tabularnewline
67 & 129.1 & 127.4 & 1.7 \tabularnewline
68 & 128.4 & 129.4 & -0.999999999999972 \tabularnewline
69 & 126.5 & 128.7 & -2.19999999999999 \tabularnewline
70 & 117.1 & 126.8 & -9.7 \tabularnewline
71 & 114.2 & 117.4 & -3.19999999999999 \tabularnewline
72 & 109.1 & 114.5 & -5.40000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201693&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]62.9[/C][C]65.6[/C][C]-2.7[/C][/ROW]
[ROW][C]4[/C][C]63.5[/C][C]63.2[/C][C]0.300000000000004[/C][/ROW]
[ROW][C]5[/C][C]62.1[/C][C]63.8[/C][C]-1.7[/C][/ROW]
[ROW][C]6[/C][C]59.3[/C][C]62.4[/C][C]-3.1[/C][/ROW]
[ROW][C]7[/C][C]61.6[/C][C]59.6[/C][C]2.00000000000001[/C][/ROW]
[ROW][C]8[/C][C]61.5[/C][C]61.9[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]9[/C][C]60.1[/C][C]61.8[/C][C]-1.7[/C][/ROW]
[ROW][C]10[/C][C]59.5[/C][C]60.4[/C][C]-0.899999999999999[/C][/ROW]
[ROW][C]11[/C][C]62.7[/C][C]59.8[/C][C]2.90000000000001[/C][/ROW]
[ROW][C]12[/C][C]65.5[/C][C]63[/C][C]2.5[/C][/ROW]
[ROW][C]13[/C][C]63.8[/C][C]65.8[/C][C]-2[/C][/ROW]
[ROW][C]14[/C][C]63.8[/C][C]64.1[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]15[/C][C]62.7[/C][C]64.1[/C][C]-1.39999999999999[/C][/ROW]
[ROW][C]16[/C][C]62.3[/C][C]63[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]17[/C][C]62.4[/C][C]62.6[/C][C]-0.199999999999996[/C][/ROW]
[ROW][C]18[/C][C]64.8[/C][C]62.7[/C][C]2.1[/C][/ROW]
[ROW][C]19[/C][C]66.4[/C][C]65.1[/C][C]1.30000000000001[/C][/ROW]
[ROW][C]20[/C][C]65.1[/C][C]66.7[/C][C]-1.60000000000001[/C][/ROW]
[ROW][C]21[/C][C]67.4[/C][C]65.4[/C][C]2.00000000000001[/C][/ROW]
[ROW][C]22[/C][C]68.8[/C][C]67.7[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]23[/C][C]68.6[/C][C]69.1[/C][C]-0.5[/C][/ROW]
[ROW][C]24[/C][C]71.5[/C][C]68.9[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]25[/C][C]75[/C][C]71.8[/C][C]3.2[/C][/ROW]
[ROW][C]26[/C][C]84.3[/C][C]75.3[/C][C]9[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]84.6[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]28[/C][C]79.1[/C][C]84.3[/C][C]-5.2[/C][/ROW]
[ROW][C]29[/C][C]78.8[/C][C]79.4[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]30[/C][C]82.7[/C][C]79.1[/C][C]3.60000000000001[/C][/ROW]
[ROW][C]31[/C][C]85.3[/C][C]83[/C][C]2.3[/C][/ROW]
[ROW][C]32[/C][C]84.5[/C][C]85.6[/C][C]-1.09999999999999[/C][/ROW]
[ROW][C]33[/C][C]80.8[/C][C]84.8[/C][C]-4[/C][/ROW]
[ROW][C]34[/C][C]70.1[/C][C]81.1[/C][C]-11[/C][/ROW]
[ROW][C]35[/C][C]68.2[/C][C]70.4[/C][C]-2.19999999999999[/C][/ROW]
[ROW][C]36[/C][C]68.1[/C][C]68.5[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]37[/C][C]72.3[/C][C]68.4[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]38[/C][C]73.1[/C][C]72.6[/C][C]0.5[/C][/ROW]
[ROW][C]39[/C][C]71.5[/C][C]73.4[/C][C]-1.89999999999999[/C][/ROW]
[ROW][C]40[/C][C]74.1[/C][C]71.8[/C][C]2.3[/C][/ROW]
[ROW][C]41[/C][C]80.3[/C][C]74.4[/C][C]5.90000000000001[/C][/ROW]
[ROW][C]42[/C][C]80.6[/C][C]80.6[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]81.4[/C][C]80.9[/C][C]0.500000000000014[/C][/ROW]
[ROW][C]44[/C][C]87.4[/C][C]81.7[/C][C]5.7[/C][/ROW]
[ROW][C]45[/C][C]89.3[/C][C]87.7[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]46[/C][C]93.2[/C][C]89.6[/C][C]3.60000000000001[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]93.5[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]93.1[/C][C]3.7[/C][/ROW]
[ROW][C]49[/C][C]100.3[/C][C]97.1[/C][C]3.2[/C][/ROW]
[ROW][C]50[/C][C]95.6[/C][C]100.6[/C][C]-5[/C][/ROW]
[ROW][C]51[/C][C]89[/C][C]95.9[/C][C]-6.89999999999999[/C][/ROW]
[ROW][C]52[/C][C]87.4[/C][C]89.3[/C][C]-1.89999999999999[/C][/ROW]
[ROW][C]53[/C][C]86.7[/C][C]87.7[/C][C]-1[/C][/ROW]
[ROW][C]54[/C][C]92.8[/C][C]87[/C][C]5.8[/C][/ROW]
[ROW][C]55[/C][C]98.6[/C][C]93.1[/C][C]5.5[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]98.9[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]57[/C][C]105.5[/C][C]101.1[/C][C]4.40000000000001[/C][/ROW]
[ROW][C]58[/C][C]107.8[/C][C]105.8[/C][C]2[/C][/ROW]
[ROW][C]59[/C][C]113.7[/C][C]108.1[/C][C]5.60000000000001[/C][/ROW]
[ROW][C]60[/C][C]120.3[/C][C]114[/C][C]6.3[/C][/ROW]
[ROW][C]61[/C][C]126.5[/C][C]120.6[/C][C]5.90000000000001[/C][/ROW]
[ROW][C]62[/C][C]134.8[/C][C]126.8[/C][C]8.00000000000001[/C][/ROW]
[ROW][C]63[/C][C]134.5[/C][C]135.1[/C][C]-0.600000000000023[/C][/ROW]
[ROW][C]64[/C][C]133.1[/C][C]134.8[/C][C]-1.70000000000002[/C][/ROW]
[ROW][C]65[/C][C]128.8[/C][C]133.4[/C][C]-4.59999999999997[/C][/ROW]
[ROW][C]66[/C][C]127.1[/C][C]129.1[/C][C]-2.00000000000003[/C][/ROW]
[ROW][C]67[/C][C]129.1[/C][C]127.4[/C][C]1.7[/C][/ROW]
[ROW][C]68[/C][C]128.4[/C][C]129.4[/C][C]-0.999999999999972[/C][/ROW]
[ROW][C]69[/C][C]126.5[/C][C]128.7[/C][C]-2.19999999999999[/C][/ROW]
[ROW][C]70[/C][C]117.1[/C][C]126.8[/C][C]-9.7[/C][/ROW]
[ROW][C]71[/C][C]114.2[/C][C]117.4[/C][C]-3.19999999999999[/C][/ROW]
[ROW][C]72[/C][C]109.1[/C][C]114.5[/C][C]-5.40000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201693&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
362.965.6-2.7
463.563.20.300000000000004
562.163.8-1.7
659.362.4-3.1
761.659.62.00000000000001
861.561.9-0.399999999999999
960.161.8-1.7
1059.560.4-0.899999999999999
1162.759.82.90000000000001
1265.5632.5
1363.865.8-2
1463.864.1-0.299999999999997
1562.764.1-1.39999999999999
1662.363-0.700000000000003
1762.462.6-0.199999999999996
1864.862.72.1
1966.465.11.30000000000001
2065.166.7-1.60000000000001
2167.465.42.00000000000001
2268.867.71.09999999999999
2368.669.1-0.5
2471.568.92.60000000000001
257571.83.2
2684.375.39
278484.6-0.599999999999994
2879.184.3-5.2
2978.879.4-0.599999999999994
3082.779.13.60000000000001
3185.3832.3
3284.585.6-1.09999999999999
3380.884.8-4
3470.181.1-11
3568.270.4-2.19999999999999
3668.168.5-0.400000000000006
3772.368.43.90000000000001
3873.172.60.5
3971.573.4-1.89999999999999
4074.171.82.3
4180.374.45.90000000000001
4280.680.60
4381.480.90.500000000000014
4487.481.75.7
4589.387.71.59999999999999
4693.289.63.60000000000001
4792.893.5-0.700000000000003
4896.893.13.7
49100.397.13.2
5095.6100.6-5
518995.9-6.89999999999999
5287.489.3-1.89999999999999
5386.787.7-1
5492.8875.8
5598.693.15.5
56100.898.91.90000000000001
57105.5101.14.40000000000001
58107.8105.82
59113.7108.15.60000000000001
60120.31146.3
61126.5120.65.90000000000001
62134.8126.88.00000000000001
63134.5135.1-0.600000000000023
64133.1134.8-1.70000000000002
65128.8133.4-4.59999999999997
66127.1129.1-2.00000000000003
67129.1127.41.7
68128.4129.4-0.999999999999972
69126.5128.7-2.19999999999999
70117.1126.8-9.7
71114.2117.4-3.19999999999999
72109.1114.5-5.40000000000001






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73109.4102.001058495942116.798941504058
74109.799.2363165777563120.163683422244
7511097.1846573927418122.815342607258
76110.395.5021169918844125.097883008116
77110.694.0554638353822127.144536164618
78110.992.7763686783577129.023631321642
79111.291.6242408151489130.775759184851
80111.590.5726331555125132.427366844487
81111.889.6031754878266133.996824512173
82112.188.7024925728254135.497507427175
83112.487.8604871852524136.939512814748
84112.787.0693147854836138.330685214516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 109.4 & 102.001058495942 & 116.798941504058 \tabularnewline
74 & 109.7 & 99.2363165777563 & 120.163683422244 \tabularnewline
75 & 110 & 97.1846573927418 & 122.815342607258 \tabularnewline
76 & 110.3 & 95.5021169918844 & 125.097883008116 \tabularnewline
77 & 110.6 & 94.0554638353822 & 127.144536164618 \tabularnewline
78 & 110.9 & 92.7763686783577 & 129.023631321642 \tabularnewline
79 & 111.2 & 91.6242408151489 & 130.775759184851 \tabularnewline
80 & 111.5 & 90.5726331555125 & 132.427366844487 \tabularnewline
81 & 111.8 & 89.6031754878266 & 133.996824512173 \tabularnewline
82 & 112.1 & 88.7024925728254 & 135.497507427175 \tabularnewline
83 & 112.4 & 87.8604871852524 & 136.939512814748 \tabularnewline
84 & 112.7 & 87.0693147854836 & 138.330685214516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201693&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]109.4[/C][C]102.001058495942[/C][C]116.798941504058[/C][/ROW]
[ROW][C]74[/C][C]109.7[/C][C]99.2363165777563[/C][C]120.163683422244[/C][/ROW]
[ROW][C]75[/C][C]110[/C][C]97.1846573927418[/C][C]122.815342607258[/C][/ROW]
[ROW][C]76[/C][C]110.3[/C][C]95.5021169918844[/C][C]125.097883008116[/C][/ROW]
[ROW][C]77[/C][C]110.6[/C][C]94.0554638353822[/C][C]127.144536164618[/C][/ROW]
[ROW][C]78[/C][C]110.9[/C][C]92.7763686783577[/C][C]129.023631321642[/C][/ROW]
[ROW][C]79[/C][C]111.2[/C][C]91.6242408151489[/C][C]130.775759184851[/C][/ROW]
[ROW][C]80[/C][C]111.5[/C][C]90.5726331555125[/C][C]132.427366844487[/C][/ROW]
[ROW][C]81[/C][C]111.8[/C][C]89.6031754878266[/C][C]133.996824512173[/C][/ROW]
[ROW][C]82[/C][C]112.1[/C][C]88.7024925728254[/C][C]135.497507427175[/C][/ROW]
[ROW][C]83[/C][C]112.4[/C][C]87.8604871852524[/C][C]136.939512814748[/C][/ROW]
[ROW][C]84[/C][C]112.7[/C][C]87.0693147854836[/C][C]138.330685214516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201693&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73109.4102.001058495942116.798941504058
74109.799.2363165777563120.163683422244
7511097.1846573927418122.815342607258
76110.395.5021169918844125.097883008116
77110.694.0554638353822127.144536164618
78110.992.7763686783577129.023631321642
79111.291.6242408151489130.775759184851
80111.590.5726331555125132.427366844487
81111.889.6031754878266133.996824512173
82112.188.7024925728254135.497507427175
83112.487.8604871852524136.939512814748
84112.787.0693147854836138.330685214516


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')