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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 04:37:21 -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/2013/Dec/14/t13870138847z2qc6xerak1c6n.htm/, Retrieved Fri, 26 Apr 2024 11:50:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232308, Retrieved Fri, 26 Apr 2024 11:50:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 09:37:21] [76c30f62b7052b57088120e90a652e05] [Current]
- R PD    [Exponential Smoothing] [] [2014-01-10 12:43:38] [0b3be05215961a0fa3a77d7bd3c5f728]
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Dataseries X:
55,7
59,2
59,8
61,6
65,8
64,2
67
62,8
65,5
75,2
80,9
83,2
83,7
86,4
85,9
80,4
81,8
87,5
83,7
87
99,7
101,4
101,9
115,7
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5
140
149,4
144,3
154,4
151,4
145,5
136,8
146,6
145,1
133,6
131,4
127,5
130,1
131,1
132,3
128,6
125,1
128,7
156,1
163,2
159,8
157,4
156,2
152,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ yule.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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232308&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232308&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 time5 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\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=232308&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=232308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232308&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1383.773.027083333333410.6729166666667
1486.486.6303030303031-0.230303030303062
1585.985.40113636363640.498863636363652
1680.479.8178030303030.582196969696966
1781.881.7678030303030.0321969696969688
1887.587.2053030303030.294696969696957
1983.790.930303030303-7.23030303030301
208779.13446969696977.8655303030303
2199.789.413636363636410.2863636363636
22101.4109.463636363636-8.06363636363638
23101.9107.58446969697-5.68446969696971
24115.7104.4969696969711.2030303030303
25123.2116.4678030303036.73219696969699
26136.9126.13030303030310.7696969696969
27146.8135.90113636363610.8988636363637
28149.6140.7178030303038.88219696969693
29146.5150.967803030303-4.467803030303
30157151.9053030303035.09469696969694
31147.9160.430303030303-12.530303030303
32133.6143.33446969697-9.73446969696971
33128.7136.013636363636-7.31363636363636
34100.8138.463636363636-37.6636363636364
3591.8106.98446969697-15.1844696969697
3689.394.3969696969697-5.09696969696969
3796.790.0678030303036.63219696969699
3891.699.6303030303031-8.03030303030307
3993.390.60113636363632.69886363636365
4093.387.2178030303036.08219696969697
4110194.6678030303036.33219696969698
42100.4106.405303030303-6.00530303030304
4386.9103.830303030303-16.930303030303
4483.982.33446969696971.5655303030303
4580.386.3136363636364-6.01363636363638
4687.790.0636363636364-2.36363636363637
4792.793.8844696969697-1.18446969696971
4895.595.29696969696970.203030303030303
499296.267803030303-4.26780303030301
5087.494.9303030303031-7.53030303030306
5186.886.40113636363640.398863636363643
5283.780.7178030303032.98219696969697
538585.067803030303-0.0678030303030255
5481.790.405303030303-8.70530303030304
5590.985.1303030303035.76969696969699
56101.586.334469696969715.1655303030303
57113.8103.9136363636369.88636363636363
58120.1123.563636363636-3.46363636363638
59122.1126.28446969697-4.18446969696971
60132.5124.696969696977.80303030303031
61140133.2678030303036.73219696969699
62149.4142.9303030303036.46969696969694
63144.3148.401136363636-4.10113636363633
64154.4138.21780303030316.1821969696969
65151.4155.767803030303-4.36780303030301
66145.5156.805303030303-11.3053030303031
67136.8148.930303030303-12.130303030303
68146.6132.2344696969714.3655303030303
69145.1149.013636363636-3.91363636363636
70133.6154.863636363636-21.2636363636364
71131.4139.78446969697-8.38446969696972
72127.5133.99696969697-6.4969696969697
73130.1128.2678030303031.83219696969698
74131.1133.030303030303-1.93030303030307
75132.3130.1011363636362.19886363636368
76128.6126.2178030303032.38219696969693
77125.1129.967803030303-4.86780303030301
78128.7130.505303030303-1.80530303030307
79156.1132.13030303030323.969696969697
80163.2151.5344696969711.6655303030303
81159.8165.613636363636-5.81363636363633
82157.4169.563636363636-12.1636363636364
83156.2163.58446969697-7.38446969696975
84152.5158.79696969697-6.29696969696968

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83.7 & 73.0270833333334 & 10.6729166666667 \tabularnewline
14 & 86.4 & 86.6303030303031 & -0.230303030303062 \tabularnewline
15 & 85.9 & 85.4011363636364 & 0.498863636363652 \tabularnewline
16 & 80.4 & 79.817803030303 & 0.582196969696966 \tabularnewline
17 & 81.8 & 81.767803030303 & 0.0321969696969688 \tabularnewline
18 & 87.5 & 87.205303030303 & 0.294696969696957 \tabularnewline
19 & 83.7 & 90.930303030303 & -7.23030303030301 \tabularnewline
20 & 87 & 79.1344696969697 & 7.8655303030303 \tabularnewline
21 & 99.7 & 89.4136363636364 & 10.2863636363636 \tabularnewline
22 & 101.4 & 109.463636363636 & -8.06363636363638 \tabularnewline
23 & 101.9 & 107.58446969697 & -5.68446969696971 \tabularnewline
24 & 115.7 & 104.49696969697 & 11.2030303030303 \tabularnewline
25 & 123.2 & 116.467803030303 & 6.73219696969699 \tabularnewline
26 & 136.9 & 126.130303030303 & 10.7696969696969 \tabularnewline
27 & 146.8 & 135.901136363636 & 10.8988636363637 \tabularnewline
28 & 149.6 & 140.717803030303 & 8.88219696969693 \tabularnewline
29 & 146.5 & 150.967803030303 & -4.467803030303 \tabularnewline
30 & 157 & 151.905303030303 & 5.09469696969694 \tabularnewline
31 & 147.9 & 160.430303030303 & -12.530303030303 \tabularnewline
32 & 133.6 & 143.33446969697 & -9.73446969696971 \tabularnewline
33 & 128.7 & 136.013636363636 & -7.31363636363636 \tabularnewline
34 & 100.8 & 138.463636363636 & -37.6636363636364 \tabularnewline
35 & 91.8 & 106.98446969697 & -15.1844696969697 \tabularnewline
36 & 89.3 & 94.3969696969697 & -5.09696969696969 \tabularnewline
37 & 96.7 & 90.067803030303 & 6.63219696969699 \tabularnewline
38 & 91.6 & 99.6303030303031 & -8.03030303030307 \tabularnewline
39 & 93.3 & 90.6011363636363 & 2.69886363636365 \tabularnewline
40 & 93.3 & 87.217803030303 & 6.08219696969697 \tabularnewline
41 & 101 & 94.667803030303 & 6.33219696969698 \tabularnewline
42 & 100.4 & 106.405303030303 & -6.00530303030304 \tabularnewline
43 & 86.9 & 103.830303030303 & -16.930303030303 \tabularnewline
44 & 83.9 & 82.3344696969697 & 1.5655303030303 \tabularnewline
45 & 80.3 & 86.3136363636364 & -6.01363636363638 \tabularnewline
46 & 87.7 & 90.0636363636364 & -2.36363636363637 \tabularnewline
47 & 92.7 & 93.8844696969697 & -1.18446969696971 \tabularnewline
48 & 95.5 & 95.2969696969697 & 0.203030303030303 \tabularnewline
49 & 92 & 96.267803030303 & -4.26780303030301 \tabularnewline
50 & 87.4 & 94.9303030303031 & -7.53030303030306 \tabularnewline
51 & 86.8 & 86.4011363636364 & 0.398863636363643 \tabularnewline
52 & 83.7 & 80.717803030303 & 2.98219696969697 \tabularnewline
53 & 85 & 85.067803030303 & -0.0678030303030255 \tabularnewline
54 & 81.7 & 90.405303030303 & -8.70530303030304 \tabularnewline
55 & 90.9 & 85.130303030303 & 5.76969696969699 \tabularnewline
56 & 101.5 & 86.3344696969697 & 15.1655303030303 \tabularnewline
57 & 113.8 & 103.913636363636 & 9.88636363636363 \tabularnewline
58 & 120.1 & 123.563636363636 & -3.46363636363638 \tabularnewline
59 & 122.1 & 126.28446969697 & -4.18446969696971 \tabularnewline
60 & 132.5 & 124.69696969697 & 7.80303030303031 \tabularnewline
61 & 140 & 133.267803030303 & 6.73219696969699 \tabularnewline
62 & 149.4 & 142.930303030303 & 6.46969696969694 \tabularnewline
63 & 144.3 & 148.401136363636 & -4.10113636363633 \tabularnewline
64 & 154.4 & 138.217803030303 & 16.1821969696969 \tabularnewline
65 & 151.4 & 155.767803030303 & -4.36780303030301 \tabularnewline
66 & 145.5 & 156.805303030303 & -11.3053030303031 \tabularnewline
67 & 136.8 & 148.930303030303 & -12.130303030303 \tabularnewline
68 & 146.6 & 132.23446969697 & 14.3655303030303 \tabularnewline
69 & 145.1 & 149.013636363636 & -3.91363636363636 \tabularnewline
70 & 133.6 & 154.863636363636 & -21.2636363636364 \tabularnewline
71 & 131.4 & 139.78446969697 & -8.38446969696972 \tabularnewline
72 & 127.5 & 133.99696969697 & -6.4969696969697 \tabularnewline
73 & 130.1 & 128.267803030303 & 1.83219696969698 \tabularnewline
74 & 131.1 & 133.030303030303 & -1.93030303030307 \tabularnewline
75 & 132.3 & 130.101136363636 & 2.19886363636368 \tabularnewline
76 & 128.6 & 126.217803030303 & 2.38219696969693 \tabularnewline
77 & 125.1 & 129.967803030303 & -4.86780303030301 \tabularnewline
78 & 128.7 & 130.505303030303 & -1.80530303030307 \tabularnewline
79 & 156.1 & 132.130303030303 & 23.969696969697 \tabularnewline
80 & 163.2 & 151.53446969697 & 11.6655303030303 \tabularnewline
81 & 159.8 & 165.613636363636 & -5.81363636363633 \tabularnewline
82 & 157.4 & 169.563636363636 & -12.1636363636364 \tabularnewline
83 & 156.2 & 163.58446969697 & -7.38446969696975 \tabularnewline
84 & 152.5 & 158.79696969697 & -6.29696969696968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232308&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]83.7[/C][C]73.0270833333334[/C][C]10.6729166666667[/C][/ROW]
[ROW][C]14[/C][C]86.4[/C][C]86.6303030303031[/C][C]-0.230303030303062[/C][/ROW]
[ROW][C]15[/C][C]85.9[/C][C]85.4011363636364[/C][C]0.498863636363652[/C][/ROW]
[ROW][C]16[/C][C]80.4[/C][C]79.817803030303[/C][C]0.582196969696966[/C][/ROW]
[ROW][C]17[/C][C]81.8[/C][C]81.767803030303[/C][C]0.0321969696969688[/C][/ROW]
[ROW][C]18[/C][C]87.5[/C][C]87.205303030303[/C][C]0.294696969696957[/C][/ROW]
[ROW][C]19[/C][C]83.7[/C][C]90.930303030303[/C][C]-7.23030303030301[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]79.1344696969697[/C][C]7.8655303030303[/C][/ROW]
[ROW][C]21[/C][C]99.7[/C][C]89.4136363636364[/C][C]10.2863636363636[/C][/ROW]
[ROW][C]22[/C][C]101.4[/C][C]109.463636363636[/C][C]-8.06363636363638[/C][/ROW]
[ROW][C]23[/C][C]101.9[/C][C]107.58446969697[/C][C]-5.68446969696971[/C][/ROW]
[ROW][C]24[/C][C]115.7[/C][C]104.49696969697[/C][C]11.2030303030303[/C][/ROW]
[ROW][C]25[/C][C]123.2[/C][C]116.467803030303[/C][C]6.73219696969699[/C][/ROW]
[ROW][C]26[/C][C]136.9[/C][C]126.130303030303[/C][C]10.7696969696969[/C][/ROW]
[ROW][C]27[/C][C]146.8[/C][C]135.901136363636[/C][C]10.8988636363637[/C][/ROW]
[ROW][C]28[/C][C]149.6[/C][C]140.717803030303[/C][C]8.88219696969693[/C][/ROW]
[ROW][C]29[/C][C]146.5[/C][C]150.967803030303[/C][C]-4.467803030303[/C][/ROW]
[ROW][C]30[/C][C]157[/C][C]151.905303030303[/C][C]5.09469696969694[/C][/ROW]
[ROW][C]31[/C][C]147.9[/C][C]160.430303030303[/C][C]-12.530303030303[/C][/ROW]
[ROW][C]32[/C][C]133.6[/C][C]143.33446969697[/C][C]-9.73446969696971[/C][/ROW]
[ROW][C]33[/C][C]128.7[/C][C]136.013636363636[/C][C]-7.31363636363636[/C][/ROW]
[ROW][C]34[/C][C]100.8[/C][C]138.463636363636[/C][C]-37.6636363636364[/C][/ROW]
[ROW][C]35[/C][C]91.8[/C][C]106.98446969697[/C][C]-15.1844696969697[/C][/ROW]
[ROW][C]36[/C][C]89.3[/C][C]94.3969696969697[/C][C]-5.09696969696969[/C][/ROW]
[ROW][C]37[/C][C]96.7[/C][C]90.067803030303[/C][C]6.63219696969699[/C][/ROW]
[ROW][C]38[/C][C]91.6[/C][C]99.6303030303031[/C][C]-8.03030303030307[/C][/ROW]
[ROW][C]39[/C][C]93.3[/C][C]90.6011363636363[/C][C]2.69886363636365[/C][/ROW]
[ROW][C]40[/C][C]93.3[/C][C]87.217803030303[/C][C]6.08219696969697[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]94.667803030303[/C][C]6.33219696969698[/C][/ROW]
[ROW][C]42[/C][C]100.4[/C][C]106.405303030303[/C][C]-6.00530303030304[/C][/ROW]
[ROW][C]43[/C][C]86.9[/C][C]103.830303030303[/C][C]-16.930303030303[/C][/ROW]
[ROW][C]44[/C][C]83.9[/C][C]82.3344696969697[/C][C]1.5655303030303[/C][/ROW]
[ROW][C]45[/C][C]80.3[/C][C]86.3136363636364[/C][C]-6.01363636363638[/C][/ROW]
[ROW][C]46[/C][C]87.7[/C][C]90.0636363636364[/C][C]-2.36363636363637[/C][/ROW]
[ROW][C]47[/C][C]92.7[/C][C]93.8844696969697[/C][C]-1.18446969696971[/C][/ROW]
[ROW][C]48[/C][C]95.5[/C][C]95.2969696969697[/C][C]0.203030303030303[/C][/ROW]
[ROW][C]49[/C][C]92[/C][C]96.267803030303[/C][C]-4.26780303030301[/C][/ROW]
[ROW][C]50[/C][C]87.4[/C][C]94.9303030303031[/C][C]-7.53030303030306[/C][/ROW]
[ROW][C]51[/C][C]86.8[/C][C]86.4011363636364[/C][C]0.398863636363643[/C][/ROW]
[ROW][C]52[/C][C]83.7[/C][C]80.717803030303[/C][C]2.98219696969697[/C][/ROW]
[ROW][C]53[/C][C]85[/C][C]85.067803030303[/C][C]-0.0678030303030255[/C][/ROW]
[ROW][C]54[/C][C]81.7[/C][C]90.405303030303[/C][C]-8.70530303030304[/C][/ROW]
[ROW][C]55[/C][C]90.9[/C][C]85.130303030303[/C][C]5.76969696969699[/C][/ROW]
[ROW][C]56[/C][C]101.5[/C][C]86.3344696969697[/C][C]15.1655303030303[/C][/ROW]
[ROW][C]57[/C][C]113.8[/C][C]103.913636363636[/C][C]9.88636363636363[/C][/ROW]
[ROW][C]58[/C][C]120.1[/C][C]123.563636363636[/C][C]-3.46363636363638[/C][/ROW]
[ROW][C]59[/C][C]122.1[/C][C]126.28446969697[/C][C]-4.18446969696971[/C][/ROW]
[ROW][C]60[/C][C]132.5[/C][C]124.69696969697[/C][C]7.80303030303031[/C][/ROW]
[ROW][C]61[/C][C]140[/C][C]133.267803030303[/C][C]6.73219696969699[/C][/ROW]
[ROW][C]62[/C][C]149.4[/C][C]142.930303030303[/C][C]6.46969696969694[/C][/ROW]
[ROW][C]63[/C][C]144.3[/C][C]148.401136363636[/C][C]-4.10113636363633[/C][/ROW]
[ROW][C]64[/C][C]154.4[/C][C]138.217803030303[/C][C]16.1821969696969[/C][/ROW]
[ROW][C]65[/C][C]151.4[/C][C]155.767803030303[/C][C]-4.36780303030301[/C][/ROW]
[ROW][C]66[/C][C]145.5[/C][C]156.805303030303[/C][C]-11.3053030303031[/C][/ROW]
[ROW][C]67[/C][C]136.8[/C][C]148.930303030303[/C][C]-12.130303030303[/C][/ROW]
[ROW][C]68[/C][C]146.6[/C][C]132.23446969697[/C][C]14.3655303030303[/C][/ROW]
[ROW][C]69[/C][C]145.1[/C][C]149.013636363636[/C][C]-3.91363636363636[/C][/ROW]
[ROW][C]70[/C][C]133.6[/C][C]154.863636363636[/C][C]-21.2636363636364[/C][/ROW]
[ROW][C]71[/C][C]131.4[/C][C]139.78446969697[/C][C]-8.38446969696972[/C][/ROW]
[ROW][C]72[/C][C]127.5[/C][C]133.99696969697[/C][C]-6.4969696969697[/C][/ROW]
[ROW][C]73[/C][C]130.1[/C][C]128.267803030303[/C][C]1.83219696969698[/C][/ROW]
[ROW][C]74[/C][C]131.1[/C][C]133.030303030303[/C][C]-1.93030303030307[/C][/ROW]
[ROW][C]75[/C][C]132.3[/C][C]130.101136363636[/C][C]2.19886363636368[/C][/ROW]
[ROW][C]76[/C][C]128.6[/C][C]126.217803030303[/C][C]2.38219696969693[/C][/ROW]
[ROW][C]77[/C][C]125.1[/C][C]129.967803030303[/C][C]-4.86780303030301[/C][/ROW]
[ROW][C]78[/C][C]128.7[/C][C]130.505303030303[/C][C]-1.80530303030307[/C][/ROW]
[ROW][C]79[/C][C]156.1[/C][C]132.130303030303[/C][C]23.969696969697[/C][/ROW]
[ROW][C]80[/C][C]163.2[/C][C]151.53446969697[/C][C]11.6655303030303[/C][/ROW]
[ROW][C]81[/C][C]159.8[/C][C]165.613636363636[/C][C]-5.81363636363633[/C][/ROW]
[ROW][C]82[/C][C]157.4[/C][C]169.563636363636[/C][C]-12.1636363636364[/C][/ROW]
[ROW][C]83[/C][C]156.2[/C][C]163.58446969697[/C][C]-7.38446969696975[/C][/ROW]
[ROW][C]84[/C][C]152.5[/C][C]158.79696969697[/C][C]-6.29696969696968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232308&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232308&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
1383.773.027083333333410.6729166666667
1486.486.6303030303031-0.230303030303062
1585.985.40113636363640.498863636363652
1680.479.8178030303030.582196969696966
1781.881.7678030303030.0321969696969688
1887.587.2053030303030.294696969696957
1983.790.930303030303-7.23030303030301
208779.13446969696977.8655303030303
2199.789.413636363636410.2863636363636
22101.4109.463636363636-8.06363636363638
23101.9107.58446969697-5.68446969696971
24115.7104.4969696969711.2030303030303
25123.2116.4678030303036.73219696969699
26136.9126.13030303030310.7696969696969
27146.8135.90113636363610.8988636363637
28149.6140.7178030303038.88219696969693
29146.5150.967803030303-4.467803030303
30157151.9053030303035.09469696969694
31147.9160.430303030303-12.530303030303
32133.6143.33446969697-9.73446969696971
33128.7136.013636363636-7.31363636363636
34100.8138.463636363636-37.6636363636364
3591.8106.98446969697-15.1844696969697
3689.394.3969696969697-5.09696969696969
3796.790.0678030303036.63219696969699
3891.699.6303030303031-8.03030303030307
3993.390.60113636363632.69886363636365
4093.387.2178030303036.08219696969697
4110194.6678030303036.33219696969698
42100.4106.405303030303-6.00530303030304
4386.9103.830303030303-16.930303030303
4483.982.33446969696971.5655303030303
4580.386.3136363636364-6.01363636363638
4687.790.0636363636364-2.36363636363637
4792.793.8844696969697-1.18446969696971
4895.595.29696969696970.203030303030303
499296.267803030303-4.26780303030301
5087.494.9303030303031-7.53030303030306
5186.886.40113636363640.398863636363643
5283.780.7178030303032.98219696969697
538585.067803030303-0.0678030303030255
5481.790.405303030303-8.70530303030304
5590.985.1303030303035.76969696969699
56101.586.334469696969715.1655303030303
57113.8103.9136363636369.88636363636363
58120.1123.563636363636-3.46363636363638
59122.1126.28446969697-4.18446969696971
60132.5124.696969696977.80303030303031
61140133.2678030303036.73219696969699
62149.4142.9303030303036.46969696969694
63144.3148.401136363636-4.10113636363633
64154.4138.21780303030316.1821969696969
65151.4155.767803030303-4.36780303030301
66145.5156.805303030303-11.3053030303031
67136.8148.930303030303-12.130303030303
68146.6132.2344696969714.3655303030303
69145.1149.013636363636-3.91363636363636
70133.6154.863636363636-21.2636363636364
71131.4139.78446969697-8.38446969696972
72127.5133.99696969697-6.4969696969697
73130.1128.2678030303031.83219696969698
74131.1133.030303030303-1.93030303030307
75132.3130.1011363636362.19886363636368
76128.6126.2178030303032.38219696969693
77125.1129.967803030303-4.86780303030301
78128.7130.505303030303-1.80530303030307
79156.1132.13030303030323.969696969697
80163.2151.5344696969711.6655303030303
81159.8165.613636363636-5.81363636363633
82157.4169.563636363636-12.1636363636364
83156.2163.58446969697-7.38446969696975
84152.5158.79696969697-6.29696969696968







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85153.267803030303134.45124145681172.084364603796
86156.198106060606129.587469486144182.808742635068
87155.199242424242122.608001755205187.79048309328
88149.117045454545111.48392230756186.750168601531
89150.484848484848108.409737703708192.559959265988
90155.890151515152109.799176946433201.98112608387
91159.320454545454109.536512092659209.10439699825
92154.754924242424101.533651093501207.976197391348
93157.168560606061100.718875885583213.618245326539
94166.932196969697107.429004664658226.435389274736
95173.116666666667110.709192082772235.524141250561
96175.713636363636110.531155025561240.896117701711

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 153.267803030303 & 134.45124145681 & 172.084364603796 \tabularnewline
86 & 156.198106060606 & 129.587469486144 & 182.808742635068 \tabularnewline
87 & 155.199242424242 & 122.608001755205 & 187.79048309328 \tabularnewline
88 & 149.117045454545 & 111.48392230756 & 186.750168601531 \tabularnewline
89 & 150.484848484848 & 108.409737703708 & 192.559959265988 \tabularnewline
90 & 155.890151515152 & 109.799176946433 & 201.98112608387 \tabularnewline
91 & 159.320454545454 & 109.536512092659 & 209.10439699825 \tabularnewline
92 & 154.754924242424 & 101.533651093501 & 207.976197391348 \tabularnewline
93 & 157.168560606061 & 100.718875885583 & 213.618245326539 \tabularnewline
94 & 166.932196969697 & 107.429004664658 & 226.435389274736 \tabularnewline
95 & 173.116666666667 & 110.709192082772 & 235.524141250561 \tabularnewline
96 & 175.713636363636 & 110.531155025561 & 240.896117701711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232308&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]85[/C][C]153.267803030303[/C][C]134.45124145681[/C][C]172.084364603796[/C][/ROW]
[ROW][C]86[/C][C]156.198106060606[/C][C]129.587469486144[/C][C]182.808742635068[/C][/ROW]
[ROW][C]87[/C][C]155.199242424242[/C][C]122.608001755205[/C][C]187.79048309328[/C][/ROW]
[ROW][C]88[/C][C]149.117045454545[/C][C]111.48392230756[/C][C]186.750168601531[/C][/ROW]
[ROW][C]89[/C][C]150.484848484848[/C][C]108.409737703708[/C][C]192.559959265988[/C][/ROW]
[ROW][C]90[/C][C]155.890151515152[/C][C]109.799176946433[/C][C]201.98112608387[/C][/ROW]
[ROW][C]91[/C][C]159.320454545454[/C][C]109.536512092659[/C][C]209.10439699825[/C][/ROW]
[ROW][C]92[/C][C]154.754924242424[/C][C]101.533651093501[/C][C]207.976197391348[/C][/ROW]
[ROW][C]93[/C][C]157.168560606061[/C][C]100.718875885583[/C][C]213.618245326539[/C][/ROW]
[ROW][C]94[/C][C]166.932196969697[/C][C]107.429004664658[/C][C]226.435389274736[/C][/ROW]
[ROW][C]95[/C][C]173.116666666667[/C][C]110.709192082772[/C][C]235.524141250561[/C][/ROW]
[ROW][C]96[/C][C]175.713636363636[/C][C]110.531155025561[/C][C]240.896117701711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232308&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232308&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
85153.267803030303134.45124145681172.084364603796
86156.198106060606129.587469486144182.808742635068
87155.199242424242122.608001755205187.79048309328
88149.117045454545111.48392230756186.750168601531
89150.484848484848108.409737703708192.559959265988
90155.890151515152109.799176946433201.98112608387
91159.320454545454109.536512092659209.10439699825
92154.754924242424101.533651093501207.976197391348
93157.168560606061100.718875885583213.618245326539
94166.932196969697107.429004664658226.435389274736
95173.116666666667110.709192082772235.524141250561
96175.713636363636110.531155025561240.896117701711



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')