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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 24 May 2012 08:34:39 -0400
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/May/24/t1337862886ecv81sroyg3uswy.htm/, Retrieved Sun, 05 May 2024 19:47:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167315, Retrieved Sun, 05 May 2024 19:47:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-24 12:34:39] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
111
111
112
115
115
115
116
116
112
110
111
111
108
109
112
113
114
115
116
114
115
117
121
119
119
119
122
123
127
130
131
126
125
121
114
109
108
110
110
111
113
116
115
117
116
115
117
117
119
118
122
124
125
125
124
124
125
125
126
129
131
132
135
137
138
136
136
136
138
138
138
138




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167315&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167315&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955647489977
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955647489977 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167315&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999955647489977[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167315&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
alpha0.999955647489977
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21111110
31121111
4115111.999955647493.00004435251002
5115114.9998669405030.000133059497215982
6115114.9999999940985.90152637869323e-09
71161151.00000000000026
8116115.999955647494.43525100166653e-05
9112115.999999998033-3.99999999803285
10110112.00017741004-2.00017741004001
11111110.0000887128890.999911287111374
12111110.9999556514254.4348575386266e-05
13108110.999999998033-2.99999999803303
14109108.000133057530.999866942470021
15112108.9999556533913.00004434660859
16113111.9998669405031.00013305949695
17114112.9999556415881.00004435841154
18115113.9999556455231.00004435447742
19116114.9999556455231.00004435447725
20114115.999955645523-1.99995564552275
21115114.0000887030530.999911296947189
22117114.9999556514242.00004434857583
23121116.9999112930134.00008870698701
24119120.999822586026-1.99982258602553
25119119.000088697151-8.86971512841228e-05
26119119.000000003934-3.93394827824523e-09
271221192.99999999999983
28123121.999866942471.00013305753006
29127122.9999556415894.00004435841146
30130126.9998225879923.0001774120075
31131129.9998669346011.00013306539873
32126130.999955641588-4.9999556415882
33125126.000221760583-1.0002217605827
34121125.000044362346-4.00004436234566
35114121.000177412008-7.00017741200767
36109114.000310475439-5.00031047543882
37108109.00022177632-1.00022177632047
38110108.0000443623461.99995563765364
39110109.9999112969488.8703052469441e-05
40111109.9999999960661.0000000039342
41113110.999955647492.0000443525102
42116112.9999112930133.00008870698719
43115115.999866938536-0.999866938535561
44117115.0000443466081.99995565339158
45116116.999911296947-0.999911296946834
46115116.000044348576-1.00004434857583
47117115.0000443544771.999955645523
48117116.9999112969478.87030528105015e-05
49119116.9999999960662.0000000039342
50118118.99991129498-0.999911294979782
51122118.0000443485763.99995565142427
52124121.9998225919272.00017740807311
53125123.9999112871111.00008871288854
54125124.9999556435554.43564446612754e-05
55124124.999999998033-0.999999998032678
56124124.00004435251-4.43525099314002e-05
57125124.0000000019670.999999998032848
58125124.999955647494.43525099314002e-05
59126124.9999999980331.00000000196715
60129125.999955647493.00004435251012
61131128.9998669405032.00013305949722
62132130.9999112890781.00008871092157
63135131.9999556435553.00004435644456
64137134.9998669405032.00013305949739
65138136.9999112890781.00008871092157
66136137.999955643555-1.99995564355544
67136136.000088703053-8.87030527394472e-05
68136136.000000003934-3.93418986277538e-09
691381361.99999999999983
70138137.999911294988.87050200333306e-05
71138137.9999999960663.9343035496131e-09
721381381.70530256582424e-13

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 111 & 111 & 0 \tabularnewline
3 & 112 & 111 & 1 \tabularnewline
4 & 115 & 111.99995564749 & 3.00004435251002 \tabularnewline
5 & 115 & 114.999866940503 & 0.000133059497215982 \tabularnewline
6 & 115 & 114.999999994098 & 5.90152637869323e-09 \tabularnewline
7 & 116 & 115 & 1.00000000000026 \tabularnewline
8 & 116 & 115.99995564749 & 4.43525100166653e-05 \tabularnewline
9 & 112 & 115.999999998033 & -3.99999999803285 \tabularnewline
10 & 110 & 112.00017741004 & -2.00017741004001 \tabularnewline
11 & 111 & 110.000088712889 & 0.999911287111374 \tabularnewline
12 & 111 & 110.999955651425 & 4.4348575386266e-05 \tabularnewline
13 & 108 & 110.999999998033 & -2.99999999803303 \tabularnewline
14 & 109 & 108.00013305753 & 0.999866942470021 \tabularnewline
15 & 112 & 108.999955653391 & 3.00004434660859 \tabularnewline
16 & 113 & 111.999866940503 & 1.00013305949695 \tabularnewline
17 & 114 & 112.999955641588 & 1.00004435841154 \tabularnewline
18 & 115 & 113.999955645523 & 1.00004435447742 \tabularnewline
19 & 116 & 114.999955645523 & 1.00004435447725 \tabularnewline
20 & 114 & 115.999955645523 & -1.99995564552275 \tabularnewline
21 & 115 & 114.000088703053 & 0.999911296947189 \tabularnewline
22 & 117 & 114.999955651424 & 2.00004434857583 \tabularnewline
23 & 121 & 116.999911293013 & 4.00008870698701 \tabularnewline
24 & 119 & 120.999822586026 & -1.99982258602553 \tabularnewline
25 & 119 & 119.000088697151 & -8.86971512841228e-05 \tabularnewline
26 & 119 & 119.000000003934 & -3.93394827824523e-09 \tabularnewline
27 & 122 & 119 & 2.99999999999983 \tabularnewline
28 & 123 & 121.99986694247 & 1.00013305753006 \tabularnewline
29 & 127 & 122.999955641589 & 4.00004435841146 \tabularnewline
30 & 130 & 126.999822587992 & 3.0001774120075 \tabularnewline
31 & 131 & 129.999866934601 & 1.00013306539873 \tabularnewline
32 & 126 & 130.999955641588 & -4.9999556415882 \tabularnewline
33 & 125 & 126.000221760583 & -1.0002217605827 \tabularnewline
34 & 121 & 125.000044362346 & -4.00004436234566 \tabularnewline
35 & 114 & 121.000177412008 & -7.00017741200767 \tabularnewline
36 & 109 & 114.000310475439 & -5.00031047543882 \tabularnewline
37 & 108 & 109.00022177632 & -1.00022177632047 \tabularnewline
38 & 110 & 108.000044362346 & 1.99995563765364 \tabularnewline
39 & 110 & 109.999911296948 & 8.8703052469441e-05 \tabularnewline
40 & 111 & 109.999999996066 & 1.0000000039342 \tabularnewline
41 & 113 & 110.99995564749 & 2.0000443525102 \tabularnewline
42 & 116 & 112.999911293013 & 3.00008870698719 \tabularnewline
43 & 115 & 115.999866938536 & -0.999866938535561 \tabularnewline
44 & 117 & 115.000044346608 & 1.99995565339158 \tabularnewline
45 & 116 & 116.999911296947 & -0.999911296946834 \tabularnewline
46 & 115 & 116.000044348576 & -1.00004434857583 \tabularnewline
47 & 117 & 115.000044354477 & 1.999955645523 \tabularnewline
48 & 117 & 116.999911296947 & 8.87030528105015e-05 \tabularnewline
49 & 119 & 116.999999996066 & 2.0000000039342 \tabularnewline
50 & 118 & 118.99991129498 & -0.999911294979782 \tabularnewline
51 & 122 & 118.000044348576 & 3.99995565142427 \tabularnewline
52 & 124 & 121.999822591927 & 2.00017740807311 \tabularnewline
53 & 125 & 123.999911287111 & 1.00008871288854 \tabularnewline
54 & 125 & 124.999955643555 & 4.43564446612754e-05 \tabularnewline
55 & 124 & 124.999999998033 & -0.999999998032678 \tabularnewline
56 & 124 & 124.00004435251 & -4.43525099314002e-05 \tabularnewline
57 & 125 & 124.000000001967 & 0.999999998032848 \tabularnewline
58 & 125 & 124.99995564749 & 4.43525099314002e-05 \tabularnewline
59 & 126 & 124.999999998033 & 1.00000000196715 \tabularnewline
60 & 129 & 125.99995564749 & 3.00004435251012 \tabularnewline
61 & 131 & 128.999866940503 & 2.00013305949722 \tabularnewline
62 & 132 & 130.999911289078 & 1.00008871092157 \tabularnewline
63 & 135 & 131.999955643555 & 3.00004435644456 \tabularnewline
64 & 137 & 134.999866940503 & 2.00013305949739 \tabularnewline
65 & 138 & 136.999911289078 & 1.00008871092157 \tabularnewline
66 & 136 & 137.999955643555 & -1.99995564355544 \tabularnewline
67 & 136 & 136.000088703053 & -8.87030527394472e-05 \tabularnewline
68 & 136 & 136.000000003934 & -3.93418986277538e-09 \tabularnewline
69 & 138 & 136 & 1.99999999999983 \tabularnewline
70 & 138 & 137.99991129498 & 8.87050200333306e-05 \tabularnewline
71 & 138 & 137.999999996066 & 3.9343035496131e-09 \tabularnewline
72 & 138 & 138 & 1.70530256582424e-13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167315&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]2[/C][C]111[/C][C]111[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]112[/C][C]111[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]115[/C][C]111.99995564749[/C][C]3.00004435251002[/C][/ROW]
[ROW][C]5[/C][C]115[/C][C]114.999866940503[/C][C]0.000133059497215982[/C][/ROW]
[ROW][C]6[/C][C]115[/C][C]114.999999994098[/C][C]5.90152637869323e-09[/C][/ROW]
[ROW][C]7[/C][C]116[/C][C]115[/C][C]1.00000000000026[/C][/ROW]
[ROW][C]8[/C][C]116[/C][C]115.99995564749[/C][C]4.43525100166653e-05[/C][/ROW]
[ROW][C]9[/C][C]112[/C][C]115.999999998033[/C][C]-3.99999999803285[/C][/ROW]
[ROW][C]10[/C][C]110[/C][C]112.00017741004[/C][C]-2.00017741004001[/C][/ROW]
[ROW][C]11[/C][C]111[/C][C]110.000088712889[/C][C]0.999911287111374[/C][/ROW]
[ROW][C]12[/C][C]111[/C][C]110.999955651425[/C][C]4.4348575386266e-05[/C][/ROW]
[ROW][C]13[/C][C]108[/C][C]110.999999998033[/C][C]-2.99999999803303[/C][/ROW]
[ROW][C]14[/C][C]109[/C][C]108.00013305753[/C][C]0.999866942470021[/C][/ROW]
[ROW][C]15[/C][C]112[/C][C]108.999955653391[/C][C]3.00004434660859[/C][/ROW]
[ROW][C]16[/C][C]113[/C][C]111.999866940503[/C][C]1.00013305949695[/C][/ROW]
[ROW][C]17[/C][C]114[/C][C]112.999955641588[/C][C]1.00004435841154[/C][/ROW]
[ROW][C]18[/C][C]115[/C][C]113.999955645523[/C][C]1.00004435447742[/C][/ROW]
[ROW][C]19[/C][C]116[/C][C]114.999955645523[/C][C]1.00004435447725[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]115.999955645523[/C][C]-1.99995564552275[/C][/ROW]
[ROW][C]21[/C][C]115[/C][C]114.000088703053[/C][C]0.999911296947189[/C][/ROW]
[ROW][C]22[/C][C]117[/C][C]114.999955651424[/C][C]2.00004434857583[/C][/ROW]
[ROW][C]23[/C][C]121[/C][C]116.999911293013[/C][C]4.00008870698701[/C][/ROW]
[ROW][C]24[/C][C]119[/C][C]120.999822586026[/C][C]-1.99982258602553[/C][/ROW]
[ROW][C]25[/C][C]119[/C][C]119.000088697151[/C][C]-8.86971512841228e-05[/C][/ROW]
[ROW][C]26[/C][C]119[/C][C]119.000000003934[/C][C]-3.93394827824523e-09[/C][/ROW]
[ROW][C]27[/C][C]122[/C][C]119[/C][C]2.99999999999983[/C][/ROW]
[ROW][C]28[/C][C]123[/C][C]121.99986694247[/C][C]1.00013305753006[/C][/ROW]
[ROW][C]29[/C][C]127[/C][C]122.999955641589[/C][C]4.00004435841146[/C][/ROW]
[ROW][C]30[/C][C]130[/C][C]126.999822587992[/C][C]3.0001774120075[/C][/ROW]
[ROW][C]31[/C][C]131[/C][C]129.999866934601[/C][C]1.00013306539873[/C][/ROW]
[ROW][C]32[/C][C]126[/C][C]130.999955641588[/C][C]-4.9999556415882[/C][/ROW]
[ROW][C]33[/C][C]125[/C][C]126.000221760583[/C][C]-1.0002217605827[/C][/ROW]
[ROW][C]34[/C][C]121[/C][C]125.000044362346[/C][C]-4.00004436234566[/C][/ROW]
[ROW][C]35[/C][C]114[/C][C]121.000177412008[/C][C]-7.00017741200767[/C][/ROW]
[ROW][C]36[/C][C]109[/C][C]114.000310475439[/C][C]-5.00031047543882[/C][/ROW]
[ROW][C]37[/C][C]108[/C][C]109.00022177632[/C][C]-1.00022177632047[/C][/ROW]
[ROW][C]38[/C][C]110[/C][C]108.000044362346[/C][C]1.99995563765364[/C][/ROW]
[ROW][C]39[/C][C]110[/C][C]109.999911296948[/C][C]8.8703052469441e-05[/C][/ROW]
[ROW][C]40[/C][C]111[/C][C]109.999999996066[/C][C]1.0000000039342[/C][/ROW]
[ROW][C]41[/C][C]113[/C][C]110.99995564749[/C][C]2.0000443525102[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]112.999911293013[/C][C]3.00008870698719[/C][/ROW]
[ROW][C]43[/C][C]115[/C][C]115.999866938536[/C][C]-0.999866938535561[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]115.000044346608[/C][C]1.99995565339158[/C][/ROW]
[ROW][C]45[/C][C]116[/C][C]116.999911296947[/C][C]-0.999911296946834[/C][/ROW]
[ROW][C]46[/C][C]115[/C][C]116.000044348576[/C][C]-1.00004434857583[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]115.000044354477[/C][C]1.999955645523[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]116.999911296947[/C][C]8.87030528105015e-05[/C][/ROW]
[ROW][C]49[/C][C]119[/C][C]116.999999996066[/C][C]2.0000000039342[/C][/ROW]
[ROW][C]50[/C][C]118[/C][C]118.99991129498[/C][C]-0.999911294979782[/C][/ROW]
[ROW][C]51[/C][C]122[/C][C]118.000044348576[/C][C]3.99995565142427[/C][/ROW]
[ROW][C]52[/C][C]124[/C][C]121.999822591927[/C][C]2.00017740807311[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]123.999911287111[/C][C]1.00008871288854[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]124.999955643555[/C][C]4.43564446612754e-05[/C][/ROW]
[ROW][C]55[/C][C]124[/C][C]124.999999998033[/C][C]-0.999999998032678[/C][/ROW]
[ROW][C]56[/C][C]124[/C][C]124.00004435251[/C][C]-4.43525099314002e-05[/C][/ROW]
[ROW][C]57[/C][C]125[/C][C]124.000000001967[/C][C]0.999999998032848[/C][/ROW]
[ROW][C]58[/C][C]125[/C][C]124.99995564749[/C][C]4.43525099314002e-05[/C][/ROW]
[ROW][C]59[/C][C]126[/C][C]124.999999998033[/C][C]1.00000000196715[/C][/ROW]
[ROW][C]60[/C][C]129[/C][C]125.99995564749[/C][C]3.00004435251012[/C][/ROW]
[ROW][C]61[/C][C]131[/C][C]128.999866940503[/C][C]2.00013305949722[/C][/ROW]
[ROW][C]62[/C][C]132[/C][C]130.999911289078[/C][C]1.00008871092157[/C][/ROW]
[ROW][C]63[/C][C]135[/C][C]131.999955643555[/C][C]3.00004435644456[/C][/ROW]
[ROW][C]64[/C][C]137[/C][C]134.999866940503[/C][C]2.00013305949739[/C][/ROW]
[ROW][C]65[/C][C]138[/C][C]136.999911289078[/C][C]1.00008871092157[/C][/ROW]
[ROW][C]66[/C][C]136[/C][C]137.999955643555[/C][C]-1.99995564355544[/C][/ROW]
[ROW][C]67[/C][C]136[/C][C]136.000088703053[/C][C]-8.87030527394472e-05[/C][/ROW]
[ROW][C]68[/C][C]136[/C][C]136.000000003934[/C][C]-3.93418986277538e-09[/C][/ROW]
[ROW][C]69[/C][C]138[/C][C]136[/C][C]1.99999999999983[/C][/ROW]
[ROW][C]70[/C][C]138[/C][C]137.99991129498[/C][C]8.87050200333306e-05[/C][/ROW]
[ROW][C]71[/C][C]138[/C][C]137.999999996066[/C][C]3.9343035496131e-09[/C][/ROW]
[ROW][C]72[/C][C]138[/C][C]138[/C][C]1.70530256582424e-13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167315&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
21111110
31121111
4115111.999955647493.00004435251002
5115114.9998669405030.000133059497215982
6115114.9999999940985.90152637869323e-09
71161151.00000000000026
8116115.999955647494.43525100166653e-05
9112115.999999998033-3.99999999803285
10110112.00017741004-2.00017741004001
11111110.0000887128890.999911287111374
12111110.9999556514254.4348575386266e-05
13108110.999999998033-2.99999999803303
14109108.000133057530.999866942470021
15112108.9999556533913.00004434660859
16113111.9998669405031.00013305949695
17114112.9999556415881.00004435841154
18115113.9999556455231.00004435447742
19116114.9999556455231.00004435447725
20114115.999955645523-1.99995564552275
21115114.0000887030530.999911296947189
22117114.9999556514242.00004434857583
23121116.9999112930134.00008870698701
24119120.999822586026-1.99982258602553
25119119.000088697151-8.86971512841228e-05
26119119.000000003934-3.93394827824523e-09
271221192.99999999999983
28123121.999866942471.00013305753006
29127122.9999556415894.00004435841146
30130126.9998225879923.0001774120075
31131129.9998669346011.00013306539873
32126130.999955641588-4.9999556415882
33125126.000221760583-1.0002217605827
34121125.000044362346-4.00004436234566
35114121.000177412008-7.00017741200767
36109114.000310475439-5.00031047543882
37108109.00022177632-1.00022177632047
38110108.0000443623461.99995563765364
39110109.9999112969488.8703052469441e-05
40111109.9999999960661.0000000039342
41113110.999955647492.0000443525102
42116112.9999112930133.00008870698719
43115115.999866938536-0.999866938535561
44117115.0000443466081.99995565339158
45116116.999911296947-0.999911296946834
46115116.000044348576-1.00004434857583
47117115.0000443544771.999955645523
48117116.9999112969478.87030528105015e-05
49119116.9999999960662.0000000039342
50118118.99991129498-0.999911294979782
51122118.0000443485763.99995565142427
52124121.9998225919272.00017740807311
53125123.9999112871111.00008871288854
54125124.9999556435554.43564446612754e-05
55124124.999999998033-0.999999998032678
56124124.00004435251-4.43525099314002e-05
57125124.0000000019670.999999998032848
58125124.999955647494.43525099314002e-05
59126124.9999999980331.00000000196715
60129125.999955647493.00004435251012
61131128.9998669405032.00013305949722
62132130.9999112890781.00008871092157
63135131.9999556435553.00004435644456
64137134.9998669405032.00013305949739
65138136.9999112890781.00008871092157
66136137.999955643555-1.99995564355544
67136136.000088703053-8.87030527394472e-05
68136136.000000003934-3.93418986277538e-09
691381361.99999999999983
70138137.999911294988.87050200333306e-05
71138137.9999999960663.9343035496131e-09
721381381.70530256582424e-13







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73138133.804559026349142.195440973651
74138132.066882050722143.933117949278
75138130.733497936648145.266502063352
76138129.609397168657146.390602831343
77138128.619041652902147.380958347098
78138127.723690198002148.276309801998
79138126.900328528137149.099671471863
80138126.133961468968149.866038531032
81138125.414173286725150.585826713275
82138124.733380321527151.266619678473
83138124.085857506483151.914142493517
84138123.467157023949152.532842976051

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 138 & 133.804559026349 & 142.195440973651 \tabularnewline
74 & 138 & 132.066882050722 & 143.933117949278 \tabularnewline
75 & 138 & 130.733497936648 & 145.266502063352 \tabularnewline
76 & 138 & 129.609397168657 & 146.390602831343 \tabularnewline
77 & 138 & 128.619041652902 & 147.380958347098 \tabularnewline
78 & 138 & 127.723690198002 & 148.276309801998 \tabularnewline
79 & 138 & 126.900328528137 & 149.099671471863 \tabularnewline
80 & 138 & 126.133961468968 & 149.866038531032 \tabularnewline
81 & 138 & 125.414173286725 & 150.585826713275 \tabularnewline
82 & 138 & 124.733380321527 & 151.266619678473 \tabularnewline
83 & 138 & 124.085857506483 & 151.914142493517 \tabularnewline
84 & 138 & 123.467157023949 & 152.532842976051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167315&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]138[/C][C]133.804559026349[/C][C]142.195440973651[/C][/ROW]
[ROW][C]74[/C][C]138[/C][C]132.066882050722[/C][C]143.933117949278[/C][/ROW]
[ROW][C]75[/C][C]138[/C][C]130.733497936648[/C][C]145.266502063352[/C][/ROW]
[ROW][C]76[/C][C]138[/C][C]129.609397168657[/C][C]146.390602831343[/C][/ROW]
[ROW][C]77[/C][C]138[/C][C]128.619041652902[/C][C]147.380958347098[/C][/ROW]
[ROW][C]78[/C][C]138[/C][C]127.723690198002[/C][C]148.276309801998[/C][/ROW]
[ROW][C]79[/C][C]138[/C][C]126.900328528137[/C][C]149.099671471863[/C][/ROW]
[ROW][C]80[/C][C]138[/C][C]126.133961468968[/C][C]149.866038531032[/C][/ROW]
[ROW][C]81[/C][C]138[/C][C]125.414173286725[/C][C]150.585826713275[/C][/ROW]
[ROW][C]82[/C][C]138[/C][C]124.733380321527[/C][C]151.266619678473[/C][/ROW]
[ROW][C]83[/C][C]138[/C][C]124.085857506483[/C][C]151.914142493517[/C][/ROW]
[ROW][C]84[/C][C]138[/C][C]123.467157023949[/C][C]152.532842976051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167315&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
73138133.804559026349142.195440973651
74138132.066882050722143.933117949278
75138130.733497936648145.266502063352
76138129.609397168657146.390602831343
77138128.619041652902147.380958347098
78138127.723690198002148.276309801998
79138126.900328528137149.099671471863
80138126.133961468968149.866038531032
81138125.414173286725150.585826713275
82138124.733380321527151.266619678473
83138124.085857506483151.914142493517
84138123.467157023949152.532842976051



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