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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 09:14:01 -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/13/t1386944114o47xkm5n4t2fpqc.htm/, Retrieved Tue, 19 Nov 2019 08:23:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232299, Retrieved Tue, 19 Nov 2019 08:23:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 14:14:01] [a51ebb1a550b3d5f2cc4b9cf02171f8b] [Current]
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Dataseries X:
71,4
75,8
79,2
84,4
84,4
87,2
92,4
88,5
94,8
100,9
110
107,9
111,2
116,7
125,8
131,5
146,2
155,4
157,5
137,2
121,3
89,1
69,6
56,7
58,5
56,4
60,5
64,6
73,2
84,6
80,4
88,4
84,6
90,8
94,9
93,1
96,6
93,1
98,3
105
95,6
94,3
95,3
97,1
98,1
104,4
107,8
114,3
118,7
124,1
134,2
142,4
133,8
131
133,2
125,9
126,2
122,7
126,6
124,8
128
134,1
138,8
134
124
110,4
116,7
124,7
126
122,8
120,2
121,2




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=232299&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=232299&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232299&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
alpha0.99992908472251
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99992908472251 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232299&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]0.99992908472251[/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=232299&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232299&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
alpha0.99992908472251
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
275.871.44.39999999999999
379.275.7996879727793.40031202722096
484.479.1997588659295.20024113407096
584.484.3996312234570.000368776543041349
687.284.39999997384812.80000002615189
792.487.19980143722125.20019856277882
888.592.3996312264759-3.89963122647592
994.888.50027654343056.29972345656947
10100.994.7995532533636.10044674663703
11110100.8995673851269.10043261487384
12107.9109.999354640296-2.09935464029583
13111.2107.9001488763173.29985112368313
14116.7111.1997659901425.5002340098581
15125.8116.6996099493799.10039005062106
16131.5125.7993546433145.70064535668571
17146.2131.49959573715314.7004042628473
18155.4146.1989575167529.20104248324753
19157.5155.3993475055192.1006524944809
20137.2157.499851031645-20.2998510316455
21121.3137.201439569569-15.9014395695689
2289.1121.301127655-32.2011276549996
2369.689.1022835519031-19.5022835519031
2456.769.6013830098498-12.9013830098498
2558.556.70091490515611.79908509484385
2656.458.4998724173813-2.09987241738127
2760.556.40014891303524.09985108696483
2864.660.49970925792254.10029074207749
2973.264.59970922674428.60029077325576
3084.673.199390107993311.4006098920067
3180.484.599191522586-4.19919152258595
3288.480.40029778683217.99970221316795
3384.688.3994326988977-3.79943269889773
3490.884.60026943782416.19973056217586
3594.990.79956034438684.10043965561319
3693.194.899709216184-1.799709216184
3796.693.10012762687853.49987237312153
3893.196.5997518055795-3.49975180557948
3998.393.10024818587045.19975181412957
4010598.29963125815726.70036874184278
4195.6104.999524841491-9.3995248414914
4294.395.6006665699124-1.30066656991241
4395.394.30009223713070.99990776286927
4497.195.29992909126351.80007090873646
4598.197.0998723474721.00012765252799
46104.498.099929075676.30007092433002
47107.8104.3995532287223.4004467712778
48114.3107.7997588563746.50024114362637
49118.7114.2995390335964.40046096640445
50124.1118.6996879400895.4003120599105
51134.2124.09961703537210.1003829646283
52142.4134.1992837285398.20071627146069
53133.8142.39941844393-8.59941844392998
54131133.800609830145-2.80060983014522
55133.2131.0001986060232.19980139397674
56125.9133.199844000474-7.29984400047371
57126.2125.9005176704630.299482329537071
58122.7126.199978762128-3.4999787621275
59126.6122.7002482019653.89975179803487
60124.8126.599723448019-1.79972344801909
61128124.8001276278883.19987237211228
62134.1127.9997730801636.1002269198372
63138.8134.0995674007154.7004325992848
64134138.799666667518-4.79966666751793
65124134.000340369694-10.0003403696936
66110.4124.000709176912-13.6007091769123
67116.7110.4009644980656.29903550193467
68124.7116.6995533021498.00044669785053
69126124.6994326461021.30056735389762
70122.8125.999907769905-3.19990776990521
71120.2122.800226922347-2.60022692234743
72121.2120.2001843958140.999815604186267

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 75.8 & 71.4 & 4.39999999999999 \tabularnewline
3 & 79.2 & 75.799687972779 & 3.40031202722096 \tabularnewline
4 & 84.4 & 79.199758865929 & 5.20024113407096 \tabularnewline
5 & 84.4 & 84.399631223457 & 0.000368776543041349 \tabularnewline
6 & 87.2 & 84.3999999738481 & 2.80000002615189 \tabularnewline
7 & 92.4 & 87.1998014372212 & 5.20019856277882 \tabularnewline
8 & 88.5 & 92.3996312264759 & -3.89963122647592 \tabularnewline
9 & 94.8 & 88.5002765434305 & 6.29972345656947 \tabularnewline
10 & 100.9 & 94.799553253363 & 6.10044674663703 \tabularnewline
11 & 110 & 100.899567385126 & 9.10043261487384 \tabularnewline
12 & 107.9 & 109.999354640296 & -2.09935464029583 \tabularnewline
13 & 111.2 & 107.900148876317 & 3.29985112368313 \tabularnewline
14 & 116.7 & 111.199765990142 & 5.5002340098581 \tabularnewline
15 & 125.8 & 116.699609949379 & 9.10039005062106 \tabularnewline
16 & 131.5 & 125.799354643314 & 5.70064535668571 \tabularnewline
17 & 146.2 & 131.499595737153 & 14.7004042628473 \tabularnewline
18 & 155.4 & 146.198957516752 & 9.20104248324753 \tabularnewline
19 & 157.5 & 155.399347505519 & 2.1006524944809 \tabularnewline
20 & 137.2 & 157.499851031645 & -20.2998510316455 \tabularnewline
21 & 121.3 & 137.201439569569 & -15.9014395695689 \tabularnewline
22 & 89.1 & 121.301127655 & -32.2011276549996 \tabularnewline
23 & 69.6 & 89.1022835519031 & -19.5022835519031 \tabularnewline
24 & 56.7 & 69.6013830098498 & -12.9013830098498 \tabularnewline
25 & 58.5 & 56.7009149051561 & 1.79908509484385 \tabularnewline
26 & 56.4 & 58.4998724173813 & -2.09987241738127 \tabularnewline
27 & 60.5 & 56.4001489130352 & 4.09985108696483 \tabularnewline
28 & 64.6 & 60.4997092579225 & 4.10029074207749 \tabularnewline
29 & 73.2 & 64.5997092267442 & 8.60029077325576 \tabularnewline
30 & 84.6 & 73.1993901079933 & 11.4006098920067 \tabularnewline
31 & 80.4 & 84.599191522586 & -4.19919152258595 \tabularnewline
32 & 88.4 & 80.4002977868321 & 7.99970221316795 \tabularnewline
33 & 84.6 & 88.3994326988977 & -3.79943269889773 \tabularnewline
34 & 90.8 & 84.6002694378241 & 6.19973056217586 \tabularnewline
35 & 94.9 & 90.7995603443868 & 4.10043965561319 \tabularnewline
36 & 93.1 & 94.899709216184 & -1.799709216184 \tabularnewline
37 & 96.6 & 93.1001276268785 & 3.49987237312153 \tabularnewline
38 & 93.1 & 96.5997518055795 & -3.49975180557948 \tabularnewline
39 & 98.3 & 93.1002481858704 & 5.19975181412957 \tabularnewline
40 & 105 & 98.2996312581572 & 6.70036874184278 \tabularnewline
41 & 95.6 & 104.999524841491 & -9.3995248414914 \tabularnewline
42 & 94.3 & 95.6006665699124 & -1.30066656991241 \tabularnewline
43 & 95.3 & 94.3000922371307 & 0.99990776286927 \tabularnewline
44 & 97.1 & 95.2999290912635 & 1.80007090873646 \tabularnewline
45 & 98.1 & 97.099872347472 & 1.00012765252799 \tabularnewline
46 & 104.4 & 98.09992907567 & 6.30007092433002 \tabularnewline
47 & 107.8 & 104.399553228722 & 3.4004467712778 \tabularnewline
48 & 114.3 & 107.799758856374 & 6.50024114362637 \tabularnewline
49 & 118.7 & 114.299539033596 & 4.40046096640445 \tabularnewline
50 & 124.1 & 118.699687940089 & 5.4003120599105 \tabularnewline
51 & 134.2 & 124.099617035372 & 10.1003829646283 \tabularnewline
52 & 142.4 & 134.199283728539 & 8.20071627146069 \tabularnewline
53 & 133.8 & 142.39941844393 & -8.59941844392998 \tabularnewline
54 & 131 & 133.800609830145 & -2.80060983014522 \tabularnewline
55 & 133.2 & 131.000198606023 & 2.19980139397674 \tabularnewline
56 & 125.9 & 133.199844000474 & -7.29984400047371 \tabularnewline
57 & 126.2 & 125.900517670463 & 0.299482329537071 \tabularnewline
58 & 122.7 & 126.199978762128 & -3.4999787621275 \tabularnewline
59 & 126.6 & 122.700248201965 & 3.89975179803487 \tabularnewline
60 & 124.8 & 126.599723448019 & -1.79972344801909 \tabularnewline
61 & 128 & 124.800127627888 & 3.19987237211228 \tabularnewline
62 & 134.1 & 127.999773080163 & 6.1002269198372 \tabularnewline
63 & 138.8 & 134.099567400715 & 4.7004325992848 \tabularnewline
64 & 134 & 138.799666667518 & -4.79966666751793 \tabularnewline
65 & 124 & 134.000340369694 & -10.0003403696936 \tabularnewline
66 & 110.4 & 124.000709176912 & -13.6007091769123 \tabularnewline
67 & 116.7 & 110.400964498065 & 6.29903550193467 \tabularnewline
68 & 124.7 & 116.699553302149 & 8.00044669785053 \tabularnewline
69 & 126 & 124.699432646102 & 1.30056735389762 \tabularnewline
70 & 122.8 & 125.999907769905 & -3.19990776990521 \tabularnewline
71 & 120.2 & 122.800226922347 & -2.60022692234743 \tabularnewline
72 & 121.2 & 120.200184395814 & 0.999815604186267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232299&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]75.8[/C][C]71.4[/C][C]4.39999999999999[/C][/ROW]
[ROW][C]3[/C][C]79.2[/C][C]75.799687972779[/C][C]3.40031202722096[/C][/ROW]
[ROW][C]4[/C][C]84.4[/C][C]79.199758865929[/C][C]5.20024113407096[/C][/ROW]
[ROW][C]5[/C][C]84.4[/C][C]84.399631223457[/C][C]0.000368776543041349[/C][/ROW]
[ROW][C]6[/C][C]87.2[/C][C]84.3999999738481[/C][C]2.80000002615189[/C][/ROW]
[ROW][C]7[/C][C]92.4[/C][C]87.1998014372212[/C][C]5.20019856277882[/C][/ROW]
[ROW][C]8[/C][C]88.5[/C][C]92.3996312264759[/C][C]-3.89963122647592[/C][/ROW]
[ROW][C]9[/C][C]94.8[/C][C]88.5002765434305[/C][C]6.29972345656947[/C][/ROW]
[ROW][C]10[/C][C]100.9[/C][C]94.799553253363[/C][C]6.10044674663703[/C][/ROW]
[ROW][C]11[/C][C]110[/C][C]100.899567385126[/C][C]9.10043261487384[/C][/ROW]
[ROW][C]12[/C][C]107.9[/C][C]109.999354640296[/C][C]-2.09935464029583[/C][/ROW]
[ROW][C]13[/C][C]111.2[/C][C]107.900148876317[/C][C]3.29985112368313[/C][/ROW]
[ROW][C]14[/C][C]116.7[/C][C]111.199765990142[/C][C]5.5002340098581[/C][/ROW]
[ROW][C]15[/C][C]125.8[/C][C]116.699609949379[/C][C]9.10039005062106[/C][/ROW]
[ROW][C]16[/C][C]131.5[/C][C]125.799354643314[/C][C]5.70064535668571[/C][/ROW]
[ROW][C]17[/C][C]146.2[/C][C]131.499595737153[/C][C]14.7004042628473[/C][/ROW]
[ROW][C]18[/C][C]155.4[/C][C]146.198957516752[/C][C]9.20104248324753[/C][/ROW]
[ROW][C]19[/C][C]157.5[/C][C]155.399347505519[/C][C]2.1006524944809[/C][/ROW]
[ROW][C]20[/C][C]137.2[/C][C]157.499851031645[/C][C]-20.2998510316455[/C][/ROW]
[ROW][C]21[/C][C]121.3[/C][C]137.201439569569[/C][C]-15.9014395695689[/C][/ROW]
[ROW][C]22[/C][C]89.1[/C][C]121.301127655[/C][C]-32.2011276549996[/C][/ROW]
[ROW][C]23[/C][C]69.6[/C][C]89.1022835519031[/C][C]-19.5022835519031[/C][/ROW]
[ROW][C]24[/C][C]56.7[/C][C]69.6013830098498[/C][C]-12.9013830098498[/C][/ROW]
[ROW][C]25[/C][C]58.5[/C][C]56.7009149051561[/C][C]1.79908509484385[/C][/ROW]
[ROW][C]26[/C][C]56.4[/C][C]58.4998724173813[/C][C]-2.09987241738127[/C][/ROW]
[ROW][C]27[/C][C]60.5[/C][C]56.4001489130352[/C][C]4.09985108696483[/C][/ROW]
[ROW][C]28[/C][C]64.6[/C][C]60.4997092579225[/C][C]4.10029074207749[/C][/ROW]
[ROW][C]29[/C][C]73.2[/C][C]64.5997092267442[/C][C]8.60029077325576[/C][/ROW]
[ROW][C]30[/C][C]84.6[/C][C]73.1993901079933[/C][C]11.4006098920067[/C][/ROW]
[ROW][C]31[/C][C]80.4[/C][C]84.599191522586[/C][C]-4.19919152258595[/C][/ROW]
[ROW][C]32[/C][C]88.4[/C][C]80.4002977868321[/C][C]7.99970221316795[/C][/ROW]
[ROW][C]33[/C][C]84.6[/C][C]88.3994326988977[/C][C]-3.79943269889773[/C][/ROW]
[ROW][C]34[/C][C]90.8[/C][C]84.6002694378241[/C][C]6.19973056217586[/C][/ROW]
[ROW][C]35[/C][C]94.9[/C][C]90.7995603443868[/C][C]4.10043965561319[/C][/ROW]
[ROW][C]36[/C][C]93.1[/C][C]94.899709216184[/C][C]-1.799709216184[/C][/ROW]
[ROW][C]37[/C][C]96.6[/C][C]93.1001276268785[/C][C]3.49987237312153[/C][/ROW]
[ROW][C]38[/C][C]93.1[/C][C]96.5997518055795[/C][C]-3.49975180557948[/C][/ROW]
[ROW][C]39[/C][C]98.3[/C][C]93.1002481858704[/C][C]5.19975181412957[/C][/ROW]
[ROW][C]40[/C][C]105[/C][C]98.2996312581572[/C][C]6.70036874184278[/C][/ROW]
[ROW][C]41[/C][C]95.6[/C][C]104.999524841491[/C][C]-9.3995248414914[/C][/ROW]
[ROW][C]42[/C][C]94.3[/C][C]95.6006665699124[/C][C]-1.30066656991241[/C][/ROW]
[ROW][C]43[/C][C]95.3[/C][C]94.3000922371307[/C][C]0.99990776286927[/C][/ROW]
[ROW][C]44[/C][C]97.1[/C][C]95.2999290912635[/C][C]1.80007090873646[/C][/ROW]
[ROW][C]45[/C][C]98.1[/C][C]97.099872347472[/C][C]1.00012765252799[/C][/ROW]
[ROW][C]46[/C][C]104.4[/C][C]98.09992907567[/C][C]6.30007092433002[/C][/ROW]
[ROW][C]47[/C][C]107.8[/C][C]104.399553228722[/C][C]3.4004467712778[/C][/ROW]
[ROW][C]48[/C][C]114.3[/C][C]107.799758856374[/C][C]6.50024114362637[/C][/ROW]
[ROW][C]49[/C][C]118.7[/C][C]114.299539033596[/C][C]4.40046096640445[/C][/ROW]
[ROW][C]50[/C][C]124.1[/C][C]118.699687940089[/C][C]5.4003120599105[/C][/ROW]
[ROW][C]51[/C][C]134.2[/C][C]124.099617035372[/C][C]10.1003829646283[/C][/ROW]
[ROW][C]52[/C][C]142.4[/C][C]134.199283728539[/C][C]8.20071627146069[/C][/ROW]
[ROW][C]53[/C][C]133.8[/C][C]142.39941844393[/C][C]-8.59941844392998[/C][/ROW]
[ROW][C]54[/C][C]131[/C][C]133.800609830145[/C][C]-2.80060983014522[/C][/ROW]
[ROW][C]55[/C][C]133.2[/C][C]131.000198606023[/C][C]2.19980139397674[/C][/ROW]
[ROW][C]56[/C][C]125.9[/C][C]133.199844000474[/C][C]-7.29984400047371[/C][/ROW]
[ROW][C]57[/C][C]126.2[/C][C]125.900517670463[/C][C]0.299482329537071[/C][/ROW]
[ROW][C]58[/C][C]122.7[/C][C]126.199978762128[/C][C]-3.4999787621275[/C][/ROW]
[ROW][C]59[/C][C]126.6[/C][C]122.700248201965[/C][C]3.89975179803487[/C][/ROW]
[ROW][C]60[/C][C]124.8[/C][C]126.599723448019[/C][C]-1.79972344801909[/C][/ROW]
[ROW][C]61[/C][C]128[/C][C]124.800127627888[/C][C]3.19987237211228[/C][/ROW]
[ROW][C]62[/C][C]134.1[/C][C]127.999773080163[/C][C]6.1002269198372[/C][/ROW]
[ROW][C]63[/C][C]138.8[/C][C]134.099567400715[/C][C]4.7004325992848[/C][/ROW]
[ROW][C]64[/C][C]134[/C][C]138.799666667518[/C][C]-4.79966666751793[/C][/ROW]
[ROW][C]65[/C][C]124[/C][C]134.000340369694[/C][C]-10.0003403696936[/C][/ROW]
[ROW][C]66[/C][C]110.4[/C][C]124.000709176912[/C][C]-13.6007091769123[/C][/ROW]
[ROW][C]67[/C][C]116.7[/C][C]110.400964498065[/C][C]6.29903550193467[/C][/ROW]
[ROW][C]68[/C][C]124.7[/C][C]116.699553302149[/C][C]8.00044669785053[/C][/ROW]
[ROW][C]69[/C][C]126[/C][C]124.699432646102[/C][C]1.30056735389762[/C][/ROW]
[ROW][C]70[/C][C]122.8[/C][C]125.999907769905[/C][C]-3.19990776990521[/C][/ROW]
[ROW][C]71[/C][C]120.2[/C][C]122.800226922347[/C][C]-2.60022692234743[/C][/ROW]
[ROW][C]72[/C][C]121.2[/C][C]120.200184395814[/C][C]0.999815604186267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232299&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232299&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
275.871.44.39999999999999
379.275.7996879727793.40031202722096
484.479.1997588659295.20024113407096
584.484.3996312234570.000368776543041349
687.284.39999997384812.80000002615189
792.487.19980143722125.20019856277882
888.592.3996312264759-3.89963122647592
994.888.50027654343056.29972345656947
10100.994.7995532533636.10044674663703
11110100.8995673851269.10043261487384
12107.9109.999354640296-2.09935464029583
13111.2107.9001488763173.29985112368313
14116.7111.1997659901425.5002340098581
15125.8116.6996099493799.10039005062106
16131.5125.7993546433145.70064535668571
17146.2131.49959573715314.7004042628473
18155.4146.1989575167529.20104248324753
19157.5155.3993475055192.1006524944809
20137.2157.499851031645-20.2998510316455
21121.3137.201439569569-15.9014395695689
2289.1121.301127655-32.2011276549996
2369.689.1022835519031-19.5022835519031
2456.769.6013830098498-12.9013830098498
2558.556.70091490515611.79908509484385
2656.458.4998724173813-2.09987241738127
2760.556.40014891303524.09985108696483
2864.660.49970925792254.10029074207749
2973.264.59970922674428.60029077325576
3084.673.199390107993311.4006098920067
3180.484.599191522586-4.19919152258595
3288.480.40029778683217.99970221316795
3384.688.3994326988977-3.79943269889773
3490.884.60026943782416.19973056217586
3594.990.79956034438684.10043965561319
3693.194.899709216184-1.799709216184
3796.693.10012762687853.49987237312153
3893.196.5997518055795-3.49975180557948
3998.393.10024818587045.19975181412957
4010598.29963125815726.70036874184278
4195.6104.999524841491-9.3995248414914
4294.395.6006665699124-1.30066656991241
4395.394.30009223713070.99990776286927
4497.195.29992909126351.80007090873646
4598.197.0998723474721.00012765252799
46104.498.099929075676.30007092433002
47107.8104.3995532287223.4004467712778
48114.3107.7997588563746.50024114362637
49118.7114.2995390335964.40046096640445
50124.1118.6996879400895.4003120599105
51134.2124.09961703537210.1003829646283
52142.4134.1992837285398.20071627146069
53133.8142.39941844393-8.59941844392998
54131133.800609830145-2.80060983014522
55133.2131.0001986060232.19980139397674
56125.9133.199844000474-7.29984400047371
57126.2125.9005176704630.299482329537071
58122.7126.199978762128-3.4999787621275
59126.6122.7002482019653.89975179803487
60124.8126.599723448019-1.79972344801909
61128124.8001276278883.19987237211228
62134.1127.9997730801636.1002269198372
63138.8134.0995674007154.7004325992848
64134138.799666667518-4.79966666751793
65124134.000340369694-10.0003403696936
66110.4124.000709176912-13.6007091769123
67116.7110.4009644980656.29903550193467
68124.7116.6995533021498.00044669785053
69126124.6994326461021.30056735389762
70122.8125.999907769905-3.19990776990521
71120.2122.800226922347-2.60022692234743
72121.2120.2001843958140.999815604186267







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73121.199929097799105.446991374804136.952866820794
74121.19992909779998.9227008346363143.477157360962
75121.19992909779993.916330521483148.483527674115
76121.19992909779989.6957293228792152.704128872719
77121.19992909779985.9772878617623156.422570333836
78121.19992909779982.6155500328581159.78430816274
79121.19992909779979.524106850223162.875751345375
80121.19992909779976.6466574761094165.753200719489
81121.19992909779973.9440949142768168.455763281321
82121.19992909779971.3879454335737171.011912762024
83121.19992909779968.9567135693732173.443144626225
84121.19992909779966.633699422898175.7661587727

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 121.199929097799 & 105.446991374804 & 136.952866820794 \tabularnewline
74 & 121.199929097799 & 98.9227008346363 & 143.477157360962 \tabularnewline
75 & 121.199929097799 & 93.916330521483 & 148.483527674115 \tabularnewline
76 & 121.199929097799 & 89.6957293228792 & 152.704128872719 \tabularnewline
77 & 121.199929097799 & 85.9772878617623 & 156.422570333836 \tabularnewline
78 & 121.199929097799 & 82.6155500328581 & 159.78430816274 \tabularnewline
79 & 121.199929097799 & 79.524106850223 & 162.875751345375 \tabularnewline
80 & 121.199929097799 & 76.6466574761094 & 165.753200719489 \tabularnewline
81 & 121.199929097799 & 73.9440949142768 & 168.455763281321 \tabularnewline
82 & 121.199929097799 & 71.3879454335737 & 171.011912762024 \tabularnewline
83 & 121.199929097799 & 68.9567135693732 & 173.443144626225 \tabularnewline
84 & 121.199929097799 & 66.633699422898 & 175.7661587727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232299&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]121.199929097799[/C][C]105.446991374804[/C][C]136.952866820794[/C][/ROW]
[ROW][C]74[/C][C]121.199929097799[/C][C]98.9227008346363[/C][C]143.477157360962[/C][/ROW]
[ROW][C]75[/C][C]121.199929097799[/C][C]93.916330521483[/C][C]148.483527674115[/C][/ROW]
[ROW][C]76[/C][C]121.199929097799[/C][C]89.6957293228792[/C][C]152.704128872719[/C][/ROW]
[ROW][C]77[/C][C]121.199929097799[/C][C]85.9772878617623[/C][C]156.422570333836[/C][/ROW]
[ROW][C]78[/C][C]121.199929097799[/C][C]82.6155500328581[/C][C]159.78430816274[/C][/ROW]
[ROW][C]79[/C][C]121.199929097799[/C][C]79.524106850223[/C][C]162.875751345375[/C][/ROW]
[ROW][C]80[/C][C]121.199929097799[/C][C]76.6466574761094[/C][C]165.753200719489[/C][/ROW]
[ROW][C]81[/C][C]121.199929097799[/C][C]73.9440949142768[/C][C]168.455763281321[/C][/ROW]
[ROW][C]82[/C][C]121.199929097799[/C][C]71.3879454335737[/C][C]171.011912762024[/C][/ROW]
[ROW][C]83[/C][C]121.199929097799[/C][C]68.9567135693732[/C][C]173.443144626225[/C][/ROW]
[ROW][C]84[/C][C]121.199929097799[/C][C]66.633699422898[/C][C]175.7661587727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232299&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232299&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
73121.199929097799105.446991374804136.952866820794
74121.19992909779998.9227008346363143.477157360962
75121.19992909779993.916330521483148.483527674115
76121.19992909779989.6957293228792152.704128872719
77121.19992909779985.9772878617623156.422570333836
78121.19992909779982.6155500328581159.78430816274
79121.19992909779979.524106850223162.875751345375
80121.19992909779976.6466574761094165.753200719489
81121.19992909779973.9440949142768168.455763281321
82121.19992909779971.3879454335737171.011912762024
83121.19992909779968.9567135693732173.443144626225
84121.19992909779966.633699422898175.7661587727



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