Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 15 Jan 2011 09:22:02 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/15/t1295083378hwj8dbnl2n3p2z7.htm/, Retrieved Thu, 31 Oct 2024 22:52:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117320, Retrieved Thu, 31 Oct 2024 22:52:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact217
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Oefening 10 2 ] [2011-01-15 09:22:02] [208cd78e8ef15d69f7248238ad0efe72] [Current]
Feedback Forum

Post a new message
Dataseries X:
78.1
66.7
79
65.2
66.5
77.2
80.2
77.9
78
86.8
92.9
185.8
91
79.1
84.2
70.1
71.3
79.6
92.3
78.7
82.5
98.2
115.4
205.6
94
83.2
80.3
70.4
71.1
78.8
86.3
77.5
80.1
89.8
99.9
218
85.4
77.5
78.6
68.8
64.8
79.8
94.3
79.9
87.5
99.1
109.9
273.6
91.3
80.6
80.4
71.8
75.5
86.6
91.5
86.8
84.6
88.6
102.1
260.3
79
70.6
79.3
66.8
61.2
72.5
83.5
75.8
83.4
89.4
104.9
251.6
80
76.3
81.1
63.1
63.5
78.8
91.7
83.8
83.8
95.8
108.9
258.2
88.7
79.5
74.3
70.5
59.1
73.2
81.2
75
74.6
89.5
107
246.4
83.6
72.1
68.7
60.1
61.1
72.7
85.3
71.4
75.2
89.8
100.9
222.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117320&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117320&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 time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.202668867194516
beta0.0361437398259691
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.202668867194516 \tabularnewline
beta & 0.0361437398259691 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117320&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]0.202668867194516[/C][/ROW]
[ROW][C]beta[/C][C]0.0361437398259691[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117320&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
alpha0.202668867194516
beta0.0361437398259691
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139188.09073183760692.90926816239312
1479.176.87329553841152.22670446158848
1584.282.8505025734381.34949742656197
1670.169.01814573884671.08185426115332
1771.369.68947077763471.61052922236534
1879.677.22973923798972.37026076201026
1992.387.11634428860525.18365571139479
2078.785.5444416107519-6.84444161075187
2182.584.205514429794-1.70551442979406
2298.292.9080945464645.29190545353599
23115.4100.38426481385615.0157351861442
24205.6196.845312730278.75468726972954
2594106.417054500701-12.4170545007014
2683.291.7097731065047-8.50977310650472
2780.394.8935116008563-14.5935116008563
2870.477.5817227413766-7.18172274137662
2971.176.9043943348688-5.80439433486879
3078.883.3979177075786-4.59791770757859
3186.393.914725388047-7.61472538804696
3277.579.864090092618-2.36409009261804
3380.183.2689140735638-3.16891407356385
3489.896.9817464180764-7.18174641807644
3599.9109.319212890896-9.4192128908961
36218195.29314291123922.7068570887611
3785.490.371082648054-4.97108264805395
3877.579.90222471164-2.40222471163999
3978.679.131717771645-0.531717771645091
4068.870.3411711063421-1.54117110634215
4164.871.7082163191013-6.90821631910134
4279.878.73492757833171.06507242166825
4394.387.8304718261066.46952817389402
4479.980.7603608180068-0.860360818006839
4587.583.77883740969963.72116259030041
4699.195.68959361012023.41040638987981
47109.9108.4684237510751.431576248925
48273.6222.41473673667251.1852632633285
4991.3101.562640129634-10.2626401296337
5080.692.3975772484612-11.7975772484612
5180.491.4735139396573-11.0735139396573
5271.879.9235596060426-8.12355960604263
5375.575.8109847655769-0.310984765576919
5486.690.7141643328644-4.11416433286442
5591.5103.213303879361-11.7133038793611
5686.886.62468164311350.175318356886478
5784.693.5245674170871-8.92456741708712
5888.6102.550537618654-13.9505376186541
59102.1110.031774821288-7.93177482128804
60260.3261.48071595557-1.18071595557046
617980.3678716777832-1.3678716777832
6270.671.1933367828603-0.59333678286032
6379.372.61110433046126.68889566953878
6466.866.63700317159010.162996828409902
6561.270.1176405671158-8.91764056711581
6672.579.8656559948387-7.36565599483866
6783.585.2445015194096-1.74450151940964
6875.879.8261500314943-4.02615003149432
6983.478.25886632406695.1411336759331
7089.485.871147533833.52885246617002
71104.9101.5648939163013.33510608369942
72251.6260.633676763997-9.03367676399748
738077.6760984482082.32390155179208
7476.369.7904165711536.50958342884701
7581.178.42919068467652.67080931532351
7663.166.38312799317-3.28312799316996
7763.561.8455064755751.65449352442499
7878.874.97149127331683.82850872668324
7991.787.18084787589344.51915212410664
8083.881.33847809610032.46152190389965
8183.888.5686912908092-4.76869129080919
8295.892.98773301721432.81226698278569
83108.9108.4772161893090.42278381069066
84258.2257.1678593474661.03214065253366
8588.785.45390686966073.24609313033926
8679.581.2471014758121-1.74710147581214
8774.385.2458490309654-10.9458490309654
8870.565.68722967629754.81277032370252
8959.166.7809938570242-7.6809938570242
9073.279.7336713928898-6.53367139288984
9181.290.3029984040844-9.10299840408436
927579.8688352820427-4.86883528204272
9374.679.6044479095331-5.00444790953311
9489.589.7744248869431-0.274424886943137
95107102.4646934511734.53530654882677
96246.4252.236372272151-5.83637227215129
9783.680.60702214977522.9929778502248
9872.172.077217386490.0227826135099605
9968.768.8227110399023-0.122711039902256
10060.163.8242178936079-3.72421789360791
10161.152.96537322823698.13462677176308
10272.769.89327338846422.80672661153582
10385.380.23051703790475.06948296209534
10471.476.0720343238506-4.67203432385058
10575.275.7681754027945-0.568175402794523
10689.890.6699091439106-0.869909143910562
107100.9107.131345980209-6.23134598020853
108222.7246.429334884454-23.7293348844543

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 91 & 88.0907318376069 & 2.90926816239312 \tabularnewline
14 & 79.1 & 76.8732955384115 & 2.22670446158848 \tabularnewline
15 & 84.2 & 82.850502573438 & 1.34949742656197 \tabularnewline
16 & 70.1 & 69.0181457388467 & 1.08185426115332 \tabularnewline
17 & 71.3 & 69.6894707776347 & 1.61052922236534 \tabularnewline
18 & 79.6 & 77.2297392379897 & 2.37026076201026 \tabularnewline
19 & 92.3 & 87.1163442886052 & 5.18365571139479 \tabularnewline
20 & 78.7 & 85.5444416107519 & -6.84444161075187 \tabularnewline
21 & 82.5 & 84.205514429794 & -1.70551442979406 \tabularnewline
22 & 98.2 & 92.908094546464 & 5.29190545353599 \tabularnewline
23 & 115.4 & 100.384264813856 & 15.0157351861442 \tabularnewline
24 & 205.6 & 196.84531273027 & 8.75468726972954 \tabularnewline
25 & 94 & 106.417054500701 & -12.4170545007014 \tabularnewline
26 & 83.2 & 91.7097731065047 & -8.50977310650472 \tabularnewline
27 & 80.3 & 94.8935116008563 & -14.5935116008563 \tabularnewline
28 & 70.4 & 77.5817227413766 & -7.18172274137662 \tabularnewline
29 & 71.1 & 76.9043943348688 & -5.80439433486879 \tabularnewline
30 & 78.8 & 83.3979177075786 & -4.59791770757859 \tabularnewline
31 & 86.3 & 93.914725388047 & -7.61472538804696 \tabularnewline
32 & 77.5 & 79.864090092618 & -2.36409009261804 \tabularnewline
33 & 80.1 & 83.2689140735638 & -3.16891407356385 \tabularnewline
34 & 89.8 & 96.9817464180764 & -7.18174641807644 \tabularnewline
35 & 99.9 & 109.319212890896 & -9.4192128908961 \tabularnewline
36 & 218 & 195.293142911239 & 22.7068570887611 \tabularnewline
37 & 85.4 & 90.371082648054 & -4.97108264805395 \tabularnewline
38 & 77.5 & 79.90222471164 & -2.40222471163999 \tabularnewline
39 & 78.6 & 79.131717771645 & -0.531717771645091 \tabularnewline
40 & 68.8 & 70.3411711063421 & -1.54117110634215 \tabularnewline
41 & 64.8 & 71.7082163191013 & -6.90821631910134 \tabularnewline
42 & 79.8 & 78.7349275783317 & 1.06507242166825 \tabularnewline
43 & 94.3 & 87.830471826106 & 6.46952817389402 \tabularnewline
44 & 79.9 & 80.7603608180068 & -0.860360818006839 \tabularnewline
45 & 87.5 & 83.7788374096996 & 3.72116259030041 \tabularnewline
46 & 99.1 & 95.6895936101202 & 3.41040638987981 \tabularnewline
47 & 109.9 & 108.468423751075 & 1.431576248925 \tabularnewline
48 & 273.6 & 222.414736736672 & 51.1852632633285 \tabularnewline
49 & 91.3 & 101.562640129634 & -10.2626401296337 \tabularnewline
50 & 80.6 & 92.3975772484612 & -11.7975772484612 \tabularnewline
51 & 80.4 & 91.4735139396573 & -11.0735139396573 \tabularnewline
52 & 71.8 & 79.9235596060426 & -8.12355960604263 \tabularnewline
53 & 75.5 & 75.8109847655769 & -0.310984765576919 \tabularnewline
54 & 86.6 & 90.7141643328644 & -4.11416433286442 \tabularnewline
55 & 91.5 & 103.213303879361 & -11.7133038793611 \tabularnewline
56 & 86.8 & 86.6246816431135 & 0.175318356886478 \tabularnewline
57 & 84.6 & 93.5245674170871 & -8.92456741708712 \tabularnewline
58 & 88.6 & 102.550537618654 & -13.9505376186541 \tabularnewline
59 & 102.1 & 110.031774821288 & -7.93177482128804 \tabularnewline
60 & 260.3 & 261.48071595557 & -1.18071595557046 \tabularnewline
61 & 79 & 80.3678716777832 & -1.3678716777832 \tabularnewline
62 & 70.6 & 71.1933367828603 & -0.59333678286032 \tabularnewline
63 & 79.3 & 72.6111043304612 & 6.68889566953878 \tabularnewline
64 & 66.8 & 66.6370031715901 & 0.162996828409902 \tabularnewline
65 & 61.2 & 70.1176405671158 & -8.91764056711581 \tabularnewline
66 & 72.5 & 79.8656559948387 & -7.36565599483866 \tabularnewline
67 & 83.5 & 85.2445015194096 & -1.74450151940964 \tabularnewline
68 & 75.8 & 79.8261500314943 & -4.02615003149432 \tabularnewline
69 & 83.4 & 78.2588663240669 & 5.1411336759331 \tabularnewline
70 & 89.4 & 85.87114753383 & 3.52885246617002 \tabularnewline
71 & 104.9 & 101.564893916301 & 3.33510608369942 \tabularnewline
72 & 251.6 & 260.633676763997 & -9.03367676399748 \tabularnewline
73 & 80 & 77.676098448208 & 2.32390155179208 \tabularnewline
74 & 76.3 & 69.790416571153 & 6.50958342884701 \tabularnewline
75 & 81.1 & 78.4291906846765 & 2.67080931532351 \tabularnewline
76 & 63.1 & 66.38312799317 & -3.28312799316996 \tabularnewline
77 & 63.5 & 61.845506475575 & 1.65449352442499 \tabularnewline
78 & 78.8 & 74.9714912733168 & 3.82850872668324 \tabularnewline
79 & 91.7 & 87.1808478758934 & 4.51915212410664 \tabularnewline
80 & 83.8 & 81.3384780961003 & 2.46152190389965 \tabularnewline
81 & 83.8 & 88.5686912908092 & -4.76869129080919 \tabularnewline
82 & 95.8 & 92.9877330172143 & 2.81226698278569 \tabularnewline
83 & 108.9 & 108.477216189309 & 0.42278381069066 \tabularnewline
84 & 258.2 & 257.167859347466 & 1.03214065253366 \tabularnewline
85 & 88.7 & 85.4539068696607 & 3.24609313033926 \tabularnewline
86 & 79.5 & 81.2471014758121 & -1.74710147581214 \tabularnewline
87 & 74.3 & 85.2458490309654 & -10.9458490309654 \tabularnewline
88 & 70.5 & 65.6872296762975 & 4.81277032370252 \tabularnewline
89 & 59.1 & 66.7809938570242 & -7.6809938570242 \tabularnewline
90 & 73.2 & 79.7336713928898 & -6.53367139288984 \tabularnewline
91 & 81.2 & 90.3029984040844 & -9.10299840408436 \tabularnewline
92 & 75 & 79.8688352820427 & -4.86883528204272 \tabularnewline
93 & 74.6 & 79.6044479095331 & -5.00444790953311 \tabularnewline
94 & 89.5 & 89.7744248869431 & -0.274424886943137 \tabularnewline
95 & 107 & 102.464693451173 & 4.53530654882677 \tabularnewline
96 & 246.4 & 252.236372272151 & -5.83637227215129 \tabularnewline
97 & 83.6 & 80.6070221497752 & 2.9929778502248 \tabularnewline
98 & 72.1 & 72.07721738649 & 0.0227826135099605 \tabularnewline
99 & 68.7 & 68.8227110399023 & -0.122711039902256 \tabularnewline
100 & 60.1 & 63.8242178936079 & -3.72421789360791 \tabularnewline
101 & 61.1 & 52.9653732282369 & 8.13462677176308 \tabularnewline
102 & 72.7 & 69.8932733884642 & 2.80672661153582 \tabularnewline
103 & 85.3 & 80.2305170379047 & 5.06948296209534 \tabularnewline
104 & 71.4 & 76.0720343238506 & -4.67203432385058 \tabularnewline
105 & 75.2 & 75.7681754027945 & -0.568175402794523 \tabularnewline
106 & 89.8 & 90.6699091439106 & -0.869909143910562 \tabularnewline
107 & 100.9 & 107.131345980209 & -6.23134598020853 \tabularnewline
108 & 222.7 & 246.429334884454 & -23.7293348844543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117320&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]91[/C][C]88.0907318376069[/C][C]2.90926816239312[/C][/ROW]
[ROW][C]14[/C][C]79.1[/C][C]76.8732955384115[/C][C]2.22670446158848[/C][/ROW]
[ROW][C]15[/C][C]84.2[/C][C]82.850502573438[/C][C]1.34949742656197[/C][/ROW]
[ROW][C]16[/C][C]70.1[/C][C]69.0181457388467[/C][C]1.08185426115332[/C][/ROW]
[ROW][C]17[/C][C]71.3[/C][C]69.6894707776347[/C][C]1.61052922236534[/C][/ROW]
[ROW][C]18[/C][C]79.6[/C][C]77.2297392379897[/C][C]2.37026076201026[/C][/ROW]
[ROW][C]19[/C][C]92.3[/C][C]87.1163442886052[/C][C]5.18365571139479[/C][/ROW]
[ROW][C]20[/C][C]78.7[/C][C]85.5444416107519[/C][C]-6.84444161075187[/C][/ROW]
[ROW][C]21[/C][C]82.5[/C][C]84.205514429794[/C][C]-1.70551442979406[/C][/ROW]
[ROW][C]22[/C][C]98.2[/C][C]92.908094546464[/C][C]5.29190545353599[/C][/ROW]
[ROW][C]23[/C][C]115.4[/C][C]100.384264813856[/C][C]15.0157351861442[/C][/ROW]
[ROW][C]24[/C][C]205.6[/C][C]196.84531273027[/C][C]8.75468726972954[/C][/ROW]
[ROW][C]25[/C][C]94[/C][C]106.417054500701[/C][C]-12.4170545007014[/C][/ROW]
[ROW][C]26[/C][C]83.2[/C][C]91.7097731065047[/C][C]-8.50977310650472[/C][/ROW]
[ROW][C]27[/C][C]80.3[/C][C]94.8935116008563[/C][C]-14.5935116008563[/C][/ROW]
[ROW][C]28[/C][C]70.4[/C][C]77.5817227413766[/C][C]-7.18172274137662[/C][/ROW]
[ROW][C]29[/C][C]71.1[/C][C]76.9043943348688[/C][C]-5.80439433486879[/C][/ROW]
[ROW][C]30[/C][C]78.8[/C][C]83.3979177075786[/C][C]-4.59791770757859[/C][/ROW]
[ROW][C]31[/C][C]86.3[/C][C]93.914725388047[/C][C]-7.61472538804696[/C][/ROW]
[ROW][C]32[/C][C]77.5[/C][C]79.864090092618[/C][C]-2.36409009261804[/C][/ROW]
[ROW][C]33[/C][C]80.1[/C][C]83.2689140735638[/C][C]-3.16891407356385[/C][/ROW]
[ROW][C]34[/C][C]89.8[/C][C]96.9817464180764[/C][C]-7.18174641807644[/C][/ROW]
[ROW][C]35[/C][C]99.9[/C][C]109.319212890896[/C][C]-9.4192128908961[/C][/ROW]
[ROW][C]36[/C][C]218[/C][C]195.293142911239[/C][C]22.7068570887611[/C][/ROW]
[ROW][C]37[/C][C]85.4[/C][C]90.371082648054[/C][C]-4.97108264805395[/C][/ROW]
[ROW][C]38[/C][C]77.5[/C][C]79.90222471164[/C][C]-2.40222471163999[/C][/ROW]
[ROW][C]39[/C][C]78.6[/C][C]79.131717771645[/C][C]-0.531717771645091[/C][/ROW]
[ROW][C]40[/C][C]68.8[/C][C]70.3411711063421[/C][C]-1.54117110634215[/C][/ROW]
[ROW][C]41[/C][C]64.8[/C][C]71.7082163191013[/C][C]-6.90821631910134[/C][/ROW]
[ROW][C]42[/C][C]79.8[/C][C]78.7349275783317[/C][C]1.06507242166825[/C][/ROW]
[ROW][C]43[/C][C]94.3[/C][C]87.830471826106[/C][C]6.46952817389402[/C][/ROW]
[ROW][C]44[/C][C]79.9[/C][C]80.7603608180068[/C][C]-0.860360818006839[/C][/ROW]
[ROW][C]45[/C][C]87.5[/C][C]83.7788374096996[/C][C]3.72116259030041[/C][/ROW]
[ROW][C]46[/C][C]99.1[/C][C]95.6895936101202[/C][C]3.41040638987981[/C][/ROW]
[ROW][C]47[/C][C]109.9[/C][C]108.468423751075[/C][C]1.431576248925[/C][/ROW]
[ROW][C]48[/C][C]273.6[/C][C]222.414736736672[/C][C]51.1852632633285[/C][/ROW]
[ROW][C]49[/C][C]91.3[/C][C]101.562640129634[/C][C]-10.2626401296337[/C][/ROW]
[ROW][C]50[/C][C]80.6[/C][C]92.3975772484612[/C][C]-11.7975772484612[/C][/ROW]
[ROW][C]51[/C][C]80.4[/C][C]91.4735139396573[/C][C]-11.0735139396573[/C][/ROW]
[ROW][C]52[/C][C]71.8[/C][C]79.9235596060426[/C][C]-8.12355960604263[/C][/ROW]
[ROW][C]53[/C][C]75.5[/C][C]75.8109847655769[/C][C]-0.310984765576919[/C][/ROW]
[ROW][C]54[/C][C]86.6[/C][C]90.7141643328644[/C][C]-4.11416433286442[/C][/ROW]
[ROW][C]55[/C][C]91.5[/C][C]103.213303879361[/C][C]-11.7133038793611[/C][/ROW]
[ROW][C]56[/C][C]86.8[/C][C]86.6246816431135[/C][C]0.175318356886478[/C][/ROW]
[ROW][C]57[/C][C]84.6[/C][C]93.5245674170871[/C][C]-8.92456741708712[/C][/ROW]
[ROW][C]58[/C][C]88.6[/C][C]102.550537618654[/C][C]-13.9505376186541[/C][/ROW]
[ROW][C]59[/C][C]102.1[/C][C]110.031774821288[/C][C]-7.93177482128804[/C][/ROW]
[ROW][C]60[/C][C]260.3[/C][C]261.48071595557[/C][C]-1.18071595557046[/C][/ROW]
[ROW][C]61[/C][C]79[/C][C]80.3678716777832[/C][C]-1.3678716777832[/C][/ROW]
[ROW][C]62[/C][C]70.6[/C][C]71.1933367828603[/C][C]-0.59333678286032[/C][/ROW]
[ROW][C]63[/C][C]79.3[/C][C]72.6111043304612[/C][C]6.68889566953878[/C][/ROW]
[ROW][C]64[/C][C]66.8[/C][C]66.6370031715901[/C][C]0.162996828409902[/C][/ROW]
[ROW][C]65[/C][C]61.2[/C][C]70.1176405671158[/C][C]-8.91764056711581[/C][/ROW]
[ROW][C]66[/C][C]72.5[/C][C]79.8656559948387[/C][C]-7.36565599483866[/C][/ROW]
[ROW][C]67[/C][C]83.5[/C][C]85.2445015194096[/C][C]-1.74450151940964[/C][/ROW]
[ROW][C]68[/C][C]75.8[/C][C]79.8261500314943[/C][C]-4.02615003149432[/C][/ROW]
[ROW][C]69[/C][C]83.4[/C][C]78.2588663240669[/C][C]5.1411336759331[/C][/ROW]
[ROW][C]70[/C][C]89.4[/C][C]85.87114753383[/C][C]3.52885246617002[/C][/ROW]
[ROW][C]71[/C][C]104.9[/C][C]101.564893916301[/C][C]3.33510608369942[/C][/ROW]
[ROW][C]72[/C][C]251.6[/C][C]260.633676763997[/C][C]-9.03367676399748[/C][/ROW]
[ROW][C]73[/C][C]80[/C][C]77.676098448208[/C][C]2.32390155179208[/C][/ROW]
[ROW][C]74[/C][C]76.3[/C][C]69.790416571153[/C][C]6.50958342884701[/C][/ROW]
[ROW][C]75[/C][C]81.1[/C][C]78.4291906846765[/C][C]2.67080931532351[/C][/ROW]
[ROW][C]76[/C][C]63.1[/C][C]66.38312799317[/C][C]-3.28312799316996[/C][/ROW]
[ROW][C]77[/C][C]63.5[/C][C]61.845506475575[/C][C]1.65449352442499[/C][/ROW]
[ROW][C]78[/C][C]78.8[/C][C]74.9714912733168[/C][C]3.82850872668324[/C][/ROW]
[ROW][C]79[/C][C]91.7[/C][C]87.1808478758934[/C][C]4.51915212410664[/C][/ROW]
[ROW][C]80[/C][C]83.8[/C][C]81.3384780961003[/C][C]2.46152190389965[/C][/ROW]
[ROW][C]81[/C][C]83.8[/C][C]88.5686912908092[/C][C]-4.76869129080919[/C][/ROW]
[ROW][C]82[/C][C]95.8[/C][C]92.9877330172143[/C][C]2.81226698278569[/C][/ROW]
[ROW][C]83[/C][C]108.9[/C][C]108.477216189309[/C][C]0.42278381069066[/C][/ROW]
[ROW][C]84[/C][C]258.2[/C][C]257.167859347466[/C][C]1.03214065253366[/C][/ROW]
[ROW][C]85[/C][C]88.7[/C][C]85.4539068696607[/C][C]3.24609313033926[/C][/ROW]
[ROW][C]86[/C][C]79.5[/C][C]81.2471014758121[/C][C]-1.74710147581214[/C][/ROW]
[ROW][C]87[/C][C]74.3[/C][C]85.2458490309654[/C][C]-10.9458490309654[/C][/ROW]
[ROW][C]88[/C][C]70.5[/C][C]65.6872296762975[/C][C]4.81277032370252[/C][/ROW]
[ROW][C]89[/C][C]59.1[/C][C]66.7809938570242[/C][C]-7.6809938570242[/C][/ROW]
[ROW][C]90[/C][C]73.2[/C][C]79.7336713928898[/C][C]-6.53367139288984[/C][/ROW]
[ROW][C]91[/C][C]81.2[/C][C]90.3029984040844[/C][C]-9.10299840408436[/C][/ROW]
[ROW][C]92[/C][C]75[/C][C]79.8688352820427[/C][C]-4.86883528204272[/C][/ROW]
[ROW][C]93[/C][C]74.6[/C][C]79.6044479095331[/C][C]-5.00444790953311[/C][/ROW]
[ROW][C]94[/C][C]89.5[/C][C]89.7744248869431[/C][C]-0.274424886943137[/C][/ROW]
[ROW][C]95[/C][C]107[/C][C]102.464693451173[/C][C]4.53530654882677[/C][/ROW]
[ROW][C]96[/C][C]246.4[/C][C]252.236372272151[/C][C]-5.83637227215129[/C][/ROW]
[ROW][C]97[/C][C]83.6[/C][C]80.6070221497752[/C][C]2.9929778502248[/C][/ROW]
[ROW][C]98[/C][C]72.1[/C][C]72.07721738649[/C][C]0.0227826135099605[/C][/ROW]
[ROW][C]99[/C][C]68.7[/C][C]68.8227110399023[/C][C]-0.122711039902256[/C][/ROW]
[ROW][C]100[/C][C]60.1[/C][C]63.8242178936079[/C][C]-3.72421789360791[/C][/ROW]
[ROW][C]101[/C][C]61.1[/C][C]52.9653732282369[/C][C]8.13462677176308[/C][/ROW]
[ROW][C]102[/C][C]72.7[/C][C]69.8932733884642[/C][C]2.80672661153582[/C][/ROW]
[ROW][C]103[/C][C]85.3[/C][C]80.2305170379047[/C][C]5.06948296209534[/C][/ROW]
[ROW][C]104[/C][C]71.4[/C][C]76.0720343238506[/C][C]-4.67203432385058[/C][/ROW]
[ROW][C]105[/C][C]75.2[/C][C]75.7681754027945[/C][C]-0.568175402794523[/C][/ROW]
[ROW][C]106[/C][C]89.8[/C][C]90.6699091439106[/C][C]-0.869909143910562[/C][/ROW]
[ROW][C]107[/C][C]100.9[/C][C]107.131345980209[/C][C]-6.23134598020853[/C][/ROW]
[ROW][C]108[/C][C]222.7[/C][C]246.429334884454[/C][C]-23.7293348844543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117320&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
139188.09073183760692.90926816239312
1479.176.87329553841152.22670446158848
1584.282.8505025734381.34949742656197
1670.169.01814573884671.08185426115332
1771.369.68947077763471.61052922236534
1879.677.22973923798972.37026076201026
1992.387.11634428860525.18365571139479
2078.785.5444416107519-6.84444161075187
2182.584.205514429794-1.70551442979406
2298.292.9080945464645.29190545353599
23115.4100.38426481385615.0157351861442
24205.6196.845312730278.75468726972954
2594106.417054500701-12.4170545007014
2683.291.7097731065047-8.50977310650472
2780.394.8935116008563-14.5935116008563
2870.477.5817227413766-7.18172274137662
2971.176.9043943348688-5.80439433486879
3078.883.3979177075786-4.59791770757859
3186.393.914725388047-7.61472538804696
3277.579.864090092618-2.36409009261804
3380.183.2689140735638-3.16891407356385
3489.896.9817464180764-7.18174641807644
3599.9109.319212890896-9.4192128908961
36218195.29314291123922.7068570887611
3785.490.371082648054-4.97108264805395
3877.579.90222471164-2.40222471163999
3978.679.131717771645-0.531717771645091
4068.870.3411711063421-1.54117110634215
4164.871.7082163191013-6.90821631910134
4279.878.73492757833171.06507242166825
4394.387.8304718261066.46952817389402
4479.980.7603608180068-0.860360818006839
4587.583.77883740969963.72116259030041
4699.195.68959361012023.41040638987981
47109.9108.4684237510751.431576248925
48273.6222.41473673667251.1852632633285
4991.3101.562640129634-10.2626401296337
5080.692.3975772484612-11.7975772484612
5180.491.4735139396573-11.0735139396573
5271.879.9235596060426-8.12355960604263
5375.575.8109847655769-0.310984765576919
5486.690.7141643328644-4.11416433286442
5591.5103.213303879361-11.7133038793611
5686.886.62468164311350.175318356886478
5784.693.5245674170871-8.92456741708712
5888.6102.550537618654-13.9505376186541
59102.1110.031774821288-7.93177482128804
60260.3261.48071595557-1.18071595557046
617980.3678716777832-1.3678716777832
6270.671.1933367828603-0.59333678286032
6379.372.61110433046126.68889566953878
6466.866.63700317159010.162996828409902
6561.270.1176405671158-8.91764056711581
6672.579.8656559948387-7.36565599483866
6783.585.2445015194096-1.74450151940964
6875.879.8261500314943-4.02615003149432
6983.478.25886632406695.1411336759331
7089.485.871147533833.52885246617002
71104.9101.5648939163013.33510608369942
72251.6260.633676763997-9.03367676399748
738077.6760984482082.32390155179208
7476.369.7904165711536.50958342884701
7581.178.42919068467652.67080931532351
7663.166.38312799317-3.28312799316996
7763.561.8455064755751.65449352442499
7878.874.97149127331683.82850872668324
7991.787.18084787589344.51915212410664
8083.881.33847809610032.46152190389965
8183.888.5686912908092-4.76869129080919
8295.892.98773301721432.81226698278569
83108.9108.4772161893090.42278381069066
84258.2257.1678593474661.03214065253366
8588.785.45390686966073.24609313033926
8679.581.2471014758121-1.74710147581214
8774.385.2458490309654-10.9458490309654
8870.565.68722967629754.81277032370252
8959.166.7809938570242-7.6809938570242
9073.279.7336713928898-6.53367139288984
9181.290.3029984040844-9.10299840408436
927579.8688352820427-4.86883528204272
9374.679.6044479095331-5.00444790953311
9489.589.7744248869431-0.274424886943137
95107102.4646934511734.53530654882677
96246.4252.236372272151-5.83637227215129
9783.680.60702214977522.9929778502248
9872.172.077217386490.0227826135099605
9968.768.8227110399023-0.122711039902256
10060.163.8242178936079-3.72421789360791
10161.152.96537322823698.13462677176308
10272.769.89327338846422.80672661153582
10385.380.23051703790475.06948296209534
10471.476.0720343238506-4.67203432385058
10575.275.7681754027945-0.568175402794523
10689.890.6699091439106-0.869909143910562
107100.9107.131345980209-6.23134598020853
108222.7246.429334884454-23.7293348844543







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10978.060522088837161.32189091570394.7991532619712
11066.380948623810449.277232861016883.4846643866041
11162.830695305258145.344431377337180.3169592331792
11254.811254185175236.925258497917672.6972498724329
11354.015675131686635.713068541792272.3182817215811
11464.840307712259846.104534621100483.5760808034192
11576.185790162421557.000632719011195.370947605832
11662.968439854303443.318027777542882.618851931064
11766.653588743847146.522405279268486.7847722084257
11881.204051673497860.5769361890322101.831167157963
11993.347483201157872.2096309037197114.485335498596
120219.782858241138198.119817464553241.445899017723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 78.0605220888371 & 61.321890915703 & 94.7991532619712 \tabularnewline
110 & 66.3809486238104 & 49.2772328610168 & 83.4846643866041 \tabularnewline
111 & 62.8306953052581 & 45.3444313773371 & 80.3169592331792 \tabularnewline
112 & 54.8112541851752 & 36.9252584979176 & 72.6972498724329 \tabularnewline
113 & 54.0156751316866 & 35.7130685417922 & 72.3182817215811 \tabularnewline
114 & 64.8403077122598 & 46.1045346211004 & 83.5760808034192 \tabularnewline
115 & 76.1857901624215 & 57.0006327190111 & 95.370947605832 \tabularnewline
116 & 62.9684398543034 & 43.3180277775428 & 82.618851931064 \tabularnewline
117 & 66.6535887438471 & 46.5224052792684 & 86.7847722084257 \tabularnewline
118 & 81.2040516734978 & 60.5769361890322 & 101.831167157963 \tabularnewline
119 & 93.3474832011578 & 72.2096309037197 & 114.485335498596 \tabularnewline
120 & 219.782858241138 & 198.119817464553 & 241.445899017723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117320&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]109[/C][C]78.0605220888371[/C][C]61.321890915703[/C][C]94.7991532619712[/C][/ROW]
[ROW][C]110[/C][C]66.3809486238104[/C][C]49.2772328610168[/C][C]83.4846643866041[/C][/ROW]
[ROW][C]111[/C][C]62.8306953052581[/C][C]45.3444313773371[/C][C]80.3169592331792[/C][/ROW]
[ROW][C]112[/C][C]54.8112541851752[/C][C]36.9252584979176[/C][C]72.6972498724329[/C][/ROW]
[ROW][C]113[/C][C]54.0156751316866[/C][C]35.7130685417922[/C][C]72.3182817215811[/C][/ROW]
[ROW][C]114[/C][C]64.8403077122598[/C][C]46.1045346211004[/C][C]83.5760808034192[/C][/ROW]
[ROW][C]115[/C][C]76.1857901624215[/C][C]57.0006327190111[/C][C]95.370947605832[/C][/ROW]
[ROW][C]116[/C][C]62.9684398543034[/C][C]43.3180277775428[/C][C]82.618851931064[/C][/ROW]
[ROW][C]117[/C][C]66.6535887438471[/C][C]46.5224052792684[/C][C]86.7847722084257[/C][/ROW]
[ROW][C]118[/C][C]81.2040516734978[/C][C]60.5769361890322[/C][C]101.831167157963[/C][/ROW]
[ROW][C]119[/C][C]93.3474832011578[/C][C]72.2096309037197[/C][C]114.485335498596[/C][/ROW]
[ROW][C]120[/C][C]219.782858241138[/C][C]198.119817464553[/C][C]241.445899017723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117320&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
10978.060522088837161.32189091570394.7991532619712
11066.380948623810449.277232861016883.4846643866041
11162.830695305258145.344431377337180.3169592331792
11254.811254185175236.925258497917672.6972498724329
11354.015675131686635.713068541792272.3182817215811
11464.840307712259846.104534621100483.5760808034192
11576.185790162421557.000632719011195.370947605832
11662.968439854303443.318027777542882.618851931064
11766.653588743847146.522405279268486.7847722084257
11881.204051673497860.5769361890322101.831167157963
11993.347483201157872.2096309037197114.485335498596
120219.782858241138198.119817464553241.445899017723



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')