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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 14:49:25 +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/2010/Aug/17/t1282056551x95rzg3b4t7z7c1.htm/, Retrieved Sat, 27 Apr 2024 12:50:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79139, Retrieved Sat, 27 Apr 2024 12:50:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQuaglia Laura
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2010-08-17 14:49:25] [f9e29edf9cfe01f572cce0cb5a360ea2] [Current]
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Dataseries X:
93
92
91
89
87
86
87
89
90
90
91
93
93
87
89
92
98
92
92
87
92
98
101
102
102
90
87
92
105
90
88
83
98
109
118
118
115
107
101
111
128
115
111
105
120
132
135
142
139
127
113
130
143
139
137
134
139
157
152
153
147
132
117
123
139
134
134
128
118
144
140
151
144
135
122
124
146
146
147
148
132
161
159
173




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79139&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79139&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.975824090716957
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.975824090716957 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79139&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]0.975824090716957[/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=79139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79139&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
alpha0.975824090716957
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
29293-1
39192.024175909283-1.02417590928304
48991.0247603838727-2.0247603838727
58789.0489504233604-2.04895042336041
68687.0495352395606-1.04953523956061
78786.0253734687410.97462653125902
88986.97643751739542.02356248260456
99088.9510785369921.04892146300801
109089.97464136986530.0253586301347184
119189.99938693205831.00061306794169
129390.9758092692422.02419073075798
139392.95106334852160.0489366514783853
148792.9988169119532-5.99881691195324
158987.1450268534691.85497314653104
169288.9551543374873.04484566251301
179891.92638808748226.07361191251778
189297.8531649093826-5.85316490938256
199292.141505583868-0.141505583867925
208792.0034210261586-5.00342102615863
219287.12096225283334.87903774716672
229891.8820448260366.11795517396405
2310197.85209287071653.14790712928348
24102100.9238964828111.076103517189
25102101.9739842189890.0260157810107273
2690101.999371044838-11.9993710448384
278790.2900957058336-3.29009570583359
289287.07954105531684.92045894468323
2910591.881043430922413.1189565690776
3090104.682837296098-14.6828372960978
318890.3549709424881-2.35497094248814
328388.0569335638698-5.05693356386979
339883.122255967090514.8777440329095
3410997.64031700992411.359682990076
35118108.7253693345489.2746306654522
36118117.7757773703980.224222629601698
37115117.994579214048-2.99457921404755
38107115.07239667542-8.0723966754197
39101107.195157529722-6.19515752972168
40111101.1497735664339.85022643356729
41128110.76186181932517.2381381806753
42115127.583252335135-12.5832523351354
43111115.30421156694-4.30421156693987
44105111.104058228377-6.10405822837737
45120105.14757115798814.8524288420123
46132119.64092902768312.3590709723173
47135131.7012082213513.29879177864944
48142134.9202487092167.07975129078429
49139141.828840575047-2.82884057504748
50127139.068389793119-12.0683897931185
51113127.291764296831-14.2917642968308
52130113.34551639713516.6544836028652
53143129.59736271526113.4026372847388
54139142.675979056851-3.67597905685062
55137139.088870136205-2.08887013620478
56134137.050500334917-3.05050033491693
57139134.0737486193654.92625138063516
58157138.88090339351618.1190966064837
59152156.561954364151-4.56195436415095
60153152.1102893948610.889710605138902
61147152.978490437122-5.97849043712199
62132147.144535442457-15.1445354424574
63117132.366132914991-15.3661329149907
64123117.3714902353845.628509764616
65139122.86392565853216.1360743414681
66134138.609895730536-4.60989573053624
67134134.111448420986-0.111448420985738
68128134.002694366915-6.00269436691548
69118128.145120594468-10.1451205944684
70144118.24526751515725.7547324848426
71140143.377355923837-3.3773559238374
72151140.08165065043110.9183493495688
73144150.736038976604-6.73603897660425
74135144.162849867225-9.16284986722542
75122135.221520227164-13.2215202271642
76124122.3196422735961.68035772640415
77146123.95937582404322.0406241759566
78146145.467147869380.532852130619574
79147145.9871178152291.01288218477114
80148146.9755126521871.02448734781345
81132147.975232086818-15.9752320868176
82161132.38621576170628.6137842382935
83159160.30823574801-1.30823574801045
84173159.03162778876513.9683722112353

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92 & 93 & -1 \tabularnewline
3 & 91 & 92.024175909283 & -1.02417590928304 \tabularnewline
4 & 89 & 91.0247603838727 & -2.0247603838727 \tabularnewline
5 & 87 & 89.0489504233604 & -2.04895042336041 \tabularnewline
6 & 86 & 87.0495352395606 & -1.04953523956061 \tabularnewline
7 & 87 & 86.025373468741 & 0.97462653125902 \tabularnewline
8 & 89 & 86.9764375173954 & 2.02356248260456 \tabularnewline
9 & 90 & 88.951078536992 & 1.04892146300801 \tabularnewline
10 & 90 & 89.9746413698653 & 0.0253586301347184 \tabularnewline
11 & 91 & 89.9993869320583 & 1.00061306794169 \tabularnewline
12 & 93 & 90.975809269242 & 2.02419073075798 \tabularnewline
13 & 93 & 92.9510633485216 & 0.0489366514783853 \tabularnewline
14 & 87 & 92.9988169119532 & -5.99881691195324 \tabularnewline
15 & 89 & 87.145026853469 & 1.85497314653104 \tabularnewline
16 & 92 & 88.955154337487 & 3.04484566251301 \tabularnewline
17 & 98 & 91.9263880874822 & 6.07361191251778 \tabularnewline
18 & 92 & 97.8531649093826 & -5.85316490938256 \tabularnewline
19 & 92 & 92.141505583868 & -0.141505583867925 \tabularnewline
20 & 87 & 92.0034210261586 & -5.00342102615863 \tabularnewline
21 & 92 & 87.1209622528333 & 4.87903774716672 \tabularnewline
22 & 98 & 91.882044826036 & 6.11795517396405 \tabularnewline
23 & 101 & 97.8520928707165 & 3.14790712928348 \tabularnewline
24 & 102 & 100.923896482811 & 1.076103517189 \tabularnewline
25 & 102 & 101.973984218989 & 0.0260157810107273 \tabularnewline
26 & 90 & 101.999371044838 & -11.9993710448384 \tabularnewline
27 & 87 & 90.2900957058336 & -3.29009570583359 \tabularnewline
28 & 92 & 87.0795410553168 & 4.92045894468323 \tabularnewline
29 & 105 & 91.8810434309224 & 13.1189565690776 \tabularnewline
30 & 90 & 104.682837296098 & -14.6828372960978 \tabularnewline
31 & 88 & 90.3549709424881 & -2.35497094248814 \tabularnewline
32 & 83 & 88.0569335638698 & -5.05693356386979 \tabularnewline
33 & 98 & 83.1222559670905 & 14.8777440329095 \tabularnewline
34 & 109 & 97.640317009924 & 11.359682990076 \tabularnewline
35 & 118 & 108.725369334548 & 9.2746306654522 \tabularnewline
36 & 118 & 117.775777370398 & 0.224222629601698 \tabularnewline
37 & 115 & 117.994579214048 & -2.99457921404755 \tabularnewline
38 & 107 & 115.07239667542 & -8.0723966754197 \tabularnewline
39 & 101 & 107.195157529722 & -6.19515752972168 \tabularnewline
40 & 111 & 101.149773566433 & 9.85022643356729 \tabularnewline
41 & 128 & 110.761861819325 & 17.2381381806753 \tabularnewline
42 & 115 & 127.583252335135 & -12.5832523351354 \tabularnewline
43 & 111 & 115.30421156694 & -4.30421156693987 \tabularnewline
44 & 105 & 111.104058228377 & -6.10405822837737 \tabularnewline
45 & 120 & 105.147571157988 & 14.8524288420123 \tabularnewline
46 & 132 & 119.640929027683 & 12.3590709723173 \tabularnewline
47 & 135 & 131.701208221351 & 3.29879177864944 \tabularnewline
48 & 142 & 134.920248709216 & 7.07975129078429 \tabularnewline
49 & 139 & 141.828840575047 & -2.82884057504748 \tabularnewline
50 & 127 & 139.068389793119 & -12.0683897931185 \tabularnewline
51 & 113 & 127.291764296831 & -14.2917642968308 \tabularnewline
52 & 130 & 113.345516397135 & 16.6544836028652 \tabularnewline
53 & 143 & 129.597362715261 & 13.4026372847388 \tabularnewline
54 & 139 & 142.675979056851 & -3.67597905685062 \tabularnewline
55 & 137 & 139.088870136205 & -2.08887013620478 \tabularnewline
56 & 134 & 137.050500334917 & -3.05050033491693 \tabularnewline
57 & 139 & 134.073748619365 & 4.92625138063516 \tabularnewline
58 & 157 & 138.880903393516 & 18.1190966064837 \tabularnewline
59 & 152 & 156.561954364151 & -4.56195436415095 \tabularnewline
60 & 153 & 152.110289394861 & 0.889710605138902 \tabularnewline
61 & 147 & 152.978490437122 & -5.97849043712199 \tabularnewline
62 & 132 & 147.144535442457 & -15.1445354424574 \tabularnewline
63 & 117 & 132.366132914991 & -15.3661329149907 \tabularnewline
64 & 123 & 117.371490235384 & 5.628509764616 \tabularnewline
65 & 139 & 122.863925658532 & 16.1360743414681 \tabularnewline
66 & 134 & 138.609895730536 & -4.60989573053624 \tabularnewline
67 & 134 & 134.111448420986 & -0.111448420985738 \tabularnewline
68 & 128 & 134.002694366915 & -6.00269436691548 \tabularnewline
69 & 118 & 128.145120594468 & -10.1451205944684 \tabularnewline
70 & 144 & 118.245267515157 & 25.7547324848426 \tabularnewline
71 & 140 & 143.377355923837 & -3.3773559238374 \tabularnewline
72 & 151 & 140.081650650431 & 10.9183493495688 \tabularnewline
73 & 144 & 150.736038976604 & -6.73603897660425 \tabularnewline
74 & 135 & 144.162849867225 & -9.16284986722542 \tabularnewline
75 & 122 & 135.221520227164 & -13.2215202271642 \tabularnewline
76 & 124 & 122.319642273596 & 1.68035772640415 \tabularnewline
77 & 146 & 123.959375824043 & 22.0406241759566 \tabularnewline
78 & 146 & 145.46714786938 & 0.532852130619574 \tabularnewline
79 & 147 & 145.987117815229 & 1.01288218477114 \tabularnewline
80 & 148 & 146.975512652187 & 1.02448734781345 \tabularnewline
81 & 132 & 147.975232086818 & -15.9752320868176 \tabularnewline
82 & 161 & 132.386215761706 & 28.6137842382935 \tabularnewline
83 & 159 & 160.30823574801 & -1.30823574801045 \tabularnewline
84 & 173 & 159.031627788765 & 13.9683722112353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79139&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]92[/C][C]93[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]91[/C][C]92.024175909283[/C][C]-1.02417590928304[/C][/ROW]
[ROW][C]4[/C][C]89[/C][C]91.0247603838727[/C][C]-2.0247603838727[/C][/ROW]
[ROW][C]5[/C][C]87[/C][C]89.0489504233604[/C][C]-2.04895042336041[/C][/ROW]
[ROW][C]6[/C][C]86[/C][C]87.0495352395606[/C][C]-1.04953523956061[/C][/ROW]
[ROW][C]7[/C][C]87[/C][C]86.025373468741[/C][C]0.97462653125902[/C][/ROW]
[ROW][C]8[/C][C]89[/C][C]86.9764375173954[/C][C]2.02356248260456[/C][/ROW]
[ROW][C]9[/C][C]90[/C][C]88.951078536992[/C][C]1.04892146300801[/C][/ROW]
[ROW][C]10[/C][C]90[/C][C]89.9746413698653[/C][C]0.0253586301347184[/C][/ROW]
[ROW][C]11[/C][C]91[/C][C]89.9993869320583[/C][C]1.00061306794169[/C][/ROW]
[ROW][C]12[/C][C]93[/C][C]90.975809269242[/C][C]2.02419073075798[/C][/ROW]
[ROW][C]13[/C][C]93[/C][C]92.9510633485216[/C][C]0.0489366514783853[/C][/ROW]
[ROW][C]14[/C][C]87[/C][C]92.9988169119532[/C][C]-5.99881691195324[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]87.145026853469[/C][C]1.85497314653104[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]88.955154337487[/C][C]3.04484566251301[/C][/ROW]
[ROW][C]17[/C][C]98[/C][C]91.9263880874822[/C][C]6.07361191251778[/C][/ROW]
[ROW][C]18[/C][C]92[/C][C]97.8531649093826[/C][C]-5.85316490938256[/C][/ROW]
[ROW][C]19[/C][C]92[/C][C]92.141505583868[/C][C]-0.141505583867925[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]92.0034210261586[/C][C]-5.00342102615863[/C][/ROW]
[ROW][C]21[/C][C]92[/C][C]87.1209622528333[/C][C]4.87903774716672[/C][/ROW]
[ROW][C]22[/C][C]98[/C][C]91.882044826036[/C][C]6.11795517396405[/C][/ROW]
[ROW][C]23[/C][C]101[/C][C]97.8520928707165[/C][C]3.14790712928348[/C][/ROW]
[ROW][C]24[/C][C]102[/C][C]100.923896482811[/C][C]1.076103517189[/C][/ROW]
[ROW][C]25[/C][C]102[/C][C]101.973984218989[/C][C]0.0260157810107273[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]101.999371044838[/C][C]-11.9993710448384[/C][/ROW]
[ROW][C]27[/C][C]87[/C][C]90.2900957058336[/C][C]-3.29009570583359[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]87.0795410553168[/C][C]4.92045894468323[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]91.8810434309224[/C][C]13.1189565690776[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]104.682837296098[/C][C]-14.6828372960978[/C][/ROW]
[ROW][C]31[/C][C]88[/C][C]90.3549709424881[/C][C]-2.35497094248814[/C][/ROW]
[ROW][C]32[/C][C]83[/C][C]88.0569335638698[/C][C]-5.05693356386979[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]83.1222559670905[/C][C]14.8777440329095[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]97.640317009924[/C][C]11.359682990076[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]108.725369334548[/C][C]9.2746306654522[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.775777370398[/C][C]0.224222629601698[/C][/ROW]
[ROW][C]37[/C][C]115[/C][C]117.994579214048[/C][C]-2.99457921404755[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]115.07239667542[/C][C]-8.0723966754197[/C][/ROW]
[ROW][C]39[/C][C]101[/C][C]107.195157529722[/C][C]-6.19515752972168[/C][/ROW]
[ROW][C]40[/C][C]111[/C][C]101.149773566433[/C][C]9.85022643356729[/C][/ROW]
[ROW][C]41[/C][C]128[/C][C]110.761861819325[/C][C]17.2381381806753[/C][/ROW]
[ROW][C]42[/C][C]115[/C][C]127.583252335135[/C][C]-12.5832523351354[/C][/ROW]
[ROW][C]43[/C][C]111[/C][C]115.30421156694[/C][C]-4.30421156693987[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]111.104058228377[/C][C]-6.10405822837737[/C][/ROW]
[ROW][C]45[/C][C]120[/C][C]105.147571157988[/C][C]14.8524288420123[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]119.640929027683[/C][C]12.3590709723173[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]131.701208221351[/C][C]3.29879177864944[/C][/ROW]
[ROW][C]48[/C][C]142[/C][C]134.920248709216[/C][C]7.07975129078429[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]141.828840575047[/C][C]-2.82884057504748[/C][/ROW]
[ROW][C]50[/C][C]127[/C][C]139.068389793119[/C][C]-12.0683897931185[/C][/ROW]
[ROW][C]51[/C][C]113[/C][C]127.291764296831[/C][C]-14.2917642968308[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]113.345516397135[/C][C]16.6544836028652[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]129.597362715261[/C][C]13.4026372847388[/C][/ROW]
[ROW][C]54[/C][C]139[/C][C]142.675979056851[/C][C]-3.67597905685062[/C][/ROW]
[ROW][C]55[/C][C]137[/C][C]139.088870136205[/C][C]-2.08887013620478[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]137.050500334917[/C][C]-3.05050033491693[/C][/ROW]
[ROW][C]57[/C][C]139[/C][C]134.073748619365[/C][C]4.92625138063516[/C][/ROW]
[ROW][C]58[/C][C]157[/C][C]138.880903393516[/C][C]18.1190966064837[/C][/ROW]
[ROW][C]59[/C][C]152[/C][C]156.561954364151[/C][C]-4.56195436415095[/C][/ROW]
[ROW][C]60[/C][C]153[/C][C]152.110289394861[/C][C]0.889710605138902[/C][/ROW]
[ROW][C]61[/C][C]147[/C][C]152.978490437122[/C][C]-5.97849043712199[/C][/ROW]
[ROW][C]62[/C][C]132[/C][C]147.144535442457[/C][C]-15.1445354424574[/C][/ROW]
[ROW][C]63[/C][C]117[/C][C]132.366132914991[/C][C]-15.3661329149907[/C][/ROW]
[ROW][C]64[/C][C]123[/C][C]117.371490235384[/C][C]5.628509764616[/C][/ROW]
[ROW][C]65[/C][C]139[/C][C]122.863925658532[/C][C]16.1360743414681[/C][/ROW]
[ROW][C]66[/C][C]134[/C][C]138.609895730536[/C][C]-4.60989573053624[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]134.111448420986[/C][C]-0.111448420985738[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]134.002694366915[/C][C]-6.00269436691548[/C][/ROW]
[ROW][C]69[/C][C]118[/C][C]128.145120594468[/C][C]-10.1451205944684[/C][/ROW]
[ROW][C]70[/C][C]144[/C][C]118.245267515157[/C][C]25.7547324848426[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]143.377355923837[/C][C]-3.3773559238374[/C][/ROW]
[ROW][C]72[/C][C]151[/C][C]140.081650650431[/C][C]10.9183493495688[/C][/ROW]
[ROW][C]73[/C][C]144[/C][C]150.736038976604[/C][C]-6.73603897660425[/C][/ROW]
[ROW][C]74[/C][C]135[/C][C]144.162849867225[/C][C]-9.16284986722542[/C][/ROW]
[ROW][C]75[/C][C]122[/C][C]135.221520227164[/C][C]-13.2215202271642[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]122.319642273596[/C][C]1.68035772640415[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]123.959375824043[/C][C]22.0406241759566[/C][/ROW]
[ROW][C]78[/C][C]146[/C][C]145.46714786938[/C][C]0.532852130619574[/C][/ROW]
[ROW][C]79[/C][C]147[/C][C]145.987117815229[/C][C]1.01288218477114[/C][/ROW]
[ROW][C]80[/C][C]148[/C][C]146.975512652187[/C][C]1.02448734781345[/C][/ROW]
[ROW][C]81[/C][C]132[/C][C]147.975232086818[/C][C]-15.9752320868176[/C][/ROW]
[ROW][C]82[/C][C]161[/C][C]132.386215761706[/C][C]28.6137842382935[/C][/ROW]
[ROW][C]83[/C][C]159[/C][C]160.30823574801[/C][C]-1.30823574801045[/C][/ROW]
[ROW][C]84[/C][C]173[/C][C]159.031627788765[/C][C]13.9683722112353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79139&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79139&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
29293-1
39192.024175909283-1.02417590928304
48991.0247603838727-2.0247603838727
58789.0489504233604-2.04895042336041
68687.0495352395606-1.04953523956061
78786.0253734687410.97462653125902
88986.97643751739542.02356248260456
99088.9510785369921.04892146300801
109089.97464136986530.0253586301347184
119189.99938693205831.00061306794169
129390.9758092692422.02419073075798
139392.95106334852160.0489366514783853
148792.9988169119532-5.99881691195324
158987.1450268534691.85497314653104
169288.9551543374873.04484566251301
179891.92638808748226.07361191251778
189297.8531649093826-5.85316490938256
199292.141505583868-0.141505583867925
208792.0034210261586-5.00342102615863
219287.12096225283334.87903774716672
229891.8820448260366.11795517396405
2310197.85209287071653.14790712928348
24102100.9238964828111.076103517189
25102101.9739842189890.0260157810107273
2690101.999371044838-11.9993710448384
278790.2900957058336-3.29009570583359
289287.07954105531684.92045894468323
2910591.881043430922413.1189565690776
3090104.682837296098-14.6828372960978
318890.3549709424881-2.35497094248814
328388.0569335638698-5.05693356386979
339883.122255967090514.8777440329095
3410997.64031700992411.359682990076
35118108.7253693345489.2746306654522
36118117.7757773703980.224222629601698
37115117.994579214048-2.99457921404755
38107115.07239667542-8.0723966754197
39101107.195157529722-6.19515752972168
40111101.1497735664339.85022643356729
41128110.76186181932517.2381381806753
42115127.583252335135-12.5832523351354
43111115.30421156694-4.30421156693987
44105111.104058228377-6.10405822837737
45120105.14757115798814.8524288420123
46132119.64092902768312.3590709723173
47135131.7012082213513.29879177864944
48142134.9202487092167.07975129078429
49139141.828840575047-2.82884057504748
50127139.068389793119-12.0683897931185
51113127.291764296831-14.2917642968308
52130113.34551639713516.6544836028652
53143129.59736271526113.4026372847388
54139142.675979056851-3.67597905685062
55137139.088870136205-2.08887013620478
56134137.050500334917-3.05050033491693
57139134.0737486193654.92625138063516
58157138.88090339351618.1190966064837
59152156.561954364151-4.56195436415095
60153152.1102893948610.889710605138902
61147152.978490437122-5.97849043712199
62132147.144535442457-15.1445354424574
63117132.366132914991-15.3661329149907
64123117.3714902353845.628509764616
65139122.86392565853216.1360743414681
66134138.609895730536-4.60989573053624
67134134.111448420986-0.111448420985738
68128134.002694366915-6.00269436691548
69118128.145120594468-10.1451205944684
70144118.24526751515725.7547324848426
71140143.377355923837-3.3773559238374
72151140.08165065043110.9183493495688
73144150.736038976604-6.73603897660425
74135144.162849867225-9.16284986722542
75122135.221520227164-13.2215202271642
76124122.3196422735961.68035772640415
77146123.95937582404322.0406241759566
78146145.467147869380.532852130619574
79147145.9871178152291.01288218477114
80148146.9755126521871.02448734781345
81132147.975232086818-15.9752320868176
82161132.38621576170628.6137842382935
83159160.30823574801-1.30823574801045
84173159.03162778876513.9683722112353







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85172.662301900589154.070183847756191.254419953423
86172.662301900589146.684963317133198.639640484045
87172.662301900589140.976699711764204.347904089415
88172.662301900589136.150212775787209.174391025392
89172.662301900589131.891136618658213.433467182521
90172.662301900589128.036713000995217.287890800183
91172.662301900589124.489711656504220.834892144675
92172.662301900589121.186543363064224.138060438115
93172.662301900589118.082919500249227.24168430093
94172.662301900589115.146527982545230.178075818634
95172.662301900589112.35293682699232.971666974188
96172.662301900589109.683140412287235.641463388892

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 172.662301900589 & 154.070183847756 & 191.254419953423 \tabularnewline
86 & 172.662301900589 & 146.684963317133 & 198.639640484045 \tabularnewline
87 & 172.662301900589 & 140.976699711764 & 204.347904089415 \tabularnewline
88 & 172.662301900589 & 136.150212775787 & 209.174391025392 \tabularnewline
89 & 172.662301900589 & 131.891136618658 & 213.433467182521 \tabularnewline
90 & 172.662301900589 & 128.036713000995 & 217.287890800183 \tabularnewline
91 & 172.662301900589 & 124.489711656504 & 220.834892144675 \tabularnewline
92 & 172.662301900589 & 121.186543363064 & 224.138060438115 \tabularnewline
93 & 172.662301900589 & 118.082919500249 & 227.24168430093 \tabularnewline
94 & 172.662301900589 & 115.146527982545 & 230.178075818634 \tabularnewline
95 & 172.662301900589 & 112.35293682699 & 232.971666974188 \tabularnewline
96 & 172.662301900589 & 109.683140412287 & 235.641463388892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79139&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]172.662301900589[/C][C]154.070183847756[/C][C]191.254419953423[/C][/ROW]
[ROW][C]86[/C][C]172.662301900589[/C][C]146.684963317133[/C][C]198.639640484045[/C][/ROW]
[ROW][C]87[/C][C]172.662301900589[/C][C]140.976699711764[/C][C]204.347904089415[/C][/ROW]
[ROW][C]88[/C][C]172.662301900589[/C][C]136.150212775787[/C][C]209.174391025392[/C][/ROW]
[ROW][C]89[/C][C]172.662301900589[/C][C]131.891136618658[/C][C]213.433467182521[/C][/ROW]
[ROW][C]90[/C][C]172.662301900589[/C][C]128.036713000995[/C][C]217.287890800183[/C][/ROW]
[ROW][C]91[/C][C]172.662301900589[/C][C]124.489711656504[/C][C]220.834892144675[/C][/ROW]
[ROW][C]92[/C][C]172.662301900589[/C][C]121.186543363064[/C][C]224.138060438115[/C][/ROW]
[ROW][C]93[/C][C]172.662301900589[/C][C]118.082919500249[/C][C]227.24168430093[/C][/ROW]
[ROW][C]94[/C][C]172.662301900589[/C][C]115.146527982545[/C][C]230.178075818634[/C][/ROW]
[ROW][C]95[/C][C]172.662301900589[/C][C]112.35293682699[/C][C]232.971666974188[/C][/ROW]
[ROW][C]96[/C][C]172.662301900589[/C][C]109.683140412287[/C][C]235.641463388892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79139&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79139&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
85172.662301900589154.070183847756191.254419953423
86172.662301900589146.684963317133198.639640484045
87172.662301900589140.976699711764204.347904089415
88172.662301900589136.150212775787209.174391025392
89172.662301900589131.891136618658213.433467182521
90172.662301900589128.036713000995217.287890800183
91172.662301900589124.489711656504220.834892144675
92172.662301900589121.186543363064224.138060438115
93172.662301900589118.082919500249227.24168430093
94172.662301900589115.146527982545230.178075818634
95172.662301900589112.35293682699232.971666974188
96172.662301900589109.683140412287235.641463388892



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')