Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Jun 2010 11:16:31 +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/Jun/03/t1275563907lrw6sh97olh64xt.htm/, Retrieved Sun, 05 May 2024 13:58:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77343, Retrieved Sun, 05 May 2024 13:58:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-03 11:16:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
77
70
67
76
85
106
108
120
108
111
109
104
104
117
111
110
116
118
115
111
112
97
106
93
95
97
81
71
75
70
72
80
78
80
81
99
87
100
95
128
112
104
102
108
103
99
96
85
78
74
106
100
109
87
107
106
109
83
84
83
65
68
61
75
66
78
68
68
174
64
48
45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77343&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77343&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.573314480838667
beta0.0612762739836527
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.573314480838667 \tabularnewline
beta & 0.0612762739836527 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77343&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]0.573314480838667[/C][/ROW]
[ROW][C]beta[/C][C]0.0612762739836527[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77343&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
alpha0.573314480838667
beta0.0612762739836527
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
367634
47658.433780224181317.5662197758187
58562.262382101010622.7376178989894
610669.854607003656536.1453929963435
710886.40351197247621.5964880275239
812095.370016089176524.6299839108235
9108106.9409328254551.05906717454477
10111105.0355073092075.96449269079287
11109106.1519693351432.84803066485692
12104105.581771508089-1.58177150808878
13104102.4163354051091.58366459489058
14117101.12132470629115.8786752937094
15111108.5796776414362.42032235856384
16110108.4071892672671.5928107327329
17116107.8162328521838.18376714781692
18118111.2914676397036.70853236029654
19115114.1566035615110.843396438488796
20111113.688801129271-2.68880112927089
21112111.1014795519630.898520448036791
2297110.602386922525-13.6023869225255
23106101.3118544354724.68814556452767
2493102.672246335831-9.67224633583125
259595.4598260318778-0.459826031877768
269793.51286573875813.48713426124188
278193.9512599693995-12.9512599693995
287184.5102995335033-13.5102995335033
297574.27420902631830.725790973681683
307072.2253728118176-2.22537281181764
317268.40641303683513.59358696316488
328068.049791941338911.9502080586611
337872.90396041371275.0960395862873
348074.0075616487095.99243835129106
358175.83559908245915.16440091754092
369977.370339039594821.6296609604052
378789.1047134411431-2.10471344114313
3810087.157887510804712.8421124891953
399594.23144412751820.768555872481755
4012894.410055710523233.5899442894768
41112114.585678618271-2.58567861827107
42104113.930456682489-9.93045668248864
43102108.715504468623-6.71550446862338
44108105.1078113793862.89218862061426
45103107.10995211551-4.10995211550997
4699104.953279188854-5.95327918885415
4796101.530658035858-5.53065803585783
488598.156036511712-13.1560365117120
497889.9474959553871-11.9474959553871
507482.012106795492-8.01210679549206
5110676.051463308357529.9485366916425
5210092.90631575492657.09368424507348
5310996.907355544310412.0926444556896
5487104.199193167075-17.1991931670749
5510794.093378561283712.9066214387163
56106101.7010804615544.29891953844636
57109104.5248857318094.47511426819088
5883107.606919330432-24.6069193304317
598493.1513467045852-9.15134670458518
608387.2351856011425-4.23518560114248
616583.9887463421642-18.9887463421642
626871.6167914849716-3.61679148497156
636167.9307409809361-6.93074098093612
647562.101274324827512.8987256751725
656668.0934677023753-2.09346770237528
667865.416874792480312.5831252075197
676871.5966375536399-3.59663755363991
686868.3739560812232-0.373956081223227
6917466.9857472718381107.014252728162
7064130.924225897852-66.9242258978518
714892.7901694014725-44.7901694014725
724565.7723835994909-20.7723835994909

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 67 & 63 & 4 \tabularnewline
4 & 76 & 58.4337802241813 & 17.5662197758187 \tabularnewline
5 & 85 & 62.2623821010106 & 22.7376178989894 \tabularnewline
6 & 106 & 69.8546070036565 & 36.1453929963435 \tabularnewline
7 & 108 & 86.403511972476 & 21.5964880275239 \tabularnewline
8 & 120 & 95.3700160891765 & 24.6299839108235 \tabularnewline
9 & 108 & 106.940932825455 & 1.05906717454477 \tabularnewline
10 & 111 & 105.035507309207 & 5.96449269079287 \tabularnewline
11 & 109 & 106.151969335143 & 2.84803066485692 \tabularnewline
12 & 104 & 105.581771508089 & -1.58177150808878 \tabularnewline
13 & 104 & 102.416335405109 & 1.58366459489058 \tabularnewline
14 & 117 & 101.121324706291 & 15.8786752937094 \tabularnewline
15 & 111 & 108.579677641436 & 2.42032235856384 \tabularnewline
16 & 110 & 108.407189267267 & 1.5928107327329 \tabularnewline
17 & 116 & 107.816232852183 & 8.18376714781692 \tabularnewline
18 & 118 & 111.291467639703 & 6.70853236029654 \tabularnewline
19 & 115 & 114.156603561511 & 0.843396438488796 \tabularnewline
20 & 111 & 113.688801129271 & -2.68880112927089 \tabularnewline
21 & 112 & 111.101479551963 & 0.898520448036791 \tabularnewline
22 & 97 & 110.602386922525 & -13.6023869225255 \tabularnewline
23 & 106 & 101.311854435472 & 4.68814556452767 \tabularnewline
24 & 93 & 102.672246335831 & -9.67224633583125 \tabularnewline
25 & 95 & 95.4598260318778 & -0.459826031877768 \tabularnewline
26 & 97 & 93.5128657387581 & 3.48713426124188 \tabularnewline
27 & 81 & 93.9512599693995 & -12.9512599693995 \tabularnewline
28 & 71 & 84.5102995335033 & -13.5102995335033 \tabularnewline
29 & 75 & 74.2742090263183 & 0.725790973681683 \tabularnewline
30 & 70 & 72.2253728118176 & -2.22537281181764 \tabularnewline
31 & 72 & 68.4064130368351 & 3.59358696316488 \tabularnewline
32 & 80 & 68.0497919413389 & 11.9502080586611 \tabularnewline
33 & 78 & 72.9039604137127 & 5.0960395862873 \tabularnewline
34 & 80 & 74.007561648709 & 5.99243835129106 \tabularnewline
35 & 81 & 75.8355990824591 & 5.16440091754092 \tabularnewline
36 & 99 & 77.3703390395948 & 21.6296609604052 \tabularnewline
37 & 87 & 89.1047134411431 & -2.10471344114313 \tabularnewline
38 & 100 & 87.1578875108047 & 12.8421124891953 \tabularnewline
39 & 95 & 94.2314441275182 & 0.768555872481755 \tabularnewline
40 & 128 & 94.4100557105232 & 33.5899442894768 \tabularnewline
41 & 112 & 114.585678618271 & -2.58567861827107 \tabularnewline
42 & 104 & 113.930456682489 & -9.93045668248864 \tabularnewline
43 & 102 & 108.715504468623 & -6.71550446862338 \tabularnewline
44 & 108 & 105.107811379386 & 2.89218862061426 \tabularnewline
45 & 103 & 107.10995211551 & -4.10995211550997 \tabularnewline
46 & 99 & 104.953279188854 & -5.95327918885415 \tabularnewline
47 & 96 & 101.530658035858 & -5.53065803585783 \tabularnewline
48 & 85 & 98.156036511712 & -13.1560365117120 \tabularnewline
49 & 78 & 89.9474959553871 & -11.9474959553871 \tabularnewline
50 & 74 & 82.012106795492 & -8.01210679549206 \tabularnewline
51 & 106 & 76.0514633083575 & 29.9485366916425 \tabularnewline
52 & 100 & 92.9063157549265 & 7.09368424507348 \tabularnewline
53 & 109 & 96.9073555443104 & 12.0926444556896 \tabularnewline
54 & 87 & 104.199193167075 & -17.1991931670749 \tabularnewline
55 & 107 & 94.0933785612837 & 12.9066214387163 \tabularnewline
56 & 106 & 101.701080461554 & 4.29891953844636 \tabularnewline
57 & 109 & 104.524885731809 & 4.47511426819088 \tabularnewline
58 & 83 & 107.606919330432 & -24.6069193304317 \tabularnewline
59 & 84 & 93.1513467045852 & -9.15134670458518 \tabularnewline
60 & 83 & 87.2351856011425 & -4.23518560114248 \tabularnewline
61 & 65 & 83.9887463421642 & -18.9887463421642 \tabularnewline
62 & 68 & 71.6167914849716 & -3.61679148497156 \tabularnewline
63 & 61 & 67.9307409809361 & -6.93074098093612 \tabularnewline
64 & 75 & 62.1012743248275 & 12.8987256751725 \tabularnewline
65 & 66 & 68.0934677023753 & -2.09346770237528 \tabularnewline
66 & 78 & 65.4168747924803 & 12.5831252075197 \tabularnewline
67 & 68 & 71.5966375536399 & -3.59663755363991 \tabularnewline
68 & 68 & 68.3739560812232 & -0.373956081223227 \tabularnewline
69 & 174 & 66.9857472718381 & 107.014252728162 \tabularnewline
70 & 64 & 130.924225897852 & -66.9242258978518 \tabularnewline
71 & 48 & 92.7901694014725 & -44.7901694014725 \tabularnewline
72 & 45 & 65.7723835994909 & -20.7723835994909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77343&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]3[/C][C]67[/C][C]63[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]76[/C][C]58.4337802241813[/C][C]17.5662197758187[/C][/ROW]
[ROW][C]5[/C][C]85[/C][C]62.2623821010106[/C][C]22.7376178989894[/C][/ROW]
[ROW][C]6[/C][C]106[/C][C]69.8546070036565[/C][C]36.1453929963435[/C][/ROW]
[ROW][C]7[/C][C]108[/C][C]86.403511972476[/C][C]21.5964880275239[/C][/ROW]
[ROW][C]8[/C][C]120[/C][C]95.3700160891765[/C][C]24.6299839108235[/C][/ROW]
[ROW][C]9[/C][C]108[/C][C]106.940932825455[/C][C]1.05906717454477[/C][/ROW]
[ROW][C]10[/C][C]111[/C][C]105.035507309207[/C][C]5.96449269079287[/C][/ROW]
[ROW][C]11[/C][C]109[/C][C]106.151969335143[/C][C]2.84803066485692[/C][/ROW]
[ROW][C]12[/C][C]104[/C][C]105.581771508089[/C][C]-1.58177150808878[/C][/ROW]
[ROW][C]13[/C][C]104[/C][C]102.416335405109[/C][C]1.58366459489058[/C][/ROW]
[ROW][C]14[/C][C]117[/C][C]101.121324706291[/C][C]15.8786752937094[/C][/ROW]
[ROW][C]15[/C][C]111[/C][C]108.579677641436[/C][C]2.42032235856384[/C][/ROW]
[ROW][C]16[/C][C]110[/C][C]108.407189267267[/C][C]1.5928107327329[/C][/ROW]
[ROW][C]17[/C][C]116[/C][C]107.816232852183[/C][C]8.18376714781692[/C][/ROW]
[ROW][C]18[/C][C]118[/C][C]111.291467639703[/C][C]6.70853236029654[/C][/ROW]
[ROW][C]19[/C][C]115[/C][C]114.156603561511[/C][C]0.843396438488796[/C][/ROW]
[ROW][C]20[/C][C]111[/C][C]113.688801129271[/C][C]-2.68880112927089[/C][/ROW]
[ROW][C]21[/C][C]112[/C][C]111.101479551963[/C][C]0.898520448036791[/C][/ROW]
[ROW][C]22[/C][C]97[/C][C]110.602386922525[/C][C]-13.6023869225255[/C][/ROW]
[ROW][C]23[/C][C]106[/C][C]101.311854435472[/C][C]4.68814556452767[/C][/ROW]
[ROW][C]24[/C][C]93[/C][C]102.672246335831[/C][C]-9.67224633583125[/C][/ROW]
[ROW][C]25[/C][C]95[/C][C]95.4598260318778[/C][C]-0.459826031877768[/C][/ROW]
[ROW][C]26[/C][C]97[/C][C]93.5128657387581[/C][C]3.48713426124188[/C][/ROW]
[ROW][C]27[/C][C]81[/C][C]93.9512599693995[/C][C]-12.9512599693995[/C][/ROW]
[ROW][C]28[/C][C]71[/C][C]84.5102995335033[/C][C]-13.5102995335033[/C][/ROW]
[ROW][C]29[/C][C]75[/C][C]74.2742090263183[/C][C]0.725790973681683[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]72.2253728118176[/C][C]-2.22537281181764[/C][/ROW]
[ROW][C]31[/C][C]72[/C][C]68.4064130368351[/C][C]3.59358696316488[/C][/ROW]
[ROW][C]32[/C][C]80[/C][C]68.0497919413389[/C][C]11.9502080586611[/C][/ROW]
[ROW][C]33[/C][C]78[/C][C]72.9039604137127[/C][C]5.0960395862873[/C][/ROW]
[ROW][C]34[/C][C]80[/C][C]74.007561648709[/C][C]5.99243835129106[/C][/ROW]
[ROW][C]35[/C][C]81[/C][C]75.8355990824591[/C][C]5.16440091754092[/C][/ROW]
[ROW][C]36[/C][C]99[/C][C]77.3703390395948[/C][C]21.6296609604052[/C][/ROW]
[ROW][C]37[/C][C]87[/C][C]89.1047134411431[/C][C]-2.10471344114313[/C][/ROW]
[ROW][C]38[/C][C]100[/C][C]87.1578875108047[/C][C]12.8421124891953[/C][/ROW]
[ROW][C]39[/C][C]95[/C][C]94.2314441275182[/C][C]0.768555872481755[/C][/ROW]
[ROW][C]40[/C][C]128[/C][C]94.4100557105232[/C][C]33.5899442894768[/C][/ROW]
[ROW][C]41[/C][C]112[/C][C]114.585678618271[/C][C]-2.58567861827107[/C][/ROW]
[ROW][C]42[/C][C]104[/C][C]113.930456682489[/C][C]-9.93045668248864[/C][/ROW]
[ROW][C]43[/C][C]102[/C][C]108.715504468623[/C][C]-6.71550446862338[/C][/ROW]
[ROW][C]44[/C][C]108[/C][C]105.107811379386[/C][C]2.89218862061426[/C][/ROW]
[ROW][C]45[/C][C]103[/C][C]107.10995211551[/C][C]-4.10995211550997[/C][/ROW]
[ROW][C]46[/C][C]99[/C][C]104.953279188854[/C][C]-5.95327918885415[/C][/ROW]
[ROW][C]47[/C][C]96[/C][C]101.530658035858[/C][C]-5.53065803585783[/C][/ROW]
[ROW][C]48[/C][C]85[/C][C]98.156036511712[/C][C]-13.1560365117120[/C][/ROW]
[ROW][C]49[/C][C]78[/C][C]89.9474959553871[/C][C]-11.9474959553871[/C][/ROW]
[ROW][C]50[/C][C]74[/C][C]82.012106795492[/C][C]-8.01210679549206[/C][/ROW]
[ROW][C]51[/C][C]106[/C][C]76.0514633083575[/C][C]29.9485366916425[/C][/ROW]
[ROW][C]52[/C][C]100[/C][C]92.9063157549265[/C][C]7.09368424507348[/C][/ROW]
[ROW][C]53[/C][C]109[/C][C]96.9073555443104[/C][C]12.0926444556896[/C][/ROW]
[ROW][C]54[/C][C]87[/C][C]104.199193167075[/C][C]-17.1991931670749[/C][/ROW]
[ROW][C]55[/C][C]107[/C][C]94.0933785612837[/C][C]12.9066214387163[/C][/ROW]
[ROW][C]56[/C][C]106[/C][C]101.701080461554[/C][C]4.29891953844636[/C][/ROW]
[ROW][C]57[/C][C]109[/C][C]104.524885731809[/C][C]4.47511426819088[/C][/ROW]
[ROW][C]58[/C][C]83[/C][C]107.606919330432[/C][C]-24.6069193304317[/C][/ROW]
[ROW][C]59[/C][C]84[/C][C]93.1513467045852[/C][C]-9.15134670458518[/C][/ROW]
[ROW][C]60[/C][C]83[/C][C]87.2351856011425[/C][C]-4.23518560114248[/C][/ROW]
[ROW][C]61[/C][C]65[/C][C]83.9887463421642[/C][C]-18.9887463421642[/C][/ROW]
[ROW][C]62[/C][C]68[/C][C]71.6167914849716[/C][C]-3.61679148497156[/C][/ROW]
[ROW][C]63[/C][C]61[/C][C]67.9307409809361[/C][C]-6.93074098093612[/C][/ROW]
[ROW][C]64[/C][C]75[/C][C]62.1012743248275[/C][C]12.8987256751725[/C][/ROW]
[ROW][C]65[/C][C]66[/C][C]68.0934677023753[/C][C]-2.09346770237528[/C][/ROW]
[ROW][C]66[/C][C]78[/C][C]65.4168747924803[/C][C]12.5831252075197[/C][/ROW]
[ROW][C]67[/C][C]68[/C][C]71.5966375536399[/C][C]-3.59663755363991[/C][/ROW]
[ROW][C]68[/C][C]68[/C][C]68.3739560812232[/C][C]-0.373956081223227[/C][/ROW]
[ROW][C]69[/C][C]174[/C][C]66.9857472718381[/C][C]107.014252728162[/C][/ROW]
[ROW][C]70[/C][C]64[/C][C]130.924225897852[/C][C]-66.9242258978518[/C][/ROW]
[ROW][C]71[/C][C]48[/C][C]92.7901694014725[/C][C]-44.7901694014725[/C][/ROW]
[ROW][C]72[/C][C]45[/C][C]65.7723835994909[/C][C]-20.7723835994909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77343&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77343&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
367634
47658.433780224181317.5662197758187
58562.262382101010622.7376178989894
610669.854607003656536.1453929963435
710886.40351197247621.5964880275239
812095.370016089176524.6299839108235
9108106.9409328254551.05906717454477
10111105.0355073092075.96449269079287
11109106.1519693351432.84803066485692
12104105.581771508089-1.58177150808878
13104102.4163354051091.58366459489058
14117101.12132470629115.8786752937094
15111108.5796776414362.42032235856384
16110108.4071892672671.5928107327329
17116107.8162328521838.18376714781692
18118111.2914676397036.70853236029654
19115114.1566035615110.843396438488796
20111113.688801129271-2.68880112927089
21112111.1014795519630.898520448036791
2297110.602386922525-13.6023869225255
23106101.3118544354724.68814556452767
2493102.672246335831-9.67224633583125
259595.4598260318778-0.459826031877768
269793.51286573875813.48713426124188
278193.9512599693995-12.9512599693995
287184.5102995335033-13.5102995335033
297574.27420902631830.725790973681683
307072.2253728118176-2.22537281181764
317268.40641303683513.59358696316488
328068.049791941338911.9502080586611
337872.90396041371275.0960395862873
348074.0075616487095.99243835129106
358175.83559908245915.16440091754092
369977.370339039594821.6296609604052
378789.1047134411431-2.10471344114313
3810087.157887510804712.8421124891953
399594.23144412751820.768555872481755
4012894.410055710523233.5899442894768
41112114.585678618271-2.58567861827107
42104113.930456682489-9.93045668248864
43102108.715504468623-6.71550446862338
44108105.1078113793862.89218862061426
45103107.10995211551-4.10995211550997
4699104.953279188854-5.95327918885415
4796101.530658035858-5.53065803585783
488598.156036511712-13.1560365117120
497889.9474959553871-11.9474959553871
507482.012106795492-8.01210679549206
5110676.051463308357529.9485366916425
5210092.90631575492657.09368424507348
5310996.907355544310412.0926444556896
5487104.199193167075-17.1991931670749
5510794.093378561283712.9066214387163
56106101.7010804615544.29891953844636
57109104.5248857318094.47511426819088
5883107.606919330432-24.6069193304317
598493.1513467045852-9.15134670458518
608387.2351856011425-4.23518560114248
616583.9887463421642-18.9887463421642
626871.6167914849716-3.61679148497156
636167.9307409809361-6.93074098093612
647562.101274324827512.8987256751725
656668.0934677023753-2.09346770237528
667865.416874792480312.5831252075197
676871.5966375536399-3.59663755363991
686868.3739560812232-0.373956081223227
6917466.9857472718381107.014252728162
7064130.924225897852-66.9242258978518
714892.7901694014725-44.7901694014725
724565.7723835994909-20.7723835994909







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7351.794596411203112.238068603637591.3511242187687
7449.7259175420393.4227183652077996.0291167188702
7547.6572386728749-5.18286480304995100.497342148800
7645.5885598037109-13.6807573404367104.857876947858
7743.5198809345468-22.132040063258109.171801932352
7841.4512020653827-30.5759253366122113.478329467378
7939.3825231962187-39.0388465094208117.803892901858
8037.3138443270546-47.5392604093633122.166949063473
8135.2451654578906-56.090390439128126.580721354909
8233.1764865887265-64.7018900215527131.054863199006
8331.1078077195624-73.3809003425036135.596515781628
8429.0391288503984-82.1327493535649140.211007054362

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 51.7945964112031 & 12.2380686036375 & 91.3511242187687 \tabularnewline
74 & 49.725917542039 & 3.42271836520779 & 96.0291167188702 \tabularnewline
75 & 47.6572386728749 & -5.18286480304995 & 100.497342148800 \tabularnewline
76 & 45.5885598037109 & -13.6807573404367 & 104.857876947858 \tabularnewline
77 & 43.5198809345468 & -22.132040063258 & 109.171801932352 \tabularnewline
78 & 41.4512020653827 & -30.5759253366122 & 113.478329467378 \tabularnewline
79 & 39.3825231962187 & -39.0388465094208 & 117.803892901858 \tabularnewline
80 & 37.3138443270546 & -47.5392604093633 & 122.166949063473 \tabularnewline
81 & 35.2451654578906 & -56.090390439128 & 126.580721354909 \tabularnewline
82 & 33.1764865887265 & -64.7018900215527 & 131.054863199006 \tabularnewline
83 & 31.1078077195624 & -73.3809003425036 & 135.596515781628 \tabularnewline
84 & 29.0391288503984 & -82.1327493535649 & 140.211007054362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77343&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]51.7945964112031[/C][C]12.2380686036375[/C][C]91.3511242187687[/C][/ROW]
[ROW][C]74[/C][C]49.725917542039[/C][C]3.42271836520779[/C][C]96.0291167188702[/C][/ROW]
[ROW][C]75[/C][C]47.6572386728749[/C][C]-5.18286480304995[/C][C]100.497342148800[/C][/ROW]
[ROW][C]76[/C][C]45.5885598037109[/C][C]-13.6807573404367[/C][C]104.857876947858[/C][/ROW]
[ROW][C]77[/C][C]43.5198809345468[/C][C]-22.132040063258[/C][C]109.171801932352[/C][/ROW]
[ROW][C]78[/C][C]41.4512020653827[/C][C]-30.5759253366122[/C][C]113.478329467378[/C][/ROW]
[ROW][C]79[/C][C]39.3825231962187[/C][C]-39.0388465094208[/C][C]117.803892901858[/C][/ROW]
[ROW][C]80[/C][C]37.3138443270546[/C][C]-47.5392604093633[/C][C]122.166949063473[/C][/ROW]
[ROW][C]81[/C][C]35.2451654578906[/C][C]-56.090390439128[/C][C]126.580721354909[/C][/ROW]
[ROW][C]82[/C][C]33.1764865887265[/C][C]-64.7018900215527[/C][C]131.054863199006[/C][/ROW]
[ROW][C]83[/C][C]31.1078077195624[/C][C]-73.3809003425036[/C][C]135.596515781628[/C][/ROW]
[ROW][C]84[/C][C]29.0391288503984[/C][C]-82.1327493535649[/C][C]140.211007054362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77343&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77343&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
7351.794596411203112.238068603637591.3511242187687
7449.7259175420393.4227183652077996.0291167188702
7547.6572386728749-5.18286480304995100.497342148800
7645.5885598037109-13.6807573404367104.857876947858
7743.5198809345468-22.132040063258109.171801932352
7841.4512020653827-30.5759253366122113.478329467378
7939.3825231962187-39.0388465094208117.803892901858
8037.3138443270546-47.5392604093633122.166949063473
8135.2451654578906-56.090390439128126.580721354909
8233.1764865887265-64.7018900215527131.054863199006
8331.1078077195624-73.3809003425036135.596515781628
8429.0391288503984-82.1327493535649140.211007054362



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