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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Aug 2012 15:03:38 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/13/t1344884688dv02dn0jdniby2z.htm/, Retrieved Sat, 27 Apr 2024 23:41:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169301, Retrieved Sat, 27 Apr 2024 23:41:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Puyenbroeck Willem
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdsreeks 2 stap 27] [2012-08-13 19:03:38] [d94b10b2615af2e11b32dea0ad6a3c7b] [Current]
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Dataseries X:
1200
1400
1210
1260
1320
1320
1310
1260
1340
1180
1330
1390
1130
1340
1140
1290
1260
1280
1330
1270
1300
1150
1410
1250
1030
1320
1160
1300
1190
1310
1290
1320
1300
1230
1330
1220
1010
1290
1170
1240
1260
1260
1310
1360
1250
1170
1360
1140
1030
1260
1210
1190
1230
1350
1300
1340
1270
1220
1400
1120
1000
1260
1260
1150
1240
1360
1350
1280
1320
1210
1370
1060
1040
1260
1210
1200
1200
1290
1400
1280
1280
1220
1350
1000
980
1240
1190
1200
1150
1270
1410
1420
1260
1300
1410
1000
950
1280
1330
1190
1170
1270
1340
1470
1270
1280
1430
980




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169301&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169301&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0240942222896128
beta0.14173454654716
gamma0.959898381687373

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0240942222896128 \tabularnewline
beta & 0.14173454654716 \tabularnewline
gamma & 0.959898381687373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169301&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]0.0240942222896128[/C][/ROW]
[ROW][C]beta[/C][C]0.14173454654716[/C][/ROW]
[ROW][C]gamma[/C][C]0.959898381687373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169301&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
alpha0.0240942222896128
beta0.14173454654716
gamma0.959898381687373







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311301147.95673076923-17.9567307692305
1413401354.5009255273-14.5009255272976
1511401153.57886480117-13.5788648011687
1612901304.29931547624-14.2993154762448
1712601269.95357552375-9.95357552375413
1812801290.26188483115-10.261884831147
1913301295.9443881630934.0556118369079
2012701250.3109864693919.6890135306071
2113001334.39867042225-34.3986704222534
2211501173.31568279704-23.3156827970406
2314101322.0034417966187.9965582033858
2412501386.59035615041-136.59035615041
2510301105.14490285022-75.1449028502186
2613201312.898607436397.10139256361322
2711601112.7846868818647.2153131181437
2813001263.92653021236.0734697880036
2911901234.66896710513-44.6689671051302
3013101253.5369918372656.4630081627365
3112901302.25533285395-12.2553328539454
3213201241.8025853695978.1974146304108
3313001276.5867330196723.4132669803273
3412301127.43080972696102.569190273042
3513301384.00748772984-54.0074877298373
3612201234.88342612994-14.8834261299428
3710101014.44318372616-4.44318372615771
3812901301.70022623831-11.7002262383057
3911701139.4005624005530.5994375994487
4012401280.33770204596-40.3377020459602
4112601173.9739969382186.0260030617935
4212601291.54682387412-31.5468238741173
4313101274.2891480661235.7108519338822
4413601300.4071844057459.5928155942645
4512501284.04098924809-34.040989248093
4611701208.07355623734-38.0735562373447
4713601314.5267521456945.4732478543085
4811401204.73117765222-64.7311776522233
491030992.98108722124837.0189127787518
5012601274.69162160699-14.6916216069892
5112101152.1874162373357.8125837626742
5211901227.66381868279-37.663818682795
5312301240.08283985375-10.0828398537462
5413501245.21757295957104.782427040433
5513001294.731520270225.26847972978408
5613401342.86590475718-2.8659047571814
5712701237.4460624987132.5539375012854
5812201159.6976355718360.3023644281704
5914001347.5132884976152.4867115023851
6011201135.40240219965-15.4024021996454
6110001021.0777231945-21.077723194502
6212601253.669570881746.33042911825783
6312601200.3854605509159.6145394490916
6411501187.26576118028-37.2657611802838
6512401226.3327234727813.6672765272192
6613601340.5244890683819.4755109316245
6713501295.3524055121754.6475944878282
6812801337.81621065921-57.8162106592133
6913201264.8247078060955.1752921939087
7012101214.26454604516-4.26454604516084
7113701393.63185926932-23.6318592693158
7210601116.25932284121-56.2593228412068
731040995.66310805609144.3368919439088
7412601255.758957565064.24104243494367
7512101252.58508834937-42.5850883493681
7612001146.1449698082553.8550301917453
7712001235.32775073312-35.3277507331161
7812901353.8204570737-63.8204570737032
7914001339.3455894322760.654410567731
8012801276.377877728233.62212227176747
8112801310.70010202173-30.7001020217324
8212201202.0824222998517.9175777001451
8313501363.61028536493-13.610285364932
8410001055.71780726156-55.717807261557
859801029.17508079577-49.1750807957692
8612401248.9427730415-8.94277304150182
8711901201.0264403996-11.0264403996005
8812001185.2372439087514.7627560912501
8911501189.34913492778-39.3491349277801
9012701280.45488824894-10.4548882489412
9114101383.4534960393326.5465039606677
9214201265.70464961965154.295350380348
9312601271.48655875641-11.4865587564143
9413001208.9224040738191.0775959261889
9514101342.9754604975567.0245395024547
961000998.1529310267971.84706897320257
97950979.894995320595-29.8949953205947
9812801238.650278998741.3497210013004
9913301191.00015375426138.999846245743
10011901204.50298331626-14.5029833162621
10111701158.6380845898411.3619154101648
10212701279.62489500444-9.62489500444076
10313401418.90008279685-78.9000827968521
10414701419.516593329850.4834066701983
10512701268.377812322871.62218767713398
10612801303.13349004114-23.1334900411393
10714301412.4374249831917.5625750168133
1089801005.73280906241-25.732809062414

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1130 & 1147.95673076923 & -17.9567307692305 \tabularnewline
14 & 1340 & 1354.5009255273 & -14.5009255272976 \tabularnewline
15 & 1140 & 1153.57886480117 & -13.5788648011687 \tabularnewline
16 & 1290 & 1304.29931547624 & -14.2993154762448 \tabularnewline
17 & 1260 & 1269.95357552375 & -9.95357552375413 \tabularnewline
18 & 1280 & 1290.26188483115 & -10.261884831147 \tabularnewline
19 & 1330 & 1295.94438816309 & 34.0556118369079 \tabularnewline
20 & 1270 & 1250.31098646939 & 19.6890135306071 \tabularnewline
21 & 1300 & 1334.39867042225 & -34.3986704222534 \tabularnewline
22 & 1150 & 1173.31568279704 & -23.3156827970406 \tabularnewline
23 & 1410 & 1322.00344179661 & 87.9965582033858 \tabularnewline
24 & 1250 & 1386.59035615041 & -136.59035615041 \tabularnewline
25 & 1030 & 1105.14490285022 & -75.1449028502186 \tabularnewline
26 & 1320 & 1312.89860743639 & 7.10139256361322 \tabularnewline
27 & 1160 & 1112.78468688186 & 47.2153131181437 \tabularnewline
28 & 1300 & 1263.926530212 & 36.0734697880036 \tabularnewline
29 & 1190 & 1234.66896710513 & -44.6689671051302 \tabularnewline
30 & 1310 & 1253.53699183726 & 56.4630081627365 \tabularnewline
31 & 1290 & 1302.25533285395 & -12.2553328539454 \tabularnewline
32 & 1320 & 1241.80258536959 & 78.1974146304108 \tabularnewline
33 & 1300 & 1276.58673301967 & 23.4132669803273 \tabularnewline
34 & 1230 & 1127.43080972696 & 102.569190273042 \tabularnewline
35 & 1330 & 1384.00748772984 & -54.0074877298373 \tabularnewline
36 & 1220 & 1234.88342612994 & -14.8834261299428 \tabularnewline
37 & 1010 & 1014.44318372616 & -4.44318372615771 \tabularnewline
38 & 1290 & 1301.70022623831 & -11.7002262383057 \tabularnewline
39 & 1170 & 1139.40056240055 & 30.5994375994487 \tabularnewline
40 & 1240 & 1280.33770204596 & -40.3377020459602 \tabularnewline
41 & 1260 & 1173.97399693821 & 86.0260030617935 \tabularnewline
42 & 1260 & 1291.54682387412 & -31.5468238741173 \tabularnewline
43 & 1310 & 1274.28914806612 & 35.7108519338822 \tabularnewline
44 & 1360 & 1300.40718440574 & 59.5928155942645 \tabularnewline
45 & 1250 & 1284.04098924809 & -34.040989248093 \tabularnewline
46 & 1170 & 1208.07355623734 & -38.0735562373447 \tabularnewline
47 & 1360 & 1314.52675214569 & 45.4732478543085 \tabularnewline
48 & 1140 & 1204.73117765222 & -64.7311776522233 \tabularnewline
49 & 1030 & 992.981087221248 & 37.0189127787518 \tabularnewline
50 & 1260 & 1274.69162160699 & -14.6916216069892 \tabularnewline
51 & 1210 & 1152.18741623733 & 57.8125837626742 \tabularnewline
52 & 1190 & 1227.66381868279 & -37.663818682795 \tabularnewline
53 & 1230 & 1240.08283985375 & -10.0828398537462 \tabularnewline
54 & 1350 & 1245.21757295957 & 104.782427040433 \tabularnewline
55 & 1300 & 1294.73152027022 & 5.26847972978408 \tabularnewline
56 & 1340 & 1342.86590475718 & -2.8659047571814 \tabularnewline
57 & 1270 & 1237.44606249871 & 32.5539375012854 \tabularnewline
58 & 1220 & 1159.69763557183 & 60.3023644281704 \tabularnewline
59 & 1400 & 1347.51328849761 & 52.4867115023851 \tabularnewline
60 & 1120 & 1135.40240219965 & -15.4024021996454 \tabularnewline
61 & 1000 & 1021.0777231945 & -21.077723194502 \tabularnewline
62 & 1260 & 1253.66957088174 & 6.33042911825783 \tabularnewline
63 & 1260 & 1200.38546055091 & 59.6145394490916 \tabularnewline
64 & 1150 & 1187.26576118028 & -37.2657611802838 \tabularnewline
65 & 1240 & 1226.33272347278 & 13.6672765272192 \tabularnewline
66 & 1360 & 1340.52448906838 & 19.4755109316245 \tabularnewline
67 & 1350 & 1295.35240551217 & 54.6475944878282 \tabularnewline
68 & 1280 & 1337.81621065921 & -57.8162106592133 \tabularnewline
69 & 1320 & 1264.82470780609 & 55.1752921939087 \tabularnewline
70 & 1210 & 1214.26454604516 & -4.26454604516084 \tabularnewline
71 & 1370 & 1393.63185926932 & -23.6318592693158 \tabularnewline
72 & 1060 & 1116.25932284121 & -56.2593228412068 \tabularnewline
73 & 1040 & 995.663108056091 & 44.3368919439088 \tabularnewline
74 & 1260 & 1255.75895756506 & 4.24104243494367 \tabularnewline
75 & 1210 & 1252.58508834937 & -42.5850883493681 \tabularnewline
76 & 1200 & 1146.14496980825 & 53.8550301917453 \tabularnewline
77 & 1200 & 1235.32775073312 & -35.3277507331161 \tabularnewline
78 & 1290 & 1353.8204570737 & -63.8204570737032 \tabularnewline
79 & 1400 & 1339.34558943227 & 60.654410567731 \tabularnewline
80 & 1280 & 1276.37787772823 & 3.62212227176747 \tabularnewline
81 & 1280 & 1310.70010202173 & -30.7001020217324 \tabularnewline
82 & 1220 & 1202.08242229985 & 17.9175777001451 \tabularnewline
83 & 1350 & 1363.61028536493 & -13.610285364932 \tabularnewline
84 & 1000 & 1055.71780726156 & -55.717807261557 \tabularnewline
85 & 980 & 1029.17508079577 & -49.1750807957692 \tabularnewline
86 & 1240 & 1248.9427730415 & -8.94277304150182 \tabularnewline
87 & 1190 & 1201.0264403996 & -11.0264403996005 \tabularnewline
88 & 1200 & 1185.23724390875 & 14.7627560912501 \tabularnewline
89 & 1150 & 1189.34913492778 & -39.3491349277801 \tabularnewline
90 & 1270 & 1280.45488824894 & -10.4548882489412 \tabularnewline
91 & 1410 & 1383.45349603933 & 26.5465039606677 \tabularnewline
92 & 1420 & 1265.70464961965 & 154.295350380348 \tabularnewline
93 & 1260 & 1271.48655875641 & -11.4865587564143 \tabularnewline
94 & 1300 & 1208.92240407381 & 91.0775959261889 \tabularnewline
95 & 1410 & 1342.97546049755 & 67.0245395024547 \tabularnewline
96 & 1000 & 998.152931026797 & 1.84706897320257 \tabularnewline
97 & 950 & 979.894995320595 & -29.8949953205947 \tabularnewline
98 & 1280 & 1238.6502789987 & 41.3497210013004 \tabularnewline
99 & 1330 & 1191.00015375426 & 138.999846245743 \tabularnewline
100 & 1190 & 1204.50298331626 & -14.5029833162621 \tabularnewline
101 & 1170 & 1158.63808458984 & 11.3619154101648 \tabularnewline
102 & 1270 & 1279.62489500444 & -9.62489500444076 \tabularnewline
103 & 1340 & 1418.90008279685 & -78.9000827968521 \tabularnewline
104 & 1470 & 1419.5165933298 & 50.4834066701983 \tabularnewline
105 & 1270 & 1268.37781232287 & 1.62218767713398 \tabularnewline
106 & 1280 & 1303.13349004114 & -23.1334900411393 \tabularnewline
107 & 1430 & 1412.43742498319 & 17.5625750168133 \tabularnewline
108 & 980 & 1005.73280906241 & -25.732809062414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169301&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]1130[/C][C]1147.95673076923[/C][C]-17.9567307692305[/C][/ROW]
[ROW][C]14[/C][C]1340[/C][C]1354.5009255273[/C][C]-14.5009255272976[/C][/ROW]
[ROW][C]15[/C][C]1140[/C][C]1153.57886480117[/C][C]-13.5788648011687[/C][/ROW]
[ROW][C]16[/C][C]1290[/C][C]1304.29931547624[/C][C]-14.2993154762448[/C][/ROW]
[ROW][C]17[/C][C]1260[/C][C]1269.95357552375[/C][C]-9.95357552375413[/C][/ROW]
[ROW][C]18[/C][C]1280[/C][C]1290.26188483115[/C][C]-10.261884831147[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1295.94438816309[/C][C]34.0556118369079[/C][/ROW]
[ROW][C]20[/C][C]1270[/C][C]1250.31098646939[/C][C]19.6890135306071[/C][/ROW]
[ROW][C]21[/C][C]1300[/C][C]1334.39867042225[/C][C]-34.3986704222534[/C][/ROW]
[ROW][C]22[/C][C]1150[/C][C]1173.31568279704[/C][C]-23.3156827970406[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]1322.00344179661[/C][C]87.9965582033858[/C][/ROW]
[ROW][C]24[/C][C]1250[/C][C]1386.59035615041[/C][C]-136.59035615041[/C][/ROW]
[ROW][C]25[/C][C]1030[/C][C]1105.14490285022[/C][C]-75.1449028502186[/C][/ROW]
[ROW][C]26[/C][C]1320[/C][C]1312.89860743639[/C][C]7.10139256361322[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1112.78468688186[/C][C]47.2153131181437[/C][/ROW]
[ROW][C]28[/C][C]1300[/C][C]1263.926530212[/C][C]36.0734697880036[/C][/ROW]
[ROW][C]29[/C][C]1190[/C][C]1234.66896710513[/C][C]-44.6689671051302[/C][/ROW]
[ROW][C]30[/C][C]1310[/C][C]1253.53699183726[/C][C]56.4630081627365[/C][/ROW]
[ROW][C]31[/C][C]1290[/C][C]1302.25533285395[/C][C]-12.2553328539454[/C][/ROW]
[ROW][C]32[/C][C]1320[/C][C]1241.80258536959[/C][C]78.1974146304108[/C][/ROW]
[ROW][C]33[/C][C]1300[/C][C]1276.58673301967[/C][C]23.4132669803273[/C][/ROW]
[ROW][C]34[/C][C]1230[/C][C]1127.43080972696[/C][C]102.569190273042[/C][/ROW]
[ROW][C]35[/C][C]1330[/C][C]1384.00748772984[/C][C]-54.0074877298373[/C][/ROW]
[ROW][C]36[/C][C]1220[/C][C]1234.88342612994[/C][C]-14.8834261299428[/C][/ROW]
[ROW][C]37[/C][C]1010[/C][C]1014.44318372616[/C][C]-4.44318372615771[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1301.70022623831[/C][C]-11.7002262383057[/C][/ROW]
[ROW][C]39[/C][C]1170[/C][C]1139.40056240055[/C][C]30.5994375994487[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1280.33770204596[/C][C]-40.3377020459602[/C][/ROW]
[ROW][C]41[/C][C]1260[/C][C]1173.97399693821[/C][C]86.0260030617935[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1291.54682387412[/C][C]-31.5468238741173[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1274.28914806612[/C][C]35.7108519338822[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1300.40718440574[/C][C]59.5928155942645[/C][/ROW]
[ROW][C]45[/C][C]1250[/C][C]1284.04098924809[/C][C]-34.040989248093[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1208.07355623734[/C][C]-38.0735562373447[/C][/ROW]
[ROW][C]47[/C][C]1360[/C][C]1314.52675214569[/C][C]45.4732478543085[/C][/ROW]
[ROW][C]48[/C][C]1140[/C][C]1204.73117765222[/C][C]-64.7311776522233[/C][/ROW]
[ROW][C]49[/C][C]1030[/C][C]992.981087221248[/C][C]37.0189127787518[/C][/ROW]
[ROW][C]50[/C][C]1260[/C][C]1274.69162160699[/C][C]-14.6916216069892[/C][/ROW]
[ROW][C]51[/C][C]1210[/C][C]1152.18741623733[/C][C]57.8125837626742[/C][/ROW]
[ROW][C]52[/C][C]1190[/C][C]1227.66381868279[/C][C]-37.663818682795[/C][/ROW]
[ROW][C]53[/C][C]1230[/C][C]1240.08283985375[/C][C]-10.0828398537462[/C][/ROW]
[ROW][C]54[/C][C]1350[/C][C]1245.21757295957[/C][C]104.782427040433[/C][/ROW]
[ROW][C]55[/C][C]1300[/C][C]1294.73152027022[/C][C]5.26847972978408[/C][/ROW]
[ROW][C]56[/C][C]1340[/C][C]1342.86590475718[/C][C]-2.8659047571814[/C][/ROW]
[ROW][C]57[/C][C]1270[/C][C]1237.44606249871[/C][C]32.5539375012854[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1159.69763557183[/C][C]60.3023644281704[/C][/ROW]
[ROW][C]59[/C][C]1400[/C][C]1347.51328849761[/C][C]52.4867115023851[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]1135.40240219965[/C][C]-15.4024021996454[/C][/ROW]
[ROW][C]61[/C][C]1000[/C][C]1021.0777231945[/C][C]-21.077723194502[/C][/ROW]
[ROW][C]62[/C][C]1260[/C][C]1253.66957088174[/C][C]6.33042911825783[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1200.38546055091[/C][C]59.6145394490916[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1187.26576118028[/C][C]-37.2657611802838[/C][/ROW]
[ROW][C]65[/C][C]1240[/C][C]1226.33272347278[/C][C]13.6672765272192[/C][/ROW]
[ROW][C]66[/C][C]1360[/C][C]1340.52448906838[/C][C]19.4755109316245[/C][/ROW]
[ROW][C]67[/C][C]1350[/C][C]1295.35240551217[/C][C]54.6475944878282[/C][/ROW]
[ROW][C]68[/C][C]1280[/C][C]1337.81621065921[/C][C]-57.8162106592133[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1264.82470780609[/C][C]55.1752921939087[/C][/ROW]
[ROW][C]70[/C][C]1210[/C][C]1214.26454604516[/C][C]-4.26454604516084[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1393.63185926932[/C][C]-23.6318592693158[/C][/ROW]
[ROW][C]72[/C][C]1060[/C][C]1116.25932284121[/C][C]-56.2593228412068[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]995.663108056091[/C][C]44.3368919439088[/C][/ROW]
[ROW][C]74[/C][C]1260[/C][C]1255.75895756506[/C][C]4.24104243494367[/C][/ROW]
[ROW][C]75[/C][C]1210[/C][C]1252.58508834937[/C][C]-42.5850883493681[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1146.14496980825[/C][C]53.8550301917453[/C][/ROW]
[ROW][C]77[/C][C]1200[/C][C]1235.32775073312[/C][C]-35.3277507331161[/C][/ROW]
[ROW][C]78[/C][C]1290[/C][C]1353.8204570737[/C][C]-63.8204570737032[/C][/ROW]
[ROW][C]79[/C][C]1400[/C][C]1339.34558943227[/C][C]60.654410567731[/C][/ROW]
[ROW][C]80[/C][C]1280[/C][C]1276.37787772823[/C][C]3.62212227176747[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1310.70010202173[/C][C]-30.7001020217324[/C][/ROW]
[ROW][C]82[/C][C]1220[/C][C]1202.08242229985[/C][C]17.9175777001451[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1363.61028536493[/C][C]-13.610285364932[/C][/ROW]
[ROW][C]84[/C][C]1000[/C][C]1055.71780726156[/C][C]-55.717807261557[/C][/ROW]
[ROW][C]85[/C][C]980[/C][C]1029.17508079577[/C][C]-49.1750807957692[/C][/ROW]
[ROW][C]86[/C][C]1240[/C][C]1248.9427730415[/C][C]-8.94277304150182[/C][/ROW]
[ROW][C]87[/C][C]1190[/C][C]1201.0264403996[/C][C]-11.0264403996005[/C][/ROW]
[ROW][C]88[/C][C]1200[/C][C]1185.23724390875[/C][C]14.7627560912501[/C][/ROW]
[ROW][C]89[/C][C]1150[/C][C]1189.34913492778[/C][C]-39.3491349277801[/C][/ROW]
[ROW][C]90[/C][C]1270[/C][C]1280.45488824894[/C][C]-10.4548882489412[/C][/ROW]
[ROW][C]91[/C][C]1410[/C][C]1383.45349603933[/C][C]26.5465039606677[/C][/ROW]
[ROW][C]92[/C][C]1420[/C][C]1265.70464961965[/C][C]154.295350380348[/C][/ROW]
[ROW][C]93[/C][C]1260[/C][C]1271.48655875641[/C][C]-11.4865587564143[/C][/ROW]
[ROW][C]94[/C][C]1300[/C][C]1208.92240407381[/C][C]91.0775959261889[/C][/ROW]
[ROW][C]95[/C][C]1410[/C][C]1342.97546049755[/C][C]67.0245395024547[/C][/ROW]
[ROW][C]96[/C][C]1000[/C][C]998.152931026797[/C][C]1.84706897320257[/C][/ROW]
[ROW][C]97[/C][C]950[/C][C]979.894995320595[/C][C]-29.8949953205947[/C][/ROW]
[ROW][C]98[/C][C]1280[/C][C]1238.6502789987[/C][C]41.3497210013004[/C][/ROW]
[ROW][C]99[/C][C]1330[/C][C]1191.00015375426[/C][C]138.999846245743[/C][/ROW]
[ROW][C]100[/C][C]1190[/C][C]1204.50298331626[/C][C]-14.5029833162621[/C][/ROW]
[ROW][C]101[/C][C]1170[/C][C]1158.63808458984[/C][C]11.3619154101648[/C][/ROW]
[ROW][C]102[/C][C]1270[/C][C]1279.62489500444[/C][C]-9.62489500444076[/C][/ROW]
[ROW][C]103[/C][C]1340[/C][C]1418.90008279685[/C][C]-78.9000827968521[/C][/ROW]
[ROW][C]104[/C][C]1470[/C][C]1419.5165933298[/C][C]50.4834066701983[/C][/ROW]
[ROW][C]105[/C][C]1270[/C][C]1268.37781232287[/C][C]1.62218767713398[/C][/ROW]
[ROW][C]106[/C][C]1280[/C][C]1303.13349004114[/C][C]-23.1334900411393[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1412.43742498319[/C][C]17.5625750168133[/C][/ROW]
[ROW][C]108[/C][C]980[/C][C]1005.73280906241[/C][C]-25.732809062414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169301&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
1311301147.95673076923-17.9567307692305
1413401354.5009255273-14.5009255272976
1511401153.57886480117-13.5788648011687
1612901304.29931547624-14.2993154762448
1712601269.95357552375-9.95357552375413
1812801290.26188483115-10.261884831147
1913301295.9443881630934.0556118369079
2012701250.3109864693919.6890135306071
2113001334.39867042225-34.3986704222534
2211501173.31568279704-23.3156827970406
2314101322.0034417966187.9965582033858
2412501386.59035615041-136.59035615041
2510301105.14490285022-75.1449028502186
2613201312.898607436397.10139256361322
2711601112.7846868818647.2153131181437
2813001263.92653021236.0734697880036
2911901234.66896710513-44.6689671051302
3013101253.5369918372656.4630081627365
3112901302.25533285395-12.2553328539454
3213201241.8025853695978.1974146304108
3313001276.5867330196723.4132669803273
3412301127.43080972696102.569190273042
3513301384.00748772984-54.0074877298373
3612201234.88342612994-14.8834261299428
3710101014.44318372616-4.44318372615771
3812901301.70022623831-11.7002262383057
3911701139.4005624005530.5994375994487
4012401280.33770204596-40.3377020459602
4112601173.9739969382186.0260030617935
4212601291.54682387412-31.5468238741173
4313101274.2891480661235.7108519338822
4413601300.4071844057459.5928155942645
4512501284.04098924809-34.040989248093
4611701208.07355623734-38.0735562373447
4713601314.5267521456945.4732478543085
4811401204.73117765222-64.7311776522233
491030992.98108722124837.0189127787518
5012601274.69162160699-14.6916216069892
5112101152.1874162373357.8125837626742
5211901227.66381868279-37.663818682795
5312301240.08283985375-10.0828398537462
5413501245.21757295957104.782427040433
5513001294.731520270225.26847972978408
5613401342.86590475718-2.8659047571814
5712701237.4460624987132.5539375012854
5812201159.6976355718360.3023644281704
5914001347.5132884976152.4867115023851
6011201135.40240219965-15.4024021996454
6110001021.0777231945-21.077723194502
6212601253.669570881746.33042911825783
6312601200.3854605509159.6145394490916
6411501187.26576118028-37.2657611802838
6512401226.3327234727813.6672765272192
6613601340.5244890683819.4755109316245
6713501295.3524055121754.6475944878282
6812801337.81621065921-57.8162106592133
6913201264.8247078060955.1752921939087
7012101214.26454604516-4.26454604516084
7113701393.63185926932-23.6318592693158
7210601116.25932284121-56.2593228412068
731040995.66310805609144.3368919439088
7412601255.758957565064.24104243494367
7512101252.58508834937-42.5850883493681
7612001146.1449698082553.8550301917453
7712001235.32775073312-35.3277507331161
7812901353.8204570737-63.8204570737032
7914001339.3455894322760.654410567731
8012801276.377877728233.62212227176747
8112801310.70010202173-30.7001020217324
8212201202.0824222998517.9175777001451
8313501363.61028536493-13.610285364932
8410001055.71780726156-55.717807261557
859801029.17508079577-49.1750807957692
8612401248.9427730415-8.94277304150182
8711901201.0264403996-11.0264403996005
8812001185.2372439087514.7627560912501
8911501189.34913492778-39.3491349277801
9012701280.45488824894-10.4548882489412
9114101383.4534960393326.5465039606677
9214201265.70464961965154.295350380348
9312601271.48655875641-11.4865587564143
9413001208.9224040738191.0775959261889
9514101342.9754604975567.0245395024547
961000998.1529310267971.84706897320257
97950979.894995320595-29.8949953205947
9812801238.650278998741.3497210013004
9913301191.00015375426138.999846245743
10011901204.50298331626-14.5029833162621
10111701158.6380845898411.3619154101648
10212701279.62489500444-9.62489500444076
10313401418.90008279685-78.9000827968521
10414701419.516593329850.4834066701983
10512701268.377812322871.62218767713398
10612801303.13349004114-23.1334900411393
10714301412.4374249831917.5625750168133
1089801005.73280906241-25.732809062414







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109957.347132022569861.7214658037841052.97279824135
1101283.936542935441188.274700891381379.59838497951
1111326.998555135131231.291017620461422.70609264981
1121193.113388027631097.349535429961288.87724062529
1131171.634925777661075.80304440241267.46680715291
1141272.456884072461176.544173283831368.3695948611
1151346.870628013011250.863208736991442.87804728904
1161470.661832894071374.544757581941566.7789082062
1171272.43358898041176.190853122821368.67632483798
1181283.85289409991187.467449371921380.23833882788
1191431.809179472171335.262948578811528.35541036553
120984.035696588796887.3095898686011080.76180330899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 957.347132022569 & 861.721465803784 & 1052.97279824135 \tabularnewline
110 & 1283.93654293544 & 1188.27470089138 & 1379.59838497951 \tabularnewline
111 & 1326.99855513513 & 1231.29101762046 & 1422.70609264981 \tabularnewline
112 & 1193.11338802763 & 1097.34953542996 & 1288.87724062529 \tabularnewline
113 & 1171.63492577766 & 1075.8030444024 & 1267.46680715291 \tabularnewline
114 & 1272.45688407246 & 1176.54417328383 & 1368.3695948611 \tabularnewline
115 & 1346.87062801301 & 1250.86320873699 & 1442.87804728904 \tabularnewline
116 & 1470.66183289407 & 1374.54475758194 & 1566.7789082062 \tabularnewline
117 & 1272.4335889804 & 1176.19085312282 & 1368.67632483798 \tabularnewline
118 & 1283.8528940999 & 1187.46744937192 & 1380.23833882788 \tabularnewline
119 & 1431.80917947217 & 1335.26294857881 & 1528.35541036553 \tabularnewline
120 & 984.035696588796 & 887.309589868601 & 1080.76180330899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169301&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]957.347132022569[/C][C]861.721465803784[/C][C]1052.97279824135[/C][/ROW]
[ROW][C]110[/C][C]1283.93654293544[/C][C]1188.27470089138[/C][C]1379.59838497951[/C][/ROW]
[ROW][C]111[/C][C]1326.99855513513[/C][C]1231.29101762046[/C][C]1422.70609264981[/C][/ROW]
[ROW][C]112[/C][C]1193.11338802763[/C][C]1097.34953542996[/C][C]1288.87724062529[/C][/ROW]
[ROW][C]113[/C][C]1171.63492577766[/C][C]1075.8030444024[/C][C]1267.46680715291[/C][/ROW]
[ROW][C]114[/C][C]1272.45688407246[/C][C]1176.54417328383[/C][C]1368.3695948611[/C][/ROW]
[ROW][C]115[/C][C]1346.87062801301[/C][C]1250.86320873699[/C][C]1442.87804728904[/C][/ROW]
[ROW][C]116[/C][C]1470.66183289407[/C][C]1374.54475758194[/C][C]1566.7789082062[/C][/ROW]
[ROW][C]117[/C][C]1272.4335889804[/C][C]1176.19085312282[/C][C]1368.67632483798[/C][/ROW]
[ROW][C]118[/C][C]1283.8528940999[/C][C]1187.46744937192[/C][C]1380.23833882788[/C][/ROW]
[ROW][C]119[/C][C]1431.80917947217[/C][C]1335.26294857881[/C][C]1528.35541036553[/C][/ROW]
[ROW][C]120[/C][C]984.035696588796[/C][C]887.309589868601[/C][C]1080.76180330899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169301&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
109957.347132022569861.7214658037841052.97279824135
1101283.936542935441188.274700891381379.59838497951
1111326.998555135131231.291017620461422.70609264981
1121193.113388027631097.349535429961288.87724062529
1131171.634925777661075.80304440241267.46680715291
1141272.456884072461176.544173283831368.3695948611
1151346.870628013011250.863208736991442.87804728904
1161470.661832894071374.544757581941566.7789082062
1171272.43358898041176.190853122821368.67632483798
1181283.85289409991187.467449371921380.23833882788
1191431.809179472171335.262948578811528.35541036553
120984.035696588796887.3095898686011080.76180330899



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')