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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 12 Aug 2016 11:11:27 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/12/t1470996732sksca6l4votx2m4.htm/, Retrieved Sun, 05 May 2024 09:30:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296416, Retrieved Sun, 05 May 2024 09:30:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reeks B Stap 28] [2016-08-12 10:11:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1410
1425
1380
1395
1395
1350
1410
1260
1335
1275
1245
1410
1440
1350
1410
1380
1395
1455
1395
1170
1215
1305
1080
1320
1380
1380
1425
1425
1335
1440
1170
1170
1140
1290
1110
1530
1335
1560
1380
1350
1425
1485
1260
1110
1260
1440
1185
1515
1350
1455
1380
1470
1335
1500
1320
1110
1290
1410
1140
1515
1305
1470
1380
1425
1320
1470
1365
1095
1320
1230
1035
1485
1200
1440
1365
1425
1410
1515
1335
990
1290
1260
1110
1470
1230
1620
1395
1455
1395
1515
1320
1110
1290
1215
1125
1335
1185
1500
1335
1455
1350
1485
1365
1095
1275
1260
1245
1425




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296416&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296416&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.15308162522971
beta0.00940485503733336
gamma0.766853296758206

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.15308162522971 \tabularnewline
beta & 0.00940485503733336 \tabularnewline
gamma & 0.766853296758206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296416&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]0.15308162522971[/C][/ROW]
[ROW][C]beta[/C][C]0.00940485503733336[/C][/ROW]
[ROW][C]gamma[/C][C]0.766853296758206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296416&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
alpha0.15308162522971
beta0.00940485503733336
gamma0.766853296758206







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314401428.345352564111.6546474358975
1413501342.64405893867.35594106139706
1514101410.67030278045-0.670302780449902
1613801382.46691112855-2.46691112854978
1713951400.85994011298-5.85994011298135
1814551468.72512208875-13.725122088749
1913951390.991529022634.00847097736641
2011701241.60339424197-71.6033942419731
2112151305.53738408878-90.5373840887783
2213051228.9425803757676.0574196242351
2310801209.20988063516-129.209880635156
2413201347.86850414322-27.868504143225
2513801375.194760045134.8052399548676
2613801285.2935845203594.7064154796526
2714251361.2450823857263.7549176142763
2814251341.5961757261683.4038242738407
2913351370.91341821786-35.9134182178598
3014401429.0091842989710.9908157010295
3111701366.55138575042-196.551385750422
3211701137.0403707838632.959629216138
3311401204.52086199149-64.520861991492
3412901239.9799185547350.0200814452689
3511101082.7847426077427.2152573922624
3615301311.26847895349218.731521046506
3713351397.98197060162-62.9819706016156
3815601356.41057839131203.589421608689
3913801429.40434665298-49.4043466529811
4013501405.50724958866-55.5072495886623
4114251336.1809273831988.8190726168102
4214851444.1262498847440.8737501152552
4312601251.787977871758.21202212824619
4411101203.31179719477-93.3117971947661
4512601188.601372048671.3986279513983
4614401319.90170488904120.09829511096
4711851159.3687308370825.6312691629207
4815151512.735656196162.26434380383603
4913501383.7812057112-33.7812057112035
5014551520.28143812878-65.2814381287776
5113801387.8925410565-7.89254105649798
5214701366.53269815414103.46730184586
5313351415.65198312617-80.6519831261735
5415001466.6467808733633.353219126644
5513201252.0649223739967.9350776260092
5611101147.00157488644-37.0015748864364
5712901248.1716755213441.8283244786603
5814101406.818634957173.18136504282552
5911401167.111449416-27.1114494159967
6015151497.2289456687517.7710543312471
6113051347.26083830474-42.2608383047441
6214701462.015348643427.98465135658375
6313801378.230104394121.76989560588231
6414251430.80336127791-5.80336127791179
6513201343.58944669404-23.5894466940383
6614701477.41632471369-7.41632471369144
6713651279.0491008811785.9508991188291
6810951108.61329307617-13.6132930761703
6913201264.6164501773655.3835498226429
7012301400.31394838379-170.313948383789
7110351114.1992190543-79.1992190543012
7214851465.2429679504319.7570320495736
7312001276.34374038251-76.3437403825058
7414401418.2175638241921.7824361758078
7513651332.2323586114632.7676413885383
7614251384.4009852262440.5990147737648
7714101292.57456664525117.425433354752
7815151458.530616921956.4693830781009
7913351330.712130413274.28786958672913
809901083.12499972486-93.1249997248608
8112901271.6656999912118.3343000087873
8212601254.954803360435.04519663957149
8311101054.9575176268955.0424823731071
8414701491.11042578775-21.11042578775
8512301233.773372039-3.77337203900333
8616201450.82214786263169.17785213737
8713951395.08367924672-0.0836792467164287
8814551447.810988294237.18901170577101
8913951401.21929763802-6.21929763802063
9015151508.934286269416.06571373058887
9113201339.71276168035-19.7127616803457
9211101025.3538054332684.6461945667443
9312901313.9207456961-23.9207456961046
9412151282.47391380621-67.4739138062146
9511251104.1055282644120.8944717355882
9613351485.78230781901-150.782307819007
9711851219.87767747092-34.8776774709197
9815001544.46849367161-44.4684936716142
9913351345.76641310978-10.7664131097772
10014551401.2370249414753.7629750585313
10113501352.7891114877-2.78911148770385
10214851468.7351355172516.2648644827464
10313651284.0747403773480.9252596226611
10410951052.7856683535442.2143316464612
10512751264.1727227781810.8272772218199
10612601209.6348385999350.3651614000676
10712451106.74282382226138.25717617774
10814251395.102527404729.897472595303

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1440 & 1428.3453525641 & 11.6546474358975 \tabularnewline
14 & 1350 & 1342.6440589386 & 7.35594106139706 \tabularnewline
15 & 1410 & 1410.67030278045 & -0.670302780449902 \tabularnewline
16 & 1380 & 1382.46691112855 & -2.46691112854978 \tabularnewline
17 & 1395 & 1400.85994011298 & -5.85994011298135 \tabularnewline
18 & 1455 & 1468.72512208875 & -13.725122088749 \tabularnewline
19 & 1395 & 1390.99152902263 & 4.00847097736641 \tabularnewline
20 & 1170 & 1241.60339424197 & -71.6033942419731 \tabularnewline
21 & 1215 & 1305.53738408878 & -90.5373840887783 \tabularnewline
22 & 1305 & 1228.94258037576 & 76.0574196242351 \tabularnewline
23 & 1080 & 1209.20988063516 & -129.209880635156 \tabularnewline
24 & 1320 & 1347.86850414322 & -27.868504143225 \tabularnewline
25 & 1380 & 1375.19476004513 & 4.8052399548676 \tabularnewline
26 & 1380 & 1285.29358452035 & 94.7064154796526 \tabularnewline
27 & 1425 & 1361.24508238572 & 63.7549176142763 \tabularnewline
28 & 1425 & 1341.59617572616 & 83.4038242738407 \tabularnewline
29 & 1335 & 1370.91341821786 & -35.9134182178598 \tabularnewline
30 & 1440 & 1429.00918429897 & 10.9908157010295 \tabularnewline
31 & 1170 & 1366.55138575042 & -196.551385750422 \tabularnewline
32 & 1170 & 1137.04037078386 & 32.959629216138 \tabularnewline
33 & 1140 & 1204.52086199149 & -64.520861991492 \tabularnewline
34 & 1290 & 1239.97991855473 & 50.0200814452689 \tabularnewline
35 & 1110 & 1082.78474260774 & 27.2152573922624 \tabularnewline
36 & 1530 & 1311.26847895349 & 218.731521046506 \tabularnewline
37 & 1335 & 1397.98197060162 & -62.9819706016156 \tabularnewline
38 & 1560 & 1356.41057839131 & 203.589421608689 \tabularnewline
39 & 1380 & 1429.40434665298 & -49.4043466529811 \tabularnewline
40 & 1350 & 1405.50724958866 & -55.5072495886623 \tabularnewline
41 & 1425 & 1336.18092738319 & 88.8190726168102 \tabularnewline
42 & 1485 & 1444.12624988474 & 40.8737501152552 \tabularnewline
43 & 1260 & 1251.78797787175 & 8.21202212824619 \tabularnewline
44 & 1110 & 1203.31179719477 & -93.3117971947661 \tabularnewline
45 & 1260 & 1188.6013720486 & 71.3986279513983 \tabularnewline
46 & 1440 & 1319.90170488904 & 120.09829511096 \tabularnewline
47 & 1185 & 1159.36873083708 & 25.6312691629207 \tabularnewline
48 & 1515 & 1512.73565619616 & 2.26434380383603 \tabularnewline
49 & 1350 & 1383.7812057112 & -33.7812057112035 \tabularnewline
50 & 1455 & 1520.28143812878 & -65.2814381287776 \tabularnewline
51 & 1380 & 1387.8925410565 & -7.89254105649798 \tabularnewline
52 & 1470 & 1366.53269815414 & 103.46730184586 \tabularnewline
53 & 1335 & 1415.65198312617 & -80.6519831261735 \tabularnewline
54 & 1500 & 1466.64678087336 & 33.353219126644 \tabularnewline
55 & 1320 & 1252.06492237399 & 67.9350776260092 \tabularnewline
56 & 1110 & 1147.00157488644 & -37.0015748864364 \tabularnewline
57 & 1290 & 1248.17167552134 & 41.8283244786603 \tabularnewline
58 & 1410 & 1406.81863495717 & 3.18136504282552 \tabularnewline
59 & 1140 & 1167.111449416 & -27.1114494159967 \tabularnewline
60 & 1515 & 1497.22894566875 & 17.7710543312471 \tabularnewline
61 & 1305 & 1347.26083830474 & -42.2608383047441 \tabularnewline
62 & 1470 & 1462.01534864342 & 7.98465135658375 \tabularnewline
63 & 1380 & 1378.23010439412 & 1.76989560588231 \tabularnewline
64 & 1425 & 1430.80336127791 & -5.80336127791179 \tabularnewline
65 & 1320 & 1343.58944669404 & -23.5894466940383 \tabularnewline
66 & 1470 & 1477.41632471369 & -7.41632471369144 \tabularnewline
67 & 1365 & 1279.04910088117 & 85.9508991188291 \tabularnewline
68 & 1095 & 1108.61329307617 & -13.6132930761703 \tabularnewline
69 & 1320 & 1264.61645017736 & 55.3835498226429 \tabularnewline
70 & 1230 & 1400.31394838379 & -170.313948383789 \tabularnewline
71 & 1035 & 1114.1992190543 & -79.1992190543012 \tabularnewline
72 & 1485 & 1465.24296795043 & 19.7570320495736 \tabularnewline
73 & 1200 & 1276.34374038251 & -76.3437403825058 \tabularnewline
74 & 1440 & 1418.21756382419 & 21.7824361758078 \tabularnewline
75 & 1365 & 1332.23235861146 & 32.7676413885383 \tabularnewline
76 & 1425 & 1384.40098522624 & 40.5990147737648 \tabularnewline
77 & 1410 & 1292.57456664525 & 117.425433354752 \tabularnewline
78 & 1515 & 1458.5306169219 & 56.4693830781009 \tabularnewline
79 & 1335 & 1330.71213041327 & 4.28786958672913 \tabularnewline
80 & 990 & 1083.12499972486 & -93.1249997248608 \tabularnewline
81 & 1290 & 1271.66569999121 & 18.3343000087873 \tabularnewline
82 & 1260 & 1254.95480336043 & 5.04519663957149 \tabularnewline
83 & 1110 & 1054.95751762689 & 55.0424823731071 \tabularnewline
84 & 1470 & 1491.11042578775 & -21.11042578775 \tabularnewline
85 & 1230 & 1233.773372039 & -3.77337203900333 \tabularnewline
86 & 1620 & 1450.82214786263 & 169.17785213737 \tabularnewline
87 & 1395 & 1395.08367924672 & -0.0836792467164287 \tabularnewline
88 & 1455 & 1447.81098829423 & 7.18901170577101 \tabularnewline
89 & 1395 & 1401.21929763802 & -6.21929763802063 \tabularnewline
90 & 1515 & 1508.93428626941 & 6.06571373058887 \tabularnewline
91 & 1320 & 1339.71276168035 & -19.7127616803457 \tabularnewline
92 & 1110 & 1025.35380543326 & 84.6461945667443 \tabularnewline
93 & 1290 & 1313.9207456961 & -23.9207456961046 \tabularnewline
94 & 1215 & 1282.47391380621 & -67.4739138062146 \tabularnewline
95 & 1125 & 1104.10552826441 & 20.8944717355882 \tabularnewline
96 & 1335 & 1485.78230781901 & -150.782307819007 \tabularnewline
97 & 1185 & 1219.87767747092 & -34.8776774709197 \tabularnewline
98 & 1500 & 1544.46849367161 & -44.4684936716142 \tabularnewline
99 & 1335 & 1345.76641310978 & -10.7664131097772 \tabularnewline
100 & 1455 & 1401.23702494147 & 53.7629750585313 \tabularnewline
101 & 1350 & 1352.7891114877 & -2.78911148770385 \tabularnewline
102 & 1485 & 1468.73513551725 & 16.2648644827464 \tabularnewline
103 & 1365 & 1284.07474037734 & 80.9252596226611 \tabularnewline
104 & 1095 & 1052.78566835354 & 42.2143316464612 \tabularnewline
105 & 1275 & 1264.17272277818 & 10.8272772218199 \tabularnewline
106 & 1260 & 1209.63483859993 & 50.3651614000676 \tabularnewline
107 & 1245 & 1106.74282382226 & 138.25717617774 \tabularnewline
108 & 1425 & 1395.1025274047 & 29.897472595303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296416&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]1440[/C][C]1428.3453525641[/C][C]11.6546474358975[/C][/ROW]
[ROW][C]14[/C][C]1350[/C][C]1342.6440589386[/C][C]7.35594106139706[/C][/ROW]
[ROW][C]15[/C][C]1410[/C][C]1410.67030278045[/C][C]-0.670302780449902[/C][/ROW]
[ROW][C]16[/C][C]1380[/C][C]1382.46691112855[/C][C]-2.46691112854978[/C][/ROW]
[ROW][C]17[/C][C]1395[/C][C]1400.85994011298[/C][C]-5.85994011298135[/C][/ROW]
[ROW][C]18[/C][C]1455[/C][C]1468.72512208875[/C][C]-13.725122088749[/C][/ROW]
[ROW][C]19[/C][C]1395[/C][C]1390.99152902263[/C][C]4.00847097736641[/C][/ROW]
[ROW][C]20[/C][C]1170[/C][C]1241.60339424197[/C][C]-71.6033942419731[/C][/ROW]
[ROW][C]21[/C][C]1215[/C][C]1305.53738408878[/C][C]-90.5373840887783[/C][/ROW]
[ROW][C]22[/C][C]1305[/C][C]1228.94258037576[/C][C]76.0574196242351[/C][/ROW]
[ROW][C]23[/C][C]1080[/C][C]1209.20988063516[/C][C]-129.209880635156[/C][/ROW]
[ROW][C]24[/C][C]1320[/C][C]1347.86850414322[/C][C]-27.868504143225[/C][/ROW]
[ROW][C]25[/C][C]1380[/C][C]1375.19476004513[/C][C]4.8052399548676[/C][/ROW]
[ROW][C]26[/C][C]1380[/C][C]1285.29358452035[/C][C]94.7064154796526[/C][/ROW]
[ROW][C]27[/C][C]1425[/C][C]1361.24508238572[/C][C]63.7549176142763[/C][/ROW]
[ROW][C]28[/C][C]1425[/C][C]1341.59617572616[/C][C]83.4038242738407[/C][/ROW]
[ROW][C]29[/C][C]1335[/C][C]1370.91341821786[/C][C]-35.9134182178598[/C][/ROW]
[ROW][C]30[/C][C]1440[/C][C]1429.00918429897[/C][C]10.9908157010295[/C][/ROW]
[ROW][C]31[/C][C]1170[/C][C]1366.55138575042[/C][C]-196.551385750422[/C][/ROW]
[ROW][C]32[/C][C]1170[/C][C]1137.04037078386[/C][C]32.959629216138[/C][/ROW]
[ROW][C]33[/C][C]1140[/C][C]1204.52086199149[/C][C]-64.520861991492[/C][/ROW]
[ROW][C]34[/C][C]1290[/C][C]1239.97991855473[/C][C]50.0200814452689[/C][/ROW]
[ROW][C]35[/C][C]1110[/C][C]1082.78474260774[/C][C]27.2152573922624[/C][/ROW]
[ROW][C]36[/C][C]1530[/C][C]1311.26847895349[/C][C]218.731521046506[/C][/ROW]
[ROW][C]37[/C][C]1335[/C][C]1397.98197060162[/C][C]-62.9819706016156[/C][/ROW]
[ROW][C]38[/C][C]1560[/C][C]1356.41057839131[/C][C]203.589421608689[/C][/ROW]
[ROW][C]39[/C][C]1380[/C][C]1429.40434665298[/C][C]-49.4043466529811[/C][/ROW]
[ROW][C]40[/C][C]1350[/C][C]1405.50724958866[/C][C]-55.5072495886623[/C][/ROW]
[ROW][C]41[/C][C]1425[/C][C]1336.18092738319[/C][C]88.8190726168102[/C][/ROW]
[ROW][C]42[/C][C]1485[/C][C]1444.12624988474[/C][C]40.8737501152552[/C][/ROW]
[ROW][C]43[/C][C]1260[/C][C]1251.78797787175[/C][C]8.21202212824619[/C][/ROW]
[ROW][C]44[/C][C]1110[/C][C]1203.31179719477[/C][C]-93.3117971947661[/C][/ROW]
[ROW][C]45[/C][C]1260[/C][C]1188.6013720486[/C][C]71.3986279513983[/C][/ROW]
[ROW][C]46[/C][C]1440[/C][C]1319.90170488904[/C][C]120.09829511096[/C][/ROW]
[ROW][C]47[/C][C]1185[/C][C]1159.36873083708[/C][C]25.6312691629207[/C][/ROW]
[ROW][C]48[/C][C]1515[/C][C]1512.73565619616[/C][C]2.26434380383603[/C][/ROW]
[ROW][C]49[/C][C]1350[/C][C]1383.7812057112[/C][C]-33.7812057112035[/C][/ROW]
[ROW][C]50[/C][C]1455[/C][C]1520.28143812878[/C][C]-65.2814381287776[/C][/ROW]
[ROW][C]51[/C][C]1380[/C][C]1387.8925410565[/C][C]-7.89254105649798[/C][/ROW]
[ROW][C]52[/C][C]1470[/C][C]1366.53269815414[/C][C]103.46730184586[/C][/ROW]
[ROW][C]53[/C][C]1335[/C][C]1415.65198312617[/C][C]-80.6519831261735[/C][/ROW]
[ROW][C]54[/C][C]1500[/C][C]1466.64678087336[/C][C]33.353219126644[/C][/ROW]
[ROW][C]55[/C][C]1320[/C][C]1252.06492237399[/C][C]67.9350776260092[/C][/ROW]
[ROW][C]56[/C][C]1110[/C][C]1147.00157488644[/C][C]-37.0015748864364[/C][/ROW]
[ROW][C]57[/C][C]1290[/C][C]1248.17167552134[/C][C]41.8283244786603[/C][/ROW]
[ROW][C]58[/C][C]1410[/C][C]1406.81863495717[/C][C]3.18136504282552[/C][/ROW]
[ROW][C]59[/C][C]1140[/C][C]1167.111449416[/C][C]-27.1114494159967[/C][/ROW]
[ROW][C]60[/C][C]1515[/C][C]1497.22894566875[/C][C]17.7710543312471[/C][/ROW]
[ROW][C]61[/C][C]1305[/C][C]1347.26083830474[/C][C]-42.2608383047441[/C][/ROW]
[ROW][C]62[/C][C]1470[/C][C]1462.01534864342[/C][C]7.98465135658375[/C][/ROW]
[ROW][C]63[/C][C]1380[/C][C]1378.23010439412[/C][C]1.76989560588231[/C][/ROW]
[ROW][C]64[/C][C]1425[/C][C]1430.80336127791[/C][C]-5.80336127791179[/C][/ROW]
[ROW][C]65[/C][C]1320[/C][C]1343.58944669404[/C][C]-23.5894466940383[/C][/ROW]
[ROW][C]66[/C][C]1470[/C][C]1477.41632471369[/C][C]-7.41632471369144[/C][/ROW]
[ROW][C]67[/C][C]1365[/C][C]1279.04910088117[/C][C]85.9508991188291[/C][/ROW]
[ROW][C]68[/C][C]1095[/C][C]1108.61329307617[/C][C]-13.6132930761703[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1264.61645017736[/C][C]55.3835498226429[/C][/ROW]
[ROW][C]70[/C][C]1230[/C][C]1400.31394838379[/C][C]-170.313948383789[/C][/ROW]
[ROW][C]71[/C][C]1035[/C][C]1114.1992190543[/C][C]-79.1992190543012[/C][/ROW]
[ROW][C]72[/C][C]1485[/C][C]1465.24296795043[/C][C]19.7570320495736[/C][/ROW]
[ROW][C]73[/C][C]1200[/C][C]1276.34374038251[/C][C]-76.3437403825058[/C][/ROW]
[ROW][C]74[/C][C]1440[/C][C]1418.21756382419[/C][C]21.7824361758078[/C][/ROW]
[ROW][C]75[/C][C]1365[/C][C]1332.23235861146[/C][C]32.7676413885383[/C][/ROW]
[ROW][C]76[/C][C]1425[/C][C]1384.40098522624[/C][C]40.5990147737648[/C][/ROW]
[ROW][C]77[/C][C]1410[/C][C]1292.57456664525[/C][C]117.425433354752[/C][/ROW]
[ROW][C]78[/C][C]1515[/C][C]1458.5306169219[/C][C]56.4693830781009[/C][/ROW]
[ROW][C]79[/C][C]1335[/C][C]1330.71213041327[/C][C]4.28786958672913[/C][/ROW]
[ROW][C]80[/C][C]990[/C][C]1083.12499972486[/C][C]-93.1249997248608[/C][/ROW]
[ROW][C]81[/C][C]1290[/C][C]1271.66569999121[/C][C]18.3343000087873[/C][/ROW]
[ROW][C]82[/C][C]1260[/C][C]1254.95480336043[/C][C]5.04519663957149[/C][/ROW]
[ROW][C]83[/C][C]1110[/C][C]1054.95751762689[/C][C]55.0424823731071[/C][/ROW]
[ROW][C]84[/C][C]1470[/C][C]1491.11042578775[/C][C]-21.11042578775[/C][/ROW]
[ROW][C]85[/C][C]1230[/C][C]1233.773372039[/C][C]-3.77337203900333[/C][/ROW]
[ROW][C]86[/C][C]1620[/C][C]1450.82214786263[/C][C]169.17785213737[/C][/ROW]
[ROW][C]87[/C][C]1395[/C][C]1395.08367924672[/C][C]-0.0836792467164287[/C][/ROW]
[ROW][C]88[/C][C]1455[/C][C]1447.81098829423[/C][C]7.18901170577101[/C][/ROW]
[ROW][C]89[/C][C]1395[/C][C]1401.21929763802[/C][C]-6.21929763802063[/C][/ROW]
[ROW][C]90[/C][C]1515[/C][C]1508.93428626941[/C][C]6.06571373058887[/C][/ROW]
[ROW][C]91[/C][C]1320[/C][C]1339.71276168035[/C][C]-19.7127616803457[/C][/ROW]
[ROW][C]92[/C][C]1110[/C][C]1025.35380543326[/C][C]84.6461945667443[/C][/ROW]
[ROW][C]93[/C][C]1290[/C][C]1313.9207456961[/C][C]-23.9207456961046[/C][/ROW]
[ROW][C]94[/C][C]1215[/C][C]1282.47391380621[/C][C]-67.4739138062146[/C][/ROW]
[ROW][C]95[/C][C]1125[/C][C]1104.10552826441[/C][C]20.8944717355882[/C][/ROW]
[ROW][C]96[/C][C]1335[/C][C]1485.78230781901[/C][C]-150.782307819007[/C][/ROW]
[ROW][C]97[/C][C]1185[/C][C]1219.87767747092[/C][C]-34.8776774709197[/C][/ROW]
[ROW][C]98[/C][C]1500[/C][C]1544.46849367161[/C][C]-44.4684936716142[/C][/ROW]
[ROW][C]99[/C][C]1335[/C][C]1345.76641310978[/C][C]-10.7664131097772[/C][/ROW]
[ROW][C]100[/C][C]1455[/C][C]1401.23702494147[/C][C]53.7629750585313[/C][/ROW]
[ROW][C]101[/C][C]1350[/C][C]1352.7891114877[/C][C]-2.78911148770385[/C][/ROW]
[ROW][C]102[/C][C]1485[/C][C]1468.73513551725[/C][C]16.2648644827464[/C][/ROW]
[ROW][C]103[/C][C]1365[/C][C]1284.07474037734[/C][C]80.9252596226611[/C][/ROW]
[ROW][C]104[/C][C]1095[/C][C]1052.78566835354[/C][C]42.2143316464612[/C][/ROW]
[ROW][C]105[/C][C]1275[/C][C]1264.17272277818[/C][C]10.8272772218199[/C][/ROW]
[ROW][C]106[/C][C]1260[/C][C]1209.63483859993[/C][C]50.3651614000676[/C][/ROW]
[ROW][C]107[/C][C]1245[/C][C]1106.74282382226[/C][C]138.25717617774[/C][/ROW]
[ROW][C]108[/C][C]1425[/C][C]1395.1025274047[/C][C]29.897472595303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296416&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
1314401428.345352564111.6546474358975
1413501342.64405893867.35594106139706
1514101410.67030278045-0.670302780449902
1613801382.46691112855-2.46691112854978
1713951400.85994011298-5.85994011298135
1814551468.72512208875-13.725122088749
1913951390.991529022634.00847097736641
2011701241.60339424197-71.6033942419731
2112151305.53738408878-90.5373840887783
2213051228.9425803757676.0574196242351
2310801209.20988063516-129.209880635156
2413201347.86850414322-27.868504143225
2513801375.194760045134.8052399548676
2613801285.2935845203594.7064154796526
2714251361.2450823857263.7549176142763
2814251341.5961757261683.4038242738407
2913351370.91341821786-35.9134182178598
3014401429.0091842989710.9908157010295
3111701366.55138575042-196.551385750422
3211701137.0403707838632.959629216138
3311401204.52086199149-64.520861991492
3412901239.9799185547350.0200814452689
3511101082.7847426077427.2152573922624
3615301311.26847895349218.731521046506
3713351397.98197060162-62.9819706016156
3815601356.41057839131203.589421608689
3913801429.40434665298-49.4043466529811
4013501405.50724958866-55.5072495886623
4114251336.1809273831988.8190726168102
4214851444.1262498847440.8737501152552
4312601251.787977871758.21202212824619
4411101203.31179719477-93.3117971947661
4512601188.601372048671.3986279513983
4614401319.90170488904120.09829511096
4711851159.3687308370825.6312691629207
4815151512.735656196162.26434380383603
4913501383.7812057112-33.7812057112035
5014551520.28143812878-65.2814381287776
5113801387.8925410565-7.89254105649798
5214701366.53269815414103.46730184586
5313351415.65198312617-80.6519831261735
5415001466.6467808733633.353219126644
5513201252.0649223739967.9350776260092
5611101147.00157488644-37.0015748864364
5712901248.1716755213441.8283244786603
5814101406.818634957173.18136504282552
5911401167.111449416-27.1114494159967
6015151497.2289456687517.7710543312471
6113051347.26083830474-42.2608383047441
6214701462.015348643427.98465135658375
6313801378.230104394121.76989560588231
6414251430.80336127791-5.80336127791179
6513201343.58944669404-23.5894466940383
6614701477.41632471369-7.41632471369144
6713651279.0491008811785.9508991188291
6810951108.61329307617-13.6132930761703
6913201264.6164501773655.3835498226429
7012301400.31394838379-170.313948383789
7110351114.1992190543-79.1992190543012
7214851465.2429679504319.7570320495736
7312001276.34374038251-76.3437403825058
7414401418.2175638241921.7824361758078
7513651332.2323586114632.7676413885383
7614251384.4009852262440.5990147737648
7714101292.57456664525117.425433354752
7815151458.530616921956.4693830781009
7913351330.712130413274.28786958672913
809901083.12499972486-93.1249997248608
8112901271.6656999912118.3343000087873
8212601254.954803360435.04519663957149
8311101054.9575176268955.0424823731071
8414701491.11042578775-21.11042578775
8512301233.773372039-3.77337203900333
8616201450.82214786263169.17785213737
8713951395.08367924672-0.0836792467164287
8814551447.810988294237.18901170577101
8913951401.21929763802-6.21929763802063
9015151508.934286269416.06571373058887
9113201339.71276168035-19.7127616803457
9211101025.3538054332684.6461945667443
9312901313.9207456961-23.9207456961046
9412151282.47391380621-67.4739138062146
9511251104.1055282644120.8944717355882
9613351485.78230781901-150.782307819007
9711851219.87767747092-34.8776774709197
9815001544.46849367161-44.4684936716142
9913351345.76641310978-10.7664131097772
10014551401.2370249414753.7629750585313
10113501352.7891114877-2.78911148770385
10214851468.7351355172516.2648644827464
10313651284.0747403773480.9252596226611
10410951052.7856683535442.2143316464612
10512751264.1727227781810.8272772218199
10612601209.6348385999350.3651614000676
10712451106.74282382226138.25717617774
10814251395.102527404729.897472595303







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091232.606868691341096.253185823941368.96055155875
1101556.832705152661418.860777196761694.80463310857
1111387.414942054641247.81376070391527.01612340538
1121487.047372010361345.806037061628.28870696072
1131394.167775321151251.275492215741537.06005842656
1141523.446492694071378.892570135131668.000415253
1151378.798203539041232.57205115191525.02435592618
1161110.37064864898962.4617747079871258.27952258998
1171295.240954206681145.638963418091444.84294499528
1181265.038577275391113.733168616951416.34398593382
1191211.761212438131058.742177054481364.78024782179
1201408.623800675451253.881019828151563.36658152276

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1232.60686869134 & 1096.25318582394 & 1368.96055155875 \tabularnewline
110 & 1556.83270515266 & 1418.86077719676 & 1694.80463310857 \tabularnewline
111 & 1387.41494205464 & 1247.8137607039 & 1527.01612340538 \tabularnewline
112 & 1487.04737201036 & 1345.80603706 & 1628.28870696072 \tabularnewline
113 & 1394.16777532115 & 1251.27549221574 & 1537.06005842656 \tabularnewline
114 & 1523.44649269407 & 1378.89257013513 & 1668.000415253 \tabularnewline
115 & 1378.79820353904 & 1232.5720511519 & 1525.02435592618 \tabularnewline
116 & 1110.37064864898 & 962.461774707987 & 1258.27952258998 \tabularnewline
117 & 1295.24095420668 & 1145.63896341809 & 1444.84294499528 \tabularnewline
118 & 1265.03857727539 & 1113.73316861695 & 1416.34398593382 \tabularnewline
119 & 1211.76121243813 & 1058.74217705448 & 1364.78024782179 \tabularnewline
120 & 1408.62380067545 & 1253.88101982815 & 1563.36658152276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296416&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]1232.60686869134[/C][C]1096.25318582394[/C][C]1368.96055155875[/C][/ROW]
[ROW][C]110[/C][C]1556.83270515266[/C][C]1418.86077719676[/C][C]1694.80463310857[/C][/ROW]
[ROW][C]111[/C][C]1387.41494205464[/C][C]1247.8137607039[/C][C]1527.01612340538[/C][/ROW]
[ROW][C]112[/C][C]1487.04737201036[/C][C]1345.80603706[/C][C]1628.28870696072[/C][/ROW]
[ROW][C]113[/C][C]1394.16777532115[/C][C]1251.27549221574[/C][C]1537.06005842656[/C][/ROW]
[ROW][C]114[/C][C]1523.44649269407[/C][C]1378.89257013513[/C][C]1668.000415253[/C][/ROW]
[ROW][C]115[/C][C]1378.79820353904[/C][C]1232.5720511519[/C][C]1525.02435592618[/C][/ROW]
[ROW][C]116[/C][C]1110.37064864898[/C][C]962.461774707987[/C][C]1258.27952258998[/C][/ROW]
[ROW][C]117[/C][C]1295.24095420668[/C][C]1145.63896341809[/C][C]1444.84294499528[/C][/ROW]
[ROW][C]118[/C][C]1265.03857727539[/C][C]1113.73316861695[/C][C]1416.34398593382[/C][/ROW]
[ROW][C]119[/C][C]1211.76121243813[/C][C]1058.74217705448[/C][C]1364.78024782179[/C][/ROW]
[ROW][C]120[/C][C]1408.62380067545[/C][C]1253.88101982815[/C][C]1563.36658152276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296416&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296416&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
1091232.606868691341096.253185823941368.96055155875
1101556.832705152661418.860777196761694.80463310857
1111387.414942054641247.81376070391527.01612340538
1121487.047372010361345.806037061628.28870696072
1131394.167775321151251.275492215741537.06005842656
1141523.446492694071378.892570135131668.000415253
1151378.798203539041232.57205115191525.02435592618
1161110.37064864898962.4617747079871258.27952258998
1171295.240954206681145.638963418091444.84294499528
1181265.038577275391113.733168616951416.34398593382
1191211.761212438131058.742177054481364.78024782179
1201408.623800675451253.881019828151563.36658152276



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')