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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 05 Jan 2015 14:54:31 +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/2015/Jan/05/t1420469724oj3g61jyxbuorrw.htm/, Retrieved Tue, 14 May 2024 14:53:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271973, Retrieved Tue, 14 May 2024 14:53:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [verkopen BMW] [2015-01-05 14:54:31] [8f795c08ce5b45f0e59533fe19a9a846] [Current]
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Dataseries X:
2135
1157
1290
1071
1169
1431
945
1034
1100
1297
921
236
1990
966
1326
908
1206
1861
929
1296
1332
1352
1040
148
2090
1435
1124
1319
1436
1774
1566
1385
1147
1274
625
52
1990
1154
954
887
825
966
954
770
1838
1371
589
116
1898
712
1175
1240
1329
1550
1201
938
1030
1060
1035
635
2565
910
1304
1331
1681
1983
1021
1061
1292
1274
1024
568
2570
1125
1600
1492
2492
3523
990
869
1310
979
1244
442
2956
1055
2004
1462
1144
1454
4060
1538
1388
1547
4473
1570
1535
1352




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271973&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271973&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.351268811826333
beta0.369793646308356
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.351268811826333 \tabularnewline
beta & 0.369793646308356 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271973&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]0.351268811826333[/C][/ROW]
[ROW][C]beta[/C][C]0.369793646308356[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271973&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
alpha0.351268811826333
beta0.369793646308356
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312901791111
41071-264.4248111029581335.42481110296
51169-455.5485424841611624.54854248416
61431-334.088183253381765.08818325338
794566.0189837935492878.981016206451
81034269.041313997498764.958686002502
91100531.376974876889568.623025123111
101297798.608452182218498.391547817782
119211105.90935620901-184.909356209012
122361149.16879758215-913.168797582148
131990817.9955460319921172.00445396801
149661371.51845798121-405.518457981207
1513261318.231150120247.76884987975882
169081411.12793393124-503.127933931244
1712061259.20781499231-53.2078149923118
1818611258.41906744875602.580932551252
199291566.26189425015-637.261894250155
2012961355.80821223692-59.8082122369224
2113321340.42709315386-8.427093153859
2213521341.9999048147110.0000951852935
2310401351.34459514063-311.344595140626
241481207.36819689252-1059.36819689252
252090663.0257129060341426.97428709397
2614351177.41744201615257.582557983852
2711241314.49752291517-190.497522915169
2813191269.4359942678549.5640057321461
2914361315.13880795527120.861192044729
3017741401.58560277773372.414397222274
3115661624.77069665012-58.7706966501207
3213851688.85977922136-303.859779221365
3311471627.38624489421-480.386244894207
3412741441.50374878634-167.503748786336
356251343.76888509929-718.768885099287
3652959.025868252532-907.025868252532
371990390.3341283007651599.66587169923
381154909.95677481675244.04322518325
39954985.091941668091-31.0919416680914
40887959.541956205833-72.5419562058331
41825910.008892732432-85.0088927324323
42966845.054185284607120.945814715393
43954868.15543865339185.8445613466085
44770890.077665276203-120.077665276203
451838824.0681105690041013.931889431
4613711288.1074297929582.8925702070519
475891435.86916768945-846.869167689448
481161147.02886173337-1031.02886173337
491898659.5714688351111238.42853116489
507121130.17179748509-418.171797485086
511175964.540845595949210.459154404051
5212401047.06634872173192.933651278272
5313291148.49718681824180.50281318176
5415501269.0082285545280.991771445496
5512011461.31788830487-260.317888304865
569381429.66784087797-491.667840877974
5710301252.88560537798-222.885605377985
5810601141.56602052603-81.5660205260258
5910351069.29241902329-34.2924190232898
606351009.17007786286-374.170077862855
612565781.0557541555581783.94424584444
629101542.74864539742-632.748645397416
6313041373.3405613632-69.3405613632017
6413311392.83303643182-61.8330364318197
6516811406.93074649014274.069253509856
6619831574.62122173159408.378778268406
6710211842.53761200505-821.537612005053
6810611571.70748277069-510.707482770687
6912921343.72292671327-51.7229267132668
7012741270.2466786033.75332139699549
7110241216.74505134579-192.745051345787
725681069.18267509969-501.182675099691
732570748.1736679376181821.82633206238
7411251479.81500365563-354.815003655634
7516001400.78072802969199.219271970306
7614921542.23939485671-50.2393948567064
7724921589.54506678197902.454933218029
7835232088.728709045691434.27129095431
799902961.03035308084-1971.03035308084
808692381.12485468084-1512.12485468084
8113101765.99810136243-455.998101362435
829791462.62296395706-483.62296395706
8312441086.72291394888157.277086051118
84442956.380880683569-514.380880683569
852956523.2898312146652432.71016878534
8610551441.42164442901-386.421644429009
8720041319.08537264075684.914627359248
8814621662.04445817262-200.044458172618
8911441668.15984728073-524.159847280728
9014541492.33683030995-38.3368303099489
9140601482.188448989242577.81155101076
9215382725.86132311326-1187.86132311326
9313882492.47116871066-1104.47116871066
9415472144.90591123829-597.905911238286
9544731897.615060809962575.38493919004
9615703099.53702943336-1529.53702943336
9715352660.84570259232-1125.84570259232
9813522217.71459766242-865.714597662423

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1290 & 179 & 1111 \tabularnewline
4 & 1071 & -264.424811102958 & 1335.42481110296 \tabularnewline
5 & 1169 & -455.548542484161 & 1624.54854248416 \tabularnewline
6 & 1431 & -334.08818325338 & 1765.08818325338 \tabularnewline
7 & 945 & 66.0189837935492 & 878.981016206451 \tabularnewline
8 & 1034 & 269.041313997498 & 764.958686002502 \tabularnewline
9 & 1100 & 531.376974876889 & 568.623025123111 \tabularnewline
10 & 1297 & 798.608452182218 & 498.391547817782 \tabularnewline
11 & 921 & 1105.90935620901 & -184.909356209012 \tabularnewline
12 & 236 & 1149.16879758215 & -913.168797582148 \tabularnewline
13 & 1990 & 817.995546031992 & 1172.00445396801 \tabularnewline
14 & 966 & 1371.51845798121 & -405.518457981207 \tabularnewline
15 & 1326 & 1318.23115012024 & 7.76884987975882 \tabularnewline
16 & 908 & 1411.12793393124 & -503.127933931244 \tabularnewline
17 & 1206 & 1259.20781499231 & -53.2078149923118 \tabularnewline
18 & 1861 & 1258.41906744875 & 602.580932551252 \tabularnewline
19 & 929 & 1566.26189425015 & -637.261894250155 \tabularnewline
20 & 1296 & 1355.80821223692 & -59.8082122369224 \tabularnewline
21 & 1332 & 1340.42709315386 & -8.427093153859 \tabularnewline
22 & 1352 & 1341.99990481471 & 10.0000951852935 \tabularnewline
23 & 1040 & 1351.34459514063 & -311.344595140626 \tabularnewline
24 & 148 & 1207.36819689252 & -1059.36819689252 \tabularnewline
25 & 2090 & 663.025712906034 & 1426.97428709397 \tabularnewline
26 & 1435 & 1177.41744201615 & 257.582557983852 \tabularnewline
27 & 1124 & 1314.49752291517 & -190.497522915169 \tabularnewline
28 & 1319 & 1269.43599426785 & 49.5640057321461 \tabularnewline
29 & 1436 & 1315.13880795527 & 120.861192044729 \tabularnewline
30 & 1774 & 1401.58560277773 & 372.414397222274 \tabularnewline
31 & 1566 & 1624.77069665012 & -58.7706966501207 \tabularnewline
32 & 1385 & 1688.85977922136 & -303.859779221365 \tabularnewline
33 & 1147 & 1627.38624489421 & -480.386244894207 \tabularnewline
34 & 1274 & 1441.50374878634 & -167.503748786336 \tabularnewline
35 & 625 & 1343.76888509929 & -718.768885099287 \tabularnewline
36 & 52 & 959.025868252532 & -907.025868252532 \tabularnewline
37 & 1990 & 390.334128300765 & 1599.66587169923 \tabularnewline
38 & 1154 & 909.95677481675 & 244.04322518325 \tabularnewline
39 & 954 & 985.091941668091 & -31.0919416680914 \tabularnewline
40 & 887 & 959.541956205833 & -72.5419562058331 \tabularnewline
41 & 825 & 910.008892732432 & -85.0088927324323 \tabularnewline
42 & 966 & 845.054185284607 & 120.945814715393 \tabularnewline
43 & 954 & 868.155438653391 & 85.8445613466085 \tabularnewline
44 & 770 & 890.077665276203 & -120.077665276203 \tabularnewline
45 & 1838 & 824.068110569004 & 1013.931889431 \tabularnewline
46 & 1371 & 1288.10742979295 & 82.8925702070519 \tabularnewline
47 & 589 & 1435.86916768945 & -846.869167689448 \tabularnewline
48 & 116 & 1147.02886173337 & -1031.02886173337 \tabularnewline
49 & 1898 & 659.571468835111 & 1238.42853116489 \tabularnewline
50 & 712 & 1130.17179748509 & -418.171797485086 \tabularnewline
51 & 1175 & 964.540845595949 & 210.459154404051 \tabularnewline
52 & 1240 & 1047.06634872173 & 192.933651278272 \tabularnewline
53 & 1329 & 1148.49718681824 & 180.50281318176 \tabularnewline
54 & 1550 & 1269.0082285545 & 280.991771445496 \tabularnewline
55 & 1201 & 1461.31788830487 & -260.317888304865 \tabularnewline
56 & 938 & 1429.66784087797 & -491.667840877974 \tabularnewline
57 & 1030 & 1252.88560537798 & -222.885605377985 \tabularnewline
58 & 1060 & 1141.56602052603 & -81.5660205260258 \tabularnewline
59 & 1035 & 1069.29241902329 & -34.2924190232898 \tabularnewline
60 & 635 & 1009.17007786286 & -374.170077862855 \tabularnewline
61 & 2565 & 781.055754155558 & 1783.94424584444 \tabularnewline
62 & 910 & 1542.74864539742 & -632.748645397416 \tabularnewline
63 & 1304 & 1373.3405613632 & -69.3405613632017 \tabularnewline
64 & 1331 & 1392.83303643182 & -61.8330364318197 \tabularnewline
65 & 1681 & 1406.93074649014 & 274.069253509856 \tabularnewline
66 & 1983 & 1574.62122173159 & 408.378778268406 \tabularnewline
67 & 1021 & 1842.53761200505 & -821.537612005053 \tabularnewline
68 & 1061 & 1571.70748277069 & -510.707482770687 \tabularnewline
69 & 1292 & 1343.72292671327 & -51.7229267132668 \tabularnewline
70 & 1274 & 1270.246678603 & 3.75332139699549 \tabularnewline
71 & 1024 & 1216.74505134579 & -192.745051345787 \tabularnewline
72 & 568 & 1069.18267509969 & -501.182675099691 \tabularnewline
73 & 2570 & 748.173667937618 & 1821.82633206238 \tabularnewline
74 & 1125 & 1479.81500365563 & -354.815003655634 \tabularnewline
75 & 1600 & 1400.78072802969 & 199.219271970306 \tabularnewline
76 & 1492 & 1542.23939485671 & -50.2393948567064 \tabularnewline
77 & 2492 & 1589.54506678197 & 902.454933218029 \tabularnewline
78 & 3523 & 2088.72870904569 & 1434.27129095431 \tabularnewline
79 & 990 & 2961.03035308084 & -1971.03035308084 \tabularnewline
80 & 869 & 2381.12485468084 & -1512.12485468084 \tabularnewline
81 & 1310 & 1765.99810136243 & -455.998101362435 \tabularnewline
82 & 979 & 1462.62296395706 & -483.62296395706 \tabularnewline
83 & 1244 & 1086.72291394888 & 157.277086051118 \tabularnewline
84 & 442 & 956.380880683569 & -514.380880683569 \tabularnewline
85 & 2956 & 523.289831214665 & 2432.71016878534 \tabularnewline
86 & 1055 & 1441.42164442901 & -386.421644429009 \tabularnewline
87 & 2004 & 1319.08537264075 & 684.914627359248 \tabularnewline
88 & 1462 & 1662.04445817262 & -200.044458172618 \tabularnewline
89 & 1144 & 1668.15984728073 & -524.159847280728 \tabularnewline
90 & 1454 & 1492.33683030995 & -38.3368303099489 \tabularnewline
91 & 4060 & 1482.18844898924 & 2577.81155101076 \tabularnewline
92 & 1538 & 2725.86132311326 & -1187.86132311326 \tabularnewline
93 & 1388 & 2492.47116871066 & -1104.47116871066 \tabularnewline
94 & 1547 & 2144.90591123829 & -597.905911238286 \tabularnewline
95 & 4473 & 1897.61506080996 & 2575.38493919004 \tabularnewline
96 & 1570 & 3099.53702943336 & -1529.53702943336 \tabularnewline
97 & 1535 & 2660.84570259232 & -1125.84570259232 \tabularnewline
98 & 1352 & 2217.71459766242 & -865.714597662423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271973&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]1290[/C][C]179[/C][C]1111[/C][/ROW]
[ROW][C]4[/C][C]1071[/C][C]-264.424811102958[/C][C]1335.42481110296[/C][/ROW]
[ROW][C]5[/C][C]1169[/C][C]-455.548542484161[/C][C]1624.54854248416[/C][/ROW]
[ROW][C]6[/C][C]1431[/C][C]-334.08818325338[/C][C]1765.08818325338[/C][/ROW]
[ROW][C]7[/C][C]945[/C][C]66.0189837935492[/C][C]878.981016206451[/C][/ROW]
[ROW][C]8[/C][C]1034[/C][C]269.041313997498[/C][C]764.958686002502[/C][/ROW]
[ROW][C]9[/C][C]1100[/C][C]531.376974876889[/C][C]568.623025123111[/C][/ROW]
[ROW][C]10[/C][C]1297[/C][C]798.608452182218[/C][C]498.391547817782[/C][/ROW]
[ROW][C]11[/C][C]921[/C][C]1105.90935620901[/C][C]-184.909356209012[/C][/ROW]
[ROW][C]12[/C][C]236[/C][C]1149.16879758215[/C][C]-913.168797582148[/C][/ROW]
[ROW][C]13[/C][C]1990[/C][C]817.995546031992[/C][C]1172.00445396801[/C][/ROW]
[ROW][C]14[/C][C]966[/C][C]1371.51845798121[/C][C]-405.518457981207[/C][/ROW]
[ROW][C]15[/C][C]1326[/C][C]1318.23115012024[/C][C]7.76884987975882[/C][/ROW]
[ROW][C]16[/C][C]908[/C][C]1411.12793393124[/C][C]-503.127933931244[/C][/ROW]
[ROW][C]17[/C][C]1206[/C][C]1259.20781499231[/C][C]-53.2078149923118[/C][/ROW]
[ROW][C]18[/C][C]1861[/C][C]1258.41906744875[/C][C]602.580932551252[/C][/ROW]
[ROW][C]19[/C][C]929[/C][C]1566.26189425015[/C][C]-637.261894250155[/C][/ROW]
[ROW][C]20[/C][C]1296[/C][C]1355.80821223692[/C][C]-59.8082122369224[/C][/ROW]
[ROW][C]21[/C][C]1332[/C][C]1340.42709315386[/C][C]-8.427093153859[/C][/ROW]
[ROW][C]22[/C][C]1352[/C][C]1341.99990481471[/C][C]10.0000951852935[/C][/ROW]
[ROW][C]23[/C][C]1040[/C][C]1351.34459514063[/C][C]-311.344595140626[/C][/ROW]
[ROW][C]24[/C][C]148[/C][C]1207.36819689252[/C][C]-1059.36819689252[/C][/ROW]
[ROW][C]25[/C][C]2090[/C][C]663.025712906034[/C][C]1426.97428709397[/C][/ROW]
[ROW][C]26[/C][C]1435[/C][C]1177.41744201615[/C][C]257.582557983852[/C][/ROW]
[ROW][C]27[/C][C]1124[/C][C]1314.49752291517[/C][C]-190.497522915169[/C][/ROW]
[ROW][C]28[/C][C]1319[/C][C]1269.43599426785[/C][C]49.5640057321461[/C][/ROW]
[ROW][C]29[/C][C]1436[/C][C]1315.13880795527[/C][C]120.861192044729[/C][/ROW]
[ROW][C]30[/C][C]1774[/C][C]1401.58560277773[/C][C]372.414397222274[/C][/ROW]
[ROW][C]31[/C][C]1566[/C][C]1624.77069665012[/C][C]-58.7706966501207[/C][/ROW]
[ROW][C]32[/C][C]1385[/C][C]1688.85977922136[/C][C]-303.859779221365[/C][/ROW]
[ROW][C]33[/C][C]1147[/C][C]1627.38624489421[/C][C]-480.386244894207[/C][/ROW]
[ROW][C]34[/C][C]1274[/C][C]1441.50374878634[/C][C]-167.503748786336[/C][/ROW]
[ROW][C]35[/C][C]625[/C][C]1343.76888509929[/C][C]-718.768885099287[/C][/ROW]
[ROW][C]36[/C][C]52[/C][C]959.025868252532[/C][C]-907.025868252532[/C][/ROW]
[ROW][C]37[/C][C]1990[/C][C]390.334128300765[/C][C]1599.66587169923[/C][/ROW]
[ROW][C]38[/C][C]1154[/C][C]909.95677481675[/C][C]244.04322518325[/C][/ROW]
[ROW][C]39[/C][C]954[/C][C]985.091941668091[/C][C]-31.0919416680914[/C][/ROW]
[ROW][C]40[/C][C]887[/C][C]959.541956205833[/C][C]-72.5419562058331[/C][/ROW]
[ROW][C]41[/C][C]825[/C][C]910.008892732432[/C][C]-85.0088927324323[/C][/ROW]
[ROW][C]42[/C][C]966[/C][C]845.054185284607[/C][C]120.945814715393[/C][/ROW]
[ROW][C]43[/C][C]954[/C][C]868.155438653391[/C][C]85.8445613466085[/C][/ROW]
[ROW][C]44[/C][C]770[/C][C]890.077665276203[/C][C]-120.077665276203[/C][/ROW]
[ROW][C]45[/C][C]1838[/C][C]824.068110569004[/C][C]1013.931889431[/C][/ROW]
[ROW][C]46[/C][C]1371[/C][C]1288.10742979295[/C][C]82.8925702070519[/C][/ROW]
[ROW][C]47[/C][C]589[/C][C]1435.86916768945[/C][C]-846.869167689448[/C][/ROW]
[ROW][C]48[/C][C]116[/C][C]1147.02886173337[/C][C]-1031.02886173337[/C][/ROW]
[ROW][C]49[/C][C]1898[/C][C]659.571468835111[/C][C]1238.42853116489[/C][/ROW]
[ROW][C]50[/C][C]712[/C][C]1130.17179748509[/C][C]-418.171797485086[/C][/ROW]
[ROW][C]51[/C][C]1175[/C][C]964.540845595949[/C][C]210.459154404051[/C][/ROW]
[ROW][C]52[/C][C]1240[/C][C]1047.06634872173[/C][C]192.933651278272[/C][/ROW]
[ROW][C]53[/C][C]1329[/C][C]1148.49718681824[/C][C]180.50281318176[/C][/ROW]
[ROW][C]54[/C][C]1550[/C][C]1269.0082285545[/C][C]280.991771445496[/C][/ROW]
[ROW][C]55[/C][C]1201[/C][C]1461.31788830487[/C][C]-260.317888304865[/C][/ROW]
[ROW][C]56[/C][C]938[/C][C]1429.66784087797[/C][C]-491.667840877974[/C][/ROW]
[ROW][C]57[/C][C]1030[/C][C]1252.88560537798[/C][C]-222.885605377985[/C][/ROW]
[ROW][C]58[/C][C]1060[/C][C]1141.56602052603[/C][C]-81.5660205260258[/C][/ROW]
[ROW][C]59[/C][C]1035[/C][C]1069.29241902329[/C][C]-34.2924190232898[/C][/ROW]
[ROW][C]60[/C][C]635[/C][C]1009.17007786286[/C][C]-374.170077862855[/C][/ROW]
[ROW][C]61[/C][C]2565[/C][C]781.055754155558[/C][C]1783.94424584444[/C][/ROW]
[ROW][C]62[/C][C]910[/C][C]1542.74864539742[/C][C]-632.748645397416[/C][/ROW]
[ROW][C]63[/C][C]1304[/C][C]1373.3405613632[/C][C]-69.3405613632017[/C][/ROW]
[ROW][C]64[/C][C]1331[/C][C]1392.83303643182[/C][C]-61.8330364318197[/C][/ROW]
[ROW][C]65[/C][C]1681[/C][C]1406.93074649014[/C][C]274.069253509856[/C][/ROW]
[ROW][C]66[/C][C]1983[/C][C]1574.62122173159[/C][C]408.378778268406[/C][/ROW]
[ROW][C]67[/C][C]1021[/C][C]1842.53761200505[/C][C]-821.537612005053[/C][/ROW]
[ROW][C]68[/C][C]1061[/C][C]1571.70748277069[/C][C]-510.707482770687[/C][/ROW]
[ROW][C]69[/C][C]1292[/C][C]1343.72292671327[/C][C]-51.7229267132668[/C][/ROW]
[ROW][C]70[/C][C]1274[/C][C]1270.246678603[/C][C]3.75332139699549[/C][/ROW]
[ROW][C]71[/C][C]1024[/C][C]1216.74505134579[/C][C]-192.745051345787[/C][/ROW]
[ROW][C]72[/C][C]568[/C][C]1069.18267509969[/C][C]-501.182675099691[/C][/ROW]
[ROW][C]73[/C][C]2570[/C][C]748.173667937618[/C][C]1821.82633206238[/C][/ROW]
[ROW][C]74[/C][C]1125[/C][C]1479.81500365563[/C][C]-354.815003655634[/C][/ROW]
[ROW][C]75[/C][C]1600[/C][C]1400.78072802969[/C][C]199.219271970306[/C][/ROW]
[ROW][C]76[/C][C]1492[/C][C]1542.23939485671[/C][C]-50.2393948567064[/C][/ROW]
[ROW][C]77[/C][C]2492[/C][C]1589.54506678197[/C][C]902.454933218029[/C][/ROW]
[ROW][C]78[/C][C]3523[/C][C]2088.72870904569[/C][C]1434.27129095431[/C][/ROW]
[ROW][C]79[/C][C]990[/C][C]2961.03035308084[/C][C]-1971.03035308084[/C][/ROW]
[ROW][C]80[/C][C]869[/C][C]2381.12485468084[/C][C]-1512.12485468084[/C][/ROW]
[ROW][C]81[/C][C]1310[/C][C]1765.99810136243[/C][C]-455.998101362435[/C][/ROW]
[ROW][C]82[/C][C]979[/C][C]1462.62296395706[/C][C]-483.62296395706[/C][/ROW]
[ROW][C]83[/C][C]1244[/C][C]1086.72291394888[/C][C]157.277086051118[/C][/ROW]
[ROW][C]84[/C][C]442[/C][C]956.380880683569[/C][C]-514.380880683569[/C][/ROW]
[ROW][C]85[/C][C]2956[/C][C]523.289831214665[/C][C]2432.71016878534[/C][/ROW]
[ROW][C]86[/C][C]1055[/C][C]1441.42164442901[/C][C]-386.421644429009[/C][/ROW]
[ROW][C]87[/C][C]2004[/C][C]1319.08537264075[/C][C]684.914627359248[/C][/ROW]
[ROW][C]88[/C][C]1462[/C][C]1662.04445817262[/C][C]-200.044458172618[/C][/ROW]
[ROW][C]89[/C][C]1144[/C][C]1668.15984728073[/C][C]-524.159847280728[/C][/ROW]
[ROW][C]90[/C][C]1454[/C][C]1492.33683030995[/C][C]-38.3368303099489[/C][/ROW]
[ROW][C]91[/C][C]4060[/C][C]1482.18844898924[/C][C]2577.81155101076[/C][/ROW]
[ROW][C]92[/C][C]1538[/C][C]2725.86132311326[/C][C]-1187.86132311326[/C][/ROW]
[ROW][C]93[/C][C]1388[/C][C]2492.47116871066[/C][C]-1104.47116871066[/C][/ROW]
[ROW][C]94[/C][C]1547[/C][C]2144.90591123829[/C][C]-597.905911238286[/C][/ROW]
[ROW][C]95[/C][C]4473[/C][C]1897.61506080996[/C][C]2575.38493919004[/C][/ROW]
[ROW][C]96[/C][C]1570[/C][C]3099.53702943336[/C][C]-1529.53702943336[/C][/ROW]
[ROW][C]97[/C][C]1535[/C][C]2660.84570259232[/C][C]-1125.84570259232[/C][/ROW]
[ROW][C]98[/C][C]1352[/C][C]2217.71459766242[/C][C]-865.714597662423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271973&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
312901791111
41071-264.4248111029581335.42481110296
51169-455.5485424841611624.54854248416
61431-334.088183253381765.08818325338
794566.0189837935492878.981016206451
81034269.041313997498764.958686002502
91100531.376974876889568.623025123111
101297798.608452182218498.391547817782
119211105.90935620901-184.909356209012
122361149.16879758215-913.168797582148
131990817.9955460319921172.00445396801
149661371.51845798121-405.518457981207
1513261318.231150120247.76884987975882
169081411.12793393124-503.127933931244
1712061259.20781499231-53.2078149923118
1818611258.41906744875602.580932551252
199291566.26189425015-637.261894250155
2012961355.80821223692-59.8082122369224
2113321340.42709315386-8.427093153859
2213521341.9999048147110.0000951852935
2310401351.34459514063-311.344595140626
241481207.36819689252-1059.36819689252
252090663.0257129060341426.97428709397
2614351177.41744201615257.582557983852
2711241314.49752291517-190.497522915169
2813191269.4359942678549.5640057321461
2914361315.13880795527120.861192044729
3017741401.58560277773372.414397222274
3115661624.77069665012-58.7706966501207
3213851688.85977922136-303.859779221365
3311471627.38624489421-480.386244894207
3412741441.50374878634-167.503748786336
356251343.76888509929-718.768885099287
3652959.025868252532-907.025868252532
371990390.3341283007651599.66587169923
381154909.95677481675244.04322518325
39954985.091941668091-31.0919416680914
40887959.541956205833-72.5419562058331
41825910.008892732432-85.0088927324323
42966845.054185284607120.945814715393
43954868.15543865339185.8445613466085
44770890.077665276203-120.077665276203
451838824.0681105690041013.931889431
4613711288.1074297929582.8925702070519
475891435.86916768945-846.869167689448
481161147.02886173337-1031.02886173337
491898659.5714688351111238.42853116489
507121130.17179748509-418.171797485086
511175964.540845595949210.459154404051
5212401047.06634872173192.933651278272
5313291148.49718681824180.50281318176
5415501269.0082285545280.991771445496
5512011461.31788830487-260.317888304865
569381429.66784087797-491.667840877974
5710301252.88560537798-222.885605377985
5810601141.56602052603-81.5660205260258
5910351069.29241902329-34.2924190232898
606351009.17007786286-374.170077862855
612565781.0557541555581783.94424584444
629101542.74864539742-632.748645397416
6313041373.3405613632-69.3405613632017
6413311392.83303643182-61.8330364318197
6516811406.93074649014274.069253509856
6619831574.62122173159408.378778268406
6710211842.53761200505-821.537612005053
6810611571.70748277069-510.707482770687
6912921343.72292671327-51.7229267132668
7012741270.2466786033.75332139699549
7110241216.74505134579-192.745051345787
725681069.18267509969-501.182675099691
732570748.1736679376181821.82633206238
7411251479.81500365563-354.815003655634
7516001400.78072802969199.219271970306
7614921542.23939485671-50.2393948567064
7724921589.54506678197902.454933218029
7835232088.728709045691434.27129095431
799902961.03035308084-1971.03035308084
808692381.12485468084-1512.12485468084
8113101765.99810136243-455.998101362435
829791462.62296395706-483.62296395706
8312441086.72291394888157.277086051118
84442956.380880683569-514.380880683569
852956523.2898312146652432.71016878534
8610551441.42164442901-386.421644429009
8720041319.08537264075684.914627359248
8814621662.04445817262-200.044458172618
8911441668.15984728073-524.159847280728
9014541492.33683030995-38.3368303099489
9140601482.188448989242577.81155101076
9215382725.86132311326-1187.86132311326
9313882492.47116871066-1104.47116871066
9415472144.90591123829-597.905911238286
9544731897.615060809962575.38493919004
9615703099.53702943336-1529.53702943336
9715352660.84570259232-1125.84570259232
9813522217.71459766242-865.714597662423







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
991753.5057296386939.87824179797283467.13321747941
1001593.39539971656-308.283751599083495.07455103219
1011433.28506979442-737.6301962998693604.2003358887
1021273.17473987228-1241.797377825653788.14685757021
1031113.06440995014-1811.335642528254037.46446242853
104952.954080028002-2437.187941576794343.0961016328
105792.843750105864-3111.899983306094697.58748351781
106632.733420183725-3829.675665671135095.14250603859
107472.623090261587-4586.069793876345531.31597439951
108312.512760339449-5377.650440731296002.67596141019
109152.402430417311-6201.725567787676506.53042862229
110-7.70789950482776-7056.142255868167040.7264568585

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
99 & 1753.50572963869 & 39.8782417979728 & 3467.13321747941 \tabularnewline
100 & 1593.39539971656 & -308.28375159908 & 3495.07455103219 \tabularnewline
101 & 1433.28506979442 & -737.630196299869 & 3604.2003358887 \tabularnewline
102 & 1273.17473987228 & -1241.79737782565 & 3788.14685757021 \tabularnewline
103 & 1113.06440995014 & -1811.33564252825 & 4037.46446242853 \tabularnewline
104 & 952.954080028002 & -2437.18794157679 & 4343.0961016328 \tabularnewline
105 & 792.843750105864 & -3111.89998330609 & 4697.58748351781 \tabularnewline
106 & 632.733420183725 & -3829.67566567113 & 5095.14250603859 \tabularnewline
107 & 472.623090261587 & -4586.06979387634 & 5531.31597439951 \tabularnewline
108 & 312.512760339449 & -5377.65044073129 & 6002.67596141019 \tabularnewline
109 & 152.402430417311 & -6201.72556778767 & 6506.53042862229 \tabularnewline
110 & -7.70789950482776 & -7056.14225586816 & 7040.7264568585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271973&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]99[/C][C]1753.50572963869[/C][C]39.8782417979728[/C][C]3467.13321747941[/C][/ROW]
[ROW][C]100[/C][C]1593.39539971656[/C][C]-308.28375159908[/C][C]3495.07455103219[/C][/ROW]
[ROW][C]101[/C][C]1433.28506979442[/C][C]-737.630196299869[/C][C]3604.2003358887[/C][/ROW]
[ROW][C]102[/C][C]1273.17473987228[/C][C]-1241.79737782565[/C][C]3788.14685757021[/C][/ROW]
[ROW][C]103[/C][C]1113.06440995014[/C][C]-1811.33564252825[/C][C]4037.46446242853[/C][/ROW]
[ROW][C]104[/C][C]952.954080028002[/C][C]-2437.18794157679[/C][C]4343.0961016328[/C][/ROW]
[ROW][C]105[/C][C]792.843750105864[/C][C]-3111.89998330609[/C][C]4697.58748351781[/C][/ROW]
[ROW][C]106[/C][C]632.733420183725[/C][C]-3829.67566567113[/C][C]5095.14250603859[/C][/ROW]
[ROW][C]107[/C][C]472.623090261587[/C][C]-4586.06979387634[/C][C]5531.31597439951[/C][/ROW]
[ROW][C]108[/C][C]312.512760339449[/C][C]-5377.65044073129[/C][C]6002.67596141019[/C][/ROW]
[ROW][C]109[/C][C]152.402430417311[/C][C]-6201.72556778767[/C][C]6506.53042862229[/C][/ROW]
[ROW][C]110[/C][C]-7.70789950482776[/C][C]-7056.14225586816[/C][C]7040.7264568585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271973&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271973&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
991753.5057296386939.87824179797283467.13321747941
1001593.39539971656-308.283751599083495.07455103219
1011433.28506979442-737.6301962998693604.2003358887
1021273.17473987228-1241.797377825653788.14685757021
1031113.06440995014-1811.335642528254037.46446242853
104952.954080028002-2437.187941576794343.0961016328
105792.843750105864-3111.899983306094697.58748351781
106632.733420183725-3829.675665671135095.14250603859
107472.623090261587-4586.069793876345531.31597439951
108312.512760339449-5377.650440731296002.67596141019
109152.402430417311-6201.725567787676506.53042862229
110-7.70789950482776-7056.142255868167040.7264568585



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