Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 14 Aug 2016 19:43:25 +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/14/t14712002319rw7ws6qc72z4vy.htm/, Retrieved Fri, 03 May 2024 10:52:33 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 10:52:33 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
193
223
254
284
294
304
314
314
314
314
324
335
335
335
345
365
365
385
385
385
395
395
405
405
416
416
426
436
446
446
466
476
476
476
476
486
497
507
517
527
527
547
547
557
557
557
567
567
598
598
618
628
638
669
679
689
689
689
689
709
719
729
790
831
942
952
962
1013
1033
1033
1043
1043
1053
1114
1155
1215
1236
1296
1317
1327
1347
1367
1367
1387
1408
1468
1479
1499
1499
1509
1519
1529
1539
1590
1620
1620
1651
1671
1691
1711
1721
1732
1732
1742
1762
1782
1813
1883
1904
1924
1934
1964
1985
1995
1995
2035
2066
2086
2157
2157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.154187802300169
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.154187802300169 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.154187802300169[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha1
beta0.154187802300169
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32542531
4284284.1541878023-0.154187802300157
5294314.130413923922-20.130413923922
6304321.0265496416-17.0265496415997
7314328.401263371607-14.4012633716067
8314336.180764221993-22.1807642219928
9314332.760760933265-18.7607609332655
10314329.868080435486-15.8680804354864
11324327.421415986416-3.42141598641643
12335336.893875374716-1.89387537471623
13335347.601862892858-12.6018628928583
14335345.65880934852-10.6588093485204
15345344.0153509599360.984649040064426
16365354.1671718314610.8328281685399
17365375.837461799463-10.8374617994626
18385374.16645738209110.8335426179086
19385395.836857509472-10.836857509472
20385394.165946266246-9.16594626624641
21395392.7526691554522.24733084454755
22395403.099180159415-8.09918015941463
23405401.8503853702013.14961462979869
24405412.336017528062-7.33601752806243
25416411.2048931077754.79510689222502
26416422.944240101282-6.94424010128154
27426421.873522981424.12647701857975
28436432.5097754041573.49022459584279
29446443.0479254641242.95207453587579
30446453.503099349037-7.5030993490372
31466452.34621294996913.6537870500307
32476474.4514603682881.54853963171195
33476484.690226290876-8.69022629087641
34476483.350299397595-7.35029939759505
35476482.216972887232-6.21697288723158
36486481.258391500794.74160849921037
37497491.9894896946515.01051030534933
38507503.7620492670353.23795073296515
39517514.2613017745072.73869822549307
40527524.6835756350592.31642436494087
41527535.040740017084-8.04074001708386
42547533.80095598498313.1990440150173
43547555.836087574121-8.83608757412139
44557554.4736706501362.52632934986423
45557564.863199820478-7.8631998204778
46557563.650790321111-6.65079032111123
47567562.625319577944.37468042206012
48567573.299841937983-6.29984193798293
49598572.32848315472725.6715168452731
50598607.286717918811-9.28671791881129
51618605.85481929232812.1451807076718
52628627.7274580141830.272541985817497
53638637.769480664010.230519335989811
54669647.80502393381421.1949760661857
55679682.073030713264-3.07303071326407
56689691.599206861185-2.59920686118494
57689701.198440867535-12.1984408675353
58689699.317590078682-10.3175900786815
59689697.726743539416-8.72674353941557
60709696.38118613183612.6188138681641
61719718.3268533098030.673146690196972
62729728.430644318590.569355681409888
63790738.51843201983451.4815679801662
64831807.45626184566223.5437381543376
65942852.0864190896189.9135809103897
66952976.949996527122-24.9499965271218
67962983.103011395208-21.103011395208
681013989.84918444626523.1508155537346
6910331044.41875781795-11.4187578179524
7010331062.658124645-29.6581246450044
7110431058.08520358565-15.0852035856467
7210431065.75924919753-22.7592491975252
7310531062.25005058176-9.2500505817568
7411141070.8238056113943.1761943886097
7511551138.4810481358516.518951864145
7612151182.0280690200932.9719309799102
7712361247.11193859548-11.1119385954751
7812961266.3986132041429.6013867958557
7913171330.96278597923-13.9627859792345
8013271349.80989469511-22.8098946951088
8113471356.29288716137-9.29288716137171
8213671374.86003731294-7.86003731293636
8313671393.64811543366-26.6481154336573
8413871389.5393010795-2.53930107950055
8514081409.14777182667-1.14777182667376
8614681429.9707994111838.029200588823
8714791495.8344382732-16.8344382731998
8814991504.2387732329-5.2387732328973
8914991523.43101830137-24.4310183013679
9015091519.66405328152-10.6640532815247
9115191528.01978634243-9.0197863424346
9215291536.62904530908-7.62904530907758
9315391545.45273957922-6.45273957922245
9415901554.4578058446935.5421941553132
9516201610.937978650429.06202134957948
9616201642.33523180671-22.3352318067093
9716511638.8914115005712.108588499432
9816711671.75840815025-0.758408150252535
9916911691.64147086432-0.641470864318535
10017111711.54256388151-0.54256388150975
10117211731.45890714901-10.4589071490122
10217321739.84627124124-7.84627124124449
10317321749.63647192231-17.6364719223061
10417421746.91714307628-4.91714307627694
10517621756.158979591755.84102040824973
10617821777.059593691694.94040630831114
10718131797.8213440828415.1786559171628
10818831831.1617076805851.8382923194249
10919041909.1545400483-5.15454004830099
11019241929.35977284639-5.35977284638511
11119341948.53336125037-14.533361250373
11219641956.292494219147.70750578085654
11319851987.48089759671-2.48089759670961
11419952008.09837344854-13.0983734485412
11519952016.0787640328-21.0787640328037
11620352012.8286757313822.1713242686183
11720662056.247223494449.75277650555563
11820862088.75098267016-2.75098267016074
11921572108.3268146980848.6731853019173
12021572186.83162617073-29.8316261707346

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 254 & 253 & 1 \tabularnewline
4 & 284 & 284.1541878023 & -0.154187802300157 \tabularnewline
5 & 294 & 314.130413923922 & -20.130413923922 \tabularnewline
6 & 304 & 321.0265496416 & -17.0265496415997 \tabularnewline
7 & 314 & 328.401263371607 & -14.4012633716067 \tabularnewline
8 & 314 & 336.180764221993 & -22.1807642219928 \tabularnewline
9 & 314 & 332.760760933265 & -18.7607609332655 \tabularnewline
10 & 314 & 329.868080435486 & -15.8680804354864 \tabularnewline
11 & 324 & 327.421415986416 & -3.42141598641643 \tabularnewline
12 & 335 & 336.893875374716 & -1.89387537471623 \tabularnewline
13 & 335 & 347.601862892858 & -12.6018628928583 \tabularnewline
14 & 335 & 345.65880934852 & -10.6588093485204 \tabularnewline
15 & 345 & 344.015350959936 & 0.984649040064426 \tabularnewline
16 & 365 & 354.16717183146 & 10.8328281685399 \tabularnewline
17 & 365 & 375.837461799463 & -10.8374617994626 \tabularnewline
18 & 385 & 374.166457382091 & 10.8335426179086 \tabularnewline
19 & 385 & 395.836857509472 & -10.836857509472 \tabularnewline
20 & 385 & 394.165946266246 & -9.16594626624641 \tabularnewline
21 & 395 & 392.752669155452 & 2.24733084454755 \tabularnewline
22 & 395 & 403.099180159415 & -8.09918015941463 \tabularnewline
23 & 405 & 401.850385370201 & 3.14961462979869 \tabularnewline
24 & 405 & 412.336017528062 & -7.33601752806243 \tabularnewline
25 & 416 & 411.204893107775 & 4.79510689222502 \tabularnewline
26 & 416 & 422.944240101282 & -6.94424010128154 \tabularnewline
27 & 426 & 421.87352298142 & 4.12647701857975 \tabularnewline
28 & 436 & 432.509775404157 & 3.49022459584279 \tabularnewline
29 & 446 & 443.047925464124 & 2.95207453587579 \tabularnewline
30 & 446 & 453.503099349037 & -7.5030993490372 \tabularnewline
31 & 466 & 452.346212949969 & 13.6537870500307 \tabularnewline
32 & 476 & 474.451460368288 & 1.54853963171195 \tabularnewline
33 & 476 & 484.690226290876 & -8.69022629087641 \tabularnewline
34 & 476 & 483.350299397595 & -7.35029939759505 \tabularnewline
35 & 476 & 482.216972887232 & -6.21697288723158 \tabularnewline
36 & 486 & 481.25839150079 & 4.74160849921037 \tabularnewline
37 & 497 & 491.989489694651 & 5.01051030534933 \tabularnewline
38 & 507 & 503.762049267035 & 3.23795073296515 \tabularnewline
39 & 517 & 514.261301774507 & 2.73869822549307 \tabularnewline
40 & 527 & 524.683575635059 & 2.31642436494087 \tabularnewline
41 & 527 & 535.040740017084 & -8.04074001708386 \tabularnewline
42 & 547 & 533.800955984983 & 13.1990440150173 \tabularnewline
43 & 547 & 555.836087574121 & -8.83608757412139 \tabularnewline
44 & 557 & 554.473670650136 & 2.52632934986423 \tabularnewline
45 & 557 & 564.863199820478 & -7.8631998204778 \tabularnewline
46 & 557 & 563.650790321111 & -6.65079032111123 \tabularnewline
47 & 567 & 562.62531957794 & 4.37468042206012 \tabularnewline
48 & 567 & 573.299841937983 & -6.29984193798293 \tabularnewline
49 & 598 & 572.328483154727 & 25.6715168452731 \tabularnewline
50 & 598 & 607.286717918811 & -9.28671791881129 \tabularnewline
51 & 618 & 605.854819292328 & 12.1451807076718 \tabularnewline
52 & 628 & 627.727458014183 & 0.272541985817497 \tabularnewline
53 & 638 & 637.76948066401 & 0.230519335989811 \tabularnewline
54 & 669 & 647.805023933814 & 21.1949760661857 \tabularnewline
55 & 679 & 682.073030713264 & -3.07303071326407 \tabularnewline
56 & 689 & 691.599206861185 & -2.59920686118494 \tabularnewline
57 & 689 & 701.198440867535 & -12.1984408675353 \tabularnewline
58 & 689 & 699.317590078682 & -10.3175900786815 \tabularnewline
59 & 689 & 697.726743539416 & -8.72674353941557 \tabularnewline
60 & 709 & 696.381186131836 & 12.6188138681641 \tabularnewline
61 & 719 & 718.326853309803 & 0.673146690196972 \tabularnewline
62 & 729 & 728.43064431859 & 0.569355681409888 \tabularnewline
63 & 790 & 738.518432019834 & 51.4815679801662 \tabularnewline
64 & 831 & 807.456261845662 & 23.5437381543376 \tabularnewline
65 & 942 & 852.08641908961 & 89.9135809103897 \tabularnewline
66 & 952 & 976.949996527122 & -24.9499965271218 \tabularnewline
67 & 962 & 983.103011395208 & -21.103011395208 \tabularnewline
68 & 1013 & 989.849184446265 & 23.1508155537346 \tabularnewline
69 & 1033 & 1044.41875781795 & -11.4187578179524 \tabularnewline
70 & 1033 & 1062.658124645 & -29.6581246450044 \tabularnewline
71 & 1043 & 1058.08520358565 & -15.0852035856467 \tabularnewline
72 & 1043 & 1065.75924919753 & -22.7592491975252 \tabularnewline
73 & 1053 & 1062.25005058176 & -9.2500505817568 \tabularnewline
74 & 1114 & 1070.82380561139 & 43.1761943886097 \tabularnewline
75 & 1155 & 1138.48104813585 & 16.518951864145 \tabularnewline
76 & 1215 & 1182.02806902009 & 32.9719309799102 \tabularnewline
77 & 1236 & 1247.11193859548 & -11.1119385954751 \tabularnewline
78 & 1296 & 1266.39861320414 & 29.6013867958557 \tabularnewline
79 & 1317 & 1330.96278597923 & -13.9627859792345 \tabularnewline
80 & 1327 & 1349.80989469511 & -22.8098946951088 \tabularnewline
81 & 1347 & 1356.29288716137 & -9.29288716137171 \tabularnewline
82 & 1367 & 1374.86003731294 & -7.86003731293636 \tabularnewline
83 & 1367 & 1393.64811543366 & -26.6481154336573 \tabularnewline
84 & 1387 & 1389.5393010795 & -2.53930107950055 \tabularnewline
85 & 1408 & 1409.14777182667 & -1.14777182667376 \tabularnewline
86 & 1468 & 1429.97079941118 & 38.029200588823 \tabularnewline
87 & 1479 & 1495.8344382732 & -16.8344382731998 \tabularnewline
88 & 1499 & 1504.2387732329 & -5.2387732328973 \tabularnewline
89 & 1499 & 1523.43101830137 & -24.4310183013679 \tabularnewline
90 & 1509 & 1519.66405328152 & -10.6640532815247 \tabularnewline
91 & 1519 & 1528.01978634243 & -9.0197863424346 \tabularnewline
92 & 1529 & 1536.62904530908 & -7.62904530907758 \tabularnewline
93 & 1539 & 1545.45273957922 & -6.45273957922245 \tabularnewline
94 & 1590 & 1554.45780584469 & 35.5421941553132 \tabularnewline
95 & 1620 & 1610.93797865042 & 9.06202134957948 \tabularnewline
96 & 1620 & 1642.33523180671 & -22.3352318067093 \tabularnewline
97 & 1651 & 1638.89141150057 & 12.108588499432 \tabularnewline
98 & 1671 & 1671.75840815025 & -0.758408150252535 \tabularnewline
99 & 1691 & 1691.64147086432 & -0.641470864318535 \tabularnewline
100 & 1711 & 1711.54256388151 & -0.54256388150975 \tabularnewline
101 & 1721 & 1731.45890714901 & -10.4589071490122 \tabularnewline
102 & 1732 & 1739.84627124124 & -7.84627124124449 \tabularnewline
103 & 1732 & 1749.63647192231 & -17.6364719223061 \tabularnewline
104 & 1742 & 1746.91714307628 & -4.91714307627694 \tabularnewline
105 & 1762 & 1756.15897959175 & 5.84102040824973 \tabularnewline
106 & 1782 & 1777.05959369169 & 4.94040630831114 \tabularnewline
107 & 1813 & 1797.82134408284 & 15.1786559171628 \tabularnewline
108 & 1883 & 1831.16170768058 & 51.8382923194249 \tabularnewline
109 & 1904 & 1909.1545400483 & -5.15454004830099 \tabularnewline
110 & 1924 & 1929.35977284639 & -5.35977284638511 \tabularnewline
111 & 1934 & 1948.53336125037 & -14.533361250373 \tabularnewline
112 & 1964 & 1956.29249421914 & 7.70750578085654 \tabularnewline
113 & 1985 & 1987.48089759671 & -2.48089759670961 \tabularnewline
114 & 1995 & 2008.09837344854 & -13.0983734485412 \tabularnewline
115 & 1995 & 2016.0787640328 & -21.0787640328037 \tabularnewline
116 & 2035 & 2012.82867573138 & 22.1713242686183 \tabularnewline
117 & 2066 & 2056.24722349444 & 9.75277650555563 \tabularnewline
118 & 2086 & 2088.75098267016 & -2.75098267016074 \tabularnewline
119 & 2157 & 2108.32681469808 & 48.6731853019173 \tabularnewline
120 & 2157 & 2186.83162617073 & -29.8316261707346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]254[/C][C]253[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]284[/C][C]284.1541878023[/C][C]-0.154187802300157[/C][/ROW]
[ROW][C]5[/C][C]294[/C][C]314.130413923922[/C][C]-20.130413923922[/C][/ROW]
[ROW][C]6[/C][C]304[/C][C]321.0265496416[/C][C]-17.0265496415997[/C][/ROW]
[ROW][C]7[/C][C]314[/C][C]328.401263371607[/C][C]-14.4012633716067[/C][/ROW]
[ROW][C]8[/C][C]314[/C][C]336.180764221993[/C][C]-22.1807642219928[/C][/ROW]
[ROW][C]9[/C][C]314[/C][C]332.760760933265[/C][C]-18.7607609332655[/C][/ROW]
[ROW][C]10[/C][C]314[/C][C]329.868080435486[/C][C]-15.8680804354864[/C][/ROW]
[ROW][C]11[/C][C]324[/C][C]327.421415986416[/C][C]-3.42141598641643[/C][/ROW]
[ROW][C]12[/C][C]335[/C][C]336.893875374716[/C][C]-1.89387537471623[/C][/ROW]
[ROW][C]13[/C][C]335[/C][C]347.601862892858[/C][C]-12.6018628928583[/C][/ROW]
[ROW][C]14[/C][C]335[/C][C]345.65880934852[/C][C]-10.6588093485204[/C][/ROW]
[ROW][C]15[/C][C]345[/C][C]344.015350959936[/C][C]0.984649040064426[/C][/ROW]
[ROW][C]16[/C][C]365[/C][C]354.16717183146[/C][C]10.8328281685399[/C][/ROW]
[ROW][C]17[/C][C]365[/C][C]375.837461799463[/C][C]-10.8374617994626[/C][/ROW]
[ROW][C]18[/C][C]385[/C][C]374.166457382091[/C][C]10.8335426179086[/C][/ROW]
[ROW][C]19[/C][C]385[/C][C]395.836857509472[/C][C]-10.836857509472[/C][/ROW]
[ROW][C]20[/C][C]385[/C][C]394.165946266246[/C][C]-9.16594626624641[/C][/ROW]
[ROW][C]21[/C][C]395[/C][C]392.752669155452[/C][C]2.24733084454755[/C][/ROW]
[ROW][C]22[/C][C]395[/C][C]403.099180159415[/C][C]-8.09918015941463[/C][/ROW]
[ROW][C]23[/C][C]405[/C][C]401.850385370201[/C][C]3.14961462979869[/C][/ROW]
[ROW][C]24[/C][C]405[/C][C]412.336017528062[/C][C]-7.33601752806243[/C][/ROW]
[ROW][C]25[/C][C]416[/C][C]411.204893107775[/C][C]4.79510689222502[/C][/ROW]
[ROW][C]26[/C][C]416[/C][C]422.944240101282[/C][C]-6.94424010128154[/C][/ROW]
[ROW][C]27[/C][C]426[/C][C]421.87352298142[/C][C]4.12647701857975[/C][/ROW]
[ROW][C]28[/C][C]436[/C][C]432.509775404157[/C][C]3.49022459584279[/C][/ROW]
[ROW][C]29[/C][C]446[/C][C]443.047925464124[/C][C]2.95207453587579[/C][/ROW]
[ROW][C]30[/C][C]446[/C][C]453.503099349037[/C][C]-7.5030993490372[/C][/ROW]
[ROW][C]31[/C][C]466[/C][C]452.346212949969[/C][C]13.6537870500307[/C][/ROW]
[ROW][C]32[/C][C]476[/C][C]474.451460368288[/C][C]1.54853963171195[/C][/ROW]
[ROW][C]33[/C][C]476[/C][C]484.690226290876[/C][C]-8.69022629087641[/C][/ROW]
[ROW][C]34[/C][C]476[/C][C]483.350299397595[/C][C]-7.35029939759505[/C][/ROW]
[ROW][C]35[/C][C]476[/C][C]482.216972887232[/C][C]-6.21697288723158[/C][/ROW]
[ROW][C]36[/C][C]486[/C][C]481.25839150079[/C][C]4.74160849921037[/C][/ROW]
[ROW][C]37[/C][C]497[/C][C]491.989489694651[/C][C]5.01051030534933[/C][/ROW]
[ROW][C]38[/C][C]507[/C][C]503.762049267035[/C][C]3.23795073296515[/C][/ROW]
[ROW][C]39[/C][C]517[/C][C]514.261301774507[/C][C]2.73869822549307[/C][/ROW]
[ROW][C]40[/C][C]527[/C][C]524.683575635059[/C][C]2.31642436494087[/C][/ROW]
[ROW][C]41[/C][C]527[/C][C]535.040740017084[/C][C]-8.04074001708386[/C][/ROW]
[ROW][C]42[/C][C]547[/C][C]533.800955984983[/C][C]13.1990440150173[/C][/ROW]
[ROW][C]43[/C][C]547[/C][C]555.836087574121[/C][C]-8.83608757412139[/C][/ROW]
[ROW][C]44[/C][C]557[/C][C]554.473670650136[/C][C]2.52632934986423[/C][/ROW]
[ROW][C]45[/C][C]557[/C][C]564.863199820478[/C][C]-7.8631998204778[/C][/ROW]
[ROW][C]46[/C][C]557[/C][C]563.650790321111[/C][C]-6.65079032111123[/C][/ROW]
[ROW][C]47[/C][C]567[/C][C]562.62531957794[/C][C]4.37468042206012[/C][/ROW]
[ROW][C]48[/C][C]567[/C][C]573.299841937983[/C][C]-6.29984193798293[/C][/ROW]
[ROW][C]49[/C][C]598[/C][C]572.328483154727[/C][C]25.6715168452731[/C][/ROW]
[ROW][C]50[/C][C]598[/C][C]607.286717918811[/C][C]-9.28671791881129[/C][/ROW]
[ROW][C]51[/C][C]618[/C][C]605.854819292328[/C][C]12.1451807076718[/C][/ROW]
[ROW][C]52[/C][C]628[/C][C]627.727458014183[/C][C]0.272541985817497[/C][/ROW]
[ROW][C]53[/C][C]638[/C][C]637.76948066401[/C][C]0.230519335989811[/C][/ROW]
[ROW][C]54[/C][C]669[/C][C]647.805023933814[/C][C]21.1949760661857[/C][/ROW]
[ROW][C]55[/C][C]679[/C][C]682.073030713264[/C][C]-3.07303071326407[/C][/ROW]
[ROW][C]56[/C][C]689[/C][C]691.599206861185[/C][C]-2.59920686118494[/C][/ROW]
[ROW][C]57[/C][C]689[/C][C]701.198440867535[/C][C]-12.1984408675353[/C][/ROW]
[ROW][C]58[/C][C]689[/C][C]699.317590078682[/C][C]-10.3175900786815[/C][/ROW]
[ROW][C]59[/C][C]689[/C][C]697.726743539416[/C][C]-8.72674353941557[/C][/ROW]
[ROW][C]60[/C][C]709[/C][C]696.381186131836[/C][C]12.6188138681641[/C][/ROW]
[ROW][C]61[/C][C]719[/C][C]718.326853309803[/C][C]0.673146690196972[/C][/ROW]
[ROW][C]62[/C][C]729[/C][C]728.43064431859[/C][C]0.569355681409888[/C][/ROW]
[ROW][C]63[/C][C]790[/C][C]738.518432019834[/C][C]51.4815679801662[/C][/ROW]
[ROW][C]64[/C][C]831[/C][C]807.456261845662[/C][C]23.5437381543376[/C][/ROW]
[ROW][C]65[/C][C]942[/C][C]852.08641908961[/C][C]89.9135809103897[/C][/ROW]
[ROW][C]66[/C][C]952[/C][C]976.949996527122[/C][C]-24.9499965271218[/C][/ROW]
[ROW][C]67[/C][C]962[/C][C]983.103011395208[/C][C]-21.103011395208[/C][/ROW]
[ROW][C]68[/C][C]1013[/C][C]989.849184446265[/C][C]23.1508155537346[/C][/ROW]
[ROW][C]69[/C][C]1033[/C][C]1044.41875781795[/C][C]-11.4187578179524[/C][/ROW]
[ROW][C]70[/C][C]1033[/C][C]1062.658124645[/C][C]-29.6581246450044[/C][/ROW]
[ROW][C]71[/C][C]1043[/C][C]1058.08520358565[/C][C]-15.0852035856467[/C][/ROW]
[ROW][C]72[/C][C]1043[/C][C]1065.75924919753[/C][C]-22.7592491975252[/C][/ROW]
[ROW][C]73[/C][C]1053[/C][C]1062.25005058176[/C][C]-9.2500505817568[/C][/ROW]
[ROW][C]74[/C][C]1114[/C][C]1070.82380561139[/C][C]43.1761943886097[/C][/ROW]
[ROW][C]75[/C][C]1155[/C][C]1138.48104813585[/C][C]16.518951864145[/C][/ROW]
[ROW][C]76[/C][C]1215[/C][C]1182.02806902009[/C][C]32.9719309799102[/C][/ROW]
[ROW][C]77[/C][C]1236[/C][C]1247.11193859548[/C][C]-11.1119385954751[/C][/ROW]
[ROW][C]78[/C][C]1296[/C][C]1266.39861320414[/C][C]29.6013867958557[/C][/ROW]
[ROW][C]79[/C][C]1317[/C][C]1330.96278597923[/C][C]-13.9627859792345[/C][/ROW]
[ROW][C]80[/C][C]1327[/C][C]1349.80989469511[/C][C]-22.8098946951088[/C][/ROW]
[ROW][C]81[/C][C]1347[/C][C]1356.29288716137[/C][C]-9.29288716137171[/C][/ROW]
[ROW][C]82[/C][C]1367[/C][C]1374.86003731294[/C][C]-7.86003731293636[/C][/ROW]
[ROW][C]83[/C][C]1367[/C][C]1393.64811543366[/C][C]-26.6481154336573[/C][/ROW]
[ROW][C]84[/C][C]1387[/C][C]1389.5393010795[/C][C]-2.53930107950055[/C][/ROW]
[ROW][C]85[/C][C]1408[/C][C]1409.14777182667[/C][C]-1.14777182667376[/C][/ROW]
[ROW][C]86[/C][C]1468[/C][C]1429.97079941118[/C][C]38.029200588823[/C][/ROW]
[ROW][C]87[/C][C]1479[/C][C]1495.8344382732[/C][C]-16.8344382731998[/C][/ROW]
[ROW][C]88[/C][C]1499[/C][C]1504.2387732329[/C][C]-5.2387732328973[/C][/ROW]
[ROW][C]89[/C][C]1499[/C][C]1523.43101830137[/C][C]-24.4310183013679[/C][/ROW]
[ROW][C]90[/C][C]1509[/C][C]1519.66405328152[/C][C]-10.6640532815247[/C][/ROW]
[ROW][C]91[/C][C]1519[/C][C]1528.01978634243[/C][C]-9.0197863424346[/C][/ROW]
[ROW][C]92[/C][C]1529[/C][C]1536.62904530908[/C][C]-7.62904530907758[/C][/ROW]
[ROW][C]93[/C][C]1539[/C][C]1545.45273957922[/C][C]-6.45273957922245[/C][/ROW]
[ROW][C]94[/C][C]1590[/C][C]1554.45780584469[/C][C]35.5421941553132[/C][/ROW]
[ROW][C]95[/C][C]1620[/C][C]1610.93797865042[/C][C]9.06202134957948[/C][/ROW]
[ROW][C]96[/C][C]1620[/C][C]1642.33523180671[/C][C]-22.3352318067093[/C][/ROW]
[ROW][C]97[/C][C]1651[/C][C]1638.89141150057[/C][C]12.108588499432[/C][/ROW]
[ROW][C]98[/C][C]1671[/C][C]1671.75840815025[/C][C]-0.758408150252535[/C][/ROW]
[ROW][C]99[/C][C]1691[/C][C]1691.64147086432[/C][C]-0.641470864318535[/C][/ROW]
[ROW][C]100[/C][C]1711[/C][C]1711.54256388151[/C][C]-0.54256388150975[/C][/ROW]
[ROW][C]101[/C][C]1721[/C][C]1731.45890714901[/C][C]-10.4589071490122[/C][/ROW]
[ROW][C]102[/C][C]1732[/C][C]1739.84627124124[/C][C]-7.84627124124449[/C][/ROW]
[ROW][C]103[/C][C]1732[/C][C]1749.63647192231[/C][C]-17.6364719223061[/C][/ROW]
[ROW][C]104[/C][C]1742[/C][C]1746.91714307628[/C][C]-4.91714307627694[/C][/ROW]
[ROW][C]105[/C][C]1762[/C][C]1756.15897959175[/C][C]5.84102040824973[/C][/ROW]
[ROW][C]106[/C][C]1782[/C][C]1777.05959369169[/C][C]4.94040630831114[/C][/ROW]
[ROW][C]107[/C][C]1813[/C][C]1797.82134408284[/C][C]15.1786559171628[/C][/ROW]
[ROW][C]108[/C][C]1883[/C][C]1831.16170768058[/C][C]51.8382923194249[/C][/ROW]
[ROW][C]109[/C][C]1904[/C][C]1909.1545400483[/C][C]-5.15454004830099[/C][/ROW]
[ROW][C]110[/C][C]1924[/C][C]1929.35977284639[/C][C]-5.35977284638511[/C][/ROW]
[ROW][C]111[/C][C]1934[/C][C]1948.53336125037[/C][C]-14.533361250373[/C][/ROW]
[ROW][C]112[/C][C]1964[/C][C]1956.29249421914[/C][C]7.70750578085654[/C][/ROW]
[ROW][C]113[/C][C]1985[/C][C]1987.48089759671[/C][C]-2.48089759670961[/C][/ROW]
[ROW][C]114[/C][C]1995[/C][C]2008.09837344854[/C][C]-13.0983734485412[/C][/ROW]
[ROW][C]115[/C][C]1995[/C][C]2016.0787640328[/C][C]-21.0787640328037[/C][/ROW]
[ROW][C]116[/C][C]2035[/C][C]2012.82867573138[/C][C]22.1713242686183[/C][/ROW]
[ROW][C]117[/C][C]2066[/C][C]2056.24722349444[/C][C]9.75277650555563[/C][/ROW]
[ROW][C]118[/C][C]2086[/C][C]2088.75098267016[/C][C]-2.75098267016074[/C][/ROW]
[ROW][C]119[/C][C]2157[/C][C]2108.32681469808[/C][C]48.6731853019173[/C][/ROW]
[ROW][C]120[/C][C]2157[/C][C]2186.83162617073[/C][C]-29.8316261707346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
32542531
4284284.1541878023-0.154187802300157
5294314.130413923922-20.130413923922
6304321.0265496416-17.0265496415997
7314328.401263371607-14.4012633716067
8314336.180764221993-22.1807642219928
9314332.760760933265-18.7607609332655
10314329.868080435486-15.8680804354864
11324327.421415986416-3.42141598641643
12335336.893875374716-1.89387537471623
13335347.601862892858-12.6018628928583
14335345.65880934852-10.6588093485204
15345344.0153509599360.984649040064426
16365354.1671718314610.8328281685399
17365375.837461799463-10.8374617994626
18385374.16645738209110.8335426179086
19385395.836857509472-10.836857509472
20385394.165946266246-9.16594626624641
21395392.7526691554522.24733084454755
22395403.099180159415-8.09918015941463
23405401.8503853702013.14961462979869
24405412.336017528062-7.33601752806243
25416411.2048931077754.79510689222502
26416422.944240101282-6.94424010128154
27426421.873522981424.12647701857975
28436432.5097754041573.49022459584279
29446443.0479254641242.95207453587579
30446453.503099349037-7.5030993490372
31466452.34621294996913.6537870500307
32476474.4514603682881.54853963171195
33476484.690226290876-8.69022629087641
34476483.350299397595-7.35029939759505
35476482.216972887232-6.21697288723158
36486481.258391500794.74160849921037
37497491.9894896946515.01051030534933
38507503.7620492670353.23795073296515
39517514.2613017745072.73869822549307
40527524.6835756350592.31642436494087
41527535.040740017084-8.04074001708386
42547533.80095598498313.1990440150173
43547555.836087574121-8.83608757412139
44557554.4736706501362.52632934986423
45557564.863199820478-7.8631998204778
46557563.650790321111-6.65079032111123
47567562.625319577944.37468042206012
48567573.299841937983-6.29984193798293
49598572.32848315472725.6715168452731
50598607.286717918811-9.28671791881129
51618605.85481929232812.1451807076718
52628627.7274580141830.272541985817497
53638637.769480664010.230519335989811
54669647.80502393381421.1949760661857
55679682.073030713264-3.07303071326407
56689691.599206861185-2.59920686118494
57689701.198440867535-12.1984408675353
58689699.317590078682-10.3175900786815
59689697.726743539416-8.72674353941557
60709696.38118613183612.6188138681641
61719718.3268533098030.673146690196972
62729728.430644318590.569355681409888
63790738.51843201983451.4815679801662
64831807.45626184566223.5437381543376
65942852.0864190896189.9135809103897
66952976.949996527122-24.9499965271218
67962983.103011395208-21.103011395208
681013989.84918444626523.1508155537346
6910331044.41875781795-11.4187578179524
7010331062.658124645-29.6581246450044
7110431058.08520358565-15.0852035856467
7210431065.75924919753-22.7592491975252
7310531062.25005058176-9.2500505817568
7411141070.8238056113943.1761943886097
7511551138.4810481358516.518951864145
7612151182.0280690200932.9719309799102
7712361247.11193859548-11.1119385954751
7812961266.3986132041429.6013867958557
7913171330.96278597923-13.9627859792345
8013271349.80989469511-22.8098946951088
8113471356.29288716137-9.29288716137171
8213671374.86003731294-7.86003731293636
8313671393.64811543366-26.6481154336573
8413871389.5393010795-2.53930107950055
8514081409.14777182667-1.14777182667376
8614681429.9707994111838.029200588823
8714791495.8344382732-16.8344382731998
8814991504.2387732329-5.2387732328973
8914991523.43101830137-24.4310183013679
9015091519.66405328152-10.6640532815247
9115191528.01978634243-9.0197863424346
9215291536.62904530908-7.62904530907758
9315391545.45273957922-6.45273957922245
9415901554.4578058446935.5421941553132
9516201610.937978650429.06202134957948
9616201642.33523180671-22.3352318067093
9716511638.8914115005712.108588499432
9816711671.75840815025-0.758408150252535
9916911691.64147086432-0.641470864318535
10017111711.54256388151-0.54256388150975
10117211731.45890714901-10.4589071490122
10217321739.84627124124-7.84627124124449
10317321749.63647192231-17.6364719223061
10417421746.91714307628-4.91714307627694
10517621756.158979591755.84102040824973
10617821777.059593691694.94040630831114
10718131797.8213440828415.1786559171628
10818831831.1617076805851.8382923194249
10919041909.1545400483-5.15454004830099
11019241929.35977284639-5.35977284638511
11119341948.53336125037-14.533361250373
11219641956.292494219147.70750578085654
11319851987.48089759671-2.48089759670961
11419952008.09837344854-13.0983734485412
11519952016.0787640328-21.0787640328037
11620352012.8286757313822.1713242686183
11720662056.247223494449.75277650555563
11820862088.75098267016-2.75098267016074
11921572108.3268146980848.6731853019173
12021572186.83162617073-29.8316261707346







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212182.231953292432146.281939705282218.18196687957
1222207.463906584862152.563286365332262.36452680439
1232232.695859877292160.401498016422304.99022173816
1242257.927813169712168.535171793522347.32045454591
1252283.159766462142176.533138865352389.78639405894
1262308.391719754572184.204338010772432.57910149838
1272333.6236730472191.453706339852475.79363975415
1282358.855626339432198.23162580962519.47962686926
1292384.087579631862204.512339109622563.6628201541
1302409.319532924292210.283499234652608.35556661392
1312434.551486216712215.540647381732653.5623250517
1322459.783439509142220.284102650622699.28277636767

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2182.23195329243 & 2146.28193970528 & 2218.18196687957 \tabularnewline
122 & 2207.46390658486 & 2152.56328636533 & 2262.36452680439 \tabularnewline
123 & 2232.69585987729 & 2160.40149801642 & 2304.99022173816 \tabularnewline
124 & 2257.92781316971 & 2168.53517179352 & 2347.32045454591 \tabularnewline
125 & 2283.15976646214 & 2176.53313886535 & 2389.78639405894 \tabularnewline
126 & 2308.39171975457 & 2184.20433801077 & 2432.57910149838 \tabularnewline
127 & 2333.623673047 & 2191.45370633985 & 2475.79363975415 \tabularnewline
128 & 2358.85562633943 & 2198.2316258096 & 2519.47962686926 \tabularnewline
129 & 2384.08757963186 & 2204.51233910962 & 2563.6628201541 \tabularnewline
130 & 2409.31953292429 & 2210.28349923465 & 2608.35556661392 \tabularnewline
131 & 2434.55148621671 & 2215.54064738173 & 2653.5623250517 \tabularnewline
132 & 2459.78343950914 & 2220.28410265062 & 2699.28277636767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121[/C][C]2182.23195329243[/C][C]2146.28193970528[/C][C]2218.18196687957[/C][/ROW]
[ROW][C]122[/C][C]2207.46390658486[/C][C]2152.56328636533[/C][C]2262.36452680439[/C][/ROW]
[ROW][C]123[/C][C]2232.69585987729[/C][C]2160.40149801642[/C][C]2304.99022173816[/C][/ROW]
[ROW][C]124[/C][C]2257.92781316971[/C][C]2168.53517179352[/C][C]2347.32045454591[/C][/ROW]
[ROW][C]125[/C][C]2283.15976646214[/C][C]2176.53313886535[/C][C]2389.78639405894[/C][/ROW]
[ROW][C]126[/C][C]2308.39171975457[/C][C]2184.20433801077[/C][C]2432.57910149838[/C][/ROW]
[ROW][C]127[/C][C]2333.623673047[/C][C]2191.45370633985[/C][C]2475.79363975415[/C][/ROW]
[ROW][C]128[/C][C]2358.85562633943[/C][C]2198.2316258096[/C][C]2519.47962686926[/C][/ROW]
[ROW][C]129[/C][C]2384.08757963186[/C][C]2204.51233910962[/C][C]2563.6628201541[/C][/ROW]
[ROW][C]130[/C][C]2409.31953292429[/C][C]2210.28349923465[/C][C]2608.35556661392[/C][/ROW]
[ROW][C]131[/C][C]2434.55148621671[/C][C]2215.54064738173[/C][C]2653.5623250517[/C][/ROW]
[ROW][C]132[/C][C]2459.78343950914[/C][C]2220.28410265062[/C][C]2699.28277636767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1212182.231953292432146.281939705282218.18196687957
1222207.463906584862152.563286365332262.36452680439
1232232.695859877292160.401498016422304.99022173816
1242257.927813169712168.535171793522347.32045454591
1252283.159766462142176.533138865352389.78639405894
1262308.391719754572184.204338010772432.57910149838
1272333.6236730472191.453706339852475.79363975415
1282358.855626339432198.23162580962519.47962686926
1292384.087579631862204.512339109622563.6628201541
1302409.319532924292210.283499234652608.35556661392
1312434.551486216712215.540647381732653.5623250517
1322459.783439509142220.284102650622699.28277636767



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')