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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Dec 2016 14:20:01 +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/Dec/20/t1482240080ywdu5rxj78g0ui9.htm/, Retrieved Sun, 28 Apr 2024 08:13:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301651, Retrieved Sun, 28 Apr 2024 08:13:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ES 2A] [2016-12-20 13:20:01] [94c1b173d9287822f5e2740a4a602bdd] [Current]
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Dataseries X:
2880
2160
2040
2360
2160
3300
2700
3900
4620
3860
4040
3460
2820
2040
2100
1820
1840
2680
3060
3540
4700
4880
3960
2440
2440
2340
2340
2220
1560
2940
2280
2400
2700
3100
3160
3520
2300
2680
2140
2320
1940
2260
2300
2980
2800
3060
3140
2740
2480
1720
2060
1920
2000
2820
2440
2700
2880
3100
3060
2040
1880
2180
1820
1700
1700
1680
2240
2400
2920
3380
2700
1900
1960
2040
1860
1720
2340
2060
2200
2520
2700
2000
2120
1780
1820
1480
1780
1600
1720
2100
2000
2420
2660
3140
2280
2220
1860
1980
1520
1540
1660
2500
1660
2220
2160
2540
2540
2340




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301651&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301651&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.980879852637059
beta0.107720278277293
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.980879852637059 \tabularnewline
beta & 0.107720278277293 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301651&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]0.980879852637059[/C][/ROW]
[ROW][C]beta[/C][C]0.107720278277293[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301651&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
alpha0.980879852637059
beta0.107720278277293
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
320401440600
423601371.92430199183988.075698008172
521601788.9049586332371.095041366803
633001639.911863244191660.08813675581
727002930.67211803071-230.67211803071
839002342.450766644751557.54923335525
946203672.83137635528947.168623644722
1038604504.58039664092-644.58039664092
1140403706.90808834724333.091911652765
1234603903.40955786235-443.409557862355
1328203291.40543798438-471.405437984379
1420402602.1317180251-562.131718025096
1521001764.47121477328335.528785226724
1618201842.76000343903-22.7600034390259
1718401567.2057011039272.794298896102
1826801610.378282413381069.62171758662
1930602548.15975140969511.840248590314
2035402992.90598900484547.094010995163
2147003530.038241058891169.96175894111
2248804801.7478386540878.2521613459185
2339605010.88966132277-1050.88966132277
2424404001.44133395482-1561.44133395482
2524402326.22024982348113.779750176519
2623402306.2118182675533.7881817324546
2723402211.31135011122128.688649888776
2822202223.09416565798-3.09416565798301
2915602105.2869409544-545.286940954398
3029401398.038373727191541.96162627281
3122802901.05454229839-621.054542298389
3224002216.79070314123183.209296858772
3327002340.77107353507359.228926464932
3431002675.36191439254424.638085607456
3531603118.9788180607741.0211819392266
3635203190.6479545653329.352045434705
3723003579.93457739027-1279.93457739027
3826802255.46565448961424.53434551039
3921402647.73253269196-507.732532691959
4023202071.91026300779248.089736992207
4119402263.67215286952-323.672152869524
4222601860.40491418014399.595085819856
4323002208.7974147709391.2025852290667
4429802264.3304493271715.669550672902
4528003008.00865932239-208.008659322385
4630602823.6911925218236.308807478197
4731403100.1643194408439.8356805591643
4827403188.12997850865-448.129978508653
4924802750.11024869846-270.110248698456
5017202458.16646059744-738.166460597442
5120601629.12061580425430.879384195748
5219201992.29528307764-72.2952830776369
5320001854.27729021393145.722709786067
5428201945.50591039784874.494089602158
5524402843.97130874736-403.971308747364
5627002445.73188422286254.268115777142
5728802720.01238398672159.987616013283
5831002918.71943664478181.280563355216
5930603157.46653463404-97.4665346340448
6020403112.49784275538-1072.49784275538
6118801997.81976512886-117.81976512886
6221801807.11726655368372.882733446321
6318202137.13399471382-317.133994713824
6417001756.81863200409-56.8186320040877
6517001625.8378702797974.16212972021
6616801631.1695176961648.8304823038402
6722401616.81332306108623.186676938921
6824002231.67785776296168.322142237035
6929202418.1599617697501.840038230296
7033802984.80779542816395.192204571843
7127003488.60318320342-788.603183203418
7219002747.91319999757-847.913199997566
7319601859.45615582461100.543844175387
7420401911.94504537031128.054954629686
7518602004.94939871362-144.94939871362
7617201814.85383439613-94.8538343961279
7723401663.87368196211676.126318037892
7820602340.57237454122-280.572374541218
7922002049.21913486766150.780865132339
8025202196.90320168323.096798320003
8127002547.74711358844152.25288641156
8220002747.10081340675-747.100813406749
8321201985.35743060858134.642569391417
8417802102.72478868467-322.724788684666
8518201737.3704088062482.6295911937643
8614801778.35066969992-298.350669699921
8717801414.11114253848365.888857461519
8816001740.07083965178-140.070839651781
8917201554.94488756102165.055112438976
9021001686.55066497159413.449335028409
9120002105.48665659499-105.486656594991
9224202004.2630004526415.736999547401
9326602458.22416922314201.775830776861
9431402723.63490387189416.365096128106
9522803243.52533247432-963.525332474315
9622202308.10232723545-88.1023272354482
9718602222.05516114802-362.055161148019
9819801829.03819579301150.96180420699
9915201955.17995827647-435.179958276471
10015401460.4056775951979.5943224048133
10116601478.97310538585181.026894614154
10225001616.16111913379883.838880866207
10316602536.11024163916-876.110241639165
10422201637.19035001141582.809649988585
10521602230.87563353469-70.8756335346902
10625402175.88542692782364.11457307218
10725402586.0409327899-46.0409327899042
10823402589.01845158709-249.018451587091

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2040 & 1440 & 600 \tabularnewline
4 & 2360 & 1371.92430199183 & 988.075698008172 \tabularnewline
5 & 2160 & 1788.9049586332 & 371.095041366803 \tabularnewline
6 & 3300 & 1639.91186324419 & 1660.08813675581 \tabularnewline
7 & 2700 & 2930.67211803071 & -230.67211803071 \tabularnewline
8 & 3900 & 2342.45076664475 & 1557.54923335525 \tabularnewline
9 & 4620 & 3672.83137635528 & 947.168623644722 \tabularnewline
10 & 3860 & 4504.58039664092 & -644.58039664092 \tabularnewline
11 & 4040 & 3706.90808834724 & 333.091911652765 \tabularnewline
12 & 3460 & 3903.40955786235 & -443.409557862355 \tabularnewline
13 & 2820 & 3291.40543798438 & -471.405437984379 \tabularnewline
14 & 2040 & 2602.1317180251 & -562.131718025096 \tabularnewline
15 & 2100 & 1764.47121477328 & 335.528785226724 \tabularnewline
16 & 1820 & 1842.76000343903 & -22.7600034390259 \tabularnewline
17 & 1840 & 1567.2057011039 & 272.794298896102 \tabularnewline
18 & 2680 & 1610.37828241338 & 1069.62171758662 \tabularnewline
19 & 3060 & 2548.15975140969 & 511.840248590314 \tabularnewline
20 & 3540 & 2992.90598900484 & 547.094010995163 \tabularnewline
21 & 4700 & 3530.03824105889 & 1169.96175894111 \tabularnewline
22 & 4880 & 4801.74783865408 & 78.2521613459185 \tabularnewline
23 & 3960 & 5010.88966132277 & -1050.88966132277 \tabularnewline
24 & 2440 & 4001.44133395482 & -1561.44133395482 \tabularnewline
25 & 2440 & 2326.22024982348 & 113.779750176519 \tabularnewline
26 & 2340 & 2306.21181826755 & 33.7881817324546 \tabularnewline
27 & 2340 & 2211.31135011122 & 128.688649888776 \tabularnewline
28 & 2220 & 2223.09416565798 & -3.09416565798301 \tabularnewline
29 & 1560 & 2105.2869409544 & -545.286940954398 \tabularnewline
30 & 2940 & 1398.03837372719 & 1541.96162627281 \tabularnewline
31 & 2280 & 2901.05454229839 & -621.054542298389 \tabularnewline
32 & 2400 & 2216.79070314123 & 183.209296858772 \tabularnewline
33 & 2700 & 2340.77107353507 & 359.228926464932 \tabularnewline
34 & 3100 & 2675.36191439254 & 424.638085607456 \tabularnewline
35 & 3160 & 3118.97881806077 & 41.0211819392266 \tabularnewline
36 & 3520 & 3190.6479545653 & 329.352045434705 \tabularnewline
37 & 2300 & 3579.93457739027 & -1279.93457739027 \tabularnewline
38 & 2680 & 2255.46565448961 & 424.53434551039 \tabularnewline
39 & 2140 & 2647.73253269196 & -507.732532691959 \tabularnewline
40 & 2320 & 2071.91026300779 & 248.089736992207 \tabularnewline
41 & 1940 & 2263.67215286952 & -323.672152869524 \tabularnewline
42 & 2260 & 1860.40491418014 & 399.595085819856 \tabularnewline
43 & 2300 & 2208.79741477093 & 91.2025852290667 \tabularnewline
44 & 2980 & 2264.3304493271 & 715.669550672902 \tabularnewline
45 & 2800 & 3008.00865932239 & -208.008659322385 \tabularnewline
46 & 3060 & 2823.6911925218 & 236.308807478197 \tabularnewline
47 & 3140 & 3100.16431944084 & 39.8356805591643 \tabularnewline
48 & 2740 & 3188.12997850865 & -448.129978508653 \tabularnewline
49 & 2480 & 2750.11024869846 & -270.110248698456 \tabularnewline
50 & 1720 & 2458.16646059744 & -738.166460597442 \tabularnewline
51 & 2060 & 1629.12061580425 & 430.879384195748 \tabularnewline
52 & 1920 & 1992.29528307764 & -72.2952830776369 \tabularnewline
53 & 2000 & 1854.27729021393 & 145.722709786067 \tabularnewline
54 & 2820 & 1945.50591039784 & 874.494089602158 \tabularnewline
55 & 2440 & 2843.97130874736 & -403.971308747364 \tabularnewline
56 & 2700 & 2445.73188422286 & 254.268115777142 \tabularnewline
57 & 2880 & 2720.01238398672 & 159.987616013283 \tabularnewline
58 & 3100 & 2918.71943664478 & 181.280563355216 \tabularnewline
59 & 3060 & 3157.46653463404 & -97.4665346340448 \tabularnewline
60 & 2040 & 3112.49784275538 & -1072.49784275538 \tabularnewline
61 & 1880 & 1997.81976512886 & -117.81976512886 \tabularnewline
62 & 2180 & 1807.11726655368 & 372.882733446321 \tabularnewline
63 & 1820 & 2137.13399471382 & -317.133994713824 \tabularnewline
64 & 1700 & 1756.81863200409 & -56.8186320040877 \tabularnewline
65 & 1700 & 1625.83787027979 & 74.16212972021 \tabularnewline
66 & 1680 & 1631.16951769616 & 48.8304823038402 \tabularnewline
67 & 2240 & 1616.81332306108 & 623.186676938921 \tabularnewline
68 & 2400 & 2231.67785776296 & 168.322142237035 \tabularnewline
69 & 2920 & 2418.1599617697 & 501.840038230296 \tabularnewline
70 & 3380 & 2984.80779542816 & 395.192204571843 \tabularnewline
71 & 2700 & 3488.60318320342 & -788.603183203418 \tabularnewline
72 & 1900 & 2747.91319999757 & -847.913199997566 \tabularnewline
73 & 1960 & 1859.45615582461 & 100.543844175387 \tabularnewline
74 & 2040 & 1911.94504537031 & 128.054954629686 \tabularnewline
75 & 1860 & 2004.94939871362 & -144.94939871362 \tabularnewline
76 & 1720 & 1814.85383439613 & -94.8538343961279 \tabularnewline
77 & 2340 & 1663.87368196211 & 676.126318037892 \tabularnewline
78 & 2060 & 2340.57237454122 & -280.572374541218 \tabularnewline
79 & 2200 & 2049.21913486766 & 150.780865132339 \tabularnewline
80 & 2520 & 2196.90320168 & 323.096798320003 \tabularnewline
81 & 2700 & 2547.74711358844 & 152.25288641156 \tabularnewline
82 & 2000 & 2747.10081340675 & -747.100813406749 \tabularnewline
83 & 2120 & 1985.35743060858 & 134.642569391417 \tabularnewline
84 & 1780 & 2102.72478868467 & -322.724788684666 \tabularnewline
85 & 1820 & 1737.37040880624 & 82.6295911937643 \tabularnewline
86 & 1480 & 1778.35066969992 & -298.350669699921 \tabularnewline
87 & 1780 & 1414.11114253848 & 365.888857461519 \tabularnewline
88 & 1600 & 1740.07083965178 & -140.070839651781 \tabularnewline
89 & 1720 & 1554.94488756102 & 165.055112438976 \tabularnewline
90 & 2100 & 1686.55066497159 & 413.449335028409 \tabularnewline
91 & 2000 & 2105.48665659499 & -105.486656594991 \tabularnewline
92 & 2420 & 2004.2630004526 & 415.736999547401 \tabularnewline
93 & 2660 & 2458.22416922314 & 201.775830776861 \tabularnewline
94 & 3140 & 2723.63490387189 & 416.365096128106 \tabularnewline
95 & 2280 & 3243.52533247432 & -963.525332474315 \tabularnewline
96 & 2220 & 2308.10232723545 & -88.1023272354482 \tabularnewline
97 & 1860 & 2222.05516114802 & -362.055161148019 \tabularnewline
98 & 1980 & 1829.03819579301 & 150.96180420699 \tabularnewline
99 & 1520 & 1955.17995827647 & -435.179958276471 \tabularnewline
100 & 1540 & 1460.40567759519 & 79.5943224048133 \tabularnewline
101 & 1660 & 1478.97310538585 & 181.026894614154 \tabularnewline
102 & 2500 & 1616.16111913379 & 883.838880866207 \tabularnewline
103 & 1660 & 2536.11024163916 & -876.110241639165 \tabularnewline
104 & 2220 & 1637.19035001141 & 582.809649988585 \tabularnewline
105 & 2160 & 2230.87563353469 & -70.8756335346902 \tabularnewline
106 & 2540 & 2175.88542692782 & 364.11457307218 \tabularnewline
107 & 2540 & 2586.0409327899 & -46.0409327899042 \tabularnewline
108 & 2340 & 2589.01845158709 & -249.018451587091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301651&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]2040[/C][C]1440[/C][C]600[/C][/ROW]
[ROW][C]4[/C][C]2360[/C][C]1371.92430199183[/C][C]988.075698008172[/C][/ROW]
[ROW][C]5[/C][C]2160[/C][C]1788.9049586332[/C][C]371.095041366803[/C][/ROW]
[ROW][C]6[/C][C]3300[/C][C]1639.91186324419[/C][C]1660.08813675581[/C][/ROW]
[ROW][C]7[/C][C]2700[/C][C]2930.67211803071[/C][C]-230.67211803071[/C][/ROW]
[ROW][C]8[/C][C]3900[/C][C]2342.45076664475[/C][C]1557.54923335525[/C][/ROW]
[ROW][C]9[/C][C]4620[/C][C]3672.83137635528[/C][C]947.168623644722[/C][/ROW]
[ROW][C]10[/C][C]3860[/C][C]4504.58039664092[/C][C]-644.58039664092[/C][/ROW]
[ROW][C]11[/C][C]4040[/C][C]3706.90808834724[/C][C]333.091911652765[/C][/ROW]
[ROW][C]12[/C][C]3460[/C][C]3903.40955786235[/C][C]-443.409557862355[/C][/ROW]
[ROW][C]13[/C][C]2820[/C][C]3291.40543798438[/C][C]-471.405437984379[/C][/ROW]
[ROW][C]14[/C][C]2040[/C][C]2602.1317180251[/C][C]-562.131718025096[/C][/ROW]
[ROW][C]15[/C][C]2100[/C][C]1764.47121477328[/C][C]335.528785226724[/C][/ROW]
[ROW][C]16[/C][C]1820[/C][C]1842.76000343903[/C][C]-22.7600034390259[/C][/ROW]
[ROW][C]17[/C][C]1840[/C][C]1567.2057011039[/C][C]272.794298896102[/C][/ROW]
[ROW][C]18[/C][C]2680[/C][C]1610.37828241338[/C][C]1069.62171758662[/C][/ROW]
[ROW][C]19[/C][C]3060[/C][C]2548.15975140969[/C][C]511.840248590314[/C][/ROW]
[ROW][C]20[/C][C]3540[/C][C]2992.90598900484[/C][C]547.094010995163[/C][/ROW]
[ROW][C]21[/C][C]4700[/C][C]3530.03824105889[/C][C]1169.96175894111[/C][/ROW]
[ROW][C]22[/C][C]4880[/C][C]4801.74783865408[/C][C]78.2521613459185[/C][/ROW]
[ROW][C]23[/C][C]3960[/C][C]5010.88966132277[/C][C]-1050.88966132277[/C][/ROW]
[ROW][C]24[/C][C]2440[/C][C]4001.44133395482[/C][C]-1561.44133395482[/C][/ROW]
[ROW][C]25[/C][C]2440[/C][C]2326.22024982348[/C][C]113.779750176519[/C][/ROW]
[ROW][C]26[/C][C]2340[/C][C]2306.21181826755[/C][C]33.7881817324546[/C][/ROW]
[ROW][C]27[/C][C]2340[/C][C]2211.31135011122[/C][C]128.688649888776[/C][/ROW]
[ROW][C]28[/C][C]2220[/C][C]2223.09416565798[/C][C]-3.09416565798301[/C][/ROW]
[ROW][C]29[/C][C]1560[/C][C]2105.2869409544[/C][C]-545.286940954398[/C][/ROW]
[ROW][C]30[/C][C]2940[/C][C]1398.03837372719[/C][C]1541.96162627281[/C][/ROW]
[ROW][C]31[/C][C]2280[/C][C]2901.05454229839[/C][C]-621.054542298389[/C][/ROW]
[ROW][C]32[/C][C]2400[/C][C]2216.79070314123[/C][C]183.209296858772[/C][/ROW]
[ROW][C]33[/C][C]2700[/C][C]2340.77107353507[/C][C]359.228926464932[/C][/ROW]
[ROW][C]34[/C][C]3100[/C][C]2675.36191439254[/C][C]424.638085607456[/C][/ROW]
[ROW][C]35[/C][C]3160[/C][C]3118.97881806077[/C][C]41.0211819392266[/C][/ROW]
[ROW][C]36[/C][C]3520[/C][C]3190.6479545653[/C][C]329.352045434705[/C][/ROW]
[ROW][C]37[/C][C]2300[/C][C]3579.93457739027[/C][C]-1279.93457739027[/C][/ROW]
[ROW][C]38[/C][C]2680[/C][C]2255.46565448961[/C][C]424.53434551039[/C][/ROW]
[ROW][C]39[/C][C]2140[/C][C]2647.73253269196[/C][C]-507.732532691959[/C][/ROW]
[ROW][C]40[/C][C]2320[/C][C]2071.91026300779[/C][C]248.089736992207[/C][/ROW]
[ROW][C]41[/C][C]1940[/C][C]2263.67215286952[/C][C]-323.672152869524[/C][/ROW]
[ROW][C]42[/C][C]2260[/C][C]1860.40491418014[/C][C]399.595085819856[/C][/ROW]
[ROW][C]43[/C][C]2300[/C][C]2208.79741477093[/C][C]91.2025852290667[/C][/ROW]
[ROW][C]44[/C][C]2980[/C][C]2264.3304493271[/C][C]715.669550672902[/C][/ROW]
[ROW][C]45[/C][C]2800[/C][C]3008.00865932239[/C][C]-208.008659322385[/C][/ROW]
[ROW][C]46[/C][C]3060[/C][C]2823.6911925218[/C][C]236.308807478197[/C][/ROW]
[ROW][C]47[/C][C]3140[/C][C]3100.16431944084[/C][C]39.8356805591643[/C][/ROW]
[ROW][C]48[/C][C]2740[/C][C]3188.12997850865[/C][C]-448.129978508653[/C][/ROW]
[ROW][C]49[/C][C]2480[/C][C]2750.11024869846[/C][C]-270.110248698456[/C][/ROW]
[ROW][C]50[/C][C]1720[/C][C]2458.16646059744[/C][C]-738.166460597442[/C][/ROW]
[ROW][C]51[/C][C]2060[/C][C]1629.12061580425[/C][C]430.879384195748[/C][/ROW]
[ROW][C]52[/C][C]1920[/C][C]1992.29528307764[/C][C]-72.2952830776369[/C][/ROW]
[ROW][C]53[/C][C]2000[/C][C]1854.27729021393[/C][C]145.722709786067[/C][/ROW]
[ROW][C]54[/C][C]2820[/C][C]1945.50591039784[/C][C]874.494089602158[/C][/ROW]
[ROW][C]55[/C][C]2440[/C][C]2843.97130874736[/C][C]-403.971308747364[/C][/ROW]
[ROW][C]56[/C][C]2700[/C][C]2445.73188422286[/C][C]254.268115777142[/C][/ROW]
[ROW][C]57[/C][C]2880[/C][C]2720.01238398672[/C][C]159.987616013283[/C][/ROW]
[ROW][C]58[/C][C]3100[/C][C]2918.71943664478[/C][C]181.280563355216[/C][/ROW]
[ROW][C]59[/C][C]3060[/C][C]3157.46653463404[/C][C]-97.4665346340448[/C][/ROW]
[ROW][C]60[/C][C]2040[/C][C]3112.49784275538[/C][C]-1072.49784275538[/C][/ROW]
[ROW][C]61[/C][C]1880[/C][C]1997.81976512886[/C][C]-117.81976512886[/C][/ROW]
[ROW][C]62[/C][C]2180[/C][C]1807.11726655368[/C][C]372.882733446321[/C][/ROW]
[ROW][C]63[/C][C]1820[/C][C]2137.13399471382[/C][C]-317.133994713824[/C][/ROW]
[ROW][C]64[/C][C]1700[/C][C]1756.81863200409[/C][C]-56.8186320040877[/C][/ROW]
[ROW][C]65[/C][C]1700[/C][C]1625.83787027979[/C][C]74.16212972021[/C][/ROW]
[ROW][C]66[/C][C]1680[/C][C]1631.16951769616[/C][C]48.8304823038402[/C][/ROW]
[ROW][C]67[/C][C]2240[/C][C]1616.81332306108[/C][C]623.186676938921[/C][/ROW]
[ROW][C]68[/C][C]2400[/C][C]2231.67785776296[/C][C]168.322142237035[/C][/ROW]
[ROW][C]69[/C][C]2920[/C][C]2418.1599617697[/C][C]501.840038230296[/C][/ROW]
[ROW][C]70[/C][C]3380[/C][C]2984.80779542816[/C][C]395.192204571843[/C][/ROW]
[ROW][C]71[/C][C]2700[/C][C]3488.60318320342[/C][C]-788.603183203418[/C][/ROW]
[ROW][C]72[/C][C]1900[/C][C]2747.91319999757[/C][C]-847.913199997566[/C][/ROW]
[ROW][C]73[/C][C]1960[/C][C]1859.45615582461[/C][C]100.543844175387[/C][/ROW]
[ROW][C]74[/C][C]2040[/C][C]1911.94504537031[/C][C]128.054954629686[/C][/ROW]
[ROW][C]75[/C][C]1860[/C][C]2004.94939871362[/C][C]-144.94939871362[/C][/ROW]
[ROW][C]76[/C][C]1720[/C][C]1814.85383439613[/C][C]-94.8538343961279[/C][/ROW]
[ROW][C]77[/C][C]2340[/C][C]1663.87368196211[/C][C]676.126318037892[/C][/ROW]
[ROW][C]78[/C][C]2060[/C][C]2340.57237454122[/C][C]-280.572374541218[/C][/ROW]
[ROW][C]79[/C][C]2200[/C][C]2049.21913486766[/C][C]150.780865132339[/C][/ROW]
[ROW][C]80[/C][C]2520[/C][C]2196.90320168[/C][C]323.096798320003[/C][/ROW]
[ROW][C]81[/C][C]2700[/C][C]2547.74711358844[/C][C]152.25288641156[/C][/ROW]
[ROW][C]82[/C][C]2000[/C][C]2747.10081340675[/C][C]-747.100813406749[/C][/ROW]
[ROW][C]83[/C][C]2120[/C][C]1985.35743060858[/C][C]134.642569391417[/C][/ROW]
[ROW][C]84[/C][C]1780[/C][C]2102.72478868467[/C][C]-322.724788684666[/C][/ROW]
[ROW][C]85[/C][C]1820[/C][C]1737.37040880624[/C][C]82.6295911937643[/C][/ROW]
[ROW][C]86[/C][C]1480[/C][C]1778.35066969992[/C][C]-298.350669699921[/C][/ROW]
[ROW][C]87[/C][C]1780[/C][C]1414.11114253848[/C][C]365.888857461519[/C][/ROW]
[ROW][C]88[/C][C]1600[/C][C]1740.07083965178[/C][C]-140.070839651781[/C][/ROW]
[ROW][C]89[/C][C]1720[/C][C]1554.94488756102[/C][C]165.055112438976[/C][/ROW]
[ROW][C]90[/C][C]2100[/C][C]1686.55066497159[/C][C]413.449335028409[/C][/ROW]
[ROW][C]91[/C][C]2000[/C][C]2105.48665659499[/C][C]-105.486656594991[/C][/ROW]
[ROW][C]92[/C][C]2420[/C][C]2004.2630004526[/C][C]415.736999547401[/C][/ROW]
[ROW][C]93[/C][C]2660[/C][C]2458.22416922314[/C][C]201.775830776861[/C][/ROW]
[ROW][C]94[/C][C]3140[/C][C]2723.63490387189[/C][C]416.365096128106[/C][/ROW]
[ROW][C]95[/C][C]2280[/C][C]3243.52533247432[/C][C]-963.525332474315[/C][/ROW]
[ROW][C]96[/C][C]2220[/C][C]2308.10232723545[/C][C]-88.1023272354482[/C][/ROW]
[ROW][C]97[/C][C]1860[/C][C]2222.05516114802[/C][C]-362.055161148019[/C][/ROW]
[ROW][C]98[/C][C]1980[/C][C]1829.03819579301[/C][C]150.96180420699[/C][/ROW]
[ROW][C]99[/C][C]1520[/C][C]1955.17995827647[/C][C]-435.179958276471[/C][/ROW]
[ROW][C]100[/C][C]1540[/C][C]1460.40567759519[/C][C]79.5943224048133[/C][/ROW]
[ROW][C]101[/C][C]1660[/C][C]1478.97310538585[/C][C]181.026894614154[/C][/ROW]
[ROW][C]102[/C][C]2500[/C][C]1616.16111913379[/C][C]883.838880866207[/C][/ROW]
[ROW][C]103[/C][C]1660[/C][C]2536.11024163916[/C][C]-876.110241639165[/C][/ROW]
[ROW][C]104[/C][C]2220[/C][C]1637.19035001141[/C][C]582.809649988585[/C][/ROW]
[ROW][C]105[/C][C]2160[/C][C]2230.87563353469[/C][C]-70.8756335346902[/C][/ROW]
[ROW][C]106[/C][C]2540[/C][C]2175.88542692782[/C][C]364.11457307218[/C][/ROW]
[ROW][C]107[/C][C]2540[/C][C]2586.0409327899[/C][C]-46.0409327899042[/C][/ROW]
[ROW][C]108[/C][C]2340[/C][C]2589.01845158709[/C][C]-249.018451587091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301651&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
320401440600
423601371.92430199183988.075698008172
521601788.9049586332371.095041366803
633001639.911863244191660.08813675581
727002930.67211803071-230.67211803071
839002342.450766644751557.54923335525
946203672.83137635528947.168623644722
1038604504.58039664092-644.58039664092
1140403706.90808834724333.091911652765
1234603903.40955786235-443.409557862355
1328203291.40543798438-471.405437984379
1420402602.1317180251-562.131718025096
1521001764.47121477328335.528785226724
1618201842.76000343903-22.7600034390259
1718401567.2057011039272.794298896102
1826801610.378282413381069.62171758662
1930602548.15975140969511.840248590314
2035402992.90598900484547.094010995163
2147003530.038241058891169.96175894111
2248804801.7478386540878.2521613459185
2339605010.88966132277-1050.88966132277
2424404001.44133395482-1561.44133395482
2524402326.22024982348113.779750176519
2623402306.2118182675533.7881817324546
2723402211.31135011122128.688649888776
2822202223.09416565798-3.09416565798301
2915602105.2869409544-545.286940954398
3029401398.038373727191541.96162627281
3122802901.05454229839-621.054542298389
3224002216.79070314123183.209296858772
3327002340.77107353507359.228926464932
3431002675.36191439254424.638085607456
3531603118.9788180607741.0211819392266
3635203190.6479545653329.352045434705
3723003579.93457739027-1279.93457739027
3826802255.46565448961424.53434551039
3921402647.73253269196-507.732532691959
4023202071.91026300779248.089736992207
4119402263.67215286952-323.672152869524
4222601860.40491418014399.595085819856
4323002208.7974147709391.2025852290667
4429802264.3304493271715.669550672902
4528003008.00865932239-208.008659322385
4630602823.6911925218236.308807478197
4731403100.1643194408439.8356805591643
4827403188.12997850865-448.129978508653
4924802750.11024869846-270.110248698456
5017202458.16646059744-738.166460597442
5120601629.12061580425430.879384195748
5219201992.29528307764-72.2952830776369
5320001854.27729021393145.722709786067
5428201945.50591039784874.494089602158
5524402843.97130874736-403.971308747364
5627002445.73188422286254.268115777142
5728802720.01238398672159.987616013283
5831002918.71943664478181.280563355216
5930603157.46653463404-97.4665346340448
6020403112.49784275538-1072.49784275538
6118801997.81976512886-117.81976512886
6221801807.11726655368372.882733446321
6318202137.13399471382-317.133994713824
6417001756.81863200409-56.8186320040877
6517001625.8378702797974.16212972021
6616801631.1695176961648.8304823038402
6722401616.81332306108623.186676938921
6824002231.67785776296168.322142237035
6929202418.1599617697501.840038230296
7033802984.80779542816395.192204571843
7127003488.60318320342-788.603183203418
7219002747.91319999757-847.913199997566
7319601859.45615582461100.543844175387
7420401911.94504537031128.054954629686
7518602004.94939871362-144.94939871362
7617201814.85383439613-94.8538343961279
7723401663.87368196211676.126318037892
7820602340.57237454122-280.572374541218
7922002049.21913486766150.780865132339
8025202196.90320168323.096798320003
8127002547.74711358844152.25288641156
8220002747.10081340675-747.100813406749
8321201985.35743060858134.642569391417
8417802102.72478868467-322.724788684666
8518201737.3704088062482.6295911937643
8614801778.35066969992-298.350669699921
8717801414.11114253848365.888857461519
8816001740.07083965178-140.070839651781
8917201554.94488756102165.055112438976
9021001686.55066497159413.449335028409
9120002105.48665659499-105.486656594991
9224202004.2630004526415.736999547401
9326602458.22416922314201.775830776861
9431402723.63490387189416.365096128106
9522803243.52533247432-963.525332474315
9622202308.10232723545-88.1023272354482
9718602222.05516114802-362.055161148019
9819801829.03819579301150.96180420699
9915201955.17995827647-435.179958276471
10015401460.4056775951979.5943224048133
10116601478.97310538585181.026894614154
10225001616.16111913379883.838880866207
10316602536.11024163916-876.110241639165
10422201637.19035001141582.809649988585
10521602230.87563353469-70.8756335346902
10625402175.88542692782364.11457307218
10725402586.0409327899-46.0409327899042
10823402589.01845158709-249.018451587091







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092366.587960031181265.651676640883467.52424342148
1102388.41465057192762.6891133392794014.14018780456
1112410.24134111266320.8064339877034499.67624823762
1122432.0680316534-99.21388412058884963.3499474274
1132453.89472219415-511.7412216432435419.53066603154
1142475.72141273489-923.6354065491925875.07823201897
1152497.54810327563-1338.640389011556333.73659556281
1162519.37479381637-1758.966701780246797.71628941299
1172541.20148435711-2185.983884285477268.3868529997
1182563.02817489786-2620.564414126097746.6207639218
1192584.8548654386-3063.270586629868232.98031750706
1202606.68155597934-3514.463091911348727.82620387002
1212628.50824652008-3974.367450796119231.38394383628
1222650.33493706082-4443.116370635699743.78624475734
1232672.16162760157-4920.7776618101410265.1009170133
1242693.98831814231-5407.3731464038610795.3497826885
1252715.81500868305-5902.8917588790111334.5217762451
1262737.64169922379-6407.298796021911882.5821944695

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2366.58796003118 & 1265.65167664088 & 3467.52424342148 \tabularnewline
110 & 2388.41465057192 & 762.689113339279 & 4014.14018780456 \tabularnewline
111 & 2410.24134111266 & 320.806433987703 & 4499.67624823762 \tabularnewline
112 & 2432.0680316534 & -99.2138841205888 & 4963.3499474274 \tabularnewline
113 & 2453.89472219415 & -511.741221643243 & 5419.53066603154 \tabularnewline
114 & 2475.72141273489 & -923.635406549192 & 5875.07823201897 \tabularnewline
115 & 2497.54810327563 & -1338.64038901155 & 6333.73659556281 \tabularnewline
116 & 2519.37479381637 & -1758.96670178024 & 6797.71628941299 \tabularnewline
117 & 2541.20148435711 & -2185.98388428547 & 7268.3868529997 \tabularnewline
118 & 2563.02817489786 & -2620.56441412609 & 7746.6207639218 \tabularnewline
119 & 2584.8548654386 & -3063.27058662986 & 8232.98031750706 \tabularnewline
120 & 2606.68155597934 & -3514.46309191134 & 8727.82620387002 \tabularnewline
121 & 2628.50824652008 & -3974.36745079611 & 9231.38394383628 \tabularnewline
122 & 2650.33493706082 & -4443.11637063569 & 9743.78624475734 \tabularnewline
123 & 2672.16162760157 & -4920.77766181014 & 10265.1009170133 \tabularnewline
124 & 2693.98831814231 & -5407.37314640386 & 10795.3497826885 \tabularnewline
125 & 2715.81500868305 & -5902.89175887901 & 11334.5217762451 \tabularnewline
126 & 2737.64169922379 & -6407.2987960219 & 11882.5821944695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301651&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]2366.58796003118[/C][C]1265.65167664088[/C][C]3467.52424342148[/C][/ROW]
[ROW][C]110[/C][C]2388.41465057192[/C][C]762.689113339279[/C][C]4014.14018780456[/C][/ROW]
[ROW][C]111[/C][C]2410.24134111266[/C][C]320.806433987703[/C][C]4499.67624823762[/C][/ROW]
[ROW][C]112[/C][C]2432.0680316534[/C][C]-99.2138841205888[/C][C]4963.3499474274[/C][/ROW]
[ROW][C]113[/C][C]2453.89472219415[/C][C]-511.741221643243[/C][C]5419.53066603154[/C][/ROW]
[ROW][C]114[/C][C]2475.72141273489[/C][C]-923.635406549192[/C][C]5875.07823201897[/C][/ROW]
[ROW][C]115[/C][C]2497.54810327563[/C][C]-1338.64038901155[/C][C]6333.73659556281[/C][/ROW]
[ROW][C]116[/C][C]2519.37479381637[/C][C]-1758.96670178024[/C][C]6797.71628941299[/C][/ROW]
[ROW][C]117[/C][C]2541.20148435711[/C][C]-2185.98388428547[/C][C]7268.3868529997[/C][/ROW]
[ROW][C]118[/C][C]2563.02817489786[/C][C]-2620.56441412609[/C][C]7746.6207639218[/C][/ROW]
[ROW][C]119[/C][C]2584.8548654386[/C][C]-3063.27058662986[/C][C]8232.98031750706[/C][/ROW]
[ROW][C]120[/C][C]2606.68155597934[/C][C]-3514.46309191134[/C][C]8727.82620387002[/C][/ROW]
[ROW][C]121[/C][C]2628.50824652008[/C][C]-3974.36745079611[/C][C]9231.38394383628[/C][/ROW]
[ROW][C]122[/C][C]2650.33493706082[/C][C]-4443.11637063569[/C][C]9743.78624475734[/C][/ROW]
[ROW][C]123[/C][C]2672.16162760157[/C][C]-4920.77766181014[/C][C]10265.1009170133[/C][/ROW]
[ROW][C]124[/C][C]2693.98831814231[/C][C]-5407.37314640386[/C][C]10795.3497826885[/C][/ROW]
[ROW][C]125[/C][C]2715.81500868305[/C][C]-5902.89175887901[/C][C]11334.5217762451[/C][/ROW]
[ROW][C]126[/C][C]2737.64169922379[/C][C]-6407.2987960219[/C][C]11882.5821944695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301651&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301651&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
1092366.587960031181265.651676640883467.52424342148
1102388.41465057192762.6891133392794014.14018780456
1112410.24134111266320.8064339877034499.67624823762
1122432.0680316534-99.21388412058884963.3499474274
1132453.89472219415-511.7412216432435419.53066603154
1142475.72141273489-923.6354065491925875.07823201897
1152497.54810327563-1338.640389011556333.73659556281
1162519.37479381637-1758.966701780246797.71628941299
1172541.20148435711-2185.983884285477268.3868529997
1182563.02817489786-2620.564414126097746.6207639218
1192584.8548654386-3063.270586629868232.98031750706
1202606.68155597934-3514.463091911348727.82620387002
1212628.50824652008-3974.367450796119231.38394383628
1222650.33493706082-4443.116370635699743.78624475734
1232672.16162760157-4920.7776618101410265.1009170133
1242693.98831814231-5407.3731464038610795.3497826885
1252715.81500868305-5902.8917588790111334.5217762451
1262737.64169922379-6407.298796021911882.5821944695



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')