Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 18:18:54 +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/2016/Nov/26/t1480184609v6fgcpc6upb5n52.htm/, Retrieved Sat, 04 May 2024 00:33:52 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 00:33:52 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95,83
95,87
96,06
96,06
96,15
96,26
96,28
96,36
96,38
96,43
96,47
96,55
96,71
96,87
96,99
97,1
97,26
97,31
97,33
97,33
97,45
97,61
97,59
97,6
97,96
98,36
98,36
98,51
98,77
98,78
98,89
98,86
99,04
99,09
99,1
99,12
99,37
99,46
99,6
99,88
99,88
100,01
100,02
100,19
100,2
100,35
100,47
100,58
101,4
101,67
101,82
101,85
101,98
102,06
102,16
102,2
102,35
102,47
102,55
102,62
102,8
102,87
102,94
102,95
102,94
103,05
103,09
103,1
103,13
103,19
103,36
103,42





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999950460721084
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999950460721084 \tabularnewline
beta & FALSE \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]0.999950460721084[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/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
alpha0.999950460721084
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
295.8795.830.0400000000000063
396.0695.86999801842890.190001981571143
496.0696.05999058743889.41256115538636e-06
596.1596.05999999953370.09000000046629
696.2696.14999554146490.11000445853513
796.2896.25999455045840.0200054495415571
896.3696.27999900894450.0800009910555417
996.3896.35999603680860.0200039631913995
1096.4396.37999900901810.0500009909819141
1196.4796.4299975229870.0400024770130329
1296.5596.46999801830610.0800019816938544
1396.7196.54999603675950.160003963240484
1496.8796.7099920735190.160007926480972
1596.9996.86999207332270.120007926677289
1697.196.98999405489380.110005945106153
1797.2697.09999455038480.160005449615213
1897.3197.25999207344540.0500079265545992
1997.3397.30999752264340.0200024773566128
2097.3397.32999900909179.90908304743243e-07
2197.4597.32999999995090.120000000049089
2297.6197.44999405528650.160005944713461
2397.5997.6099920734209-0.0199920734208803
2497.697.59000099039290.00999900960708544
2597.9697.59999950465630.360000495343726
2698.3697.9599821658350.400017834164956
2798.3698.35998018340491.98165950564544e-05
2898.5198.35999999901830.150000000981706
2998.7798.50999256910810.260007430891875
3098.7898.76998711941940.0100128805806463
3198.8998.77999950396910.110000496030892
3298.8698.8899945506547-0.0299945506547488
3399.0498.86000148590840.179998514091594
3499.0999.03999108300340.0500089169965889
3599.199.08999752259430.0100024774056777
3699.1299.09999950448450.0200004955155322
3799.3799.11999900918990.250000990810122
3899.4699.36998761513120.0900123848687997
3999.699.45999554085140.140004459148642
4099.8899.599993064280.280006935719953
4199.8899.87998612865831.38713416788505e-05
42100.0199.87999999931280.13000000068719
43100.02100.0099935598940.0100064401062809
44100.19100.0199995042880.170000495711818
45100.2100.1899915782980.0100084217019827
46100.35100.199999504190.150000495809977
47100.47100.3499925690840.120007430916402
48100.58100.4699940549180.110005945081596
49101.4100.5799945503850.820005449615195
50101.67101.3999593775210.270040622478675
51101.82101.6699866223820.150013377617697
52101.85101.8199925684450.0300074315545515
53101.98101.8499985134530.130001486546533
54102.06101.979993559820.0800064401799006
55102.16102.0599960365390.100003963461347
56102.2102.1599950458760.0400049541242424
57102.35102.1999980181830.150001981816573
58102.47102.349992569010.120007430990029
59102.55102.4699940549180.0800059450815951
60102.62102.5499960365630.0700039634368466
61102.8102.6199965320540.180003467945866
62102.87102.7999910827580.0700089172420064
63102.94102.8699965318090.070003468191274
64102.95102.9399965320790.0100034679213366
65102.94102.949999504435-0.00999950443541309
66103.05102.9400004953680.109999504631759
67103.09103.0499945507040.0400054492961459
68103.1103.0899980181590.0100019818410999
69103.13103.0999995045090.0300004954909667
70103.19103.1299985137970.0600014862029212
71103.36103.189997027570.170002972430353
72103.42103.3599915781750.0600084218246764

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 95.87 & 95.83 & 0.0400000000000063 \tabularnewline
3 & 96.06 & 95.8699980184289 & 0.190001981571143 \tabularnewline
4 & 96.06 & 96.0599905874388 & 9.41256115538636e-06 \tabularnewline
5 & 96.15 & 96.0599999995337 & 0.09000000046629 \tabularnewline
6 & 96.26 & 96.1499955414649 & 0.11000445853513 \tabularnewline
7 & 96.28 & 96.2599945504584 & 0.0200054495415571 \tabularnewline
8 & 96.36 & 96.2799990089445 & 0.0800009910555417 \tabularnewline
9 & 96.38 & 96.3599960368086 & 0.0200039631913995 \tabularnewline
10 & 96.43 & 96.3799990090181 & 0.0500009909819141 \tabularnewline
11 & 96.47 & 96.429997522987 & 0.0400024770130329 \tabularnewline
12 & 96.55 & 96.4699980183061 & 0.0800019816938544 \tabularnewline
13 & 96.71 & 96.5499960367595 & 0.160003963240484 \tabularnewline
14 & 96.87 & 96.709992073519 & 0.160007926480972 \tabularnewline
15 & 96.99 & 96.8699920733227 & 0.120007926677289 \tabularnewline
16 & 97.1 & 96.9899940548938 & 0.110005945106153 \tabularnewline
17 & 97.26 & 97.0999945503848 & 0.160005449615213 \tabularnewline
18 & 97.31 & 97.2599920734454 & 0.0500079265545992 \tabularnewline
19 & 97.33 & 97.3099975226434 & 0.0200024773566128 \tabularnewline
20 & 97.33 & 97.3299990090917 & 9.90908304743243e-07 \tabularnewline
21 & 97.45 & 97.3299999999509 & 0.120000000049089 \tabularnewline
22 & 97.61 & 97.4499940552865 & 0.160005944713461 \tabularnewline
23 & 97.59 & 97.6099920734209 & -0.0199920734208803 \tabularnewline
24 & 97.6 & 97.5900009903929 & 0.00999900960708544 \tabularnewline
25 & 97.96 & 97.5999995046563 & 0.360000495343726 \tabularnewline
26 & 98.36 & 97.959982165835 & 0.400017834164956 \tabularnewline
27 & 98.36 & 98.3599801834049 & 1.98165950564544e-05 \tabularnewline
28 & 98.51 & 98.3599999990183 & 0.150000000981706 \tabularnewline
29 & 98.77 & 98.5099925691081 & 0.260007430891875 \tabularnewline
30 & 98.78 & 98.7699871194194 & 0.0100128805806463 \tabularnewline
31 & 98.89 & 98.7799995039691 & 0.110000496030892 \tabularnewline
32 & 98.86 & 98.8899945506547 & -0.0299945506547488 \tabularnewline
33 & 99.04 & 98.8600014859084 & 0.179998514091594 \tabularnewline
34 & 99.09 & 99.0399910830034 & 0.0500089169965889 \tabularnewline
35 & 99.1 & 99.0899975225943 & 0.0100024774056777 \tabularnewline
36 & 99.12 & 99.0999995044845 & 0.0200004955155322 \tabularnewline
37 & 99.37 & 99.1199990091899 & 0.250000990810122 \tabularnewline
38 & 99.46 & 99.3699876151312 & 0.0900123848687997 \tabularnewline
39 & 99.6 & 99.4599955408514 & 0.140004459148642 \tabularnewline
40 & 99.88 & 99.59999306428 & 0.280006935719953 \tabularnewline
41 & 99.88 & 99.8799861286583 & 1.38713416788505e-05 \tabularnewline
42 & 100.01 & 99.8799999993128 & 0.13000000068719 \tabularnewline
43 & 100.02 & 100.009993559894 & 0.0100064401062809 \tabularnewline
44 & 100.19 & 100.019999504288 & 0.170000495711818 \tabularnewline
45 & 100.2 & 100.189991578298 & 0.0100084217019827 \tabularnewline
46 & 100.35 & 100.19999950419 & 0.150000495809977 \tabularnewline
47 & 100.47 & 100.349992569084 & 0.120007430916402 \tabularnewline
48 & 100.58 & 100.469994054918 & 0.110005945081596 \tabularnewline
49 & 101.4 & 100.579994550385 & 0.820005449615195 \tabularnewline
50 & 101.67 & 101.399959377521 & 0.270040622478675 \tabularnewline
51 & 101.82 & 101.669986622382 & 0.150013377617697 \tabularnewline
52 & 101.85 & 101.819992568445 & 0.0300074315545515 \tabularnewline
53 & 101.98 & 101.849998513453 & 0.130001486546533 \tabularnewline
54 & 102.06 & 101.97999355982 & 0.0800064401799006 \tabularnewline
55 & 102.16 & 102.059996036539 & 0.100003963461347 \tabularnewline
56 & 102.2 & 102.159995045876 & 0.0400049541242424 \tabularnewline
57 & 102.35 & 102.199998018183 & 0.150001981816573 \tabularnewline
58 & 102.47 & 102.34999256901 & 0.120007430990029 \tabularnewline
59 & 102.55 & 102.469994054918 & 0.0800059450815951 \tabularnewline
60 & 102.62 & 102.549996036563 & 0.0700039634368466 \tabularnewline
61 & 102.8 & 102.619996532054 & 0.180003467945866 \tabularnewline
62 & 102.87 & 102.799991082758 & 0.0700089172420064 \tabularnewline
63 & 102.94 & 102.869996531809 & 0.070003468191274 \tabularnewline
64 & 102.95 & 102.939996532079 & 0.0100034679213366 \tabularnewline
65 & 102.94 & 102.949999504435 & -0.00999950443541309 \tabularnewline
66 & 103.05 & 102.940000495368 & 0.109999504631759 \tabularnewline
67 & 103.09 & 103.049994550704 & 0.0400054492961459 \tabularnewline
68 & 103.1 & 103.089998018159 & 0.0100019818410999 \tabularnewline
69 & 103.13 & 103.099999504509 & 0.0300004954909667 \tabularnewline
70 & 103.19 & 103.129998513797 & 0.0600014862029212 \tabularnewline
71 & 103.36 & 103.18999702757 & 0.170002972430353 \tabularnewline
72 & 103.42 & 103.359991578175 & 0.0600084218246764 \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]2[/C][C]95.87[/C][C]95.83[/C][C]0.0400000000000063[/C][/ROW]
[ROW][C]3[/C][C]96.06[/C][C]95.8699980184289[/C][C]0.190001981571143[/C][/ROW]
[ROW][C]4[/C][C]96.06[/C][C]96.0599905874388[/C][C]9.41256115538636e-06[/C][/ROW]
[ROW][C]5[/C][C]96.15[/C][C]96.0599999995337[/C][C]0.09000000046629[/C][/ROW]
[ROW][C]6[/C][C]96.26[/C][C]96.1499955414649[/C][C]0.11000445853513[/C][/ROW]
[ROW][C]7[/C][C]96.28[/C][C]96.2599945504584[/C][C]0.0200054495415571[/C][/ROW]
[ROW][C]8[/C][C]96.36[/C][C]96.2799990089445[/C][C]0.0800009910555417[/C][/ROW]
[ROW][C]9[/C][C]96.38[/C][C]96.3599960368086[/C][C]0.0200039631913995[/C][/ROW]
[ROW][C]10[/C][C]96.43[/C][C]96.3799990090181[/C][C]0.0500009909819141[/C][/ROW]
[ROW][C]11[/C][C]96.47[/C][C]96.429997522987[/C][C]0.0400024770130329[/C][/ROW]
[ROW][C]12[/C][C]96.55[/C][C]96.4699980183061[/C][C]0.0800019816938544[/C][/ROW]
[ROW][C]13[/C][C]96.71[/C][C]96.5499960367595[/C][C]0.160003963240484[/C][/ROW]
[ROW][C]14[/C][C]96.87[/C][C]96.709992073519[/C][C]0.160007926480972[/C][/ROW]
[ROW][C]15[/C][C]96.99[/C][C]96.8699920733227[/C][C]0.120007926677289[/C][/ROW]
[ROW][C]16[/C][C]97.1[/C][C]96.9899940548938[/C][C]0.110005945106153[/C][/ROW]
[ROW][C]17[/C][C]97.26[/C][C]97.0999945503848[/C][C]0.160005449615213[/C][/ROW]
[ROW][C]18[/C][C]97.31[/C][C]97.2599920734454[/C][C]0.0500079265545992[/C][/ROW]
[ROW][C]19[/C][C]97.33[/C][C]97.3099975226434[/C][C]0.0200024773566128[/C][/ROW]
[ROW][C]20[/C][C]97.33[/C][C]97.3299990090917[/C][C]9.90908304743243e-07[/C][/ROW]
[ROW][C]21[/C][C]97.45[/C][C]97.3299999999509[/C][C]0.120000000049089[/C][/ROW]
[ROW][C]22[/C][C]97.61[/C][C]97.4499940552865[/C][C]0.160005944713461[/C][/ROW]
[ROW][C]23[/C][C]97.59[/C][C]97.6099920734209[/C][C]-0.0199920734208803[/C][/ROW]
[ROW][C]24[/C][C]97.6[/C][C]97.5900009903929[/C][C]0.00999900960708544[/C][/ROW]
[ROW][C]25[/C][C]97.96[/C][C]97.5999995046563[/C][C]0.360000495343726[/C][/ROW]
[ROW][C]26[/C][C]98.36[/C][C]97.959982165835[/C][C]0.400017834164956[/C][/ROW]
[ROW][C]27[/C][C]98.36[/C][C]98.3599801834049[/C][C]1.98165950564544e-05[/C][/ROW]
[ROW][C]28[/C][C]98.51[/C][C]98.3599999990183[/C][C]0.150000000981706[/C][/ROW]
[ROW][C]29[/C][C]98.77[/C][C]98.5099925691081[/C][C]0.260007430891875[/C][/ROW]
[ROW][C]30[/C][C]98.78[/C][C]98.7699871194194[/C][C]0.0100128805806463[/C][/ROW]
[ROW][C]31[/C][C]98.89[/C][C]98.7799995039691[/C][C]0.110000496030892[/C][/ROW]
[ROW][C]32[/C][C]98.86[/C][C]98.8899945506547[/C][C]-0.0299945506547488[/C][/ROW]
[ROW][C]33[/C][C]99.04[/C][C]98.8600014859084[/C][C]0.179998514091594[/C][/ROW]
[ROW][C]34[/C][C]99.09[/C][C]99.0399910830034[/C][C]0.0500089169965889[/C][/ROW]
[ROW][C]35[/C][C]99.1[/C][C]99.0899975225943[/C][C]0.0100024774056777[/C][/ROW]
[ROW][C]36[/C][C]99.12[/C][C]99.0999995044845[/C][C]0.0200004955155322[/C][/ROW]
[ROW][C]37[/C][C]99.37[/C][C]99.1199990091899[/C][C]0.250000990810122[/C][/ROW]
[ROW][C]38[/C][C]99.46[/C][C]99.3699876151312[/C][C]0.0900123848687997[/C][/ROW]
[ROW][C]39[/C][C]99.6[/C][C]99.4599955408514[/C][C]0.140004459148642[/C][/ROW]
[ROW][C]40[/C][C]99.88[/C][C]99.59999306428[/C][C]0.280006935719953[/C][/ROW]
[ROW][C]41[/C][C]99.88[/C][C]99.8799861286583[/C][C]1.38713416788505e-05[/C][/ROW]
[ROW][C]42[/C][C]100.01[/C][C]99.8799999993128[/C][C]0.13000000068719[/C][/ROW]
[ROW][C]43[/C][C]100.02[/C][C]100.009993559894[/C][C]0.0100064401062809[/C][/ROW]
[ROW][C]44[/C][C]100.19[/C][C]100.019999504288[/C][C]0.170000495711818[/C][/ROW]
[ROW][C]45[/C][C]100.2[/C][C]100.189991578298[/C][C]0.0100084217019827[/C][/ROW]
[ROW][C]46[/C][C]100.35[/C][C]100.19999950419[/C][C]0.150000495809977[/C][/ROW]
[ROW][C]47[/C][C]100.47[/C][C]100.349992569084[/C][C]0.120007430916402[/C][/ROW]
[ROW][C]48[/C][C]100.58[/C][C]100.469994054918[/C][C]0.110005945081596[/C][/ROW]
[ROW][C]49[/C][C]101.4[/C][C]100.579994550385[/C][C]0.820005449615195[/C][/ROW]
[ROW][C]50[/C][C]101.67[/C][C]101.399959377521[/C][C]0.270040622478675[/C][/ROW]
[ROW][C]51[/C][C]101.82[/C][C]101.669986622382[/C][C]0.150013377617697[/C][/ROW]
[ROW][C]52[/C][C]101.85[/C][C]101.819992568445[/C][C]0.0300074315545515[/C][/ROW]
[ROW][C]53[/C][C]101.98[/C][C]101.849998513453[/C][C]0.130001486546533[/C][/ROW]
[ROW][C]54[/C][C]102.06[/C][C]101.97999355982[/C][C]0.0800064401799006[/C][/ROW]
[ROW][C]55[/C][C]102.16[/C][C]102.059996036539[/C][C]0.100003963461347[/C][/ROW]
[ROW][C]56[/C][C]102.2[/C][C]102.159995045876[/C][C]0.0400049541242424[/C][/ROW]
[ROW][C]57[/C][C]102.35[/C][C]102.199998018183[/C][C]0.150001981816573[/C][/ROW]
[ROW][C]58[/C][C]102.47[/C][C]102.34999256901[/C][C]0.120007430990029[/C][/ROW]
[ROW][C]59[/C][C]102.55[/C][C]102.469994054918[/C][C]0.0800059450815951[/C][/ROW]
[ROW][C]60[/C][C]102.62[/C][C]102.549996036563[/C][C]0.0700039634368466[/C][/ROW]
[ROW][C]61[/C][C]102.8[/C][C]102.619996532054[/C][C]0.180003467945866[/C][/ROW]
[ROW][C]62[/C][C]102.87[/C][C]102.799991082758[/C][C]0.0700089172420064[/C][/ROW]
[ROW][C]63[/C][C]102.94[/C][C]102.869996531809[/C][C]0.070003468191274[/C][/ROW]
[ROW][C]64[/C][C]102.95[/C][C]102.939996532079[/C][C]0.0100034679213366[/C][/ROW]
[ROW][C]65[/C][C]102.94[/C][C]102.949999504435[/C][C]-0.00999950443541309[/C][/ROW]
[ROW][C]66[/C][C]103.05[/C][C]102.940000495368[/C][C]0.109999504631759[/C][/ROW]
[ROW][C]67[/C][C]103.09[/C][C]103.049994550704[/C][C]0.0400054492961459[/C][/ROW]
[ROW][C]68[/C][C]103.1[/C][C]103.089998018159[/C][C]0.0100019818410999[/C][/ROW]
[ROW][C]69[/C][C]103.13[/C][C]103.099999504509[/C][C]0.0300004954909667[/C][/ROW]
[ROW][C]70[/C][C]103.19[/C][C]103.129998513797[/C][C]0.0600014862029212[/C][/ROW]
[ROW][C]71[/C][C]103.36[/C][C]103.18999702757[/C][C]0.170002972430353[/C][/ROW]
[ROW][C]72[/C][C]103.42[/C][C]103.359991578175[/C][C]0.0600084218246764[/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
295.8795.830.0400000000000063
396.0695.86999801842890.190001981571143
496.0696.05999058743889.41256115538636e-06
596.1596.05999999953370.09000000046629
696.2696.14999554146490.11000445853513
796.2896.25999455045840.0200054495415571
896.3696.27999900894450.0800009910555417
996.3896.35999603680860.0200039631913995
1096.4396.37999900901810.0500009909819141
1196.4796.4299975229870.0400024770130329
1296.5596.46999801830610.0800019816938544
1396.7196.54999603675950.160003963240484
1496.8796.7099920735190.160007926480972
1596.9996.86999207332270.120007926677289
1697.196.98999405489380.110005945106153
1797.2697.09999455038480.160005449615213
1897.3197.25999207344540.0500079265545992
1997.3397.30999752264340.0200024773566128
2097.3397.32999900909179.90908304743243e-07
2197.4597.32999999995090.120000000049089
2297.6197.44999405528650.160005944713461
2397.5997.6099920734209-0.0199920734208803
2497.697.59000099039290.00999900960708544
2597.9697.59999950465630.360000495343726
2698.3697.9599821658350.400017834164956
2798.3698.35998018340491.98165950564544e-05
2898.5198.35999999901830.150000000981706
2998.7798.50999256910810.260007430891875
3098.7898.76998711941940.0100128805806463
3198.8998.77999950396910.110000496030892
3298.8698.8899945506547-0.0299945506547488
3399.0498.86000148590840.179998514091594
3499.0999.03999108300340.0500089169965889
3599.199.08999752259430.0100024774056777
3699.1299.09999950448450.0200004955155322
3799.3799.11999900918990.250000990810122
3899.4699.36998761513120.0900123848687997
3999.699.45999554085140.140004459148642
4099.8899.599993064280.280006935719953
4199.8899.87998612865831.38713416788505e-05
42100.0199.87999999931280.13000000068719
43100.02100.0099935598940.0100064401062809
44100.19100.0199995042880.170000495711818
45100.2100.1899915782980.0100084217019827
46100.35100.199999504190.150000495809977
47100.47100.3499925690840.120007430916402
48100.58100.4699940549180.110005945081596
49101.4100.5799945503850.820005449615195
50101.67101.3999593775210.270040622478675
51101.82101.6699866223820.150013377617697
52101.85101.8199925684450.0300074315545515
53101.98101.8499985134530.130001486546533
54102.06101.979993559820.0800064401799006
55102.16102.0599960365390.100003963461347
56102.2102.1599950458760.0400049541242424
57102.35102.1999980181830.150001981816573
58102.47102.349992569010.120007430990029
59102.55102.4699940549180.0800059450815951
60102.62102.5499960365630.0700039634368466
61102.8102.6199965320540.180003467945866
62102.87102.7999910827580.0700089172420064
63102.94102.8699965318090.070003468191274
64102.95102.9399965320790.0100034679213366
65102.94102.949999504435-0.00999950443541309
66103.05102.9400004953680.109999504631759
67103.09103.0499945507040.0400054492961459
68103.1103.0899980181590.0100019818410999
69103.13103.0999995045090.0300004954909667
70103.19103.1299985137970.0600014862029212
71103.36103.189997027570.170002972430353
72103.42103.3599915781750.0600084218246764







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73103.419997027226103.180210989431103.659783065021
74103.419997027226103.080896760004103.759097294448
75103.419997027226103.004689143195103.835304911257
76103.419997027226102.940442769767103.899551284685
77103.419997027226102.883840396049103.956153658403
78103.419997027226102.83266783464104.007326219812
79103.419997027226102.785609741909104.054384312543
80103.419997027226102.741809092299104.098184962153
81103.419997027226102.700670590628104.139323463824
82103.419997027226102.661760804339104.178233250113
83103.419997027226102.624752525826104.215241528626
84103.419997027226102.589391546679104.250602507773

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 103.419997027226 & 103.180210989431 & 103.659783065021 \tabularnewline
74 & 103.419997027226 & 103.080896760004 & 103.759097294448 \tabularnewline
75 & 103.419997027226 & 103.004689143195 & 103.835304911257 \tabularnewline
76 & 103.419997027226 & 102.940442769767 & 103.899551284685 \tabularnewline
77 & 103.419997027226 & 102.883840396049 & 103.956153658403 \tabularnewline
78 & 103.419997027226 & 102.83266783464 & 104.007326219812 \tabularnewline
79 & 103.419997027226 & 102.785609741909 & 104.054384312543 \tabularnewline
80 & 103.419997027226 & 102.741809092299 & 104.098184962153 \tabularnewline
81 & 103.419997027226 & 102.700670590628 & 104.139323463824 \tabularnewline
82 & 103.419997027226 & 102.661760804339 & 104.178233250113 \tabularnewline
83 & 103.419997027226 & 102.624752525826 & 104.215241528626 \tabularnewline
84 & 103.419997027226 & 102.589391546679 & 104.250602507773 \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]73[/C][C]103.419997027226[/C][C]103.180210989431[/C][C]103.659783065021[/C][/ROW]
[ROW][C]74[/C][C]103.419997027226[/C][C]103.080896760004[/C][C]103.759097294448[/C][/ROW]
[ROW][C]75[/C][C]103.419997027226[/C][C]103.004689143195[/C][C]103.835304911257[/C][/ROW]
[ROW][C]76[/C][C]103.419997027226[/C][C]102.940442769767[/C][C]103.899551284685[/C][/ROW]
[ROW][C]77[/C][C]103.419997027226[/C][C]102.883840396049[/C][C]103.956153658403[/C][/ROW]
[ROW][C]78[/C][C]103.419997027226[/C][C]102.83266783464[/C][C]104.007326219812[/C][/ROW]
[ROW][C]79[/C][C]103.419997027226[/C][C]102.785609741909[/C][C]104.054384312543[/C][/ROW]
[ROW][C]80[/C][C]103.419997027226[/C][C]102.741809092299[/C][C]104.098184962153[/C][/ROW]
[ROW][C]81[/C][C]103.419997027226[/C][C]102.700670590628[/C][C]104.139323463824[/C][/ROW]
[ROW][C]82[/C][C]103.419997027226[/C][C]102.661760804339[/C][C]104.178233250113[/C][/ROW]
[ROW][C]83[/C][C]103.419997027226[/C][C]102.624752525826[/C][C]104.215241528626[/C][/ROW]
[ROW][C]84[/C][C]103.419997027226[/C][C]102.589391546679[/C][C]104.250602507773[/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
73103.419997027226103.180210989431103.659783065021
74103.419997027226103.080896760004103.759097294448
75103.419997027226103.004689143195103.835304911257
76103.419997027226102.940442769767103.899551284685
77103.419997027226102.883840396049103.956153658403
78103.419997027226102.83266783464104.007326219812
79103.419997027226102.785609741909104.054384312543
80103.419997027226102.741809092299104.098184962153
81103.419997027226102.700670590628104.139323463824
82103.419997027226102.661760804339104.178233250113
83103.419997027226102.624752525826104.215241528626
84103.419997027226102.589391546679104.250602507773



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')