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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:37:21 +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/07/t1481107084reqhniy2yhm84kl.htm/, Retrieved Wed, 08 May 2024 02:43:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297986, Retrieved Wed, 08 May 2024 02:43:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double smoothing] [2016-12-07 10:37:21] [c0b73e623858a81821526bb2f691ccd9] [Current]
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Dataseries X:
7360
4820
2600
5520
3180
4080
3360
4960
4640
5420
4880
4780
4860
3780
4120
3980
3060
4420
3340
4220
5780
5440
4200
3720
4040
3920
3160
3500
2780
3340
3100
3100
4400
3480
5100
4260
3640
2900
3820
2980
2860
2420
2680
4420
3160
3160
4300
2820
3240
2520
3480
2740
2240
3700
2600
3160
3800
3440
2180
2300
3160
1800
2620
2820
2180
2300
2560
2860
2620
3960
3960
2320
3400
2640
2340
2340
1960
2100
2280
2320
2660
2520
2120
1800
2300
2420
1920
1720
2000
1960
2860
2160
2360
2300
2360
2260
2460
2200
1620
1740
1720
2460
1840
2160
2460
2860
2700
2420




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297986&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297986&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.538712603003287
beta0.708690501430818
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.538712603003287 \tabularnewline
beta & 0.708690501430818 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297986&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]0.538712603003287[/C][/ROW]
[ROW][C]beta[/C][C]0.708690501430818[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297986&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
alpha0.538712603003287
beta0.708690501430818
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326002280320
4552034.55779448089245485.44220551911
531802666.03929915733513.960700842674
640802815.541237455941264.45876254406
733603852.09164472163-492.091644721631
849603754.49521327791205.5047867221
946405031.65360021902-391.653600219016
1054205298.87692594398121.123074056024
1148805888.58193697693-1008.58193697693
1247805484.64369991018-704.643699910183
1348604975.42159426563-115.421594265627
1437804739.55514838221-959.555148382206
1541203682.60386939388437.396130606115
1639803545.19716569642434.802834303585
1730603572.39266614439-512.392666144387
1844202893.700482282481526.29951771752
1933403895.9888717844-555.988871784396
2042203564.25655066926655.743449330742
2157804135.649767476941644.35023252306
2254405867.39877956248-427.398779562475
2342006319.89796678724-2119.89796678724
2437205051.29079550373-1331.29079550373
2540403699.25537433364340.744625666358
2639203378.05616239337541.943837606629
2731603372.14909350699-212.149093506994
2835002879.00827079277620.991729207231
2927803071.77344517323-291.773445173226
3033402661.4271033617678.572896638296
3131003032.8844681500867.1155318499164
3231003100.56544595398-0.56544595397645
3344003131.569951789611268.43004821039
3434804330.46018753117-850.460187531168
3551004063.188429233141036.81157076686
3642605208.44819723993-948.448197239925
3736404922.12447651506-1282.12447651506
3829003966.55500902583-1066.55500902583
3938202719.925620806761100.07437919324
4029803060.473741809-80.4737418089976
4128602734.32240580856125.677594191441
4224202567.20864798363-147.208647983633
4326802196.8862403821483.113759617896
4444202350.569872709242069.43012729076
4531604148.89020319304-988.890203193039
4631603922.11582670716-762.11582670716
4743003526.54669987459773.453300125407
4828204253.49740577153-1433.49740577153
4932403244.25458906223-4.25458906222957
5025203003.33857130647-483.338571306467
5134802319.804730700451160.19526929955
5227402964.60321901245-224.603219012451
5322402777.64417872794-537.644178727942
5437002216.783962258071483.21603774193
5526003310.84958085014-710.849580850137
5631602951.55588711252208.444112887483
5738003167.07719068304632.922809316957
5834403852.90810733503-412.908107335033
5921803817.69646294259-1637.69646294259
6023002497.43531312398-197.435313123985
6131601877.684042828821282.31595717118
6218002544.65666452894-744.656664528936
6326201835.37819172765784.621808272352
6428202249.49461572572570.505384274281
6521802766.07165717658-586.071657176577
6623002435.83533695735-135.835336957352
6725602296.28771326365263.71228673635
6828602472.66163989261387.33836010739
6926202863.512724937-243.512724937001
7039602821.547968810311138.45203118969
7139603958.703834816121.29616518387866
7223204483.75435482363-2163.75435482363
7334003016.38564382577383.614356174227
7426403067.77304446805-427.773044468053
7523402518.74041763102-178.740417631015
7623402035.6251985678304.374801432201
7719601928.9746020404531.0253979595536
7821001686.912128932413.087871067999
7922801808.38042114392471.619578856083
8023202141.435642882178.564357117998
8126602384.79071368464275.209286315363
8225202785.27916610348-265.279166103483
8321202793.32126349204-673.321263492039
8418002324.48500862692-524.485008626923
8523001735.59056871432564.409431285679
8624201948.77780448447471.222195515531
8719202291.66734955929-371.667349559286
8817202038.58632544894-318.586325448939
8920001692.47066987097307.529330129028
9019601801.06011177246158.939888227542
9128601890.28269940073969.717300599271
9221602786.50045779116-626.500457791157
9323602583.6299315977-223.629931597704
9423002512.41328708076-212.413287080762
9523602366.14393837131-6.14393837131001
9622602328.64885153237-68.6488515323713
9724602231.27278703544228.72721296456
9822002381.42054713008-181.420547130081
9916202241.35371171292-621.353711712917
10017401627.06860237013112.931397629874
10117201451.46714161714268.532858382856
10224601462.21075903275997.789240967253
10318402246.75046061725-406.750460617251
10421602119.3575273781640.6424726218402
10524602248.49730948141211.50269051859
10628602550.42924825959309.570751740408
10727003023.3797654252-323.379765425201
10824203031.89177184644-611.891771846439

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2600 & 2280 & 320 \tabularnewline
4 & 5520 & 34.5577944808924 & 5485.44220551911 \tabularnewline
5 & 3180 & 2666.03929915733 & 513.960700842674 \tabularnewline
6 & 4080 & 2815.54123745594 & 1264.45876254406 \tabularnewline
7 & 3360 & 3852.09164472163 & -492.091644721631 \tabularnewline
8 & 4960 & 3754.4952132779 & 1205.5047867221 \tabularnewline
9 & 4640 & 5031.65360021902 & -391.653600219016 \tabularnewline
10 & 5420 & 5298.87692594398 & 121.123074056024 \tabularnewline
11 & 4880 & 5888.58193697693 & -1008.58193697693 \tabularnewline
12 & 4780 & 5484.64369991018 & -704.643699910183 \tabularnewline
13 & 4860 & 4975.42159426563 & -115.421594265627 \tabularnewline
14 & 3780 & 4739.55514838221 & -959.555148382206 \tabularnewline
15 & 4120 & 3682.60386939388 & 437.396130606115 \tabularnewline
16 & 3980 & 3545.19716569642 & 434.802834303585 \tabularnewline
17 & 3060 & 3572.39266614439 & -512.392666144387 \tabularnewline
18 & 4420 & 2893.70048228248 & 1526.29951771752 \tabularnewline
19 & 3340 & 3895.9888717844 & -555.988871784396 \tabularnewline
20 & 4220 & 3564.25655066926 & 655.743449330742 \tabularnewline
21 & 5780 & 4135.64976747694 & 1644.35023252306 \tabularnewline
22 & 5440 & 5867.39877956248 & -427.398779562475 \tabularnewline
23 & 4200 & 6319.89796678724 & -2119.89796678724 \tabularnewline
24 & 3720 & 5051.29079550373 & -1331.29079550373 \tabularnewline
25 & 4040 & 3699.25537433364 & 340.744625666358 \tabularnewline
26 & 3920 & 3378.05616239337 & 541.943837606629 \tabularnewline
27 & 3160 & 3372.14909350699 & -212.149093506994 \tabularnewline
28 & 3500 & 2879.00827079277 & 620.991729207231 \tabularnewline
29 & 2780 & 3071.77344517323 & -291.773445173226 \tabularnewline
30 & 3340 & 2661.4271033617 & 678.572896638296 \tabularnewline
31 & 3100 & 3032.88446815008 & 67.1155318499164 \tabularnewline
32 & 3100 & 3100.56544595398 & -0.56544595397645 \tabularnewline
33 & 4400 & 3131.56995178961 & 1268.43004821039 \tabularnewline
34 & 3480 & 4330.46018753117 & -850.460187531168 \tabularnewline
35 & 5100 & 4063.18842923314 & 1036.81157076686 \tabularnewline
36 & 4260 & 5208.44819723993 & -948.448197239925 \tabularnewline
37 & 3640 & 4922.12447651506 & -1282.12447651506 \tabularnewline
38 & 2900 & 3966.55500902583 & -1066.55500902583 \tabularnewline
39 & 3820 & 2719.92562080676 & 1100.07437919324 \tabularnewline
40 & 2980 & 3060.473741809 & -80.4737418089976 \tabularnewline
41 & 2860 & 2734.32240580856 & 125.677594191441 \tabularnewline
42 & 2420 & 2567.20864798363 & -147.208647983633 \tabularnewline
43 & 2680 & 2196.8862403821 & 483.113759617896 \tabularnewline
44 & 4420 & 2350.56987270924 & 2069.43012729076 \tabularnewline
45 & 3160 & 4148.89020319304 & -988.890203193039 \tabularnewline
46 & 3160 & 3922.11582670716 & -762.11582670716 \tabularnewline
47 & 4300 & 3526.54669987459 & 773.453300125407 \tabularnewline
48 & 2820 & 4253.49740577153 & -1433.49740577153 \tabularnewline
49 & 3240 & 3244.25458906223 & -4.25458906222957 \tabularnewline
50 & 2520 & 3003.33857130647 & -483.338571306467 \tabularnewline
51 & 3480 & 2319.80473070045 & 1160.19526929955 \tabularnewline
52 & 2740 & 2964.60321901245 & -224.603219012451 \tabularnewline
53 & 2240 & 2777.64417872794 & -537.644178727942 \tabularnewline
54 & 3700 & 2216.78396225807 & 1483.21603774193 \tabularnewline
55 & 2600 & 3310.84958085014 & -710.849580850137 \tabularnewline
56 & 3160 & 2951.55588711252 & 208.444112887483 \tabularnewline
57 & 3800 & 3167.07719068304 & 632.922809316957 \tabularnewline
58 & 3440 & 3852.90810733503 & -412.908107335033 \tabularnewline
59 & 2180 & 3817.69646294259 & -1637.69646294259 \tabularnewline
60 & 2300 & 2497.43531312398 & -197.435313123985 \tabularnewline
61 & 3160 & 1877.68404282882 & 1282.31595717118 \tabularnewline
62 & 1800 & 2544.65666452894 & -744.656664528936 \tabularnewline
63 & 2620 & 1835.37819172765 & 784.621808272352 \tabularnewline
64 & 2820 & 2249.49461572572 & 570.505384274281 \tabularnewline
65 & 2180 & 2766.07165717658 & -586.071657176577 \tabularnewline
66 & 2300 & 2435.83533695735 & -135.835336957352 \tabularnewline
67 & 2560 & 2296.28771326365 & 263.71228673635 \tabularnewline
68 & 2860 & 2472.66163989261 & 387.33836010739 \tabularnewline
69 & 2620 & 2863.512724937 & -243.512724937001 \tabularnewline
70 & 3960 & 2821.54796881031 & 1138.45203118969 \tabularnewline
71 & 3960 & 3958.70383481612 & 1.29616518387866 \tabularnewline
72 & 2320 & 4483.75435482363 & -2163.75435482363 \tabularnewline
73 & 3400 & 3016.38564382577 & 383.614356174227 \tabularnewline
74 & 2640 & 3067.77304446805 & -427.773044468053 \tabularnewline
75 & 2340 & 2518.74041763102 & -178.740417631015 \tabularnewline
76 & 2340 & 2035.6251985678 & 304.374801432201 \tabularnewline
77 & 1960 & 1928.97460204045 & 31.0253979595536 \tabularnewline
78 & 2100 & 1686.912128932 & 413.087871067999 \tabularnewline
79 & 2280 & 1808.38042114392 & 471.619578856083 \tabularnewline
80 & 2320 & 2141.435642882 & 178.564357117998 \tabularnewline
81 & 2660 & 2384.79071368464 & 275.209286315363 \tabularnewline
82 & 2520 & 2785.27916610348 & -265.279166103483 \tabularnewline
83 & 2120 & 2793.32126349204 & -673.321263492039 \tabularnewline
84 & 1800 & 2324.48500862692 & -524.485008626923 \tabularnewline
85 & 2300 & 1735.59056871432 & 564.409431285679 \tabularnewline
86 & 2420 & 1948.77780448447 & 471.222195515531 \tabularnewline
87 & 1920 & 2291.66734955929 & -371.667349559286 \tabularnewline
88 & 1720 & 2038.58632544894 & -318.586325448939 \tabularnewline
89 & 2000 & 1692.47066987097 & 307.529330129028 \tabularnewline
90 & 1960 & 1801.06011177246 & 158.939888227542 \tabularnewline
91 & 2860 & 1890.28269940073 & 969.717300599271 \tabularnewline
92 & 2160 & 2786.50045779116 & -626.500457791157 \tabularnewline
93 & 2360 & 2583.6299315977 & -223.629931597704 \tabularnewline
94 & 2300 & 2512.41328708076 & -212.413287080762 \tabularnewline
95 & 2360 & 2366.14393837131 & -6.14393837131001 \tabularnewline
96 & 2260 & 2328.64885153237 & -68.6488515323713 \tabularnewline
97 & 2460 & 2231.27278703544 & 228.72721296456 \tabularnewline
98 & 2200 & 2381.42054713008 & -181.420547130081 \tabularnewline
99 & 1620 & 2241.35371171292 & -621.353711712917 \tabularnewline
100 & 1740 & 1627.06860237013 & 112.931397629874 \tabularnewline
101 & 1720 & 1451.46714161714 & 268.532858382856 \tabularnewline
102 & 2460 & 1462.21075903275 & 997.789240967253 \tabularnewline
103 & 1840 & 2246.75046061725 & -406.750460617251 \tabularnewline
104 & 2160 & 2119.35752737816 & 40.6424726218402 \tabularnewline
105 & 2460 & 2248.49730948141 & 211.50269051859 \tabularnewline
106 & 2860 & 2550.42924825959 & 309.570751740408 \tabularnewline
107 & 2700 & 3023.3797654252 & -323.379765425201 \tabularnewline
108 & 2420 & 3031.89177184644 & -611.891771846439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297986&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]2600[/C][C]2280[/C][C]320[/C][/ROW]
[ROW][C]4[/C][C]5520[/C][C]34.5577944808924[/C][C]5485.44220551911[/C][/ROW]
[ROW][C]5[/C][C]3180[/C][C]2666.03929915733[/C][C]513.960700842674[/C][/ROW]
[ROW][C]6[/C][C]4080[/C][C]2815.54123745594[/C][C]1264.45876254406[/C][/ROW]
[ROW][C]7[/C][C]3360[/C][C]3852.09164472163[/C][C]-492.091644721631[/C][/ROW]
[ROW][C]8[/C][C]4960[/C][C]3754.4952132779[/C][C]1205.5047867221[/C][/ROW]
[ROW][C]9[/C][C]4640[/C][C]5031.65360021902[/C][C]-391.653600219016[/C][/ROW]
[ROW][C]10[/C][C]5420[/C][C]5298.87692594398[/C][C]121.123074056024[/C][/ROW]
[ROW][C]11[/C][C]4880[/C][C]5888.58193697693[/C][C]-1008.58193697693[/C][/ROW]
[ROW][C]12[/C][C]4780[/C][C]5484.64369991018[/C][C]-704.643699910183[/C][/ROW]
[ROW][C]13[/C][C]4860[/C][C]4975.42159426563[/C][C]-115.421594265627[/C][/ROW]
[ROW][C]14[/C][C]3780[/C][C]4739.55514838221[/C][C]-959.555148382206[/C][/ROW]
[ROW][C]15[/C][C]4120[/C][C]3682.60386939388[/C][C]437.396130606115[/C][/ROW]
[ROW][C]16[/C][C]3980[/C][C]3545.19716569642[/C][C]434.802834303585[/C][/ROW]
[ROW][C]17[/C][C]3060[/C][C]3572.39266614439[/C][C]-512.392666144387[/C][/ROW]
[ROW][C]18[/C][C]4420[/C][C]2893.70048228248[/C][C]1526.29951771752[/C][/ROW]
[ROW][C]19[/C][C]3340[/C][C]3895.9888717844[/C][C]-555.988871784396[/C][/ROW]
[ROW][C]20[/C][C]4220[/C][C]3564.25655066926[/C][C]655.743449330742[/C][/ROW]
[ROW][C]21[/C][C]5780[/C][C]4135.64976747694[/C][C]1644.35023252306[/C][/ROW]
[ROW][C]22[/C][C]5440[/C][C]5867.39877956248[/C][C]-427.398779562475[/C][/ROW]
[ROW][C]23[/C][C]4200[/C][C]6319.89796678724[/C][C]-2119.89796678724[/C][/ROW]
[ROW][C]24[/C][C]3720[/C][C]5051.29079550373[/C][C]-1331.29079550373[/C][/ROW]
[ROW][C]25[/C][C]4040[/C][C]3699.25537433364[/C][C]340.744625666358[/C][/ROW]
[ROW][C]26[/C][C]3920[/C][C]3378.05616239337[/C][C]541.943837606629[/C][/ROW]
[ROW][C]27[/C][C]3160[/C][C]3372.14909350699[/C][C]-212.149093506994[/C][/ROW]
[ROW][C]28[/C][C]3500[/C][C]2879.00827079277[/C][C]620.991729207231[/C][/ROW]
[ROW][C]29[/C][C]2780[/C][C]3071.77344517323[/C][C]-291.773445173226[/C][/ROW]
[ROW][C]30[/C][C]3340[/C][C]2661.4271033617[/C][C]678.572896638296[/C][/ROW]
[ROW][C]31[/C][C]3100[/C][C]3032.88446815008[/C][C]67.1155318499164[/C][/ROW]
[ROW][C]32[/C][C]3100[/C][C]3100.56544595398[/C][C]-0.56544595397645[/C][/ROW]
[ROW][C]33[/C][C]4400[/C][C]3131.56995178961[/C][C]1268.43004821039[/C][/ROW]
[ROW][C]34[/C][C]3480[/C][C]4330.46018753117[/C][C]-850.460187531168[/C][/ROW]
[ROW][C]35[/C][C]5100[/C][C]4063.18842923314[/C][C]1036.81157076686[/C][/ROW]
[ROW][C]36[/C][C]4260[/C][C]5208.44819723993[/C][C]-948.448197239925[/C][/ROW]
[ROW][C]37[/C][C]3640[/C][C]4922.12447651506[/C][C]-1282.12447651506[/C][/ROW]
[ROW][C]38[/C][C]2900[/C][C]3966.55500902583[/C][C]-1066.55500902583[/C][/ROW]
[ROW][C]39[/C][C]3820[/C][C]2719.92562080676[/C][C]1100.07437919324[/C][/ROW]
[ROW][C]40[/C][C]2980[/C][C]3060.473741809[/C][C]-80.4737418089976[/C][/ROW]
[ROW][C]41[/C][C]2860[/C][C]2734.32240580856[/C][C]125.677594191441[/C][/ROW]
[ROW][C]42[/C][C]2420[/C][C]2567.20864798363[/C][C]-147.208647983633[/C][/ROW]
[ROW][C]43[/C][C]2680[/C][C]2196.8862403821[/C][C]483.113759617896[/C][/ROW]
[ROW][C]44[/C][C]4420[/C][C]2350.56987270924[/C][C]2069.43012729076[/C][/ROW]
[ROW][C]45[/C][C]3160[/C][C]4148.89020319304[/C][C]-988.890203193039[/C][/ROW]
[ROW][C]46[/C][C]3160[/C][C]3922.11582670716[/C][C]-762.11582670716[/C][/ROW]
[ROW][C]47[/C][C]4300[/C][C]3526.54669987459[/C][C]773.453300125407[/C][/ROW]
[ROW][C]48[/C][C]2820[/C][C]4253.49740577153[/C][C]-1433.49740577153[/C][/ROW]
[ROW][C]49[/C][C]3240[/C][C]3244.25458906223[/C][C]-4.25458906222957[/C][/ROW]
[ROW][C]50[/C][C]2520[/C][C]3003.33857130647[/C][C]-483.338571306467[/C][/ROW]
[ROW][C]51[/C][C]3480[/C][C]2319.80473070045[/C][C]1160.19526929955[/C][/ROW]
[ROW][C]52[/C][C]2740[/C][C]2964.60321901245[/C][C]-224.603219012451[/C][/ROW]
[ROW][C]53[/C][C]2240[/C][C]2777.64417872794[/C][C]-537.644178727942[/C][/ROW]
[ROW][C]54[/C][C]3700[/C][C]2216.78396225807[/C][C]1483.21603774193[/C][/ROW]
[ROW][C]55[/C][C]2600[/C][C]3310.84958085014[/C][C]-710.849580850137[/C][/ROW]
[ROW][C]56[/C][C]3160[/C][C]2951.55588711252[/C][C]208.444112887483[/C][/ROW]
[ROW][C]57[/C][C]3800[/C][C]3167.07719068304[/C][C]632.922809316957[/C][/ROW]
[ROW][C]58[/C][C]3440[/C][C]3852.90810733503[/C][C]-412.908107335033[/C][/ROW]
[ROW][C]59[/C][C]2180[/C][C]3817.69646294259[/C][C]-1637.69646294259[/C][/ROW]
[ROW][C]60[/C][C]2300[/C][C]2497.43531312398[/C][C]-197.435313123985[/C][/ROW]
[ROW][C]61[/C][C]3160[/C][C]1877.68404282882[/C][C]1282.31595717118[/C][/ROW]
[ROW][C]62[/C][C]1800[/C][C]2544.65666452894[/C][C]-744.656664528936[/C][/ROW]
[ROW][C]63[/C][C]2620[/C][C]1835.37819172765[/C][C]784.621808272352[/C][/ROW]
[ROW][C]64[/C][C]2820[/C][C]2249.49461572572[/C][C]570.505384274281[/C][/ROW]
[ROW][C]65[/C][C]2180[/C][C]2766.07165717658[/C][C]-586.071657176577[/C][/ROW]
[ROW][C]66[/C][C]2300[/C][C]2435.83533695735[/C][C]-135.835336957352[/C][/ROW]
[ROW][C]67[/C][C]2560[/C][C]2296.28771326365[/C][C]263.71228673635[/C][/ROW]
[ROW][C]68[/C][C]2860[/C][C]2472.66163989261[/C][C]387.33836010739[/C][/ROW]
[ROW][C]69[/C][C]2620[/C][C]2863.512724937[/C][C]-243.512724937001[/C][/ROW]
[ROW][C]70[/C][C]3960[/C][C]2821.54796881031[/C][C]1138.45203118969[/C][/ROW]
[ROW][C]71[/C][C]3960[/C][C]3958.70383481612[/C][C]1.29616518387866[/C][/ROW]
[ROW][C]72[/C][C]2320[/C][C]4483.75435482363[/C][C]-2163.75435482363[/C][/ROW]
[ROW][C]73[/C][C]3400[/C][C]3016.38564382577[/C][C]383.614356174227[/C][/ROW]
[ROW][C]74[/C][C]2640[/C][C]3067.77304446805[/C][C]-427.773044468053[/C][/ROW]
[ROW][C]75[/C][C]2340[/C][C]2518.74041763102[/C][C]-178.740417631015[/C][/ROW]
[ROW][C]76[/C][C]2340[/C][C]2035.6251985678[/C][C]304.374801432201[/C][/ROW]
[ROW][C]77[/C][C]1960[/C][C]1928.97460204045[/C][C]31.0253979595536[/C][/ROW]
[ROW][C]78[/C][C]2100[/C][C]1686.912128932[/C][C]413.087871067999[/C][/ROW]
[ROW][C]79[/C][C]2280[/C][C]1808.38042114392[/C][C]471.619578856083[/C][/ROW]
[ROW][C]80[/C][C]2320[/C][C]2141.435642882[/C][C]178.564357117998[/C][/ROW]
[ROW][C]81[/C][C]2660[/C][C]2384.79071368464[/C][C]275.209286315363[/C][/ROW]
[ROW][C]82[/C][C]2520[/C][C]2785.27916610348[/C][C]-265.279166103483[/C][/ROW]
[ROW][C]83[/C][C]2120[/C][C]2793.32126349204[/C][C]-673.321263492039[/C][/ROW]
[ROW][C]84[/C][C]1800[/C][C]2324.48500862692[/C][C]-524.485008626923[/C][/ROW]
[ROW][C]85[/C][C]2300[/C][C]1735.59056871432[/C][C]564.409431285679[/C][/ROW]
[ROW][C]86[/C][C]2420[/C][C]1948.77780448447[/C][C]471.222195515531[/C][/ROW]
[ROW][C]87[/C][C]1920[/C][C]2291.66734955929[/C][C]-371.667349559286[/C][/ROW]
[ROW][C]88[/C][C]1720[/C][C]2038.58632544894[/C][C]-318.586325448939[/C][/ROW]
[ROW][C]89[/C][C]2000[/C][C]1692.47066987097[/C][C]307.529330129028[/C][/ROW]
[ROW][C]90[/C][C]1960[/C][C]1801.06011177246[/C][C]158.939888227542[/C][/ROW]
[ROW][C]91[/C][C]2860[/C][C]1890.28269940073[/C][C]969.717300599271[/C][/ROW]
[ROW][C]92[/C][C]2160[/C][C]2786.50045779116[/C][C]-626.500457791157[/C][/ROW]
[ROW][C]93[/C][C]2360[/C][C]2583.6299315977[/C][C]-223.629931597704[/C][/ROW]
[ROW][C]94[/C][C]2300[/C][C]2512.41328708076[/C][C]-212.413287080762[/C][/ROW]
[ROW][C]95[/C][C]2360[/C][C]2366.14393837131[/C][C]-6.14393837131001[/C][/ROW]
[ROW][C]96[/C][C]2260[/C][C]2328.64885153237[/C][C]-68.6488515323713[/C][/ROW]
[ROW][C]97[/C][C]2460[/C][C]2231.27278703544[/C][C]228.72721296456[/C][/ROW]
[ROW][C]98[/C][C]2200[/C][C]2381.42054713008[/C][C]-181.420547130081[/C][/ROW]
[ROW][C]99[/C][C]1620[/C][C]2241.35371171292[/C][C]-621.353711712917[/C][/ROW]
[ROW][C]100[/C][C]1740[/C][C]1627.06860237013[/C][C]112.931397629874[/C][/ROW]
[ROW][C]101[/C][C]1720[/C][C]1451.46714161714[/C][C]268.532858382856[/C][/ROW]
[ROW][C]102[/C][C]2460[/C][C]1462.21075903275[/C][C]997.789240967253[/C][/ROW]
[ROW][C]103[/C][C]1840[/C][C]2246.75046061725[/C][C]-406.750460617251[/C][/ROW]
[ROW][C]104[/C][C]2160[/C][C]2119.35752737816[/C][C]40.6424726218402[/C][/ROW]
[ROW][C]105[/C][C]2460[/C][C]2248.49730948141[/C][C]211.50269051859[/C][/ROW]
[ROW][C]106[/C][C]2860[/C][C]2550.42924825959[/C][C]309.570751740408[/C][/ROW]
[ROW][C]107[/C][C]2700[/C][C]3023.3797654252[/C][C]-323.379765425201[/C][/ROW]
[ROW][C]108[/C][C]2420[/C][C]3031.89177184644[/C][C]-611.891771846439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297986&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297986&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
326002280320
4552034.55779448089245485.44220551911
531802666.03929915733513.960700842674
640802815.541237455941264.45876254406
733603852.09164472163-492.091644721631
849603754.49521327791205.5047867221
946405031.65360021902-391.653600219016
1054205298.87692594398121.123074056024
1148805888.58193697693-1008.58193697693
1247805484.64369991018-704.643699910183
1348604975.42159426563-115.421594265627
1437804739.55514838221-959.555148382206
1541203682.60386939388437.396130606115
1639803545.19716569642434.802834303585
1730603572.39266614439-512.392666144387
1844202893.700482282481526.29951771752
1933403895.9888717844-555.988871784396
2042203564.25655066926655.743449330742
2157804135.649767476941644.35023252306
2254405867.39877956248-427.398779562475
2342006319.89796678724-2119.89796678724
2437205051.29079550373-1331.29079550373
2540403699.25537433364340.744625666358
2639203378.05616239337541.943837606629
2731603372.14909350699-212.149093506994
2835002879.00827079277620.991729207231
2927803071.77344517323-291.773445173226
3033402661.4271033617678.572896638296
3131003032.8844681500867.1155318499164
3231003100.56544595398-0.56544595397645
3344003131.569951789611268.43004821039
3434804330.46018753117-850.460187531168
3551004063.188429233141036.81157076686
3642605208.44819723993-948.448197239925
3736404922.12447651506-1282.12447651506
3829003966.55500902583-1066.55500902583
3938202719.925620806761100.07437919324
4029803060.473741809-80.4737418089976
4128602734.32240580856125.677594191441
4224202567.20864798363-147.208647983633
4326802196.8862403821483.113759617896
4444202350.569872709242069.43012729076
4531604148.89020319304-988.890203193039
4631603922.11582670716-762.11582670716
4743003526.54669987459773.453300125407
4828204253.49740577153-1433.49740577153
4932403244.25458906223-4.25458906222957
5025203003.33857130647-483.338571306467
5134802319.804730700451160.19526929955
5227402964.60321901245-224.603219012451
5322402777.64417872794-537.644178727942
5437002216.783962258071483.21603774193
5526003310.84958085014-710.849580850137
5631602951.55588711252208.444112887483
5738003167.07719068304632.922809316957
5834403852.90810733503-412.908107335033
5921803817.69646294259-1637.69646294259
6023002497.43531312398-197.435313123985
6131601877.684042828821282.31595717118
6218002544.65666452894-744.656664528936
6326201835.37819172765784.621808272352
6428202249.49461572572570.505384274281
6521802766.07165717658-586.071657176577
6623002435.83533695735-135.835336957352
6725602296.28771326365263.71228673635
6828602472.66163989261387.33836010739
6926202863.512724937-243.512724937001
7039602821.547968810311138.45203118969
7139603958.703834816121.29616518387866
7223204483.75435482363-2163.75435482363
7334003016.38564382577383.614356174227
7426403067.77304446805-427.773044468053
7523402518.74041763102-178.740417631015
7623402035.6251985678304.374801432201
7719601928.9746020404531.0253979595536
7821001686.912128932413.087871067999
7922801808.38042114392471.619578856083
8023202141.435642882178.564357117998
8126602384.79071368464275.209286315363
8225202785.27916610348-265.279166103483
8321202793.32126349204-673.321263492039
8418002324.48500862692-524.485008626923
8523001735.59056871432564.409431285679
8624201948.77780448447471.222195515531
8719202291.66734955929-371.667349559286
8817202038.58632544894-318.586325448939
8920001692.47066987097307.529330129028
9019601801.06011177246158.939888227542
9128601890.28269940073969.717300599271
9221602786.50045779116-626.500457791157
9323602583.6299315977-223.629931597704
9423002512.41328708076-212.413287080762
9523602366.14393837131-6.14393837131001
9622602328.64885153237-68.6488515323713
9724602231.27278703544228.72721296456
9822002381.42054713008-181.420547130081
9916202241.35371171292-621.353711712917
10017401627.06860237013112.931397629874
10117201451.46714161714268.532858382856
10224601462.21075903275997.789240967253
10318402246.75046061725-406.750460617251
10421602119.3575273781640.6424726218402
10524602248.49730948141211.50269051859
10628602550.42924825959309.570751740408
10727003023.3797654252-323.379765425201
10824203031.89177184644-611.891771846439







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092651.37037478319822.3780819640514480.36266760233
1102600.48278688763114.5952364771655086.3703372981
1112549.59519899207-893.1999903582815992.39038834242
1122498.70761109651-2120.815119418457118.23034161147
1132447.82002320095-3520.116268520448415.75631492234
1142396.93243530539-5063.418141690619857.28301230139
1152346.04484740983-6733.430013485511425.5197083052
1162295.15725951427-8518.3312931615313108.6458121901
1172244.26967161872-10409.426055808714897.9653990461
1182193.38208372316-12399.954698623316786.7188660697
1192142.4944958276-14484.444349427118769.4333410823
1202091.60690793204-16658.327448428820841.5412642928

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2651.37037478319 & 822.378081964051 & 4480.36266760233 \tabularnewline
110 & 2600.48278688763 & 114.595236477165 & 5086.3703372981 \tabularnewline
111 & 2549.59519899207 & -893.199990358281 & 5992.39038834242 \tabularnewline
112 & 2498.70761109651 & -2120.81511941845 & 7118.23034161147 \tabularnewline
113 & 2447.82002320095 & -3520.11626852044 & 8415.75631492234 \tabularnewline
114 & 2396.93243530539 & -5063.41814169061 & 9857.28301230139 \tabularnewline
115 & 2346.04484740983 & -6733.4300134855 & 11425.5197083052 \tabularnewline
116 & 2295.15725951427 & -8518.33129316153 & 13108.6458121901 \tabularnewline
117 & 2244.26967161872 & -10409.4260558087 & 14897.9653990461 \tabularnewline
118 & 2193.38208372316 & -12399.9546986233 & 16786.7188660697 \tabularnewline
119 & 2142.4944958276 & -14484.4443494271 & 18769.4333410823 \tabularnewline
120 & 2091.60690793204 & -16658.3274484288 & 20841.5412642928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297986&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]2651.37037478319[/C][C]822.378081964051[/C][C]4480.36266760233[/C][/ROW]
[ROW][C]110[/C][C]2600.48278688763[/C][C]114.595236477165[/C][C]5086.3703372981[/C][/ROW]
[ROW][C]111[/C][C]2549.59519899207[/C][C]-893.199990358281[/C][C]5992.39038834242[/C][/ROW]
[ROW][C]112[/C][C]2498.70761109651[/C][C]-2120.81511941845[/C][C]7118.23034161147[/C][/ROW]
[ROW][C]113[/C][C]2447.82002320095[/C][C]-3520.11626852044[/C][C]8415.75631492234[/C][/ROW]
[ROW][C]114[/C][C]2396.93243530539[/C][C]-5063.41814169061[/C][C]9857.28301230139[/C][/ROW]
[ROW][C]115[/C][C]2346.04484740983[/C][C]-6733.4300134855[/C][C]11425.5197083052[/C][/ROW]
[ROW][C]116[/C][C]2295.15725951427[/C][C]-8518.33129316153[/C][C]13108.6458121901[/C][/ROW]
[ROW][C]117[/C][C]2244.26967161872[/C][C]-10409.4260558087[/C][C]14897.9653990461[/C][/ROW]
[ROW][C]118[/C][C]2193.38208372316[/C][C]-12399.9546986233[/C][C]16786.7188660697[/C][/ROW]
[ROW][C]119[/C][C]2142.4944958276[/C][C]-14484.4443494271[/C][C]18769.4333410823[/C][/ROW]
[ROW][C]120[/C][C]2091.60690793204[/C][C]-16658.3274484288[/C][C]20841.5412642928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297986&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297986&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
1092651.37037478319822.3780819640514480.36266760233
1102600.48278688763114.5952364771655086.3703372981
1112549.59519899207-893.1999903582815992.39038834242
1122498.70761109651-2120.815119418457118.23034161147
1132447.82002320095-3520.116268520448415.75631492234
1142396.93243530539-5063.418141690619857.28301230139
1152346.04484740983-6733.430013485511425.5197083052
1162295.15725951427-8518.3312931615313108.6458121901
1172244.26967161872-10409.426055808714897.9653990461
1182193.38208372316-12399.954698623316786.7188660697
1192142.4944958276-14484.444349427118769.4333410823
1202091.60690793204-16658.327448428820841.5412642928



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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')