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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 computationThu, 15 Dec 2016 20:14:45 +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/15/t1481829966pza8n0vogamripp.htm/, Retrieved Sat, 18 May 2024 07:07:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299974, Retrieved Sat, 18 May 2024 07:07:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2099 - r0481974] [2016-12-15 19:14:45] [ee2f08b6fcfe19fae25bd9410e008f6d] [Current]
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Dataseries X:
2490
2560
2890
3420
2700
3290
2650
3060
3200
4600
4370
3340
2410
1920
2620
2840
2880
2380
2820
2480
3230
3860
5050
3630
1700
2590
2130
2350
2680
2270
2810
2200
3420
4300
3440
2670
2460
1920
2890
2600
2860
2010
2470
2210
3530
3790
3520
2510
1860
1760
1540
2240
2600
3060
2040
2230
2720
3740
3100
2100
3630
1620
1870
1680
1830
4620
1560
2800
1810
4260
2770
3280
1830
2590
1760
2950
2020
2530
2530
2220
2250
2630
3550
2670
2260
2170
2430
1700
2200
3140
1900
2260
3580
3050
3130
2350
1650
1760
2010
1910
1850
2030
2110
1900
2170
2690
3620
1920
1480
3910
2120
1980
2040
1820
1700
2210
2070
2650
3260
1590
1880
1390
1890
1640
1840
1620




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=299974&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=299974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299974&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
alpha0.00778085163077724
beta1
gamma0.230071128002228

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00778085163077724 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.230071128002228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299974&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]0.00778085163077724[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.230071128002228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299974&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
alpha0.00778085163077724
beta1
gamma0.230071128002228







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1324102606.08707264957-196.087072649574
1419202107.43393383488-187.433933834884
1526202803.22306151304-183.223061513043
1628403024.28598857367-184.285988573672
1728803036.82340988849-156.823409888491
1823802465.43762710222-85.437627102217
1928202491.44250900018328.557490999819
2024802906.14174924428-426.141749244281
2132303049.5697076163180.430292383702
2238604456.62121438234-596.621214382336
2350504204.23437751587845.765622484128
2436303183.40131544421446.598684555786
2517002218.59103056928-518.591030569276
2625901715.22396370989874.776036290107
2721302424.32423020423-294.324230204228
2823502647.50056639912-297.500566399123
2926802667.765877262112.2341227378984
3022702117.64654503278152.35345496722
3128102245.51409454113564.485905458869
3222002497.10654133012-297.106541330119
3334202788.35233036381631.647669636188
3443004033.38443714795266.61556285205
3534404135.55633663387-695.55633663387
3626703018.18800064865-348.188000648649
3724601827.25477124821632.745228751787
3819201660.27928084989259.720719150115
3928902102.27888813861787.72111186139
4026002346.13694371174253.863056288259
4128602458.67653187993401.323468120071
4220101963.8763316722846.1236683277161
4324702204.47787117119265.522128828807
4422102274.21131444752-64.211314447522
4535302798.2506263973731.749373602695
4637903980.47507907201-190.475079072013
4735203875.63168271556-355.631682715562
4825102859.03753853839-349.037538538386
4918601910.85119132457-50.8511913245702
5017601666.9084708359893.0915291640245
5115402240.35362286981-700.353622869809
5222402351.39467693441-111.394676934413
5326002492.54376640139107.456233598614
5430601909.874243961361150.12575603864
5520402213.24300468171-173.243004681714
5622302204.9692915011325.0307084988735
5727202912.77872928377-192.778729283769
5837403871.46271136094-131.46271136094
5931003724.01498287119-624.014982871187
6021002699.38826760917-599.388267609166
6136301807.926669679871822.07333032013
6216201616.591649925833.40835007416899
6318702012.68811090288-142.688110902883
6416802271.33307106789-591.333071067887
6518302463.78967061076-633.78967061076
6646202112.689057867912507.31094213209
6715602134.39283092542-574.392830925422
6828002175.01353211355624.986467886448
6918102849.19113612367-1039.19113612367
7042603820.1225311733439.877468826704
7127703573.96145618001-803.961456180012
7232802561.43773287977718.56226712023
7318302251.14063163275-421.140631632749
7425901627.8668559271962.133144072898
7517602006.21364522628-246.21364522628
7629502168.97213719539781.027862804611
7720202380.42913548121-360.429135481208
7825302768.65029634055-238.650296340548
7925302064.26915588246465.730844117539
8022202393.64679002436-173.646790024355
8122502682.36461290789-432.364612907893
8226304001.03684885105-1371.03684885105
8335503448.12608054182101.873919458183
8426702788.54743363598-118.547433635978
8522602203.3846865842856.6153134157162
8621701895.14097216178274.859027838215
8724301982.48763978949447.512360210515
8817002380.73143072067-680.731430720666
8922002304.4558669751-104.455866975105
9031402708.67429131818431.325708681818
9119002161.72171563487-261.721715634867
9222602325.23996159863-65.239961598626
9335802542.342985897661037.65701410234
9430503656.21230727785-606.212307277851
9531303449.4811051996-319.481105199596
9623502737.0185224593-387.018522459297
9716502188.37679862109-538.376798621095
9817601919.31851582524-159.318515825243
9920102033.31620129421-23.3162012942068
10019102157.29231827045-247.292318270454
10118502206.26692508334-356.266925083337
10220302719.20037836369-689.200378363685
10321101984.96655487883125.033445121173
10419002179.00336072767-279.003360727675
10521702627.20649170488-457.206491704877
10626903323.54206022969-633.542060229687
10736203151.20249589326468.797504106743
10819202404.73837031119-484.738370311186
10914801795.30622974858-315.30622974858
11039101590.773243057642319.22675694236
11121201750.64587737495369.354122625052
11219801825.14614058039154.853859419611
11320401854.10032086823185.899679131773
11418202301.19579903612-481.195799036122
11517001762.01885673472-62.0188567347166
11622101868.47522700642341.52477299358
11720702291.76335561785-221.763355617851
11826502962.44590963884-312.445909638835
11932603059.51539646017200.484603539828
12015902106.46925756398-516.469257563984
12118801548.40125740367331.598742596329
12213901968.2818813844-578.281881384396
12318901655.91188325792234.088116742077
12416401674.76213265862-34.7621326586193
12518401702.22153618391137.778463816089
12616201989.17638467265-369.176384672649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2410 & 2606.08707264957 & -196.087072649574 \tabularnewline
14 & 1920 & 2107.43393383488 & -187.433933834884 \tabularnewline
15 & 2620 & 2803.22306151304 & -183.223061513043 \tabularnewline
16 & 2840 & 3024.28598857367 & -184.285988573672 \tabularnewline
17 & 2880 & 3036.82340988849 & -156.823409888491 \tabularnewline
18 & 2380 & 2465.43762710222 & -85.437627102217 \tabularnewline
19 & 2820 & 2491.44250900018 & 328.557490999819 \tabularnewline
20 & 2480 & 2906.14174924428 & -426.141749244281 \tabularnewline
21 & 3230 & 3049.5697076163 & 180.430292383702 \tabularnewline
22 & 3860 & 4456.62121438234 & -596.621214382336 \tabularnewline
23 & 5050 & 4204.23437751587 & 845.765622484128 \tabularnewline
24 & 3630 & 3183.40131544421 & 446.598684555786 \tabularnewline
25 & 1700 & 2218.59103056928 & -518.591030569276 \tabularnewline
26 & 2590 & 1715.22396370989 & 874.776036290107 \tabularnewline
27 & 2130 & 2424.32423020423 & -294.324230204228 \tabularnewline
28 & 2350 & 2647.50056639912 & -297.500566399123 \tabularnewline
29 & 2680 & 2667.7658772621 & 12.2341227378984 \tabularnewline
30 & 2270 & 2117.64654503278 & 152.35345496722 \tabularnewline
31 & 2810 & 2245.51409454113 & 564.485905458869 \tabularnewline
32 & 2200 & 2497.10654133012 & -297.106541330119 \tabularnewline
33 & 3420 & 2788.35233036381 & 631.647669636188 \tabularnewline
34 & 4300 & 4033.38443714795 & 266.61556285205 \tabularnewline
35 & 3440 & 4135.55633663387 & -695.55633663387 \tabularnewline
36 & 2670 & 3018.18800064865 & -348.188000648649 \tabularnewline
37 & 2460 & 1827.25477124821 & 632.745228751787 \tabularnewline
38 & 1920 & 1660.27928084989 & 259.720719150115 \tabularnewline
39 & 2890 & 2102.27888813861 & 787.72111186139 \tabularnewline
40 & 2600 & 2346.13694371174 & 253.863056288259 \tabularnewline
41 & 2860 & 2458.67653187993 & 401.323468120071 \tabularnewline
42 & 2010 & 1963.87633167228 & 46.1236683277161 \tabularnewline
43 & 2470 & 2204.47787117119 & 265.522128828807 \tabularnewline
44 & 2210 & 2274.21131444752 & -64.211314447522 \tabularnewline
45 & 3530 & 2798.2506263973 & 731.749373602695 \tabularnewline
46 & 3790 & 3980.47507907201 & -190.475079072013 \tabularnewline
47 & 3520 & 3875.63168271556 & -355.631682715562 \tabularnewline
48 & 2510 & 2859.03753853839 & -349.037538538386 \tabularnewline
49 & 1860 & 1910.85119132457 & -50.8511913245702 \tabularnewline
50 & 1760 & 1666.90847083598 & 93.0915291640245 \tabularnewline
51 & 1540 & 2240.35362286981 & -700.353622869809 \tabularnewline
52 & 2240 & 2351.39467693441 & -111.394676934413 \tabularnewline
53 & 2600 & 2492.54376640139 & 107.456233598614 \tabularnewline
54 & 3060 & 1909.87424396136 & 1150.12575603864 \tabularnewline
55 & 2040 & 2213.24300468171 & -173.243004681714 \tabularnewline
56 & 2230 & 2204.96929150113 & 25.0307084988735 \tabularnewline
57 & 2720 & 2912.77872928377 & -192.778729283769 \tabularnewline
58 & 3740 & 3871.46271136094 & -131.46271136094 \tabularnewline
59 & 3100 & 3724.01498287119 & -624.014982871187 \tabularnewline
60 & 2100 & 2699.38826760917 & -599.388267609166 \tabularnewline
61 & 3630 & 1807.92666967987 & 1822.07333032013 \tabularnewline
62 & 1620 & 1616.59164992583 & 3.40835007416899 \tabularnewline
63 & 1870 & 2012.68811090288 & -142.688110902883 \tabularnewline
64 & 1680 & 2271.33307106789 & -591.333071067887 \tabularnewline
65 & 1830 & 2463.78967061076 & -633.78967061076 \tabularnewline
66 & 4620 & 2112.68905786791 & 2507.31094213209 \tabularnewline
67 & 1560 & 2134.39283092542 & -574.392830925422 \tabularnewline
68 & 2800 & 2175.01353211355 & 624.986467886448 \tabularnewline
69 & 1810 & 2849.19113612367 & -1039.19113612367 \tabularnewline
70 & 4260 & 3820.1225311733 & 439.877468826704 \tabularnewline
71 & 2770 & 3573.96145618001 & -803.961456180012 \tabularnewline
72 & 3280 & 2561.43773287977 & 718.56226712023 \tabularnewline
73 & 1830 & 2251.14063163275 & -421.140631632749 \tabularnewline
74 & 2590 & 1627.8668559271 & 962.133144072898 \tabularnewline
75 & 1760 & 2006.21364522628 & -246.21364522628 \tabularnewline
76 & 2950 & 2168.97213719539 & 781.027862804611 \tabularnewline
77 & 2020 & 2380.42913548121 & -360.429135481208 \tabularnewline
78 & 2530 & 2768.65029634055 & -238.650296340548 \tabularnewline
79 & 2530 & 2064.26915588246 & 465.730844117539 \tabularnewline
80 & 2220 & 2393.64679002436 & -173.646790024355 \tabularnewline
81 & 2250 & 2682.36461290789 & -432.364612907893 \tabularnewline
82 & 2630 & 4001.03684885105 & -1371.03684885105 \tabularnewline
83 & 3550 & 3448.12608054182 & 101.873919458183 \tabularnewline
84 & 2670 & 2788.54743363598 & -118.547433635978 \tabularnewline
85 & 2260 & 2203.38468658428 & 56.6153134157162 \tabularnewline
86 & 2170 & 1895.14097216178 & 274.859027838215 \tabularnewline
87 & 2430 & 1982.48763978949 & 447.512360210515 \tabularnewline
88 & 1700 & 2380.73143072067 & -680.731430720666 \tabularnewline
89 & 2200 & 2304.4558669751 & -104.455866975105 \tabularnewline
90 & 3140 & 2708.67429131818 & 431.325708681818 \tabularnewline
91 & 1900 & 2161.72171563487 & -261.721715634867 \tabularnewline
92 & 2260 & 2325.23996159863 & -65.239961598626 \tabularnewline
93 & 3580 & 2542.34298589766 & 1037.65701410234 \tabularnewline
94 & 3050 & 3656.21230727785 & -606.212307277851 \tabularnewline
95 & 3130 & 3449.4811051996 & -319.481105199596 \tabularnewline
96 & 2350 & 2737.0185224593 & -387.018522459297 \tabularnewline
97 & 1650 & 2188.37679862109 & -538.376798621095 \tabularnewline
98 & 1760 & 1919.31851582524 & -159.318515825243 \tabularnewline
99 & 2010 & 2033.31620129421 & -23.3162012942068 \tabularnewline
100 & 1910 & 2157.29231827045 & -247.292318270454 \tabularnewline
101 & 1850 & 2206.26692508334 & -356.266925083337 \tabularnewline
102 & 2030 & 2719.20037836369 & -689.200378363685 \tabularnewline
103 & 2110 & 1984.96655487883 & 125.033445121173 \tabularnewline
104 & 1900 & 2179.00336072767 & -279.003360727675 \tabularnewline
105 & 2170 & 2627.20649170488 & -457.206491704877 \tabularnewline
106 & 2690 & 3323.54206022969 & -633.542060229687 \tabularnewline
107 & 3620 & 3151.20249589326 & 468.797504106743 \tabularnewline
108 & 1920 & 2404.73837031119 & -484.738370311186 \tabularnewline
109 & 1480 & 1795.30622974858 & -315.30622974858 \tabularnewline
110 & 3910 & 1590.77324305764 & 2319.22675694236 \tabularnewline
111 & 2120 & 1750.64587737495 & 369.354122625052 \tabularnewline
112 & 1980 & 1825.14614058039 & 154.853859419611 \tabularnewline
113 & 2040 & 1854.10032086823 & 185.899679131773 \tabularnewline
114 & 1820 & 2301.19579903612 & -481.195799036122 \tabularnewline
115 & 1700 & 1762.01885673472 & -62.0188567347166 \tabularnewline
116 & 2210 & 1868.47522700642 & 341.52477299358 \tabularnewline
117 & 2070 & 2291.76335561785 & -221.763355617851 \tabularnewline
118 & 2650 & 2962.44590963884 & -312.445909638835 \tabularnewline
119 & 3260 & 3059.51539646017 & 200.484603539828 \tabularnewline
120 & 1590 & 2106.46925756398 & -516.469257563984 \tabularnewline
121 & 1880 & 1548.40125740367 & 331.598742596329 \tabularnewline
122 & 1390 & 1968.2818813844 & -578.281881384396 \tabularnewline
123 & 1890 & 1655.91188325792 & 234.088116742077 \tabularnewline
124 & 1640 & 1674.76213265862 & -34.7621326586193 \tabularnewline
125 & 1840 & 1702.22153618391 & 137.778463816089 \tabularnewline
126 & 1620 & 1989.17638467265 & -369.176384672649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299974&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]13[/C][C]2410[/C][C]2606.08707264957[/C][C]-196.087072649574[/C][/ROW]
[ROW][C]14[/C][C]1920[/C][C]2107.43393383488[/C][C]-187.433933834884[/C][/ROW]
[ROW][C]15[/C][C]2620[/C][C]2803.22306151304[/C][C]-183.223061513043[/C][/ROW]
[ROW][C]16[/C][C]2840[/C][C]3024.28598857367[/C][C]-184.285988573672[/C][/ROW]
[ROW][C]17[/C][C]2880[/C][C]3036.82340988849[/C][C]-156.823409888491[/C][/ROW]
[ROW][C]18[/C][C]2380[/C][C]2465.43762710222[/C][C]-85.437627102217[/C][/ROW]
[ROW][C]19[/C][C]2820[/C][C]2491.44250900018[/C][C]328.557490999819[/C][/ROW]
[ROW][C]20[/C][C]2480[/C][C]2906.14174924428[/C][C]-426.141749244281[/C][/ROW]
[ROW][C]21[/C][C]3230[/C][C]3049.5697076163[/C][C]180.430292383702[/C][/ROW]
[ROW][C]22[/C][C]3860[/C][C]4456.62121438234[/C][C]-596.621214382336[/C][/ROW]
[ROW][C]23[/C][C]5050[/C][C]4204.23437751587[/C][C]845.765622484128[/C][/ROW]
[ROW][C]24[/C][C]3630[/C][C]3183.40131544421[/C][C]446.598684555786[/C][/ROW]
[ROW][C]25[/C][C]1700[/C][C]2218.59103056928[/C][C]-518.591030569276[/C][/ROW]
[ROW][C]26[/C][C]2590[/C][C]1715.22396370989[/C][C]874.776036290107[/C][/ROW]
[ROW][C]27[/C][C]2130[/C][C]2424.32423020423[/C][C]-294.324230204228[/C][/ROW]
[ROW][C]28[/C][C]2350[/C][C]2647.50056639912[/C][C]-297.500566399123[/C][/ROW]
[ROW][C]29[/C][C]2680[/C][C]2667.7658772621[/C][C]12.2341227378984[/C][/ROW]
[ROW][C]30[/C][C]2270[/C][C]2117.64654503278[/C][C]152.35345496722[/C][/ROW]
[ROW][C]31[/C][C]2810[/C][C]2245.51409454113[/C][C]564.485905458869[/C][/ROW]
[ROW][C]32[/C][C]2200[/C][C]2497.10654133012[/C][C]-297.106541330119[/C][/ROW]
[ROW][C]33[/C][C]3420[/C][C]2788.35233036381[/C][C]631.647669636188[/C][/ROW]
[ROW][C]34[/C][C]4300[/C][C]4033.38443714795[/C][C]266.61556285205[/C][/ROW]
[ROW][C]35[/C][C]3440[/C][C]4135.55633663387[/C][C]-695.55633663387[/C][/ROW]
[ROW][C]36[/C][C]2670[/C][C]3018.18800064865[/C][C]-348.188000648649[/C][/ROW]
[ROW][C]37[/C][C]2460[/C][C]1827.25477124821[/C][C]632.745228751787[/C][/ROW]
[ROW][C]38[/C][C]1920[/C][C]1660.27928084989[/C][C]259.720719150115[/C][/ROW]
[ROW][C]39[/C][C]2890[/C][C]2102.27888813861[/C][C]787.72111186139[/C][/ROW]
[ROW][C]40[/C][C]2600[/C][C]2346.13694371174[/C][C]253.863056288259[/C][/ROW]
[ROW][C]41[/C][C]2860[/C][C]2458.67653187993[/C][C]401.323468120071[/C][/ROW]
[ROW][C]42[/C][C]2010[/C][C]1963.87633167228[/C][C]46.1236683277161[/C][/ROW]
[ROW][C]43[/C][C]2470[/C][C]2204.47787117119[/C][C]265.522128828807[/C][/ROW]
[ROW][C]44[/C][C]2210[/C][C]2274.21131444752[/C][C]-64.211314447522[/C][/ROW]
[ROW][C]45[/C][C]3530[/C][C]2798.2506263973[/C][C]731.749373602695[/C][/ROW]
[ROW][C]46[/C][C]3790[/C][C]3980.47507907201[/C][C]-190.475079072013[/C][/ROW]
[ROW][C]47[/C][C]3520[/C][C]3875.63168271556[/C][C]-355.631682715562[/C][/ROW]
[ROW][C]48[/C][C]2510[/C][C]2859.03753853839[/C][C]-349.037538538386[/C][/ROW]
[ROW][C]49[/C][C]1860[/C][C]1910.85119132457[/C][C]-50.8511913245702[/C][/ROW]
[ROW][C]50[/C][C]1760[/C][C]1666.90847083598[/C][C]93.0915291640245[/C][/ROW]
[ROW][C]51[/C][C]1540[/C][C]2240.35362286981[/C][C]-700.353622869809[/C][/ROW]
[ROW][C]52[/C][C]2240[/C][C]2351.39467693441[/C][C]-111.394676934413[/C][/ROW]
[ROW][C]53[/C][C]2600[/C][C]2492.54376640139[/C][C]107.456233598614[/C][/ROW]
[ROW][C]54[/C][C]3060[/C][C]1909.87424396136[/C][C]1150.12575603864[/C][/ROW]
[ROW][C]55[/C][C]2040[/C][C]2213.24300468171[/C][C]-173.243004681714[/C][/ROW]
[ROW][C]56[/C][C]2230[/C][C]2204.96929150113[/C][C]25.0307084988735[/C][/ROW]
[ROW][C]57[/C][C]2720[/C][C]2912.77872928377[/C][C]-192.778729283769[/C][/ROW]
[ROW][C]58[/C][C]3740[/C][C]3871.46271136094[/C][C]-131.46271136094[/C][/ROW]
[ROW][C]59[/C][C]3100[/C][C]3724.01498287119[/C][C]-624.014982871187[/C][/ROW]
[ROW][C]60[/C][C]2100[/C][C]2699.38826760917[/C][C]-599.388267609166[/C][/ROW]
[ROW][C]61[/C][C]3630[/C][C]1807.92666967987[/C][C]1822.07333032013[/C][/ROW]
[ROW][C]62[/C][C]1620[/C][C]1616.59164992583[/C][C]3.40835007416899[/C][/ROW]
[ROW][C]63[/C][C]1870[/C][C]2012.68811090288[/C][C]-142.688110902883[/C][/ROW]
[ROW][C]64[/C][C]1680[/C][C]2271.33307106789[/C][C]-591.333071067887[/C][/ROW]
[ROW][C]65[/C][C]1830[/C][C]2463.78967061076[/C][C]-633.78967061076[/C][/ROW]
[ROW][C]66[/C][C]4620[/C][C]2112.68905786791[/C][C]2507.31094213209[/C][/ROW]
[ROW][C]67[/C][C]1560[/C][C]2134.39283092542[/C][C]-574.392830925422[/C][/ROW]
[ROW][C]68[/C][C]2800[/C][C]2175.01353211355[/C][C]624.986467886448[/C][/ROW]
[ROW][C]69[/C][C]1810[/C][C]2849.19113612367[/C][C]-1039.19113612367[/C][/ROW]
[ROW][C]70[/C][C]4260[/C][C]3820.1225311733[/C][C]439.877468826704[/C][/ROW]
[ROW][C]71[/C][C]2770[/C][C]3573.96145618001[/C][C]-803.961456180012[/C][/ROW]
[ROW][C]72[/C][C]3280[/C][C]2561.43773287977[/C][C]718.56226712023[/C][/ROW]
[ROW][C]73[/C][C]1830[/C][C]2251.14063163275[/C][C]-421.140631632749[/C][/ROW]
[ROW][C]74[/C][C]2590[/C][C]1627.8668559271[/C][C]962.133144072898[/C][/ROW]
[ROW][C]75[/C][C]1760[/C][C]2006.21364522628[/C][C]-246.21364522628[/C][/ROW]
[ROW][C]76[/C][C]2950[/C][C]2168.97213719539[/C][C]781.027862804611[/C][/ROW]
[ROW][C]77[/C][C]2020[/C][C]2380.42913548121[/C][C]-360.429135481208[/C][/ROW]
[ROW][C]78[/C][C]2530[/C][C]2768.65029634055[/C][C]-238.650296340548[/C][/ROW]
[ROW][C]79[/C][C]2530[/C][C]2064.26915588246[/C][C]465.730844117539[/C][/ROW]
[ROW][C]80[/C][C]2220[/C][C]2393.64679002436[/C][C]-173.646790024355[/C][/ROW]
[ROW][C]81[/C][C]2250[/C][C]2682.36461290789[/C][C]-432.364612907893[/C][/ROW]
[ROW][C]82[/C][C]2630[/C][C]4001.03684885105[/C][C]-1371.03684885105[/C][/ROW]
[ROW][C]83[/C][C]3550[/C][C]3448.12608054182[/C][C]101.873919458183[/C][/ROW]
[ROW][C]84[/C][C]2670[/C][C]2788.54743363598[/C][C]-118.547433635978[/C][/ROW]
[ROW][C]85[/C][C]2260[/C][C]2203.38468658428[/C][C]56.6153134157162[/C][/ROW]
[ROW][C]86[/C][C]2170[/C][C]1895.14097216178[/C][C]274.859027838215[/C][/ROW]
[ROW][C]87[/C][C]2430[/C][C]1982.48763978949[/C][C]447.512360210515[/C][/ROW]
[ROW][C]88[/C][C]1700[/C][C]2380.73143072067[/C][C]-680.731430720666[/C][/ROW]
[ROW][C]89[/C][C]2200[/C][C]2304.4558669751[/C][C]-104.455866975105[/C][/ROW]
[ROW][C]90[/C][C]3140[/C][C]2708.67429131818[/C][C]431.325708681818[/C][/ROW]
[ROW][C]91[/C][C]1900[/C][C]2161.72171563487[/C][C]-261.721715634867[/C][/ROW]
[ROW][C]92[/C][C]2260[/C][C]2325.23996159863[/C][C]-65.239961598626[/C][/ROW]
[ROW][C]93[/C][C]3580[/C][C]2542.34298589766[/C][C]1037.65701410234[/C][/ROW]
[ROW][C]94[/C][C]3050[/C][C]3656.21230727785[/C][C]-606.212307277851[/C][/ROW]
[ROW][C]95[/C][C]3130[/C][C]3449.4811051996[/C][C]-319.481105199596[/C][/ROW]
[ROW][C]96[/C][C]2350[/C][C]2737.0185224593[/C][C]-387.018522459297[/C][/ROW]
[ROW][C]97[/C][C]1650[/C][C]2188.37679862109[/C][C]-538.376798621095[/C][/ROW]
[ROW][C]98[/C][C]1760[/C][C]1919.31851582524[/C][C]-159.318515825243[/C][/ROW]
[ROW][C]99[/C][C]2010[/C][C]2033.31620129421[/C][C]-23.3162012942068[/C][/ROW]
[ROW][C]100[/C][C]1910[/C][C]2157.29231827045[/C][C]-247.292318270454[/C][/ROW]
[ROW][C]101[/C][C]1850[/C][C]2206.26692508334[/C][C]-356.266925083337[/C][/ROW]
[ROW][C]102[/C][C]2030[/C][C]2719.20037836369[/C][C]-689.200378363685[/C][/ROW]
[ROW][C]103[/C][C]2110[/C][C]1984.96655487883[/C][C]125.033445121173[/C][/ROW]
[ROW][C]104[/C][C]1900[/C][C]2179.00336072767[/C][C]-279.003360727675[/C][/ROW]
[ROW][C]105[/C][C]2170[/C][C]2627.20649170488[/C][C]-457.206491704877[/C][/ROW]
[ROW][C]106[/C][C]2690[/C][C]3323.54206022969[/C][C]-633.542060229687[/C][/ROW]
[ROW][C]107[/C][C]3620[/C][C]3151.20249589326[/C][C]468.797504106743[/C][/ROW]
[ROW][C]108[/C][C]1920[/C][C]2404.73837031119[/C][C]-484.738370311186[/C][/ROW]
[ROW][C]109[/C][C]1480[/C][C]1795.30622974858[/C][C]-315.30622974858[/C][/ROW]
[ROW][C]110[/C][C]3910[/C][C]1590.77324305764[/C][C]2319.22675694236[/C][/ROW]
[ROW][C]111[/C][C]2120[/C][C]1750.64587737495[/C][C]369.354122625052[/C][/ROW]
[ROW][C]112[/C][C]1980[/C][C]1825.14614058039[/C][C]154.853859419611[/C][/ROW]
[ROW][C]113[/C][C]2040[/C][C]1854.10032086823[/C][C]185.899679131773[/C][/ROW]
[ROW][C]114[/C][C]1820[/C][C]2301.19579903612[/C][C]-481.195799036122[/C][/ROW]
[ROW][C]115[/C][C]1700[/C][C]1762.01885673472[/C][C]-62.0188567347166[/C][/ROW]
[ROW][C]116[/C][C]2210[/C][C]1868.47522700642[/C][C]341.52477299358[/C][/ROW]
[ROW][C]117[/C][C]2070[/C][C]2291.76335561785[/C][C]-221.763355617851[/C][/ROW]
[ROW][C]118[/C][C]2650[/C][C]2962.44590963884[/C][C]-312.445909638835[/C][/ROW]
[ROW][C]119[/C][C]3260[/C][C]3059.51539646017[/C][C]200.484603539828[/C][/ROW]
[ROW][C]120[/C][C]1590[/C][C]2106.46925756398[/C][C]-516.469257563984[/C][/ROW]
[ROW][C]121[/C][C]1880[/C][C]1548.40125740367[/C][C]331.598742596329[/C][/ROW]
[ROW][C]122[/C][C]1390[/C][C]1968.2818813844[/C][C]-578.281881384396[/C][/ROW]
[ROW][C]123[/C][C]1890[/C][C]1655.91188325792[/C][C]234.088116742077[/C][/ROW]
[ROW][C]124[/C][C]1640[/C][C]1674.76213265862[/C][C]-34.7621326586193[/C][/ROW]
[ROW][C]125[/C][C]1840[/C][C]1702.22153618391[/C][C]137.778463816089[/C][/ROW]
[ROW][C]126[/C][C]1620[/C][C]1989.17638467265[/C][C]-369.176384672649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299974&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
1324102606.08707264957-196.087072649574
1419202107.43393383488-187.433933834884
1526202803.22306151304-183.223061513043
1628403024.28598857367-184.285988573672
1728803036.82340988849-156.823409888491
1823802465.43762710222-85.437627102217
1928202491.44250900018328.557490999819
2024802906.14174924428-426.141749244281
2132303049.5697076163180.430292383702
2238604456.62121438234-596.621214382336
2350504204.23437751587845.765622484128
2436303183.40131544421446.598684555786
2517002218.59103056928-518.591030569276
2625901715.22396370989874.776036290107
2721302424.32423020423-294.324230204228
2823502647.50056639912-297.500566399123
2926802667.765877262112.2341227378984
3022702117.64654503278152.35345496722
3128102245.51409454113564.485905458869
3222002497.10654133012-297.106541330119
3334202788.35233036381631.647669636188
3443004033.38443714795266.61556285205
3534404135.55633663387-695.55633663387
3626703018.18800064865-348.188000648649
3724601827.25477124821632.745228751787
3819201660.27928084989259.720719150115
3928902102.27888813861787.72111186139
4026002346.13694371174253.863056288259
4128602458.67653187993401.323468120071
4220101963.8763316722846.1236683277161
4324702204.47787117119265.522128828807
4422102274.21131444752-64.211314447522
4535302798.2506263973731.749373602695
4637903980.47507907201-190.475079072013
4735203875.63168271556-355.631682715562
4825102859.03753853839-349.037538538386
4918601910.85119132457-50.8511913245702
5017601666.9084708359893.0915291640245
5115402240.35362286981-700.353622869809
5222402351.39467693441-111.394676934413
5326002492.54376640139107.456233598614
5430601909.874243961361150.12575603864
5520402213.24300468171-173.243004681714
5622302204.9692915011325.0307084988735
5727202912.77872928377-192.778729283769
5837403871.46271136094-131.46271136094
5931003724.01498287119-624.014982871187
6021002699.38826760917-599.388267609166
6136301807.926669679871822.07333032013
6216201616.591649925833.40835007416899
6318702012.68811090288-142.688110902883
6416802271.33307106789-591.333071067887
6518302463.78967061076-633.78967061076
6646202112.689057867912507.31094213209
6715602134.39283092542-574.392830925422
6828002175.01353211355624.986467886448
6918102849.19113612367-1039.19113612367
7042603820.1225311733439.877468826704
7127703573.96145618001-803.961456180012
7232802561.43773287977718.56226712023
7318302251.14063163275-421.140631632749
7425901627.8668559271962.133144072898
7517602006.21364522628-246.21364522628
7629502168.97213719539781.027862804611
7720202380.42913548121-360.429135481208
7825302768.65029634055-238.650296340548
7925302064.26915588246465.730844117539
8022202393.64679002436-173.646790024355
8122502682.36461290789-432.364612907893
8226304001.03684885105-1371.03684885105
8335503448.12608054182101.873919458183
8426702788.54743363598-118.547433635978
8522602203.3846865842856.6153134157162
8621701895.14097216178274.859027838215
8724301982.48763978949447.512360210515
8817002380.73143072067-680.731430720666
8922002304.4558669751-104.455866975105
9031402708.67429131818431.325708681818
9119002161.72171563487-261.721715634867
9222602325.23996159863-65.239961598626
9335802542.342985897661037.65701410234
9430503656.21230727785-606.212307277851
9531303449.4811051996-319.481105199596
9623502737.0185224593-387.018522459297
9716502188.37679862109-538.376798621095
9817601919.31851582524-159.318515825243
9920102033.31620129421-23.3162012942068
10019102157.29231827045-247.292318270454
10118502206.26692508334-356.266925083337
10220302719.20037836369-689.200378363685
10321101984.96655487883125.033445121173
10419002179.00336072767-279.003360727675
10521702627.20649170488-457.206491704877
10626903323.54206022969-633.542060229687
10736203151.20249589326468.797504106743
10819202404.73837031119-484.738370311186
10914801795.30622974858-315.30622974858
11039101590.773243057642319.22675694236
11121201750.64587737495369.354122625052
11219801825.14614058039154.853859419611
11320401854.10032086823185.899679131773
11418202301.19579903612-481.195799036122
11517001762.01885673472-62.0188567347166
11622101868.47522700642341.52477299358
11720702291.76335561785-221.763355617851
11826502962.44590963884-312.445909638835
11932603059.51539646017200.484603539828
12015902106.46925756398-516.469257563984
12118801548.40125740367331.598742596329
12213901968.2818813844-578.281881384396
12318901655.91188325792234.088116742077
12416401674.76213265862-34.7621326586193
12518401702.22153618391137.778463816089
12616201989.17638467265-369.176384672649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1271539.95178088407385.7589915110942694.14457025705
1281732.88521437644578.5526799867192887.21774876616
1292016.14383948911861.4969406502843170.79073832794
1302660.792122234841505.586564492773815.99767997691
1312872.757402275651716.679480453014028.83532409829
1321748.29687078696590.963899894032905.6298416799
1331385.67628248022226.6372341028532544.71533085759
1341590.51927400845429.2556544010332751.78289361587
1351467.84787265154303.7748750901862631.92087021289
1361421.43236720646253.9003263605632588.96440805236
1371486.74951306561315.0456831966162658.45334293461
1381654.03167212974477.3823438716892830.6810003878

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 1539.95178088407 & 385.758991511094 & 2694.14457025705 \tabularnewline
128 & 1732.88521437644 & 578.552679986719 & 2887.21774876616 \tabularnewline
129 & 2016.14383948911 & 861.496940650284 & 3170.79073832794 \tabularnewline
130 & 2660.79212223484 & 1505.58656449277 & 3815.99767997691 \tabularnewline
131 & 2872.75740227565 & 1716.67948045301 & 4028.83532409829 \tabularnewline
132 & 1748.29687078696 & 590.96389989403 & 2905.6298416799 \tabularnewline
133 & 1385.67628248022 & 226.637234102853 & 2544.71533085759 \tabularnewline
134 & 1590.51927400845 & 429.255654401033 & 2751.78289361587 \tabularnewline
135 & 1467.84787265154 & 303.774875090186 & 2631.92087021289 \tabularnewline
136 & 1421.43236720646 & 253.900326360563 & 2588.96440805236 \tabularnewline
137 & 1486.74951306561 & 315.045683196616 & 2658.45334293461 \tabularnewline
138 & 1654.03167212974 & 477.382343871689 & 2830.6810003878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299974&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]127[/C][C]1539.95178088407[/C][C]385.758991511094[/C][C]2694.14457025705[/C][/ROW]
[ROW][C]128[/C][C]1732.88521437644[/C][C]578.552679986719[/C][C]2887.21774876616[/C][/ROW]
[ROW][C]129[/C][C]2016.14383948911[/C][C]861.496940650284[/C][C]3170.79073832794[/C][/ROW]
[ROW][C]130[/C][C]2660.79212223484[/C][C]1505.58656449277[/C][C]3815.99767997691[/C][/ROW]
[ROW][C]131[/C][C]2872.75740227565[/C][C]1716.67948045301[/C][C]4028.83532409829[/C][/ROW]
[ROW][C]132[/C][C]1748.29687078696[/C][C]590.96389989403[/C][C]2905.6298416799[/C][/ROW]
[ROW][C]133[/C][C]1385.67628248022[/C][C]226.637234102853[/C][C]2544.71533085759[/C][/ROW]
[ROW][C]134[/C][C]1590.51927400845[/C][C]429.255654401033[/C][C]2751.78289361587[/C][/ROW]
[ROW][C]135[/C][C]1467.84787265154[/C][C]303.774875090186[/C][C]2631.92087021289[/C][/ROW]
[ROW][C]136[/C][C]1421.43236720646[/C][C]253.900326360563[/C][C]2588.96440805236[/C][/ROW]
[ROW][C]137[/C][C]1486.74951306561[/C][C]315.045683196616[/C][C]2658.45334293461[/C][/ROW]
[ROW][C]138[/C][C]1654.03167212974[/C][C]477.382343871689[/C][C]2830.6810003878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299974&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299974&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
1271539.95178088407385.7589915110942694.14457025705
1281732.88521437644578.5526799867192887.21774876616
1292016.14383948911861.4969406502843170.79073832794
1302660.792122234841505.586564492773815.99767997691
1312872.757402275651716.679480453014028.83532409829
1321748.29687078696590.963899894032905.6298416799
1331385.67628248022226.6372341028532544.71533085759
1341590.51927400845429.2556544010332751.78289361587
1351467.84787265154303.7748750901862631.92087021289
1361421.43236720646253.9003263605632588.96440805236
1371486.74951306561315.0456831966162658.45334293461
1381654.03167212974477.3823438716892830.6810003878



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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')