Free Statistics

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 computationSun, 18 Dec 2016 14:29:07 +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/18/t14820677643px9gd1d4ni1zqx.htm/, Retrieved Thu, 09 May 2024 02:10:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301071, Retrieved Thu, 09 May 2024 02:10:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- R  D    [Exponential Smoothing] [] [2016-12-18 13:29:07] [404ac5ee4f7301873f6a96ef36861981] [Current]
- R P       [Exponential Smoothing] [] [2016-12-20 23:20:29] [683f400e1b95307fc738e729f07c4fce]
- RMP       [ARIMA Backward Selection] [] [2016-12-20 23:27:16] [683f400e1b95307fc738e729f07c4fce]
- RMP       [ARIMA Forecasting] [] [2016-12-20 23:32:48] [683f400e1b95307fc738e729f07c4fce]
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Dataseries X:
2280
3640
3950
3860
3500
4740
3690
4810
6150
4530
4760
4670
3510
2990
3240
2700
2610
3280
3170
3440
4710
4320
3650
3340
3050
2960
2810
2670
2440
2580
2520
2860
3500
3460
3310
3050
2730
2760
2800
2490
2310
2350
2370
2560
2740
2830
3010
2500
2630
2270
2410
2210
2330
2690
3150
2330
2260
2330
2240
2230
2270
2220
2290
2240
2110
2240
2230
2320
2320
2540
2530
2400
2470
2290
2110
2050
2170
2070
2330
2190
2260
2300
2220
2220
2380
2280
2150
2190
2080
2120
2140
2130
2210
2210
2190
2160
2290
2270
2200
2120
2050
2080
2180
2070
2170
2240
2320
2250




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=301071&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=301071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301071&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
alpha0.816731721690792
beta0.0620122241103173
gamma0.82293034264525

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.816731721690792 \tabularnewline
beta & 0.0620122241103173 \tabularnewline
gamma & 0.82293034264525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301071&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]0.816731721690792[/C][/ROW]
[ROW][C]beta[/C][C]0.0620122241103173[/C][/ROW]
[ROW][C]gamma[/C][C]0.82293034264525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301071&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
alpha0.816731721690792
beta0.0620122241103173
gamma0.82293034264525







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
438603446.11111111111413.88888888889
535003841.77633823858-341.776338238579
647404009.62240404196730.377595958042
736904884.21044700963-1194.21044700963
848103811.72078083997998.279219160033
961505262.80009067338887.199909326618
1045306010.22017191721-1480.22017191721
1147605055.32735646828-295.327356468284
1246705388.13203603603-718.132036036026
1335104341.08107209913-831.081072099131
1429904001.6416755388-1011.6416755388
1532403555.9430732478-315.943073247797
1627002711.00725092524-11.0072509252377
1726102946.32040655908-336.32040655908
1832803123.50839668921156.491603310794
1931702700.74913477121469.250865228793
2034403293.90002610361146.099973896388
2147103978.5122611342731.4877388658
2243204140.75381065506179.246189344942
2336504501.83786415771-851.837864157712
2433404462.6719825698-1122.6719825698
2530502936.34969398298113.650306017019
2629602994.1068716482-34.1068716482027
2728103529.1297376223-719.129737622299
2826702486.45830186879183.541698131206
2924402550.16016040511-110.160160405107
3025802887.04934533888-307.049345338881
3125202305.2406048393214.759395160699
3228602339.89014394749520.109856052509
3335003183.51454777067316.485452229328
3434603242.91242919361217.087570806392
3533103378.88175808987-68.8817580898681
3630503734.28338101012-684.283381010118
3727302934.17980874356-204.179808743559
3827602634.47067624829125.529323751711
3928003017.20037456881-217.200374568808
4024902656.00204157942-166.002041579421
4123102424.14919430816-114.149194308158
4223502534.24682836565-184.246828365654
4323702184.16375071349185.836249286513
4425602241.78783446612318.212165533882
4527402710.6338926270729.3661073729318
4628302617.84613759585212.153862404148
4730102745.27814264302264.721857356978
4825003152.51387283036-652.513872830362
4926302521.4850062681108.514993731902
5022702558.05536716358-288.055367163583
5124102333.3442940138676.6557059861402
5222102407.41662830879-197.416628308793
5323302113.6079040333216.392095966703
5426902360.743181315329.256818685
5531502617.42512531029532.574874689708
5623303036.84219791188-706.842197911876
5722602554.8144700814-294.8144700814
5823302308.7036706715921.2963293284142
5922402073.96548472239166.034515277608
6022302361.54089379942-131.540893799415
6122702299.28130763955-29.281307639551
6222202045.32773396433174.672266035669
6322902295.77989864183-5.77989864182882
6422402358.72672363801-118.726723638013
6521102065.0206699435444.9793300564561
6622402178.305394074961.6946059251027
6722302278.7160412322-48.7160412322046
6823202069.81500685982250.184993140185
6923202366.54719068443-46.5471906844327
7025402369.74790012794170.252099872056
7125302403.70099098111126.299009018885
7224002567.1613319897-167.161331989703
7324702511.10292000629-41.1029200062862
7422902361.65546469835-71.6554646983504
7521102305.00409935802-195.004099358016
7620502229.6300165565-179.630016556502
7721701939.83185838042230.168141619581
7820702103.76951345854-33.7695134585424
7923302163.24879080718166.751209192819
8021902236.54828453108-46.5482845310753
8122602139.05418726727120.945812732733
8223002367.34986324402-67.3498632440242
8322202217.639335066772.3606649332296
8422202188.1857443722731.8142556277303
8523802313.6064332456766.3935667543255
8622802288.73546896333-8.73546896332664
8721502259.19295436165-109.192954361654
8821902272.05362680471-82.0536268047094
8920802104.4818317342-24.4818317342033
9021202036.0019913074283.9980086925784
9121402209.59946219637-69.5994621963696
9221302060.371493721769.6285062782981
9322102089.37090631711120.629093682886
9422102275.83204739514-65.8320473951371
9521902156.9808189669233.0191810330784
9621602168.21965054608-8.21965054607699
9722902219.246231683470.753768316602
9822702231.6969414952438.3030585047559
9922002246.13890125729-46.1389012572909
10021202281.29278995882-161.292789958817
10120502090.76367798673-40.7636779867289
10220802015.3236027225164.6763972774934
10321802116.6587572375363.3412427624744
10420702132.19240990682-62.1924099068228
10521702058.48684171919111.513158280812
10622402203.5797320125136.4202679874907
10723202182.53611362538137.463886374624
10822502312.5485511681-62.5485511680954

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
4 & 3860 & 3446.11111111111 & 413.88888888889 \tabularnewline
5 & 3500 & 3841.77633823858 & -341.776338238579 \tabularnewline
6 & 4740 & 4009.62240404196 & 730.377595958042 \tabularnewline
7 & 3690 & 4884.21044700963 & -1194.21044700963 \tabularnewline
8 & 4810 & 3811.72078083997 & 998.279219160033 \tabularnewline
9 & 6150 & 5262.80009067338 & 887.199909326618 \tabularnewline
10 & 4530 & 6010.22017191721 & -1480.22017191721 \tabularnewline
11 & 4760 & 5055.32735646828 & -295.327356468284 \tabularnewline
12 & 4670 & 5388.13203603603 & -718.132036036026 \tabularnewline
13 & 3510 & 4341.08107209913 & -831.081072099131 \tabularnewline
14 & 2990 & 4001.6416755388 & -1011.6416755388 \tabularnewline
15 & 3240 & 3555.9430732478 & -315.943073247797 \tabularnewline
16 & 2700 & 2711.00725092524 & -11.0072509252377 \tabularnewline
17 & 2610 & 2946.32040655908 & -336.32040655908 \tabularnewline
18 & 3280 & 3123.50839668921 & 156.491603310794 \tabularnewline
19 & 3170 & 2700.74913477121 & 469.250865228793 \tabularnewline
20 & 3440 & 3293.90002610361 & 146.099973896388 \tabularnewline
21 & 4710 & 3978.5122611342 & 731.4877388658 \tabularnewline
22 & 4320 & 4140.75381065506 & 179.246189344942 \tabularnewline
23 & 3650 & 4501.83786415771 & -851.837864157712 \tabularnewline
24 & 3340 & 4462.6719825698 & -1122.6719825698 \tabularnewline
25 & 3050 & 2936.34969398298 & 113.650306017019 \tabularnewline
26 & 2960 & 2994.1068716482 & -34.1068716482027 \tabularnewline
27 & 2810 & 3529.1297376223 & -719.129737622299 \tabularnewline
28 & 2670 & 2486.45830186879 & 183.541698131206 \tabularnewline
29 & 2440 & 2550.16016040511 & -110.160160405107 \tabularnewline
30 & 2580 & 2887.04934533888 & -307.049345338881 \tabularnewline
31 & 2520 & 2305.2406048393 & 214.759395160699 \tabularnewline
32 & 2860 & 2339.89014394749 & 520.109856052509 \tabularnewline
33 & 3500 & 3183.51454777067 & 316.485452229328 \tabularnewline
34 & 3460 & 3242.91242919361 & 217.087570806392 \tabularnewline
35 & 3310 & 3378.88175808987 & -68.8817580898681 \tabularnewline
36 & 3050 & 3734.28338101012 & -684.283381010118 \tabularnewline
37 & 2730 & 2934.17980874356 & -204.179808743559 \tabularnewline
38 & 2760 & 2634.47067624829 & 125.529323751711 \tabularnewline
39 & 2800 & 3017.20037456881 & -217.200374568808 \tabularnewline
40 & 2490 & 2656.00204157942 & -166.002041579421 \tabularnewline
41 & 2310 & 2424.14919430816 & -114.149194308158 \tabularnewline
42 & 2350 & 2534.24682836565 & -184.246828365654 \tabularnewline
43 & 2370 & 2184.16375071349 & 185.836249286513 \tabularnewline
44 & 2560 & 2241.78783446612 & 318.212165533882 \tabularnewline
45 & 2740 & 2710.63389262707 & 29.3661073729318 \tabularnewline
46 & 2830 & 2617.84613759585 & 212.153862404148 \tabularnewline
47 & 3010 & 2745.27814264302 & 264.721857356978 \tabularnewline
48 & 2500 & 3152.51387283036 & -652.513872830362 \tabularnewline
49 & 2630 & 2521.4850062681 & 108.514993731902 \tabularnewline
50 & 2270 & 2558.05536716358 & -288.055367163583 \tabularnewline
51 & 2410 & 2333.34429401386 & 76.6557059861402 \tabularnewline
52 & 2210 & 2407.41662830879 & -197.416628308793 \tabularnewline
53 & 2330 & 2113.6079040333 & 216.392095966703 \tabularnewline
54 & 2690 & 2360.743181315 & 329.256818685 \tabularnewline
55 & 3150 & 2617.42512531029 & 532.574874689708 \tabularnewline
56 & 2330 & 3036.84219791188 & -706.842197911876 \tabularnewline
57 & 2260 & 2554.8144700814 & -294.8144700814 \tabularnewline
58 & 2330 & 2308.70367067159 & 21.2963293284142 \tabularnewline
59 & 2240 & 2073.96548472239 & 166.034515277608 \tabularnewline
60 & 2230 & 2361.54089379942 & -131.540893799415 \tabularnewline
61 & 2270 & 2299.28130763955 & -29.281307639551 \tabularnewline
62 & 2220 & 2045.32773396433 & 174.672266035669 \tabularnewline
63 & 2290 & 2295.77989864183 & -5.77989864182882 \tabularnewline
64 & 2240 & 2358.72672363801 & -118.726723638013 \tabularnewline
65 & 2110 & 2065.02066994354 & 44.9793300564561 \tabularnewline
66 & 2240 & 2178.3053940749 & 61.6946059251027 \tabularnewline
67 & 2230 & 2278.7160412322 & -48.7160412322046 \tabularnewline
68 & 2320 & 2069.81500685982 & 250.184993140185 \tabularnewline
69 & 2320 & 2366.54719068443 & -46.5471906844327 \tabularnewline
70 & 2540 & 2369.74790012794 & 170.252099872056 \tabularnewline
71 & 2530 & 2403.70099098111 & 126.299009018885 \tabularnewline
72 & 2400 & 2567.1613319897 & -167.161331989703 \tabularnewline
73 & 2470 & 2511.10292000629 & -41.1029200062862 \tabularnewline
74 & 2290 & 2361.65546469835 & -71.6554646983504 \tabularnewline
75 & 2110 & 2305.00409935802 & -195.004099358016 \tabularnewline
76 & 2050 & 2229.6300165565 & -179.630016556502 \tabularnewline
77 & 2170 & 1939.83185838042 & 230.168141619581 \tabularnewline
78 & 2070 & 2103.76951345854 & -33.7695134585424 \tabularnewline
79 & 2330 & 2163.24879080718 & 166.751209192819 \tabularnewline
80 & 2190 & 2236.54828453108 & -46.5482845310753 \tabularnewline
81 & 2260 & 2139.05418726727 & 120.945812732733 \tabularnewline
82 & 2300 & 2367.34986324402 & -67.3498632440242 \tabularnewline
83 & 2220 & 2217.63933506677 & 2.3606649332296 \tabularnewline
84 & 2220 & 2188.18574437227 & 31.8142556277303 \tabularnewline
85 & 2380 & 2313.60643324567 & 66.3935667543255 \tabularnewline
86 & 2280 & 2288.73546896333 & -8.73546896332664 \tabularnewline
87 & 2150 & 2259.19295436165 & -109.192954361654 \tabularnewline
88 & 2190 & 2272.05362680471 & -82.0536268047094 \tabularnewline
89 & 2080 & 2104.4818317342 & -24.4818317342033 \tabularnewline
90 & 2120 & 2036.00199130742 & 83.9980086925784 \tabularnewline
91 & 2140 & 2209.59946219637 & -69.5994621963696 \tabularnewline
92 & 2130 & 2060.3714937217 & 69.6285062782981 \tabularnewline
93 & 2210 & 2089.37090631711 & 120.629093682886 \tabularnewline
94 & 2210 & 2275.83204739514 & -65.8320473951371 \tabularnewline
95 & 2190 & 2156.98081896692 & 33.0191810330784 \tabularnewline
96 & 2160 & 2168.21965054608 & -8.21965054607699 \tabularnewline
97 & 2290 & 2219.2462316834 & 70.753768316602 \tabularnewline
98 & 2270 & 2231.69694149524 & 38.3030585047559 \tabularnewline
99 & 2200 & 2246.13890125729 & -46.1389012572909 \tabularnewline
100 & 2120 & 2281.29278995882 & -161.292789958817 \tabularnewline
101 & 2050 & 2090.76367798673 & -40.7636779867289 \tabularnewline
102 & 2080 & 2015.32360272251 & 64.6763972774934 \tabularnewline
103 & 2180 & 2116.65875723753 & 63.3412427624744 \tabularnewline
104 & 2070 & 2132.19240990682 & -62.1924099068228 \tabularnewline
105 & 2170 & 2058.48684171919 & 111.513158280812 \tabularnewline
106 & 2240 & 2203.57973201251 & 36.4202679874907 \tabularnewline
107 & 2320 & 2182.53611362538 & 137.463886374624 \tabularnewline
108 & 2250 & 2312.5485511681 & -62.5485511680954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301071&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]4[/C][C]3860[/C][C]3446.11111111111[/C][C]413.88888888889[/C][/ROW]
[ROW][C]5[/C][C]3500[/C][C]3841.77633823858[/C][C]-341.776338238579[/C][/ROW]
[ROW][C]6[/C][C]4740[/C][C]4009.62240404196[/C][C]730.377595958042[/C][/ROW]
[ROW][C]7[/C][C]3690[/C][C]4884.21044700963[/C][C]-1194.21044700963[/C][/ROW]
[ROW][C]8[/C][C]4810[/C][C]3811.72078083997[/C][C]998.279219160033[/C][/ROW]
[ROW][C]9[/C][C]6150[/C][C]5262.80009067338[/C][C]887.199909326618[/C][/ROW]
[ROW][C]10[/C][C]4530[/C][C]6010.22017191721[/C][C]-1480.22017191721[/C][/ROW]
[ROW][C]11[/C][C]4760[/C][C]5055.32735646828[/C][C]-295.327356468284[/C][/ROW]
[ROW][C]12[/C][C]4670[/C][C]5388.13203603603[/C][C]-718.132036036026[/C][/ROW]
[ROW][C]13[/C][C]3510[/C][C]4341.08107209913[/C][C]-831.081072099131[/C][/ROW]
[ROW][C]14[/C][C]2990[/C][C]4001.6416755388[/C][C]-1011.6416755388[/C][/ROW]
[ROW][C]15[/C][C]3240[/C][C]3555.9430732478[/C][C]-315.943073247797[/C][/ROW]
[ROW][C]16[/C][C]2700[/C][C]2711.00725092524[/C][C]-11.0072509252377[/C][/ROW]
[ROW][C]17[/C][C]2610[/C][C]2946.32040655908[/C][C]-336.32040655908[/C][/ROW]
[ROW][C]18[/C][C]3280[/C][C]3123.50839668921[/C][C]156.491603310794[/C][/ROW]
[ROW][C]19[/C][C]3170[/C][C]2700.74913477121[/C][C]469.250865228793[/C][/ROW]
[ROW][C]20[/C][C]3440[/C][C]3293.90002610361[/C][C]146.099973896388[/C][/ROW]
[ROW][C]21[/C][C]4710[/C][C]3978.5122611342[/C][C]731.4877388658[/C][/ROW]
[ROW][C]22[/C][C]4320[/C][C]4140.75381065506[/C][C]179.246189344942[/C][/ROW]
[ROW][C]23[/C][C]3650[/C][C]4501.83786415771[/C][C]-851.837864157712[/C][/ROW]
[ROW][C]24[/C][C]3340[/C][C]4462.6719825698[/C][C]-1122.6719825698[/C][/ROW]
[ROW][C]25[/C][C]3050[/C][C]2936.34969398298[/C][C]113.650306017019[/C][/ROW]
[ROW][C]26[/C][C]2960[/C][C]2994.1068716482[/C][C]-34.1068716482027[/C][/ROW]
[ROW][C]27[/C][C]2810[/C][C]3529.1297376223[/C][C]-719.129737622299[/C][/ROW]
[ROW][C]28[/C][C]2670[/C][C]2486.45830186879[/C][C]183.541698131206[/C][/ROW]
[ROW][C]29[/C][C]2440[/C][C]2550.16016040511[/C][C]-110.160160405107[/C][/ROW]
[ROW][C]30[/C][C]2580[/C][C]2887.04934533888[/C][C]-307.049345338881[/C][/ROW]
[ROW][C]31[/C][C]2520[/C][C]2305.2406048393[/C][C]214.759395160699[/C][/ROW]
[ROW][C]32[/C][C]2860[/C][C]2339.89014394749[/C][C]520.109856052509[/C][/ROW]
[ROW][C]33[/C][C]3500[/C][C]3183.51454777067[/C][C]316.485452229328[/C][/ROW]
[ROW][C]34[/C][C]3460[/C][C]3242.91242919361[/C][C]217.087570806392[/C][/ROW]
[ROW][C]35[/C][C]3310[/C][C]3378.88175808987[/C][C]-68.8817580898681[/C][/ROW]
[ROW][C]36[/C][C]3050[/C][C]3734.28338101012[/C][C]-684.283381010118[/C][/ROW]
[ROW][C]37[/C][C]2730[/C][C]2934.17980874356[/C][C]-204.179808743559[/C][/ROW]
[ROW][C]38[/C][C]2760[/C][C]2634.47067624829[/C][C]125.529323751711[/C][/ROW]
[ROW][C]39[/C][C]2800[/C][C]3017.20037456881[/C][C]-217.200374568808[/C][/ROW]
[ROW][C]40[/C][C]2490[/C][C]2656.00204157942[/C][C]-166.002041579421[/C][/ROW]
[ROW][C]41[/C][C]2310[/C][C]2424.14919430816[/C][C]-114.149194308158[/C][/ROW]
[ROW][C]42[/C][C]2350[/C][C]2534.24682836565[/C][C]-184.246828365654[/C][/ROW]
[ROW][C]43[/C][C]2370[/C][C]2184.16375071349[/C][C]185.836249286513[/C][/ROW]
[ROW][C]44[/C][C]2560[/C][C]2241.78783446612[/C][C]318.212165533882[/C][/ROW]
[ROW][C]45[/C][C]2740[/C][C]2710.63389262707[/C][C]29.3661073729318[/C][/ROW]
[ROW][C]46[/C][C]2830[/C][C]2617.84613759585[/C][C]212.153862404148[/C][/ROW]
[ROW][C]47[/C][C]3010[/C][C]2745.27814264302[/C][C]264.721857356978[/C][/ROW]
[ROW][C]48[/C][C]2500[/C][C]3152.51387283036[/C][C]-652.513872830362[/C][/ROW]
[ROW][C]49[/C][C]2630[/C][C]2521.4850062681[/C][C]108.514993731902[/C][/ROW]
[ROW][C]50[/C][C]2270[/C][C]2558.05536716358[/C][C]-288.055367163583[/C][/ROW]
[ROW][C]51[/C][C]2410[/C][C]2333.34429401386[/C][C]76.6557059861402[/C][/ROW]
[ROW][C]52[/C][C]2210[/C][C]2407.41662830879[/C][C]-197.416628308793[/C][/ROW]
[ROW][C]53[/C][C]2330[/C][C]2113.6079040333[/C][C]216.392095966703[/C][/ROW]
[ROW][C]54[/C][C]2690[/C][C]2360.743181315[/C][C]329.256818685[/C][/ROW]
[ROW][C]55[/C][C]3150[/C][C]2617.42512531029[/C][C]532.574874689708[/C][/ROW]
[ROW][C]56[/C][C]2330[/C][C]3036.84219791188[/C][C]-706.842197911876[/C][/ROW]
[ROW][C]57[/C][C]2260[/C][C]2554.8144700814[/C][C]-294.8144700814[/C][/ROW]
[ROW][C]58[/C][C]2330[/C][C]2308.70367067159[/C][C]21.2963293284142[/C][/ROW]
[ROW][C]59[/C][C]2240[/C][C]2073.96548472239[/C][C]166.034515277608[/C][/ROW]
[ROW][C]60[/C][C]2230[/C][C]2361.54089379942[/C][C]-131.540893799415[/C][/ROW]
[ROW][C]61[/C][C]2270[/C][C]2299.28130763955[/C][C]-29.281307639551[/C][/ROW]
[ROW][C]62[/C][C]2220[/C][C]2045.32773396433[/C][C]174.672266035669[/C][/ROW]
[ROW][C]63[/C][C]2290[/C][C]2295.77989864183[/C][C]-5.77989864182882[/C][/ROW]
[ROW][C]64[/C][C]2240[/C][C]2358.72672363801[/C][C]-118.726723638013[/C][/ROW]
[ROW][C]65[/C][C]2110[/C][C]2065.02066994354[/C][C]44.9793300564561[/C][/ROW]
[ROW][C]66[/C][C]2240[/C][C]2178.3053940749[/C][C]61.6946059251027[/C][/ROW]
[ROW][C]67[/C][C]2230[/C][C]2278.7160412322[/C][C]-48.7160412322046[/C][/ROW]
[ROW][C]68[/C][C]2320[/C][C]2069.81500685982[/C][C]250.184993140185[/C][/ROW]
[ROW][C]69[/C][C]2320[/C][C]2366.54719068443[/C][C]-46.5471906844327[/C][/ROW]
[ROW][C]70[/C][C]2540[/C][C]2369.74790012794[/C][C]170.252099872056[/C][/ROW]
[ROW][C]71[/C][C]2530[/C][C]2403.70099098111[/C][C]126.299009018885[/C][/ROW]
[ROW][C]72[/C][C]2400[/C][C]2567.1613319897[/C][C]-167.161331989703[/C][/ROW]
[ROW][C]73[/C][C]2470[/C][C]2511.10292000629[/C][C]-41.1029200062862[/C][/ROW]
[ROW][C]74[/C][C]2290[/C][C]2361.65546469835[/C][C]-71.6554646983504[/C][/ROW]
[ROW][C]75[/C][C]2110[/C][C]2305.00409935802[/C][C]-195.004099358016[/C][/ROW]
[ROW][C]76[/C][C]2050[/C][C]2229.6300165565[/C][C]-179.630016556502[/C][/ROW]
[ROW][C]77[/C][C]2170[/C][C]1939.83185838042[/C][C]230.168141619581[/C][/ROW]
[ROW][C]78[/C][C]2070[/C][C]2103.76951345854[/C][C]-33.7695134585424[/C][/ROW]
[ROW][C]79[/C][C]2330[/C][C]2163.24879080718[/C][C]166.751209192819[/C][/ROW]
[ROW][C]80[/C][C]2190[/C][C]2236.54828453108[/C][C]-46.5482845310753[/C][/ROW]
[ROW][C]81[/C][C]2260[/C][C]2139.05418726727[/C][C]120.945812732733[/C][/ROW]
[ROW][C]82[/C][C]2300[/C][C]2367.34986324402[/C][C]-67.3498632440242[/C][/ROW]
[ROW][C]83[/C][C]2220[/C][C]2217.63933506677[/C][C]2.3606649332296[/C][/ROW]
[ROW][C]84[/C][C]2220[/C][C]2188.18574437227[/C][C]31.8142556277303[/C][/ROW]
[ROW][C]85[/C][C]2380[/C][C]2313.60643324567[/C][C]66.3935667543255[/C][/ROW]
[ROW][C]86[/C][C]2280[/C][C]2288.73546896333[/C][C]-8.73546896332664[/C][/ROW]
[ROW][C]87[/C][C]2150[/C][C]2259.19295436165[/C][C]-109.192954361654[/C][/ROW]
[ROW][C]88[/C][C]2190[/C][C]2272.05362680471[/C][C]-82.0536268047094[/C][/ROW]
[ROW][C]89[/C][C]2080[/C][C]2104.4818317342[/C][C]-24.4818317342033[/C][/ROW]
[ROW][C]90[/C][C]2120[/C][C]2036.00199130742[/C][C]83.9980086925784[/C][/ROW]
[ROW][C]91[/C][C]2140[/C][C]2209.59946219637[/C][C]-69.5994621963696[/C][/ROW]
[ROW][C]92[/C][C]2130[/C][C]2060.3714937217[/C][C]69.6285062782981[/C][/ROW]
[ROW][C]93[/C][C]2210[/C][C]2089.37090631711[/C][C]120.629093682886[/C][/ROW]
[ROW][C]94[/C][C]2210[/C][C]2275.83204739514[/C][C]-65.8320473951371[/C][/ROW]
[ROW][C]95[/C][C]2190[/C][C]2156.98081896692[/C][C]33.0191810330784[/C][/ROW]
[ROW][C]96[/C][C]2160[/C][C]2168.21965054608[/C][C]-8.21965054607699[/C][/ROW]
[ROW][C]97[/C][C]2290[/C][C]2219.2462316834[/C][C]70.753768316602[/C][/ROW]
[ROW][C]98[/C][C]2270[/C][C]2231.69694149524[/C][C]38.3030585047559[/C][/ROW]
[ROW][C]99[/C][C]2200[/C][C]2246.13890125729[/C][C]-46.1389012572909[/C][/ROW]
[ROW][C]100[/C][C]2120[/C][C]2281.29278995882[/C][C]-161.292789958817[/C][/ROW]
[ROW][C]101[/C][C]2050[/C][C]2090.76367798673[/C][C]-40.7636779867289[/C][/ROW]
[ROW][C]102[/C][C]2080[/C][C]2015.32360272251[/C][C]64.6763972774934[/C][/ROW]
[ROW][C]103[/C][C]2180[/C][C]2116.65875723753[/C][C]63.3412427624744[/C][/ROW]
[ROW][C]104[/C][C]2070[/C][C]2132.19240990682[/C][C]-62.1924099068228[/C][/ROW]
[ROW][C]105[/C][C]2170[/C][C]2058.48684171919[/C][C]111.513158280812[/C][/ROW]
[ROW][C]106[/C][C]2240[/C][C]2203.57973201251[/C][C]36.4202679874907[/C][/ROW]
[ROW][C]107[/C][C]2320[/C][C]2182.53611362538[/C][C]137.463886374624[/C][/ROW]
[ROW][C]108[/C][C]2250[/C][C]2312.5485511681[/C][C]-62.5485511680954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301071&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301071&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
438603446.11111111111413.88888888889
535003841.77633823858-341.776338238579
647404009.62240404196730.377595958042
736904884.21044700963-1194.21044700963
848103811.72078083997998.279219160033
961505262.80009067338887.199909326618
1045306010.22017191721-1480.22017191721
1147605055.32735646828-295.327356468284
1246705388.13203603603-718.132036036026
1335104341.08107209913-831.081072099131
1429904001.6416755388-1011.6416755388
1532403555.9430732478-315.943073247797
1627002711.00725092524-11.0072509252377
1726102946.32040655908-336.32040655908
1832803123.50839668921156.491603310794
1931702700.74913477121469.250865228793
2034403293.90002610361146.099973896388
2147103978.5122611342731.4877388658
2243204140.75381065506179.246189344942
2336504501.83786415771-851.837864157712
2433404462.6719825698-1122.6719825698
2530502936.34969398298113.650306017019
2629602994.1068716482-34.1068716482027
2728103529.1297376223-719.129737622299
2826702486.45830186879183.541698131206
2924402550.16016040511-110.160160405107
3025802887.04934533888-307.049345338881
3125202305.2406048393214.759395160699
3228602339.89014394749520.109856052509
3335003183.51454777067316.485452229328
3434603242.91242919361217.087570806392
3533103378.88175808987-68.8817580898681
3630503734.28338101012-684.283381010118
3727302934.17980874356-204.179808743559
3827602634.47067624829125.529323751711
3928003017.20037456881-217.200374568808
4024902656.00204157942-166.002041579421
4123102424.14919430816-114.149194308158
4223502534.24682836565-184.246828365654
4323702184.16375071349185.836249286513
4425602241.78783446612318.212165533882
4527402710.6338926270729.3661073729318
4628302617.84613759585212.153862404148
4730102745.27814264302264.721857356978
4825003152.51387283036-652.513872830362
4926302521.4850062681108.514993731902
5022702558.05536716358-288.055367163583
5124102333.3442940138676.6557059861402
5222102407.41662830879-197.416628308793
5323302113.6079040333216.392095966703
5426902360.743181315329.256818685
5531502617.42512531029532.574874689708
5623303036.84219791188-706.842197911876
5722602554.8144700814-294.8144700814
5823302308.7036706715921.2963293284142
5922402073.96548472239166.034515277608
6022302361.54089379942-131.540893799415
6122702299.28130763955-29.281307639551
6222202045.32773396433174.672266035669
6322902295.77989864183-5.77989864182882
6422402358.72672363801-118.726723638013
6521102065.0206699435444.9793300564561
6622402178.305394074961.6946059251027
6722302278.7160412322-48.7160412322046
6823202069.81500685982250.184993140185
6923202366.54719068443-46.5471906844327
7025402369.74790012794170.252099872056
7125302403.70099098111126.299009018885
7224002567.1613319897-167.161331989703
7324702511.10292000629-41.1029200062862
7422902361.65546469835-71.6554646983504
7521102305.00409935802-195.004099358016
7620502229.6300165565-179.630016556502
7721701939.83185838042230.168141619581
7820702103.76951345854-33.7695134585424
7923302163.24879080718166.751209192819
8021902236.54828453108-46.5482845310753
8122602139.05418726727120.945812732733
8223002367.34986324402-67.3498632440242
8322202217.639335066772.3606649332296
8422202188.1857443722731.8142556277303
8523802313.6064332456766.3935667543255
8622802288.73546896333-8.73546896332664
8721502259.19295436165-109.192954361654
8821902272.05362680471-82.0536268047094
8920802104.4818317342-24.4818317342033
9021202036.0019913074283.9980086925784
9121402209.59946219637-69.5994621963696
9221302060.371493721769.6285062782981
9322102089.37090631711120.629093682886
9422102275.83204739514-65.8320473951371
9521902156.9808189669233.0191810330784
9621602168.21965054608-8.21965054607699
9722902219.246231683470.753768316602
9822702231.6969414952438.3030585047559
9922002246.13890125729-46.1389012572909
10021202281.29278995882-161.292789958817
10120502090.76367798673-40.7636779867289
10220802015.3236027225164.6763972774934
10321802116.6587572375363.3412427624744
10420702132.19240990682-62.1924099068228
10521702058.48684171919111.513158280812
10622402203.5797320125136.4202679874907
10723202182.53611362538137.463886374624
10822502312.5485511681-62.5485511680954







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092309.793288680181550.852819816663068.7337575437
1102278.0374434891273.380712144833282.69417483318
1112262.44556483821039.840058966143485.05107071027
1122320.20907476946831.3739441129763809.04420542595
1132288.45322957829610.6292593333053966.27719982328
1142272.86135092749408.8586430213494136.86405883363
1152330.62486085875231.6682488305954429.58147288691
1162298.8690156675819.4401639954144578.29786733974
1172283.27713701678-177.5738418316364744.12811586519
1182341.04064694804-346.4753679834485028.55666187952
1192309.28480175687-559.72691806775178.29652158143
1202293.69292310607-758.9115082896985346.29735450183

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2309.79328868018 & 1550.85281981666 & 3068.7337575437 \tabularnewline
110 & 2278.037443489 & 1273.38071214483 & 3282.69417483318 \tabularnewline
111 & 2262.4455648382 & 1039.84005896614 & 3485.05107071027 \tabularnewline
112 & 2320.20907476946 & 831.373944112976 & 3809.04420542595 \tabularnewline
113 & 2288.45322957829 & 610.629259333305 & 3966.27719982328 \tabularnewline
114 & 2272.86135092749 & 408.858643021349 & 4136.86405883363 \tabularnewline
115 & 2330.62486085875 & 231.668248830595 & 4429.58147288691 \tabularnewline
116 & 2298.86901566758 & 19.440163995414 & 4578.29786733974 \tabularnewline
117 & 2283.27713701678 & -177.573841831636 & 4744.12811586519 \tabularnewline
118 & 2341.04064694804 & -346.475367983448 & 5028.55666187952 \tabularnewline
119 & 2309.28480175687 & -559.7269180677 & 5178.29652158143 \tabularnewline
120 & 2293.69292310607 & -758.911508289698 & 5346.29735450183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301071&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]2309.79328868018[/C][C]1550.85281981666[/C][C]3068.7337575437[/C][/ROW]
[ROW][C]110[/C][C]2278.037443489[/C][C]1273.38071214483[/C][C]3282.69417483318[/C][/ROW]
[ROW][C]111[/C][C]2262.4455648382[/C][C]1039.84005896614[/C][C]3485.05107071027[/C][/ROW]
[ROW][C]112[/C][C]2320.20907476946[/C][C]831.373944112976[/C][C]3809.04420542595[/C][/ROW]
[ROW][C]113[/C][C]2288.45322957829[/C][C]610.629259333305[/C][C]3966.27719982328[/C][/ROW]
[ROW][C]114[/C][C]2272.86135092749[/C][C]408.858643021349[/C][C]4136.86405883363[/C][/ROW]
[ROW][C]115[/C][C]2330.62486085875[/C][C]231.668248830595[/C][C]4429.58147288691[/C][/ROW]
[ROW][C]116[/C][C]2298.86901566758[/C][C]19.440163995414[/C][C]4578.29786733974[/C][/ROW]
[ROW][C]117[/C][C]2283.27713701678[/C][C]-177.573841831636[/C][C]4744.12811586519[/C][/ROW]
[ROW][C]118[/C][C]2341.04064694804[/C][C]-346.475367983448[/C][C]5028.55666187952[/C][/ROW]
[ROW][C]119[/C][C]2309.28480175687[/C][C]-559.7269180677[/C][C]5178.29652158143[/C][/ROW]
[ROW][C]120[/C][C]2293.69292310607[/C][C]-758.911508289698[/C][C]5346.29735450183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301071&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301071&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
1092309.793288680181550.852819816663068.7337575437
1102278.0374434891273.380712144833282.69417483318
1112262.44556483821039.840058966143485.05107071027
1122320.20907476946831.3739441129763809.04420542595
1132288.45322957829610.6292593333053966.27719982328
1142272.86135092749408.8586430213494136.86405883363
1152330.62486085875231.6682488305954429.58147288691
1162298.8690156675819.4401639954144578.29786733974
1172283.27713701678-177.5738418316364744.12811586519
1182341.04064694804-346.4753679834485028.55666187952
1192309.28480175687-559.72691806775178.29652158143
1202293.69292310607-758.9115082896985346.29735450183



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 3 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
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')