FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

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, 21 Dec 2016 00:20:29 +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/21/t1482276044dnlv6l1mgq3racy.htm/, Retrieved Fri, 07 Nov 2025 05:36:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301831, Retrieved Fri, 07 Nov 2025 05:36:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact328

Tree of Dependent Computations

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] [683f400e1b95307fc738e729f07c4fce]
- R P       [Exponential Smoothing] [] [2016-12-20 23:20:29] [404ac5ee4f7301873f6a96ef36861981] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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

Tables (Output of Computation)





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=301831&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=301831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301831&T=0

As an alternative you can also use a QR Code:  
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
alpha0.84676363328923
beta0.334128281429783
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.84676363328923 \tabularnewline
beta & 0.334128281429783 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301831&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]0.84676363328923[/C][/ROW]
[ROW][C]beta[/C][C]0.334128281429783[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301831&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.84676363328923
beta0.334128281429783
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
339505000-1050
438605173.82412359973-1313.82412359973
535004752.5343657277-1252.5343657277
647404028.76590674515711.234093254853
736905169.07297324135-1479.07297324135
848104036.23698881913773.763011180868
961505029.939559512551120.06044048745
1045306633.77029880742-2103.77029880742
1147604912.56356340899-152.563563408986
1246704800.40327789812-130.403277898118
1335104670.11281969817-1160.11281969817
1429903339.67374285676-349.673742856757
1532402596.55262330812643.447376691883
1627002876.41942316952-176.419423169516
1726102412.1388950918197.861104908204
1832802320.76588973133959.234110268672
1931703145.4897357407224.5102642592842
2034403185.65805392457254.341946075427
2147103492.399858159331217.60014184067
2243204959.28645237355-639.286452373548
2336504672.95717619403-1022.95717619403
2433403772.3265858133-432.326585813301
2530503249.50334319999-199.503343199988
2629602867.3813378574592.618662142555
2728102758.8220061019551.1779938980462
2826702629.6518944939840.3481055060188
2924402502.72702302815-62.727023028152
3025802270.77467027685309.225329723146
3125202441.2664475355478.7335524644568
3228602438.86207118483421.137928815167
3335002845.54484474253654.455155257472
3434603634.95563782099-174.955637820987
3533103672.55174197688-362.551741976879
3630503448.72236503101-398.722365031011
3727303081.45542715678-351.455427156779
3827602654.77594555719105.224054442809
3928002644.56683839332155.433161606677
4024902720.8493206662-230.849320666195
4123102404.72818260943-94.7281826094313
4223502177.06824927514172.931750724862
4323702224.98019218733145.019807812673
4425602290.28743433285269.71256566715
4527402537.48911897924202.510881020757
4628302785.0827942207944.9172057792139
4730102911.9401971453698.0598028546383
4825003111.5406509364-611.540650936405
4926302537.2554701836992.7445298163057
5022702585.57336238499-315.57336238499
5124102198.85807412695211.141925873047
5222102317.88403178781-107.884031787808
5323302136.24703186577193.752968134234
5426902264.84335122833425.156648771666
5531502709.67247520359440.327524796412
5623303291.92858924173-961.928589241726
5722602414.64899961431-154.648999614305
5823302177.18992608092152.810073919078
5922402243.31021406335-3.3102140633523
6022302176.2969685864253.7030314135791
6122702172.7545399513697.2454600486385
6222202233.59568855517-13.5956885551709
6322902196.7339868614193.2660131385869
6422402276.74642444667-36.7464244466742
6521102236.27247748182-126.272477481818
6622402084.26514578017155.73485421983
6722302215.1130675052414.8869324947559
6823202230.9080165260189.0919834739871
6923202334.74369209661-14.7436920966052
7025402346.48369519233193.516304807672
7125302589.32180862633-59.3218086263291
7224002601.28202095117-201.282020951171
7324702436.0872333813833.9127666186237
7422902479.64169896419-189.641698964188
7521102280.24348757405-170.243487574046
7620502049.10438157950.895618420496703
7721701963.13304201447206.866957985531
7820702110.09913028141-40.0991302814109
7923302036.59816254519293.401837454815
8021902328.50518642009-138.505186420085
8122602215.5020987905644.497901209445
8223002270.049058391229.9509416088008
8322202320.75213197745-100.752131977448
8422202232.27502938131-12.2750293813147
8523802215.24417408745164.755825912549
8622802394.73059221778-114.730592217782
8721502305.09761547488-155.097615474883
8821902137.4019033110652.5980966889392
8920802160.45682433838-80.4568243383783
9021202048.0822145550371.9177854449745
9121402085.0804149846554.9195850153542
9221302123.22342810056.77657189949605
9322102122.5179682622887.4820317377153
9422102214.90204489145-4.90204489145117
9521902227.67172095956-37.6717209595604
9621602202.03485453744-42.0348545374418
9722902160.8106215032129.189378496804
9822702301.12409296477-31.1240929647661
9922002296.88407952739-96.8840795273904
10021202209.54971332918-89.5497133291819
10120502103.08972928172-53.0897292817212
10220802012.4821799875667.5178200124446
10321802043.10337734641136.896622653586
10420702171.20386521725-101.203865217247
10521702069.0561443438100.943855656202
10622402166.6395727038773.360427296127
10723202261.622052367558.3779476325008
10822502360.43465026033-110.434650260331

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3950 & 5000 & -1050 \tabularnewline
4 & 3860 & 5173.82412359973 & -1313.82412359973 \tabularnewline
5 & 3500 & 4752.5343657277 & -1252.5343657277 \tabularnewline
6 & 4740 & 4028.76590674515 & 711.234093254853 \tabularnewline
7 & 3690 & 5169.07297324135 & -1479.07297324135 \tabularnewline
8 & 4810 & 4036.23698881913 & 773.763011180868 \tabularnewline
9 & 6150 & 5029.93955951255 & 1120.06044048745 \tabularnewline
10 & 4530 & 6633.77029880742 & -2103.77029880742 \tabularnewline
11 & 4760 & 4912.56356340899 & -152.563563408986 \tabularnewline
12 & 4670 & 4800.40327789812 & -130.403277898118 \tabularnewline
13 & 3510 & 4670.11281969817 & -1160.11281969817 \tabularnewline
14 & 2990 & 3339.67374285676 & -349.673742856757 \tabularnewline
15 & 3240 & 2596.55262330812 & 643.447376691883 \tabularnewline
16 & 2700 & 2876.41942316952 & -176.419423169516 \tabularnewline
17 & 2610 & 2412.1388950918 & 197.861104908204 \tabularnewline
18 & 3280 & 2320.76588973133 & 959.234110268672 \tabularnewline
19 & 3170 & 3145.48973574072 & 24.5102642592842 \tabularnewline
20 & 3440 & 3185.65805392457 & 254.341946075427 \tabularnewline
21 & 4710 & 3492.39985815933 & 1217.60014184067 \tabularnewline
22 & 4320 & 4959.28645237355 & -639.286452373548 \tabularnewline
23 & 3650 & 4672.95717619403 & -1022.95717619403 \tabularnewline
24 & 3340 & 3772.3265858133 & -432.326585813301 \tabularnewline
25 & 3050 & 3249.50334319999 & -199.503343199988 \tabularnewline
26 & 2960 & 2867.38133785745 & 92.618662142555 \tabularnewline
27 & 2810 & 2758.82200610195 & 51.1779938980462 \tabularnewline
28 & 2670 & 2629.65189449398 & 40.3481055060188 \tabularnewline
29 & 2440 & 2502.72702302815 & -62.727023028152 \tabularnewline
30 & 2580 & 2270.77467027685 & 309.225329723146 \tabularnewline
31 & 2520 & 2441.26644753554 & 78.7335524644568 \tabularnewline
32 & 2860 & 2438.86207118483 & 421.137928815167 \tabularnewline
33 & 3500 & 2845.54484474253 & 654.455155257472 \tabularnewline
34 & 3460 & 3634.95563782099 & -174.955637820987 \tabularnewline
35 & 3310 & 3672.55174197688 & -362.551741976879 \tabularnewline
36 & 3050 & 3448.72236503101 & -398.722365031011 \tabularnewline
37 & 2730 & 3081.45542715678 & -351.455427156779 \tabularnewline
38 & 2760 & 2654.77594555719 & 105.224054442809 \tabularnewline
39 & 2800 & 2644.56683839332 & 155.433161606677 \tabularnewline
40 & 2490 & 2720.8493206662 & -230.849320666195 \tabularnewline
41 & 2310 & 2404.72818260943 & -94.7281826094313 \tabularnewline
42 & 2350 & 2177.06824927514 & 172.931750724862 \tabularnewline
43 & 2370 & 2224.98019218733 & 145.019807812673 \tabularnewline
44 & 2560 & 2290.28743433285 & 269.71256566715 \tabularnewline
45 & 2740 & 2537.48911897924 & 202.510881020757 \tabularnewline
46 & 2830 & 2785.08279422079 & 44.9172057792139 \tabularnewline
47 & 3010 & 2911.94019714536 & 98.0598028546383 \tabularnewline
48 & 2500 & 3111.5406509364 & -611.540650936405 \tabularnewline
49 & 2630 & 2537.25547018369 & 92.7445298163057 \tabularnewline
50 & 2270 & 2585.57336238499 & -315.57336238499 \tabularnewline
51 & 2410 & 2198.85807412695 & 211.141925873047 \tabularnewline
52 & 2210 & 2317.88403178781 & -107.884031787808 \tabularnewline
53 & 2330 & 2136.24703186577 & 193.752968134234 \tabularnewline
54 & 2690 & 2264.84335122833 & 425.156648771666 \tabularnewline
55 & 3150 & 2709.67247520359 & 440.327524796412 \tabularnewline
56 & 2330 & 3291.92858924173 & -961.928589241726 \tabularnewline
57 & 2260 & 2414.64899961431 & -154.648999614305 \tabularnewline
58 & 2330 & 2177.18992608092 & 152.810073919078 \tabularnewline
59 & 2240 & 2243.31021406335 & -3.3102140633523 \tabularnewline
60 & 2230 & 2176.29696858642 & 53.7030314135791 \tabularnewline
61 & 2270 & 2172.75453995136 & 97.2454600486385 \tabularnewline
62 & 2220 & 2233.59568855517 & -13.5956885551709 \tabularnewline
63 & 2290 & 2196.73398686141 & 93.2660131385869 \tabularnewline
64 & 2240 & 2276.74642444667 & -36.7464244466742 \tabularnewline
65 & 2110 & 2236.27247748182 & -126.272477481818 \tabularnewline
66 & 2240 & 2084.26514578017 & 155.73485421983 \tabularnewline
67 & 2230 & 2215.11306750524 & 14.8869324947559 \tabularnewline
68 & 2320 & 2230.90801652601 & 89.0919834739871 \tabularnewline
69 & 2320 & 2334.74369209661 & -14.7436920966052 \tabularnewline
70 & 2540 & 2346.48369519233 & 193.516304807672 \tabularnewline
71 & 2530 & 2589.32180862633 & -59.3218086263291 \tabularnewline
72 & 2400 & 2601.28202095117 & -201.282020951171 \tabularnewline
73 & 2470 & 2436.08723338138 & 33.9127666186237 \tabularnewline
74 & 2290 & 2479.64169896419 & -189.641698964188 \tabularnewline
75 & 2110 & 2280.24348757405 & -170.243487574046 \tabularnewline
76 & 2050 & 2049.1043815795 & 0.895618420496703 \tabularnewline
77 & 2170 & 1963.13304201447 & 206.866957985531 \tabularnewline
78 & 2070 & 2110.09913028141 & -40.0991302814109 \tabularnewline
79 & 2330 & 2036.59816254519 & 293.401837454815 \tabularnewline
80 & 2190 & 2328.50518642009 & -138.505186420085 \tabularnewline
81 & 2260 & 2215.50209879056 & 44.497901209445 \tabularnewline
82 & 2300 & 2270.0490583912 & 29.9509416088008 \tabularnewline
83 & 2220 & 2320.75213197745 & -100.752131977448 \tabularnewline
84 & 2220 & 2232.27502938131 & -12.2750293813147 \tabularnewline
85 & 2380 & 2215.24417408745 & 164.755825912549 \tabularnewline
86 & 2280 & 2394.73059221778 & -114.730592217782 \tabularnewline
87 & 2150 & 2305.09761547488 & -155.097615474883 \tabularnewline
88 & 2190 & 2137.40190331106 & 52.5980966889392 \tabularnewline
89 & 2080 & 2160.45682433838 & -80.4568243383783 \tabularnewline
90 & 2120 & 2048.08221455503 & 71.9177854449745 \tabularnewline
91 & 2140 & 2085.08041498465 & 54.9195850153542 \tabularnewline
92 & 2130 & 2123.2234281005 & 6.77657189949605 \tabularnewline
93 & 2210 & 2122.51796826228 & 87.4820317377153 \tabularnewline
94 & 2210 & 2214.90204489145 & -4.90204489145117 \tabularnewline
95 & 2190 & 2227.67172095956 & -37.6717209595604 \tabularnewline
96 & 2160 & 2202.03485453744 & -42.0348545374418 \tabularnewline
97 & 2290 & 2160.8106215032 & 129.189378496804 \tabularnewline
98 & 2270 & 2301.12409296477 & -31.1240929647661 \tabularnewline
99 & 2200 & 2296.88407952739 & -96.8840795273904 \tabularnewline
100 & 2120 & 2209.54971332918 & -89.5497133291819 \tabularnewline
101 & 2050 & 2103.08972928172 & -53.0897292817212 \tabularnewline
102 & 2080 & 2012.48217998756 & 67.5178200124446 \tabularnewline
103 & 2180 & 2043.10337734641 & 136.896622653586 \tabularnewline
104 & 2070 & 2171.20386521725 & -101.203865217247 \tabularnewline
105 & 2170 & 2069.0561443438 & 100.943855656202 \tabularnewline
106 & 2240 & 2166.63957270387 & 73.360427296127 \tabularnewline
107 & 2320 & 2261.6220523675 & 58.3779476325008 \tabularnewline
108 & 2250 & 2360.43465026033 & -110.434650260331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301831&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]3950[/C][C]5000[/C][C]-1050[/C][/ROW]
[ROW][C]4[/C][C]3860[/C][C]5173.82412359973[/C][C]-1313.82412359973[/C][/ROW]
[ROW][C]5[/C][C]3500[/C][C]4752.5343657277[/C][C]-1252.5343657277[/C][/ROW]
[ROW][C]6[/C][C]4740[/C][C]4028.76590674515[/C][C]711.234093254853[/C][/ROW]
[ROW][C]7[/C][C]3690[/C][C]5169.07297324135[/C][C]-1479.07297324135[/C][/ROW]
[ROW][C]8[/C][C]4810[/C][C]4036.23698881913[/C][C]773.763011180868[/C][/ROW]
[ROW][C]9[/C][C]6150[/C][C]5029.93955951255[/C][C]1120.06044048745[/C][/ROW]
[ROW][C]10[/C][C]4530[/C][C]6633.77029880742[/C][C]-2103.77029880742[/C][/ROW]
[ROW][C]11[/C][C]4760[/C][C]4912.56356340899[/C][C]-152.563563408986[/C][/ROW]
[ROW][C]12[/C][C]4670[/C][C]4800.40327789812[/C][C]-130.403277898118[/C][/ROW]
[ROW][C]13[/C][C]3510[/C][C]4670.11281969817[/C][C]-1160.11281969817[/C][/ROW]
[ROW][C]14[/C][C]2990[/C][C]3339.67374285676[/C][C]-349.673742856757[/C][/ROW]
[ROW][C]15[/C][C]3240[/C][C]2596.55262330812[/C][C]643.447376691883[/C][/ROW]
[ROW][C]16[/C][C]2700[/C][C]2876.41942316952[/C][C]-176.419423169516[/C][/ROW]
[ROW][C]17[/C][C]2610[/C][C]2412.1388950918[/C][C]197.861104908204[/C][/ROW]
[ROW][C]18[/C][C]3280[/C][C]2320.76588973133[/C][C]959.234110268672[/C][/ROW]
[ROW][C]19[/C][C]3170[/C][C]3145.48973574072[/C][C]24.5102642592842[/C][/ROW]
[ROW][C]20[/C][C]3440[/C][C]3185.65805392457[/C][C]254.341946075427[/C][/ROW]
[ROW][C]21[/C][C]4710[/C][C]3492.39985815933[/C][C]1217.60014184067[/C][/ROW]
[ROW][C]22[/C][C]4320[/C][C]4959.28645237355[/C][C]-639.286452373548[/C][/ROW]
[ROW][C]23[/C][C]3650[/C][C]4672.95717619403[/C][C]-1022.95717619403[/C][/ROW]
[ROW][C]24[/C][C]3340[/C][C]3772.3265858133[/C][C]-432.326585813301[/C][/ROW]
[ROW][C]25[/C][C]3050[/C][C]3249.50334319999[/C][C]-199.503343199988[/C][/ROW]
[ROW][C]26[/C][C]2960[/C][C]2867.38133785745[/C][C]92.618662142555[/C][/ROW]
[ROW][C]27[/C][C]2810[/C][C]2758.82200610195[/C][C]51.1779938980462[/C][/ROW]
[ROW][C]28[/C][C]2670[/C][C]2629.65189449398[/C][C]40.3481055060188[/C][/ROW]
[ROW][C]29[/C][C]2440[/C][C]2502.72702302815[/C][C]-62.727023028152[/C][/ROW]
[ROW][C]30[/C][C]2580[/C][C]2270.77467027685[/C][C]309.225329723146[/C][/ROW]
[ROW][C]31[/C][C]2520[/C][C]2441.26644753554[/C][C]78.7335524644568[/C][/ROW]
[ROW][C]32[/C][C]2860[/C][C]2438.86207118483[/C][C]421.137928815167[/C][/ROW]
[ROW][C]33[/C][C]3500[/C][C]2845.54484474253[/C][C]654.455155257472[/C][/ROW]
[ROW][C]34[/C][C]3460[/C][C]3634.95563782099[/C][C]-174.955637820987[/C][/ROW]
[ROW][C]35[/C][C]3310[/C][C]3672.55174197688[/C][C]-362.551741976879[/C][/ROW]
[ROW][C]36[/C][C]3050[/C][C]3448.72236503101[/C][C]-398.722365031011[/C][/ROW]
[ROW][C]37[/C][C]2730[/C][C]3081.45542715678[/C][C]-351.455427156779[/C][/ROW]
[ROW][C]38[/C][C]2760[/C][C]2654.77594555719[/C][C]105.224054442809[/C][/ROW]
[ROW][C]39[/C][C]2800[/C][C]2644.56683839332[/C][C]155.433161606677[/C][/ROW]
[ROW][C]40[/C][C]2490[/C][C]2720.8493206662[/C][C]-230.849320666195[/C][/ROW]
[ROW][C]41[/C][C]2310[/C][C]2404.72818260943[/C][C]-94.7281826094313[/C][/ROW]
[ROW][C]42[/C][C]2350[/C][C]2177.06824927514[/C][C]172.931750724862[/C][/ROW]
[ROW][C]43[/C][C]2370[/C][C]2224.98019218733[/C][C]145.019807812673[/C][/ROW]
[ROW][C]44[/C][C]2560[/C][C]2290.28743433285[/C][C]269.71256566715[/C][/ROW]
[ROW][C]45[/C][C]2740[/C][C]2537.48911897924[/C][C]202.510881020757[/C][/ROW]
[ROW][C]46[/C][C]2830[/C][C]2785.08279422079[/C][C]44.9172057792139[/C][/ROW]
[ROW][C]47[/C][C]3010[/C][C]2911.94019714536[/C][C]98.0598028546383[/C][/ROW]
[ROW][C]48[/C][C]2500[/C][C]3111.5406509364[/C][C]-611.540650936405[/C][/ROW]
[ROW][C]49[/C][C]2630[/C][C]2537.25547018369[/C][C]92.7445298163057[/C][/ROW]
[ROW][C]50[/C][C]2270[/C][C]2585.57336238499[/C][C]-315.57336238499[/C][/ROW]
[ROW][C]51[/C][C]2410[/C][C]2198.85807412695[/C][C]211.141925873047[/C][/ROW]
[ROW][C]52[/C][C]2210[/C][C]2317.88403178781[/C][C]-107.884031787808[/C][/ROW]
[ROW][C]53[/C][C]2330[/C][C]2136.24703186577[/C][C]193.752968134234[/C][/ROW]
[ROW][C]54[/C][C]2690[/C][C]2264.84335122833[/C][C]425.156648771666[/C][/ROW]
[ROW][C]55[/C][C]3150[/C][C]2709.67247520359[/C][C]440.327524796412[/C][/ROW]
[ROW][C]56[/C][C]2330[/C][C]3291.92858924173[/C][C]-961.928589241726[/C][/ROW]
[ROW][C]57[/C][C]2260[/C][C]2414.64899961431[/C][C]-154.648999614305[/C][/ROW]
[ROW][C]58[/C][C]2330[/C][C]2177.18992608092[/C][C]152.810073919078[/C][/ROW]
[ROW][C]59[/C][C]2240[/C][C]2243.31021406335[/C][C]-3.3102140633523[/C][/ROW]
[ROW][C]60[/C][C]2230[/C][C]2176.29696858642[/C][C]53.7030314135791[/C][/ROW]
[ROW][C]61[/C][C]2270[/C][C]2172.75453995136[/C][C]97.2454600486385[/C][/ROW]
[ROW][C]62[/C][C]2220[/C][C]2233.59568855517[/C][C]-13.5956885551709[/C][/ROW]
[ROW][C]63[/C][C]2290[/C][C]2196.73398686141[/C][C]93.2660131385869[/C][/ROW]
[ROW][C]64[/C][C]2240[/C][C]2276.74642444667[/C][C]-36.7464244466742[/C][/ROW]
[ROW][C]65[/C][C]2110[/C][C]2236.27247748182[/C][C]-126.272477481818[/C][/ROW]
[ROW][C]66[/C][C]2240[/C][C]2084.26514578017[/C][C]155.73485421983[/C][/ROW]
[ROW][C]67[/C][C]2230[/C][C]2215.11306750524[/C][C]14.8869324947559[/C][/ROW]
[ROW][C]68[/C][C]2320[/C][C]2230.90801652601[/C][C]89.0919834739871[/C][/ROW]
[ROW][C]69[/C][C]2320[/C][C]2334.74369209661[/C][C]-14.7436920966052[/C][/ROW]
[ROW][C]70[/C][C]2540[/C][C]2346.48369519233[/C][C]193.516304807672[/C][/ROW]
[ROW][C]71[/C][C]2530[/C][C]2589.32180862633[/C][C]-59.3218086263291[/C][/ROW]
[ROW][C]72[/C][C]2400[/C][C]2601.28202095117[/C][C]-201.282020951171[/C][/ROW]
[ROW][C]73[/C][C]2470[/C][C]2436.08723338138[/C][C]33.9127666186237[/C][/ROW]
[ROW][C]74[/C][C]2290[/C][C]2479.64169896419[/C][C]-189.641698964188[/C][/ROW]
[ROW][C]75[/C][C]2110[/C][C]2280.24348757405[/C][C]-170.243487574046[/C][/ROW]
[ROW][C]76[/C][C]2050[/C][C]2049.1043815795[/C][C]0.895618420496703[/C][/ROW]
[ROW][C]77[/C][C]2170[/C][C]1963.13304201447[/C][C]206.866957985531[/C][/ROW]
[ROW][C]78[/C][C]2070[/C][C]2110.09913028141[/C][C]-40.0991302814109[/C][/ROW]
[ROW][C]79[/C][C]2330[/C][C]2036.59816254519[/C][C]293.401837454815[/C][/ROW]
[ROW][C]80[/C][C]2190[/C][C]2328.50518642009[/C][C]-138.505186420085[/C][/ROW]
[ROW][C]81[/C][C]2260[/C][C]2215.50209879056[/C][C]44.497901209445[/C][/ROW]
[ROW][C]82[/C][C]2300[/C][C]2270.0490583912[/C][C]29.9509416088008[/C][/ROW]
[ROW][C]83[/C][C]2220[/C][C]2320.75213197745[/C][C]-100.752131977448[/C][/ROW]
[ROW][C]84[/C][C]2220[/C][C]2232.27502938131[/C][C]-12.2750293813147[/C][/ROW]
[ROW][C]85[/C][C]2380[/C][C]2215.24417408745[/C][C]164.755825912549[/C][/ROW]
[ROW][C]86[/C][C]2280[/C][C]2394.73059221778[/C][C]-114.730592217782[/C][/ROW]
[ROW][C]87[/C][C]2150[/C][C]2305.09761547488[/C][C]-155.097615474883[/C][/ROW]
[ROW][C]88[/C][C]2190[/C][C]2137.40190331106[/C][C]52.5980966889392[/C][/ROW]
[ROW][C]89[/C][C]2080[/C][C]2160.45682433838[/C][C]-80.4568243383783[/C][/ROW]
[ROW][C]90[/C][C]2120[/C][C]2048.08221455503[/C][C]71.9177854449745[/C][/ROW]
[ROW][C]91[/C][C]2140[/C][C]2085.08041498465[/C][C]54.9195850153542[/C][/ROW]
[ROW][C]92[/C][C]2130[/C][C]2123.2234281005[/C][C]6.77657189949605[/C][/ROW]
[ROW][C]93[/C][C]2210[/C][C]2122.51796826228[/C][C]87.4820317377153[/C][/ROW]
[ROW][C]94[/C][C]2210[/C][C]2214.90204489145[/C][C]-4.90204489145117[/C][/ROW]
[ROW][C]95[/C][C]2190[/C][C]2227.67172095956[/C][C]-37.6717209595604[/C][/ROW]
[ROW][C]96[/C][C]2160[/C][C]2202.03485453744[/C][C]-42.0348545374418[/C][/ROW]
[ROW][C]97[/C][C]2290[/C][C]2160.8106215032[/C][C]129.189378496804[/C][/ROW]
[ROW][C]98[/C][C]2270[/C][C]2301.12409296477[/C][C]-31.1240929647661[/C][/ROW]
[ROW][C]99[/C][C]2200[/C][C]2296.88407952739[/C][C]-96.8840795273904[/C][/ROW]
[ROW][C]100[/C][C]2120[/C][C]2209.54971332918[/C][C]-89.5497133291819[/C][/ROW]
[ROW][C]101[/C][C]2050[/C][C]2103.08972928172[/C][C]-53.0897292817212[/C][/ROW]
[ROW][C]102[/C][C]2080[/C][C]2012.48217998756[/C][C]67.5178200124446[/C][/ROW]
[ROW][C]103[/C][C]2180[/C][C]2043.10337734641[/C][C]136.896622653586[/C][/ROW]
[ROW][C]104[/C][C]2070[/C][C]2171.20386521725[/C][C]-101.203865217247[/C][/ROW]
[ROW][C]105[/C][C]2170[/C][C]2069.0561443438[/C][C]100.943855656202[/C][/ROW]
[ROW][C]106[/C][C]2240[/C][C]2166.63957270387[/C][C]73.360427296127[/C][/ROW]
[ROW][C]107[/C][C]2320[/C][C]2261.6220523675[/C][C]58.3779476325008[/C][/ROW]
[ROW][C]108[/C][C]2250[/C][C]2360.43465026033[/C][C]-110.434650260331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301831&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301831&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
339505000-1050
438605173.82412359973-1313.82412359973
535004752.5343657277-1252.5343657277
647404028.76590674515711.234093254853
736905169.07297324135-1479.07297324135
848104036.23698881913773.763011180868
961505029.939559512551120.06044048745
1045306633.77029880742-2103.77029880742
1147604912.56356340899-152.563563408986
1246704800.40327789812-130.403277898118
1335104670.11281969817-1160.11281969817
1429903339.67374285676-349.673742856757
1532402596.55262330812643.447376691883
1627002876.41942316952-176.419423169516
1726102412.1388950918197.861104908204
1832802320.76588973133959.234110268672
1931703145.4897357407224.5102642592842
2034403185.65805392457254.341946075427
2147103492.399858159331217.60014184067
2243204959.28645237355-639.286452373548
2336504672.95717619403-1022.95717619403
2433403772.3265858133-432.326585813301
2530503249.50334319999-199.503343199988
2629602867.3813378574592.618662142555
2728102758.8220061019551.1779938980462
2826702629.6518944939840.3481055060188
2924402502.72702302815-62.727023028152
3025802270.77467027685309.225329723146
3125202441.2664475355478.7335524644568
3228602438.86207118483421.137928815167
3335002845.54484474253654.455155257472
3434603634.95563782099-174.955637820987
3533103672.55174197688-362.551741976879
3630503448.72236503101-398.722365031011
3727303081.45542715678-351.455427156779
3827602654.77594555719105.224054442809
3928002644.56683839332155.433161606677
4024902720.8493206662-230.849320666195
4123102404.72818260943-94.7281826094313
4223502177.06824927514172.931750724862
4323702224.98019218733145.019807812673
4425602290.28743433285269.71256566715
4527402537.48911897924202.510881020757
4628302785.0827942207944.9172057792139
4730102911.9401971453698.0598028546383
4825003111.5406509364-611.540650936405
4926302537.2554701836992.7445298163057
5022702585.57336238499-315.57336238499
5124102198.85807412695211.141925873047
5222102317.88403178781-107.884031787808
5323302136.24703186577193.752968134234
5426902264.84335122833425.156648771666
5531502709.67247520359440.327524796412
5623303291.92858924173-961.928589241726
5722602414.64899961431-154.648999614305
5823302177.18992608092152.810073919078
5922402243.31021406335-3.3102140633523
6022302176.2969685864253.7030314135791
6122702172.7545399513697.2454600486385
6222202233.59568855517-13.5956885551709
6322902196.7339868614193.2660131385869
6422402276.74642444667-36.7464244466742
6521102236.27247748182-126.272477481818
6622402084.26514578017155.73485421983
6722302215.1130675052414.8869324947559
6823202230.9080165260189.0919834739871
6923202334.74369209661-14.7436920966052
7025402346.48369519233193.516304807672
7125302589.32180862633-59.3218086263291
7224002601.28202095117-201.282020951171
7324702436.0872333813833.9127666186237
7422902479.64169896419-189.641698964188
7521102280.24348757405-170.243487574046
7620502049.10438157950.895618420496703
7721701963.13304201447206.866957985531
7820702110.09913028141-40.0991302814109
7923302036.59816254519293.401837454815
8021902328.50518642009-138.505186420085
8122602215.5020987905644.497901209445
8223002270.049058391229.9509416088008
8322202320.75213197745-100.752131977448
8422202232.27502938131-12.2750293813147
8523802215.24417408745164.755825912549
8622802394.73059221778-114.730592217782
8721502305.09761547488-155.097615474883
8821902137.4019033110652.5980966889392
8920802160.45682433838-80.4568243383783
9021202048.0822145550371.9177854449745
9121402085.0804149846554.9195850153542
9221302123.22342810056.77657189949605
9322102122.5179682622887.4820317377153
9422102214.90204489145-4.90204489145117
9521902227.67172095956-37.6717209595604
9621602202.03485453744-42.0348545374418
9722902160.8106215032129.189378496804
9822702301.12409296477-31.1240929647661
9922002296.88407952739-96.8840795273904
10021202209.54971332918-89.5497133291819
10120502103.08972928172-53.0897292817212
10220802012.4821799875667.5178200124446
10321802043.10337734641136.896622653586
10420702171.20386521725-101.203865217247
10521702069.0561443438100.943855656202
10622402166.6395727038773.360427296127
10723202261.622052367558.3779476325008
10822502360.43465026033-110.434650260331






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092285.057860295231362.911114483543207.20460610691
1102303.19311602559911.9421401357283694.44409191544
1112321.32837175594415.4281995167034227.22854399519
1122339.4636274863-125.7182482307594804.64550320336
1132357.59888321666-709.2751626243115424.47292905763
1142375.73413894702-1332.955408356776084.42368625081
1152393.86939467738-1994.666284762596782.40507411735
1162412.00465040774-2692.547892277697516.55719309316
1172430.1399061381-3424.956199470068285.23601174625
1182448.27516186846-4190.434436992149086.98476072905
1192466.41041759881-4987.685057440119920.50589263774
1202484.54567332917-5815.5453827108310784.6367293692

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2285.05786029523 & 1362.91111448354 & 3207.20460610691 \tabularnewline
110 & 2303.19311602559 & 911.942140135728 & 3694.44409191544 \tabularnewline
111 & 2321.32837175594 & 415.428199516703 & 4227.22854399519 \tabularnewline
112 & 2339.4636274863 & -125.718248230759 & 4804.64550320336 \tabularnewline
113 & 2357.59888321666 & -709.275162624311 & 5424.47292905763 \tabularnewline
114 & 2375.73413894702 & -1332.95540835677 & 6084.42368625081 \tabularnewline
115 & 2393.86939467738 & -1994.66628476259 & 6782.40507411735 \tabularnewline
116 & 2412.00465040774 & -2692.54789227769 & 7516.55719309316 \tabularnewline
117 & 2430.1399061381 & -3424.95619947006 & 8285.23601174625 \tabularnewline
118 & 2448.27516186846 & -4190.43443699214 & 9086.98476072905 \tabularnewline
119 & 2466.41041759881 & -4987.68505744011 & 9920.50589263774 \tabularnewline
120 & 2484.54567332917 & -5815.54538271083 & 10784.6367293692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301831&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]2285.05786029523[/C][C]1362.91111448354[/C][C]3207.20460610691[/C][/ROW]
[ROW][C]110[/C][C]2303.19311602559[/C][C]911.942140135728[/C][C]3694.44409191544[/C][/ROW]
[ROW][C]111[/C][C]2321.32837175594[/C][C]415.428199516703[/C][C]4227.22854399519[/C][/ROW]
[ROW][C]112[/C][C]2339.4636274863[/C][C]-125.718248230759[/C][C]4804.64550320336[/C][/ROW]
[ROW][C]113[/C][C]2357.59888321666[/C][C]-709.275162624311[/C][C]5424.47292905763[/C][/ROW]
[ROW][C]114[/C][C]2375.73413894702[/C][C]-1332.95540835677[/C][C]6084.42368625081[/C][/ROW]
[ROW][C]115[/C][C]2393.86939467738[/C][C]-1994.66628476259[/C][C]6782.40507411735[/C][/ROW]
[ROW][C]116[/C][C]2412.00465040774[/C][C]-2692.54789227769[/C][C]7516.55719309316[/C][/ROW]
[ROW][C]117[/C][C]2430.1399061381[/C][C]-3424.95619947006[/C][C]8285.23601174625[/C][/ROW]
[ROW][C]118[/C][C]2448.27516186846[/C][C]-4190.43443699214[/C][C]9086.98476072905[/C][/ROW]
[ROW][C]119[/C][C]2466.41041759881[/C][C]-4987.68505744011[/C][C]9920.50589263774[/C][/ROW]
[ROW][C]120[/C][C]2484.54567332917[/C][C]-5815.54538271083[/C][C]10784.6367293692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301831&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301831&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092285.057860295231362.911114483543207.20460610691
1102303.19311602559911.9421401357283694.44409191544
1112321.32837175594415.4281995167034227.22854399519
1122339.4636274863-125.7182482307594804.64550320336
1132357.59888321666-709.2751626243115424.47292905763
1142375.73413894702-1332.955408356776084.42368625081
1152393.86939467738-1994.666284762596782.40507411735
1162412.00465040774-2692.547892277697516.55719309316
1172430.1399061381-3424.956199470068285.23601174625
1182448.27516186846-4190.434436992149086.98476072905
1192466.41041759881-4987.685057440119920.50589263774
1202484.54567332917-5815.5453827108310784.6367293692


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3 ; par2 = Triple ; par3 = additive ; par4 = 11 ;
Parameters (R input):
par1 = 3 ; par2 = Triple ; par3 = additive ; par4 = 11 ;
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')