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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 16:06:40 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481123216ahpyztb4rlf9a27.htm/, Retrieved Tue, 07 May 2024 14:01:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298187, Retrieved Tue, 07 May 2024 14:01:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper N2163] [2016-12-07 15:06:40] [1e2703d0f11438bcd65480dae45a3781] [Current]
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Dataseries X:
3875
3755
4670
4335
4945
4600
4395
4345
4390
4490
4395
4690
4590
4630
5375
4655
4975
4810
4445
4660
4215
4825
4250
3945
4390
4315
4835
4835
4970
4690
4700
4855
4610
4900
4250
4105
4740
4565
5155
5320
5430
4690
4540
4575
4660
4850
4200
4360
4655
4585
5315
5115
5100
5735
5260
5050
5165
5190
4720
5275
4605
4825
5595
5160
5320
5540
4970
5445
5305
5145
4895
4555
4980
4930
5810
5210
5450
5510
5010
5495
5125
5190
4565
4255
4875
4650
5295
5045
5430
5325
4920
5445
4895
5175
4545
4220
4595
4360
4750
4985
5140
4995
5150
5240
4875
5170
4715
4370
5160
4930
5600
5385
5425
5375
5365




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298187&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298187&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.515202719214325
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.515202719214325 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298187&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]0.515202719214325[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298187&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
alpha0.515202719214325
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
237553875-120
346703813.17567369428856.824326305719
443354254.6138964959780.38610350403
549454296.02903560829648.970964391709
646004630.38064115404-30.3806411540427
743954614.72845222001-219.728452220005
843454501.5237561475-156.523756147504
943904420.88229135867-30.88229135867
1044904404.9716508751185.0283491248856
1143954448.77848755456-53.7784875545603
1246904421.07166453122268.928335468783
1345904559.6242742385230.3757257614834
1446304575.2739307489454.726069251059
1553754603.468950439771.531049561002
1646555000.96384513111-345.963845131108
1749754822.72233136972152.277668630282
1848104901.17620032366-91.1762003236563
1944454854.20197398928-409.201973989278
2046604643.3800042821316.6199957178669
2142154651.94267126931-436.942671269308
2248254426.82861889059398.171381109411
2342504631.96759715148-381.967597151481
2439454435.17685244728-490.176852447275
2543904182.63640517052207.36359482948
2643154289.4706930927325.5293069072741
2748354302.62346143101532.376538568989
2848354576.90530174766258.094698252336
2949704709.87639210207260.123607897932
3046904843.89278222292-153.892782222923
3147004764.60680235422-64.6068023542157
3248554731.32120210158123.678797898419
3346104795.04085508801-185.040855088006
3449004699.70730338092200.292696619079
3542504802.89864531784-552.89864531784
3641054518.04375980017-413.043759800173
3747404305.24249159661434.757508403385
3845654529.2307421248835.7692578751166
3951554547.65916104642607.340838953578
4053204860.56281276521459.437187234786
4154305097.26610093676332.733899063243
4246905268.69151050892-578.691510508925
4345404970.54807070848-430.548070708482
4445754748.72853392699-173.728533926991
4546604659.223120842690.776879157312578
4648504659.62337109704190.376628902965
4742004757.7059279827-557.705927982699
4843604470.37431736406-110.374317364063
4946554413.50916892667241.490831073327
5045854537.9259017609847.0740982390216
5153154562.17860517828752.821394821715
5251154950.03423487315164.965765126846
5351005035.0250456437864.974954356223
5457355068.50031880893666.499681191071
5552605411.88276691405-151.88276691405
5650505333.63235239814-283.632352398135
5751655187.50419318546-22.5041931854603
5851905175.9099716625914.0900283374131
5947205183.16919257583-463.16919257583
6052754944.54316510446330.456834895542
6146055114.7954250256-509.795425025601
6248254852.14743580939-27.1474358093892
6355954838.1610030607756.838996939305
6451605228.08651229127-68.0865122912674
6553205193.00815601699126.991843983013
6655405258.43469935508281.565300644923
6749705403.49790788374-433.49790788374
6854455180.15860696832264.841393031684
6953055316.60561281875-11.6056128187502
7051455310.62636953638-165.626369536381
7148955225.29521357764-330.295213577641
7245555055.12622139896-500.126221398965
7349804797.45983218383182.540167816167
7449304891.5050230085638.4949769914383
7558104911.33773983064898.662260169356
7652105374.33097992519-164.330979925187
7754505289.66721221658160.332787783424
7855105372.27110046181137.72889953819
7950105443.22940401828-433.229404018282
8054955220.02843702446274.971562975538
8151255361.69453397607-236.694533976071
8251905239.74886644843-49.7488664484317
8345655214.11811517637-649.118115176369
8442554879.69069714623-624.690697146227
8548754557.8483513086317.151648691402
8646504721.24574311772-71.2457431177154
8752954684.53974253102610.460257468977
8850454999.0505271513245.9494728486834
8954305022.72382050942407.276179490577
9053255232.5536156541992.4463843458107
9149205280.18224425068-360.182244250684
9254455094.61537260001350.384627399987
9348955275.13448540739-380.134485407385
9451755079.2881648583695.7118351416375
9545455128.59916258433-583.599162584327
9642204827.92728708968-607.927287089678
9745954514.7214956964980.278504303511
9843604556.08119940812-196.081199408117
9947504455.05963228625294.940367713751
10049854607.01371173845377.986288261553
10151404801.75327527653338.246724723471
10249954976.018907619418.9810923805999
10351504985.79801802754164.201981972456
10452405070.39532564013169.604674359865
10548755157.7761150618-282.776115061797
10651705012.0890916531157.910908346903
10747155093.44522102702-378.445221027025
10843704898.46921408024-528.469214080235
10951604626.20043796504533.799562034959
11049304901.2154238408728.7845761591325
11156004916.04531574948683.954684250515
11253855268.42062889473116.579371105275
11354255328.4826378924696.517362107541
11453755378.20864530166-3.20864530165818
11553655376.55554251725-11.5555425172497

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3755 & 3875 & -120 \tabularnewline
3 & 4670 & 3813.17567369428 & 856.824326305719 \tabularnewline
4 & 4335 & 4254.61389649597 & 80.38610350403 \tabularnewline
5 & 4945 & 4296.02903560829 & 648.970964391709 \tabularnewline
6 & 4600 & 4630.38064115404 & -30.3806411540427 \tabularnewline
7 & 4395 & 4614.72845222001 & -219.728452220005 \tabularnewline
8 & 4345 & 4501.5237561475 & -156.523756147504 \tabularnewline
9 & 4390 & 4420.88229135867 & -30.88229135867 \tabularnewline
10 & 4490 & 4404.97165087511 & 85.0283491248856 \tabularnewline
11 & 4395 & 4448.77848755456 & -53.7784875545603 \tabularnewline
12 & 4690 & 4421.07166453122 & 268.928335468783 \tabularnewline
13 & 4590 & 4559.62427423852 & 30.3757257614834 \tabularnewline
14 & 4630 & 4575.27393074894 & 54.726069251059 \tabularnewline
15 & 5375 & 4603.468950439 & 771.531049561002 \tabularnewline
16 & 4655 & 5000.96384513111 & -345.963845131108 \tabularnewline
17 & 4975 & 4822.72233136972 & 152.277668630282 \tabularnewline
18 & 4810 & 4901.17620032366 & -91.1762003236563 \tabularnewline
19 & 4445 & 4854.20197398928 & -409.201973989278 \tabularnewline
20 & 4660 & 4643.38000428213 & 16.6199957178669 \tabularnewline
21 & 4215 & 4651.94267126931 & -436.942671269308 \tabularnewline
22 & 4825 & 4426.82861889059 & 398.171381109411 \tabularnewline
23 & 4250 & 4631.96759715148 & -381.967597151481 \tabularnewline
24 & 3945 & 4435.17685244728 & -490.176852447275 \tabularnewline
25 & 4390 & 4182.63640517052 & 207.36359482948 \tabularnewline
26 & 4315 & 4289.47069309273 & 25.5293069072741 \tabularnewline
27 & 4835 & 4302.62346143101 & 532.376538568989 \tabularnewline
28 & 4835 & 4576.90530174766 & 258.094698252336 \tabularnewline
29 & 4970 & 4709.87639210207 & 260.123607897932 \tabularnewline
30 & 4690 & 4843.89278222292 & -153.892782222923 \tabularnewline
31 & 4700 & 4764.60680235422 & -64.6068023542157 \tabularnewline
32 & 4855 & 4731.32120210158 & 123.678797898419 \tabularnewline
33 & 4610 & 4795.04085508801 & -185.040855088006 \tabularnewline
34 & 4900 & 4699.70730338092 & 200.292696619079 \tabularnewline
35 & 4250 & 4802.89864531784 & -552.89864531784 \tabularnewline
36 & 4105 & 4518.04375980017 & -413.043759800173 \tabularnewline
37 & 4740 & 4305.24249159661 & 434.757508403385 \tabularnewline
38 & 4565 & 4529.23074212488 & 35.7692578751166 \tabularnewline
39 & 5155 & 4547.65916104642 & 607.340838953578 \tabularnewline
40 & 5320 & 4860.56281276521 & 459.437187234786 \tabularnewline
41 & 5430 & 5097.26610093676 & 332.733899063243 \tabularnewline
42 & 4690 & 5268.69151050892 & -578.691510508925 \tabularnewline
43 & 4540 & 4970.54807070848 & -430.548070708482 \tabularnewline
44 & 4575 & 4748.72853392699 & -173.728533926991 \tabularnewline
45 & 4660 & 4659.22312084269 & 0.776879157312578 \tabularnewline
46 & 4850 & 4659.62337109704 & 190.376628902965 \tabularnewline
47 & 4200 & 4757.7059279827 & -557.705927982699 \tabularnewline
48 & 4360 & 4470.37431736406 & -110.374317364063 \tabularnewline
49 & 4655 & 4413.50916892667 & 241.490831073327 \tabularnewline
50 & 4585 & 4537.92590176098 & 47.0740982390216 \tabularnewline
51 & 5315 & 4562.17860517828 & 752.821394821715 \tabularnewline
52 & 5115 & 4950.03423487315 & 164.965765126846 \tabularnewline
53 & 5100 & 5035.02504564378 & 64.974954356223 \tabularnewline
54 & 5735 & 5068.50031880893 & 666.499681191071 \tabularnewline
55 & 5260 & 5411.88276691405 & -151.88276691405 \tabularnewline
56 & 5050 & 5333.63235239814 & -283.632352398135 \tabularnewline
57 & 5165 & 5187.50419318546 & -22.5041931854603 \tabularnewline
58 & 5190 & 5175.90997166259 & 14.0900283374131 \tabularnewline
59 & 4720 & 5183.16919257583 & -463.16919257583 \tabularnewline
60 & 5275 & 4944.54316510446 & 330.456834895542 \tabularnewline
61 & 4605 & 5114.7954250256 & -509.795425025601 \tabularnewline
62 & 4825 & 4852.14743580939 & -27.1474358093892 \tabularnewline
63 & 5595 & 4838.1610030607 & 756.838996939305 \tabularnewline
64 & 5160 & 5228.08651229127 & -68.0865122912674 \tabularnewline
65 & 5320 & 5193.00815601699 & 126.991843983013 \tabularnewline
66 & 5540 & 5258.43469935508 & 281.565300644923 \tabularnewline
67 & 4970 & 5403.49790788374 & -433.49790788374 \tabularnewline
68 & 5445 & 5180.15860696832 & 264.841393031684 \tabularnewline
69 & 5305 & 5316.60561281875 & -11.6056128187502 \tabularnewline
70 & 5145 & 5310.62636953638 & -165.626369536381 \tabularnewline
71 & 4895 & 5225.29521357764 & -330.295213577641 \tabularnewline
72 & 4555 & 5055.12622139896 & -500.126221398965 \tabularnewline
73 & 4980 & 4797.45983218383 & 182.540167816167 \tabularnewline
74 & 4930 & 4891.50502300856 & 38.4949769914383 \tabularnewline
75 & 5810 & 4911.33773983064 & 898.662260169356 \tabularnewline
76 & 5210 & 5374.33097992519 & -164.330979925187 \tabularnewline
77 & 5450 & 5289.66721221658 & 160.332787783424 \tabularnewline
78 & 5510 & 5372.27110046181 & 137.72889953819 \tabularnewline
79 & 5010 & 5443.22940401828 & -433.229404018282 \tabularnewline
80 & 5495 & 5220.02843702446 & 274.971562975538 \tabularnewline
81 & 5125 & 5361.69453397607 & -236.694533976071 \tabularnewline
82 & 5190 & 5239.74886644843 & -49.7488664484317 \tabularnewline
83 & 4565 & 5214.11811517637 & -649.118115176369 \tabularnewline
84 & 4255 & 4879.69069714623 & -624.690697146227 \tabularnewline
85 & 4875 & 4557.8483513086 & 317.151648691402 \tabularnewline
86 & 4650 & 4721.24574311772 & -71.2457431177154 \tabularnewline
87 & 5295 & 4684.53974253102 & 610.460257468977 \tabularnewline
88 & 5045 & 4999.05052715132 & 45.9494728486834 \tabularnewline
89 & 5430 & 5022.72382050942 & 407.276179490577 \tabularnewline
90 & 5325 & 5232.55361565419 & 92.4463843458107 \tabularnewline
91 & 4920 & 5280.18224425068 & -360.182244250684 \tabularnewline
92 & 5445 & 5094.61537260001 & 350.384627399987 \tabularnewline
93 & 4895 & 5275.13448540739 & -380.134485407385 \tabularnewline
94 & 5175 & 5079.28816485836 & 95.7118351416375 \tabularnewline
95 & 4545 & 5128.59916258433 & -583.599162584327 \tabularnewline
96 & 4220 & 4827.92728708968 & -607.927287089678 \tabularnewline
97 & 4595 & 4514.72149569649 & 80.278504303511 \tabularnewline
98 & 4360 & 4556.08119940812 & -196.081199408117 \tabularnewline
99 & 4750 & 4455.05963228625 & 294.940367713751 \tabularnewline
100 & 4985 & 4607.01371173845 & 377.986288261553 \tabularnewline
101 & 5140 & 4801.75327527653 & 338.246724723471 \tabularnewline
102 & 4995 & 4976.0189076194 & 18.9810923805999 \tabularnewline
103 & 5150 & 4985.79801802754 & 164.201981972456 \tabularnewline
104 & 5240 & 5070.39532564013 & 169.604674359865 \tabularnewline
105 & 4875 & 5157.7761150618 & -282.776115061797 \tabularnewline
106 & 5170 & 5012.0890916531 & 157.910908346903 \tabularnewline
107 & 4715 & 5093.44522102702 & -378.445221027025 \tabularnewline
108 & 4370 & 4898.46921408024 & -528.469214080235 \tabularnewline
109 & 5160 & 4626.20043796504 & 533.799562034959 \tabularnewline
110 & 4930 & 4901.21542384087 & 28.7845761591325 \tabularnewline
111 & 5600 & 4916.04531574948 & 683.954684250515 \tabularnewline
112 & 5385 & 5268.42062889473 & 116.579371105275 \tabularnewline
113 & 5425 & 5328.48263789246 & 96.517362107541 \tabularnewline
114 & 5375 & 5378.20864530166 & -3.20864530165818 \tabularnewline
115 & 5365 & 5376.55554251725 & -11.5555425172497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298187&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3755[/C][C]3875[/C][C]-120[/C][/ROW]
[ROW][C]3[/C][C]4670[/C][C]3813.17567369428[/C][C]856.824326305719[/C][/ROW]
[ROW][C]4[/C][C]4335[/C][C]4254.61389649597[/C][C]80.38610350403[/C][/ROW]
[ROW][C]5[/C][C]4945[/C][C]4296.02903560829[/C][C]648.970964391709[/C][/ROW]
[ROW][C]6[/C][C]4600[/C][C]4630.38064115404[/C][C]-30.3806411540427[/C][/ROW]
[ROW][C]7[/C][C]4395[/C][C]4614.72845222001[/C][C]-219.728452220005[/C][/ROW]
[ROW][C]8[/C][C]4345[/C][C]4501.5237561475[/C][C]-156.523756147504[/C][/ROW]
[ROW][C]9[/C][C]4390[/C][C]4420.88229135867[/C][C]-30.88229135867[/C][/ROW]
[ROW][C]10[/C][C]4490[/C][C]4404.97165087511[/C][C]85.0283491248856[/C][/ROW]
[ROW][C]11[/C][C]4395[/C][C]4448.77848755456[/C][C]-53.7784875545603[/C][/ROW]
[ROW][C]12[/C][C]4690[/C][C]4421.07166453122[/C][C]268.928335468783[/C][/ROW]
[ROW][C]13[/C][C]4590[/C][C]4559.62427423852[/C][C]30.3757257614834[/C][/ROW]
[ROW][C]14[/C][C]4630[/C][C]4575.27393074894[/C][C]54.726069251059[/C][/ROW]
[ROW][C]15[/C][C]5375[/C][C]4603.468950439[/C][C]771.531049561002[/C][/ROW]
[ROW][C]16[/C][C]4655[/C][C]5000.96384513111[/C][C]-345.963845131108[/C][/ROW]
[ROW][C]17[/C][C]4975[/C][C]4822.72233136972[/C][C]152.277668630282[/C][/ROW]
[ROW][C]18[/C][C]4810[/C][C]4901.17620032366[/C][C]-91.1762003236563[/C][/ROW]
[ROW][C]19[/C][C]4445[/C][C]4854.20197398928[/C][C]-409.201973989278[/C][/ROW]
[ROW][C]20[/C][C]4660[/C][C]4643.38000428213[/C][C]16.6199957178669[/C][/ROW]
[ROW][C]21[/C][C]4215[/C][C]4651.94267126931[/C][C]-436.942671269308[/C][/ROW]
[ROW][C]22[/C][C]4825[/C][C]4426.82861889059[/C][C]398.171381109411[/C][/ROW]
[ROW][C]23[/C][C]4250[/C][C]4631.96759715148[/C][C]-381.967597151481[/C][/ROW]
[ROW][C]24[/C][C]3945[/C][C]4435.17685244728[/C][C]-490.176852447275[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4182.63640517052[/C][C]207.36359482948[/C][/ROW]
[ROW][C]26[/C][C]4315[/C][C]4289.47069309273[/C][C]25.5293069072741[/C][/ROW]
[ROW][C]27[/C][C]4835[/C][C]4302.62346143101[/C][C]532.376538568989[/C][/ROW]
[ROW][C]28[/C][C]4835[/C][C]4576.90530174766[/C][C]258.094698252336[/C][/ROW]
[ROW][C]29[/C][C]4970[/C][C]4709.87639210207[/C][C]260.123607897932[/C][/ROW]
[ROW][C]30[/C][C]4690[/C][C]4843.89278222292[/C][C]-153.892782222923[/C][/ROW]
[ROW][C]31[/C][C]4700[/C][C]4764.60680235422[/C][C]-64.6068023542157[/C][/ROW]
[ROW][C]32[/C][C]4855[/C][C]4731.32120210158[/C][C]123.678797898419[/C][/ROW]
[ROW][C]33[/C][C]4610[/C][C]4795.04085508801[/C][C]-185.040855088006[/C][/ROW]
[ROW][C]34[/C][C]4900[/C][C]4699.70730338092[/C][C]200.292696619079[/C][/ROW]
[ROW][C]35[/C][C]4250[/C][C]4802.89864531784[/C][C]-552.89864531784[/C][/ROW]
[ROW][C]36[/C][C]4105[/C][C]4518.04375980017[/C][C]-413.043759800173[/C][/ROW]
[ROW][C]37[/C][C]4740[/C][C]4305.24249159661[/C][C]434.757508403385[/C][/ROW]
[ROW][C]38[/C][C]4565[/C][C]4529.23074212488[/C][C]35.7692578751166[/C][/ROW]
[ROW][C]39[/C][C]5155[/C][C]4547.65916104642[/C][C]607.340838953578[/C][/ROW]
[ROW][C]40[/C][C]5320[/C][C]4860.56281276521[/C][C]459.437187234786[/C][/ROW]
[ROW][C]41[/C][C]5430[/C][C]5097.26610093676[/C][C]332.733899063243[/C][/ROW]
[ROW][C]42[/C][C]4690[/C][C]5268.69151050892[/C][C]-578.691510508925[/C][/ROW]
[ROW][C]43[/C][C]4540[/C][C]4970.54807070848[/C][C]-430.548070708482[/C][/ROW]
[ROW][C]44[/C][C]4575[/C][C]4748.72853392699[/C][C]-173.728533926991[/C][/ROW]
[ROW][C]45[/C][C]4660[/C][C]4659.22312084269[/C][C]0.776879157312578[/C][/ROW]
[ROW][C]46[/C][C]4850[/C][C]4659.62337109704[/C][C]190.376628902965[/C][/ROW]
[ROW][C]47[/C][C]4200[/C][C]4757.7059279827[/C][C]-557.705927982699[/C][/ROW]
[ROW][C]48[/C][C]4360[/C][C]4470.37431736406[/C][C]-110.374317364063[/C][/ROW]
[ROW][C]49[/C][C]4655[/C][C]4413.50916892667[/C][C]241.490831073327[/C][/ROW]
[ROW][C]50[/C][C]4585[/C][C]4537.92590176098[/C][C]47.0740982390216[/C][/ROW]
[ROW][C]51[/C][C]5315[/C][C]4562.17860517828[/C][C]752.821394821715[/C][/ROW]
[ROW][C]52[/C][C]5115[/C][C]4950.03423487315[/C][C]164.965765126846[/C][/ROW]
[ROW][C]53[/C][C]5100[/C][C]5035.02504564378[/C][C]64.974954356223[/C][/ROW]
[ROW][C]54[/C][C]5735[/C][C]5068.50031880893[/C][C]666.499681191071[/C][/ROW]
[ROW][C]55[/C][C]5260[/C][C]5411.88276691405[/C][C]-151.88276691405[/C][/ROW]
[ROW][C]56[/C][C]5050[/C][C]5333.63235239814[/C][C]-283.632352398135[/C][/ROW]
[ROW][C]57[/C][C]5165[/C][C]5187.50419318546[/C][C]-22.5041931854603[/C][/ROW]
[ROW][C]58[/C][C]5190[/C][C]5175.90997166259[/C][C]14.0900283374131[/C][/ROW]
[ROW][C]59[/C][C]4720[/C][C]5183.16919257583[/C][C]-463.16919257583[/C][/ROW]
[ROW][C]60[/C][C]5275[/C][C]4944.54316510446[/C][C]330.456834895542[/C][/ROW]
[ROW][C]61[/C][C]4605[/C][C]5114.7954250256[/C][C]-509.795425025601[/C][/ROW]
[ROW][C]62[/C][C]4825[/C][C]4852.14743580939[/C][C]-27.1474358093892[/C][/ROW]
[ROW][C]63[/C][C]5595[/C][C]4838.1610030607[/C][C]756.838996939305[/C][/ROW]
[ROW][C]64[/C][C]5160[/C][C]5228.08651229127[/C][C]-68.0865122912674[/C][/ROW]
[ROW][C]65[/C][C]5320[/C][C]5193.00815601699[/C][C]126.991843983013[/C][/ROW]
[ROW][C]66[/C][C]5540[/C][C]5258.43469935508[/C][C]281.565300644923[/C][/ROW]
[ROW][C]67[/C][C]4970[/C][C]5403.49790788374[/C][C]-433.49790788374[/C][/ROW]
[ROW][C]68[/C][C]5445[/C][C]5180.15860696832[/C][C]264.841393031684[/C][/ROW]
[ROW][C]69[/C][C]5305[/C][C]5316.60561281875[/C][C]-11.6056128187502[/C][/ROW]
[ROW][C]70[/C][C]5145[/C][C]5310.62636953638[/C][C]-165.626369536381[/C][/ROW]
[ROW][C]71[/C][C]4895[/C][C]5225.29521357764[/C][C]-330.295213577641[/C][/ROW]
[ROW][C]72[/C][C]4555[/C][C]5055.12622139896[/C][C]-500.126221398965[/C][/ROW]
[ROW][C]73[/C][C]4980[/C][C]4797.45983218383[/C][C]182.540167816167[/C][/ROW]
[ROW][C]74[/C][C]4930[/C][C]4891.50502300856[/C][C]38.4949769914383[/C][/ROW]
[ROW][C]75[/C][C]5810[/C][C]4911.33773983064[/C][C]898.662260169356[/C][/ROW]
[ROW][C]76[/C][C]5210[/C][C]5374.33097992519[/C][C]-164.330979925187[/C][/ROW]
[ROW][C]77[/C][C]5450[/C][C]5289.66721221658[/C][C]160.332787783424[/C][/ROW]
[ROW][C]78[/C][C]5510[/C][C]5372.27110046181[/C][C]137.72889953819[/C][/ROW]
[ROW][C]79[/C][C]5010[/C][C]5443.22940401828[/C][C]-433.229404018282[/C][/ROW]
[ROW][C]80[/C][C]5495[/C][C]5220.02843702446[/C][C]274.971562975538[/C][/ROW]
[ROW][C]81[/C][C]5125[/C][C]5361.69453397607[/C][C]-236.694533976071[/C][/ROW]
[ROW][C]82[/C][C]5190[/C][C]5239.74886644843[/C][C]-49.7488664484317[/C][/ROW]
[ROW][C]83[/C][C]4565[/C][C]5214.11811517637[/C][C]-649.118115176369[/C][/ROW]
[ROW][C]84[/C][C]4255[/C][C]4879.69069714623[/C][C]-624.690697146227[/C][/ROW]
[ROW][C]85[/C][C]4875[/C][C]4557.8483513086[/C][C]317.151648691402[/C][/ROW]
[ROW][C]86[/C][C]4650[/C][C]4721.24574311772[/C][C]-71.2457431177154[/C][/ROW]
[ROW][C]87[/C][C]5295[/C][C]4684.53974253102[/C][C]610.460257468977[/C][/ROW]
[ROW][C]88[/C][C]5045[/C][C]4999.05052715132[/C][C]45.9494728486834[/C][/ROW]
[ROW][C]89[/C][C]5430[/C][C]5022.72382050942[/C][C]407.276179490577[/C][/ROW]
[ROW][C]90[/C][C]5325[/C][C]5232.55361565419[/C][C]92.4463843458107[/C][/ROW]
[ROW][C]91[/C][C]4920[/C][C]5280.18224425068[/C][C]-360.182244250684[/C][/ROW]
[ROW][C]92[/C][C]5445[/C][C]5094.61537260001[/C][C]350.384627399987[/C][/ROW]
[ROW][C]93[/C][C]4895[/C][C]5275.13448540739[/C][C]-380.134485407385[/C][/ROW]
[ROW][C]94[/C][C]5175[/C][C]5079.28816485836[/C][C]95.7118351416375[/C][/ROW]
[ROW][C]95[/C][C]4545[/C][C]5128.59916258433[/C][C]-583.599162584327[/C][/ROW]
[ROW][C]96[/C][C]4220[/C][C]4827.92728708968[/C][C]-607.927287089678[/C][/ROW]
[ROW][C]97[/C][C]4595[/C][C]4514.72149569649[/C][C]80.278504303511[/C][/ROW]
[ROW][C]98[/C][C]4360[/C][C]4556.08119940812[/C][C]-196.081199408117[/C][/ROW]
[ROW][C]99[/C][C]4750[/C][C]4455.05963228625[/C][C]294.940367713751[/C][/ROW]
[ROW][C]100[/C][C]4985[/C][C]4607.01371173845[/C][C]377.986288261553[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]4801.75327527653[/C][C]338.246724723471[/C][/ROW]
[ROW][C]102[/C][C]4995[/C][C]4976.0189076194[/C][C]18.9810923805999[/C][/ROW]
[ROW][C]103[/C][C]5150[/C][C]4985.79801802754[/C][C]164.201981972456[/C][/ROW]
[ROW][C]104[/C][C]5240[/C][C]5070.39532564013[/C][C]169.604674359865[/C][/ROW]
[ROW][C]105[/C][C]4875[/C][C]5157.7761150618[/C][C]-282.776115061797[/C][/ROW]
[ROW][C]106[/C][C]5170[/C][C]5012.0890916531[/C][C]157.910908346903[/C][/ROW]
[ROW][C]107[/C][C]4715[/C][C]5093.44522102702[/C][C]-378.445221027025[/C][/ROW]
[ROW][C]108[/C][C]4370[/C][C]4898.46921408024[/C][C]-528.469214080235[/C][/ROW]
[ROW][C]109[/C][C]5160[/C][C]4626.20043796504[/C][C]533.799562034959[/C][/ROW]
[ROW][C]110[/C][C]4930[/C][C]4901.21542384087[/C][C]28.7845761591325[/C][/ROW]
[ROW][C]111[/C][C]5600[/C][C]4916.04531574948[/C][C]683.954684250515[/C][/ROW]
[ROW][C]112[/C][C]5385[/C][C]5268.42062889473[/C][C]116.579371105275[/C][/ROW]
[ROW][C]113[/C][C]5425[/C][C]5328.48263789246[/C][C]96.517362107541[/C][/ROW]
[ROW][C]114[/C][C]5375[/C][C]5378.20864530166[/C][C]-3.20864530165818[/C][/ROW]
[ROW][C]115[/C][C]5365[/C][C]5376.55554251725[/C][C]-11.5555425172497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298187&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
237553875-120
346703813.17567369428856.824326305719
443354254.6138964959780.38610350403
549454296.02903560829648.970964391709
646004630.38064115404-30.3806411540427
743954614.72845222001-219.728452220005
843454501.5237561475-156.523756147504
943904420.88229135867-30.88229135867
1044904404.9716508751185.0283491248856
1143954448.77848755456-53.7784875545603
1246904421.07166453122268.928335468783
1345904559.6242742385230.3757257614834
1446304575.2739307489454.726069251059
1553754603.468950439771.531049561002
1646555000.96384513111-345.963845131108
1749754822.72233136972152.277668630282
1848104901.17620032366-91.1762003236563
1944454854.20197398928-409.201973989278
2046604643.3800042821316.6199957178669
2142154651.94267126931-436.942671269308
2248254426.82861889059398.171381109411
2342504631.96759715148-381.967597151481
2439454435.17685244728-490.176852447275
2543904182.63640517052207.36359482948
2643154289.4706930927325.5293069072741
2748354302.62346143101532.376538568989
2848354576.90530174766258.094698252336
2949704709.87639210207260.123607897932
3046904843.89278222292-153.892782222923
3147004764.60680235422-64.6068023542157
3248554731.32120210158123.678797898419
3346104795.04085508801-185.040855088006
3449004699.70730338092200.292696619079
3542504802.89864531784-552.89864531784
3641054518.04375980017-413.043759800173
3747404305.24249159661434.757508403385
3845654529.2307421248835.7692578751166
3951554547.65916104642607.340838953578
4053204860.56281276521459.437187234786
4154305097.26610093676332.733899063243
4246905268.69151050892-578.691510508925
4345404970.54807070848-430.548070708482
4445754748.72853392699-173.728533926991
4546604659.223120842690.776879157312578
4648504659.62337109704190.376628902965
4742004757.7059279827-557.705927982699
4843604470.37431736406-110.374317364063
4946554413.50916892667241.490831073327
5045854537.9259017609847.0740982390216
5153154562.17860517828752.821394821715
5251154950.03423487315164.965765126846
5351005035.0250456437864.974954356223
5457355068.50031880893666.499681191071
5552605411.88276691405-151.88276691405
5650505333.63235239814-283.632352398135
5751655187.50419318546-22.5041931854603
5851905175.9099716625914.0900283374131
5947205183.16919257583-463.16919257583
6052754944.54316510446330.456834895542
6146055114.7954250256-509.795425025601
6248254852.14743580939-27.1474358093892
6355954838.1610030607756.838996939305
6451605228.08651229127-68.0865122912674
6553205193.00815601699126.991843983013
6655405258.43469935508281.565300644923
6749705403.49790788374-433.49790788374
6854455180.15860696832264.841393031684
6953055316.60561281875-11.6056128187502
7051455310.62636953638-165.626369536381
7148955225.29521357764-330.295213577641
7245555055.12622139896-500.126221398965
7349804797.45983218383182.540167816167
7449304891.5050230085638.4949769914383
7558104911.33773983064898.662260169356
7652105374.33097992519-164.330979925187
7754505289.66721221658160.332787783424
7855105372.27110046181137.72889953819
7950105443.22940401828-433.229404018282
8054955220.02843702446274.971562975538
8151255361.69453397607-236.694533976071
8251905239.74886644843-49.7488664484317
8345655214.11811517637-649.118115176369
8442554879.69069714623-624.690697146227
8548754557.8483513086317.151648691402
8646504721.24574311772-71.2457431177154
8752954684.53974253102610.460257468977
8850454999.0505271513245.9494728486834
8954305022.72382050942407.276179490577
9053255232.5536156541992.4463843458107
9149205280.18224425068-360.182244250684
9254455094.61537260001350.384627399987
9348955275.13448540739-380.134485407385
9451755079.2881648583695.7118351416375
9545455128.59916258433-583.599162584327
9642204827.92728708968-607.927287089678
9745954514.7214956964980.278504303511
9843604556.08119940812-196.081199408117
9947504455.05963228625294.940367713751
10049854607.01371173845377.986288261553
10151404801.75327527653338.246724723471
10249954976.018907619418.9810923805999
10351504985.79801802754164.201981972456
10452405070.39532564013169.604674359865
10548755157.7761150618-282.776115061797
10651705012.0890916531157.910908346903
10747155093.44522102702-378.445221027025
10843704898.46921408024-528.469214080235
10951604626.20043796504533.799562034959
11049304901.2154238408728.7845761591325
11156004916.04531574948683.954684250515
11253855268.42062889473116.579371105275
11354255328.4826378924696.517362107541
11453755378.20864530166-3.20864530165818
11553655376.55554251725-11.5555425172497







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1165370.602095590374670.057913552526071.14627762821
1175370.602095590374582.549410691876158.65478048887
1185370.602095590374503.831123900396237.37306728034
1195370.602095590374431.689532806676309.51465837406
1205370.602095590374364.708620245346376.4955709354
1215370.602095590374301.917592600666439.28659858007
1225370.602095590374242.616523821386498.58766735935
1235370.602095590374186.281052415136554.9231387656
1245370.602095590374132.506292957826608.69789822291
1255370.602095590374080.971877394096660.23231378664
1265370.602095590374031.4191421176709.78504906373
1275370.602095590373983.635669874776757.56852130596

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 5370.60209559037 & 4670.05791355252 & 6071.14627762821 \tabularnewline
117 & 5370.60209559037 & 4582.54941069187 & 6158.65478048887 \tabularnewline
118 & 5370.60209559037 & 4503.83112390039 & 6237.37306728034 \tabularnewline
119 & 5370.60209559037 & 4431.68953280667 & 6309.51465837406 \tabularnewline
120 & 5370.60209559037 & 4364.70862024534 & 6376.4955709354 \tabularnewline
121 & 5370.60209559037 & 4301.91759260066 & 6439.28659858007 \tabularnewline
122 & 5370.60209559037 & 4242.61652382138 & 6498.58766735935 \tabularnewline
123 & 5370.60209559037 & 4186.28105241513 & 6554.9231387656 \tabularnewline
124 & 5370.60209559037 & 4132.50629295782 & 6608.69789822291 \tabularnewline
125 & 5370.60209559037 & 4080.97187739409 & 6660.23231378664 \tabularnewline
126 & 5370.60209559037 & 4031.419142117 & 6709.78504906373 \tabularnewline
127 & 5370.60209559037 & 3983.63566987477 & 6757.56852130596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298187&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]116[/C][C]5370.60209559037[/C][C]4670.05791355252[/C][C]6071.14627762821[/C][/ROW]
[ROW][C]117[/C][C]5370.60209559037[/C][C]4582.54941069187[/C][C]6158.65478048887[/C][/ROW]
[ROW][C]118[/C][C]5370.60209559037[/C][C]4503.83112390039[/C][C]6237.37306728034[/C][/ROW]
[ROW][C]119[/C][C]5370.60209559037[/C][C]4431.68953280667[/C][C]6309.51465837406[/C][/ROW]
[ROW][C]120[/C][C]5370.60209559037[/C][C]4364.70862024534[/C][C]6376.4955709354[/C][/ROW]
[ROW][C]121[/C][C]5370.60209559037[/C][C]4301.91759260066[/C][C]6439.28659858007[/C][/ROW]
[ROW][C]122[/C][C]5370.60209559037[/C][C]4242.61652382138[/C][C]6498.58766735935[/C][/ROW]
[ROW][C]123[/C][C]5370.60209559037[/C][C]4186.28105241513[/C][C]6554.9231387656[/C][/ROW]
[ROW][C]124[/C][C]5370.60209559037[/C][C]4132.50629295782[/C][C]6608.69789822291[/C][/ROW]
[ROW][C]125[/C][C]5370.60209559037[/C][C]4080.97187739409[/C][C]6660.23231378664[/C][/ROW]
[ROW][C]126[/C][C]5370.60209559037[/C][C]4031.419142117[/C][C]6709.78504906373[/C][/ROW]
[ROW][C]127[/C][C]5370.60209559037[/C][C]3983.63566987477[/C][C]6757.56852130596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298187&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298187&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
1165370.602095590374670.057913552526071.14627762821
1175370.602095590374582.549410691876158.65478048887
1185370.602095590374503.831123900396237.37306728034
1195370.602095590374431.689532806676309.51465837406
1205370.602095590374364.708620245346376.4955709354
1215370.602095590374301.917592600666439.28659858007
1225370.602095590374242.616523821386498.58766735935
1235370.602095590374186.281052415136554.9231387656
1245370.602095590374132.506292957826608.69789822291
1255370.602095590374080.971877394096660.23231378664
1265370.602095590374031.4191421176709.78504906373
1275370.602095590373983.635669874776757.56852130596



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')