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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Dec 2016 21:39:37 +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/13/t14816616306na9idyna32l9ta.htm/, Retrieved Sun, 05 May 2024 02:10:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299225, Retrieved Sun, 05 May 2024 02:10:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-13 20:39:37] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
2650.84
2685.28
2706.04
2743.34
2768.48
2756.38
2788.68
2828.58
2853.18
2859
2900.32
2884.46
2884.3
2910.86
2916.62
2921.6
2926.58
2938.46
2942.92
2956.92
2946.78
2956.48
2968.1
2983.1
2993.04
3007.44
3024.64
3033.04
3047.94
3066.02
3096.46
3131.16
3133.54
3118.68
3133.5
3108.9
3136.04
3129.3
3136.1
3143.72
3199.24
3205.78
3191.44
3172.72
3211.92
3268.38
3289.52
3316.28
3348.6
3400.44
3425.68
3456.3
3454.46
3514.48
3546
3596.3
3616.2
3598.08
3595.28
3610.7
3628.74
3641.84
3637.66
3661.64
3686.56
3718.38
3728.88
3723.42
3726.34
3764.84
3782.26
3771.32
3766.66
3774.6
3795.42
3829.48
3873.62
3856.16
3875.42
3893.52
3918.86
3918.24
3942.22
3938.7
3997.98
3997.54
3973.24
3946.4
3937.48
3920.12
3940.74
3948.68
3935.74
3958.58
3975.44
4029.24
4013.44
4030.02
4032.04
4032.48
4020.54
4093.42
4098.18




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=299225&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=299225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299225&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
alpha0.999950680880253
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999950680880253 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299225&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]0.999950680880253[/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=299225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299225&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
alpha0.999950680880253
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22685.282650.8434.4400000000001
32706.042685.2783014495220.7616985504837
42743.342706.038976051337.3010239486971
52768.482743.3381603463325.1418396536665
62756.382768.4787600266-12.0987600265994
72788.682756.3805967001932.2994032998049
82828.582788.6784070218639.901592978139
92853.182828.5780320885624.601967911442
1028592853.17878665265.82121334740168
112900.322858.9997129028841.3202870971181
122884.462900.31796211981-15.8579621198128
132884.32884.46078210073-0.160782100732831
142910.862884.3000079296326.559992070368
152916.622910.858690084575.76130991542959
162921.62916.619715857274.98028414273358
172926.582921.599754376774.98024562323008
182938.462926.5797543786711.8802456213302
192942.922938.459414076744.46058592325653
202956.922942.9197800078314.0002199921714
212946.782956.91930952147-10.1393095214739
222956.482946.780500061829.69949993817954
232968.12956.479521629211.6204783707985
242983.12968.0994268882415.0005731117644
252993.042983.099260184949.94073981506153
263007.442993.0395097314614.4004902685374
273024.643007.439289780517.2007102195039
283033.043024.639151676118.4008483238872
293047.943033.0395856775614.9004143224447
303066.023047.9392651246818.0807348753183
313096.463066.0191082740730.4408917259284
323131.163096.4584986820234.7015013179839
333133.543131.15828855252.38171144749913
343118.683133.53988253609-14.8598825360882
353133.53118.6807328763314.8192671236739
363108.93133.49926912679-24.5992691267902
373136.043108.901213214327.1387867857002
383129.33136.03866153892-6.73866153892459
393136.13129.300332344866.79966765514428
403143.723136.099664646387.62033535362343
413199.243143.7196241717755.5203758282319
423205.783199.237261783946.54273821606421
433191.443205.77967731791-14.3396773179106
443172.723191.44070722026-18.7207072202627
453211.923172.720923288839.1990767111993
463268.383211.9180667360456.4619332639586
473289.523268.3772153471521.1427846528477
483316.283289.5189572564726.7610427435284
493348.63316.2786801689332.3213198310709
503400.443348.5984059409651.841594059043
513425.683400.4374432182125.2425567817854
523456.33425.6787550593230.6212449406808
533454.463456.29848978715-1.83848978715423
543514.483454.460090672760.0199093273022
5535463514.477039870931.5229601290953
563596.33545.9984453153550.3015546846459
573616.23596.297519171619.9024808283984
583598.083616.19901842716-18.1190184271645
593595.283598.08089361404-2.80089361403907
603610.73595.2801381376115.4198618623918
613628.743610.6992395059918.0407604940137
623641.843628.7391102455713.1008897544275
633637.663641.83935387565-4.17935387564967
643661.643637.6602061220523.9797938779457
653686.563661.6388173376724.9211826623259
663718.383686.5587709092131.8212290907923
673728.883718.3784306049910.5015693950077
683723.423728.87948207184-5.45948207184119
693726.343723.420269256852.91973074315001
703764.843726.3398560014538.5001439985504
713782.263764.8381012067917.4218987932122
723771.323782.25914076729-10.939140767287
733766.663771.32053950879-4.66053950879359
743774.63766.660229853717.93977014629399
753795.423774.5996084175320.8203915824747
763829.483795.4189731566134.0610268433857
773873.623829.4783201401444.1416798598616
783856.163873.6178229712-17.4578229712051
793875.423856.1608610044619.2591389955383
803893.523875.4190501562218.100949843782
813918.863893.5191072770925.3408927229129
823918.243918.85875020948-0.618750209477639
833942.223918.2400305162223.9799694837843
843938.73942.21881732901-3.51881732901347
853997.983938.7001735449759.279826455027
863997.543997.97707637114-0.437076371140392
873973.243997.54002155622-24.300021556222
883946.43973.24119845567-26.8411984556728
893937.483946.40132378428-8.92132378428096
903920.123937.48043999184-17.3604399918363
913940.743920.1208562016220.6191437983812
923948.683940.738983081987.94101691802234
933935.743948.67960835604-12.9396083560359
943958.583935.7406381700922.839361829906
953975.443958.5788735827816.8611264172214
964029.243975.4391684240953.8008315759125
974013.444029.23734659034-15.7973465903447
984030.024013.4407791112316.5792208887719
994032.044030.019182327422.02081767258005
1004032.484032.039900335050.440099664948775
1014020.544032.47997829467-11.9399782946716
1024093.424020.5405888692272.8794111307807
1034098.184093.41640565164.76359434840515

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2685.28 & 2650.84 & 34.4400000000001 \tabularnewline
3 & 2706.04 & 2685.27830144952 & 20.7616985504837 \tabularnewline
4 & 2743.34 & 2706.0389760513 & 37.3010239486971 \tabularnewline
5 & 2768.48 & 2743.33816034633 & 25.1418396536665 \tabularnewline
6 & 2756.38 & 2768.4787600266 & -12.0987600265994 \tabularnewline
7 & 2788.68 & 2756.38059670019 & 32.2994032998049 \tabularnewline
8 & 2828.58 & 2788.67840702186 & 39.901592978139 \tabularnewline
9 & 2853.18 & 2828.57803208856 & 24.601967911442 \tabularnewline
10 & 2859 & 2853.1787866526 & 5.82121334740168 \tabularnewline
11 & 2900.32 & 2858.99971290288 & 41.3202870971181 \tabularnewline
12 & 2884.46 & 2900.31796211981 & -15.8579621198128 \tabularnewline
13 & 2884.3 & 2884.46078210073 & -0.160782100732831 \tabularnewline
14 & 2910.86 & 2884.30000792963 & 26.559992070368 \tabularnewline
15 & 2916.62 & 2910.85869008457 & 5.76130991542959 \tabularnewline
16 & 2921.6 & 2916.61971585727 & 4.98028414273358 \tabularnewline
17 & 2926.58 & 2921.59975437677 & 4.98024562323008 \tabularnewline
18 & 2938.46 & 2926.57975437867 & 11.8802456213302 \tabularnewline
19 & 2942.92 & 2938.45941407674 & 4.46058592325653 \tabularnewline
20 & 2956.92 & 2942.91978000783 & 14.0002199921714 \tabularnewline
21 & 2946.78 & 2956.91930952147 & -10.1393095214739 \tabularnewline
22 & 2956.48 & 2946.78050006182 & 9.69949993817954 \tabularnewline
23 & 2968.1 & 2956.4795216292 & 11.6204783707985 \tabularnewline
24 & 2983.1 & 2968.09942688824 & 15.0005731117644 \tabularnewline
25 & 2993.04 & 2983.09926018494 & 9.94073981506153 \tabularnewline
26 & 3007.44 & 2993.03950973146 & 14.4004902685374 \tabularnewline
27 & 3024.64 & 3007.4392897805 & 17.2007102195039 \tabularnewline
28 & 3033.04 & 3024.63915167611 & 8.4008483238872 \tabularnewline
29 & 3047.94 & 3033.03958567756 & 14.9004143224447 \tabularnewline
30 & 3066.02 & 3047.93926512468 & 18.0807348753183 \tabularnewline
31 & 3096.46 & 3066.01910827407 & 30.4408917259284 \tabularnewline
32 & 3131.16 & 3096.45849868202 & 34.7015013179839 \tabularnewline
33 & 3133.54 & 3131.1582885525 & 2.38171144749913 \tabularnewline
34 & 3118.68 & 3133.53988253609 & -14.8598825360882 \tabularnewline
35 & 3133.5 & 3118.68073287633 & 14.8192671236739 \tabularnewline
36 & 3108.9 & 3133.49926912679 & -24.5992691267902 \tabularnewline
37 & 3136.04 & 3108.9012132143 & 27.1387867857002 \tabularnewline
38 & 3129.3 & 3136.03866153892 & -6.73866153892459 \tabularnewline
39 & 3136.1 & 3129.30033234486 & 6.79966765514428 \tabularnewline
40 & 3143.72 & 3136.09966464638 & 7.62033535362343 \tabularnewline
41 & 3199.24 & 3143.71962417177 & 55.5203758282319 \tabularnewline
42 & 3205.78 & 3199.23726178394 & 6.54273821606421 \tabularnewline
43 & 3191.44 & 3205.77967731791 & -14.3396773179106 \tabularnewline
44 & 3172.72 & 3191.44070722026 & -18.7207072202627 \tabularnewline
45 & 3211.92 & 3172.7209232888 & 39.1990767111993 \tabularnewline
46 & 3268.38 & 3211.91806673604 & 56.4619332639586 \tabularnewline
47 & 3289.52 & 3268.37721534715 & 21.1427846528477 \tabularnewline
48 & 3316.28 & 3289.51895725647 & 26.7610427435284 \tabularnewline
49 & 3348.6 & 3316.27868016893 & 32.3213198310709 \tabularnewline
50 & 3400.44 & 3348.59840594096 & 51.841594059043 \tabularnewline
51 & 3425.68 & 3400.43744321821 & 25.2425567817854 \tabularnewline
52 & 3456.3 & 3425.67875505932 & 30.6212449406808 \tabularnewline
53 & 3454.46 & 3456.29848978715 & -1.83848978715423 \tabularnewline
54 & 3514.48 & 3454.4600906727 & 60.0199093273022 \tabularnewline
55 & 3546 & 3514.4770398709 & 31.5229601290953 \tabularnewline
56 & 3596.3 & 3545.99844531535 & 50.3015546846459 \tabularnewline
57 & 3616.2 & 3596.2975191716 & 19.9024808283984 \tabularnewline
58 & 3598.08 & 3616.19901842716 & -18.1190184271645 \tabularnewline
59 & 3595.28 & 3598.08089361404 & -2.80089361403907 \tabularnewline
60 & 3610.7 & 3595.28013813761 & 15.4198618623918 \tabularnewline
61 & 3628.74 & 3610.69923950599 & 18.0407604940137 \tabularnewline
62 & 3641.84 & 3628.73911024557 & 13.1008897544275 \tabularnewline
63 & 3637.66 & 3641.83935387565 & -4.17935387564967 \tabularnewline
64 & 3661.64 & 3637.66020612205 & 23.9797938779457 \tabularnewline
65 & 3686.56 & 3661.63881733767 & 24.9211826623259 \tabularnewline
66 & 3718.38 & 3686.55877090921 & 31.8212290907923 \tabularnewline
67 & 3728.88 & 3718.37843060499 & 10.5015693950077 \tabularnewline
68 & 3723.42 & 3728.87948207184 & -5.45948207184119 \tabularnewline
69 & 3726.34 & 3723.42026925685 & 2.91973074315001 \tabularnewline
70 & 3764.84 & 3726.33985600145 & 38.5001439985504 \tabularnewline
71 & 3782.26 & 3764.83810120679 & 17.4218987932122 \tabularnewline
72 & 3771.32 & 3782.25914076729 & -10.939140767287 \tabularnewline
73 & 3766.66 & 3771.32053950879 & -4.66053950879359 \tabularnewline
74 & 3774.6 & 3766.66022985371 & 7.93977014629399 \tabularnewline
75 & 3795.42 & 3774.59960841753 & 20.8203915824747 \tabularnewline
76 & 3829.48 & 3795.41897315661 & 34.0610268433857 \tabularnewline
77 & 3873.62 & 3829.47832014014 & 44.1416798598616 \tabularnewline
78 & 3856.16 & 3873.6178229712 & -17.4578229712051 \tabularnewline
79 & 3875.42 & 3856.16086100446 & 19.2591389955383 \tabularnewline
80 & 3893.52 & 3875.41905015622 & 18.100949843782 \tabularnewline
81 & 3918.86 & 3893.51910727709 & 25.3408927229129 \tabularnewline
82 & 3918.24 & 3918.85875020948 & -0.618750209477639 \tabularnewline
83 & 3942.22 & 3918.24003051622 & 23.9799694837843 \tabularnewline
84 & 3938.7 & 3942.21881732901 & -3.51881732901347 \tabularnewline
85 & 3997.98 & 3938.70017354497 & 59.279826455027 \tabularnewline
86 & 3997.54 & 3997.97707637114 & -0.437076371140392 \tabularnewline
87 & 3973.24 & 3997.54002155622 & -24.300021556222 \tabularnewline
88 & 3946.4 & 3973.24119845567 & -26.8411984556728 \tabularnewline
89 & 3937.48 & 3946.40132378428 & -8.92132378428096 \tabularnewline
90 & 3920.12 & 3937.48043999184 & -17.3604399918363 \tabularnewline
91 & 3940.74 & 3920.12085620162 & 20.6191437983812 \tabularnewline
92 & 3948.68 & 3940.73898308198 & 7.94101691802234 \tabularnewline
93 & 3935.74 & 3948.67960835604 & -12.9396083560359 \tabularnewline
94 & 3958.58 & 3935.74063817009 & 22.839361829906 \tabularnewline
95 & 3975.44 & 3958.57887358278 & 16.8611264172214 \tabularnewline
96 & 4029.24 & 3975.43916842409 & 53.8008315759125 \tabularnewline
97 & 4013.44 & 4029.23734659034 & -15.7973465903447 \tabularnewline
98 & 4030.02 & 4013.44077911123 & 16.5792208887719 \tabularnewline
99 & 4032.04 & 4030.01918232742 & 2.02081767258005 \tabularnewline
100 & 4032.48 & 4032.03990033505 & 0.440099664948775 \tabularnewline
101 & 4020.54 & 4032.47997829467 & -11.9399782946716 \tabularnewline
102 & 4093.42 & 4020.54058886922 & 72.8794111307807 \tabularnewline
103 & 4098.18 & 4093.4164056516 & 4.76359434840515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299225&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]2685.28[/C][C]2650.84[/C][C]34.4400000000001[/C][/ROW]
[ROW][C]3[/C][C]2706.04[/C][C]2685.27830144952[/C][C]20.7616985504837[/C][/ROW]
[ROW][C]4[/C][C]2743.34[/C][C]2706.0389760513[/C][C]37.3010239486971[/C][/ROW]
[ROW][C]5[/C][C]2768.48[/C][C]2743.33816034633[/C][C]25.1418396536665[/C][/ROW]
[ROW][C]6[/C][C]2756.38[/C][C]2768.4787600266[/C][C]-12.0987600265994[/C][/ROW]
[ROW][C]7[/C][C]2788.68[/C][C]2756.38059670019[/C][C]32.2994032998049[/C][/ROW]
[ROW][C]8[/C][C]2828.58[/C][C]2788.67840702186[/C][C]39.901592978139[/C][/ROW]
[ROW][C]9[/C][C]2853.18[/C][C]2828.57803208856[/C][C]24.601967911442[/C][/ROW]
[ROW][C]10[/C][C]2859[/C][C]2853.1787866526[/C][C]5.82121334740168[/C][/ROW]
[ROW][C]11[/C][C]2900.32[/C][C]2858.99971290288[/C][C]41.3202870971181[/C][/ROW]
[ROW][C]12[/C][C]2884.46[/C][C]2900.31796211981[/C][C]-15.8579621198128[/C][/ROW]
[ROW][C]13[/C][C]2884.3[/C][C]2884.46078210073[/C][C]-0.160782100732831[/C][/ROW]
[ROW][C]14[/C][C]2910.86[/C][C]2884.30000792963[/C][C]26.559992070368[/C][/ROW]
[ROW][C]15[/C][C]2916.62[/C][C]2910.85869008457[/C][C]5.76130991542959[/C][/ROW]
[ROW][C]16[/C][C]2921.6[/C][C]2916.61971585727[/C][C]4.98028414273358[/C][/ROW]
[ROW][C]17[/C][C]2926.58[/C][C]2921.59975437677[/C][C]4.98024562323008[/C][/ROW]
[ROW][C]18[/C][C]2938.46[/C][C]2926.57975437867[/C][C]11.8802456213302[/C][/ROW]
[ROW][C]19[/C][C]2942.92[/C][C]2938.45941407674[/C][C]4.46058592325653[/C][/ROW]
[ROW][C]20[/C][C]2956.92[/C][C]2942.91978000783[/C][C]14.0002199921714[/C][/ROW]
[ROW][C]21[/C][C]2946.78[/C][C]2956.91930952147[/C][C]-10.1393095214739[/C][/ROW]
[ROW][C]22[/C][C]2956.48[/C][C]2946.78050006182[/C][C]9.69949993817954[/C][/ROW]
[ROW][C]23[/C][C]2968.1[/C][C]2956.4795216292[/C][C]11.6204783707985[/C][/ROW]
[ROW][C]24[/C][C]2983.1[/C][C]2968.09942688824[/C][C]15.0005731117644[/C][/ROW]
[ROW][C]25[/C][C]2993.04[/C][C]2983.09926018494[/C][C]9.94073981506153[/C][/ROW]
[ROW][C]26[/C][C]3007.44[/C][C]2993.03950973146[/C][C]14.4004902685374[/C][/ROW]
[ROW][C]27[/C][C]3024.64[/C][C]3007.4392897805[/C][C]17.2007102195039[/C][/ROW]
[ROW][C]28[/C][C]3033.04[/C][C]3024.63915167611[/C][C]8.4008483238872[/C][/ROW]
[ROW][C]29[/C][C]3047.94[/C][C]3033.03958567756[/C][C]14.9004143224447[/C][/ROW]
[ROW][C]30[/C][C]3066.02[/C][C]3047.93926512468[/C][C]18.0807348753183[/C][/ROW]
[ROW][C]31[/C][C]3096.46[/C][C]3066.01910827407[/C][C]30.4408917259284[/C][/ROW]
[ROW][C]32[/C][C]3131.16[/C][C]3096.45849868202[/C][C]34.7015013179839[/C][/ROW]
[ROW][C]33[/C][C]3133.54[/C][C]3131.1582885525[/C][C]2.38171144749913[/C][/ROW]
[ROW][C]34[/C][C]3118.68[/C][C]3133.53988253609[/C][C]-14.8598825360882[/C][/ROW]
[ROW][C]35[/C][C]3133.5[/C][C]3118.68073287633[/C][C]14.8192671236739[/C][/ROW]
[ROW][C]36[/C][C]3108.9[/C][C]3133.49926912679[/C][C]-24.5992691267902[/C][/ROW]
[ROW][C]37[/C][C]3136.04[/C][C]3108.9012132143[/C][C]27.1387867857002[/C][/ROW]
[ROW][C]38[/C][C]3129.3[/C][C]3136.03866153892[/C][C]-6.73866153892459[/C][/ROW]
[ROW][C]39[/C][C]3136.1[/C][C]3129.30033234486[/C][C]6.79966765514428[/C][/ROW]
[ROW][C]40[/C][C]3143.72[/C][C]3136.09966464638[/C][C]7.62033535362343[/C][/ROW]
[ROW][C]41[/C][C]3199.24[/C][C]3143.71962417177[/C][C]55.5203758282319[/C][/ROW]
[ROW][C]42[/C][C]3205.78[/C][C]3199.23726178394[/C][C]6.54273821606421[/C][/ROW]
[ROW][C]43[/C][C]3191.44[/C][C]3205.77967731791[/C][C]-14.3396773179106[/C][/ROW]
[ROW][C]44[/C][C]3172.72[/C][C]3191.44070722026[/C][C]-18.7207072202627[/C][/ROW]
[ROW][C]45[/C][C]3211.92[/C][C]3172.7209232888[/C][C]39.1990767111993[/C][/ROW]
[ROW][C]46[/C][C]3268.38[/C][C]3211.91806673604[/C][C]56.4619332639586[/C][/ROW]
[ROW][C]47[/C][C]3289.52[/C][C]3268.37721534715[/C][C]21.1427846528477[/C][/ROW]
[ROW][C]48[/C][C]3316.28[/C][C]3289.51895725647[/C][C]26.7610427435284[/C][/ROW]
[ROW][C]49[/C][C]3348.6[/C][C]3316.27868016893[/C][C]32.3213198310709[/C][/ROW]
[ROW][C]50[/C][C]3400.44[/C][C]3348.59840594096[/C][C]51.841594059043[/C][/ROW]
[ROW][C]51[/C][C]3425.68[/C][C]3400.43744321821[/C][C]25.2425567817854[/C][/ROW]
[ROW][C]52[/C][C]3456.3[/C][C]3425.67875505932[/C][C]30.6212449406808[/C][/ROW]
[ROW][C]53[/C][C]3454.46[/C][C]3456.29848978715[/C][C]-1.83848978715423[/C][/ROW]
[ROW][C]54[/C][C]3514.48[/C][C]3454.4600906727[/C][C]60.0199093273022[/C][/ROW]
[ROW][C]55[/C][C]3546[/C][C]3514.4770398709[/C][C]31.5229601290953[/C][/ROW]
[ROW][C]56[/C][C]3596.3[/C][C]3545.99844531535[/C][C]50.3015546846459[/C][/ROW]
[ROW][C]57[/C][C]3616.2[/C][C]3596.2975191716[/C][C]19.9024808283984[/C][/ROW]
[ROW][C]58[/C][C]3598.08[/C][C]3616.19901842716[/C][C]-18.1190184271645[/C][/ROW]
[ROW][C]59[/C][C]3595.28[/C][C]3598.08089361404[/C][C]-2.80089361403907[/C][/ROW]
[ROW][C]60[/C][C]3610.7[/C][C]3595.28013813761[/C][C]15.4198618623918[/C][/ROW]
[ROW][C]61[/C][C]3628.74[/C][C]3610.69923950599[/C][C]18.0407604940137[/C][/ROW]
[ROW][C]62[/C][C]3641.84[/C][C]3628.73911024557[/C][C]13.1008897544275[/C][/ROW]
[ROW][C]63[/C][C]3637.66[/C][C]3641.83935387565[/C][C]-4.17935387564967[/C][/ROW]
[ROW][C]64[/C][C]3661.64[/C][C]3637.66020612205[/C][C]23.9797938779457[/C][/ROW]
[ROW][C]65[/C][C]3686.56[/C][C]3661.63881733767[/C][C]24.9211826623259[/C][/ROW]
[ROW][C]66[/C][C]3718.38[/C][C]3686.55877090921[/C][C]31.8212290907923[/C][/ROW]
[ROW][C]67[/C][C]3728.88[/C][C]3718.37843060499[/C][C]10.5015693950077[/C][/ROW]
[ROW][C]68[/C][C]3723.42[/C][C]3728.87948207184[/C][C]-5.45948207184119[/C][/ROW]
[ROW][C]69[/C][C]3726.34[/C][C]3723.42026925685[/C][C]2.91973074315001[/C][/ROW]
[ROW][C]70[/C][C]3764.84[/C][C]3726.33985600145[/C][C]38.5001439985504[/C][/ROW]
[ROW][C]71[/C][C]3782.26[/C][C]3764.83810120679[/C][C]17.4218987932122[/C][/ROW]
[ROW][C]72[/C][C]3771.32[/C][C]3782.25914076729[/C][C]-10.939140767287[/C][/ROW]
[ROW][C]73[/C][C]3766.66[/C][C]3771.32053950879[/C][C]-4.66053950879359[/C][/ROW]
[ROW][C]74[/C][C]3774.6[/C][C]3766.66022985371[/C][C]7.93977014629399[/C][/ROW]
[ROW][C]75[/C][C]3795.42[/C][C]3774.59960841753[/C][C]20.8203915824747[/C][/ROW]
[ROW][C]76[/C][C]3829.48[/C][C]3795.41897315661[/C][C]34.0610268433857[/C][/ROW]
[ROW][C]77[/C][C]3873.62[/C][C]3829.47832014014[/C][C]44.1416798598616[/C][/ROW]
[ROW][C]78[/C][C]3856.16[/C][C]3873.6178229712[/C][C]-17.4578229712051[/C][/ROW]
[ROW][C]79[/C][C]3875.42[/C][C]3856.16086100446[/C][C]19.2591389955383[/C][/ROW]
[ROW][C]80[/C][C]3893.52[/C][C]3875.41905015622[/C][C]18.100949843782[/C][/ROW]
[ROW][C]81[/C][C]3918.86[/C][C]3893.51910727709[/C][C]25.3408927229129[/C][/ROW]
[ROW][C]82[/C][C]3918.24[/C][C]3918.85875020948[/C][C]-0.618750209477639[/C][/ROW]
[ROW][C]83[/C][C]3942.22[/C][C]3918.24003051622[/C][C]23.9799694837843[/C][/ROW]
[ROW][C]84[/C][C]3938.7[/C][C]3942.21881732901[/C][C]-3.51881732901347[/C][/ROW]
[ROW][C]85[/C][C]3997.98[/C][C]3938.70017354497[/C][C]59.279826455027[/C][/ROW]
[ROW][C]86[/C][C]3997.54[/C][C]3997.97707637114[/C][C]-0.437076371140392[/C][/ROW]
[ROW][C]87[/C][C]3973.24[/C][C]3997.54002155622[/C][C]-24.300021556222[/C][/ROW]
[ROW][C]88[/C][C]3946.4[/C][C]3973.24119845567[/C][C]-26.8411984556728[/C][/ROW]
[ROW][C]89[/C][C]3937.48[/C][C]3946.40132378428[/C][C]-8.92132378428096[/C][/ROW]
[ROW][C]90[/C][C]3920.12[/C][C]3937.48043999184[/C][C]-17.3604399918363[/C][/ROW]
[ROW][C]91[/C][C]3940.74[/C][C]3920.12085620162[/C][C]20.6191437983812[/C][/ROW]
[ROW][C]92[/C][C]3948.68[/C][C]3940.73898308198[/C][C]7.94101691802234[/C][/ROW]
[ROW][C]93[/C][C]3935.74[/C][C]3948.67960835604[/C][C]-12.9396083560359[/C][/ROW]
[ROW][C]94[/C][C]3958.58[/C][C]3935.74063817009[/C][C]22.839361829906[/C][/ROW]
[ROW][C]95[/C][C]3975.44[/C][C]3958.57887358278[/C][C]16.8611264172214[/C][/ROW]
[ROW][C]96[/C][C]4029.24[/C][C]3975.43916842409[/C][C]53.8008315759125[/C][/ROW]
[ROW][C]97[/C][C]4013.44[/C][C]4029.23734659034[/C][C]-15.7973465903447[/C][/ROW]
[ROW][C]98[/C][C]4030.02[/C][C]4013.44077911123[/C][C]16.5792208887719[/C][/ROW]
[ROW][C]99[/C][C]4032.04[/C][C]4030.01918232742[/C][C]2.02081767258005[/C][/ROW]
[ROW][C]100[/C][C]4032.48[/C][C]4032.03990033505[/C][C]0.440099664948775[/C][/ROW]
[ROW][C]101[/C][C]4020.54[/C][C]4032.47997829467[/C][C]-11.9399782946716[/C][/ROW]
[ROW][C]102[/C][C]4093.42[/C][C]4020.54058886922[/C][C]72.8794111307807[/C][/ROW]
[ROW][C]103[/C][C]4098.18[/C][C]4093.4164056516[/C][C]4.76359434840515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299225&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
22685.282650.8434.4400000000001
32706.042685.2783014495220.7616985504837
42743.342706.038976051337.3010239486971
52768.482743.3381603463325.1418396536665
62756.382768.4787600266-12.0987600265994
72788.682756.3805967001932.2994032998049
82828.582788.6784070218639.901592978139
92853.182828.5780320885624.601967911442
1028592853.17878665265.82121334740168
112900.322858.9997129028841.3202870971181
122884.462900.31796211981-15.8579621198128
132884.32884.46078210073-0.160782100732831
142910.862884.3000079296326.559992070368
152916.622910.858690084575.76130991542959
162921.62916.619715857274.98028414273358
172926.582921.599754376774.98024562323008
182938.462926.5797543786711.8802456213302
192942.922938.459414076744.46058592325653
202956.922942.9197800078314.0002199921714
212946.782956.91930952147-10.1393095214739
222956.482946.780500061829.69949993817954
232968.12956.479521629211.6204783707985
242983.12968.0994268882415.0005731117644
252993.042983.099260184949.94073981506153
263007.442993.0395097314614.4004902685374
273024.643007.439289780517.2007102195039
283033.043024.639151676118.4008483238872
293047.943033.0395856775614.9004143224447
303066.023047.9392651246818.0807348753183
313096.463066.0191082740730.4408917259284
323131.163096.4584986820234.7015013179839
333133.543131.15828855252.38171144749913
343118.683133.53988253609-14.8598825360882
353133.53118.6807328763314.8192671236739
363108.93133.49926912679-24.5992691267902
373136.043108.901213214327.1387867857002
383129.33136.03866153892-6.73866153892459
393136.13129.300332344866.79966765514428
403143.723136.099664646387.62033535362343
413199.243143.7196241717755.5203758282319
423205.783199.237261783946.54273821606421
433191.443205.77967731791-14.3396773179106
443172.723191.44070722026-18.7207072202627
453211.923172.720923288839.1990767111993
463268.383211.9180667360456.4619332639586
473289.523268.3772153471521.1427846528477
483316.283289.5189572564726.7610427435284
493348.63316.2786801689332.3213198310709
503400.443348.5984059409651.841594059043
513425.683400.4374432182125.2425567817854
523456.33425.6787550593230.6212449406808
533454.463456.29848978715-1.83848978715423
543514.483454.460090672760.0199093273022
5535463514.477039870931.5229601290953
563596.33545.9984453153550.3015546846459
573616.23596.297519171619.9024808283984
583598.083616.19901842716-18.1190184271645
593595.283598.08089361404-2.80089361403907
603610.73595.2801381376115.4198618623918
613628.743610.6992395059918.0407604940137
623641.843628.7391102455713.1008897544275
633637.663641.83935387565-4.17935387564967
643661.643637.6602061220523.9797938779457
653686.563661.6388173376724.9211826623259
663718.383686.5587709092131.8212290907923
673728.883718.3784306049910.5015693950077
683723.423728.87948207184-5.45948207184119
693726.343723.420269256852.91973074315001
703764.843726.3398560014538.5001439985504
713782.263764.8381012067917.4218987932122
723771.323782.25914076729-10.939140767287
733766.663771.32053950879-4.66053950879359
743774.63766.660229853717.93977014629399
753795.423774.5996084175320.8203915824747
763829.483795.4189731566134.0610268433857
773873.623829.4783201401444.1416798598616
783856.163873.6178229712-17.4578229712051
793875.423856.1608610044619.2591389955383
803893.523875.4190501562218.100949843782
813918.863893.5191072770925.3408927229129
823918.243918.85875020948-0.618750209477639
833942.223918.2400305162223.9799694837843
843938.73942.21881732901-3.51881732901347
853997.983938.7001735449759.279826455027
863997.543997.97707637114-0.437076371140392
873973.243997.54002155622-24.300021556222
883946.43973.24119845567-26.8411984556728
893937.483946.40132378428-8.92132378428096
903920.123937.48043999184-17.3604399918363
913940.743920.1208562016220.6191437983812
923948.683940.738983081987.94101691802234
933935.743948.67960835604-12.9396083560359
943958.583935.7406381700922.839361829906
953975.443958.5788735827816.8611264172214
964029.243975.4391684240953.8008315759125
974013.444029.23734659034-15.7973465903447
984030.024013.4407791112316.5792208887719
994032.044030.019182327422.02081767258005
1004032.484032.039900335050.440099664948775
1014020.544032.47997829467-11.9399782946716
1024093.424020.5405888692272.8794111307807
1034098.184093.41640565164.76359434840515







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1044098.179765063724056.968170944744139.39135918271
1054098.179765063724039.899206924274156.46032320317
1064098.179765063724026.801537120854169.55799300659
1074098.179765063724015.759625586274180.59990454117
1084098.179765063724006.03147501614190.32805511134
1094098.179765063723997.236536831624199.12299329582
1104098.179765063723989.148745197194207.21078493025
1114098.179765063723981.620804617284214.73872551016
1124098.179765063723974.550402744034221.80912738341
1134098.179765063723967.86304627914228.49648384834
1144098.179765063723961.50249862194234.85703150554
1154098.179765063723955.425069416864240.93446071058

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
104 & 4098.17976506372 & 4056.96817094474 & 4139.39135918271 \tabularnewline
105 & 4098.17976506372 & 4039.89920692427 & 4156.46032320317 \tabularnewline
106 & 4098.17976506372 & 4026.80153712085 & 4169.55799300659 \tabularnewline
107 & 4098.17976506372 & 4015.75962558627 & 4180.59990454117 \tabularnewline
108 & 4098.17976506372 & 4006.0314750161 & 4190.32805511134 \tabularnewline
109 & 4098.17976506372 & 3997.23653683162 & 4199.12299329582 \tabularnewline
110 & 4098.17976506372 & 3989.14874519719 & 4207.21078493025 \tabularnewline
111 & 4098.17976506372 & 3981.62080461728 & 4214.73872551016 \tabularnewline
112 & 4098.17976506372 & 3974.55040274403 & 4221.80912738341 \tabularnewline
113 & 4098.17976506372 & 3967.8630462791 & 4228.49648384834 \tabularnewline
114 & 4098.17976506372 & 3961.5024986219 & 4234.85703150554 \tabularnewline
115 & 4098.17976506372 & 3955.42506941686 & 4240.93446071058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299225&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]104[/C][C]4098.17976506372[/C][C]4056.96817094474[/C][C]4139.39135918271[/C][/ROW]
[ROW][C]105[/C][C]4098.17976506372[/C][C]4039.89920692427[/C][C]4156.46032320317[/C][/ROW]
[ROW][C]106[/C][C]4098.17976506372[/C][C]4026.80153712085[/C][C]4169.55799300659[/C][/ROW]
[ROW][C]107[/C][C]4098.17976506372[/C][C]4015.75962558627[/C][C]4180.59990454117[/C][/ROW]
[ROW][C]108[/C][C]4098.17976506372[/C][C]4006.0314750161[/C][C]4190.32805511134[/C][/ROW]
[ROW][C]109[/C][C]4098.17976506372[/C][C]3997.23653683162[/C][C]4199.12299329582[/C][/ROW]
[ROW][C]110[/C][C]4098.17976506372[/C][C]3989.14874519719[/C][C]4207.21078493025[/C][/ROW]
[ROW][C]111[/C][C]4098.17976506372[/C][C]3981.62080461728[/C][C]4214.73872551016[/C][/ROW]
[ROW][C]112[/C][C]4098.17976506372[/C][C]3974.55040274403[/C][C]4221.80912738341[/C][/ROW]
[ROW][C]113[/C][C]4098.17976506372[/C][C]3967.8630462791[/C][C]4228.49648384834[/C][/ROW]
[ROW][C]114[/C][C]4098.17976506372[/C][C]3961.5024986219[/C][C]4234.85703150554[/C][/ROW]
[ROW][C]115[/C][C]4098.17976506372[/C][C]3955.42506941686[/C][C]4240.93446071058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299225&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299225&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
1044098.179765063724056.968170944744139.39135918271
1054098.179765063724039.899206924274156.46032320317
1064098.179765063724026.801537120854169.55799300659
1074098.179765063724015.759625586274180.59990454117
1084098.179765063724006.03147501614190.32805511134
1094098.179765063723997.236536831624199.12299329582
1104098.179765063723989.148745197194207.21078493025
1114098.179765063723981.620804617284214.73872551016
1124098.179765063723974.550402744034221.80912738341
1134098.179765063723967.86304627914228.49648384834
1144098.179765063723961.50249862194234.85703150554
1154098.179765063723955.425069416864240.93446071058



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
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')