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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 17 Aug 2017 00:46:47 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/17/t1502923819vzqedfny0s9wrcv.htm/, Retrieved Fri, 10 May 2024 10:18:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307527, Retrieved Fri, 10 May 2024 10:18:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 22:46:47] [a0ce0558b0177aac41d3fe22da4ea7eb] [Current]
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Dataseries X:
59400
57200
60500
48400
62700
61600
66000
68200
75900
66000
62700
78100
66000
49500
58300
44000
61600
50600
67100
60500
63800
71500
70400
83600
60500
50600
56100
40700
58300
45100
63800
60500
53900
77000
69300
79200
59400
55000
49500
40700
53900
48400
66000
63800
55000
73700
68200
88000
70400
42900
42900
42900
50600
50600
68200
62700
56100
70400
64900
93500
73700
42900
45100
37400
51700
59400
74800
73700
59400
69300
61600
88000
67100
53900
48400
36300
53900
64900
75900
71500
52800
75900
59400
91300
75900
55000
50600
34100
53900
51700
78100
78100
59400
77000
57200
89100
75900
56100
42900
29700
58300
56100
73700
84700
62700
70400
52800
91300




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=307527&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=307527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307527&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
alpha0.00926118605787278
beta1
gamma0.929768627343215

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787278 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627343215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307527&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]0.00926118605787278[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627343215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307527&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
alpha0.00926118605787278
beta1
gamma0.929768627343215







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136600068256.9978632479-2256.9978632479
144950051702.0518833194-2202.05188331936
155830060977.2211561336-2677.22115613356
164400046573.1955546582-2573.19555465822
176160063221.302510838-1621.30251083795
185060051263.2099413947-663.209941394729
196710064103.68166816842996.31833183158
206050066005.7944287242-5505.79442872421
216380073644.8440211854-9844.84402118536
227150063415.03393586548084.96606413455
237040059980.318199386210419.6818006138
248360075638.72331155417961.27668844591
256050061677.3735368292-1177.37353682923
265060045212.65040608915387.34959391095
275610054220.29780909831879.70219090175
284070040096.3984236388603.601576361194
295830057822.2906642325477.70933576754
304510046957.1518902027-1857.1518902027
316380063337.4721870704462.527812929577
326050057540.76771034692959.2322896531
335390061496.0967343057-7596.0967343057
347700068058.95731051578941.04268948434
356930067046.39889084232253.60110915772
367920080552.556871948-1352.55687194799
375940058188.51292771931211.48707228072
385500047916.88604494227083.11395505779
394950053848.6722344098-4348.67223440976
404070038573.44945735562126.55054264441
415390056293.4325606715-2393.43256067148
424840043320.290817985079.70918202001
436600062035.25244213913964.74755786094
446380058736.88291187045063.11708812965
455500053174.09777000061825.90222999937
467370075330.3179323666-1630.31793236663
476820068234.5480362778-34.5480362778326
488800078551.36455681599448.63544318415
497040058902.963875422211497.0361245778
504290054484.2672156761-11584.2672156761
514290049888.7879851372-6988.78798513715
524290040705.46285759362194.53714240642
535060054414.7330896737-3814.73308967368
545060048451.48428485772148.51571514231
556820066224.21013960261975.78986039742
566270064012.73835878-1312.73835877996
575610055443.4174386836656.582561316442
587040074428.752773437-4028.75277343702
596490068782.1830209562-3882.18302095625
609350087764.69778281455735.3022171855
617370069900.24060183493799.75939816512
624290044008.8809312993-1108.88093129932
634510043700.73960564161399.26039435843
643740043089.234776025-5689.23477602495
655170051151.8371350757548.162864924307
665940050724.3248179558675.67518204499
677480068461.07871576566338.92128423441
687370063363.855423269510336.1445767305
695940056927.44926269152472.55073730851
706930071841.4639610719-2541.46396107193
716160066585.2510540516-4985.25105405164
728800094648.1254745841-6648.12547458411
736710075002.7105311726-7902.7105311726
745390044489.62866200349410.37133799663
754840046695.01216411431704.98783588567
763630039665.2570012731-3365.25700127314
775390053625.0742087317274.925791268324
786490060809.28695436474090.71304563532
797590076436.1308922225-536.130892222456
807150074978.7104713085-3478.7104713085
815280061064.2094225146-8264.20942251456
827590071054.11315232294845.8868476771
835940063477.6410497972-4077.64104979722
849130089887.99558648311412.00441351686
857590069107.04689884446792.95310115561
865500054759.7359354436240.264064556366
875060049778.9827295312821.017270468779
883410038059.0224086505-3959.0224086505
895390055349.5020669773-1449.50206697734
905170065999.6951724214-14299.6951724214
917810076990.85959125731109.14040874274
927810072650.02433512655449.97566487348
935940054304.63205655155095.36794344848
947700076513.0737208321486.926279167936
955720060654.2294887985-3454.22948879848
968910092110.9361328233-3010.93613282326
977590076188.5157813801-288.515781380062
985610055616.7649549901483.235045009904
994290051052.6815270406-8152.68152704063
1002970034642.7900563723-4942.79005637234
1015830054023.05950946754276.94049053254
1025610052729.49968672173370.50031327827
1037370078082.1980546587-4382.19805465867
1048470077642.16159271417057.83840728595
1056270058952.96160929783747.03839070215
1067040076859.2779892381-6459.27798923806
1075280057196.8110764591-4396.81107645909
1089130088935.5360863432364.46391365697

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 66000 & 68256.9978632479 & -2256.9978632479 \tabularnewline
14 & 49500 & 51702.0518833194 & -2202.05188331936 \tabularnewline
15 & 58300 & 60977.2211561336 & -2677.22115613356 \tabularnewline
16 & 44000 & 46573.1955546582 & -2573.19555465822 \tabularnewline
17 & 61600 & 63221.302510838 & -1621.30251083795 \tabularnewline
18 & 50600 & 51263.2099413947 & -663.209941394729 \tabularnewline
19 & 67100 & 64103.6816681684 & 2996.31833183158 \tabularnewline
20 & 60500 & 66005.7944287242 & -5505.79442872421 \tabularnewline
21 & 63800 & 73644.8440211854 & -9844.84402118536 \tabularnewline
22 & 71500 & 63415.0339358654 & 8084.96606413455 \tabularnewline
23 & 70400 & 59980.3181993862 & 10419.6818006138 \tabularnewline
24 & 83600 & 75638.7233115541 & 7961.27668844591 \tabularnewline
25 & 60500 & 61677.3735368292 & -1177.37353682923 \tabularnewline
26 & 50600 & 45212.6504060891 & 5387.34959391095 \tabularnewline
27 & 56100 & 54220.2978090983 & 1879.70219090175 \tabularnewline
28 & 40700 & 40096.3984236388 & 603.601576361194 \tabularnewline
29 & 58300 & 57822.2906642325 & 477.70933576754 \tabularnewline
30 & 45100 & 46957.1518902027 & -1857.1518902027 \tabularnewline
31 & 63800 & 63337.4721870704 & 462.527812929577 \tabularnewline
32 & 60500 & 57540.7677103469 & 2959.2322896531 \tabularnewline
33 & 53900 & 61496.0967343057 & -7596.0967343057 \tabularnewline
34 & 77000 & 68058.9573105157 & 8941.04268948434 \tabularnewline
35 & 69300 & 67046.3988908423 & 2253.60110915772 \tabularnewline
36 & 79200 & 80552.556871948 & -1352.55687194799 \tabularnewline
37 & 59400 & 58188.5129277193 & 1211.48707228072 \tabularnewline
38 & 55000 & 47916.8860449422 & 7083.11395505779 \tabularnewline
39 & 49500 & 53848.6722344098 & -4348.67223440976 \tabularnewline
40 & 40700 & 38573.4494573556 & 2126.55054264441 \tabularnewline
41 & 53900 & 56293.4325606715 & -2393.43256067148 \tabularnewline
42 & 48400 & 43320.29081798 & 5079.70918202001 \tabularnewline
43 & 66000 & 62035.2524421391 & 3964.74755786094 \tabularnewline
44 & 63800 & 58736.8829118704 & 5063.11708812965 \tabularnewline
45 & 55000 & 53174.0977700006 & 1825.90222999937 \tabularnewline
46 & 73700 & 75330.3179323666 & -1630.31793236663 \tabularnewline
47 & 68200 & 68234.5480362778 & -34.5480362778326 \tabularnewline
48 & 88000 & 78551.3645568159 & 9448.63544318415 \tabularnewline
49 & 70400 & 58902.9638754222 & 11497.0361245778 \tabularnewline
50 & 42900 & 54484.2672156761 & -11584.2672156761 \tabularnewline
51 & 42900 & 49888.7879851372 & -6988.78798513715 \tabularnewline
52 & 42900 & 40705.4628575936 & 2194.53714240642 \tabularnewline
53 & 50600 & 54414.7330896737 & -3814.73308967368 \tabularnewline
54 & 50600 & 48451.4842848577 & 2148.51571514231 \tabularnewline
55 & 68200 & 66224.2101396026 & 1975.78986039742 \tabularnewline
56 & 62700 & 64012.73835878 & -1312.73835877996 \tabularnewline
57 & 56100 & 55443.4174386836 & 656.582561316442 \tabularnewline
58 & 70400 & 74428.752773437 & -4028.75277343702 \tabularnewline
59 & 64900 & 68782.1830209562 & -3882.18302095625 \tabularnewline
60 & 93500 & 87764.6977828145 & 5735.3022171855 \tabularnewline
61 & 73700 & 69900.2406018349 & 3799.75939816512 \tabularnewline
62 & 42900 & 44008.8809312993 & -1108.88093129932 \tabularnewline
63 & 45100 & 43700.7396056416 & 1399.26039435843 \tabularnewline
64 & 37400 & 43089.234776025 & -5689.23477602495 \tabularnewline
65 & 51700 & 51151.8371350757 & 548.162864924307 \tabularnewline
66 & 59400 & 50724.324817955 & 8675.67518204499 \tabularnewline
67 & 74800 & 68461.0787157656 & 6338.92128423441 \tabularnewline
68 & 73700 & 63363.8554232695 & 10336.1445767305 \tabularnewline
69 & 59400 & 56927.4492626915 & 2472.55073730851 \tabularnewline
70 & 69300 & 71841.4639610719 & -2541.46396107193 \tabularnewline
71 & 61600 & 66585.2510540516 & -4985.25105405164 \tabularnewline
72 & 88000 & 94648.1254745841 & -6648.12547458411 \tabularnewline
73 & 67100 & 75002.7105311726 & -7902.7105311726 \tabularnewline
74 & 53900 & 44489.6286620034 & 9410.37133799663 \tabularnewline
75 & 48400 & 46695.0121641143 & 1704.98783588567 \tabularnewline
76 & 36300 & 39665.2570012731 & -3365.25700127314 \tabularnewline
77 & 53900 & 53625.0742087317 & 274.925791268324 \tabularnewline
78 & 64900 & 60809.2869543647 & 4090.71304563532 \tabularnewline
79 & 75900 & 76436.1308922225 & -536.130892222456 \tabularnewline
80 & 71500 & 74978.7104713085 & -3478.7104713085 \tabularnewline
81 & 52800 & 61064.2094225146 & -8264.20942251456 \tabularnewline
82 & 75900 & 71054.1131523229 & 4845.8868476771 \tabularnewline
83 & 59400 & 63477.6410497972 & -4077.64104979722 \tabularnewline
84 & 91300 & 89887.9955864831 & 1412.00441351686 \tabularnewline
85 & 75900 & 69107.0468988444 & 6792.95310115561 \tabularnewline
86 & 55000 & 54759.7359354436 & 240.264064556366 \tabularnewline
87 & 50600 & 49778.9827295312 & 821.017270468779 \tabularnewline
88 & 34100 & 38059.0224086505 & -3959.0224086505 \tabularnewline
89 & 53900 & 55349.5020669773 & -1449.50206697734 \tabularnewline
90 & 51700 & 65999.6951724214 & -14299.6951724214 \tabularnewline
91 & 78100 & 76990.8595912573 & 1109.14040874274 \tabularnewline
92 & 78100 & 72650.0243351265 & 5449.97566487348 \tabularnewline
93 & 59400 & 54304.6320565515 & 5095.36794344848 \tabularnewline
94 & 77000 & 76513.0737208321 & 486.926279167936 \tabularnewline
95 & 57200 & 60654.2294887985 & -3454.22948879848 \tabularnewline
96 & 89100 & 92110.9361328233 & -3010.93613282326 \tabularnewline
97 & 75900 & 76188.5157813801 & -288.515781380062 \tabularnewline
98 & 56100 & 55616.7649549901 & 483.235045009904 \tabularnewline
99 & 42900 & 51052.6815270406 & -8152.68152704063 \tabularnewline
100 & 29700 & 34642.7900563723 & -4942.79005637234 \tabularnewline
101 & 58300 & 54023.0595094675 & 4276.94049053254 \tabularnewline
102 & 56100 & 52729.4996867217 & 3370.50031327827 \tabularnewline
103 & 73700 & 78082.1980546587 & -4382.19805465867 \tabularnewline
104 & 84700 & 77642.1615927141 & 7057.83840728595 \tabularnewline
105 & 62700 & 58952.9616092978 & 3747.03839070215 \tabularnewline
106 & 70400 & 76859.2779892381 & -6459.27798923806 \tabularnewline
107 & 52800 & 57196.8110764591 & -4396.81107645909 \tabularnewline
108 & 91300 & 88935.536086343 & 2364.46391365697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307527&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]66000[/C][C]68256.9978632479[/C][C]-2256.9978632479[/C][/ROW]
[ROW][C]14[/C][C]49500[/C][C]51702.0518833194[/C][C]-2202.05188331936[/C][/ROW]
[ROW][C]15[/C][C]58300[/C][C]60977.2211561336[/C][C]-2677.22115613356[/C][/ROW]
[ROW][C]16[/C][C]44000[/C][C]46573.1955546582[/C][C]-2573.19555465822[/C][/ROW]
[ROW][C]17[/C][C]61600[/C][C]63221.302510838[/C][C]-1621.30251083795[/C][/ROW]
[ROW][C]18[/C][C]50600[/C][C]51263.2099413947[/C][C]-663.209941394729[/C][/ROW]
[ROW][C]19[/C][C]67100[/C][C]64103.6816681684[/C][C]2996.31833183158[/C][/ROW]
[ROW][C]20[/C][C]60500[/C][C]66005.7944287242[/C][C]-5505.79442872421[/C][/ROW]
[ROW][C]21[/C][C]63800[/C][C]73644.8440211854[/C][C]-9844.84402118536[/C][/ROW]
[ROW][C]22[/C][C]71500[/C][C]63415.0339358654[/C][C]8084.96606413455[/C][/ROW]
[ROW][C]23[/C][C]70400[/C][C]59980.3181993862[/C][C]10419.6818006138[/C][/ROW]
[ROW][C]24[/C][C]83600[/C][C]75638.7233115541[/C][C]7961.27668844591[/C][/ROW]
[ROW][C]25[/C][C]60500[/C][C]61677.3735368292[/C][C]-1177.37353682923[/C][/ROW]
[ROW][C]26[/C][C]50600[/C][C]45212.6504060891[/C][C]5387.34959391095[/C][/ROW]
[ROW][C]27[/C][C]56100[/C][C]54220.2978090983[/C][C]1879.70219090175[/C][/ROW]
[ROW][C]28[/C][C]40700[/C][C]40096.3984236388[/C][C]603.601576361194[/C][/ROW]
[ROW][C]29[/C][C]58300[/C][C]57822.2906642325[/C][C]477.70933576754[/C][/ROW]
[ROW][C]30[/C][C]45100[/C][C]46957.1518902027[/C][C]-1857.1518902027[/C][/ROW]
[ROW][C]31[/C][C]63800[/C][C]63337.4721870704[/C][C]462.527812929577[/C][/ROW]
[ROW][C]32[/C][C]60500[/C][C]57540.7677103469[/C][C]2959.2322896531[/C][/ROW]
[ROW][C]33[/C][C]53900[/C][C]61496.0967343057[/C][C]-7596.0967343057[/C][/ROW]
[ROW][C]34[/C][C]77000[/C][C]68058.9573105157[/C][C]8941.04268948434[/C][/ROW]
[ROW][C]35[/C][C]69300[/C][C]67046.3988908423[/C][C]2253.60110915772[/C][/ROW]
[ROW][C]36[/C][C]79200[/C][C]80552.556871948[/C][C]-1352.55687194799[/C][/ROW]
[ROW][C]37[/C][C]59400[/C][C]58188.5129277193[/C][C]1211.48707228072[/C][/ROW]
[ROW][C]38[/C][C]55000[/C][C]47916.8860449422[/C][C]7083.11395505779[/C][/ROW]
[ROW][C]39[/C][C]49500[/C][C]53848.6722344098[/C][C]-4348.67223440976[/C][/ROW]
[ROW][C]40[/C][C]40700[/C][C]38573.4494573556[/C][C]2126.55054264441[/C][/ROW]
[ROW][C]41[/C][C]53900[/C][C]56293.4325606715[/C][C]-2393.43256067148[/C][/ROW]
[ROW][C]42[/C][C]48400[/C][C]43320.29081798[/C][C]5079.70918202001[/C][/ROW]
[ROW][C]43[/C][C]66000[/C][C]62035.2524421391[/C][C]3964.74755786094[/C][/ROW]
[ROW][C]44[/C][C]63800[/C][C]58736.8829118704[/C][C]5063.11708812965[/C][/ROW]
[ROW][C]45[/C][C]55000[/C][C]53174.0977700006[/C][C]1825.90222999937[/C][/ROW]
[ROW][C]46[/C][C]73700[/C][C]75330.3179323666[/C][C]-1630.31793236663[/C][/ROW]
[ROW][C]47[/C][C]68200[/C][C]68234.5480362778[/C][C]-34.5480362778326[/C][/ROW]
[ROW][C]48[/C][C]88000[/C][C]78551.3645568159[/C][C]9448.63544318415[/C][/ROW]
[ROW][C]49[/C][C]70400[/C][C]58902.9638754222[/C][C]11497.0361245778[/C][/ROW]
[ROW][C]50[/C][C]42900[/C][C]54484.2672156761[/C][C]-11584.2672156761[/C][/ROW]
[ROW][C]51[/C][C]42900[/C][C]49888.7879851372[/C][C]-6988.78798513715[/C][/ROW]
[ROW][C]52[/C][C]42900[/C][C]40705.4628575936[/C][C]2194.53714240642[/C][/ROW]
[ROW][C]53[/C][C]50600[/C][C]54414.7330896737[/C][C]-3814.73308967368[/C][/ROW]
[ROW][C]54[/C][C]50600[/C][C]48451.4842848577[/C][C]2148.51571514231[/C][/ROW]
[ROW][C]55[/C][C]68200[/C][C]66224.2101396026[/C][C]1975.78986039742[/C][/ROW]
[ROW][C]56[/C][C]62700[/C][C]64012.73835878[/C][C]-1312.73835877996[/C][/ROW]
[ROW][C]57[/C][C]56100[/C][C]55443.4174386836[/C][C]656.582561316442[/C][/ROW]
[ROW][C]58[/C][C]70400[/C][C]74428.752773437[/C][C]-4028.75277343702[/C][/ROW]
[ROW][C]59[/C][C]64900[/C][C]68782.1830209562[/C][C]-3882.18302095625[/C][/ROW]
[ROW][C]60[/C][C]93500[/C][C]87764.6977828145[/C][C]5735.3022171855[/C][/ROW]
[ROW][C]61[/C][C]73700[/C][C]69900.2406018349[/C][C]3799.75939816512[/C][/ROW]
[ROW][C]62[/C][C]42900[/C][C]44008.8809312993[/C][C]-1108.88093129932[/C][/ROW]
[ROW][C]63[/C][C]45100[/C][C]43700.7396056416[/C][C]1399.26039435843[/C][/ROW]
[ROW][C]64[/C][C]37400[/C][C]43089.234776025[/C][C]-5689.23477602495[/C][/ROW]
[ROW][C]65[/C][C]51700[/C][C]51151.8371350757[/C][C]548.162864924307[/C][/ROW]
[ROW][C]66[/C][C]59400[/C][C]50724.324817955[/C][C]8675.67518204499[/C][/ROW]
[ROW][C]67[/C][C]74800[/C][C]68461.0787157656[/C][C]6338.92128423441[/C][/ROW]
[ROW][C]68[/C][C]73700[/C][C]63363.8554232695[/C][C]10336.1445767305[/C][/ROW]
[ROW][C]69[/C][C]59400[/C][C]56927.4492626915[/C][C]2472.55073730851[/C][/ROW]
[ROW][C]70[/C][C]69300[/C][C]71841.4639610719[/C][C]-2541.46396107193[/C][/ROW]
[ROW][C]71[/C][C]61600[/C][C]66585.2510540516[/C][C]-4985.25105405164[/C][/ROW]
[ROW][C]72[/C][C]88000[/C][C]94648.1254745841[/C][C]-6648.12547458411[/C][/ROW]
[ROW][C]73[/C][C]67100[/C][C]75002.7105311726[/C][C]-7902.7105311726[/C][/ROW]
[ROW][C]74[/C][C]53900[/C][C]44489.6286620034[/C][C]9410.37133799663[/C][/ROW]
[ROW][C]75[/C][C]48400[/C][C]46695.0121641143[/C][C]1704.98783588567[/C][/ROW]
[ROW][C]76[/C][C]36300[/C][C]39665.2570012731[/C][C]-3365.25700127314[/C][/ROW]
[ROW][C]77[/C][C]53900[/C][C]53625.0742087317[/C][C]274.925791268324[/C][/ROW]
[ROW][C]78[/C][C]64900[/C][C]60809.2869543647[/C][C]4090.71304563532[/C][/ROW]
[ROW][C]79[/C][C]75900[/C][C]76436.1308922225[/C][C]-536.130892222456[/C][/ROW]
[ROW][C]80[/C][C]71500[/C][C]74978.7104713085[/C][C]-3478.7104713085[/C][/ROW]
[ROW][C]81[/C][C]52800[/C][C]61064.2094225146[/C][C]-8264.20942251456[/C][/ROW]
[ROW][C]82[/C][C]75900[/C][C]71054.1131523229[/C][C]4845.8868476771[/C][/ROW]
[ROW][C]83[/C][C]59400[/C][C]63477.6410497972[/C][C]-4077.64104979722[/C][/ROW]
[ROW][C]84[/C][C]91300[/C][C]89887.9955864831[/C][C]1412.00441351686[/C][/ROW]
[ROW][C]85[/C][C]75900[/C][C]69107.0468988444[/C][C]6792.95310115561[/C][/ROW]
[ROW][C]86[/C][C]55000[/C][C]54759.7359354436[/C][C]240.264064556366[/C][/ROW]
[ROW][C]87[/C][C]50600[/C][C]49778.9827295312[/C][C]821.017270468779[/C][/ROW]
[ROW][C]88[/C][C]34100[/C][C]38059.0224086505[/C][C]-3959.0224086505[/C][/ROW]
[ROW][C]89[/C][C]53900[/C][C]55349.5020669773[/C][C]-1449.50206697734[/C][/ROW]
[ROW][C]90[/C][C]51700[/C][C]65999.6951724214[/C][C]-14299.6951724214[/C][/ROW]
[ROW][C]91[/C][C]78100[/C][C]76990.8595912573[/C][C]1109.14040874274[/C][/ROW]
[ROW][C]92[/C][C]78100[/C][C]72650.0243351265[/C][C]5449.97566487348[/C][/ROW]
[ROW][C]93[/C][C]59400[/C][C]54304.6320565515[/C][C]5095.36794344848[/C][/ROW]
[ROW][C]94[/C][C]77000[/C][C]76513.0737208321[/C][C]486.926279167936[/C][/ROW]
[ROW][C]95[/C][C]57200[/C][C]60654.2294887985[/C][C]-3454.22948879848[/C][/ROW]
[ROW][C]96[/C][C]89100[/C][C]92110.9361328233[/C][C]-3010.93613282326[/C][/ROW]
[ROW][C]97[/C][C]75900[/C][C]76188.5157813801[/C][C]-288.515781380062[/C][/ROW]
[ROW][C]98[/C][C]56100[/C][C]55616.7649549901[/C][C]483.235045009904[/C][/ROW]
[ROW][C]99[/C][C]42900[/C][C]51052.6815270406[/C][C]-8152.68152704063[/C][/ROW]
[ROW][C]100[/C][C]29700[/C][C]34642.7900563723[/C][C]-4942.79005637234[/C][/ROW]
[ROW][C]101[/C][C]58300[/C][C]54023.0595094675[/C][C]4276.94049053254[/C][/ROW]
[ROW][C]102[/C][C]56100[/C][C]52729.4996867217[/C][C]3370.50031327827[/C][/ROW]
[ROW][C]103[/C][C]73700[/C][C]78082.1980546587[/C][C]-4382.19805465867[/C][/ROW]
[ROW][C]104[/C][C]84700[/C][C]77642.1615927141[/C][C]7057.83840728595[/C][/ROW]
[ROW][C]105[/C][C]62700[/C][C]58952.9616092978[/C][C]3747.03839070215[/C][/ROW]
[ROW][C]106[/C][C]70400[/C][C]76859.2779892381[/C][C]-6459.27798923806[/C][/ROW]
[ROW][C]107[/C][C]52800[/C][C]57196.8110764591[/C][C]-4396.81107645909[/C][/ROW]
[ROW][C]108[/C][C]91300[/C][C]88935.536086343[/C][C]2364.46391365697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307527&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
136600068256.9978632479-2256.9978632479
144950051702.0518833194-2202.05188331936
155830060977.2211561336-2677.22115613356
164400046573.1955546582-2573.19555465822
176160063221.302510838-1621.30251083795
185060051263.2099413947-663.209941394729
196710064103.68166816842996.31833183158
206050066005.7944287242-5505.79442872421
216380073644.8440211854-9844.84402118536
227150063415.03393586548084.96606413455
237040059980.318199386210419.6818006138
248360075638.72331155417961.27668844591
256050061677.3735368292-1177.37353682923
265060045212.65040608915387.34959391095
275610054220.29780909831879.70219090175
284070040096.3984236388603.601576361194
295830057822.2906642325477.70933576754
304510046957.1518902027-1857.1518902027
316380063337.4721870704462.527812929577
326050057540.76771034692959.2322896531
335390061496.0967343057-7596.0967343057
347700068058.95731051578941.04268948434
356930067046.39889084232253.60110915772
367920080552.556871948-1352.55687194799
375940058188.51292771931211.48707228072
385500047916.88604494227083.11395505779
394950053848.6722344098-4348.67223440976
404070038573.44945735562126.55054264441
415390056293.4325606715-2393.43256067148
424840043320.290817985079.70918202001
436600062035.25244213913964.74755786094
446380058736.88291187045063.11708812965
455500053174.09777000061825.90222999937
467370075330.3179323666-1630.31793236663
476820068234.5480362778-34.5480362778326
488800078551.36455681599448.63544318415
497040058902.963875422211497.0361245778
504290054484.2672156761-11584.2672156761
514290049888.7879851372-6988.78798513715
524290040705.46285759362194.53714240642
535060054414.7330896737-3814.73308967368
545060048451.48428485772148.51571514231
556820066224.21013960261975.78986039742
566270064012.73835878-1312.73835877996
575610055443.4174386836656.582561316442
587040074428.752773437-4028.75277343702
596490068782.1830209562-3882.18302095625
609350087764.69778281455735.3022171855
617370069900.24060183493799.75939816512
624290044008.8809312993-1108.88093129932
634510043700.73960564161399.26039435843
643740043089.234776025-5689.23477602495
655170051151.8371350757548.162864924307
665940050724.3248179558675.67518204499
677480068461.07871576566338.92128423441
687370063363.855423269510336.1445767305
695940056927.44926269152472.55073730851
706930071841.4639610719-2541.46396107193
716160066585.2510540516-4985.25105405164
728800094648.1254745841-6648.12547458411
736710075002.7105311726-7902.7105311726
745390044489.62866200349410.37133799663
754840046695.01216411431704.98783588567
763630039665.2570012731-3365.25700127314
775390053625.0742087317274.925791268324
786490060809.28695436474090.71304563532
797590076436.1308922225-536.130892222456
807150074978.7104713085-3478.7104713085
815280061064.2094225146-8264.20942251456
827590071054.11315232294845.8868476771
835940063477.6410497972-4077.64104979722
849130089887.99558648311412.00441351686
857590069107.04689884446792.95310115561
865500054759.7359354436240.264064556366
875060049778.9827295312821.017270468779
883410038059.0224086505-3959.0224086505
895390055349.5020669773-1449.50206697734
905170065999.6951724214-14299.6951724214
917810076990.85959125731109.14040874274
927810072650.02433512655449.97566487348
935940054304.63205655155095.36794344848
947700076513.0737208321486.926279167936
955720060654.2294887985-3454.22948879848
968910092110.9361328233-3010.93613282326
977590076188.5157813801-288.515781380062
985610055616.7649549901483.235045009904
994290051052.6815270406-8152.68152704063
1002970034642.7900563723-4942.79005637234
1015830054023.05950946754276.94049053254
1025610052729.49968672173370.50031327827
1037370078082.1980546587-4382.19805465867
1048470077642.16159271417057.83840728595
1056270058952.96160929783747.03839070215
1067040076859.2779892381-6459.27798923806
1075280057196.8110764591-4396.81107645909
1089130088935.5360863432364.46391365697







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10975502.864446131965419.971212503685585.7576797603
11055579.549168567745494.926472484365664.171864651
11142986.331796705832897.81889410353074.8446993086
11229614.647983414819519.222859507139710.0731073225
11357585.184335156847478.968330019567691.4003402941
11455429.094403315945307.359739880465550.8290667514
11573589.957950271963447.138821611383732.7770789326
11683750.008880515373579.716688916493920.3010721142
11761901.734960025251696.778211703572106.6917083469
11870293.078172357860045.487417678680540.668927037
11952571.467511956542272.525582606962870.4094413061
12090601.011596247880241.2892311405100960.733961355

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 75502.8644461319 & 65419.9712125036 & 85585.7576797603 \tabularnewline
110 & 55579.5491685677 & 45494.9264724843 & 65664.171864651 \tabularnewline
111 & 42986.3317967058 & 32897.818894103 & 53074.8446993086 \tabularnewline
112 & 29614.6479834148 & 19519.2228595071 & 39710.0731073225 \tabularnewline
113 & 57585.1843351568 & 47478.9683300195 & 67691.4003402941 \tabularnewline
114 & 55429.0944033159 & 45307.3597398804 & 65550.8290667514 \tabularnewline
115 & 73589.9579502719 & 63447.1388216113 & 83732.7770789326 \tabularnewline
116 & 83750.0088805153 & 73579.7166889164 & 93920.3010721142 \tabularnewline
117 & 61901.7349600252 & 51696.7782117035 & 72106.6917083469 \tabularnewline
118 & 70293.0781723578 & 60045.4874176786 & 80540.668927037 \tabularnewline
119 & 52571.4675119565 & 42272.5255826069 & 62870.4094413061 \tabularnewline
120 & 90601.0115962478 & 80241.2892311405 & 100960.733961355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307527&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]75502.8644461319[/C][C]65419.9712125036[/C][C]85585.7576797603[/C][/ROW]
[ROW][C]110[/C][C]55579.5491685677[/C][C]45494.9264724843[/C][C]65664.171864651[/C][/ROW]
[ROW][C]111[/C][C]42986.3317967058[/C][C]32897.818894103[/C][C]53074.8446993086[/C][/ROW]
[ROW][C]112[/C][C]29614.6479834148[/C][C]19519.2228595071[/C][C]39710.0731073225[/C][/ROW]
[ROW][C]113[/C][C]57585.1843351568[/C][C]47478.9683300195[/C][C]67691.4003402941[/C][/ROW]
[ROW][C]114[/C][C]55429.0944033159[/C][C]45307.3597398804[/C][C]65550.8290667514[/C][/ROW]
[ROW][C]115[/C][C]73589.9579502719[/C][C]63447.1388216113[/C][C]83732.7770789326[/C][/ROW]
[ROW][C]116[/C][C]83750.0088805153[/C][C]73579.7166889164[/C][C]93920.3010721142[/C][/ROW]
[ROW][C]117[/C][C]61901.7349600252[/C][C]51696.7782117035[/C][C]72106.6917083469[/C][/ROW]
[ROW][C]118[/C][C]70293.0781723578[/C][C]60045.4874176786[/C][C]80540.668927037[/C][/ROW]
[ROW][C]119[/C][C]52571.4675119565[/C][C]42272.5255826069[/C][C]62870.4094413061[/C][/ROW]
[ROW][C]120[/C][C]90601.0115962478[/C][C]80241.2892311405[/C][C]100960.733961355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307527&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307527&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
10975502.864446131965419.971212503685585.7576797603
11055579.549168567745494.926472484365664.171864651
11142986.331796705832897.81889410353074.8446993086
11229614.647983414819519.222859507139710.0731073225
11357585.184335156847478.968330019567691.4003402941
11455429.094403315945307.359739880465550.8290667514
11573589.957950271963447.138821611383732.7770789326
11683750.008880515373579.716688916493920.3010721142
11761901.734960025251696.778211703572106.6917083469
11870293.078172357860045.487417678680540.668927037
11952571.467511956542272.525582606962870.4094413061
12090601.011596247880241.2892311405100960.733961355



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')