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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 computationFri, 16 Dec 2016 15:12:45 +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/16/t1481897631kc6zwnvyr6u8zt5.htm/, Retrieved Thu, 02 May 2024 18:01:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300295, Retrieved Thu, 02 May 2024 18:01:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-16 14:12:45] [31f526a885cd288e1bc58dc4a6a7fb1f] [Current]
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Dataseries X:
2647.36
2711.22
2733.02
2831
2823.6
2833.46
2885.1
2929.78
3108.46
2921.92
2988.78
3038.84
3005.08
2816.94
3016.28
3242.68
3097.38
3057.18
3014.1
3063.66
3100.36
2964.4
3155.4
3217
3091.1
3192.64
3219.66
3478.26
3284.9
3382.2
3341.9
3402.18
3394.04
3374.1
3383.36
3626.54
3579.84
3530.72
3532.4
3636.68
3639.84
3676.98
3668.92
3718.74
3815.02
3799.9
3925.86
4226.32
4049.72
3883.56
3928.18
4377.66
4146.08
4246.12
4163.4
4144.76
4238.82
4352.28
4379.2
4451.02
4368.22
4337.82
4349.92
4079.42
4463.84
4552.72
4489
4455.9
4583.62
4512.76
4654.04
4768.44
4658.66
4589.98
4572.86
4643
4470.7
4635.34
4373.52
4348.18
4421.02
4363.52
4462.84
4567.34
4367.84
4382.64
4386.44
4489.36
4549.1
4627.66
4646.26
4728.68
4687.46
4755.26
4899.7
5042.06
4983.88
5028.08
4819.3
4889.86
4962.22
4968.92
5019.56
5099.18
5171.08
5353.5
5304.26
5636.62
5322.96
5308.46
5352.02
5358.9
5421.04
5537.66
5519.38
5643.06




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=300295&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=300295&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300295&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
alpha0.453183729409511
beta0.0156659258619362
gamma0.60491858981806

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.453183729409511 \tabularnewline
beta & 0.0156659258619362 \tabularnewline
gamma & 0.60491858981806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300295&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]0.453183729409511[/C][/ROW]
[ROW][C]beta[/C][C]0.0156659258619362[/C][/ROW]
[ROW][C]gamma[/C][C]0.60491858981806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300295&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300295&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
alpha0.453183729409511
beta0.0156659258619362
gamma0.60491858981806







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133005.082870.1938034188134.886196581196
142816.942748.6022041370668.3377958629426
153016.282990.5296195317925.7503804682106
163242.683244.20826045121-1.52826045120628
173097.383106.5338151952-9.15381519519951
183057.183064.78527136625-7.60527136625251
193014.13075.33534178933-61.2353417893323
203063.663089.43139396539-25.7713939653904
213100.363256.51866516382-156.158665163815
222964.42985.43955808731-21.0395580873133
233155.43029.23986062905126.160139370947
2432173131.676016996985.3239830030993
253091.13183.04171835499-91.9417183549908
263192.642936.15367666388256.486323336117
273219.663250.10678855007-30.446788550074
283478.263469.7424838818.51751611900136
293284.93334.61747320953-49.7174732095282
303382.23275.22961038887106.970389611128
313341.93321.0084668738620.8915331261433
323402.183385.6815659070816.4984340929168
333394.043530.7232606149-136.683260614901
343374.13315.2308028567558.8691971432509
353383.363446.56849113967-63.2084911396714
363626.543450.96709941726175.572900582736
373579.843486.5260288665293.3139711334775
383530.723442.0905918476788.6294081523256
393532.43587.11537901149-54.7153790114885
403636.683810.52247443836-173.842474438358
413639.843574.0782239567265.761776043279
423676.983620.2589051036456.7210948963552
433668.923615.8418668159953.0781331840135
443718.743694.9261473480323.8138526519683
453815.023793.9435533082621.076446691744
463799.93717.0797807824882.820219217519
473925.863821.51079056474104.349209435257
484226.323984.63723725631241.682762743687
494049.724027.2253436845322.4946563154699
503883.563952.922220562-69.3622205619954
513928.183981.58664331623-53.4066433162288
524377.664168.84571077929208.814289220706
534146.084190.45175516439-44.3717551643886
544246.124188.3296866058257.7903133941791
554163.44187.79822041069-24.3982204106869
564144.764226.14744846105-81.3874484610542
574238.824279.89296742162-41.0729674216163
584352.284198.1555310279154.124468972097
594379.24345.395914964433.8040850356047
604451.024524.85282477-73.8328247699947
614368.224352.58475508115.6352449189962
624337.824245.3732526096592.4467473903505
634349.924354.37796192906-4.45796192905618
644079.424652.63787220273-573.21787220273
654463.844232.61971814807231.220281851931
664552.724387.66991690397165.050083096028
6744894407.8074004212681.1925995787406
684455.94475.15429327091-19.2542932709121
694583.624570.8303428504212.7896571495803
704512.764578.88984695058-66.1298469505791
714654.044585.771356712968.2686432870987
724768.444744.7439553375323.696044662468
734658.664646.4619570986312.1980429013702
744589.984563.2694119211626.710588078844
754572.864610.13177638285-37.2717763828532
7646434704.85630379288-61.8563037928752
774470.74785.77016158864-315.07016158864
784635.344670.58403143338-35.2440314333817
794373.524570.0125079624-196.492507962404
804348.184474.11918404882-125.939184048823
814421.024527.11735089912-106.097350899119
824363.524449.42071102699-85.9007110269868
834462.844485.88471916024-23.0447191602352
844567.344582.16970043723-14.8297004372316
854367.844455.78945187537-87.9494518753709
864382.644324.4654318463358.1745681536659
874386.444357.0993869265129.3406130734866
884489.364467.0290997419322.3309002580718
894549.14496.0845975103353.0154024896683
904627.664636.63007271594-8.97007271593975
914646.264491.17486793892155.08513206108
924728.684576.99148229052151.688517709485
934687.464763.38339551758-75.923395517576
944755.264707.2700743966647.9899256033405
954899.74827.3815077398572.318492260154
965042.064972.4568428384869.6031571615158
974983.884863.60906370838120.270936291624
985028.084879.91558464618148.164415353816
994819.34949.36632865957-130.066328659568
1004889.864989.17755528116-99.3175552811599
1014962.224976.83091713677-14.6109171367707
1024968.925069.32278071179-100.402780711785
1035019.564939.1457500899480.4142499100599
1045099.184991.91699614228107.263003857717
1055171.085084.4890633091486.5909366908636
1065353.55145.76872531588207.731274684116
1075304.265350.20998339069-45.9499833906939
1085636.625443.84039831274192.779601687258
1095322.965411.49913542054-88.5391354205376
1105308.465344.84556137608-36.3855613760752
1115352.025239.76070570806112.259294291935
1125358.95402.41384692573-43.5138469257272
1135421.045446.6247535244-25.5847535243993
1145537.665508.9363761513428.7236238486648
1155519.385501.1757033625318.2042966374738
1165643.065538.28159783037104.778402169632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3005.08 & 2870.1938034188 & 134.886196581196 \tabularnewline
14 & 2816.94 & 2748.60220413706 & 68.3377958629426 \tabularnewline
15 & 3016.28 & 2990.52961953179 & 25.7503804682106 \tabularnewline
16 & 3242.68 & 3244.20826045121 & -1.52826045120628 \tabularnewline
17 & 3097.38 & 3106.5338151952 & -9.15381519519951 \tabularnewline
18 & 3057.18 & 3064.78527136625 & -7.60527136625251 \tabularnewline
19 & 3014.1 & 3075.33534178933 & -61.2353417893323 \tabularnewline
20 & 3063.66 & 3089.43139396539 & -25.7713939653904 \tabularnewline
21 & 3100.36 & 3256.51866516382 & -156.158665163815 \tabularnewline
22 & 2964.4 & 2985.43955808731 & -21.0395580873133 \tabularnewline
23 & 3155.4 & 3029.23986062905 & 126.160139370947 \tabularnewline
24 & 3217 & 3131.6760169969 & 85.3239830030993 \tabularnewline
25 & 3091.1 & 3183.04171835499 & -91.9417183549908 \tabularnewline
26 & 3192.64 & 2936.15367666388 & 256.486323336117 \tabularnewline
27 & 3219.66 & 3250.10678855007 & -30.446788550074 \tabularnewline
28 & 3478.26 & 3469.742483881 & 8.51751611900136 \tabularnewline
29 & 3284.9 & 3334.61747320953 & -49.7174732095282 \tabularnewline
30 & 3382.2 & 3275.22961038887 & 106.970389611128 \tabularnewline
31 & 3341.9 & 3321.00846687386 & 20.8915331261433 \tabularnewline
32 & 3402.18 & 3385.68156590708 & 16.4984340929168 \tabularnewline
33 & 3394.04 & 3530.7232606149 & -136.683260614901 \tabularnewline
34 & 3374.1 & 3315.23080285675 & 58.8691971432509 \tabularnewline
35 & 3383.36 & 3446.56849113967 & -63.2084911396714 \tabularnewline
36 & 3626.54 & 3450.96709941726 & 175.572900582736 \tabularnewline
37 & 3579.84 & 3486.52602886652 & 93.3139711334775 \tabularnewline
38 & 3530.72 & 3442.09059184767 & 88.6294081523256 \tabularnewline
39 & 3532.4 & 3587.11537901149 & -54.7153790114885 \tabularnewline
40 & 3636.68 & 3810.52247443836 & -173.842474438358 \tabularnewline
41 & 3639.84 & 3574.07822395672 & 65.761776043279 \tabularnewline
42 & 3676.98 & 3620.25890510364 & 56.7210948963552 \tabularnewline
43 & 3668.92 & 3615.84186681599 & 53.0781331840135 \tabularnewline
44 & 3718.74 & 3694.92614734803 & 23.8138526519683 \tabularnewline
45 & 3815.02 & 3793.94355330826 & 21.076446691744 \tabularnewline
46 & 3799.9 & 3717.07978078248 & 82.820219217519 \tabularnewline
47 & 3925.86 & 3821.51079056474 & 104.349209435257 \tabularnewline
48 & 4226.32 & 3984.63723725631 & 241.682762743687 \tabularnewline
49 & 4049.72 & 4027.22534368453 & 22.4946563154699 \tabularnewline
50 & 3883.56 & 3952.922220562 & -69.3622205619954 \tabularnewline
51 & 3928.18 & 3981.58664331623 & -53.4066433162288 \tabularnewline
52 & 4377.66 & 4168.84571077929 & 208.814289220706 \tabularnewline
53 & 4146.08 & 4190.45175516439 & -44.3717551643886 \tabularnewline
54 & 4246.12 & 4188.32968660582 & 57.7903133941791 \tabularnewline
55 & 4163.4 & 4187.79822041069 & -24.3982204106869 \tabularnewline
56 & 4144.76 & 4226.14744846105 & -81.3874484610542 \tabularnewline
57 & 4238.82 & 4279.89296742162 & -41.0729674216163 \tabularnewline
58 & 4352.28 & 4198.1555310279 & 154.124468972097 \tabularnewline
59 & 4379.2 & 4345.3959149644 & 33.8040850356047 \tabularnewline
60 & 4451.02 & 4524.85282477 & -73.8328247699947 \tabularnewline
61 & 4368.22 & 4352.584755081 & 15.6352449189962 \tabularnewline
62 & 4337.82 & 4245.37325260965 & 92.4467473903505 \tabularnewline
63 & 4349.92 & 4354.37796192906 & -4.45796192905618 \tabularnewline
64 & 4079.42 & 4652.63787220273 & -573.21787220273 \tabularnewline
65 & 4463.84 & 4232.61971814807 & 231.220281851931 \tabularnewline
66 & 4552.72 & 4387.66991690397 & 165.050083096028 \tabularnewline
67 & 4489 & 4407.80740042126 & 81.1925995787406 \tabularnewline
68 & 4455.9 & 4475.15429327091 & -19.2542932709121 \tabularnewline
69 & 4583.62 & 4570.83034285042 & 12.7896571495803 \tabularnewline
70 & 4512.76 & 4578.88984695058 & -66.1298469505791 \tabularnewline
71 & 4654.04 & 4585.7713567129 & 68.2686432870987 \tabularnewline
72 & 4768.44 & 4744.74395533753 & 23.696044662468 \tabularnewline
73 & 4658.66 & 4646.46195709863 & 12.1980429013702 \tabularnewline
74 & 4589.98 & 4563.26941192116 & 26.710588078844 \tabularnewline
75 & 4572.86 & 4610.13177638285 & -37.2717763828532 \tabularnewline
76 & 4643 & 4704.85630379288 & -61.8563037928752 \tabularnewline
77 & 4470.7 & 4785.77016158864 & -315.07016158864 \tabularnewline
78 & 4635.34 & 4670.58403143338 & -35.2440314333817 \tabularnewline
79 & 4373.52 & 4570.0125079624 & -196.492507962404 \tabularnewline
80 & 4348.18 & 4474.11918404882 & -125.939184048823 \tabularnewline
81 & 4421.02 & 4527.11735089912 & -106.097350899119 \tabularnewline
82 & 4363.52 & 4449.42071102699 & -85.9007110269868 \tabularnewline
83 & 4462.84 & 4485.88471916024 & -23.0447191602352 \tabularnewline
84 & 4567.34 & 4582.16970043723 & -14.8297004372316 \tabularnewline
85 & 4367.84 & 4455.78945187537 & -87.9494518753709 \tabularnewline
86 & 4382.64 & 4324.46543184633 & 58.1745681536659 \tabularnewline
87 & 4386.44 & 4357.09938692651 & 29.3406130734866 \tabularnewline
88 & 4489.36 & 4467.02909974193 & 22.3309002580718 \tabularnewline
89 & 4549.1 & 4496.08459751033 & 53.0154024896683 \tabularnewline
90 & 4627.66 & 4636.63007271594 & -8.97007271593975 \tabularnewline
91 & 4646.26 & 4491.17486793892 & 155.08513206108 \tabularnewline
92 & 4728.68 & 4576.99148229052 & 151.688517709485 \tabularnewline
93 & 4687.46 & 4763.38339551758 & -75.923395517576 \tabularnewline
94 & 4755.26 & 4707.27007439666 & 47.9899256033405 \tabularnewline
95 & 4899.7 & 4827.38150773985 & 72.318492260154 \tabularnewline
96 & 5042.06 & 4972.45684283848 & 69.6031571615158 \tabularnewline
97 & 4983.88 & 4863.60906370838 & 120.270936291624 \tabularnewline
98 & 5028.08 & 4879.91558464618 & 148.164415353816 \tabularnewline
99 & 4819.3 & 4949.36632865957 & -130.066328659568 \tabularnewline
100 & 4889.86 & 4989.17755528116 & -99.3175552811599 \tabularnewline
101 & 4962.22 & 4976.83091713677 & -14.6109171367707 \tabularnewline
102 & 4968.92 & 5069.32278071179 & -100.402780711785 \tabularnewline
103 & 5019.56 & 4939.14575008994 & 80.4142499100599 \tabularnewline
104 & 5099.18 & 4991.91699614228 & 107.263003857717 \tabularnewline
105 & 5171.08 & 5084.48906330914 & 86.5909366908636 \tabularnewline
106 & 5353.5 & 5145.76872531588 & 207.731274684116 \tabularnewline
107 & 5304.26 & 5350.20998339069 & -45.9499833906939 \tabularnewline
108 & 5636.62 & 5443.84039831274 & 192.779601687258 \tabularnewline
109 & 5322.96 & 5411.49913542054 & -88.5391354205376 \tabularnewline
110 & 5308.46 & 5344.84556137608 & -36.3855613760752 \tabularnewline
111 & 5352.02 & 5239.76070570806 & 112.259294291935 \tabularnewline
112 & 5358.9 & 5402.41384692573 & -43.5138469257272 \tabularnewline
113 & 5421.04 & 5446.6247535244 & -25.5847535243993 \tabularnewline
114 & 5537.66 & 5508.93637615134 & 28.7236238486648 \tabularnewline
115 & 5519.38 & 5501.17570336253 & 18.2042966374738 \tabularnewline
116 & 5643.06 & 5538.28159783037 & 104.778402169632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300295&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]3005.08[/C][C]2870.1938034188[/C][C]134.886196581196[/C][/ROW]
[ROW][C]14[/C][C]2816.94[/C][C]2748.60220413706[/C][C]68.3377958629426[/C][/ROW]
[ROW][C]15[/C][C]3016.28[/C][C]2990.52961953179[/C][C]25.7503804682106[/C][/ROW]
[ROW][C]16[/C][C]3242.68[/C][C]3244.20826045121[/C][C]-1.52826045120628[/C][/ROW]
[ROW][C]17[/C][C]3097.38[/C][C]3106.5338151952[/C][C]-9.15381519519951[/C][/ROW]
[ROW][C]18[/C][C]3057.18[/C][C]3064.78527136625[/C][C]-7.60527136625251[/C][/ROW]
[ROW][C]19[/C][C]3014.1[/C][C]3075.33534178933[/C][C]-61.2353417893323[/C][/ROW]
[ROW][C]20[/C][C]3063.66[/C][C]3089.43139396539[/C][C]-25.7713939653904[/C][/ROW]
[ROW][C]21[/C][C]3100.36[/C][C]3256.51866516382[/C][C]-156.158665163815[/C][/ROW]
[ROW][C]22[/C][C]2964.4[/C][C]2985.43955808731[/C][C]-21.0395580873133[/C][/ROW]
[ROW][C]23[/C][C]3155.4[/C][C]3029.23986062905[/C][C]126.160139370947[/C][/ROW]
[ROW][C]24[/C][C]3217[/C][C]3131.6760169969[/C][C]85.3239830030993[/C][/ROW]
[ROW][C]25[/C][C]3091.1[/C][C]3183.04171835499[/C][C]-91.9417183549908[/C][/ROW]
[ROW][C]26[/C][C]3192.64[/C][C]2936.15367666388[/C][C]256.486323336117[/C][/ROW]
[ROW][C]27[/C][C]3219.66[/C][C]3250.10678855007[/C][C]-30.446788550074[/C][/ROW]
[ROW][C]28[/C][C]3478.26[/C][C]3469.742483881[/C][C]8.51751611900136[/C][/ROW]
[ROW][C]29[/C][C]3284.9[/C][C]3334.61747320953[/C][C]-49.7174732095282[/C][/ROW]
[ROW][C]30[/C][C]3382.2[/C][C]3275.22961038887[/C][C]106.970389611128[/C][/ROW]
[ROW][C]31[/C][C]3341.9[/C][C]3321.00846687386[/C][C]20.8915331261433[/C][/ROW]
[ROW][C]32[/C][C]3402.18[/C][C]3385.68156590708[/C][C]16.4984340929168[/C][/ROW]
[ROW][C]33[/C][C]3394.04[/C][C]3530.7232606149[/C][C]-136.683260614901[/C][/ROW]
[ROW][C]34[/C][C]3374.1[/C][C]3315.23080285675[/C][C]58.8691971432509[/C][/ROW]
[ROW][C]35[/C][C]3383.36[/C][C]3446.56849113967[/C][C]-63.2084911396714[/C][/ROW]
[ROW][C]36[/C][C]3626.54[/C][C]3450.96709941726[/C][C]175.572900582736[/C][/ROW]
[ROW][C]37[/C][C]3579.84[/C][C]3486.52602886652[/C][C]93.3139711334775[/C][/ROW]
[ROW][C]38[/C][C]3530.72[/C][C]3442.09059184767[/C][C]88.6294081523256[/C][/ROW]
[ROW][C]39[/C][C]3532.4[/C][C]3587.11537901149[/C][C]-54.7153790114885[/C][/ROW]
[ROW][C]40[/C][C]3636.68[/C][C]3810.52247443836[/C][C]-173.842474438358[/C][/ROW]
[ROW][C]41[/C][C]3639.84[/C][C]3574.07822395672[/C][C]65.761776043279[/C][/ROW]
[ROW][C]42[/C][C]3676.98[/C][C]3620.25890510364[/C][C]56.7210948963552[/C][/ROW]
[ROW][C]43[/C][C]3668.92[/C][C]3615.84186681599[/C][C]53.0781331840135[/C][/ROW]
[ROW][C]44[/C][C]3718.74[/C][C]3694.92614734803[/C][C]23.8138526519683[/C][/ROW]
[ROW][C]45[/C][C]3815.02[/C][C]3793.94355330826[/C][C]21.076446691744[/C][/ROW]
[ROW][C]46[/C][C]3799.9[/C][C]3717.07978078248[/C][C]82.820219217519[/C][/ROW]
[ROW][C]47[/C][C]3925.86[/C][C]3821.51079056474[/C][C]104.349209435257[/C][/ROW]
[ROW][C]48[/C][C]4226.32[/C][C]3984.63723725631[/C][C]241.682762743687[/C][/ROW]
[ROW][C]49[/C][C]4049.72[/C][C]4027.22534368453[/C][C]22.4946563154699[/C][/ROW]
[ROW][C]50[/C][C]3883.56[/C][C]3952.922220562[/C][C]-69.3622205619954[/C][/ROW]
[ROW][C]51[/C][C]3928.18[/C][C]3981.58664331623[/C][C]-53.4066433162288[/C][/ROW]
[ROW][C]52[/C][C]4377.66[/C][C]4168.84571077929[/C][C]208.814289220706[/C][/ROW]
[ROW][C]53[/C][C]4146.08[/C][C]4190.45175516439[/C][C]-44.3717551643886[/C][/ROW]
[ROW][C]54[/C][C]4246.12[/C][C]4188.32968660582[/C][C]57.7903133941791[/C][/ROW]
[ROW][C]55[/C][C]4163.4[/C][C]4187.79822041069[/C][C]-24.3982204106869[/C][/ROW]
[ROW][C]56[/C][C]4144.76[/C][C]4226.14744846105[/C][C]-81.3874484610542[/C][/ROW]
[ROW][C]57[/C][C]4238.82[/C][C]4279.89296742162[/C][C]-41.0729674216163[/C][/ROW]
[ROW][C]58[/C][C]4352.28[/C][C]4198.1555310279[/C][C]154.124468972097[/C][/ROW]
[ROW][C]59[/C][C]4379.2[/C][C]4345.3959149644[/C][C]33.8040850356047[/C][/ROW]
[ROW][C]60[/C][C]4451.02[/C][C]4524.85282477[/C][C]-73.8328247699947[/C][/ROW]
[ROW][C]61[/C][C]4368.22[/C][C]4352.584755081[/C][C]15.6352449189962[/C][/ROW]
[ROW][C]62[/C][C]4337.82[/C][C]4245.37325260965[/C][C]92.4467473903505[/C][/ROW]
[ROW][C]63[/C][C]4349.92[/C][C]4354.37796192906[/C][C]-4.45796192905618[/C][/ROW]
[ROW][C]64[/C][C]4079.42[/C][C]4652.63787220273[/C][C]-573.21787220273[/C][/ROW]
[ROW][C]65[/C][C]4463.84[/C][C]4232.61971814807[/C][C]231.220281851931[/C][/ROW]
[ROW][C]66[/C][C]4552.72[/C][C]4387.66991690397[/C][C]165.050083096028[/C][/ROW]
[ROW][C]67[/C][C]4489[/C][C]4407.80740042126[/C][C]81.1925995787406[/C][/ROW]
[ROW][C]68[/C][C]4455.9[/C][C]4475.15429327091[/C][C]-19.2542932709121[/C][/ROW]
[ROW][C]69[/C][C]4583.62[/C][C]4570.83034285042[/C][C]12.7896571495803[/C][/ROW]
[ROW][C]70[/C][C]4512.76[/C][C]4578.88984695058[/C][C]-66.1298469505791[/C][/ROW]
[ROW][C]71[/C][C]4654.04[/C][C]4585.7713567129[/C][C]68.2686432870987[/C][/ROW]
[ROW][C]72[/C][C]4768.44[/C][C]4744.74395533753[/C][C]23.696044662468[/C][/ROW]
[ROW][C]73[/C][C]4658.66[/C][C]4646.46195709863[/C][C]12.1980429013702[/C][/ROW]
[ROW][C]74[/C][C]4589.98[/C][C]4563.26941192116[/C][C]26.710588078844[/C][/ROW]
[ROW][C]75[/C][C]4572.86[/C][C]4610.13177638285[/C][C]-37.2717763828532[/C][/ROW]
[ROW][C]76[/C][C]4643[/C][C]4704.85630379288[/C][C]-61.8563037928752[/C][/ROW]
[ROW][C]77[/C][C]4470.7[/C][C]4785.77016158864[/C][C]-315.07016158864[/C][/ROW]
[ROW][C]78[/C][C]4635.34[/C][C]4670.58403143338[/C][C]-35.2440314333817[/C][/ROW]
[ROW][C]79[/C][C]4373.52[/C][C]4570.0125079624[/C][C]-196.492507962404[/C][/ROW]
[ROW][C]80[/C][C]4348.18[/C][C]4474.11918404882[/C][C]-125.939184048823[/C][/ROW]
[ROW][C]81[/C][C]4421.02[/C][C]4527.11735089912[/C][C]-106.097350899119[/C][/ROW]
[ROW][C]82[/C][C]4363.52[/C][C]4449.42071102699[/C][C]-85.9007110269868[/C][/ROW]
[ROW][C]83[/C][C]4462.84[/C][C]4485.88471916024[/C][C]-23.0447191602352[/C][/ROW]
[ROW][C]84[/C][C]4567.34[/C][C]4582.16970043723[/C][C]-14.8297004372316[/C][/ROW]
[ROW][C]85[/C][C]4367.84[/C][C]4455.78945187537[/C][C]-87.9494518753709[/C][/ROW]
[ROW][C]86[/C][C]4382.64[/C][C]4324.46543184633[/C][C]58.1745681536659[/C][/ROW]
[ROW][C]87[/C][C]4386.44[/C][C]4357.09938692651[/C][C]29.3406130734866[/C][/ROW]
[ROW][C]88[/C][C]4489.36[/C][C]4467.02909974193[/C][C]22.3309002580718[/C][/ROW]
[ROW][C]89[/C][C]4549.1[/C][C]4496.08459751033[/C][C]53.0154024896683[/C][/ROW]
[ROW][C]90[/C][C]4627.66[/C][C]4636.63007271594[/C][C]-8.97007271593975[/C][/ROW]
[ROW][C]91[/C][C]4646.26[/C][C]4491.17486793892[/C][C]155.08513206108[/C][/ROW]
[ROW][C]92[/C][C]4728.68[/C][C]4576.99148229052[/C][C]151.688517709485[/C][/ROW]
[ROW][C]93[/C][C]4687.46[/C][C]4763.38339551758[/C][C]-75.923395517576[/C][/ROW]
[ROW][C]94[/C][C]4755.26[/C][C]4707.27007439666[/C][C]47.9899256033405[/C][/ROW]
[ROW][C]95[/C][C]4899.7[/C][C]4827.38150773985[/C][C]72.318492260154[/C][/ROW]
[ROW][C]96[/C][C]5042.06[/C][C]4972.45684283848[/C][C]69.6031571615158[/C][/ROW]
[ROW][C]97[/C][C]4983.88[/C][C]4863.60906370838[/C][C]120.270936291624[/C][/ROW]
[ROW][C]98[/C][C]5028.08[/C][C]4879.91558464618[/C][C]148.164415353816[/C][/ROW]
[ROW][C]99[/C][C]4819.3[/C][C]4949.36632865957[/C][C]-130.066328659568[/C][/ROW]
[ROW][C]100[/C][C]4889.86[/C][C]4989.17755528116[/C][C]-99.3175552811599[/C][/ROW]
[ROW][C]101[/C][C]4962.22[/C][C]4976.83091713677[/C][C]-14.6109171367707[/C][/ROW]
[ROW][C]102[/C][C]4968.92[/C][C]5069.32278071179[/C][C]-100.402780711785[/C][/ROW]
[ROW][C]103[/C][C]5019.56[/C][C]4939.14575008994[/C][C]80.4142499100599[/C][/ROW]
[ROW][C]104[/C][C]5099.18[/C][C]4991.91699614228[/C][C]107.263003857717[/C][/ROW]
[ROW][C]105[/C][C]5171.08[/C][C]5084.48906330914[/C][C]86.5909366908636[/C][/ROW]
[ROW][C]106[/C][C]5353.5[/C][C]5145.76872531588[/C][C]207.731274684116[/C][/ROW]
[ROW][C]107[/C][C]5304.26[/C][C]5350.20998339069[/C][C]-45.9499833906939[/C][/ROW]
[ROW][C]108[/C][C]5636.62[/C][C]5443.84039831274[/C][C]192.779601687258[/C][/ROW]
[ROW][C]109[/C][C]5322.96[/C][C]5411.49913542054[/C][C]-88.5391354205376[/C][/ROW]
[ROW][C]110[/C][C]5308.46[/C][C]5344.84556137608[/C][C]-36.3855613760752[/C][/ROW]
[ROW][C]111[/C][C]5352.02[/C][C]5239.76070570806[/C][C]112.259294291935[/C][/ROW]
[ROW][C]112[/C][C]5358.9[/C][C]5402.41384692573[/C][C]-43.5138469257272[/C][/ROW]
[ROW][C]113[/C][C]5421.04[/C][C]5446.6247535244[/C][C]-25.5847535243993[/C][/ROW]
[ROW][C]114[/C][C]5537.66[/C][C]5508.93637615134[/C][C]28.7236238486648[/C][/ROW]
[ROW][C]115[/C][C]5519.38[/C][C]5501.17570336253[/C][C]18.2042966374738[/C][/ROW]
[ROW][C]116[/C][C]5643.06[/C][C]5538.28159783037[/C][C]104.778402169632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300295&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300295&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
133005.082870.1938034188134.886196581196
142816.942748.6022041370668.3377958629426
153016.282990.5296195317925.7503804682106
163242.683244.20826045121-1.52826045120628
173097.383106.5338151952-9.15381519519951
183057.183064.78527136625-7.60527136625251
193014.13075.33534178933-61.2353417893323
203063.663089.43139396539-25.7713939653904
213100.363256.51866516382-156.158665163815
222964.42985.43955808731-21.0395580873133
233155.43029.23986062905126.160139370947
2432173131.676016996985.3239830030993
253091.13183.04171835499-91.9417183549908
263192.642936.15367666388256.486323336117
273219.663250.10678855007-30.446788550074
283478.263469.7424838818.51751611900136
293284.93334.61747320953-49.7174732095282
303382.23275.22961038887106.970389611128
313341.93321.0084668738620.8915331261433
323402.183385.6815659070816.4984340929168
333394.043530.7232606149-136.683260614901
343374.13315.2308028567558.8691971432509
353383.363446.56849113967-63.2084911396714
363626.543450.96709941726175.572900582736
373579.843486.5260288665293.3139711334775
383530.723442.0905918476788.6294081523256
393532.43587.11537901149-54.7153790114885
403636.683810.52247443836-173.842474438358
413639.843574.0782239567265.761776043279
423676.983620.2589051036456.7210948963552
433668.923615.8418668159953.0781331840135
443718.743694.9261473480323.8138526519683
453815.023793.9435533082621.076446691744
463799.93717.0797807824882.820219217519
473925.863821.51079056474104.349209435257
484226.323984.63723725631241.682762743687
494049.724027.2253436845322.4946563154699
503883.563952.922220562-69.3622205619954
513928.183981.58664331623-53.4066433162288
524377.664168.84571077929208.814289220706
534146.084190.45175516439-44.3717551643886
544246.124188.3296866058257.7903133941791
554163.44187.79822041069-24.3982204106869
564144.764226.14744846105-81.3874484610542
574238.824279.89296742162-41.0729674216163
584352.284198.1555310279154.124468972097
594379.24345.395914964433.8040850356047
604451.024524.85282477-73.8328247699947
614368.224352.58475508115.6352449189962
624337.824245.3732526096592.4467473903505
634349.924354.37796192906-4.45796192905618
644079.424652.63787220273-573.21787220273
654463.844232.61971814807231.220281851931
664552.724387.66991690397165.050083096028
6744894407.8074004212681.1925995787406
684455.94475.15429327091-19.2542932709121
694583.624570.8303428504212.7896571495803
704512.764578.88984695058-66.1298469505791
714654.044585.771356712968.2686432870987
724768.444744.7439553375323.696044662468
734658.664646.4619570986312.1980429013702
744589.984563.2694119211626.710588078844
754572.864610.13177638285-37.2717763828532
7646434704.85630379288-61.8563037928752
774470.74785.77016158864-315.07016158864
784635.344670.58403143338-35.2440314333817
794373.524570.0125079624-196.492507962404
804348.184474.11918404882-125.939184048823
814421.024527.11735089912-106.097350899119
824363.524449.42071102699-85.9007110269868
834462.844485.88471916024-23.0447191602352
844567.344582.16970043723-14.8297004372316
854367.844455.78945187537-87.9494518753709
864382.644324.4654318463358.1745681536659
874386.444357.0993869265129.3406130734866
884489.364467.0290997419322.3309002580718
894549.14496.0845975103353.0154024896683
904627.664636.63007271594-8.97007271593975
914646.264491.17486793892155.08513206108
924728.684576.99148229052151.688517709485
934687.464763.38339551758-75.923395517576
944755.264707.2700743966647.9899256033405
954899.74827.3815077398572.318492260154
965042.064972.4568428384869.6031571615158
974983.884863.60906370838120.270936291624
985028.084879.91558464618148.164415353816
994819.34949.36632865957-130.066328659568
1004889.864989.17755528116-99.3175552811599
1014962.224976.83091713677-14.6109171367707
1024968.925069.32278071179-100.402780711785
1035019.564939.1457500899480.4142499100599
1045099.184991.91699614228107.263003857717
1055171.085084.4890633091486.5909366908636
1065353.55145.76872531588207.731274684116
1075304.265350.20998339069-45.9499833906939
1085636.625443.84039831274192.779601687258
1095322.965411.49913542054-88.5391354205376
1105308.465344.84556137608-36.3855613760752
1115352.025239.76070570806112.259294291935
1125358.95402.41384692573-43.5138469257272
1135421.045446.6247535244-25.5847535243993
1145537.665508.9363761513428.7236238486648
1155519.385501.1757033625318.2042966374738
1165643.065538.28159783037104.778402169632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175626.518326207515401.790192607265851.24645980777
1185691.640882788945444.249940877075939.03182470081
1195719.568172825485450.80352948945988.33281616156
1205914.854389645265625.710323194276203.99845609626
1215702.590683776035393.856263701816011.32510385025
1225694.438075317475366.753047491076022.12310314387
1235656.394676120055310.286328687236002.50302355287
1245717.233673878695353.142249547376081.32509821
1255787.990326828715406.287170150446169.69348350698
1265880.937677524395481.938576232046279.93677881675
1275857.553470701555441.528705401166273.57823600194
1285915.7902772585482.972349739576348.60820477642

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5626.51832620751 & 5401.79019260726 & 5851.24645980777 \tabularnewline
118 & 5691.64088278894 & 5444.24994087707 & 5939.03182470081 \tabularnewline
119 & 5719.56817282548 & 5450.8035294894 & 5988.33281616156 \tabularnewline
120 & 5914.85438964526 & 5625.71032319427 & 6203.99845609626 \tabularnewline
121 & 5702.59068377603 & 5393.85626370181 & 6011.32510385025 \tabularnewline
122 & 5694.43807531747 & 5366.75304749107 & 6022.12310314387 \tabularnewline
123 & 5656.39467612005 & 5310.28632868723 & 6002.50302355287 \tabularnewline
124 & 5717.23367387869 & 5353.14224954737 & 6081.32509821 \tabularnewline
125 & 5787.99032682871 & 5406.28717015044 & 6169.69348350698 \tabularnewline
126 & 5880.93767752439 & 5481.93857623204 & 6279.93677881675 \tabularnewline
127 & 5857.55347070155 & 5441.52870540116 & 6273.57823600194 \tabularnewline
128 & 5915.790277258 & 5482.97234973957 & 6348.60820477642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300295&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]117[/C][C]5626.51832620751[/C][C]5401.79019260726[/C][C]5851.24645980777[/C][/ROW]
[ROW][C]118[/C][C]5691.64088278894[/C][C]5444.24994087707[/C][C]5939.03182470081[/C][/ROW]
[ROW][C]119[/C][C]5719.56817282548[/C][C]5450.8035294894[/C][C]5988.33281616156[/C][/ROW]
[ROW][C]120[/C][C]5914.85438964526[/C][C]5625.71032319427[/C][C]6203.99845609626[/C][/ROW]
[ROW][C]121[/C][C]5702.59068377603[/C][C]5393.85626370181[/C][C]6011.32510385025[/C][/ROW]
[ROW][C]122[/C][C]5694.43807531747[/C][C]5366.75304749107[/C][C]6022.12310314387[/C][/ROW]
[ROW][C]123[/C][C]5656.39467612005[/C][C]5310.28632868723[/C][C]6002.50302355287[/C][/ROW]
[ROW][C]124[/C][C]5717.23367387869[/C][C]5353.14224954737[/C][C]6081.32509821[/C][/ROW]
[ROW][C]125[/C][C]5787.99032682871[/C][C]5406.28717015044[/C][C]6169.69348350698[/C][/ROW]
[ROW][C]126[/C][C]5880.93767752439[/C][C]5481.93857623204[/C][C]6279.93677881675[/C][/ROW]
[ROW][C]127[/C][C]5857.55347070155[/C][C]5441.52870540116[/C][C]6273.57823600194[/C][/ROW]
[ROW][C]128[/C][C]5915.790277258[/C][C]5482.97234973957[/C][C]6348.60820477642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300295&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300295&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
1175626.518326207515401.790192607265851.24645980777
1185691.640882788945444.249940877075939.03182470081
1195719.568172825485450.80352948945988.33281616156
1205914.854389645265625.710323194276203.99845609626
1215702.590683776035393.856263701816011.32510385025
1225694.438075317475366.753047491076022.12310314387
1235656.394676120055310.286328687236002.50302355287
1245717.233673878695353.142249547376081.32509821
1255787.990326828715406.287170150446169.69348350698
1265880.937677524395481.938576232046279.93677881675
1275857.553470701555441.528705401166273.57823600194
1285915.7902772585482.972349739576348.60820477642



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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')