Free Statistics

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 computationThu, 15 Dec 2016 11:17:05 +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/15/t1481797076nrjqucw279zzdx4.htm/, Retrieved Fri, 03 May 2024 07:09:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299819, Retrieved Fri, 03 May 2024 07:09:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [F1 Exponentional ...] [2016-12-15 10:17:05] [10299735033611e1e2dae6371997f8c9] [Current]
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Dataseries X:
7235.6
7268.3
7271.3
7327.4
7339.5
7303.2
7300.7
7311.8
7329
7330.8
7328.6
7346.5
7356.9
7385.7
7394.9
7422.8
7446.6
7441.2
7476.1
7461.6
7450.2
7483.8
7479.7
7509.3
7518.6
7495.4
7507.5
7533.8
7544.7
7564.7
7573.6
7604.6
7605.6
7619.9
7661
7664.1
7663.9
7652.1
7632.8
7677.7
7677.3
7727
7746.4
7771.2
7781.2
7819.4
7819.1
7849.1
7757.8
7823
7825.6
7827
7884.7
7912
7897
7881.1
7885.8
7891.3
7920.9
7946.3
7952.3
8001.9
8007.9
8028.1
8012.5
8069.6
8082.7
8110.6
8129
8149.4
8139.7
8162.4
8207.7
8215.5
8244.6
8269
8245.6
8244.6
8287.6
8284.3
8290.6
8325
8344.2
8353.6
8367.8
8334.6
8330.2
8368.2
8384.7
8351.4
8411.4
8442.8
8443.1
8462.6
8508.5
8522.7
8559.6
8556.7
8618.9
8613.2
8634
8653.4




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=299819&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=299819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299819&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
alpha0.759784953068822
beta0.104249095398375
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.759784953068822 \tabularnewline
beta & 0.104249095398375 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299819&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]0.759784953068822[/C][/ROW]
[ROW][C]beta[/C][C]0.104249095398375[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299819&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
alpha0.759784953068822
beta0.104249095398375
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37271.37301-29.6999999999998
47327.47308.7819421404318.6180578595695
57339.57354.74989614046-15.2498961404572
67303.27373.7775913921-70.5775913920952
77300.77345.17790449953-44.4779044995294
87311.87332.88541031827-21.0854103182719
973297336.69607136951-7.69607136950617
107330.87350.07016877595-19.2701687759482
117328.67353.12411091097-24.5241109109693
127346.57350.2437082128-3.74370821279626
137356.97362.85541530362-5.95541530362243
147385.77373.3149906772412.385009322762
157394.97398.69032283617-3.79032283616743
167422.87411.4756613105311.3243386894665
177446.67436.641857877629.95814212237838
187441.27461.55879235817-20.3587923581717
197476.17461.8288194878314.2711805121708
207461.67489.54055481242-27.9405548124196
217450.27482.96736422961-32.7673642296058
227483.87470.1314353332913.6685646667056
237479.77493.65947104761-13.9594710476104
247509.37495.0904545990114.2095454009868
257518.67519.04932694795-0.449326947949885
267495.47531.83501886525-36.435018865247
277507.57514.39341885887-6.89341885886915
287533.87518.8510757296914.9489242703139
297544.77541.088274110733.61172588926729
307564.77554.997713341779.70228665823015
317573.67574.30315699224-0.703156992242839
327604.67585.6470062456918.9529937543075
337605.67613.42651083994-7.82651083994097
347619.97620.23943717792-0.339437177924992
3576617632.7140436622428.2859563377642
367664.17669.17823616232-5.07823616232236
377663.97679.89058591586-15.9905859158589
387652.17681.04533187952-28.9453318795222
397632.87670.06458695361-37.2645869536063
407677.77649.8113850108327.8886149891678
417677.37681.26957612121-3.9695761212115
4277277688.2079751986638.7920248013406
437746.47730.708591024815.6914089751963
447771.27756.9005743078914.299425692112
457781.27783.1675627334-1.96756273339997
467819.47796.9192935884922.4807064115066
477819.17831.02707839947-11.9270783994734
487849.17838.0476392074711.0523607925279
497757.87863.40305531386-105.603055313863
5078237791.7609515545431.2390484454645
517825.67826.56376717842-0.963767178417584
5278277836.82303104003-9.8230310400304
537884.77839.5731077454445.1268922545605
5479127887.6476703161924.3523296838102
5578977921.86690523635-24.8669052363493
567881.17916.72047573409-35.6204757340865
577885.87900.58225792823-14.782257928231
587891.37899.10574772242-7.8057477224238
597920.97902.3116159630518.588384036947
607946.37927.0436765288319.2563234711715
617952.37953.80846099935-1.50846099935461
628001.97964.676994164937.2230058351024
638007.98007.92143172112-0.0214317211239177
648028.18022.866408496555.23359150344822
658012.58042.21860937378-29.7186093737791
668069.68032.6607352037336.9392647962741
678082.78076.674355264816.02564473518669
688110.68097.6775445627512.9224554372504
6981298124.944374415024.05562558497513
708149.48145.795553870153.6044461298452
718139.78166.58943094687-26.8894309468742
728162.48162.084690751770.315309248228004
738207.78178.2746774752729.4253225247276
748215.58218.91270267364-3.41270267363507
758244.68234.3305808586810.2694191413248
7682698260.957338118718.04266188129259
778245.68286.52927298598-40.929272985979
788244.68271.65118802929-27.0511880292943
798287.68265.1748226158222.4251773841806
808284.38298.06608382526-13.766083825265
818290.68302.36940059209-11.7694005920912
8283258307.2575495697517.7424504302544
838344.28335.973683282898.22631671711315
848353.68358.11118278607-4.51118278606555
858367.88370.21360505001-2.41360505001103
868334.68383.71856115621-49.1185611562141
878330.28357.84726570956-27.6472657095637
888368.28346.0996834202122.1003165797865
898384.78373.9000630397810.7999369602239
908351.48393.97001372304-42.5700137230378
918411.48370.1184403642641.2815596357377
928442.88413.2458148551129.5541851448888
938443.18449.80380188045-6.70380188045237
948462.68458.282528610074.3174713899316
958508.58475.4770264331533.0229735668509
968522.78517.097180049225.60281995078185
978559.68538.3276955032121.2723044967879
988556.78573.14856270618-16.448562706184
998618.98578.0068430280140.8931569719898
1008613.28629.67151909624-16.4715190962434
10186348636.44671958219-2.44671958219078
1028653.48653.68395464999-0.283954649994484

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7271.3 & 7301 & -29.6999999999998 \tabularnewline
4 & 7327.4 & 7308.78194214043 & 18.6180578595695 \tabularnewline
5 & 7339.5 & 7354.74989614046 & -15.2498961404572 \tabularnewline
6 & 7303.2 & 7373.7775913921 & -70.5775913920952 \tabularnewline
7 & 7300.7 & 7345.17790449953 & -44.4779044995294 \tabularnewline
8 & 7311.8 & 7332.88541031827 & -21.0854103182719 \tabularnewline
9 & 7329 & 7336.69607136951 & -7.69607136950617 \tabularnewline
10 & 7330.8 & 7350.07016877595 & -19.2701687759482 \tabularnewline
11 & 7328.6 & 7353.12411091097 & -24.5241109109693 \tabularnewline
12 & 7346.5 & 7350.2437082128 & -3.74370821279626 \tabularnewline
13 & 7356.9 & 7362.85541530362 & -5.95541530362243 \tabularnewline
14 & 7385.7 & 7373.31499067724 & 12.385009322762 \tabularnewline
15 & 7394.9 & 7398.69032283617 & -3.79032283616743 \tabularnewline
16 & 7422.8 & 7411.47566131053 & 11.3243386894665 \tabularnewline
17 & 7446.6 & 7436.64185787762 & 9.95814212237838 \tabularnewline
18 & 7441.2 & 7461.55879235817 & -20.3587923581717 \tabularnewline
19 & 7476.1 & 7461.82881948783 & 14.2711805121708 \tabularnewline
20 & 7461.6 & 7489.54055481242 & -27.9405548124196 \tabularnewline
21 & 7450.2 & 7482.96736422961 & -32.7673642296058 \tabularnewline
22 & 7483.8 & 7470.13143533329 & 13.6685646667056 \tabularnewline
23 & 7479.7 & 7493.65947104761 & -13.9594710476104 \tabularnewline
24 & 7509.3 & 7495.09045459901 & 14.2095454009868 \tabularnewline
25 & 7518.6 & 7519.04932694795 & -0.449326947949885 \tabularnewline
26 & 7495.4 & 7531.83501886525 & -36.435018865247 \tabularnewline
27 & 7507.5 & 7514.39341885887 & -6.89341885886915 \tabularnewline
28 & 7533.8 & 7518.85107572969 & 14.9489242703139 \tabularnewline
29 & 7544.7 & 7541.08827411073 & 3.61172588926729 \tabularnewline
30 & 7564.7 & 7554.99771334177 & 9.70228665823015 \tabularnewline
31 & 7573.6 & 7574.30315699224 & -0.703156992242839 \tabularnewline
32 & 7604.6 & 7585.64700624569 & 18.9529937543075 \tabularnewline
33 & 7605.6 & 7613.42651083994 & -7.82651083994097 \tabularnewline
34 & 7619.9 & 7620.23943717792 & -0.339437177924992 \tabularnewline
35 & 7661 & 7632.71404366224 & 28.2859563377642 \tabularnewline
36 & 7664.1 & 7669.17823616232 & -5.07823616232236 \tabularnewline
37 & 7663.9 & 7679.89058591586 & -15.9905859158589 \tabularnewline
38 & 7652.1 & 7681.04533187952 & -28.9453318795222 \tabularnewline
39 & 7632.8 & 7670.06458695361 & -37.2645869536063 \tabularnewline
40 & 7677.7 & 7649.81138501083 & 27.8886149891678 \tabularnewline
41 & 7677.3 & 7681.26957612121 & -3.9695761212115 \tabularnewline
42 & 7727 & 7688.20797519866 & 38.7920248013406 \tabularnewline
43 & 7746.4 & 7730.7085910248 & 15.6914089751963 \tabularnewline
44 & 7771.2 & 7756.90057430789 & 14.299425692112 \tabularnewline
45 & 7781.2 & 7783.1675627334 & -1.96756273339997 \tabularnewline
46 & 7819.4 & 7796.91929358849 & 22.4807064115066 \tabularnewline
47 & 7819.1 & 7831.02707839947 & -11.9270783994734 \tabularnewline
48 & 7849.1 & 7838.04763920747 & 11.0523607925279 \tabularnewline
49 & 7757.8 & 7863.40305531386 & -105.603055313863 \tabularnewline
50 & 7823 & 7791.76095155454 & 31.2390484454645 \tabularnewline
51 & 7825.6 & 7826.56376717842 & -0.963767178417584 \tabularnewline
52 & 7827 & 7836.82303104003 & -9.8230310400304 \tabularnewline
53 & 7884.7 & 7839.57310774544 & 45.1268922545605 \tabularnewline
54 & 7912 & 7887.64767031619 & 24.3523296838102 \tabularnewline
55 & 7897 & 7921.86690523635 & -24.8669052363493 \tabularnewline
56 & 7881.1 & 7916.72047573409 & -35.6204757340865 \tabularnewline
57 & 7885.8 & 7900.58225792823 & -14.782257928231 \tabularnewline
58 & 7891.3 & 7899.10574772242 & -7.8057477224238 \tabularnewline
59 & 7920.9 & 7902.31161596305 & 18.588384036947 \tabularnewline
60 & 7946.3 & 7927.04367652883 & 19.2563234711715 \tabularnewline
61 & 7952.3 & 7953.80846099935 & -1.50846099935461 \tabularnewline
62 & 8001.9 & 7964.6769941649 & 37.2230058351024 \tabularnewline
63 & 8007.9 & 8007.92143172112 & -0.0214317211239177 \tabularnewline
64 & 8028.1 & 8022.86640849655 & 5.23359150344822 \tabularnewline
65 & 8012.5 & 8042.21860937378 & -29.7186093737791 \tabularnewline
66 & 8069.6 & 8032.66073520373 & 36.9392647962741 \tabularnewline
67 & 8082.7 & 8076.67435526481 & 6.02564473518669 \tabularnewline
68 & 8110.6 & 8097.67754456275 & 12.9224554372504 \tabularnewline
69 & 8129 & 8124.94437441502 & 4.05562558497513 \tabularnewline
70 & 8149.4 & 8145.79555387015 & 3.6044461298452 \tabularnewline
71 & 8139.7 & 8166.58943094687 & -26.8894309468742 \tabularnewline
72 & 8162.4 & 8162.08469075177 & 0.315309248228004 \tabularnewline
73 & 8207.7 & 8178.27467747527 & 29.4253225247276 \tabularnewline
74 & 8215.5 & 8218.91270267364 & -3.41270267363507 \tabularnewline
75 & 8244.6 & 8234.33058085868 & 10.2694191413248 \tabularnewline
76 & 8269 & 8260.95733811871 & 8.04266188129259 \tabularnewline
77 & 8245.6 & 8286.52927298598 & -40.929272985979 \tabularnewline
78 & 8244.6 & 8271.65118802929 & -27.0511880292943 \tabularnewline
79 & 8287.6 & 8265.17482261582 & 22.4251773841806 \tabularnewline
80 & 8284.3 & 8298.06608382526 & -13.766083825265 \tabularnewline
81 & 8290.6 & 8302.36940059209 & -11.7694005920912 \tabularnewline
82 & 8325 & 8307.25754956975 & 17.7424504302544 \tabularnewline
83 & 8344.2 & 8335.97368328289 & 8.22631671711315 \tabularnewline
84 & 8353.6 & 8358.11118278607 & -4.51118278606555 \tabularnewline
85 & 8367.8 & 8370.21360505001 & -2.41360505001103 \tabularnewline
86 & 8334.6 & 8383.71856115621 & -49.1185611562141 \tabularnewline
87 & 8330.2 & 8357.84726570956 & -27.6472657095637 \tabularnewline
88 & 8368.2 & 8346.09968342021 & 22.1003165797865 \tabularnewline
89 & 8384.7 & 8373.90006303978 & 10.7999369602239 \tabularnewline
90 & 8351.4 & 8393.97001372304 & -42.5700137230378 \tabularnewline
91 & 8411.4 & 8370.11844036426 & 41.2815596357377 \tabularnewline
92 & 8442.8 & 8413.24581485511 & 29.5541851448888 \tabularnewline
93 & 8443.1 & 8449.80380188045 & -6.70380188045237 \tabularnewline
94 & 8462.6 & 8458.28252861007 & 4.3174713899316 \tabularnewline
95 & 8508.5 & 8475.47702643315 & 33.0229735668509 \tabularnewline
96 & 8522.7 & 8517.09718004922 & 5.60281995078185 \tabularnewline
97 & 8559.6 & 8538.32769550321 & 21.2723044967879 \tabularnewline
98 & 8556.7 & 8573.14856270618 & -16.448562706184 \tabularnewline
99 & 8618.9 & 8578.00684302801 & 40.8931569719898 \tabularnewline
100 & 8613.2 & 8629.67151909624 & -16.4715190962434 \tabularnewline
101 & 8634 & 8636.44671958219 & -2.44671958219078 \tabularnewline
102 & 8653.4 & 8653.68395464999 & -0.283954649994484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299819&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]7271.3[/C][C]7301[/C][C]-29.6999999999998[/C][/ROW]
[ROW][C]4[/C][C]7327.4[/C][C]7308.78194214043[/C][C]18.6180578595695[/C][/ROW]
[ROW][C]5[/C][C]7339.5[/C][C]7354.74989614046[/C][C]-15.2498961404572[/C][/ROW]
[ROW][C]6[/C][C]7303.2[/C][C]7373.7775913921[/C][C]-70.5775913920952[/C][/ROW]
[ROW][C]7[/C][C]7300.7[/C][C]7345.17790449953[/C][C]-44.4779044995294[/C][/ROW]
[ROW][C]8[/C][C]7311.8[/C][C]7332.88541031827[/C][C]-21.0854103182719[/C][/ROW]
[ROW][C]9[/C][C]7329[/C][C]7336.69607136951[/C][C]-7.69607136950617[/C][/ROW]
[ROW][C]10[/C][C]7330.8[/C][C]7350.07016877595[/C][C]-19.2701687759482[/C][/ROW]
[ROW][C]11[/C][C]7328.6[/C][C]7353.12411091097[/C][C]-24.5241109109693[/C][/ROW]
[ROW][C]12[/C][C]7346.5[/C][C]7350.2437082128[/C][C]-3.74370821279626[/C][/ROW]
[ROW][C]13[/C][C]7356.9[/C][C]7362.85541530362[/C][C]-5.95541530362243[/C][/ROW]
[ROW][C]14[/C][C]7385.7[/C][C]7373.31499067724[/C][C]12.385009322762[/C][/ROW]
[ROW][C]15[/C][C]7394.9[/C][C]7398.69032283617[/C][C]-3.79032283616743[/C][/ROW]
[ROW][C]16[/C][C]7422.8[/C][C]7411.47566131053[/C][C]11.3243386894665[/C][/ROW]
[ROW][C]17[/C][C]7446.6[/C][C]7436.64185787762[/C][C]9.95814212237838[/C][/ROW]
[ROW][C]18[/C][C]7441.2[/C][C]7461.55879235817[/C][C]-20.3587923581717[/C][/ROW]
[ROW][C]19[/C][C]7476.1[/C][C]7461.82881948783[/C][C]14.2711805121708[/C][/ROW]
[ROW][C]20[/C][C]7461.6[/C][C]7489.54055481242[/C][C]-27.9405548124196[/C][/ROW]
[ROW][C]21[/C][C]7450.2[/C][C]7482.96736422961[/C][C]-32.7673642296058[/C][/ROW]
[ROW][C]22[/C][C]7483.8[/C][C]7470.13143533329[/C][C]13.6685646667056[/C][/ROW]
[ROW][C]23[/C][C]7479.7[/C][C]7493.65947104761[/C][C]-13.9594710476104[/C][/ROW]
[ROW][C]24[/C][C]7509.3[/C][C]7495.09045459901[/C][C]14.2095454009868[/C][/ROW]
[ROW][C]25[/C][C]7518.6[/C][C]7519.04932694795[/C][C]-0.449326947949885[/C][/ROW]
[ROW][C]26[/C][C]7495.4[/C][C]7531.83501886525[/C][C]-36.435018865247[/C][/ROW]
[ROW][C]27[/C][C]7507.5[/C][C]7514.39341885887[/C][C]-6.89341885886915[/C][/ROW]
[ROW][C]28[/C][C]7533.8[/C][C]7518.85107572969[/C][C]14.9489242703139[/C][/ROW]
[ROW][C]29[/C][C]7544.7[/C][C]7541.08827411073[/C][C]3.61172588926729[/C][/ROW]
[ROW][C]30[/C][C]7564.7[/C][C]7554.99771334177[/C][C]9.70228665823015[/C][/ROW]
[ROW][C]31[/C][C]7573.6[/C][C]7574.30315699224[/C][C]-0.703156992242839[/C][/ROW]
[ROW][C]32[/C][C]7604.6[/C][C]7585.64700624569[/C][C]18.9529937543075[/C][/ROW]
[ROW][C]33[/C][C]7605.6[/C][C]7613.42651083994[/C][C]-7.82651083994097[/C][/ROW]
[ROW][C]34[/C][C]7619.9[/C][C]7620.23943717792[/C][C]-0.339437177924992[/C][/ROW]
[ROW][C]35[/C][C]7661[/C][C]7632.71404366224[/C][C]28.2859563377642[/C][/ROW]
[ROW][C]36[/C][C]7664.1[/C][C]7669.17823616232[/C][C]-5.07823616232236[/C][/ROW]
[ROW][C]37[/C][C]7663.9[/C][C]7679.89058591586[/C][C]-15.9905859158589[/C][/ROW]
[ROW][C]38[/C][C]7652.1[/C][C]7681.04533187952[/C][C]-28.9453318795222[/C][/ROW]
[ROW][C]39[/C][C]7632.8[/C][C]7670.06458695361[/C][C]-37.2645869536063[/C][/ROW]
[ROW][C]40[/C][C]7677.7[/C][C]7649.81138501083[/C][C]27.8886149891678[/C][/ROW]
[ROW][C]41[/C][C]7677.3[/C][C]7681.26957612121[/C][C]-3.9695761212115[/C][/ROW]
[ROW][C]42[/C][C]7727[/C][C]7688.20797519866[/C][C]38.7920248013406[/C][/ROW]
[ROW][C]43[/C][C]7746.4[/C][C]7730.7085910248[/C][C]15.6914089751963[/C][/ROW]
[ROW][C]44[/C][C]7771.2[/C][C]7756.90057430789[/C][C]14.299425692112[/C][/ROW]
[ROW][C]45[/C][C]7781.2[/C][C]7783.1675627334[/C][C]-1.96756273339997[/C][/ROW]
[ROW][C]46[/C][C]7819.4[/C][C]7796.91929358849[/C][C]22.4807064115066[/C][/ROW]
[ROW][C]47[/C][C]7819.1[/C][C]7831.02707839947[/C][C]-11.9270783994734[/C][/ROW]
[ROW][C]48[/C][C]7849.1[/C][C]7838.04763920747[/C][C]11.0523607925279[/C][/ROW]
[ROW][C]49[/C][C]7757.8[/C][C]7863.40305531386[/C][C]-105.603055313863[/C][/ROW]
[ROW][C]50[/C][C]7823[/C][C]7791.76095155454[/C][C]31.2390484454645[/C][/ROW]
[ROW][C]51[/C][C]7825.6[/C][C]7826.56376717842[/C][C]-0.963767178417584[/C][/ROW]
[ROW][C]52[/C][C]7827[/C][C]7836.82303104003[/C][C]-9.8230310400304[/C][/ROW]
[ROW][C]53[/C][C]7884.7[/C][C]7839.57310774544[/C][C]45.1268922545605[/C][/ROW]
[ROW][C]54[/C][C]7912[/C][C]7887.64767031619[/C][C]24.3523296838102[/C][/ROW]
[ROW][C]55[/C][C]7897[/C][C]7921.86690523635[/C][C]-24.8669052363493[/C][/ROW]
[ROW][C]56[/C][C]7881.1[/C][C]7916.72047573409[/C][C]-35.6204757340865[/C][/ROW]
[ROW][C]57[/C][C]7885.8[/C][C]7900.58225792823[/C][C]-14.782257928231[/C][/ROW]
[ROW][C]58[/C][C]7891.3[/C][C]7899.10574772242[/C][C]-7.8057477224238[/C][/ROW]
[ROW][C]59[/C][C]7920.9[/C][C]7902.31161596305[/C][C]18.588384036947[/C][/ROW]
[ROW][C]60[/C][C]7946.3[/C][C]7927.04367652883[/C][C]19.2563234711715[/C][/ROW]
[ROW][C]61[/C][C]7952.3[/C][C]7953.80846099935[/C][C]-1.50846099935461[/C][/ROW]
[ROW][C]62[/C][C]8001.9[/C][C]7964.6769941649[/C][C]37.2230058351024[/C][/ROW]
[ROW][C]63[/C][C]8007.9[/C][C]8007.92143172112[/C][C]-0.0214317211239177[/C][/ROW]
[ROW][C]64[/C][C]8028.1[/C][C]8022.86640849655[/C][C]5.23359150344822[/C][/ROW]
[ROW][C]65[/C][C]8012.5[/C][C]8042.21860937378[/C][C]-29.7186093737791[/C][/ROW]
[ROW][C]66[/C][C]8069.6[/C][C]8032.66073520373[/C][C]36.9392647962741[/C][/ROW]
[ROW][C]67[/C][C]8082.7[/C][C]8076.67435526481[/C][C]6.02564473518669[/C][/ROW]
[ROW][C]68[/C][C]8110.6[/C][C]8097.67754456275[/C][C]12.9224554372504[/C][/ROW]
[ROW][C]69[/C][C]8129[/C][C]8124.94437441502[/C][C]4.05562558497513[/C][/ROW]
[ROW][C]70[/C][C]8149.4[/C][C]8145.79555387015[/C][C]3.6044461298452[/C][/ROW]
[ROW][C]71[/C][C]8139.7[/C][C]8166.58943094687[/C][C]-26.8894309468742[/C][/ROW]
[ROW][C]72[/C][C]8162.4[/C][C]8162.08469075177[/C][C]0.315309248228004[/C][/ROW]
[ROW][C]73[/C][C]8207.7[/C][C]8178.27467747527[/C][C]29.4253225247276[/C][/ROW]
[ROW][C]74[/C][C]8215.5[/C][C]8218.91270267364[/C][C]-3.41270267363507[/C][/ROW]
[ROW][C]75[/C][C]8244.6[/C][C]8234.33058085868[/C][C]10.2694191413248[/C][/ROW]
[ROW][C]76[/C][C]8269[/C][C]8260.95733811871[/C][C]8.04266188129259[/C][/ROW]
[ROW][C]77[/C][C]8245.6[/C][C]8286.52927298598[/C][C]-40.929272985979[/C][/ROW]
[ROW][C]78[/C][C]8244.6[/C][C]8271.65118802929[/C][C]-27.0511880292943[/C][/ROW]
[ROW][C]79[/C][C]8287.6[/C][C]8265.17482261582[/C][C]22.4251773841806[/C][/ROW]
[ROW][C]80[/C][C]8284.3[/C][C]8298.06608382526[/C][C]-13.766083825265[/C][/ROW]
[ROW][C]81[/C][C]8290.6[/C][C]8302.36940059209[/C][C]-11.7694005920912[/C][/ROW]
[ROW][C]82[/C][C]8325[/C][C]8307.25754956975[/C][C]17.7424504302544[/C][/ROW]
[ROW][C]83[/C][C]8344.2[/C][C]8335.97368328289[/C][C]8.22631671711315[/C][/ROW]
[ROW][C]84[/C][C]8353.6[/C][C]8358.11118278607[/C][C]-4.51118278606555[/C][/ROW]
[ROW][C]85[/C][C]8367.8[/C][C]8370.21360505001[/C][C]-2.41360505001103[/C][/ROW]
[ROW][C]86[/C][C]8334.6[/C][C]8383.71856115621[/C][C]-49.1185611562141[/C][/ROW]
[ROW][C]87[/C][C]8330.2[/C][C]8357.84726570956[/C][C]-27.6472657095637[/C][/ROW]
[ROW][C]88[/C][C]8368.2[/C][C]8346.09968342021[/C][C]22.1003165797865[/C][/ROW]
[ROW][C]89[/C][C]8384.7[/C][C]8373.90006303978[/C][C]10.7999369602239[/C][/ROW]
[ROW][C]90[/C][C]8351.4[/C][C]8393.97001372304[/C][C]-42.5700137230378[/C][/ROW]
[ROW][C]91[/C][C]8411.4[/C][C]8370.11844036426[/C][C]41.2815596357377[/C][/ROW]
[ROW][C]92[/C][C]8442.8[/C][C]8413.24581485511[/C][C]29.5541851448888[/C][/ROW]
[ROW][C]93[/C][C]8443.1[/C][C]8449.80380188045[/C][C]-6.70380188045237[/C][/ROW]
[ROW][C]94[/C][C]8462.6[/C][C]8458.28252861007[/C][C]4.3174713899316[/C][/ROW]
[ROW][C]95[/C][C]8508.5[/C][C]8475.47702643315[/C][C]33.0229735668509[/C][/ROW]
[ROW][C]96[/C][C]8522.7[/C][C]8517.09718004922[/C][C]5.60281995078185[/C][/ROW]
[ROW][C]97[/C][C]8559.6[/C][C]8538.32769550321[/C][C]21.2723044967879[/C][/ROW]
[ROW][C]98[/C][C]8556.7[/C][C]8573.14856270618[/C][C]-16.448562706184[/C][/ROW]
[ROW][C]99[/C][C]8618.9[/C][C]8578.00684302801[/C][C]40.8931569719898[/C][/ROW]
[ROW][C]100[/C][C]8613.2[/C][C]8629.67151909624[/C][C]-16.4715190962434[/C][/ROW]
[ROW][C]101[/C][C]8634[/C][C]8636.44671958219[/C][C]-2.44671958219078[/C][/ROW]
[ROW][C]102[/C][C]8653.4[/C][C]8653.68395464999[/C][C]-0.283954649994484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299819&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299819&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
37271.37301-29.6999999999998
47327.47308.7819421404318.6180578595695
57339.57354.74989614046-15.2498961404572
67303.27373.7775913921-70.5775913920952
77300.77345.17790449953-44.4779044995294
87311.87332.88541031827-21.0854103182719
973297336.69607136951-7.69607136950617
107330.87350.07016877595-19.2701687759482
117328.67353.12411091097-24.5241109109693
127346.57350.2437082128-3.74370821279626
137356.97362.85541530362-5.95541530362243
147385.77373.3149906772412.385009322762
157394.97398.69032283617-3.79032283616743
167422.87411.4756613105311.3243386894665
177446.67436.641857877629.95814212237838
187441.27461.55879235817-20.3587923581717
197476.17461.8288194878314.2711805121708
207461.67489.54055481242-27.9405548124196
217450.27482.96736422961-32.7673642296058
227483.87470.1314353332913.6685646667056
237479.77493.65947104761-13.9594710476104
247509.37495.0904545990114.2095454009868
257518.67519.04932694795-0.449326947949885
267495.47531.83501886525-36.435018865247
277507.57514.39341885887-6.89341885886915
287533.87518.8510757296914.9489242703139
297544.77541.088274110733.61172588926729
307564.77554.997713341779.70228665823015
317573.67574.30315699224-0.703156992242839
327604.67585.6470062456918.9529937543075
337605.67613.42651083994-7.82651083994097
347619.97620.23943717792-0.339437177924992
3576617632.7140436622428.2859563377642
367664.17669.17823616232-5.07823616232236
377663.97679.89058591586-15.9905859158589
387652.17681.04533187952-28.9453318795222
397632.87670.06458695361-37.2645869536063
407677.77649.8113850108327.8886149891678
417677.37681.26957612121-3.9695761212115
4277277688.2079751986638.7920248013406
437746.47730.708591024815.6914089751963
447771.27756.9005743078914.299425692112
457781.27783.1675627334-1.96756273339997
467819.47796.9192935884922.4807064115066
477819.17831.02707839947-11.9270783994734
487849.17838.0476392074711.0523607925279
497757.87863.40305531386-105.603055313863
5078237791.7609515545431.2390484454645
517825.67826.56376717842-0.963767178417584
5278277836.82303104003-9.8230310400304
537884.77839.5731077454445.1268922545605
5479127887.6476703161924.3523296838102
5578977921.86690523635-24.8669052363493
567881.17916.72047573409-35.6204757340865
577885.87900.58225792823-14.782257928231
587891.37899.10574772242-7.8057477224238
597920.97902.3116159630518.588384036947
607946.37927.0436765288319.2563234711715
617952.37953.80846099935-1.50846099935461
628001.97964.676994164937.2230058351024
638007.98007.92143172112-0.0214317211239177
648028.18022.866408496555.23359150344822
658012.58042.21860937378-29.7186093737791
668069.68032.6607352037336.9392647962741
678082.78076.674355264816.02564473518669
688110.68097.6775445627512.9224554372504
6981298124.944374415024.05562558497513
708149.48145.795553870153.6044461298452
718139.78166.58943094687-26.8894309468742
728162.48162.084690751770.315309248228004
738207.78178.2746774752729.4253225247276
748215.58218.91270267364-3.41270267363507
758244.68234.3305808586810.2694191413248
7682698260.957338118718.04266188129259
778245.68286.52927298598-40.929272985979
788244.68271.65118802929-27.0511880292943
798287.68265.1748226158222.4251773841806
808284.38298.06608382526-13.766083825265
818290.68302.36940059209-11.7694005920912
8283258307.2575495697517.7424504302544
838344.28335.973683282898.22631671711315
848353.68358.11118278607-4.51118278606555
858367.88370.21360505001-2.41360505001103
868334.68383.71856115621-49.1185611562141
878330.28357.84726570956-27.6472657095637
888368.28346.0996834202122.1003165797865
898384.78373.9000630397810.7999369602239
908351.48393.97001372304-42.5700137230378
918411.48370.1184403642641.2815596357377
928442.88413.2458148551129.5541851448888
938443.18449.80380188045-6.70380188045237
948462.68458.282528610074.3174713899316
958508.58475.4770264331533.0229735668509
968522.78517.097180049225.60281995078185
978559.68538.3276955032121.2723044967879
988556.78573.14856270618-16.448562706184
998618.98578.0068430280140.8931569719898
1008613.28629.67151909624-16.4715190962434
10186348636.44671958219-2.44671958219078
1028653.48653.68395464999-0.283954649994484







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1038672.541934804438623.834454050918721.24941555794
1048691.615659429288628.03593344558755.19538541306
1058710.689384054138632.955598093858788.42317001441
1068729.763108678988638.097050127858821.42916723011
1078748.836833303838643.231322906758854.44234370091
1088767.910557928688648.236492543538887.58462331384
1098786.984282553548653.042099402168920.92646570491
1108806.058007178398657.605418217548954.51059613924
1118825.131731803248661.89987832618988.36358528038
1128844.205456428098665.908858796849022.50205405934
1138863.279181052958669.622125360739056.93623674516
1148882.35290567788673.033672673789091.67213868182
1158901.426630302658676.140361694859126.71289891044
1168920.50035492758678.941029685889162.05968016912
1178939.574079552358681.435892707429197.71226639728
1188958.64780417728683.626135302299233.66947305212
1198977.721528802068685.513623400869269.92943420325
1208996.795253426918687.10070030969306.48980654422

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
103 & 8672.54193480443 & 8623.83445405091 & 8721.24941555794 \tabularnewline
104 & 8691.61565942928 & 8628.0359334455 & 8755.19538541306 \tabularnewline
105 & 8710.68938405413 & 8632.95559809385 & 8788.42317001441 \tabularnewline
106 & 8729.76310867898 & 8638.09705012785 & 8821.42916723011 \tabularnewline
107 & 8748.83683330383 & 8643.23132290675 & 8854.44234370091 \tabularnewline
108 & 8767.91055792868 & 8648.23649254353 & 8887.58462331384 \tabularnewline
109 & 8786.98428255354 & 8653.04209940216 & 8920.92646570491 \tabularnewline
110 & 8806.05800717839 & 8657.60541821754 & 8954.51059613924 \tabularnewline
111 & 8825.13173180324 & 8661.8998783261 & 8988.36358528038 \tabularnewline
112 & 8844.20545642809 & 8665.90885879684 & 9022.50205405934 \tabularnewline
113 & 8863.27918105295 & 8669.62212536073 & 9056.93623674516 \tabularnewline
114 & 8882.3529056778 & 8673.03367267378 & 9091.67213868182 \tabularnewline
115 & 8901.42663030265 & 8676.14036169485 & 9126.71289891044 \tabularnewline
116 & 8920.5003549275 & 8678.94102968588 & 9162.05968016912 \tabularnewline
117 & 8939.57407955235 & 8681.43589270742 & 9197.71226639728 \tabularnewline
118 & 8958.6478041772 & 8683.62613530229 & 9233.66947305212 \tabularnewline
119 & 8977.72152880206 & 8685.51362340086 & 9269.92943420325 \tabularnewline
120 & 8996.79525342691 & 8687.1007003096 & 9306.48980654422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299819&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]103[/C][C]8672.54193480443[/C][C]8623.83445405091[/C][C]8721.24941555794[/C][/ROW]
[ROW][C]104[/C][C]8691.61565942928[/C][C]8628.0359334455[/C][C]8755.19538541306[/C][/ROW]
[ROW][C]105[/C][C]8710.68938405413[/C][C]8632.95559809385[/C][C]8788.42317001441[/C][/ROW]
[ROW][C]106[/C][C]8729.76310867898[/C][C]8638.09705012785[/C][C]8821.42916723011[/C][/ROW]
[ROW][C]107[/C][C]8748.83683330383[/C][C]8643.23132290675[/C][C]8854.44234370091[/C][/ROW]
[ROW][C]108[/C][C]8767.91055792868[/C][C]8648.23649254353[/C][C]8887.58462331384[/C][/ROW]
[ROW][C]109[/C][C]8786.98428255354[/C][C]8653.04209940216[/C][C]8920.92646570491[/C][/ROW]
[ROW][C]110[/C][C]8806.05800717839[/C][C]8657.60541821754[/C][C]8954.51059613924[/C][/ROW]
[ROW][C]111[/C][C]8825.13173180324[/C][C]8661.8998783261[/C][C]8988.36358528038[/C][/ROW]
[ROW][C]112[/C][C]8844.20545642809[/C][C]8665.90885879684[/C][C]9022.50205405934[/C][/ROW]
[ROW][C]113[/C][C]8863.27918105295[/C][C]8669.62212536073[/C][C]9056.93623674516[/C][/ROW]
[ROW][C]114[/C][C]8882.3529056778[/C][C]8673.03367267378[/C][C]9091.67213868182[/C][/ROW]
[ROW][C]115[/C][C]8901.42663030265[/C][C]8676.14036169485[/C][C]9126.71289891044[/C][/ROW]
[ROW][C]116[/C][C]8920.5003549275[/C][C]8678.94102968588[/C][C]9162.05968016912[/C][/ROW]
[ROW][C]117[/C][C]8939.57407955235[/C][C]8681.43589270742[/C][C]9197.71226639728[/C][/ROW]
[ROW][C]118[/C][C]8958.6478041772[/C][C]8683.62613530229[/C][C]9233.66947305212[/C][/ROW]
[ROW][C]119[/C][C]8977.72152880206[/C][C]8685.51362340086[/C][C]9269.92943420325[/C][/ROW]
[ROW][C]120[/C][C]8996.79525342691[/C][C]8687.1007003096[/C][C]9306.48980654422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299819&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299819&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
1038672.541934804438623.834454050918721.24941555794
1048691.615659429288628.03593344558755.19538541306
1058710.689384054138632.955598093858788.42317001441
1068729.763108678988638.097050127858821.42916723011
1078748.836833303838643.231322906758854.44234370091
1088767.910557928688648.236492543538887.58462331384
1098786.984282553548653.042099402168920.92646570491
1108806.058007178398657.605418217548954.51059613924
1118825.131731803248661.89987832618988.36358528038
1128844.205456428098665.908858796849022.50205405934
1138863.279181052958669.622125360739056.93623674516
1148882.35290567788673.033672673789091.67213868182
1158901.426630302658676.140361694859126.71289891044
1168920.50035492758678.941029685889162.05968016912
1178939.574079552358681.435892707429197.71226639728
1188958.64780417728683.626135302299233.66947305212
1198977.721528802068685.513623400869269.92943420325
1208996.795253426918687.10070030969306.48980654422



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
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')