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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Aug 2017 17:38:25 +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/14/t15027253501nl4mjimafsdo1r.htm/, Retrieved Sun, 12 May 2024 21:36:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307244, Retrieved Sun, 12 May 2024 21:36:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [aantal verkochte ...] [2017-08-14 15:38:25] [ff90ea2d7baa48124a9630d5b785d73f] [Current]
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Dataseries X:
37800
36400
38500
30800
39900
39200
42000
43400
48300
42000
39900
49700
42000
31500
37100
28000
39200
32200
42700
38500
40600
45500
44800
53200
38500
32200
35700
25900
37100
28700
40600
38500
34300
49000
44100
50400
37800
35000
31500
25900
34300
30800
42000
40600
35000
46900
43400
56000
44800
27300
27300
27300
32200
32200
43400
39900
35700
44800
41300
59500
46900
27300
28700
23800
32900
37800
47600
46900
37800
44100
39200
56000
42700
34300
30800
23100
34300
41300
48300
45500
33600
48300
37800
58100
48300
35000
32200
21700
34300
32900
49700
49700
37800
49000
36400
56700
48300
35700
27300
18900
37100
35700
46900
53900
39900
44800
33600
58100




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=307244&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=307244&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307244&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
alpha0.00926118605787113
beta1
gamma0.929768627341843

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787113 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307244&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]0.00926118605787113[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307244&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307244&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
alpha0.00926118605787113
beta1
gamma0.929768627341843







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134200043436.2713675214-1436.27136752138
143150032901.3057439305-1401.3057439305
153710038803.6861902668-1703.68619026682
162800029637.4880802371-1637.48808023708
173920040231.7379614424-1031.73796144239
183220032622.0426899785-422.042689978542
194270040793.25197065271906.74802934726
203850042003.6873637337-3503.68736373373
214060046864.9007407545-6264.90074075449
224550040355.02159555095144.97840444905
234480038169.29339960966630.70660039036
245320048133.73301644375066.26698355627
253850039249.2377052571-749.237705257125
263220028771.68662205873428.31337794128
273570034503.82587851941196.17412148056
282590025515.8899059541384.110094045871
293710036796.0031499673303.996850032694
302870029881.8239301292-1181.82393012921
314060040305.6641190417294.335880958271
323850036616.85217931591883.14782068413
333430039133.8797400205-4833.87974002047
344900043310.24556122925689.75443877081
354410042665.89020325311434.10979674687
365040051260.7180094135-860.718009413511
373780037029.0536812762770.946318723843
383500030492.56384677614507.43615322394
393150034267.3368764405-2767.33687644048
402590024546.7405637711353.25943622905
413430035823.0934476995-1523.09344769952
423080027567.45779326173232.54220673834
434200039476.97882681532523.02117318466
444060037378.01639846113221.98360153889
453500033838.0622172811161.93778271902
464690047937.4750478622-1037.47504786219
474340043421.9851139934-21.9851139933598
485600049987.23199070276012.76800929725
494480037483.70428435977316.29571564026
502730034671.8064099704-7371.80640997038
512730031747.4105360013-4447.41053600128
522730025903.47636392251396.52363607745
533220034627.5574207047-2427.55742070473
543220030832.76272672461367.23727327542
554340042142.67917974491257.32082025507
563990040735.3789555841-835.378955584056
573570035282.1747337082417.825266291838
584480047363.7517649169-2563.75176491688
594130043770.4801042463-2470.48010424631
605950055850.26222542093649.73777457912
614690044481.97129206852418.02870793152
622730028005.6515017474-705.65150174743
632870027809.5615672346890.438432765382
642380027420.4221301974-3620.42213019739
653290032551.1690859624348.830914037582
663780032279.11579324355520.88420675649
674760043566.14100094134033.85899905874
684690040322.45345117366577.54654882636
693780036226.55862171331573.44137828673
704410045717.2952479594-1617.29524795942
713920042372.4324889461-3172.4324889461
725600060230.6253020031-4230.62530200306
734270047728.9976107425-5028.99761074253
743430028311.58187582225988.41812417781
753080029715.00774079941084.99225920062
762310025241.5271826332-2141.52718263319
773430034125.047223738174.952776261969
784130038696.81897095152603.18102904847
794830048641.1742041359-341.174204135852
804550047713.7248453693-2213.7248453693
813360038859.0423597801-5259.04235978011
824830045216.25382420853083.74617579152
833780040394.8624862399-2594.8624862399
845810057201.4517368591898.548263140896
854830043977.21166290834322.78833709167
863500034847.1046861841152.89531381592
873220031677.5344642464522.465535753567
882170024219.3778964181-2519.37789641813
893430035222.410406259-922.410406259005
903290041999.8060188105-9099.80601881049
914970048994.1833762557705.816623744322
924970046231.8336678113468.16633218895
933780034557.49312690413242.50687309589
944900048690.1378223441309.862177655938
953640038598.1460383305-2198.14603833047
965670058616.0502663414-1916.0502663414
974830048483.600951782-183.600951782049
983570035392.4867895385307.51321046146
992730032488.0700626615-5188.07006266153
1001890022045.4118540589-3145.41185405892
1013710034378.31059693522721.68940306483
1023570033555.13616428952144.86383571046
1034690049688.671489327-2788.67148932696
1045390049408.64828626754491.35171373245
1053990037515.52102409422384.47897590577
1064480048910.4496295139-4110.44962951393
1073360036397.9706850222-2797.97068502222
1085810056595.34114585671504.6588541433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 42000 & 43436.2713675214 & -1436.27136752138 \tabularnewline
14 & 31500 & 32901.3057439305 & -1401.3057439305 \tabularnewline
15 & 37100 & 38803.6861902668 & -1703.68619026682 \tabularnewline
16 & 28000 & 29637.4880802371 & -1637.48808023708 \tabularnewline
17 & 39200 & 40231.7379614424 & -1031.73796144239 \tabularnewline
18 & 32200 & 32622.0426899785 & -422.042689978542 \tabularnewline
19 & 42700 & 40793.2519706527 & 1906.74802934726 \tabularnewline
20 & 38500 & 42003.6873637337 & -3503.68736373373 \tabularnewline
21 & 40600 & 46864.9007407545 & -6264.90074075449 \tabularnewline
22 & 45500 & 40355.0215955509 & 5144.97840444905 \tabularnewline
23 & 44800 & 38169.2933996096 & 6630.70660039036 \tabularnewline
24 & 53200 & 48133.7330164437 & 5066.26698355627 \tabularnewline
25 & 38500 & 39249.2377052571 & -749.237705257125 \tabularnewline
26 & 32200 & 28771.6866220587 & 3428.31337794128 \tabularnewline
27 & 35700 & 34503.8258785194 & 1196.17412148056 \tabularnewline
28 & 25900 & 25515.8899059541 & 384.110094045871 \tabularnewline
29 & 37100 & 36796.0031499673 & 303.996850032694 \tabularnewline
30 & 28700 & 29881.8239301292 & -1181.82393012921 \tabularnewline
31 & 40600 & 40305.6641190417 & 294.335880958271 \tabularnewline
32 & 38500 & 36616.8521793159 & 1883.14782068413 \tabularnewline
33 & 34300 & 39133.8797400205 & -4833.87974002047 \tabularnewline
34 & 49000 & 43310.2455612292 & 5689.75443877081 \tabularnewline
35 & 44100 & 42665.8902032531 & 1434.10979674687 \tabularnewline
36 & 50400 & 51260.7180094135 & -860.718009413511 \tabularnewline
37 & 37800 & 37029.0536812762 & 770.946318723843 \tabularnewline
38 & 35000 & 30492.5638467761 & 4507.43615322394 \tabularnewline
39 & 31500 & 34267.3368764405 & -2767.33687644048 \tabularnewline
40 & 25900 & 24546.740563771 & 1353.25943622905 \tabularnewline
41 & 34300 & 35823.0934476995 & -1523.09344769952 \tabularnewline
42 & 30800 & 27567.4577932617 & 3232.54220673834 \tabularnewline
43 & 42000 & 39476.9788268153 & 2523.02117318466 \tabularnewline
44 & 40600 & 37378.0163984611 & 3221.98360153889 \tabularnewline
45 & 35000 & 33838.062217281 & 1161.93778271902 \tabularnewline
46 & 46900 & 47937.4750478622 & -1037.47504786219 \tabularnewline
47 & 43400 & 43421.9851139934 & -21.9851139933598 \tabularnewline
48 & 56000 & 49987.2319907027 & 6012.76800929725 \tabularnewline
49 & 44800 & 37483.7042843597 & 7316.29571564026 \tabularnewline
50 & 27300 & 34671.8064099704 & -7371.80640997038 \tabularnewline
51 & 27300 & 31747.4105360013 & -4447.41053600128 \tabularnewline
52 & 27300 & 25903.4763639225 & 1396.52363607745 \tabularnewline
53 & 32200 & 34627.5574207047 & -2427.55742070473 \tabularnewline
54 & 32200 & 30832.7627267246 & 1367.23727327542 \tabularnewline
55 & 43400 & 42142.6791797449 & 1257.32082025507 \tabularnewline
56 & 39900 & 40735.3789555841 & -835.378955584056 \tabularnewline
57 & 35700 & 35282.1747337082 & 417.825266291838 \tabularnewline
58 & 44800 & 47363.7517649169 & -2563.75176491688 \tabularnewline
59 & 41300 & 43770.4801042463 & -2470.48010424631 \tabularnewline
60 & 59500 & 55850.2622254209 & 3649.73777457912 \tabularnewline
61 & 46900 & 44481.9712920685 & 2418.02870793152 \tabularnewline
62 & 27300 & 28005.6515017474 & -705.65150174743 \tabularnewline
63 & 28700 & 27809.5615672346 & 890.438432765382 \tabularnewline
64 & 23800 & 27420.4221301974 & -3620.42213019739 \tabularnewline
65 & 32900 & 32551.1690859624 & 348.830914037582 \tabularnewline
66 & 37800 & 32279.1157932435 & 5520.88420675649 \tabularnewline
67 & 47600 & 43566.1410009413 & 4033.85899905874 \tabularnewline
68 & 46900 & 40322.4534511736 & 6577.54654882636 \tabularnewline
69 & 37800 & 36226.5586217133 & 1573.44137828673 \tabularnewline
70 & 44100 & 45717.2952479594 & -1617.29524795942 \tabularnewline
71 & 39200 & 42372.4324889461 & -3172.4324889461 \tabularnewline
72 & 56000 & 60230.6253020031 & -4230.62530200306 \tabularnewline
73 & 42700 & 47728.9976107425 & -5028.99761074253 \tabularnewline
74 & 34300 & 28311.5818758222 & 5988.41812417781 \tabularnewline
75 & 30800 & 29715.0077407994 & 1084.99225920062 \tabularnewline
76 & 23100 & 25241.5271826332 & -2141.52718263319 \tabularnewline
77 & 34300 & 34125.047223738 & 174.952776261969 \tabularnewline
78 & 41300 & 38696.8189709515 & 2603.18102904847 \tabularnewline
79 & 48300 & 48641.1742041359 & -341.174204135852 \tabularnewline
80 & 45500 & 47713.7248453693 & -2213.7248453693 \tabularnewline
81 & 33600 & 38859.0423597801 & -5259.04235978011 \tabularnewline
82 & 48300 & 45216.2538242085 & 3083.74617579152 \tabularnewline
83 & 37800 & 40394.8624862399 & -2594.8624862399 \tabularnewline
84 & 58100 & 57201.4517368591 & 898.548263140896 \tabularnewline
85 & 48300 & 43977.2116629083 & 4322.78833709167 \tabularnewline
86 & 35000 & 34847.1046861841 & 152.89531381592 \tabularnewline
87 & 32200 & 31677.5344642464 & 522.465535753567 \tabularnewline
88 & 21700 & 24219.3778964181 & -2519.37789641813 \tabularnewline
89 & 34300 & 35222.410406259 & -922.410406259005 \tabularnewline
90 & 32900 & 41999.8060188105 & -9099.80601881049 \tabularnewline
91 & 49700 & 48994.1833762557 & 705.816623744322 \tabularnewline
92 & 49700 & 46231.833667811 & 3468.16633218895 \tabularnewline
93 & 37800 & 34557.4931269041 & 3242.50687309589 \tabularnewline
94 & 49000 & 48690.1378223441 & 309.862177655938 \tabularnewline
95 & 36400 & 38598.1460383305 & -2198.14603833047 \tabularnewline
96 & 56700 & 58616.0502663414 & -1916.0502663414 \tabularnewline
97 & 48300 & 48483.600951782 & -183.600951782049 \tabularnewline
98 & 35700 & 35392.4867895385 & 307.51321046146 \tabularnewline
99 & 27300 & 32488.0700626615 & -5188.07006266153 \tabularnewline
100 & 18900 & 22045.4118540589 & -3145.41185405892 \tabularnewline
101 & 37100 & 34378.3105969352 & 2721.68940306483 \tabularnewline
102 & 35700 & 33555.1361642895 & 2144.86383571046 \tabularnewline
103 & 46900 & 49688.671489327 & -2788.67148932696 \tabularnewline
104 & 53900 & 49408.6482862675 & 4491.35171373245 \tabularnewline
105 & 39900 & 37515.5210240942 & 2384.47897590577 \tabularnewline
106 & 44800 & 48910.4496295139 & -4110.44962951393 \tabularnewline
107 & 33600 & 36397.9706850222 & -2797.97068502222 \tabularnewline
108 & 58100 & 56595.3411458567 & 1504.6588541433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307244&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]42000[/C][C]43436.2713675214[/C][C]-1436.27136752138[/C][/ROW]
[ROW][C]14[/C][C]31500[/C][C]32901.3057439305[/C][C]-1401.3057439305[/C][/ROW]
[ROW][C]15[/C][C]37100[/C][C]38803.6861902668[/C][C]-1703.68619026682[/C][/ROW]
[ROW][C]16[/C][C]28000[/C][C]29637.4880802371[/C][C]-1637.48808023708[/C][/ROW]
[ROW][C]17[/C][C]39200[/C][C]40231.7379614424[/C][C]-1031.73796144239[/C][/ROW]
[ROW][C]18[/C][C]32200[/C][C]32622.0426899785[/C][C]-422.042689978542[/C][/ROW]
[ROW][C]19[/C][C]42700[/C][C]40793.2519706527[/C][C]1906.74802934726[/C][/ROW]
[ROW][C]20[/C][C]38500[/C][C]42003.6873637337[/C][C]-3503.68736373373[/C][/ROW]
[ROW][C]21[/C][C]40600[/C][C]46864.9007407545[/C][C]-6264.90074075449[/C][/ROW]
[ROW][C]22[/C][C]45500[/C][C]40355.0215955509[/C][C]5144.97840444905[/C][/ROW]
[ROW][C]23[/C][C]44800[/C][C]38169.2933996096[/C][C]6630.70660039036[/C][/ROW]
[ROW][C]24[/C][C]53200[/C][C]48133.7330164437[/C][C]5066.26698355627[/C][/ROW]
[ROW][C]25[/C][C]38500[/C][C]39249.2377052571[/C][C]-749.237705257125[/C][/ROW]
[ROW][C]26[/C][C]32200[/C][C]28771.6866220587[/C][C]3428.31337794128[/C][/ROW]
[ROW][C]27[/C][C]35700[/C][C]34503.8258785194[/C][C]1196.17412148056[/C][/ROW]
[ROW][C]28[/C][C]25900[/C][C]25515.8899059541[/C][C]384.110094045871[/C][/ROW]
[ROW][C]29[/C][C]37100[/C][C]36796.0031499673[/C][C]303.996850032694[/C][/ROW]
[ROW][C]30[/C][C]28700[/C][C]29881.8239301292[/C][C]-1181.82393012921[/C][/ROW]
[ROW][C]31[/C][C]40600[/C][C]40305.6641190417[/C][C]294.335880958271[/C][/ROW]
[ROW][C]32[/C][C]38500[/C][C]36616.8521793159[/C][C]1883.14782068413[/C][/ROW]
[ROW][C]33[/C][C]34300[/C][C]39133.8797400205[/C][C]-4833.87974002047[/C][/ROW]
[ROW][C]34[/C][C]49000[/C][C]43310.2455612292[/C][C]5689.75443877081[/C][/ROW]
[ROW][C]35[/C][C]44100[/C][C]42665.8902032531[/C][C]1434.10979674687[/C][/ROW]
[ROW][C]36[/C][C]50400[/C][C]51260.7180094135[/C][C]-860.718009413511[/C][/ROW]
[ROW][C]37[/C][C]37800[/C][C]37029.0536812762[/C][C]770.946318723843[/C][/ROW]
[ROW][C]38[/C][C]35000[/C][C]30492.5638467761[/C][C]4507.43615322394[/C][/ROW]
[ROW][C]39[/C][C]31500[/C][C]34267.3368764405[/C][C]-2767.33687644048[/C][/ROW]
[ROW][C]40[/C][C]25900[/C][C]24546.740563771[/C][C]1353.25943622905[/C][/ROW]
[ROW][C]41[/C][C]34300[/C][C]35823.0934476995[/C][C]-1523.09344769952[/C][/ROW]
[ROW][C]42[/C][C]30800[/C][C]27567.4577932617[/C][C]3232.54220673834[/C][/ROW]
[ROW][C]43[/C][C]42000[/C][C]39476.9788268153[/C][C]2523.02117318466[/C][/ROW]
[ROW][C]44[/C][C]40600[/C][C]37378.0163984611[/C][C]3221.98360153889[/C][/ROW]
[ROW][C]45[/C][C]35000[/C][C]33838.062217281[/C][C]1161.93778271902[/C][/ROW]
[ROW][C]46[/C][C]46900[/C][C]47937.4750478622[/C][C]-1037.47504786219[/C][/ROW]
[ROW][C]47[/C][C]43400[/C][C]43421.9851139934[/C][C]-21.9851139933598[/C][/ROW]
[ROW][C]48[/C][C]56000[/C][C]49987.2319907027[/C][C]6012.76800929725[/C][/ROW]
[ROW][C]49[/C][C]44800[/C][C]37483.7042843597[/C][C]7316.29571564026[/C][/ROW]
[ROW][C]50[/C][C]27300[/C][C]34671.8064099704[/C][C]-7371.80640997038[/C][/ROW]
[ROW][C]51[/C][C]27300[/C][C]31747.4105360013[/C][C]-4447.41053600128[/C][/ROW]
[ROW][C]52[/C][C]27300[/C][C]25903.4763639225[/C][C]1396.52363607745[/C][/ROW]
[ROW][C]53[/C][C]32200[/C][C]34627.5574207047[/C][C]-2427.55742070473[/C][/ROW]
[ROW][C]54[/C][C]32200[/C][C]30832.7627267246[/C][C]1367.23727327542[/C][/ROW]
[ROW][C]55[/C][C]43400[/C][C]42142.6791797449[/C][C]1257.32082025507[/C][/ROW]
[ROW][C]56[/C][C]39900[/C][C]40735.3789555841[/C][C]-835.378955584056[/C][/ROW]
[ROW][C]57[/C][C]35700[/C][C]35282.1747337082[/C][C]417.825266291838[/C][/ROW]
[ROW][C]58[/C][C]44800[/C][C]47363.7517649169[/C][C]-2563.75176491688[/C][/ROW]
[ROW][C]59[/C][C]41300[/C][C]43770.4801042463[/C][C]-2470.48010424631[/C][/ROW]
[ROW][C]60[/C][C]59500[/C][C]55850.2622254209[/C][C]3649.73777457912[/C][/ROW]
[ROW][C]61[/C][C]46900[/C][C]44481.9712920685[/C][C]2418.02870793152[/C][/ROW]
[ROW][C]62[/C][C]27300[/C][C]28005.6515017474[/C][C]-705.65150174743[/C][/ROW]
[ROW][C]63[/C][C]28700[/C][C]27809.5615672346[/C][C]890.438432765382[/C][/ROW]
[ROW][C]64[/C][C]23800[/C][C]27420.4221301974[/C][C]-3620.42213019739[/C][/ROW]
[ROW][C]65[/C][C]32900[/C][C]32551.1690859624[/C][C]348.830914037582[/C][/ROW]
[ROW][C]66[/C][C]37800[/C][C]32279.1157932435[/C][C]5520.88420675649[/C][/ROW]
[ROW][C]67[/C][C]47600[/C][C]43566.1410009413[/C][C]4033.85899905874[/C][/ROW]
[ROW][C]68[/C][C]46900[/C][C]40322.4534511736[/C][C]6577.54654882636[/C][/ROW]
[ROW][C]69[/C][C]37800[/C][C]36226.5586217133[/C][C]1573.44137828673[/C][/ROW]
[ROW][C]70[/C][C]44100[/C][C]45717.2952479594[/C][C]-1617.29524795942[/C][/ROW]
[ROW][C]71[/C][C]39200[/C][C]42372.4324889461[/C][C]-3172.4324889461[/C][/ROW]
[ROW][C]72[/C][C]56000[/C][C]60230.6253020031[/C][C]-4230.62530200306[/C][/ROW]
[ROW][C]73[/C][C]42700[/C][C]47728.9976107425[/C][C]-5028.99761074253[/C][/ROW]
[ROW][C]74[/C][C]34300[/C][C]28311.5818758222[/C][C]5988.41812417781[/C][/ROW]
[ROW][C]75[/C][C]30800[/C][C]29715.0077407994[/C][C]1084.99225920062[/C][/ROW]
[ROW][C]76[/C][C]23100[/C][C]25241.5271826332[/C][C]-2141.52718263319[/C][/ROW]
[ROW][C]77[/C][C]34300[/C][C]34125.047223738[/C][C]174.952776261969[/C][/ROW]
[ROW][C]78[/C][C]41300[/C][C]38696.8189709515[/C][C]2603.18102904847[/C][/ROW]
[ROW][C]79[/C][C]48300[/C][C]48641.1742041359[/C][C]-341.174204135852[/C][/ROW]
[ROW][C]80[/C][C]45500[/C][C]47713.7248453693[/C][C]-2213.7248453693[/C][/ROW]
[ROW][C]81[/C][C]33600[/C][C]38859.0423597801[/C][C]-5259.04235978011[/C][/ROW]
[ROW][C]82[/C][C]48300[/C][C]45216.2538242085[/C][C]3083.74617579152[/C][/ROW]
[ROW][C]83[/C][C]37800[/C][C]40394.8624862399[/C][C]-2594.8624862399[/C][/ROW]
[ROW][C]84[/C][C]58100[/C][C]57201.4517368591[/C][C]898.548263140896[/C][/ROW]
[ROW][C]85[/C][C]48300[/C][C]43977.2116629083[/C][C]4322.78833709167[/C][/ROW]
[ROW][C]86[/C][C]35000[/C][C]34847.1046861841[/C][C]152.89531381592[/C][/ROW]
[ROW][C]87[/C][C]32200[/C][C]31677.5344642464[/C][C]522.465535753567[/C][/ROW]
[ROW][C]88[/C][C]21700[/C][C]24219.3778964181[/C][C]-2519.37789641813[/C][/ROW]
[ROW][C]89[/C][C]34300[/C][C]35222.410406259[/C][C]-922.410406259005[/C][/ROW]
[ROW][C]90[/C][C]32900[/C][C]41999.8060188105[/C][C]-9099.80601881049[/C][/ROW]
[ROW][C]91[/C][C]49700[/C][C]48994.1833762557[/C][C]705.816623744322[/C][/ROW]
[ROW][C]92[/C][C]49700[/C][C]46231.833667811[/C][C]3468.16633218895[/C][/ROW]
[ROW][C]93[/C][C]37800[/C][C]34557.4931269041[/C][C]3242.50687309589[/C][/ROW]
[ROW][C]94[/C][C]49000[/C][C]48690.1378223441[/C][C]309.862177655938[/C][/ROW]
[ROW][C]95[/C][C]36400[/C][C]38598.1460383305[/C][C]-2198.14603833047[/C][/ROW]
[ROW][C]96[/C][C]56700[/C][C]58616.0502663414[/C][C]-1916.0502663414[/C][/ROW]
[ROW][C]97[/C][C]48300[/C][C]48483.600951782[/C][C]-183.600951782049[/C][/ROW]
[ROW][C]98[/C][C]35700[/C][C]35392.4867895385[/C][C]307.51321046146[/C][/ROW]
[ROW][C]99[/C][C]27300[/C][C]32488.0700626615[/C][C]-5188.07006266153[/C][/ROW]
[ROW][C]100[/C][C]18900[/C][C]22045.4118540589[/C][C]-3145.41185405892[/C][/ROW]
[ROW][C]101[/C][C]37100[/C][C]34378.3105969352[/C][C]2721.68940306483[/C][/ROW]
[ROW][C]102[/C][C]35700[/C][C]33555.1361642895[/C][C]2144.86383571046[/C][/ROW]
[ROW][C]103[/C][C]46900[/C][C]49688.671489327[/C][C]-2788.67148932696[/C][/ROW]
[ROW][C]104[/C][C]53900[/C][C]49408.6482862675[/C][C]4491.35171373245[/C][/ROW]
[ROW][C]105[/C][C]39900[/C][C]37515.5210240942[/C][C]2384.47897590577[/C][/ROW]
[ROW][C]106[/C][C]44800[/C][C]48910.4496295139[/C][C]-4110.44962951393[/C][/ROW]
[ROW][C]107[/C][C]33600[/C][C]36397.9706850222[/C][C]-2797.97068502222[/C][/ROW]
[ROW][C]108[/C][C]58100[/C][C]56595.3411458567[/C][C]1504.6588541433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307244&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307244&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
134200043436.2713675214-1436.27136752138
143150032901.3057439305-1401.3057439305
153710038803.6861902668-1703.68619026682
162800029637.4880802371-1637.48808023708
173920040231.7379614424-1031.73796144239
183220032622.0426899785-422.042689978542
194270040793.25197065271906.74802934726
203850042003.6873637337-3503.68736373373
214060046864.9007407545-6264.90074075449
224550040355.02159555095144.97840444905
234480038169.29339960966630.70660039036
245320048133.73301644375066.26698355627
253850039249.2377052571-749.237705257125
263220028771.68662205873428.31337794128
273570034503.82587851941196.17412148056
282590025515.8899059541384.110094045871
293710036796.0031499673303.996850032694
302870029881.8239301292-1181.82393012921
314060040305.6641190417294.335880958271
323850036616.85217931591883.14782068413
333430039133.8797400205-4833.87974002047
344900043310.24556122925689.75443877081
354410042665.89020325311434.10979674687
365040051260.7180094135-860.718009413511
373780037029.0536812762770.946318723843
383500030492.56384677614507.43615322394
393150034267.3368764405-2767.33687644048
402590024546.7405637711353.25943622905
413430035823.0934476995-1523.09344769952
423080027567.45779326173232.54220673834
434200039476.97882681532523.02117318466
444060037378.01639846113221.98360153889
453500033838.0622172811161.93778271902
464690047937.4750478622-1037.47504786219
474340043421.9851139934-21.9851139933598
485600049987.23199070276012.76800929725
494480037483.70428435977316.29571564026
502730034671.8064099704-7371.80640997038
512730031747.4105360013-4447.41053600128
522730025903.47636392251396.52363607745
533220034627.5574207047-2427.55742070473
543220030832.76272672461367.23727327542
554340042142.67917974491257.32082025507
563990040735.3789555841-835.378955584056
573570035282.1747337082417.825266291838
584480047363.7517649169-2563.75176491688
594130043770.4801042463-2470.48010424631
605950055850.26222542093649.73777457912
614690044481.97129206852418.02870793152
622730028005.6515017474-705.65150174743
632870027809.5615672346890.438432765382
642380027420.4221301974-3620.42213019739
653290032551.1690859624348.830914037582
663780032279.11579324355520.88420675649
674760043566.14100094134033.85899905874
684690040322.45345117366577.54654882636
693780036226.55862171331573.44137828673
704410045717.2952479594-1617.29524795942
713920042372.4324889461-3172.4324889461
725600060230.6253020031-4230.62530200306
734270047728.9976107425-5028.99761074253
743430028311.58187582225988.41812417781
753080029715.00774079941084.99225920062
762310025241.5271826332-2141.52718263319
773430034125.047223738174.952776261969
784130038696.81897095152603.18102904847
794830048641.1742041359-341.174204135852
804550047713.7248453693-2213.7248453693
813360038859.0423597801-5259.04235978011
824830045216.25382420853083.74617579152
833780040394.8624862399-2594.8624862399
845810057201.4517368591898.548263140896
854830043977.21166290834322.78833709167
863500034847.1046861841152.89531381592
873220031677.5344642464522.465535753567
882170024219.3778964181-2519.37789641813
893430035222.410406259-922.410406259005
903290041999.8060188105-9099.80601881049
914970048994.1833762557705.816623744322
924970046231.8336678113468.16633218895
933780034557.49312690413242.50687309589
944900048690.1378223441309.862177655938
953640038598.1460383305-2198.14603833047
965670058616.0502663414-1916.0502663414
974830048483.600951782-183.600951782049
983570035392.4867895385307.51321046146
992730032488.0700626615-5188.07006266153
1001890022045.4118540589-3145.41185405892
1013710034378.31059693522721.68940306483
1023570033555.13616428952144.86383571046
1034690049688.671489327-2788.67148932696
1045390049408.64828626754491.35171373245
1053990037515.52102409422384.47897590577
1064480048910.4496295139-4110.44962951393
1073360036397.9706850222-2797.97068502222
1085810056595.34114585671504.6588541433







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10948047.277374810541630.890771592554463.6639780286
11035368.804016360128951.316846125241786.291186595
11127354.938416091820934.9756598933774.9011722936
11218845.685080358612421.323637871925270.0465228453
11336645.117304186230213.888937280643076.3456710918
11435273.060074834528831.956198102941714.1639515662
11546829.973241085140375.45197739253284.4945047782
11653295.460196684446823.456074757859767.4643186109
11739392.013156375432897.949771079845886.076541671
11844731.958836959738210.764720345751253.1529535737
11933454.570234884626900.698098025840008.4423717434
12057655.189197609651062.638601632264247.7397935869

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 48047.2773748105 & 41630.8907715925 & 54463.6639780286 \tabularnewline
110 & 35368.8040163601 & 28951.3168461252 & 41786.291186595 \tabularnewline
111 & 27354.9384160918 & 20934.97565989 & 33774.9011722936 \tabularnewline
112 & 18845.6850803586 & 12421.3236378719 & 25270.0465228453 \tabularnewline
113 & 36645.1173041862 & 30213.8889372806 & 43076.3456710918 \tabularnewline
114 & 35273.0600748345 & 28831.9561981029 & 41714.1639515662 \tabularnewline
115 & 46829.9732410851 & 40375.451977392 & 53284.4945047782 \tabularnewline
116 & 53295.4601966844 & 46823.4560747578 & 59767.4643186109 \tabularnewline
117 & 39392.0131563754 & 32897.9497710798 & 45886.076541671 \tabularnewline
118 & 44731.9588369597 & 38210.7647203457 & 51253.1529535737 \tabularnewline
119 & 33454.5702348846 & 26900.6980980258 & 40008.4423717434 \tabularnewline
120 & 57655.1891976096 & 51062.6386016322 & 64247.7397935869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307244&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]48047.2773748105[/C][C]41630.8907715925[/C][C]54463.6639780286[/C][/ROW]
[ROW][C]110[/C][C]35368.8040163601[/C][C]28951.3168461252[/C][C]41786.291186595[/C][/ROW]
[ROW][C]111[/C][C]27354.9384160918[/C][C]20934.97565989[/C][C]33774.9011722936[/C][/ROW]
[ROW][C]112[/C][C]18845.6850803586[/C][C]12421.3236378719[/C][C]25270.0465228453[/C][/ROW]
[ROW][C]113[/C][C]36645.1173041862[/C][C]30213.8889372806[/C][C]43076.3456710918[/C][/ROW]
[ROW][C]114[/C][C]35273.0600748345[/C][C]28831.9561981029[/C][C]41714.1639515662[/C][/ROW]
[ROW][C]115[/C][C]46829.9732410851[/C][C]40375.451977392[/C][C]53284.4945047782[/C][/ROW]
[ROW][C]116[/C][C]53295.4601966844[/C][C]46823.4560747578[/C][C]59767.4643186109[/C][/ROW]
[ROW][C]117[/C][C]39392.0131563754[/C][C]32897.9497710798[/C][C]45886.076541671[/C][/ROW]
[ROW][C]118[/C][C]44731.9588369597[/C][C]38210.7647203457[/C][C]51253.1529535737[/C][/ROW]
[ROW][C]119[/C][C]33454.5702348846[/C][C]26900.6980980258[/C][C]40008.4423717434[/C][/ROW]
[ROW][C]120[/C][C]57655.1891976096[/C][C]51062.6386016322[/C][C]64247.7397935869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307244&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307244&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
10948047.277374810541630.890771592554463.6639780286
11035368.804016360128951.316846125241786.291186595
11127354.938416091820934.9756598933774.9011722936
11218845.685080358612421.323637871925270.0465228453
11336645.117304186230213.888937280643076.3456710918
11435273.060074834528831.956198102941714.1639515662
11546829.973241085140375.45197739253284.4945047782
11653295.460196684446823.456074757859767.4643186109
11739392.013156375432897.949771079845886.076541671
11844731.958836959738210.764720345751253.1529535737
11933454.570234884626900.698098025840008.4423717434
12057655.189197609651062.638601632264247.7397935869



Parameters (Session):
par1 = 12additive12 ; par2 = 12Triple ; 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')