Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 17:31:31 +0000
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/Nov/28/t1480354359c6b9qnxx73zu310.htm/, Retrieved Sat, 04 May 2024 10:21:36 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 10:21:36 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
54854
53982
52301
51652
50338
51959
57648
57803
52599
51123
49604
51154
51765
50491
49332
48690
47496
48107
53970
54300
50246
48519
47602
49723
52010
50976
49795
49104
48354
49390
55323
56287
52831
51881
51382
53000
54365
53815
53107
53031
52419
53378
59398
60706
58531
57244
56843
58299
60654
59579
58823
57813
56487
57644
62444
62890
59758
58716
57485
57888
59676
58365
57337
56520
55189
56229
60766
61393
57919
56772
55820
56953




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.740554482778413
beta0.135154928124364
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740554482778413 \tabularnewline
beta & 0.135154928124364 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.740554482778413[/C][/ROW]
[ROW][C]beta[/C][C]0.135154928124364[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.740554482778413
beta0.135154928124364
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135176553381.5032051282-1616.50320512821
145049150792.0874241304-301.087424130361
154933249206.4646469339125.535353066094
164869048428.8857282666261.114271733401
174749647211.2202054392284.77979456084
184810747795.7087839065311.291216093523
195397054508.2791906345-538.27919063453
205430054135.6536151961164.34638480391
215024648935.80992128991310.19007871008
224851948421.620629841197.3793701589166
234760246970.7339257747631.266074225263
244972349084.4859082533638.514091746692
255201049943.95287809342066.04712190664
265097650928.507208870547.4927911295235
274979550252.1639212433-457.1639212433
284910449560.3691367842-456.369136784248
294835448227.8247058241126.175294175911
304939049096.1783534869293.821646513148
315532355968.0879100128-645.087910012793
325628756080.6608252184206.339174781591
335283151595.40524178521235.59475821482
345188151090.0556866803790.944313319676
355138250739.4646886842642.535311315813
365300053312.7291203989-312.729120398915
375436554192.1926690805172.807330919473
385381553415.5782812663399.421718733742
395310753068.73440615338.2655938469616
405303152993.43349857337.5665014269835
415241952476.6467996761-57.6467996761421
425337853532.7995284633-154.799528463314
435939860064.4167409187-666.416740918699
446070660615.490594924690.5094050753833
455853156533.29630932691997.70369067308
465724456775.0503506731468.949649326882
475684356413.3553721309429.644627869078
485829958825.6701001253-526.670100125302
496065459895.8022092862758.19779071377
505957959893.2201839049-314.220183904908
515882359134.4818833377-311.481883337736
525781358975.2830786986-1162.28307869855
535648757600.4378218265-1113.43782182647
545764457799.0383394038-155.038339403771
556244464147.2424076435-1703.24240764354
566289063972.596508646-1082.59650864603
575975859244.7757471823513.224252817738
585871657570.29192754671145.70807245334
595748557347.0408173365137.959182663471
605788858913.5052320361-1025.50523203606
615967659515.9179797587160.082020241287
625836558300.64145941864.3585405820413
635733757369.3404148668-32.3404148667905
645652056770.4323190985-250.432319098538
655518955749.1094788022-560.109478802151
665622956327.0892024948-98.089202494848
676076662042.4495915762-1276.4495915762
686139362114.2653265497-721.265326549685
695791957873.598528252345.4014717476748
705677255775.4773469517996.522653048341
715582054924.0742708298895.925729170209
725695356569.647038911383.352961088982

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 51765 & 53381.5032051282 & -1616.50320512821 \tabularnewline
14 & 50491 & 50792.0874241304 & -301.087424130361 \tabularnewline
15 & 49332 & 49206.4646469339 & 125.535353066094 \tabularnewline
16 & 48690 & 48428.8857282666 & 261.114271733401 \tabularnewline
17 & 47496 & 47211.2202054392 & 284.77979456084 \tabularnewline
18 & 48107 & 47795.7087839065 & 311.291216093523 \tabularnewline
19 & 53970 & 54508.2791906345 & -538.27919063453 \tabularnewline
20 & 54300 & 54135.6536151961 & 164.34638480391 \tabularnewline
21 & 50246 & 48935.8099212899 & 1310.19007871008 \tabularnewline
22 & 48519 & 48421.6206298411 & 97.3793701589166 \tabularnewline
23 & 47602 & 46970.7339257747 & 631.266074225263 \tabularnewline
24 & 49723 & 49084.4859082533 & 638.514091746692 \tabularnewline
25 & 52010 & 49943.9528780934 & 2066.04712190664 \tabularnewline
26 & 50976 & 50928.5072088705 & 47.4927911295235 \tabularnewline
27 & 49795 & 50252.1639212433 & -457.1639212433 \tabularnewline
28 & 49104 & 49560.3691367842 & -456.369136784248 \tabularnewline
29 & 48354 & 48227.8247058241 & 126.175294175911 \tabularnewline
30 & 49390 & 49096.1783534869 & 293.821646513148 \tabularnewline
31 & 55323 & 55968.0879100128 & -645.087910012793 \tabularnewline
32 & 56287 & 56080.6608252184 & 206.339174781591 \tabularnewline
33 & 52831 & 51595.4052417852 & 1235.59475821482 \tabularnewline
34 & 51881 & 51090.0556866803 & 790.944313319676 \tabularnewline
35 & 51382 & 50739.4646886842 & 642.535311315813 \tabularnewline
36 & 53000 & 53312.7291203989 & -312.729120398915 \tabularnewline
37 & 54365 & 54192.1926690805 & 172.807330919473 \tabularnewline
38 & 53815 & 53415.5782812663 & 399.421718733742 \tabularnewline
39 & 53107 & 53068.734406153 & 38.2655938469616 \tabularnewline
40 & 53031 & 52993.433498573 & 37.5665014269835 \tabularnewline
41 & 52419 & 52476.6467996761 & -57.6467996761421 \tabularnewline
42 & 53378 & 53532.7995284633 & -154.799528463314 \tabularnewline
43 & 59398 & 60064.4167409187 & -666.416740918699 \tabularnewline
44 & 60706 & 60615.4905949246 & 90.5094050753833 \tabularnewline
45 & 58531 & 56533.2963093269 & 1997.70369067308 \tabularnewline
46 & 57244 & 56775.0503506731 & 468.949649326882 \tabularnewline
47 & 56843 & 56413.3553721309 & 429.644627869078 \tabularnewline
48 & 58299 & 58825.6701001253 & -526.670100125302 \tabularnewline
49 & 60654 & 59895.8022092862 & 758.19779071377 \tabularnewline
50 & 59579 & 59893.2201839049 & -314.220183904908 \tabularnewline
51 & 58823 & 59134.4818833377 & -311.481883337736 \tabularnewline
52 & 57813 & 58975.2830786986 & -1162.28307869855 \tabularnewline
53 & 56487 & 57600.4378218265 & -1113.43782182647 \tabularnewline
54 & 57644 & 57799.0383394038 & -155.038339403771 \tabularnewline
55 & 62444 & 64147.2424076435 & -1703.24240764354 \tabularnewline
56 & 62890 & 63972.596508646 & -1082.59650864603 \tabularnewline
57 & 59758 & 59244.7757471823 & 513.224252817738 \tabularnewline
58 & 58716 & 57570.2919275467 & 1145.70807245334 \tabularnewline
59 & 57485 & 57347.0408173365 & 137.959182663471 \tabularnewline
60 & 57888 & 58913.5052320361 & -1025.50523203606 \tabularnewline
61 & 59676 & 59515.9179797587 & 160.082020241287 \tabularnewline
62 & 58365 & 58300.641459418 & 64.3585405820413 \tabularnewline
63 & 57337 & 57369.3404148668 & -32.3404148667905 \tabularnewline
64 & 56520 & 56770.4323190985 & -250.432319098538 \tabularnewline
65 & 55189 & 55749.1094788022 & -560.109478802151 \tabularnewline
66 & 56229 & 56327.0892024948 & -98.089202494848 \tabularnewline
67 & 60766 & 62042.4495915762 & -1276.4495915762 \tabularnewline
68 & 61393 & 62114.2653265497 & -721.265326549685 \tabularnewline
69 & 57919 & 57873.5985282523 & 45.4014717476748 \tabularnewline
70 & 56772 & 55775.4773469517 & 996.522653048341 \tabularnewline
71 & 55820 & 54924.0742708298 & 895.925729170209 \tabularnewline
72 & 56953 & 56569.647038911 & 383.352961088982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]51765[/C][C]53381.5032051282[/C][C]-1616.50320512821[/C][/ROW]
[ROW][C]14[/C][C]50491[/C][C]50792.0874241304[/C][C]-301.087424130361[/C][/ROW]
[ROW][C]15[/C][C]49332[/C][C]49206.4646469339[/C][C]125.535353066094[/C][/ROW]
[ROW][C]16[/C][C]48690[/C][C]48428.8857282666[/C][C]261.114271733401[/C][/ROW]
[ROW][C]17[/C][C]47496[/C][C]47211.2202054392[/C][C]284.77979456084[/C][/ROW]
[ROW][C]18[/C][C]48107[/C][C]47795.7087839065[/C][C]311.291216093523[/C][/ROW]
[ROW][C]19[/C][C]53970[/C][C]54508.2791906345[/C][C]-538.27919063453[/C][/ROW]
[ROW][C]20[/C][C]54300[/C][C]54135.6536151961[/C][C]164.34638480391[/C][/ROW]
[ROW][C]21[/C][C]50246[/C][C]48935.8099212899[/C][C]1310.19007871008[/C][/ROW]
[ROW][C]22[/C][C]48519[/C][C]48421.6206298411[/C][C]97.3793701589166[/C][/ROW]
[ROW][C]23[/C][C]47602[/C][C]46970.7339257747[/C][C]631.266074225263[/C][/ROW]
[ROW][C]24[/C][C]49723[/C][C]49084.4859082533[/C][C]638.514091746692[/C][/ROW]
[ROW][C]25[/C][C]52010[/C][C]49943.9528780934[/C][C]2066.04712190664[/C][/ROW]
[ROW][C]26[/C][C]50976[/C][C]50928.5072088705[/C][C]47.4927911295235[/C][/ROW]
[ROW][C]27[/C][C]49795[/C][C]50252.1639212433[/C][C]-457.1639212433[/C][/ROW]
[ROW][C]28[/C][C]49104[/C][C]49560.3691367842[/C][C]-456.369136784248[/C][/ROW]
[ROW][C]29[/C][C]48354[/C][C]48227.8247058241[/C][C]126.175294175911[/C][/ROW]
[ROW][C]30[/C][C]49390[/C][C]49096.1783534869[/C][C]293.821646513148[/C][/ROW]
[ROW][C]31[/C][C]55323[/C][C]55968.0879100128[/C][C]-645.087910012793[/C][/ROW]
[ROW][C]32[/C][C]56287[/C][C]56080.6608252184[/C][C]206.339174781591[/C][/ROW]
[ROW][C]33[/C][C]52831[/C][C]51595.4052417852[/C][C]1235.59475821482[/C][/ROW]
[ROW][C]34[/C][C]51881[/C][C]51090.0556866803[/C][C]790.944313319676[/C][/ROW]
[ROW][C]35[/C][C]51382[/C][C]50739.4646886842[/C][C]642.535311315813[/C][/ROW]
[ROW][C]36[/C][C]53000[/C][C]53312.7291203989[/C][C]-312.729120398915[/C][/ROW]
[ROW][C]37[/C][C]54365[/C][C]54192.1926690805[/C][C]172.807330919473[/C][/ROW]
[ROW][C]38[/C][C]53815[/C][C]53415.5782812663[/C][C]399.421718733742[/C][/ROW]
[ROW][C]39[/C][C]53107[/C][C]53068.734406153[/C][C]38.2655938469616[/C][/ROW]
[ROW][C]40[/C][C]53031[/C][C]52993.433498573[/C][C]37.5665014269835[/C][/ROW]
[ROW][C]41[/C][C]52419[/C][C]52476.6467996761[/C][C]-57.6467996761421[/C][/ROW]
[ROW][C]42[/C][C]53378[/C][C]53532.7995284633[/C][C]-154.799528463314[/C][/ROW]
[ROW][C]43[/C][C]59398[/C][C]60064.4167409187[/C][C]-666.416740918699[/C][/ROW]
[ROW][C]44[/C][C]60706[/C][C]60615.4905949246[/C][C]90.5094050753833[/C][/ROW]
[ROW][C]45[/C][C]58531[/C][C]56533.2963093269[/C][C]1997.70369067308[/C][/ROW]
[ROW][C]46[/C][C]57244[/C][C]56775.0503506731[/C][C]468.949649326882[/C][/ROW]
[ROW][C]47[/C][C]56843[/C][C]56413.3553721309[/C][C]429.644627869078[/C][/ROW]
[ROW][C]48[/C][C]58299[/C][C]58825.6701001253[/C][C]-526.670100125302[/C][/ROW]
[ROW][C]49[/C][C]60654[/C][C]59895.8022092862[/C][C]758.19779071377[/C][/ROW]
[ROW][C]50[/C][C]59579[/C][C]59893.2201839049[/C][C]-314.220183904908[/C][/ROW]
[ROW][C]51[/C][C]58823[/C][C]59134.4818833377[/C][C]-311.481883337736[/C][/ROW]
[ROW][C]52[/C][C]57813[/C][C]58975.2830786986[/C][C]-1162.28307869855[/C][/ROW]
[ROW][C]53[/C][C]56487[/C][C]57600.4378218265[/C][C]-1113.43782182647[/C][/ROW]
[ROW][C]54[/C][C]57644[/C][C]57799.0383394038[/C][C]-155.038339403771[/C][/ROW]
[ROW][C]55[/C][C]62444[/C][C]64147.2424076435[/C][C]-1703.24240764354[/C][/ROW]
[ROW][C]56[/C][C]62890[/C][C]63972.596508646[/C][C]-1082.59650864603[/C][/ROW]
[ROW][C]57[/C][C]59758[/C][C]59244.7757471823[/C][C]513.224252817738[/C][/ROW]
[ROW][C]58[/C][C]58716[/C][C]57570.2919275467[/C][C]1145.70807245334[/C][/ROW]
[ROW][C]59[/C][C]57485[/C][C]57347.0408173365[/C][C]137.959182663471[/C][/ROW]
[ROW][C]60[/C][C]57888[/C][C]58913.5052320361[/C][C]-1025.50523203606[/C][/ROW]
[ROW][C]61[/C][C]59676[/C][C]59515.9179797587[/C][C]160.082020241287[/C][/ROW]
[ROW][C]62[/C][C]58365[/C][C]58300.641459418[/C][C]64.3585405820413[/C][/ROW]
[ROW][C]63[/C][C]57337[/C][C]57369.3404148668[/C][C]-32.3404148667905[/C][/ROW]
[ROW][C]64[/C][C]56520[/C][C]56770.4323190985[/C][C]-250.432319098538[/C][/ROW]
[ROW][C]65[/C][C]55189[/C][C]55749.1094788022[/C][C]-560.109478802151[/C][/ROW]
[ROW][C]66[/C][C]56229[/C][C]56327.0892024948[/C][C]-98.089202494848[/C][/ROW]
[ROW][C]67[/C][C]60766[/C][C]62042.4495915762[/C][C]-1276.4495915762[/C][/ROW]
[ROW][C]68[/C][C]61393[/C][C]62114.2653265497[/C][C]-721.265326549685[/C][/ROW]
[ROW][C]69[/C][C]57919[/C][C]57873.5985282523[/C][C]45.4014717476748[/C][/ROW]
[ROW][C]70[/C][C]56772[/C][C]55775.4773469517[/C][C]996.522653048341[/C][/ROW]
[ROW][C]71[/C][C]55820[/C][C]54924.0742708298[/C][C]895.925729170209[/C][/ROW]
[ROW][C]72[/C][C]56953[/C][C]56569.647038911[/C][C]383.352961088982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
135176553381.5032051282-1616.50320512821
145049150792.0874241304-301.087424130361
154933249206.4646469339125.535353066094
164869048428.8857282666261.114271733401
174749647211.2202054392284.77979456084
184810747795.7087839065311.291216093523
195397054508.2791906345-538.27919063453
205430054135.6536151961164.34638480391
215024648935.80992128991310.19007871008
224851948421.620629841197.3793701589166
234760246970.7339257747631.266074225263
244972349084.4859082533638.514091746692
255201049943.95287809342066.04712190664
265097650928.507208870547.4927911295235
274979550252.1639212433-457.1639212433
284910449560.3691367842-456.369136784248
294835448227.8247058241126.175294175911
304939049096.1783534869293.821646513148
315532355968.0879100128-645.087910012793
325628756080.6608252184206.339174781591
335283151595.40524178521235.59475821482
345188151090.0556866803790.944313319676
355138250739.4646886842642.535311315813
365300053312.7291203989-312.729120398915
375436554192.1926690805172.807330919473
385381553415.5782812663399.421718733742
395310753068.73440615338.2655938469616
405303152993.43349857337.5665014269835
415241952476.6467996761-57.6467996761421
425337853532.7995284633-154.799528463314
435939860064.4167409187-666.416740918699
446070660615.490594924690.5094050753833
455853156533.29630932691997.70369067308
465724456775.0503506731468.949649326882
475684356413.3553721309429.644627869078
485829958825.6701001253-526.670100125302
496065459895.8022092862758.19779071377
505957959893.2201839049-314.220183904908
515882359134.4818833377-311.481883337736
525781358975.2830786986-1162.28307869855
535648757600.4378218265-1113.43782182647
545764457799.0383394038-155.038339403771
556244464147.2424076435-1703.24240764354
566289063972.596508646-1082.59650864603
575975859244.7757471823513.224252817738
585871657570.29192754671145.70807245334
595748557347.0408173365137.959182663471
605788858913.5052320361-1025.50523203606
615967659515.9179797587160.082020241287
625836558300.64145941864.3585405820413
635733757369.3404148668-32.3404148667905
645652056770.4323190985-250.432319098538
655518955749.1094788022-560.109478802151
665622956327.0892024948-98.089202494848
676076662042.4495915762-1276.4495915762
686139362114.2653265497-721.265326549685
695791957873.598528252345.4014717476748
705677255775.4773469517996.522653048341
715582054924.0742708298895.925729170209
725695356569.647038911383.352961088982







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7358483.651827388957004.810490571259962.4931642065
7457069.628770579955137.669602812259001.5879383476
7556003.774938904353623.041430319958384.5084474886
7655313.666983361552478.694853344458148.6391133785
7754363.957504264751064.895685698557663.0193228309
7855499.157965321751723.984380874459274.3315497691
7961013.816202695956749.397725634265278.2346797576
8062335.089557422557567.740735836567102.4383790086
8159059.795527167953775.592375339164343.9986789967
8257402.600227838651587.563918714663217.6365369627
8355915.160889772349555.367999579562274.9537799651
8456802.636775844149884.286121351763720.9874303365

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 58483.6518273889 & 57004.8104905712 & 59962.4931642065 \tabularnewline
74 & 57069.6287705799 & 55137.6696028122 & 59001.5879383476 \tabularnewline
75 & 56003.7749389043 & 53623.0414303199 & 58384.5084474886 \tabularnewline
76 & 55313.6669833615 & 52478.6948533444 & 58148.6391133785 \tabularnewline
77 & 54363.9575042647 & 51064.8956856985 & 57663.0193228309 \tabularnewline
78 & 55499.1579653217 & 51723.9843808744 & 59274.3315497691 \tabularnewline
79 & 61013.8162026959 & 56749.3977256342 & 65278.2346797576 \tabularnewline
80 & 62335.0895574225 & 57567.7407358365 & 67102.4383790086 \tabularnewline
81 & 59059.7955271679 & 53775.5923753391 & 64343.9986789967 \tabularnewline
82 & 57402.6002278386 & 51587.5639187146 & 63217.6365369627 \tabularnewline
83 & 55915.1608897723 & 49555.3679995795 & 62274.9537799651 \tabularnewline
84 & 56802.6367758441 & 49884.2861213517 & 63720.9874303365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]58483.6518273889[/C][C]57004.8104905712[/C][C]59962.4931642065[/C][/ROW]
[ROW][C]74[/C][C]57069.6287705799[/C][C]55137.6696028122[/C][C]59001.5879383476[/C][/ROW]
[ROW][C]75[/C][C]56003.7749389043[/C][C]53623.0414303199[/C][C]58384.5084474886[/C][/ROW]
[ROW][C]76[/C][C]55313.6669833615[/C][C]52478.6948533444[/C][C]58148.6391133785[/C][/ROW]
[ROW][C]77[/C][C]54363.9575042647[/C][C]51064.8956856985[/C][C]57663.0193228309[/C][/ROW]
[ROW][C]78[/C][C]55499.1579653217[/C][C]51723.9843808744[/C][C]59274.3315497691[/C][/ROW]
[ROW][C]79[/C][C]61013.8162026959[/C][C]56749.3977256342[/C][C]65278.2346797576[/C][/ROW]
[ROW][C]80[/C][C]62335.0895574225[/C][C]57567.7407358365[/C][C]67102.4383790086[/C][/ROW]
[ROW][C]81[/C][C]59059.7955271679[/C][C]53775.5923753391[/C][C]64343.9986789967[/C][/ROW]
[ROW][C]82[/C][C]57402.6002278386[/C][C]51587.5639187146[/C][C]63217.6365369627[/C][/ROW]
[ROW][C]83[/C][C]55915.1608897723[/C][C]49555.3679995795[/C][C]62274.9537799651[/C][/ROW]
[ROW][C]84[/C][C]56802.6367758441[/C][C]49884.2861213517[/C][C]63720.9874303365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7358483.651827388957004.810490571259962.4931642065
7457069.628770579955137.669602812259001.5879383476
7556003.774938904353623.041430319958384.5084474886
7655313.666983361552478.694853344458148.6391133785
7754363.957504264751064.895685698557663.0193228309
7855499.157965321751723.984380874459274.3315497691
7961013.816202695956749.397725634265278.2346797576
8062335.089557422557567.740735836567102.4383790086
8159059.795527167953775.592375339164343.9986789967
8257402.600227838651587.563918714663217.6365369627
8355915.160889772349555.367999579562274.9537799651
8456802.636775844149884.286121351763720.9874303365



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')