Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 20:44:32 +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/2011/Jan/16/t12952105537rpcnfj52vaz4n1.htm/, Retrieved Sun, 19 May 2024 01:23:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117470, Retrieved Sun, 19 May 2024 01:23:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-01-16 20:44:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117470&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117470&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'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.434895061810831
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.434895061810831 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117470&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]0.434895061810831[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117470&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
alpha0.434895061810831
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107109.712152105484-2.71215210548438
145857.96958354020170.0304164597983032
153636.1277445966824-0.12774459668244
165251.86290816481120.137091835188784
177979.4599600239307-0.459960023930705
187779.6279980698353-2.62799806983531
195452.5353043614241.46469563857601
208461.232211872579122.7677881274209
214885.879172493516-37.8791724935161
229656.724638417532339.2753615824677
2383167.882856301175-84.8828563011751
246667.1347028385988-1.13470283859881
256195.2099895082458-34.2099895082458
265343.46808962710219.53191037289793
273029.568840105820.431159894179963
287442.890116252750231.1098837472498
296985.9622315902852-16.9622315902852
305977.7094009460039-18.7094009460039
314248.1821119025566-6.18211190255661
326560.86286551224814.13713448775189
337044.243604980892925.7563950191071
3410085.285339543199214.7146604568008
3563101.593273536218-38.593273536218
3610567.945435454346237.0545645456538
378292.1827854617672-10.1827854617672
388169.737759632433811.2622403675662
397542.049013188278932.9509868117211
40102105.998614544043-3.99861454404311
41121106.47341611217414.526583887826
4298107.921527005735-9.9215270057353
437678.2912045478421-2.2912045478421
4477116.488186049249-39.4881860492494
456385.5098420440093-22.5098420440093
4637100.655582674904-63.6555826749038
473554.9861524299234-19.9861524299234
482362.2536123864517-39.2536123864517
494036.86768932377893.1323106762211
502935.1133023270487-6.11330232704866
513722.278434769810214.7215652301898
525139.464877494041111.5351225059589
532049.6151912998426-29.6151912998426
542830.7866838335932-2.78668383359322
551323.0690447967357-10.0690447967357
562222.0015794539673-0.0015794539672811
572520.14456994839974.85543005160029
581317.8948314310559-4.89483143105591
591617.5785870884904-1.5785870884904
601315.1833106324713-2.18331063247129
611623.7335877527623-7.73358775276226
621715.83681871094311.16318128905692
63916.0705550843557-7.07055508435574
641715.6619480506821.338051949318
65258.4742409160065616.5257590839934
661422.7636241575371-8.7636241575371
67810.8087440393825-2.80874403938249
68716.1523853797942-9.15238537979418
691012.3907371346961-2.39073713469611
7076.605486014664930.394513985335066
71108.573006307300471.42699369269953
7237.8845311083214-4.88453110832141

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107 & 109.712152105484 & -2.71215210548438 \tabularnewline
14 & 58 & 57.9695835402017 & 0.0304164597983032 \tabularnewline
15 & 36 & 36.1277445966824 & -0.12774459668244 \tabularnewline
16 & 52 & 51.8629081648112 & 0.137091835188784 \tabularnewline
17 & 79 & 79.4599600239307 & -0.459960023930705 \tabularnewline
18 & 77 & 79.6279980698353 & -2.62799806983531 \tabularnewline
19 & 54 & 52.535304361424 & 1.46469563857601 \tabularnewline
20 & 84 & 61.2322118725791 & 22.7677881274209 \tabularnewline
21 & 48 & 85.879172493516 & -37.8791724935161 \tabularnewline
22 & 96 & 56.7246384175323 & 39.2753615824677 \tabularnewline
23 & 83 & 167.882856301175 & -84.8828563011751 \tabularnewline
24 & 66 & 67.1347028385988 & -1.13470283859881 \tabularnewline
25 & 61 & 95.2099895082458 & -34.2099895082458 \tabularnewline
26 & 53 & 43.4680896271021 & 9.53191037289793 \tabularnewline
27 & 30 & 29.56884010582 & 0.431159894179963 \tabularnewline
28 & 74 & 42.8901162527502 & 31.1098837472498 \tabularnewline
29 & 69 & 85.9622315902852 & -16.9622315902852 \tabularnewline
30 & 59 & 77.7094009460039 & -18.7094009460039 \tabularnewline
31 & 42 & 48.1821119025566 & -6.18211190255661 \tabularnewline
32 & 65 & 60.8628655122481 & 4.13713448775189 \tabularnewline
33 & 70 & 44.2436049808929 & 25.7563950191071 \tabularnewline
34 & 100 & 85.2853395431992 & 14.7146604568008 \tabularnewline
35 & 63 & 101.593273536218 & -38.593273536218 \tabularnewline
36 & 105 & 67.9454354543462 & 37.0545645456538 \tabularnewline
37 & 82 & 92.1827854617672 & -10.1827854617672 \tabularnewline
38 & 81 & 69.7377596324338 & 11.2622403675662 \tabularnewline
39 & 75 & 42.0490131882789 & 32.9509868117211 \tabularnewline
40 & 102 & 105.998614544043 & -3.99861454404311 \tabularnewline
41 & 121 & 106.473416112174 & 14.526583887826 \tabularnewline
42 & 98 & 107.921527005735 & -9.9215270057353 \tabularnewline
43 & 76 & 78.2912045478421 & -2.2912045478421 \tabularnewline
44 & 77 & 116.488186049249 & -39.4881860492494 \tabularnewline
45 & 63 & 85.5098420440093 & -22.5098420440093 \tabularnewline
46 & 37 & 100.655582674904 & -63.6555826749038 \tabularnewline
47 & 35 & 54.9861524299234 & -19.9861524299234 \tabularnewline
48 & 23 & 62.2536123864517 & -39.2536123864517 \tabularnewline
49 & 40 & 36.8676893237789 & 3.1323106762211 \tabularnewline
50 & 29 & 35.1133023270487 & -6.11330232704866 \tabularnewline
51 & 37 & 22.2784347698102 & 14.7215652301898 \tabularnewline
52 & 51 & 39.4648774940411 & 11.5351225059589 \tabularnewline
53 & 20 & 49.6151912998426 & -29.6151912998426 \tabularnewline
54 & 28 & 30.7866838335932 & -2.78668383359322 \tabularnewline
55 & 13 & 23.0690447967357 & -10.0690447967357 \tabularnewline
56 & 22 & 22.0015794539673 & -0.0015794539672811 \tabularnewline
57 & 25 & 20.1445699483997 & 4.85543005160029 \tabularnewline
58 & 13 & 17.8948314310559 & -4.89483143105591 \tabularnewline
59 & 16 & 17.5785870884904 & -1.5785870884904 \tabularnewline
60 & 13 & 15.1833106324713 & -2.18331063247129 \tabularnewline
61 & 16 & 23.7335877527623 & -7.73358775276226 \tabularnewline
62 & 17 & 15.8368187109431 & 1.16318128905692 \tabularnewline
63 & 9 & 16.0705550843557 & -7.07055508435574 \tabularnewline
64 & 17 & 15.661948050682 & 1.338051949318 \tabularnewline
65 & 25 & 8.47424091600656 & 16.5257590839934 \tabularnewline
66 & 14 & 22.7636241575371 & -8.7636241575371 \tabularnewline
67 & 8 & 10.8087440393825 & -2.80874403938249 \tabularnewline
68 & 7 & 16.1523853797942 & -9.15238537979418 \tabularnewline
69 & 10 & 12.3907371346961 & -2.39073713469611 \tabularnewline
70 & 7 & 6.60548601466493 & 0.394513985335066 \tabularnewline
71 & 10 & 8.57300630730047 & 1.42699369269953 \tabularnewline
72 & 3 & 7.8845311083214 & -4.88453110832141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117470&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]107[/C][C]109.712152105484[/C][C]-2.71215210548438[/C][/ROW]
[ROW][C]14[/C][C]58[/C][C]57.9695835402017[/C][C]0.0304164597983032[/C][/ROW]
[ROW][C]15[/C][C]36[/C][C]36.1277445966824[/C][C]-0.12774459668244[/C][/ROW]
[ROW][C]16[/C][C]52[/C][C]51.8629081648112[/C][C]0.137091835188784[/C][/ROW]
[ROW][C]17[/C][C]79[/C][C]79.4599600239307[/C][C]-0.459960023930705[/C][/ROW]
[ROW][C]18[/C][C]77[/C][C]79.6279980698353[/C][C]-2.62799806983531[/C][/ROW]
[ROW][C]19[/C][C]54[/C][C]52.535304361424[/C][C]1.46469563857601[/C][/ROW]
[ROW][C]20[/C][C]84[/C][C]61.2322118725791[/C][C]22.7677881274209[/C][/ROW]
[ROW][C]21[/C][C]48[/C][C]85.879172493516[/C][C]-37.8791724935161[/C][/ROW]
[ROW][C]22[/C][C]96[/C][C]56.7246384175323[/C][C]39.2753615824677[/C][/ROW]
[ROW][C]23[/C][C]83[/C][C]167.882856301175[/C][C]-84.8828563011751[/C][/ROW]
[ROW][C]24[/C][C]66[/C][C]67.1347028385988[/C][C]-1.13470283859881[/C][/ROW]
[ROW][C]25[/C][C]61[/C][C]95.2099895082458[/C][C]-34.2099895082458[/C][/ROW]
[ROW][C]26[/C][C]53[/C][C]43.4680896271021[/C][C]9.53191037289793[/C][/ROW]
[ROW][C]27[/C][C]30[/C][C]29.56884010582[/C][C]0.431159894179963[/C][/ROW]
[ROW][C]28[/C][C]74[/C][C]42.8901162527502[/C][C]31.1098837472498[/C][/ROW]
[ROW][C]29[/C][C]69[/C][C]85.9622315902852[/C][C]-16.9622315902852[/C][/ROW]
[ROW][C]30[/C][C]59[/C][C]77.7094009460039[/C][C]-18.7094009460039[/C][/ROW]
[ROW][C]31[/C][C]42[/C][C]48.1821119025566[/C][C]-6.18211190255661[/C][/ROW]
[ROW][C]32[/C][C]65[/C][C]60.8628655122481[/C][C]4.13713448775189[/C][/ROW]
[ROW][C]33[/C][C]70[/C][C]44.2436049808929[/C][C]25.7563950191071[/C][/ROW]
[ROW][C]34[/C][C]100[/C][C]85.2853395431992[/C][C]14.7146604568008[/C][/ROW]
[ROW][C]35[/C][C]63[/C][C]101.593273536218[/C][C]-38.593273536218[/C][/ROW]
[ROW][C]36[/C][C]105[/C][C]67.9454354543462[/C][C]37.0545645456538[/C][/ROW]
[ROW][C]37[/C][C]82[/C][C]92.1827854617672[/C][C]-10.1827854617672[/C][/ROW]
[ROW][C]38[/C][C]81[/C][C]69.7377596324338[/C][C]11.2622403675662[/C][/ROW]
[ROW][C]39[/C][C]75[/C][C]42.0490131882789[/C][C]32.9509868117211[/C][/ROW]
[ROW][C]40[/C][C]102[/C][C]105.998614544043[/C][C]-3.99861454404311[/C][/ROW]
[ROW][C]41[/C][C]121[/C][C]106.473416112174[/C][C]14.526583887826[/C][/ROW]
[ROW][C]42[/C][C]98[/C][C]107.921527005735[/C][C]-9.9215270057353[/C][/ROW]
[ROW][C]43[/C][C]76[/C][C]78.2912045478421[/C][C]-2.2912045478421[/C][/ROW]
[ROW][C]44[/C][C]77[/C][C]116.488186049249[/C][C]-39.4881860492494[/C][/ROW]
[ROW][C]45[/C][C]63[/C][C]85.5098420440093[/C][C]-22.5098420440093[/C][/ROW]
[ROW][C]46[/C][C]37[/C][C]100.655582674904[/C][C]-63.6555826749038[/C][/ROW]
[ROW][C]47[/C][C]35[/C][C]54.9861524299234[/C][C]-19.9861524299234[/C][/ROW]
[ROW][C]48[/C][C]23[/C][C]62.2536123864517[/C][C]-39.2536123864517[/C][/ROW]
[ROW][C]49[/C][C]40[/C][C]36.8676893237789[/C][C]3.1323106762211[/C][/ROW]
[ROW][C]50[/C][C]29[/C][C]35.1133023270487[/C][C]-6.11330232704866[/C][/ROW]
[ROW][C]51[/C][C]37[/C][C]22.2784347698102[/C][C]14.7215652301898[/C][/ROW]
[ROW][C]52[/C][C]51[/C][C]39.4648774940411[/C][C]11.5351225059589[/C][/ROW]
[ROW][C]53[/C][C]20[/C][C]49.6151912998426[/C][C]-29.6151912998426[/C][/ROW]
[ROW][C]54[/C][C]28[/C][C]30.7866838335932[/C][C]-2.78668383359322[/C][/ROW]
[ROW][C]55[/C][C]13[/C][C]23.0690447967357[/C][C]-10.0690447967357[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]22.0015794539673[/C][C]-0.0015794539672811[/C][/ROW]
[ROW][C]57[/C][C]25[/C][C]20.1445699483997[/C][C]4.85543005160029[/C][/ROW]
[ROW][C]58[/C][C]13[/C][C]17.8948314310559[/C][C]-4.89483143105591[/C][/ROW]
[ROW][C]59[/C][C]16[/C][C]17.5785870884904[/C][C]-1.5785870884904[/C][/ROW]
[ROW][C]60[/C][C]13[/C][C]15.1833106324713[/C][C]-2.18331063247129[/C][/ROW]
[ROW][C]61[/C][C]16[/C][C]23.7335877527623[/C][C]-7.73358775276226[/C][/ROW]
[ROW][C]62[/C][C]17[/C][C]15.8368187109431[/C][C]1.16318128905692[/C][/ROW]
[ROW][C]63[/C][C]9[/C][C]16.0705550843557[/C][C]-7.07055508435574[/C][/ROW]
[ROW][C]64[/C][C]17[/C][C]15.661948050682[/C][C]1.338051949318[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]8.47424091600656[/C][C]16.5257590839934[/C][/ROW]
[ROW][C]66[/C][C]14[/C][C]22.7636241575371[/C][C]-8.7636241575371[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]10.8087440393825[/C][C]-2.80874403938249[/C][/ROW]
[ROW][C]68[/C][C]7[/C][C]16.1523853797942[/C][C]-9.15238537979418[/C][/ROW]
[ROW][C]69[/C][C]10[/C][C]12.3907371346961[/C][C]-2.39073713469611[/C][/ROW]
[ROW][C]70[/C][C]7[/C][C]6.60548601466493[/C][C]0.394513985335066[/C][/ROW]
[ROW][C]71[/C][C]10[/C][C]8.57300630730047[/C][C]1.42699369269953[/C][/ROW]
[ROW][C]72[/C][C]3[/C][C]7.8845311083214[/C][C]-4.88453110832141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117470&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
13107109.712152105484-2.71215210548438
145857.96958354020170.0304164597983032
153636.1277445966824-0.12774459668244
165251.86290816481120.137091835188784
177979.4599600239307-0.459960023930705
187779.6279980698353-2.62799806983531
195452.5353043614241.46469563857601
208461.232211872579122.7677881274209
214885.879172493516-37.8791724935161
229656.724638417532339.2753615824677
2383167.882856301175-84.8828563011751
246667.1347028385988-1.13470283859881
256195.2099895082458-34.2099895082458
265343.46808962710219.53191037289793
273029.568840105820.431159894179963
287442.890116252750231.1098837472498
296985.9622315902852-16.9622315902852
305977.7094009460039-18.7094009460039
314248.1821119025566-6.18211190255661
326560.86286551224814.13713448775189
337044.243604980892925.7563950191071
3410085.285339543199214.7146604568008
3563101.593273536218-38.593273536218
3610567.945435454346237.0545645456538
378292.1827854617672-10.1827854617672
388169.737759632433811.2622403675662
397542.049013188278932.9509868117211
40102105.998614544043-3.99861454404311
41121106.47341611217414.526583887826
4298107.921527005735-9.9215270057353
437678.2912045478421-2.2912045478421
4477116.488186049249-39.4881860492494
456385.5098420440093-22.5098420440093
4637100.655582674904-63.6555826749038
473554.9861524299234-19.9861524299234
482362.2536123864517-39.2536123864517
494036.86768932377893.1323106762211
502935.1133023270487-6.11330232704866
513722.278434769810214.7215652301898
525139.464877494041111.5351225059589
532049.6151912998426-29.6151912998426
542830.7866838335932-2.78668383359322
551323.0690447967357-10.0690447967357
562222.0015794539673-0.0015794539672811
572520.14456994839974.85543005160029
581317.8948314310559-4.89483143105591
591617.5785870884904-1.5785870884904
601315.1833106324713-2.18331063247129
611623.7335877527623-7.73358775276226
621715.83681871094311.16318128905692
63916.0705550843557-7.07055508435574
641715.6619480506821.338051949318
65258.4742409160065616.5257590839934
661422.7636241575371-8.7636241575371
67810.8087440393825-2.80874403938249
68716.1523853797942-9.15238537979418
691012.3907371346961-2.39073713469611
7076.605486014664930.394513985335066
71108.573006307300471.42699369269953
7237.8845311083214-4.88453110832141







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.10083159762423-34.615157321455750.8168205167041
748.1926835661484-38.753448497571655.1388156298684
755.26004867967327-41.068987964096151.5890853234426
769.4250564486454-54.902293041297873.7524059385886
777.36489625833425-52.502946497426167.2327390140946
784.80830968310635-48.109456709323857.7260760755365
793.00917633805022-45.871487879486251.8898405555866
803.39472623537472-52.225662868840959.0151153395903
815.16297917021532-71.873312386826682.1992707272572
823.43656612422804-59.87232129251266.7454535409681
834.45423749090523-76.469427732624185.3779027144346
841.77232110726812-46.035006648690549.5796488632268

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.10083159762423 & -34.6151573214557 & 50.8168205167041 \tabularnewline
74 & 8.1926835661484 & -38.7534484975716 & 55.1388156298684 \tabularnewline
75 & 5.26004867967327 & -41.0689879640961 & 51.5890853234426 \tabularnewline
76 & 9.4250564486454 & -54.9022930412978 & 73.7524059385886 \tabularnewline
77 & 7.36489625833425 & -52.5029464974261 & 67.2327390140946 \tabularnewline
78 & 4.80830968310635 & -48.1094567093238 & 57.7260760755365 \tabularnewline
79 & 3.00917633805022 & -45.8714878794862 & 51.8898405555866 \tabularnewline
80 & 3.39472623537472 & -52.2256628688409 & 59.0151153395903 \tabularnewline
81 & 5.16297917021532 & -71.8733123868266 & 82.1992707272572 \tabularnewline
82 & 3.43656612422804 & -59.872321292512 & 66.7454535409681 \tabularnewline
83 & 4.45423749090523 & -76.4694277326241 & 85.3779027144346 \tabularnewline
84 & 1.77232110726812 & -46.0350066486905 & 49.5796488632268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117470&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]8.10083159762423[/C][C]-34.6151573214557[/C][C]50.8168205167041[/C][/ROW]
[ROW][C]74[/C][C]8.1926835661484[/C][C]-38.7534484975716[/C][C]55.1388156298684[/C][/ROW]
[ROW][C]75[/C][C]5.26004867967327[/C][C]-41.0689879640961[/C][C]51.5890853234426[/C][/ROW]
[ROW][C]76[/C][C]9.4250564486454[/C][C]-54.9022930412978[/C][C]73.7524059385886[/C][/ROW]
[ROW][C]77[/C][C]7.36489625833425[/C][C]-52.5029464974261[/C][C]67.2327390140946[/C][/ROW]
[ROW][C]78[/C][C]4.80830968310635[/C][C]-48.1094567093238[/C][C]57.7260760755365[/C][/ROW]
[ROW][C]79[/C][C]3.00917633805022[/C][C]-45.8714878794862[/C][C]51.8898405555866[/C][/ROW]
[ROW][C]80[/C][C]3.39472623537472[/C][C]-52.2256628688409[/C][C]59.0151153395903[/C][/ROW]
[ROW][C]81[/C][C]5.16297917021532[/C][C]-71.8733123868266[/C][C]82.1992707272572[/C][/ROW]
[ROW][C]82[/C][C]3.43656612422804[/C][C]-59.872321292512[/C][C]66.7454535409681[/C][/ROW]
[ROW][C]83[/C][C]4.45423749090523[/C][C]-76.4694277326241[/C][C]85.3779027144346[/C][/ROW]
[ROW][C]84[/C][C]1.77232110726812[/C][C]-46.0350066486905[/C][C]49.5796488632268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117470&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117470&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
738.10083159762423-34.615157321455750.8168205167041
748.1926835661484-38.753448497571655.1388156298684
755.26004867967327-41.068987964096151.5890853234426
769.4250564486454-54.902293041297873.7524059385886
777.36489625833425-52.502946497426167.2327390140946
784.80830968310635-48.109456709323857.7260760755365
793.00917633805022-45.871487879486251.8898405555866
803.39472623537472-52.225662868840959.0151153395903
815.16297917021532-71.873312386826682.1992707272572
823.43656612422804-59.87232129251266.7454535409681
834.45423749090523-76.469427732624185.3779027144346
841.77232110726812-46.035006648690549.5796488632268



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')