Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Aug 2009 06:28:25 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f.htm/, Retrieved Mon, 06 May 2024 16:55:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42793, Retrieved Mon, 06 May 2024 16:55:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - Robbe...] [2009-08-18 12:28:25] [594470f14259f7e0de407f0568e168f2] [Current]
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Dataseries X:
12.11
11.42
11.71
12.04
12.21
12
12.36
12.32
12.96
12.79
13.19
12.34
13.25
12.54
12.77
12.96
13
13.61
13.8
14.16
14.27
14.69
15.01
15.09
15.14
14.2
13.83
14.31
14.04
14.9
14.92
15.36
15.5
15.65
16.18
15.44
15.58
15.24
15.33
16.07
15.82
15.87
15.72
17.07
16.83
17.52
17.76
17.36
17.95
16.71
17.14
16.72
17.26
17.24
17.69
18.13
18.08
18.18
18.18
17.64
17.89
16.82
16.61
16.66
17.02
16.91
17.18
18.06
17.58
17.48
17.54
17.44
17.79
16.79
16.19
16.62
16.39
16.54
17.26
18
17.29
18.16
17.82
17.48
18.31
17.04
17.03
16.97
17.11
17.12
17.69
18.5
18.27
18.45
18.35
18.03
18.49
18.07
17.8
17.88
18.12
18.68
18.8
19.64
19.56
19.3
20.07
19.82
20.29
19.36
18.74
18.87
18.87
18.91
19.31
20.06
20.72
20.42
20.58
20.58
21.18
19.87
19.83
19.48
19.49
19.4
19.89
20.44
20.07
19.75
19.54
19.07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42793&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42793&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.459863297921987
beta0.146965751748968
gamma0.668062732641707

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.459863297921987 \tabularnewline
beta & 0.146965751748968 \tabularnewline
gamma & 0.668062732641707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42793&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]0.459863297921987[/C][/ROW]
[ROW][C]beta[/C][C]0.146965751748968[/C][/ROW]
[ROW][C]gamma[/C][C]0.668062732641707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42793&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
alpha0.459863297921987
beta0.146965751748968
gamma0.668062732641707







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1313.2512.6539197346210.596080265378989
1412.5412.25699664949640.283003350503645
1512.7712.65908970316780.110910296832230
1612.9612.94831276976280.0116872302372268
171313.0220852317476-0.0220852317476012
1813.6113.6147159025095-0.00471590250949383
1913.813.8609842107814-0.0609842107813989
2014.1613.86050758014460.299492419855431
2114.2714.8243506935806-0.554350693580581
2214.6914.44919880861560.240801191384367
2315.0115.1167772122287-0.106777212228696
2415.0914.15217787676870.937822123231348
2515.1416.0103777873678-0.87037778736779
2614.214.6735890306251-0.473589030625059
2713.8314.6445012348439-0.814501234843888
2814.3114.3853483127609-0.0753483127608661
2914.0414.2990182191282-0.259018219128231
3014.914.71310553521710.186894464782881
3114.9214.9292764810236-0.00927648102361367
3215.3614.98165411407530.3783458859247
3315.515.5982526686552-0.0982526686552312
3415.6515.6543455758710-0.00434557587102091
3516.1816.01772185987780.162278140122247
3615.4415.43142414655850.00857585344152056
3715.5816.0895502007709-0.509550200770947
3815.2414.92361342164390.316386578356092
3915.3315.07555703007890.254442969921053
4016.0715.62480071498000.445199285020028
4115.8215.7486027256720.0713972743280014
4215.8716.6352319471215-0.765231947121494
4315.7216.3611111036762-0.641111103676197
4417.0716.24749826171570.822501738284338
4516.8316.917836124607-0.0878361246069908
4617.5217.02364900213580.496350997864212
4717.7617.75286736687860.00713263312136547
4817.3616.98840553609090.371594463909055
4917.9517.71955935824150.230440641758491
5016.7117.1946888973513-0.48468889735134
5117.1416.98866133003070.151338669969302
5216.7217.6423396096089-0.922339609608947
5317.2616.92378215746910.336217842530939
5417.2417.6221348011800-0.382134801180047
5517.6917.55740530867130.132594691328741
5618.1318.4378311485022-0.307831148502228
5718.0818.2148297569720-0.134829756972028
5818.1818.4900082689929-0.31000826899286
5918.1818.5890863468764-0.409086346876393
6017.6417.62023641797530.0197635820246767
6117.8918.0030216263282-0.113021626328223
6216.8216.9021048390842-0.0821048390841916
6316.6116.9817522037394-0.37175220373943
6416.6616.8337121745102-0.173712174510214
6517.0216.79597650213310.224023497866892
6616.9117.0542823246001-0.144282324600134
6717.1817.17035200476320.00964799523681137
6818.0617.69655305423730.363446945762703
6917.5817.7695492764780-0.189549276478036
7017.4817.8694792625431-0.389479262543137
7117.5417.8026563417840-0.262656341783977
7217.4417.00114311274190.438856887258133
7317.7917.47367884193570.316321158064323
7416.7916.58095483509850.209045164901493
7516.1916.6907879978106-0.500787997810566
7616.6216.54639497056150.073605029438454
7716.3916.7740268297144-0.384026829714369
7816.5416.5876713347055-0.0476713347055444
7917.2616.772986592960.487013407040003
801817.64554213454480.354457865455206
8117.2917.5241602188327-0.234160218832717
8218.1617.53215057114830.627849428851711
8317.8218.0540695375838-0.234069537583849
8417.4817.5823081803749-0.102308180374898
8518.3117.80002541580020.509974584199846
8617.0416.98556317129160.0544368287083898
8717.0316.79722320282390.232776797176061
8816.9717.2957964015063-0.325796401506281
8917.1117.2340747384349-0.124074738434860
9017.1217.3728886947149-0.252888694714855
9117.6917.7388732154873-0.0488732154873048
9218.518.36530246555930.134697534440697
9318.2717.93050648144850.339493518551457
9418.4518.5827839427230-0.132783942722952
9518.3518.4428550695268-0.0928550695268093
9618.0318.0850429512244-0.0550429512244115
9718.4918.5733969603524-0.083396960352406
9818.0717.27639884550620.793601154493786
9917.817.51090478254530.289095217454715
10017.8817.86773907009580.0122609299041692
10118.1218.0931451563350.0268548436649958
10218.6818.32450290632180.355497093678242
10318.819.1932883024889-0.393288302488916
10419.6419.8673950560483-0.227395056048291
10519.5619.36975873986740.190241260132566
10619.319.8544358722569-0.554435872256892
10720.0719.55258132395020.517418676049843
10819.8219.52712986483970.292870135160292
10920.2920.2975602736362-0.00756027363622636
11019.3619.34201230350720.0179876964928205
11118.7419.0419942751055-0.301994275105546
11218.8719.0247659626135-0.154765962613478
11318.8719.1707321350768-0.300732135076778
11418.9119.3426550929002-0.43265509290018
11519.3119.4930379739120-0.183037973912040
11620.0620.2638669442370-0.203866944236960
11720.7219.83962607451320.880373925486779
11820.4220.33821991752240.081780082477632
11920.5820.7368883577538-0.15688835775385
12020.5820.26895377639390.311046223606109
12121.1820.91763030020090.262369699799141
12219.8720.0406803843038-0.170680384303758
12319.8319.49305077275020.336949227249828
12419.4819.8416369217171-0.361636921717107
12519.4919.8436897697541-0.353689769754098
12619.419.9475753366679-0.547575336667904
12719.8920.1393742194867-0.249374219486661
12820.4420.8851028594458-0.445102859445761
12920.0720.7039113347433-0.633911334743274
13019.7520.0860800097087-0.336080009708688
13119.5420.0380452364186-0.498045236418633
13219.0719.4085519085413-0.338551908541341

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13.25 & 12.653919734621 & 0.596080265378989 \tabularnewline
14 & 12.54 & 12.2569966494964 & 0.283003350503645 \tabularnewline
15 & 12.77 & 12.6590897031678 & 0.110910296832230 \tabularnewline
16 & 12.96 & 12.9483127697628 & 0.0116872302372268 \tabularnewline
17 & 13 & 13.0220852317476 & -0.0220852317476012 \tabularnewline
18 & 13.61 & 13.6147159025095 & -0.00471590250949383 \tabularnewline
19 & 13.8 & 13.8609842107814 & -0.0609842107813989 \tabularnewline
20 & 14.16 & 13.8605075801446 & 0.299492419855431 \tabularnewline
21 & 14.27 & 14.8243506935806 & -0.554350693580581 \tabularnewline
22 & 14.69 & 14.4491988086156 & 0.240801191384367 \tabularnewline
23 & 15.01 & 15.1167772122287 & -0.106777212228696 \tabularnewline
24 & 15.09 & 14.1521778767687 & 0.937822123231348 \tabularnewline
25 & 15.14 & 16.0103777873678 & -0.87037778736779 \tabularnewline
26 & 14.2 & 14.6735890306251 & -0.473589030625059 \tabularnewline
27 & 13.83 & 14.6445012348439 & -0.814501234843888 \tabularnewline
28 & 14.31 & 14.3853483127609 & -0.0753483127608661 \tabularnewline
29 & 14.04 & 14.2990182191282 & -0.259018219128231 \tabularnewline
30 & 14.9 & 14.7131055352171 & 0.186894464782881 \tabularnewline
31 & 14.92 & 14.9292764810236 & -0.00927648102361367 \tabularnewline
32 & 15.36 & 14.9816541140753 & 0.3783458859247 \tabularnewline
33 & 15.5 & 15.5982526686552 & -0.0982526686552312 \tabularnewline
34 & 15.65 & 15.6543455758710 & -0.00434557587102091 \tabularnewline
35 & 16.18 & 16.0177218598778 & 0.162278140122247 \tabularnewline
36 & 15.44 & 15.4314241465585 & 0.00857585344152056 \tabularnewline
37 & 15.58 & 16.0895502007709 & -0.509550200770947 \tabularnewline
38 & 15.24 & 14.9236134216439 & 0.316386578356092 \tabularnewline
39 & 15.33 & 15.0755570300789 & 0.254442969921053 \tabularnewline
40 & 16.07 & 15.6248007149800 & 0.445199285020028 \tabularnewline
41 & 15.82 & 15.748602725672 & 0.0713972743280014 \tabularnewline
42 & 15.87 & 16.6352319471215 & -0.765231947121494 \tabularnewline
43 & 15.72 & 16.3611111036762 & -0.641111103676197 \tabularnewline
44 & 17.07 & 16.2474982617157 & 0.822501738284338 \tabularnewline
45 & 16.83 & 16.917836124607 & -0.0878361246069908 \tabularnewline
46 & 17.52 & 17.0236490021358 & 0.496350997864212 \tabularnewline
47 & 17.76 & 17.7528673668786 & 0.00713263312136547 \tabularnewline
48 & 17.36 & 16.9884055360909 & 0.371594463909055 \tabularnewline
49 & 17.95 & 17.7195593582415 & 0.230440641758491 \tabularnewline
50 & 16.71 & 17.1946888973513 & -0.48468889735134 \tabularnewline
51 & 17.14 & 16.9886613300307 & 0.151338669969302 \tabularnewline
52 & 16.72 & 17.6423396096089 & -0.922339609608947 \tabularnewline
53 & 17.26 & 16.9237821574691 & 0.336217842530939 \tabularnewline
54 & 17.24 & 17.6221348011800 & -0.382134801180047 \tabularnewline
55 & 17.69 & 17.5574053086713 & 0.132594691328741 \tabularnewline
56 & 18.13 & 18.4378311485022 & -0.307831148502228 \tabularnewline
57 & 18.08 & 18.2148297569720 & -0.134829756972028 \tabularnewline
58 & 18.18 & 18.4900082689929 & -0.31000826899286 \tabularnewline
59 & 18.18 & 18.5890863468764 & -0.409086346876393 \tabularnewline
60 & 17.64 & 17.6202364179753 & 0.0197635820246767 \tabularnewline
61 & 17.89 & 18.0030216263282 & -0.113021626328223 \tabularnewline
62 & 16.82 & 16.9021048390842 & -0.0821048390841916 \tabularnewline
63 & 16.61 & 16.9817522037394 & -0.37175220373943 \tabularnewline
64 & 16.66 & 16.8337121745102 & -0.173712174510214 \tabularnewline
65 & 17.02 & 16.7959765021331 & 0.224023497866892 \tabularnewline
66 & 16.91 & 17.0542823246001 & -0.144282324600134 \tabularnewline
67 & 17.18 & 17.1703520047632 & 0.00964799523681137 \tabularnewline
68 & 18.06 & 17.6965530542373 & 0.363446945762703 \tabularnewline
69 & 17.58 & 17.7695492764780 & -0.189549276478036 \tabularnewline
70 & 17.48 & 17.8694792625431 & -0.389479262543137 \tabularnewline
71 & 17.54 & 17.8026563417840 & -0.262656341783977 \tabularnewline
72 & 17.44 & 17.0011431127419 & 0.438856887258133 \tabularnewline
73 & 17.79 & 17.4736788419357 & 0.316321158064323 \tabularnewline
74 & 16.79 & 16.5809548350985 & 0.209045164901493 \tabularnewline
75 & 16.19 & 16.6907879978106 & -0.500787997810566 \tabularnewline
76 & 16.62 & 16.5463949705615 & 0.073605029438454 \tabularnewline
77 & 16.39 & 16.7740268297144 & -0.384026829714369 \tabularnewline
78 & 16.54 & 16.5876713347055 & -0.0476713347055444 \tabularnewline
79 & 17.26 & 16.77298659296 & 0.487013407040003 \tabularnewline
80 & 18 & 17.6455421345448 & 0.354457865455206 \tabularnewline
81 & 17.29 & 17.5241602188327 & -0.234160218832717 \tabularnewline
82 & 18.16 & 17.5321505711483 & 0.627849428851711 \tabularnewline
83 & 17.82 & 18.0540695375838 & -0.234069537583849 \tabularnewline
84 & 17.48 & 17.5823081803749 & -0.102308180374898 \tabularnewline
85 & 18.31 & 17.8000254158002 & 0.509974584199846 \tabularnewline
86 & 17.04 & 16.9855631712916 & 0.0544368287083898 \tabularnewline
87 & 17.03 & 16.7972232028239 & 0.232776797176061 \tabularnewline
88 & 16.97 & 17.2957964015063 & -0.325796401506281 \tabularnewline
89 & 17.11 & 17.2340747384349 & -0.124074738434860 \tabularnewline
90 & 17.12 & 17.3728886947149 & -0.252888694714855 \tabularnewline
91 & 17.69 & 17.7388732154873 & -0.0488732154873048 \tabularnewline
92 & 18.5 & 18.3653024655593 & 0.134697534440697 \tabularnewline
93 & 18.27 & 17.9305064814485 & 0.339493518551457 \tabularnewline
94 & 18.45 & 18.5827839427230 & -0.132783942722952 \tabularnewline
95 & 18.35 & 18.4428550695268 & -0.0928550695268093 \tabularnewline
96 & 18.03 & 18.0850429512244 & -0.0550429512244115 \tabularnewline
97 & 18.49 & 18.5733969603524 & -0.083396960352406 \tabularnewline
98 & 18.07 & 17.2763988455062 & 0.793601154493786 \tabularnewline
99 & 17.8 & 17.5109047825453 & 0.289095217454715 \tabularnewline
100 & 17.88 & 17.8677390700958 & 0.0122609299041692 \tabularnewline
101 & 18.12 & 18.093145156335 & 0.0268548436649958 \tabularnewline
102 & 18.68 & 18.3245029063218 & 0.355497093678242 \tabularnewline
103 & 18.8 & 19.1932883024889 & -0.393288302488916 \tabularnewline
104 & 19.64 & 19.8673950560483 & -0.227395056048291 \tabularnewline
105 & 19.56 & 19.3697587398674 & 0.190241260132566 \tabularnewline
106 & 19.3 & 19.8544358722569 & -0.554435872256892 \tabularnewline
107 & 20.07 & 19.5525813239502 & 0.517418676049843 \tabularnewline
108 & 19.82 & 19.5271298648397 & 0.292870135160292 \tabularnewline
109 & 20.29 & 20.2975602736362 & -0.00756027363622636 \tabularnewline
110 & 19.36 & 19.3420123035072 & 0.0179876964928205 \tabularnewline
111 & 18.74 & 19.0419942751055 & -0.301994275105546 \tabularnewline
112 & 18.87 & 19.0247659626135 & -0.154765962613478 \tabularnewline
113 & 18.87 & 19.1707321350768 & -0.300732135076778 \tabularnewline
114 & 18.91 & 19.3426550929002 & -0.43265509290018 \tabularnewline
115 & 19.31 & 19.4930379739120 & -0.183037973912040 \tabularnewline
116 & 20.06 & 20.2638669442370 & -0.203866944236960 \tabularnewline
117 & 20.72 & 19.8396260745132 & 0.880373925486779 \tabularnewline
118 & 20.42 & 20.3382199175224 & 0.081780082477632 \tabularnewline
119 & 20.58 & 20.7368883577538 & -0.15688835775385 \tabularnewline
120 & 20.58 & 20.2689537763939 & 0.311046223606109 \tabularnewline
121 & 21.18 & 20.9176303002009 & 0.262369699799141 \tabularnewline
122 & 19.87 & 20.0406803843038 & -0.170680384303758 \tabularnewline
123 & 19.83 & 19.4930507727502 & 0.336949227249828 \tabularnewline
124 & 19.48 & 19.8416369217171 & -0.361636921717107 \tabularnewline
125 & 19.49 & 19.8436897697541 & -0.353689769754098 \tabularnewline
126 & 19.4 & 19.9475753366679 & -0.547575336667904 \tabularnewline
127 & 19.89 & 20.1393742194867 & -0.249374219486661 \tabularnewline
128 & 20.44 & 20.8851028594458 & -0.445102859445761 \tabularnewline
129 & 20.07 & 20.7039113347433 & -0.633911334743274 \tabularnewline
130 & 19.75 & 20.0860800097087 & -0.336080009708688 \tabularnewline
131 & 19.54 & 20.0380452364186 & -0.498045236418633 \tabularnewline
132 & 19.07 & 19.4085519085413 & -0.338551908541341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42793&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]13.25[/C][C]12.653919734621[/C][C]0.596080265378989[/C][/ROW]
[ROW][C]14[/C][C]12.54[/C][C]12.2569966494964[/C][C]0.283003350503645[/C][/ROW]
[ROW][C]15[/C][C]12.77[/C][C]12.6590897031678[/C][C]0.110910296832230[/C][/ROW]
[ROW][C]16[/C][C]12.96[/C][C]12.9483127697628[/C][C]0.0116872302372268[/C][/ROW]
[ROW][C]17[/C][C]13[/C][C]13.0220852317476[/C][C]-0.0220852317476012[/C][/ROW]
[ROW][C]18[/C][C]13.61[/C][C]13.6147159025095[/C][C]-0.00471590250949383[/C][/ROW]
[ROW][C]19[/C][C]13.8[/C][C]13.8609842107814[/C][C]-0.0609842107813989[/C][/ROW]
[ROW][C]20[/C][C]14.16[/C][C]13.8605075801446[/C][C]0.299492419855431[/C][/ROW]
[ROW][C]21[/C][C]14.27[/C][C]14.8243506935806[/C][C]-0.554350693580581[/C][/ROW]
[ROW][C]22[/C][C]14.69[/C][C]14.4491988086156[/C][C]0.240801191384367[/C][/ROW]
[ROW][C]23[/C][C]15.01[/C][C]15.1167772122287[/C][C]-0.106777212228696[/C][/ROW]
[ROW][C]24[/C][C]15.09[/C][C]14.1521778767687[/C][C]0.937822123231348[/C][/ROW]
[ROW][C]25[/C][C]15.14[/C][C]16.0103777873678[/C][C]-0.87037778736779[/C][/ROW]
[ROW][C]26[/C][C]14.2[/C][C]14.6735890306251[/C][C]-0.473589030625059[/C][/ROW]
[ROW][C]27[/C][C]13.83[/C][C]14.6445012348439[/C][C]-0.814501234843888[/C][/ROW]
[ROW][C]28[/C][C]14.31[/C][C]14.3853483127609[/C][C]-0.0753483127608661[/C][/ROW]
[ROW][C]29[/C][C]14.04[/C][C]14.2990182191282[/C][C]-0.259018219128231[/C][/ROW]
[ROW][C]30[/C][C]14.9[/C][C]14.7131055352171[/C][C]0.186894464782881[/C][/ROW]
[ROW][C]31[/C][C]14.92[/C][C]14.9292764810236[/C][C]-0.00927648102361367[/C][/ROW]
[ROW][C]32[/C][C]15.36[/C][C]14.9816541140753[/C][C]0.3783458859247[/C][/ROW]
[ROW][C]33[/C][C]15.5[/C][C]15.5982526686552[/C][C]-0.0982526686552312[/C][/ROW]
[ROW][C]34[/C][C]15.65[/C][C]15.6543455758710[/C][C]-0.00434557587102091[/C][/ROW]
[ROW][C]35[/C][C]16.18[/C][C]16.0177218598778[/C][C]0.162278140122247[/C][/ROW]
[ROW][C]36[/C][C]15.44[/C][C]15.4314241465585[/C][C]0.00857585344152056[/C][/ROW]
[ROW][C]37[/C][C]15.58[/C][C]16.0895502007709[/C][C]-0.509550200770947[/C][/ROW]
[ROW][C]38[/C][C]15.24[/C][C]14.9236134216439[/C][C]0.316386578356092[/C][/ROW]
[ROW][C]39[/C][C]15.33[/C][C]15.0755570300789[/C][C]0.254442969921053[/C][/ROW]
[ROW][C]40[/C][C]16.07[/C][C]15.6248007149800[/C][C]0.445199285020028[/C][/ROW]
[ROW][C]41[/C][C]15.82[/C][C]15.748602725672[/C][C]0.0713972743280014[/C][/ROW]
[ROW][C]42[/C][C]15.87[/C][C]16.6352319471215[/C][C]-0.765231947121494[/C][/ROW]
[ROW][C]43[/C][C]15.72[/C][C]16.3611111036762[/C][C]-0.641111103676197[/C][/ROW]
[ROW][C]44[/C][C]17.07[/C][C]16.2474982617157[/C][C]0.822501738284338[/C][/ROW]
[ROW][C]45[/C][C]16.83[/C][C]16.917836124607[/C][C]-0.0878361246069908[/C][/ROW]
[ROW][C]46[/C][C]17.52[/C][C]17.0236490021358[/C][C]0.496350997864212[/C][/ROW]
[ROW][C]47[/C][C]17.76[/C][C]17.7528673668786[/C][C]0.00713263312136547[/C][/ROW]
[ROW][C]48[/C][C]17.36[/C][C]16.9884055360909[/C][C]0.371594463909055[/C][/ROW]
[ROW][C]49[/C][C]17.95[/C][C]17.7195593582415[/C][C]0.230440641758491[/C][/ROW]
[ROW][C]50[/C][C]16.71[/C][C]17.1946888973513[/C][C]-0.48468889735134[/C][/ROW]
[ROW][C]51[/C][C]17.14[/C][C]16.9886613300307[/C][C]0.151338669969302[/C][/ROW]
[ROW][C]52[/C][C]16.72[/C][C]17.6423396096089[/C][C]-0.922339609608947[/C][/ROW]
[ROW][C]53[/C][C]17.26[/C][C]16.9237821574691[/C][C]0.336217842530939[/C][/ROW]
[ROW][C]54[/C][C]17.24[/C][C]17.6221348011800[/C][C]-0.382134801180047[/C][/ROW]
[ROW][C]55[/C][C]17.69[/C][C]17.5574053086713[/C][C]0.132594691328741[/C][/ROW]
[ROW][C]56[/C][C]18.13[/C][C]18.4378311485022[/C][C]-0.307831148502228[/C][/ROW]
[ROW][C]57[/C][C]18.08[/C][C]18.2148297569720[/C][C]-0.134829756972028[/C][/ROW]
[ROW][C]58[/C][C]18.18[/C][C]18.4900082689929[/C][C]-0.31000826899286[/C][/ROW]
[ROW][C]59[/C][C]18.18[/C][C]18.5890863468764[/C][C]-0.409086346876393[/C][/ROW]
[ROW][C]60[/C][C]17.64[/C][C]17.6202364179753[/C][C]0.0197635820246767[/C][/ROW]
[ROW][C]61[/C][C]17.89[/C][C]18.0030216263282[/C][C]-0.113021626328223[/C][/ROW]
[ROW][C]62[/C][C]16.82[/C][C]16.9021048390842[/C][C]-0.0821048390841916[/C][/ROW]
[ROW][C]63[/C][C]16.61[/C][C]16.9817522037394[/C][C]-0.37175220373943[/C][/ROW]
[ROW][C]64[/C][C]16.66[/C][C]16.8337121745102[/C][C]-0.173712174510214[/C][/ROW]
[ROW][C]65[/C][C]17.02[/C][C]16.7959765021331[/C][C]0.224023497866892[/C][/ROW]
[ROW][C]66[/C][C]16.91[/C][C]17.0542823246001[/C][C]-0.144282324600134[/C][/ROW]
[ROW][C]67[/C][C]17.18[/C][C]17.1703520047632[/C][C]0.00964799523681137[/C][/ROW]
[ROW][C]68[/C][C]18.06[/C][C]17.6965530542373[/C][C]0.363446945762703[/C][/ROW]
[ROW][C]69[/C][C]17.58[/C][C]17.7695492764780[/C][C]-0.189549276478036[/C][/ROW]
[ROW][C]70[/C][C]17.48[/C][C]17.8694792625431[/C][C]-0.389479262543137[/C][/ROW]
[ROW][C]71[/C][C]17.54[/C][C]17.8026563417840[/C][C]-0.262656341783977[/C][/ROW]
[ROW][C]72[/C][C]17.44[/C][C]17.0011431127419[/C][C]0.438856887258133[/C][/ROW]
[ROW][C]73[/C][C]17.79[/C][C]17.4736788419357[/C][C]0.316321158064323[/C][/ROW]
[ROW][C]74[/C][C]16.79[/C][C]16.5809548350985[/C][C]0.209045164901493[/C][/ROW]
[ROW][C]75[/C][C]16.19[/C][C]16.6907879978106[/C][C]-0.500787997810566[/C][/ROW]
[ROW][C]76[/C][C]16.62[/C][C]16.5463949705615[/C][C]0.073605029438454[/C][/ROW]
[ROW][C]77[/C][C]16.39[/C][C]16.7740268297144[/C][C]-0.384026829714369[/C][/ROW]
[ROW][C]78[/C][C]16.54[/C][C]16.5876713347055[/C][C]-0.0476713347055444[/C][/ROW]
[ROW][C]79[/C][C]17.26[/C][C]16.77298659296[/C][C]0.487013407040003[/C][/ROW]
[ROW][C]80[/C][C]18[/C][C]17.6455421345448[/C][C]0.354457865455206[/C][/ROW]
[ROW][C]81[/C][C]17.29[/C][C]17.5241602188327[/C][C]-0.234160218832717[/C][/ROW]
[ROW][C]82[/C][C]18.16[/C][C]17.5321505711483[/C][C]0.627849428851711[/C][/ROW]
[ROW][C]83[/C][C]17.82[/C][C]18.0540695375838[/C][C]-0.234069537583849[/C][/ROW]
[ROW][C]84[/C][C]17.48[/C][C]17.5823081803749[/C][C]-0.102308180374898[/C][/ROW]
[ROW][C]85[/C][C]18.31[/C][C]17.8000254158002[/C][C]0.509974584199846[/C][/ROW]
[ROW][C]86[/C][C]17.04[/C][C]16.9855631712916[/C][C]0.0544368287083898[/C][/ROW]
[ROW][C]87[/C][C]17.03[/C][C]16.7972232028239[/C][C]0.232776797176061[/C][/ROW]
[ROW][C]88[/C][C]16.97[/C][C]17.2957964015063[/C][C]-0.325796401506281[/C][/ROW]
[ROW][C]89[/C][C]17.11[/C][C]17.2340747384349[/C][C]-0.124074738434860[/C][/ROW]
[ROW][C]90[/C][C]17.12[/C][C]17.3728886947149[/C][C]-0.252888694714855[/C][/ROW]
[ROW][C]91[/C][C]17.69[/C][C]17.7388732154873[/C][C]-0.0488732154873048[/C][/ROW]
[ROW][C]92[/C][C]18.5[/C][C]18.3653024655593[/C][C]0.134697534440697[/C][/ROW]
[ROW][C]93[/C][C]18.27[/C][C]17.9305064814485[/C][C]0.339493518551457[/C][/ROW]
[ROW][C]94[/C][C]18.45[/C][C]18.5827839427230[/C][C]-0.132783942722952[/C][/ROW]
[ROW][C]95[/C][C]18.35[/C][C]18.4428550695268[/C][C]-0.0928550695268093[/C][/ROW]
[ROW][C]96[/C][C]18.03[/C][C]18.0850429512244[/C][C]-0.0550429512244115[/C][/ROW]
[ROW][C]97[/C][C]18.49[/C][C]18.5733969603524[/C][C]-0.083396960352406[/C][/ROW]
[ROW][C]98[/C][C]18.07[/C][C]17.2763988455062[/C][C]0.793601154493786[/C][/ROW]
[ROW][C]99[/C][C]17.8[/C][C]17.5109047825453[/C][C]0.289095217454715[/C][/ROW]
[ROW][C]100[/C][C]17.88[/C][C]17.8677390700958[/C][C]0.0122609299041692[/C][/ROW]
[ROW][C]101[/C][C]18.12[/C][C]18.093145156335[/C][C]0.0268548436649958[/C][/ROW]
[ROW][C]102[/C][C]18.68[/C][C]18.3245029063218[/C][C]0.355497093678242[/C][/ROW]
[ROW][C]103[/C][C]18.8[/C][C]19.1932883024889[/C][C]-0.393288302488916[/C][/ROW]
[ROW][C]104[/C][C]19.64[/C][C]19.8673950560483[/C][C]-0.227395056048291[/C][/ROW]
[ROW][C]105[/C][C]19.56[/C][C]19.3697587398674[/C][C]0.190241260132566[/C][/ROW]
[ROW][C]106[/C][C]19.3[/C][C]19.8544358722569[/C][C]-0.554435872256892[/C][/ROW]
[ROW][C]107[/C][C]20.07[/C][C]19.5525813239502[/C][C]0.517418676049843[/C][/ROW]
[ROW][C]108[/C][C]19.82[/C][C]19.5271298648397[/C][C]0.292870135160292[/C][/ROW]
[ROW][C]109[/C][C]20.29[/C][C]20.2975602736362[/C][C]-0.00756027363622636[/C][/ROW]
[ROW][C]110[/C][C]19.36[/C][C]19.3420123035072[/C][C]0.0179876964928205[/C][/ROW]
[ROW][C]111[/C][C]18.74[/C][C]19.0419942751055[/C][C]-0.301994275105546[/C][/ROW]
[ROW][C]112[/C][C]18.87[/C][C]19.0247659626135[/C][C]-0.154765962613478[/C][/ROW]
[ROW][C]113[/C][C]18.87[/C][C]19.1707321350768[/C][C]-0.300732135076778[/C][/ROW]
[ROW][C]114[/C][C]18.91[/C][C]19.3426550929002[/C][C]-0.43265509290018[/C][/ROW]
[ROW][C]115[/C][C]19.31[/C][C]19.4930379739120[/C][C]-0.183037973912040[/C][/ROW]
[ROW][C]116[/C][C]20.06[/C][C]20.2638669442370[/C][C]-0.203866944236960[/C][/ROW]
[ROW][C]117[/C][C]20.72[/C][C]19.8396260745132[/C][C]0.880373925486779[/C][/ROW]
[ROW][C]118[/C][C]20.42[/C][C]20.3382199175224[/C][C]0.081780082477632[/C][/ROW]
[ROW][C]119[/C][C]20.58[/C][C]20.7368883577538[/C][C]-0.15688835775385[/C][/ROW]
[ROW][C]120[/C][C]20.58[/C][C]20.2689537763939[/C][C]0.311046223606109[/C][/ROW]
[ROW][C]121[/C][C]21.18[/C][C]20.9176303002009[/C][C]0.262369699799141[/C][/ROW]
[ROW][C]122[/C][C]19.87[/C][C]20.0406803843038[/C][C]-0.170680384303758[/C][/ROW]
[ROW][C]123[/C][C]19.83[/C][C]19.4930507727502[/C][C]0.336949227249828[/C][/ROW]
[ROW][C]124[/C][C]19.48[/C][C]19.8416369217171[/C][C]-0.361636921717107[/C][/ROW]
[ROW][C]125[/C][C]19.49[/C][C]19.8436897697541[/C][C]-0.353689769754098[/C][/ROW]
[ROW][C]126[/C][C]19.4[/C][C]19.9475753366679[/C][C]-0.547575336667904[/C][/ROW]
[ROW][C]127[/C][C]19.89[/C][C]20.1393742194867[/C][C]-0.249374219486661[/C][/ROW]
[ROW][C]128[/C][C]20.44[/C][C]20.8851028594458[/C][C]-0.445102859445761[/C][/ROW]
[ROW][C]129[/C][C]20.07[/C][C]20.7039113347433[/C][C]-0.633911334743274[/C][/ROW]
[ROW][C]130[/C][C]19.75[/C][C]20.0860800097087[/C][C]-0.336080009708688[/C][/ROW]
[ROW][C]131[/C][C]19.54[/C][C]20.0380452364186[/C][C]-0.498045236418633[/C][/ROW]
[ROW][C]132[/C][C]19.07[/C][C]19.4085519085413[/C][C]-0.338551908541341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42793&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
1313.2512.6539197346210.596080265378989
1412.5412.25699664949640.283003350503645
1512.7712.65908970316780.110910296832230
1612.9612.94831276976280.0116872302372268
171313.0220852317476-0.0220852317476012
1813.6113.6147159025095-0.00471590250949383
1913.813.8609842107814-0.0609842107813989
2014.1613.86050758014460.299492419855431
2114.2714.8243506935806-0.554350693580581
2214.6914.44919880861560.240801191384367
2315.0115.1167772122287-0.106777212228696
2415.0914.15217787676870.937822123231348
2515.1416.0103777873678-0.87037778736779
2614.214.6735890306251-0.473589030625059
2713.8314.6445012348439-0.814501234843888
2814.3114.3853483127609-0.0753483127608661
2914.0414.2990182191282-0.259018219128231
3014.914.71310553521710.186894464782881
3114.9214.9292764810236-0.00927648102361367
3215.3614.98165411407530.3783458859247
3315.515.5982526686552-0.0982526686552312
3415.6515.6543455758710-0.00434557587102091
3516.1816.01772185987780.162278140122247
3615.4415.43142414655850.00857585344152056
3715.5816.0895502007709-0.509550200770947
3815.2414.92361342164390.316386578356092
3915.3315.07555703007890.254442969921053
4016.0715.62480071498000.445199285020028
4115.8215.7486027256720.0713972743280014
4215.8716.6352319471215-0.765231947121494
4315.7216.3611111036762-0.641111103676197
4417.0716.24749826171570.822501738284338
4516.8316.917836124607-0.0878361246069908
4617.5217.02364900213580.496350997864212
4717.7617.75286736687860.00713263312136547
4817.3616.98840553609090.371594463909055
4917.9517.71955935824150.230440641758491
5016.7117.1946888973513-0.48468889735134
5117.1416.98866133003070.151338669969302
5216.7217.6423396096089-0.922339609608947
5317.2616.92378215746910.336217842530939
5417.2417.6221348011800-0.382134801180047
5517.6917.55740530867130.132594691328741
5618.1318.4378311485022-0.307831148502228
5718.0818.2148297569720-0.134829756972028
5818.1818.4900082689929-0.31000826899286
5918.1818.5890863468764-0.409086346876393
6017.6417.62023641797530.0197635820246767
6117.8918.0030216263282-0.113021626328223
6216.8216.9021048390842-0.0821048390841916
6316.6116.9817522037394-0.37175220373943
6416.6616.8337121745102-0.173712174510214
6517.0216.79597650213310.224023497866892
6616.9117.0542823246001-0.144282324600134
6717.1817.17035200476320.00964799523681137
6818.0617.69655305423730.363446945762703
6917.5817.7695492764780-0.189549276478036
7017.4817.8694792625431-0.389479262543137
7117.5417.8026563417840-0.262656341783977
7217.4417.00114311274190.438856887258133
7317.7917.47367884193570.316321158064323
7416.7916.58095483509850.209045164901493
7516.1916.6907879978106-0.500787997810566
7616.6216.54639497056150.073605029438454
7716.3916.7740268297144-0.384026829714369
7816.5416.5876713347055-0.0476713347055444
7917.2616.772986592960.487013407040003
801817.64554213454480.354457865455206
8117.2917.5241602188327-0.234160218832717
8218.1617.53215057114830.627849428851711
8317.8218.0540695375838-0.234069537583849
8417.4817.5823081803749-0.102308180374898
8518.3117.80002541580020.509974584199846
8617.0416.98556317129160.0544368287083898
8717.0316.79722320282390.232776797176061
8816.9717.2957964015063-0.325796401506281
8917.1117.2340747384349-0.124074738434860
9017.1217.3728886947149-0.252888694714855
9117.6917.7388732154873-0.0488732154873048
9218.518.36530246555930.134697534440697
9318.2717.93050648144850.339493518551457
9418.4518.5827839427230-0.132783942722952
9518.3518.4428550695268-0.0928550695268093
9618.0318.0850429512244-0.0550429512244115
9718.4918.5733969603524-0.083396960352406
9818.0717.27639884550620.793601154493786
9917.817.51090478254530.289095217454715
10017.8817.86773907009580.0122609299041692
10118.1218.0931451563350.0268548436649958
10218.6818.32450290632180.355497093678242
10318.819.1932883024889-0.393288302488916
10419.6419.8673950560483-0.227395056048291
10519.5619.36975873986740.190241260132566
10619.319.8544358722569-0.554435872256892
10720.0719.55258132395020.517418676049843
10819.8219.52712986483970.292870135160292
10920.2920.2975602736362-0.00756027363622636
11019.3619.34201230350720.0179876964928205
11118.7419.0419942751055-0.301994275105546
11218.8719.0247659626135-0.154765962613478
11318.8719.1707321350768-0.300732135076778
11418.9119.3426550929002-0.43265509290018
11519.3119.4930379739120-0.183037973912040
11620.0620.2638669442370-0.203866944236960
11720.7219.83962607451320.880373925486779
11820.4220.33821991752240.081780082477632
11920.5820.7368883577538-0.15688835775385
12020.5820.26895377639390.311046223606109
12121.1820.91763030020090.262369699799141
12219.8720.0406803843038-0.170680384303758
12319.8319.49305077275020.336949227249828
12419.4819.8416369217171-0.361636921717107
12519.4919.8436897697541-0.353689769754098
12619.419.9475753366679-0.547575336667904
12719.8920.1393742194867-0.249374219486661
12820.4420.8851028594458-0.445102859445761
12920.0720.7039113347433-0.633911334743274
13019.7520.0860800097087-0.336080009708688
13119.5420.0380452364186-0.498045236418633
13219.0719.4085519085413-0.338551908541341







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13319.483036428147518.89183730364520.0742355526500
13418.191195843142617.50034387155118.8820478147342
13517.716408542156116.913220504040318.5195965802719
13617.433475408386616.50809832631918.3588524904541
13717.376870364192416.314334228459118.4394064999258
13817.361017791009716.151084649941518.5709509320780
13917.691364340549416.303476888511119.0792517925878
14018.240141685552916.643873130195619.8364102409103
14118.073522492466416.31289014675819.8341548381748
14217.791416994417115.872704069933919.7101299189004
14317.767435595527515.659902156364819.8749690346902
14417.422073943508212.642198577901922.2019493091146

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 19.4830364281475 & 18.891837303645 & 20.0742355526500 \tabularnewline
134 & 18.1911958431426 & 17.500343871551 & 18.8820478147342 \tabularnewline
135 & 17.7164085421561 & 16.9132205040403 & 18.5195965802719 \tabularnewline
136 & 17.4334754083866 & 16.508098326319 & 18.3588524904541 \tabularnewline
137 & 17.3768703641924 & 16.3143342284591 & 18.4394064999258 \tabularnewline
138 & 17.3610177910097 & 16.1510846499415 & 18.5709509320780 \tabularnewline
139 & 17.6913643405494 & 16.3034768885111 & 19.0792517925878 \tabularnewline
140 & 18.2401416855529 & 16.6438731301956 & 19.8364102409103 \tabularnewline
141 & 18.0735224924664 & 16.312890146758 & 19.8341548381748 \tabularnewline
142 & 17.7914169944171 & 15.8727040699339 & 19.7101299189004 \tabularnewline
143 & 17.7674355955275 & 15.6599021563648 & 19.8749690346902 \tabularnewline
144 & 17.4220739435082 & 12.6421985779019 & 22.2019493091146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42793&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]133[/C][C]19.4830364281475[/C][C]18.891837303645[/C][C]20.0742355526500[/C][/ROW]
[ROW][C]134[/C][C]18.1911958431426[/C][C]17.500343871551[/C][C]18.8820478147342[/C][/ROW]
[ROW][C]135[/C][C]17.7164085421561[/C][C]16.9132205040403[/C][C]18.5195965802719[/C][/ROW]
[ROW][C]136[/C][C]17.4334754083866[/C][C]16.508098326319[/C][C]18.3588524904541[/C][/ROW]
[ROW][C]137[/C][C]17.3768703641924[/C][C]16.3143342284591[/C][C]18.4394064999258[/C][/ROW]
[ROW][C]138[/C][C]17.3610177910097[/C][C]16.1510846499415[/C][C]18.5709509320780[/C][/ROW]
[ROW][C]139[/C][C]17.6913643405494[/C][C]16.3034768885111[/C][C]19.0792517925878[/C][/ROW]
[ROW][C]140[/C][C]18.2401416855529[/C][C]16.6438731301956[/C][C]19.8364102409103[/C][/ROW]
[ROW][C]141[/C][C]18.0735224924664[/C][C]16.312890146758[/C][C]19.8341548381748[/C][/ROW]
[ROW][C]142[/C][C]17.7914169944171[/C][C]15.8727040699339[/C][C]19.7101299189004[/C][/ROW]
[ROW][C]143[/C][C]17.7674355955275[/C][C]15.6599021563648[/C][C]19.8749690346902[/C][/ROW]
[ROW][C]144[/C][C]17.4220739435082[/C][C]12.6421985779019[/C][C]22.2019493091146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42793&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42793&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
13319.483036428147518.89183730364520.0742355526500
13418.191195843142617.50034387155118.8820478147342
13517.716408542156116.913220504040318.5195965802719
13617.433475408386616.50809832631918.3588524904541
13717.376870364192416.314334228459118.4394064999258
13817.361017791009716.151084649941518.5709509320780
13917.691364340549416.303476888511119.0792517925878
14018.240141685552916.643873130195619.8364102409103
14118.073522492466416.31289014675819.8341548381748
14217.791416994417115.872704069933919.7101299189004
14317.767435595527515.659902156364819.8749690346902
14417.422073943508212.642198577901922.2019493091146



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')