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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 16:12:54 -0400
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/Aug/18/t1313699160rfu1vnaz0guzqxw.htm/, Retrieved Wed, 15 May 2024 20:21:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124151, Retrieved Wed, 15 May 2024 20:21:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMorel Sarah
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2011-08-18 20:12:54] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
240
150
290
210
240
240
310
310
190
230
260
320
270
250
240
250
230
230
240
300
190
270
300
330
230
260
300
330
190
260
240
270
170
230
270
320
190
300
310
360
170
280
270
260
280
300
320
370
210
310
290
450
190
290
280
310
340
220
390
410
250
310
280
450
210
390
300
310
370
250
440
360
290
300
340
600
220
410
360
250
410
290
470
350
330
250
270
580
260
450
320
240
420
380
400
370
300
310
280
560
280
480
320
170
420
310
470
420




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124151&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124151&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00717809126965481
beta1
gamma0.860544926544602

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00717809126965481 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.860544926544602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124151&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]0.00717809126965481[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.860544926544602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124151&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
alpha0.00717809126965481
beta1
gamma0.860544926544602







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13270268.4054487179491.59455128205127
14250251.710683044565-1.7106830445648
15240242.063245991823-2.06324599182284
16250250.315134708693-0.315134708692739
17230226.9106427955353.08935720446544
18230224.8027643240345.19723567596591
19240312.330655961953-72.3306559619527
20300305.866182600995-5.86618260099488
21190183.170022635236.8299773647696
22270223.11402306536846.8859769346316
23300252.01543427135347.9845657286469
24330313.35250217363716.6474978263626
25230268.446460362162-38.4464603621625
26260248.68275756104311.3172424389567
27300238.96350021041861.0364997895818
28330249.75067299931680.2493270006841
29190231.000285910814-41.0002859108142
30260231.22746939318928.7725306068106
31240253.707111494035-13.707111494035
32270305.889221522133-35.8892215221325
33170195.049904901386-25.0499049013862
34230269.983950898256-39.9839508982561
35270299.573164294261-29.5731642942612
36320333.396179241152-13.396179241152
37190240.80436499548-50.8043649954801
38300262.98014874095837.0198512590417
39310295.62010268397714.3798973160228
40360321.84846706437738.1515329356225
41170198.263219413018-28.2632194130184
42280257.3440033708922.6559966291098
43270242.59311558412427.4068844158763
44260275.520399763602-15.5203997636025
45280173.636001307625106.363998692375
46300237.24542562088962.7545743791111
47320277.69545966495742.3045403350431
48370327.60017280596542.3998271940351
49210205.5936821596554.40631784034471
50310305.7414341899134.25856581008679
51290321.10968578917-31.1096857891703
52450369.30102485648880.6989751435116
53190191.563748142585-1.56374814258459
54290296.816767168748-6.81676716874796
55280288.178611180967-8.17861118096664
56310286.18461589179723.8153841082032
57340291.00888961877848.9911103812223
58220318.828371984108-98.8283719841078
59390341.36721625832148.6327837416787
60410392.16470796505617.8352920349437
61250238.11107504732211.8889249526783
62310338.829631517904-28.8296315179037
63280324.148693797623-44.1486937976228
64450468.084386555848-18.0843865558483
65210218.958554203089-8.95855420308888
66390319.22054835076670.779451649234
67300310.082928415042-10.0829284150422
68310335.50329463761-25.5032946376095
69370361.2222614000618.77773859993914
70250261.911594679769-11.9115946797685
71440411.13502407980828.8649759201921
72360435.410955581409-75.4109555814085
73290274.87099951292215.1290004870777
74300340.110837110297-40.1108371102972
75340311.466479320728.5335206792996
76600477.919789385039122.080210614961
77220238.33039482808-18.3303948280796
78410407.3169399626052.68306003739474
79360328.78173124096731.2182687590329
80250341.797791409775-91.7977914097748
81410396.32753058138713.672469418613
82290279.40885965439610.5911403456039
83470463.8266959415886.17330405841153
84350398.881546557737-48.8815465577367
85330316.10868581342713.8913141865726
86250334.357849926958-84.3578499269584
87270363.93915915543-93.9391591554304
88580608.453257324448-28.4532573244476
89260245.75709203207514.2429079679247
90450431.1005660806218.89943391938
91320375.347622075516-55.3476220755159
92240280.306255863721-40.3062558637206
93420423.350536718074-3.35053671807384
94380301.58942196267578.4105780373254
95400481.118766536602-81.1187665366019
96370366.2824930333673.71750696663315
97300335.668429427031-35.6684294270311
98310267.41529891538242.5847010846176
99280288.427433436356-8.42743343635607
100560588.823785832203-28.8237858322033
101280261.91992606277718.0800739372229
102480450.61360725030229.3863927496984
103320330.921195372611-10.9211953726111
104170248.788036724724-78.7880367247242
105420422.592095469972-2.59209546997192
106310370.158162469354-60.1581624693543
107470410.86911396862859.130886031372
108420369.00068539438350.9993146056166

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 270 & 268.405448717949 & 1.59455128205127 \tabularnewline
14 & 250 & 251.710683044565 & -1.7106830445648 \tabularnewline
15 & 240 & 242.063245991823 & -2.06324599182284 \tabularnewline
16 & 250 & 250.315134708693 & -0.315134708692739 \tabularnewline
17 & 230 & 226.910642795535 & 3.08935720446544 \tabularnewline
18 & 230 & 224.802764324034 & 5.19723567596591 \tabularnewline
19 & 240 & 312.330655961953 & -72.3306559619527 \tabularnewline
20 & 300 & 305.866182600995 & -5.86618260099488 \tabularnewline
21 & 190 & 183.17002263523 & 6.8299773647696 \tabularnewline
22 & 270 & 223.114023065368 & 46.8859769346316 \tabularnewline
23 & 300 & 252.015434271353 & 47.9845657286469 \tabularnewline
24 & 330 & 313.352502173637 & 16.6474978263626 \tabularnewline
25 & 230 & 268.446460362162 & -38.4464603621625 \tabularnewline
26 & 260 & 248.682757561043 & 11.3172424389567 \tabularnewline
27 & 300 & 238.963500210418 & 61.0364997895818 \tabularnewline
28 & 330 & 249.750672999316 & 80.2493270006841 \tabularnewline
29 & 190 & 231.000285910814 & -41.0002859108142 \tabularnewline
30 & 260 & 231.227469393189 & 28.7725306068106 \tabularnewline
31 & 240 & 253.707111494035 & -13.707111494035 \tabularnewline
32 & 270 & 305.889221522133 & -35.8892215221325 \tabularnewline
33 & 170 & 195.049904901386 & -25.0499049013862 \tabularnewline
34 & 230 & 269.983950898256 & -39.9839508982561 \tabularnewline
35 & 270 & 299.573164294261 & -29.5731642942612 \tabularnewline
36 & 320 & 333.396179241152 & -13.396179241152 \tabularnewline
37 & 190 & 240.80436499548 & -50.8043649954801 \tabularnewline
38 & 300 & 262.980148740958 & 37.0198512590417 \tabularnewline
39 & 310 & 295.620102683977 & 14.3798973160228 \tabularnewline
40 & 360 & 321.848467064377 & 38.1515329356225 \tabularnewline
41 & 170 & 198.263219413018 & -28.2632194130184 \tabularnewline
42 & 280 & 257.34400337089 & 22.6559966291098 \tabularnewline
43 & 270 & 242.593115584124 & 27.4068844158763 \tabularnewline
44 & 260 & 275.520399763602 & -15.5203997636025 \tabularnewline
45 & 280 & 173.636001307625 & 106.363998692375 \tabularnewline
46 & 300 & 237.245425620889 & 62.7545743791111 \tabularnewline
47 & 320 & 277.695459664957 & 42.3045403350431 \tabularnewline
48 & 370 & 327.600172805965 & 42.3998271940351 \tabularnewline
49 & 210 & 205.593682159655 & 4.40631784034471 \tabularnewline
50 & 310 & 305.741434189913 & 4.25856581008679 \tabularnewline
51 & 290 & 321.10968578917 & -31.1096857891703 \tabularnewline
52 & 450 & 369.301024856488 & 80.6989751435116 \tabularnewline
53 & 190 & 191.563748142585 & -1.56374814258459 \tabularnewline
54 & 290 & 296.816767168748 & -6.81676716874796 \tabularnewline
55 & 280 & 288.178611180967 & -8.17861118096664 \tabularnewline
56 & 310 & 286.184615891797 & 23.8153841082032 \tabularnewline
57 & 340 & 291.008889618778 & 48.9911103812223 \tabularnewline
58 & 220 & 318.828371984108 & -98.8283719841078 \tabularnewline
59 & 390 & 341.367216258321 & 48.6327837416787 \tabularnewline
60 & 410 & 392.164707965056 & 17.8352920349437 \tabularnewline
61 & 250 & 238.111075047322 & 11.8889249526783 \tabularnewline
62 & 310 & 338.829631517904 & -28.8296315179037 \tabularnewline
63 & 280 & 324.148693797623 & -44.1486937976228 \tabularnewline
64 & 450 & 468.084386555848 & -18.0843865558483 \tabularnewline
65 & 210 & 218.958554203089 & -8.95855420308888 \tabularnewline
66 & 390 & 319.220548350766 & 70.779451649234 \tabularnewline
67 & 300 & 310.082928415042 & -10.0829284150422 \tabularnewline
68 & 310 & 335.50329463761 & -25.5032946376095 \tabularnewline
69 & 370 & 361.222261400061 & 8.77773859993914 \tabularnewline
70 & 250 & 261.911594679769 & -11.9115946797685 \tabularnewline
71 & 440 & 411.135024079808 & 28.8649759201921 \tabularnewline
72 & 360 & 435.410955581409 & -75.4109555814085 \tabularnewline
73 & 290 & 274.870999512922 & 15.1290004870777 \tabularnewline
74 & 300 & 340.110837110297 & -40.1108371102972 \tabularnewline
75 & 340 & 311.4664793207 & 28.5335206792996 \tabularnewline
76 & 600 & 477.919789385039 & 122.080210614961 \tabularnewline
77 & 220 & 238.33039482808 & -18.3303948280796 \tabularnewline
78 & 410 & 407.316939962605 & 2.68306003739474 \tabularnewline
79 & 360 & 328.781731240967 & 31.2182687590329 \tabularnewline
80 & 250 & 341.797791409775 & -91.7977914097748 \tabularnewline
81 & 410 & 396.327530581387 & 13.672469418613 \tabularnewline
82 & 290 & 279.408859654396 & 10.5911403456039 \tabularnewline
83 & 470 & 463.826695941588 & 6.17330405841153 \tabularnewline
84 & 350 & 398.881546557737 & -48.8815465577367 \tabularnewline
85 & 330 & 316.108685813427 & 13.8913141865726 \tabularnewline
86 & 250 & 334.357849926958 & -84.3578499269584 \tabularnewline
87 & 270 & 363.93915915543 & -93.9391591554304 \tabularnewline
88 & 580 & 608.453257324448 & -28.4532573244476 \tabularnewline
89 & 260 & 245.757092032075 & 14.2429079679247 \tabularnewline
90 & 450 & 431.10056608062 & 18.89943391938 \tabularnewline
91 & 320 & 375.347622075516 & -55.3476220755159 \tabularnewline
92 & 240 & 280.306255863721 & -40.3062558637206 \tabularnewline
93 & 420 & 423.350536718074 & -3.35053671807384 \tabularnewline
94 & 380 & 301.589421962675 & 78.4105780373254 \tabularnewline
95 & 400 & 481.118766536602 & -81.1187665366019 \tabularnewline
96 & 370 & 366.282493033367 & 3.71750696663315 \tabularnewline
97 & 300 & 335.668429427031 & -35.6684294270311 \tabularnewline
98 & 310 & 267.415298915382 & 42.5847010846176 \tabularnewline
99 & 280 & 288.427433436356 & -8.42743343635607 \tabularnewline
100 & 560 & 588.823785832203 & -28.8237858322033 \tabularnewline
101 & 280 & 261.919926062777 & 18.0800739372229 \tabularnewline
102 & 480 & 450.613607250302 & 29.3863927496984 \tabularnewline
103 & 320 & 330.921195372611 & -10.9211953726111 \tabularnewline
104 & 170 & 248.788036724724 & -78.7880367247242 \tabularnewline
105 & 420 & 422.592095469972 & -2.59209546997192 \tabularnewline
106 & 310 & 370.158162469354 & -60.1581624693543 \tabularnewline
107 & 470 & 410.869113968628 & 59.130886031372 \tabularnewline
108 & 420 & 369.000685394383 & 50.9993146056166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124151&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]270[/C][C]268.405448717949[/C][C]1.59455128205127[/C][/ROW]
[ROW][C]14[/C][C]250[/C][C]251.710683044565[/C][C]-1.7106830445648[/C][/ROW]
[ROW][C]15[/C][C]240[/C][C]242.063245991823[/C][C]-2.06324599182284[/C][/ROW]
[ROW][C]16[/C][C]250[/C][C]250.315134708693[/C][C]-0.315134708692739[/C][/ROW]
[ROW][C]17[/C][C]230[/C][C]226.910642795535[/C][C]3.08935720446544[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]224.802764324034[/C][C]5.19723567596591[/C][/ROW]
[ROW][C]19[/C][C]240[/C][C]312.330655961953[/C][C]-72.3306559619527[/C][/ROW]
[ROW][C]20[/C][C]300[/C][C]305.866182600995[/C][C]-5.86618260099488[/C][/ROW]
[ROW][C]21[/C][C]190[/C][C]183.17002263523[/C][C]6.8299773647696[/C][/ROW]
[ROW][C]22[/C][C]270[/C][C]223.114023065368[/C][C]46.8859769346316[/C][/ROW]
[ROW][C]23[/C][C]300[/C][C]252.015434271353[/C][C]47.9845657286469[/C][/ROW]
[ROW][C]24[/C][C]330[/C][C]313.352502173637[/C][C]16.6474978263626[/C][/ROW]
[ROW][C]25[/C][C]230[/C][C]268.446460362162[/C][C]-38.4464603621625[/C][/ROW]
[ROW][C]26[/C][C]260[/C][C]248.682757561043[/C][C]11.3172424389567[/C][/ROW]
[ROW][C]27[/C][C]300[/C][C]238.963500210418[/C][C]61.0364997895818[/C][/ROW]
[ROW][C]28[/C][C]330[/C][C]249.750672999316[/C][C]80.2493270006841[/C][/ROW]
[ROW][C]29[/C][C]190[/C][C]231.000285910814[/C][C]-41.0002859108142[/C][/ROW]
[ROW][C]30[/C][C]260[/C][C]231.227469393189[/C][C]28.7725306068106[/C][/ROW]
[ROW][C]31[/C][C]240[/C][C]253.707111494035[/C][C]-13.707111494035[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]305.889221522133[/C][C]-35.8892215221325[/C][/ROW]
[ROW][C]33[/C][C]170[/C][C]195.049904901386[/C][C]-25.0499049013862[/C][/ROW]
[ROW][C]34[/C][C]230[/C][C]269.983950898256[/C][C]-39.9839508982561[/C][/ROW]
[ROW][C]35[/C][C]270[/C][C]299.573164294261[/C][C]-29.5731642942612[/C][/ROW]
[ROW][C]36[/C][C]320[/C][C]333.396179241152[/C][C]-13.396179241152[/C][/ROW]
[ROW][C]37[/C][C]190[/C][C]240.80436499548[/C][C]-50.8043649954801[/C][/ROW]
[ROW][C]38[/C][C]300[/C][C]262.980148740958[/C][C]37.0198512590417[/C][/ROW]
[ROW][C]39[/C][C]310[/C][C]295.620102683977[/C][C]14.3798973160228[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]321.848467064377[/C][C]38.1515329356225[/C][/ROW]
[ROW][C]41[/C][C]170[/C][C]198.263219413018[/C][C]-28.2632194130184[/C][/ROW]
[ROW][C]42[/C][C]280[/C][C]257.34400337089[/C][C]22.6559966291098[/C][/ROW]
[ROW][C]43[/C][C]270[/C][C]242.593115584124[/C][C]27.4068844158763[/C][/ROW]
[ROW][C]44[/C][C]260[/C][C]275.520399763602[/C][C]-15.5203997636025[/C][/ROW]
[ROW][C]45[/C][C]280[/C][C]173.636001307625[/C][C]106.363998692375[/C][/ROW]
[ROW][C]46[/C][C]300[/C][C]237.245425620889[/C][C]62.7545743791111[/C][/ROW]
[ROW][C]47[/C][C]320[/C][C]277.695459664957[/C][C]42.3045403350431[/C][/ROW]
[ROW][C]48[/C][C]370[/C][C]327.600172805965[/C][C]42.3998271940351[/C][/ROW]
[ROW][C]49[/C][C]210[/C][C]205.593682159655[/C][C]4.40631784034471[/C][/ROW]
[ROW][C]50[/C][C]310[/C][C]305.741434189913[/C][C]4.25856581008679[/C][/ROW]
[ROW][C]51[/C][C]290[/C][C]321.10968578917[/C][C]-31.1096857891703[/C][/ROW]
[ROW][C]52[/C][C]450[/C][C]369.301024856488[/C][C]80.6989751435116[/C][/ROW]
[ROW][C]53[/C][C]190[/C][C]191.563748142585[/C][C]-1.56374814258459[/C][/ROW]
[ROW][C]54[/C][C]290[/C][C]296.816767168748[/C][C]-6.81676716874796[/C][/ROW]
[ROW][C]55[/C][C]280[/C][C]288.178611180967[/C][C]-8.17861118096664[/C][/ROW]
[ROW][C]56[/C][C]310[/C][C]286.184615891797[/C][C]23.8153841082032[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]291.008889618778[/C][C]48.9911103812223[/C][/ROW]
[ROW][C]58[/C][C]220[/C][C]318.828371984108[/C][C]-98.8283719841078[/C][/ROW]
[ROW][C]59[/C][C]390[/C][C]341.367216258321[/C][C]48.6327837416787[/C][/ROW]
[ROW][C]60[/C][C]410[/C][C]392.164707965056[/C][C]17.8352920349437[/C][/ROW]
[ROW][C]61[/C][C]250[/C][C]238.111075047322[/C][C]11.8889249526783[/C][/ROW]
[ROW][C]62[/C][C]310[/C][C]338.829631517904[/C][C]-28.8296315179037[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]324.148693797623[/C][C]-44.1486937976228[/C][/ROW]
[ROW][C]64[/C][C]450[/C][C]468.084386555848[/C][C]-18.0843865558483[/C][/ROW]
[ROW][C]65[/C][C]210[/C][C]218.958554203089[/C][C]-8.95855420308888[/C][/ROW]
[ROW][C]66[/C][C]390[/C][C]319.220548350766[/C][C]70.779451649234[/C][/ROW]
[ROW][C]67[/C][C]300[/C][C]310.082928415042[/C][C]-10.0829284150422[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]335.50329463761[/C][C]-25.5032946376095[/C][/ROW]
[ROW][C]69[/C][C]370[/C][C]361.222261400061[/C][C]8.77773859993914[/C][/ROW]
[ROW][C]70[/C][C]250[/C][C]261.911594679769[/C][C]-11.9115946797685[/C][/ROW]
[ROW][C]71[/C][C]440[/C][C]411.135024079808[/C][C]28.8649759201921[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]435.410955581409[/C][C]-75.4109555814085[/C][/ROW]
[ROW][C]73[/C][C]290[/C][C]274.870999512922[/C][C]15.1290004870777[/C][/ROW]
[ROW][C]74[/C][C]300[/C][C]340.110837110297[/C][C]-40.1108371102972[/C][/ROW]
[ROW][C]75[/C][C]340[/C][C]311.4664793207[/C][C]28.5335206792996[/C][/ROW]
[ROW][C]76[/C][C]600[/C][C]477.919789385039[/C][C]122.080210614961[/C][/ROW]
[ROW][C]77[/C][C]220[/C][C]238.33039482808[/C][C]-18.3303948280796[/C][/ROW]
[ROW][C]78[/C][C]410[/C][C]407.316939962605[/C][C]2.68306003739474[/C][/ROW]
[ROW][C]79[/C][C]360[/C][C]328.781731240967[/C][C]31.2182687590329[/C][/ROW]
[ROW][C]80[/C][C]250[/C][C]341.797791409775[/C][C]-91.7977914097748[/C][/ROW]
[ROW][C]81[/C][C]410[/C][C]396.327530581387[/C][C]13.672469418613[/C][/ROW]
[ROW][C]82[/C][C]290[/C][C]279.408859654396[/C][C]10.5911403456039[/C][/ROW]
[ROW][C]83[/C][C]470[/C][C]463.826695941588[/C][C]6.17330405841153[/C][/ROW]
[ROW][C]84[/C][C]350[/C][C]398.881546557737[/C][C]-48.8815465577367[/C][/ROW]
[ROW][C]85[/C][C]330[/C][C]316.108685813427[/C][C]13.8913141865726[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]334.357849926958[/C][C]-84.3578499269584[/C][/ROW]
[ROW][C]87[/C][C]270[/C][C]363.93915915543[/C][C]-93.9391591554304[/C][/ROW]
[ROW][C]88[/C][C]580[/C][C]608.453257324448[/C][C]-28.4532573244476[/C][/ROW]
[ROW][C]89[/C][C]260[/C][C]245.757092032075[/C][C]14.2429079679247[/C][/ROW]
[ROW][C]90[/C][C]450[/C][C]431.10056608062[/C][C]18.89943391938[/C][/ROW]
[ROW][C]91[/C][C]320[/C][C]375.347622075516[/C][C]-55.3476220755159[/C][/ROW]
[ROW][C]92[/C][C]240[/C][C]280.306255863721[/C][C]-40.3062558637206[/C][/ROW]
[ROW][C]93[/C][C]420[/C][C]423.350536718074[/C][C]-3.35053671807384[/C][/ROW]
[ROW][C]94[/C][C]380[/C][C]301.589421962675[/C][C]78.4105780373254[/C][/ROW]
[ROW][C]95[/C][C]400[/C][C]481.118766536602[/C][C]-81.1187665366019[/C][/ROW]
[ROW][C]96[/C][C]370[/C][C]366.282493033367[/C][C]3.71750696663315[/C][/ROW]
[ROW][C]97[/C][C]300[/C][C]335.668429427031[/C][C]-35.6684294270311[/C][/ROW]
[ROW][C]98[/C][C]310[/C][C]267.415298915382[/C][C]42.5847010846176[/C][/ROW]
[ROW][C]99[/C][C]280[/C][C]288.427433436356[/C][C]-8.42743343635607[/C][/ROW]
[ROW][C]100[/C][C]560[/C][C]588.823785832203[/C][C]-28.8237858322033[/C][/ROW]
[ROW][C]101[/C][C]280[/C][C]261.919926062777[/C][C]18.0800739372229[/C][/ROW]
[ROW][C]102[/C][C]480[/C][C]450.613607250302[/C][C]29.3863927496984[/C][/ROW]
[ROW][C]103[/C][C]320[/C][C]330.921195372611[/C][C]-10.9211953726111[/C][/ROW]
[ROW][C]104[/C][C]170[/C][C]248.788036724724[/C][C]-78.7880367247242[/C][/ROW]
[ROW][C]105[/C][C]420[/C][C]422.592095469972[/C][C]-2.59209546997192[/C][/ROW]
[ROW][C]106[/C][C]310[/C][C]370.158162469354[/C][C]-60.1581624693543[/C][/ROW]
[ROW][C]107[/C][C]470[/C][C]410.869113968628[/C][C]59.130886031372[/C][/ROW]
[ROW][C]108[/C][C]420[/C][C]369.000685394383[/C][C]50.9993146056166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124151&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
13270268.4054487179491.59455128205127
14250251.710683044565-1.7106830445648
15240242.063245991823-2.06324599182284
16250250.315134708693-0.315134708692739
17230226.9106427955353.08935720446544
18230224.8027643240345.19723567596591
19240312.330655961953-72.3306559619527
20300305.866182600995-5.86618260099488
21190183.170022635236.8299773647696
22270223.11402306536846.8859769346316
23300252.01543427135347.9845657286469
24330313.35250217363716.6474978263626
25230268.446460362162-38.4464603621625
26260248.68275756104311.3172424389567
27300238.96350021041861.0364997895818
28330249.75067299931680.2493270006841
29190231.000285910814-41.0002859108142
30260231.22746939318928.7725306068106
31240253.707111494035-13.707111494035
32270305.889221522133-35.8892215221325
33170195.049904901386-25.0499049013862
34230269.983950898256-39.9839508982561
35270299.573164294261-29.5731642942612
36320333.396179241152-13.396179241152
37190240.80436499548-50.8043649954801
38300262.98014874095837.0198512590417
39310295.62010268397714.3798973160228
40360321.84846706437738.1515329356225
41170198.263219413018-28.2632194130184
42280257.3440033708922.6559966291098
43270242.59311558412427.4068844158763
44260275.520399763602-15.5203997636025
45280173.636001307625106.363998692375
46300237.24542562088962.7545743791111
47320277.69545966495742.3045403350431
48370327.60017280596542.3998271940351
49210205.5936821596554.40631784034471
50310305.7414341899134.25856581008679
51290321.10968578917-31.1096857891703
52450369.30102485648880.6989751435116
53190191.563748142585-1.56374814258459
54290296.816767168748-6.81676716874796
55280288.178611180967-8.17861118096664
56310286.18461589179723.8153841082032
57340291.00888961877848.9911103812223
58220318.828371984108-98.8283719841078
59390341.36721625832148.6327837416787
60410392.16470796505617.8352920349437
61250238.11107504732211.8889249526783
62310338.829631517904-28.8296315179037
63280324.148693797623-44.1486937976228
64450468.084386555848-18.0843865558483
65210218.958554203089-8.95855420308888
66390319.22054835076670.779451649234
67300310.082928415042-10.0829284150422
68310335.50329463761-25.5032946376095
69370361.2222614000618.77773859993914
70250261.911594679769-11.9115946797685
71440411.13502407980828.8649759201921
72360435.410955581409-75.4109555814085
73290274.87099951292215.1290004870777
74300340.110837110297-40.1108371102972
75340311.466479320728.5335206792996
76600477.919789385039122.080210614961
77220238.33039482808-18.3303948280796
78410407.3169399626052.68306003739474
79360328.78173124096731.2182687590329
80250341.797791409775-91.7977914097748
81410396.32753058138713.672469418613
82290279.40885965439610.5911403456039
83470463.8266959415886.17330405841153
84350398.881546557737-48.8815465577367
85330316.10868581342713.8913141865726
86250334.357849926958-84.3578499269584
87270363.93915915543-93.9391591554304
88580608.453257324448-28.4532573244476
89260245.75709203207514.2429079679247
90450431.1005660806218.89943391938
91320375.347622075516-55.3476220755159
92240280.306255863721-40.3062558637206
93420423.350536718074-3.35053671807384
94380301.58942196267578.4105780373254
95400481.118766536602-81.1187665366019
96370366.2824930333673.71750696663315
97300335.668429427031-35.6684294270311
98310267.41529891538242.5847010846176
99280288.427433436356-8.42743343635607
100560588.823785832203-28.8237858322033
101280261.91992606277718.0800739372229
102480450.61360725030229.3863927496984
103320330.921195372611-10.9211953726111
104170248.788036724724-78.7880367247242
105420422.592095469972-2.59209546997192
106310370.158162469354-60.1581624693543
107470410.86911396862859.130886031372
108420369.00068539438350.9993146056166







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109304.895064969802219.342072996513390.448056943091
110303.830084427958218.268276674035389.391892181881
111280.72289652627195.141256586217366.304536466323
112563.583729293217477.966843476346649.200615110088
113276.996794550397191.324866079988362.668723020807
114475.12754539254389.376417570936560.878673214144
115320.482844137358234.62403459074406.341653683976
116180.21938088629494.2201288816191266.21863289097
117420.028447908508333.851776565565506.20511925145
118318.789227786089232.394022784949405.184432787229
119462.639253371803375.980359477693549.298147265913
120413.765102386535326.793438781063500.736765992006

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 304.895064969802 & 219.342072996513 & 390.448056943091 \tabularnewline
110 & 303.830084427958 & 218.268276674035 & 389.391892181881 \tabularnewline
111 & 280.72289652627 & 195.141256586217 & 366.304536466323 \tabularnewline
112 & 563.583729293217 & 477.966843476346 & 649.200615110088 \tabularnewline
113 & 276.996794550397 & 191.324866079988 & 362.668723020807 \tabularnewline
114 & 475.12754539254 & 389.376417570936 & 560.878673214144 \tabularnewline
115 & 320.482844137358 & 234.62403459074 & 406.341653683976 \tabularnewline
116 & 180.219380886294 & 94.2201288816191 & 266.21863289097 \tabularnewline
117 & 420.028447908508 & 333.851776565565 & 506.20511925145 \tabularnewline
118 & 318.789227786089 & 232.394022784949 & 405.184432787229 \tabularnewline
119 & 462.639253371803 & 375.980359477693 & 549.298147265913 \tabularnewline
120 & 413.765102386535 & 326.793438781063 & 500.736765992006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124151&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]304.895064969802[/C][C]219.342072996513[/C][C]390.448056943091[/C][/ROW]
[ROW][C]110[/C][C]303.830084427958[/C][C]218.268276674035[/C][C]389.391892181881[/C][/ROW]
[ROW][C]111[/C][C]280.72289652627[/C][C]195.141256586217[/C][C]366.304536466323[/C][/ROW]
[ROW][C]112[/C][C]563.583729293217[/C][C]477.966843476346[/C][C]649.200615110088[/C][/ROW]
[ROW][C]113[/C][C]276.996794550397[/C][C]191.324866079988[/C][C]362.668723020807[/C][/ROW]
[ROW][C]114[/C][C]475.12754539254[/C][C]389.376417570936[/C][C]560.878673214144[/C][/ROW]
[ROW][C]115[/C][C]320.482844137358[/C][C]234.62403459074[/C][C]406.341653683976[/C][/ROW]
[ROW][C]116[/C][C]180.219380886294[/C][C]94.2201288816191[/C][C]266.21863289097[/C][/ROW]
[ROW][C]117[/C][C]420.028447908508[/C][C]333.851776565565[/C][C]506.20511925145[/C][/ROW]
[ROW][C]118[/C][C]318.789227786089[/C][C]232.394022784949[/C][C]405.184432787229[/C][/ROW]
[ROW][C]119[/C][C]462.639253371803[/C][C]375.980359477693[/C][C]549.298147265913[/C][/ROW]
[ROW][C]120[/C][C]413.765102386535[/C][C]326.793438781063[/C][C]500.736765992006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124151&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124151&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
109304.895064969802219.342072996513390.448056943091
110303.830084427958218.268276674035389.391892181881
111280.72289652627195.141256586217366.304536466323
112563.583729293217477.966843476346649.200615110088
113276.996794550397191.324866079988362.668723020807
114475.12754539254389.376417570936560.878673214144
115320.482844137358234.62403459074406.341653683976
116180.21938088629494.2201288816191266.21863289097
117420.028447908508333.851776565565506.20511925145
118318.789227786089232.394022784949405.184432787229
119462.639253371803375.980359477693549.298147265913
120413.765102386535326.793438781063500.736765992006



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')