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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 May 2012 14:50:43 -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/2012/May/16/t1337194367smgmmugguzr29ri.htm/, Retrieved Wed, 01 May 2024 20:06:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166532, Retrieved Wed, 01 May 2024 20:06:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-16 18:50:43] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
9676
8642
9402
9610
9294
9448
10319
9548
9801
9596
8923
9746
9829
9125
9782
9441
9162
9915
10444
10209
9985
9842
9429
10132
9849
9172
10313
9819
9955
10048
10082
10541
10208
10233
9439
9963
10158
9225
10474
9757
10490
10281
10444
10640
10695
10786
9832
9747
10411
9511
10402
9701
10540
10112
10915
11183
10384
10834
9886
10216
10943
9867
10203
10837
10573
10647
11502
10656
10866
10835
9945
10331
9769
9321
9939
9336
10195
9464
10010
10213
9563
9890
9305
9391
9928
8686
9843
9627
10074
9503
10119
10000
9313
9866
9172
9241




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=166532&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=166532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166532&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
alpha0.23659807589547
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.23659807589547 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166532&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]0.23659807589547[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166532&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
alpha0.23659807589547
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
286429676-1034
394029431.35758952408-29.3575895240847
496109424.41164032976185.588359670242
592949468.32148913633-174.321489136333
694489427.0773602194420.922639780556
7103199432.02761653418886.972383465822
895489641.88357583461-93.8835758346104
998019619.67090243395181.329097566046
1095969662.57301802194-66.5730180219434
1189239646.8219700514-723.821970051396
1297469475.56708464637270.432915353633
1398299539.55099207784289.449007922161
1491259608.03407042207-483.034070422074
1597829493.74913876825288.250861231745
1694419561.9487379109-120.948737910898
1791629533.33249923919-371.332499239194
1899159445.47594440174469.524055598256
19104449556.56443254293887.435567457071
20102099766.52998028448442.470019715523
2199859871.2175355906113.7824644094
2298429898.13824774051-56.1382477405095
2394299884.85604634096-455.856046340961
24101329777.00138289137354.998617108626
2598499860.99337264483-11.9933726448271
2691729858.15576375356-686.155763753564
27103139695.81263028489617.187369715115
2898199841.83797442647-22.8379744264676
2999559836.43455361982118.565446380184
30100489864.48691010106183.513089898945
31100829907.90575407278174.094245927223
32105419949.09611768363591.903882316368
331020810089.1394373547118.860562645257
341023310117.2616177765115.738382223537
35943910144.6450963178-705.645096317807
3699639977.69082426394-14.6908242639402
37101589974.21500350977183.784996490227
38922510017.6981800578-792.698180057816
39104749830.1473158903643.852684109705
4097579982.48162211078-225.481622110785
41104909929.13310416958560.866895830417
421028110061.8331325565219.166867443475
431044410113.6875916937330.312408306312
441064010191.8388719434448.161128056639
451069510297.8729325327397.127067467296
461078610391.8324325815394.167567418523
47983210485.0917206131-653.091720613098
48974710330.5714761328-583.571476132778
491041110192.4995877323218.500412267716
50951110244.1963648572-733.196364857193
511040210070.7235156784331.276484321572
52970110149.1028944583-448.102894458329
531054010043.0826118263496.917388173702
541011210160.6523097472-48.6523097471982
551091510149.1412668731765.858733126859
561118310330.3419695387852.658030461302
571038410532.0792189427-148.079218942663
581083410497.0439606607336.956039339275
59988610576.7671112298-690.767111229756
601021610413.3329418209-197.332941820923
611094310366.6443474753576.3556525247
62986710503.0089858941-636.008985894121
631020310352.5304835793-149.530483579343
641083710317.1518588768519.848141123248
651057310440.1469288243132.85307117565
661064710471.5797098413175.420290158687
671150210513.0838129659988.916187034116
681065610747.05948004-91.0594800400413
691086610725.5149822705140.485017729474
701083510758.753467157576.2465328425387
71994510776.7932501217-831.793250121707
721033110579.9925676001-248.992567600073
73976910521.0814051936-752.081405193623
74932110343.1403918081-1022.14039180805
75993910101.3039418112-162.303941811224
76933610062.9031414684-726.903141468438
77101959890.91925683463304.080743165367
7894649962.86417558442-498.864175584424
79100109844.83387150797165.16612849203
80102139883.91185971229329.088140287711
8195639961.77348050438-398.77348050438
8298909867.424442298922.575557701095
8393059872.76577581325-567.765775813252
8493919738.43348569654-347.433485696538
8599289656.23139147908271.768608520919
8686869720.53132134392-1034.53132134392
8798439475.76320126035367.236798739648
8896279562.6507212401664.3492787598352
89100749577.87563678496.124363219997
9095039695.25770652272-192.25770652272
91101199649.76990308337469.230096916632
92100009760.78884116609239.211158833912
9393139817.38574107892-504.385741078917
9498669698.04904523053167.950954769465
9591729737.7859179738-565.785917973797
9692419603.92205841245-362.922058412445

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 8642 & 9676 & -1034 \tabularnewline
3 & 9402 & 9431.35758952408 & -29.3575895240847 \tabularnewline
4 & 9610 & 9424.41164032976 & 185.588359670242 \tabularnewline
5 & 9294 & 9468.32148913633 & -174.321489136333 \tabularnewline
6 & 9448 & 9427.07736021944 & 20.922639780556 \tabularnewline
7 & 10319 & 9432.02761653418 & 886.972383465822 \tabularnewline
8 & 9548 & 9641.88357583461 & -93.8835758346104 \tabularnewline
9 & 9801 & 9619.67090243395 & 181.329097566046 \tabularnewline
10 & 9596 & 9662.57301802194 & -66.5730180219434 \tabularnewline
11 & 8923 & 9646.8219700514 & -723.821970051396 \tabularnewline
12 & 9746 & 9475.56708464637 & 270.432915353633 \tabularnewline
13 & 9829 & 9539.55099207784 & 289.449007922161 \tabularnewline
14 & 9125 & 9608.03407042207 & -483.034070422074 \tabularnewline
15 & 9782 & 9493.74913876825 & 288.250861231745 \tabularnewline
16 & 9441 & 9561.9487379109 & -120.948737910898 \tabularnewline
17 & 9162 & 9533.33249923919 & -371.332499239194 \tabularnewline
18 & 9915 & 9445.47594440174 & 469.524055598256 \tabularnewline
19 & 10444 & 9556.56443254293 & 887.435567457071 \tabularnewline
20 & 10209 & 9766.52998028448 & 442.470019715523 \tabularnewline
21 & 9985 & 9871.2175355906 & 113.7824644094 \tabularnewline
22 & 9842 & 9898.13824774051 & -56.1382477405095 \tabularnewline
23 & 9429 & 9884.85604634096 & -455.856046340961 \tabularnewline
24 & 10132 & 9777.00138289137 & 354.998617108626 \tabularnewline
25 & 9849 & 9860.99337264483 & -11.9933726448271 \tabularnewline
26 & 9172 & 9858.15576375356 & -686.155763753564 \tabularnewline
27 & 10313 & 9695.81263028489 & 617.187369715115 \tabularnewline
28 & 9819 & 9841.83797442647 & -22.8379744264676 \tabularnewline
29 & 9955 & 9836.43455361982 & 118.565446380184 \tabularnewline
30 & 10048 & 9864.48691010106 & 183.513089898945 \tabularnewline
31 & 10082 & 9907.90575407278 & 174.094245927223 \tabularnewline
32 & 10541 & 9949.09611768363 & 591.903882316368 \tabularnewline
33 & 10208 & 10089.1394373547 & 118.860562645257 \tabularnewline
34 & 10233 & 10117.2616177765 & 115.738382223537 \tabularnewline
35 & 9439 & 10144.6450963178 & -705.645096317807 \tabularnewline
36 & 9963 & 9977.69082426394 & -14.6908242639402 \tabularnewline
37 & 10158 & 9974.21500350977 & 183.784996490227 \tabularnewline
38 & 9225 & 10017.6981800578 & -792.698180057816 \tabularnewline
39 & 10474 & 9830.1473158903 & 643.852684109705 \tabularnewline
40 & 9757 & 9982.48162211078 & -225.481622110785 \tabularnewline
41 & 10490 & 9929.13310416958 & 560.866895830417 \tabularnewline
42 & 10281 & 10061.8331325565 & 219.166867443475 \tabularnewline
43 & 10444 & 10113.6875916937 & 330.312408306312 \tabularnewline
44 & 10640 & 10191.8388719434 & 448.161128056639 \tabularnewline
45 & 10695 & 10297.8729325327 & 397.127067467296 \tabularnewline
46 & 10786 & 10391.8324325815 & 394.167567418523 \tabularnewline
47 & 9832 & 10485.0917206131 & -653.091720613098 \tabularnewline
48 & 9747 & 10330.5714761328 & -583.571476132778 \tabularnewline
49 & 10411 & 10192.4995877323 & 218.500412267716 \tabularnewline
50 & 9511 & 10244.1963648572 & -733.196364857193 \tabularnewline
51 & 10402 & 10070.7235156784 & 331.276484321572 \tabularnewline
52 & 9701 & 10149.1028944583 & -448.102894458329 \tabularnewline
53 & 10540 & 10043.0826118263 & 496.917388173702 \tabularnewline
54 & 10112 & 10160.6523097472 & -48.6523097471982 \tabularnewline
55 & 10915 & 10149.1412668731 & 765.858733126859 \tabularnewline
56 & 11183 & 10330.3419695387 & 852.658030461302 \tabularnewline
57 & 10384 & 10532.0792189427 & -148.079218942663 \tabularnewline
58 & 10834 & 10497.0439606607 & 336.956039339275 \tabularnewline
59 & 9886 & 10576.7671112298 & -690.767111229756 \tabularnewline
60 & 10216 & 10413.3329418209 & -197.332941820923 \tabularnewline
61 & 10943 & 10366.6443474753 & 576.3556525247 \tabularnewline
62 & 9867 & 10503.0089858941 & -636.008985894121 \tabularnewline
63 & 10203 & 10352.5304835793 & -149.530483579343 \tabularnewline
64 & 10837 & 10317.1518588768 & 519.848141123248 \tabularnewline
65 & 10573 & 10440.1469288243 & 132.85307117565 \tabularnewline
66 & 10647 & 10471.5797098413 & 175.420290158687 \tabularnewline
67 & 11502 & 10513.0838129659 & 988.916187034116 \tabularnewline
68 & 10656 & 10747.05948004 & -91.0594800400413 \tabularnewline
69 & 10866 & 10725.5149822705 & 140.485017729474 \tabularnewline
70 & 10835 & 10758.7534671575 & 76.2465328425387 \tabularnewline
71 & 9945 & 10776.7932501217 & -831.793250121707 \tabularnewline
72 & 10331 & 10579.9925676001 & -248.992567600073 \tabularnewline
73 & 9769 & 10521.0814051936 & -752.081405193623 \tabularnewline
74 & 9321 & 10343.1403918081 & -1022.14039180805 \tabularnewline
75 & 9939 & 10101.3039418112 & -162.303941811224 \tabularnewline
76 & 9336 & 10062.9031414684 & -726.903141468438 \tabularnewline
77 & 10195 & 9890.91925683463 & 304.080743165367 \tabularnewline
78 & 9464 & 9962.86417558442 & -498.864175584424 \tabularnewline
79 & 10010 & 9844.83387150797 & 165.16612849203 \tabularnewline
80 & 10213 & 9883.91185971229 & 329.088140287711 \tabularnewline
81 & 9563 & 9961.77348050438 & -398.77348050438 \tabularnewline
82 & 9890 & 9867.4244422989 & 22.575557701095 \tabularnewline
83 & 9305 & 9872.76577581325 & -567.765775813252 \tabularnewline
84 & 9391 & 9738.43348569654 & -347.433485696538 \tabularnewline
85 & 9928 & 9656.23139147908 & 271.768608520919 \tabularnewline
86 & 8686 & 9720.53132134392 & -1034.53132134392 \tabularnewline
87 & 9843 & 9475.76320126035 & 367.236798739648 \tabularnewline
88 & 9627 & 9562.65072124016 & 64.3492787598352 \tabularnewline
89 & 10074 & 9577.87563678 & 496.124363219997 \tabularnewline
90 & 9503 & 9695.25770652272 & -192.25770652272 \tabularnewline
91 & 10119 & 9649.76990308337 & 469.230096916632 \tabularnewline
92 & 10000 & 9760.78884116609 & 239.211158833912 \tabularnewline
93 & 9313 & 9817.38574107892 & -504.385741078917 \tabularnewline
94 & 9866 & 9698.04904523053 & 167.950954769465 \tabularnewline
95 & 9172 & 9737.7859179738 & -565.785917973797 \tabularnewline
96 & 9241 & 9603.92205841245 & -362.922058412445 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166532&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]2[/C][C]8642[/C][C]9676[/C][C]-1034[/C][/ROW]
[ROW][C]3[/C][C]9402[/C][C]9431.35758952408[/C][C]-29.3575895240847[/C][/ROW]
[ROW][C]4[/C][C]9610[/C][C]9424.41164032976[/C][C]185.588359670242[/C][/ROW]
[ROW][C]5[/C][C]9294[/C][C]9468.32148913633[/C][C]-174.321489136333[/C][/ROW]
[ROW][C]6[/C][C]9448[/C][C]9427.07736021944[/C][C]20.922639780556[/C][/ROW]
[ROW][C]7[/C][C]10319[/C][C]9432.02761653418[/C][C]886.972383465822[/C][/ROW]
[ROW][C]8[/C][C]9548[/C][C]9641.88357583461[/C][C]-93.8835758346104[/C][/ROW]
[ROW][C]9[/C][C]9801[/C][C]9619.67090243395[/C][C]181.329097566046[/C][/ROW]
[ROW][C]10[/C][C]9596[/C][C]9662.57301802194[/C][C]-66.5730180219434[/C][/ROW]
[ROW][C]11[/C][C]8923[/C][C]9646.8219700514[/C][C]-723.821970051396[/C][/ROW]
[ROW][C]12[/C][C]9746[/C][C]9475.56708464637[/C][C]270.432915353633[/C][/ROW]
[ROW][C]13[/C][C]9829[/C][C]9539.55099207784[/C][C]289.449007922161[/C][/ROW]
[ROW][C]14[/C][C]9125[/C][C]9608.03407042207[/C][C]-483.034070422074[/C][/ROW]
[ROW][C]15[/C][C]9782[/C][C]9493.74913876825[/C][C]288.250861231745[/C][/ROW]
[ROW][C]16[/C][C]9441[/C][C]9561.9487379109[/C][C]-120.948737910898[/C][/ROW]
[ROW][C]17[/C][C]9162[/C][C]9533.33249923919[/C][C]-371.332499239194[/C][/ROW]
[ROW][C]18[/C][C]9915[/C][C]9445.47594440174[/C][C]469.524055598256[/C][/ROW]
[ROW][C]19[/C][C]10444[/C][C]9556.56443254293[/C][C]887.435567457071[/C][/ROW]
[ROW][C]20[/C][C]10209[/C][C]9766.52998028448[/C][C]442.470019715523[/C][/ROW]
[ROW][C]21[/C][C]9985[/C][C]9871.2175355906[/C][C]113.7824644094[/C][/ROW]
[ROW][C]22[/C][C]9842[/C][C]9898.13824774051[/C][C]-56.1382477405095[/C][/ROW]
[ROW][C]23[/C][C]9429[/C][C]9884.85604634096[/C][C]-455.856046340961[/C][/ROW]
[ROW][C]24[/C][C]10132[/C][C]9777.00138289137[/C][C]354.998617108626[/C][/ROW]
[ROW][C]25[/C][C]9849[/C][C]9860.99337264483[/C][C]-11.9933726448271[/C][/ROW]
[ROW][C]26[/C][C]9172[/C][C]9858.15576375356[/C][C]-686.155763753564[/C][/ROW]
[ROW][C]27[/C][C]10313[/C][C]9695.81263028489[/C][C]617.187369715115[/C][/ROW]
[ROW][C]28[/C][C]9819[/C][C]9841.83797442647[/C][C]-22.8379744264676[/C][/ROW]
[ROW][C]29[/C][C]9955[/C][C]9836.43455361982[/C][C]118.565446380184[/C][/ROW]
[ROW][C]30[/C][C]10048[/C][C]9864.48691010106[/C][C]183.513089898945[/C][/ROW]
[ROW][C]31[/C][C]10082[/C][C]9907.90575407278[/C][C]174.094245927223[/C][/ROW]
[ROW][C]32[/C][C]10541[/C][C]9949.09611768363[/C][C]591.903882316368[/C][/ROW]
[ROW][C]33[/C][C]10208[/C][C]10089.1394373547[/C][C]118.860562645257[/C][/ROW]
[ROW][C]34[/C][C]10233[/C][C]10117.2616177765[/C][C]115.738382223537[/C][/ROW]
[ROW][C]35[/C][C]9439[/C][C]10144.6450963178[/C][C]-705.645096317807[/C][/ROW]
[ROW][C]36[/C][C]9963[/C][C]9977.69082426394[/C][C]-14.6908242639402[/C][/ROW]
[ROW][C]37[/C][C]10158[/C][C]9974.21500350977[/C][C]183.784996490227[/C][/ROW]
[ROW][C]38[/C][C]9225[/C][C]10017.6981800578[/C][C]-792.698180057816[/C][/ROW]
[ROW][C]39[/C][C]10474[/C][C]9830.1473158903[/C][C]643.852684109705[/C][/ROW]
[ROW][C]40[/C][C]9757[/C][C]9982.48162211078[/C][C]-225.481622110785[/C][/ROW]
[ROW][C]41[/C][C]10490[/C][C]9929.13310416958[/C][C]560.866895830417[/C][/ROW]
[ROW][C]42[/C][C]10281[/C][C]10061.8331325565[/C][C]219.166867443475[/C][/ROW]
[ROW][C]43[/C][C]10444[/C][C]10113.6875916937[/C][C]330.312408306312[/C][/ROW]
[ROW][C]44[/C][C]10640[/C][C]10191.8388719434[/C][C]448.161128056639[/C][/ROW]
[ROW][C]45[/C][C]10695[/C][C]10297.8729325327[/C][C]397.127067467296[/C][/ROW]
[ROW][C]46[/C][C]10786[/C][C]10391.8324325815[/C][C]394.167567418523[/C][/ROW]
[ROW][C]47[/C][C]9832[/C][C]10485.0917206131[/C][C]-653.091720613098[/C][/ROW]
[ROW][C]48[/C][C]9747[/C][C]10330.5714761328[/C][C]-583.571476132778[/C][/ROW]
[ROW][C]49[/C][C]10411[/C][C]10192.4995877323[/C][C]218.500412267716[/C][/ROW]
[ROW][C]50[/C][C]9511[/C][C]10244.1963648572[/C][C]-733.196364857193[/C][/ROW]
[ROW][C]51[/C][C]10402[/C][C]10070.7235156784[/C][C]331.276484321572[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10149.1028944583[/C][C]-448.102894458329[/C][/ROW]
[ROW][C]53[/C][C]10540[/C][C]10043.0826118263[/C][C]496.917388173702[/C][/ROW]
[ROW][C]54[/C][C]10112[/C][C]10160.6523097472[/C][C]-48.6523097471982[/C][/ROW]
[ROW][C]55[/C][C]10915[/C][C]10149.1412668731[/C][C]765.858733126859[/C][/ROW]
[ROW][C]56[/C][C]11183[/C][C]10330.3419695387[/C][C]852.658030461302[/C][/ROW]
[ROW][C]57[/C][C]10384[/C][C]10532.0792189427[/C][C]-148.079218942663[/C][/ROW]
[ROW][C]58[/C][C]10834[/C][C]10497.0439606607[/C][C]336.956039339275[/C][/ROW]
[ROW][C]59[/C][C]9886[/C][C]10576.7671112298[/C][C]-690.767111229756[/C][/ROW]
[ROW][C]60[/C][C]10216[/C][C]10413.3329418209[/C][C]-197.332941820923[/C][/ROW]
[ROW][C]61[/C][C]10943[/C][C]10366.6443474753[/C][C]576.3556525247[/C][/ROW]
[ROW][C]62[/C][C]9867[/C][C]10503.0089858941[/C][C]-636.008985894121[/C][/ROW]
[ROW][C]63[/C][C]10203[/C][C]10352.5304835793[/C][C]-149.530483579343[/C][/ROW]
[ROW][C]64[/C][C]10837[/C][C]10317.1518588768[/C][C]519.848141123248[/C][/ROW]
[ROW][C]65[/C][C]10573[/C][C]10440.1469288243[/C][C]132.85307117565[/C][/ROW]
[ROW][C]66[/C][C]10647[/C][C]10471.5797098413[/C][C]175.420290158687[/C][/ROW]
[ROW][C]67[/C][C]11502[/C][C]10513.0838129659[/C][C]988.916187034116[/C][/ROW]
[ROW][C]68[/C][C]10656[/C][C]10747.05948004[/C][C]-91.0594800400413[/C][/ROW]
[ROW][C]69[/C][C]10866[/C][C]10725.5149822705[/C][C]140.485017729474[/C][/ROW]
[ROW][C]70[/C][C]10835[/C][C]10758.7534671575[/C][C]76.2465328425387[/C][/ROW]
[ROW][C]71[/C][C]9945[/C][C]10776.7932501217[/C][C]-831.793250121707[/C][/ROW]
[ROW][C]72[/C][C]10331[/C][C]10579.9925676001[/C][C]-248.992567600073[/C][/ROW]
[ROW][C]73[/C][C]9769[/C][C]10521.0814051936[/C][C]-752.081405193623[/C][/ROW]
[ROW][C]74[/C][C]9321[/C][C]10343.1403918081[/C][C]-1022.14039180805[/C][/ROW]
[ROW][C]75[/C][C]9939[/C][C]10101.3039418112[/C][C]-162.303941811224[/C][/ROW]
[ROW][C]76[/C][C]9336[/C][C]10062.9031414684[/C][C]-726.903141468438[/C][/ROW]
[ROW][C]77[/C][C]10195[/C][C]9890.91925683463[/C][C]304.080743165367[/C][/ROW]
[ROW][C]78[/C][C]9464[/C][C]9962.86417558442[/C][C]-498.864175584424[/C][/ROW]
[ROW][C]79[/C][C]10010[/C][C]9844.83387150797[/C][C]165.16612849203[/C][/ROW]
[ROW][C]80[/C][C]10213[/C][C]9883.91185971229[/C][C]329.088140287711[/C][/ROW]
[ROW][C]81[/C][C]9563[/C][C]9961.77348050438[/C][C]-398.77348050438[/C][/ROW]
[ROW][C]82[/C][C]9890[/C][C]9867.4244422989[/C][C]22.575557701095[/C][/ROW]
[ROW][C]83[/C][C]9305[/C][C]9872.76577581325[/C][C]-567.765775813252[/C][/ROW]
[ROW][C]84[/C][C]9391[/C][C]9738.43348569654[/C][C]-347.433485696538[/C][/ROW]
[ROW][C]85[/C][C]9928[/C][C]9656.23139147908[/C][C]271.768608520919[/C][/ROW]
[ROW][C]86[/C][C]8686[/C][C]9720.53132134392[/C][C]-1034.53132134392[/C][/ROW]
[ROW][C]87[/C][C]9843[/C][C]9475.76320126035[/C][C]367.236798739648[/C][/ROW]
[ROW][C]88[/C][C]9627[/C][C]9562.65072124016[/C][C]64.3492787598352[/C][/ROW]
[ROW][C]89[/C][C]10074[/C][C]9577.87563678[/C][C]496.124363219997[/C][/ROW]
[ROW][C]90[/C][C]9503[/C][C]9695.25770652272[/C][C]-192.25770652272[/C][/ROW]
[ROW][C]91[/C][C]10119[/C][C]9649.76990308337[/C][C]469.230096916632[/C][/ROW]
[ROW][C]92[/C][C]10000[/C][C]9760.78884116609[/C][C]239.211158833912[/C][/ROW]
[ROW][C]93[/C][C]9313[/C][C]9817.38574107892[/C][C]-504.385741078917[/C][/ROW]
[ROW][C]94[/C][C]9866[/C][C]9698.04904523053[/C][C]167.950954769465[/C][/ROW]
[ROW][C]95[/C][C]9172[/C][C]9737.7859179738[/C][C]-565.785917973797[/C][/ROW]
[ROW][C]96[/C][C]9241[/C][C]9603.92205841245[/C][C]-362.922058412445[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166532&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166532&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
286429676-1034
394029431.35758952408-29.3575895240847
496109424.41164032976185.588359670242
592949468.32148913633-174.321489136333
694489427.0773602194420.922639780556
7103199432.02761653418886.972383465822
895489641.88357583461-93.8835758346104
998019619.67090243395181.329097566046
1095969662.57301802194-66.5730180219434
1189239646.8219700514-723.821970051396
1297469475.56708464637270.432915353633
1398299539.55099207784289.449007922161
1491259608.03407042207-483.034070422074
1597829493.74913876825288.250861231745
1694419561.9487379109-120.948737910898
1791629533.33249923919-371.332499239194
1899159445.47594440174469.524055598256
19104449556.56443254293887.435567457071
20102099766.52998028448442.470019715523
2199859871.2175355906113.7824644094
2298429898.13824774051-56.1382477405095
2394299884.85604634096-455.856046340961
24101329777.00138289137354.998617108626
2598499860.99337264483-11.9933726448271
2691729858.15576375356-686.155763753564
27103139695.81263028489617.187369715115
2898199841.83797442647-22.8379744264676
2999559836.43455361982118.565446380184
30100489864.48691010106183.513089898945
31100829907.90575407278174.094245927223
32105419949.09611768363591.903882316368
331020810089.1394373547118.860562645257
341023310117.2616177765115.738382223537
35943910144.6450963178-705.645096317807
3699639977.69082426394-14.6908242639402
37101589974.21500350977183.784996490227
38922510017.6981800578-792.698180057816
39104749830.1473158903643.852684109705
4097579982.48162211078-225.481622110785
41104909929.13310416958560.866895830417
421028110061.8331325565219.166867443475
431044410113.6875916937330.312408306312
441064010191.8388719434448.161128056639
451069510297.8729325327397.127067467296
461078610391.8324325815394.167567418523
47983210485.0917206131-653.091720613098
48974710330.5714761328-583.571476132778
491041110192.4995877323218.500412267716
50951110244.1963648572-733.196364857193
511040210070.7235156784331.276484321572
52970110149.1028944583-448.102894458329
531054010043.0826118263496.917388173702
541011210160.6523097472-48.6523097471982
551091510149.1412668731765.858733126859
561118310330.3419695387852.658030461302
571038410532.0792189427-148.079218942663
581083410497.0439606607336.956039339275
59988610576.7671112298-690.767111229756
601021610413.3329418209-197.332941820923
611094310366.6443474753576.3556525247
62986710503.0089858941-636.008985894121
631020310352.5304835793-149.530483579343
641083710317.1518588768519.848141123248
651057310440.1469288243132.85307117565
661064710471.5797098413175.420290158687
671150210513.0838129659988.916187034116
681065610747.05948004-91.0594800400413
691086610725.5149822705140.485017729474
701083510758.753467157576.2465328425387
71994510776.7932501217-831.793250121707
721033110579.9925676001-248.992567600073
73976910521.0814051936-752.081405193623
74932110343.1403918081-1022.14039180805
75993910101.3039418112-162.303941811224
76933610062.9031414684-726.903141468438
77101959890.91925683463304.080743165367
7894649962.86417558442-498.864175584424
79100109844.83387150797165.16612849203
80102139883.91185971229329.088140287711
8195639961.77348050438-398.77348050438
8298909867.424442298922.575557701095
8393059872.76577581325-567.765775813252
8493919738.43348569654-347.433485696538
8599289656.23139147908271.768608520919
8686869720.53132134392-1034.53132134392
8798439475.76320126035367.236798739648
8896279562.6507212401664.3492787598352
89100749577.87563678496.124363219997
9095039695.25770652272-192.25770652272
91101199649.76990308337469.230096916632
92100009760.78884116609239.211158833912
9393139817.38574107892-504.385741078917
9498669698.04904523053167.950954769465
9591729737.7859179738-565.785917973797
9692419603.92205841245-362.922058412445







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
979518.055397692048588.8026738873110447.3081214968
989518.055397692048563.1476621944710472.9631331896
999518.055397692048538.1641068195910497.9466885645
1009518.055397692048513.8018935695710522.3089018145
1019518.055397692048490.0168482412710546.0939471428
1029518.055397692048466.7697953120710569.341000072
1039518.055397692048444.025800154810592.0849952293
1049518.055397692048421.7535528515810614.3572425325
1059518.055397692048399.9248625508310636.1859328332
1069518.055397692048378.5142390541610657.5965563299
1079518.055397692048357.4985439169510678.6122514671
1089518.055397692048336.856697447710699.2540979364

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 9518.05539769204 & 8588.80267388731 & 10447.3081214968 \tabularnewline
98 & 9518.05539769204 & 8563.14766219447 & 10472.9631331896 \tabularnewline
99 & 9518.05539769204 & 8538.16410681959 & 10497.9466885645 \tabularnewline
100 & 9518.05539769204 & 8513.80189356957 & 10522.3089018145 \tabularnewline
101 & 9518.05539769204 & 8490.01684824127 & 10546.0939471428 \tabularnewline
102 & 9518.05539769204 & 8466.76979531207 & 10569.341000072 \tabularnewline
103 & 9518.05539769204 & 8444.0258001548 & 10592.0849952293 \tabularnewline
104 & 9518.05539769204 & 8421.75355285158 & 10614.3572425325 \tabularnewline
105 & 9518.05539769204 & 8399.92486255083 & 10636.1859328332 \tabularnewline
106 & 9518.05539769204 & 8378.51423905416 & 10657.5965563299 \tabularnewline
107 & 9518.05539769204 & 8357.49854391695 & 10678.6122514671 \tabularnewline
108 & 9518.05539769204 & 8336.8566974477 & 10699.2540979364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166532&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]97[/C][C]9518.05539769204[/C][C]8588.80267388731[/C][C]10447.3081214968[/C][/ROW]
[ROW][C]98[/C][C]9518.05539769204[/C][C]8563.14766219447[/C][C]10472.9631331896[/C][/ROW]
[ROW][C]99[/C][C]9518.05539769204[/C][C]8538.16410681959[/C][C]10497.9466885645[/C][/ROW]
[ROW][C]100[/C][C]9518.05539769204[/C][C]8513.80189356957[/C][C]10522.3089018145[/C][/ROW]
[ROW][C]101[/C][C]9518.05539769204[/C][C]8490.01684824127[/C][C]10546.0939471428[/C][/ROW]
[ROW][C]102[/C][C]9518.05539769204[/C][C]8466.76979531207[/C][C]10569.341000072[/C][/ROW]
[ROW][C]103[/C][C]9518.05539769204[/C][C]8444.0258001548[/C][C]10592.0849952293[/C][/ROW]
[ROW][C]104[/C][C]9518.05539769204[/C][C]8421.75355285158[/C][C]10614.3572425325[/C][/ROW]
[ROW][C]105[/C][C]9518.05539769204[/C][C]8399.92486255083[/C][C]10636.1859328332[/C][/ROW]
[ROW][C]106[/C][C]9518.05539769204[/C][C]8378.51423905416[/C][C]10657.5965563299[/C][/ROW]
[ROW][C]107[/C][C]9518.05539769204[/C][C]8357.49854391695[/C][C]10678.6122514671[/C][/ROW]
[ROW][C]108[/C][C]9518.05539769204[/C][C]8336.8566974477[/C][C]10699.2540979364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166532&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166532&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
979518.055397692048588.8026738873110447.3081214968
989518.055397692048563.1476621944710472.9631331896
999518.055397692048538.1641068195910497.9466885645
1009518.055397692048513.8018935695710522.3089018145
1019518.055397692048490.0168482412710546.0939471428
1029518.055397692048466.7697953120710569.341000072
1039518.055397692048444.025800154810592.0849952293
1049518.055397692048421.7535528515810614.3572425325
1059518.055397692048399.9248625508310636.1859328332
1069518.055397692048378.5142390541610657.5965563299
1079518.055397692048357.4985439169510678.6122514671
1089518.055397692048336.856697447710699.2540979364



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')