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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Dec 2015 14:57:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/25/t1451056569fda8qk8s4yjsqum.htm/, Retrieved Thu, 16 May 2024 13:57:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287090, Retrieved Thu, 16 May 2024 13:57:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-12-25 14:57:47] [e7bd1b63287b3004f428c98394187272] [Current]
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Dataseries X:
62239,3
64816,6
62625,3
67923
64363,7
67342
64411,2
69174,5
66290,2
69336,8
66712,2
72225,9
68229,5
71096,3
68407,9
74522,4
71798,4
75074,3
72694,6
78789,4
74814,5
78303,2
75431,6
82600,7
78830,5
82168,1
79493,2
86876,6
83478,5
87003,2
83672,7
90914,2
86448
90577,7
86621,1
91418,5
84275,4
87677,9
85149,6
92600
87111,3
92293,9
89060
97281,6
91812
95980,4
92043,7
100079,2
94384,8
97900,5
93630,8
102255,2
95251,8
100001,8
95689,8
104298
97435,1
101220,2
97537
105834,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287090&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287090&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287090&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.987929494235697
beta0.0156525552200263
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.987929494235697 \tabularnewline
beta & 0.0156525552200263 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287090&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]0.987929494235697[/C][/ROW]
[ROW][C]beta[/C][C]0.0156525552200263[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287090&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287090&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
alpha0.987929494235697
beta0.0156525552200263
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
564363.763223.33544157781140.36455842216
66734267471.6781419928-129.678141992845
764411.264582.0572413641-170.857241364094
869174.569777.5176914552-603.017691455156
966290.265530.0284493296760.171550670413
1069336.869462.4976946375-125.697694637536
1166712.266477.9904332887234.209566711259
1272225.972245.4598819664-19.5598819664156
1368229.568421.7118147574-192.211814757364
1471096.371478.4588700459-382.158870045896
1568407.968154.2787285912253.621271408774
1674522.474059.1867417554463.213258244548
1771798.470575.42488805581222.97511194424
1875074.375194.3787684566-120.078768456631
1972694.671972.0442103468722.555789653168
2078789.478700.261415209289.1385847907513
2174814.574631.1592790364183.340720963606
2278303.278340.3120816755-37.1120816755138
2375431.675069.1456296076362.454370392385
2482600.781647.9800331925952.719966807534
2578830.578228.4036333226602.096366677404
2682168.182536.5502578647-368.450257864723
2779493.278779.7500004015713.44999959851
2886876.686046.2064100812830.393589918793
2983478.582274.00430659331204.49569340669
3087003.287385.9105659825-382.710565982488
3183672.783431.6349282123241.065071787671
3290914.290575.8105522507338.389447749287
338644886103.0183050935344.981694906543
3490577.790471.3987887822106.301211217826
3586621.186852.0939409499-230.99394094992
3691418.593760.6499370987-2342.1499370987
3784275.486577.2369203655-2301.83692036553
3887677.988169.4516922063-491.551692206267
3985149.684014.4095287681135.19047123201
409260092072.8081123428527.191887657173
4187111.387636.2738061318-524.973806131748
4292293.991128.07798826811165.8220117319
438906088444.5776701432615.422329856781
4497281.696300.8018443891980.798155610901
459181292053.6784931916-241.678493191561
4695980.496070.9897940233-90.5897940233262
4792043.791981.971359882261.7286401177844
48100079.299528.412083977550.78791602295
4994384.894678.3918040098-293.591804009833
5097900.598751.6156523403-851.115652340261
5193630.893812.7537004801-181.953700480095
52102255.2101229.9772161331025.22278386701
5395251.896703.4940310131-1451.69403101306
54100001.899636.8331727392364.966827260767
5595689.895802.5584463665-112.758446366468
56104298103452.353835186845.646164813981
5797435.198589.2613166042-1154.16131660424
58101220.2101923.989190044-703.789190044175
599753796951.9127264197585.08727358027
60105834.9105432.949061932401.950938067544

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 64363.7 & 63223.3354415778 & 1140.36455842216 \tabularnewline
6 & 67342 & 67471.6781419928 & -129.678141992845 \tabularnewline
7 & 64411.2 & 64582.0572413641 & -170.857241364094 \tabularnewline
8 & 69174.5 & 69777.5176914552 & -603.017691455156 \tabularnewline
9 & 66290.2 & 65530.0284493296 & 760.171550670413 \tabularnewline
10 & 69336.8 & 69462.4976946375 & -125.697694637536 \tabularnewline
11 & 66712.2 & 66477.9904332887 & 234.209566711259 \tabularnewline
12 & 72225.9 & 72245.4598819664 & -19.5598819664156 \tabularnewline
13 & 68229.5 & 68421.7118147574 & -192.211814757364 \tabularnewline
14 & 71096.3 & 71478.4588700459 & -382.158870045896 \tabularnewline
15 & 68407.9 & 68154.2787285912 & 253.621271408774 \tabularnewline
16 & 74522.4 & 74059.1867417554 & 463.213258244548 \tabularnewline
17 & 71798.4 & 70575.4248880558 & 1222.97511194424 \tabularnewline
18 & 75074.3 & 75194.3787684566 & -120.078768456631 \tabularnewline
19 & 72694.6 & 71972.0442103468 & 722.555789653168 \tabularnewline
20 & 78789.4 & 78700.2614152092 & 89.1385847907513 \tabularnewline
21 & 74814.5 & 74631.1592790364 & 183.340720963606 \tabularnewline
22 & 78303.2 & 78340.3120816755 & -37.1120816755138 \tabularnewline
23 & 75431.6 & 75069.1456296076 & 362.454370392385 \tabularnewline
24 & 82600.7 & 81647.9800331925 & 952.719966807534 \tabularnewline
25 & 78830.5 & 78228.4036333226 & 602.096366677404 \tabularnewline
26 & 82168.1 & 82536.5502578647 & -368.450257864723 \tabularnewline
27 & 79493.2 & 78779.7500004015 & 713.44999959851 \tabularnewline
28 & 86876.6 & 86046.2064100812 & 830.393589918793 \tabularnewline
29 & 83478.5 & 82274.0043065933 & 1204.49569340669 \tabularnewline
30 & 87003.2 & 87385.9105659825 & -382.710565982488 \tabularnewline
31 & 83672.7 & 83431.6349282123 & 241.065071787671 \tabularnewline
32 & 90914.2 & 90575.8105522507 & 338.389447749287 \tabularnewline
33 & 86448 & 86103.0183050935 & 344.981694906543 \tabularnewline
34 & 90577.7 & 90471.3987887822 & 106.301211217826 \tabularnewline
35 & 86621.1 & 86852.0939409499 & -230.99394094992 \tabularnewline
36 & 91418.5 & 93760.6499370987 & -2342.1499370987 \tabularnewline
37 & 84275.4 & 86577.2369203655 & -2301.83692036553 \tabularnewline
38 & 87677.9 & 88169.4516922063 & -491.551692206267 \tabularnewline
39 & 85149.6 & 84014.409528768 & 1135.19047123201 \tabularnewline
40 & 92600 & 92072.8081123428 & 527.191887657173 \tabularnewline
41 & 87111.3 & 87636.2738061318 & -524.973806131748 \tabularnewline
42 & 92293.9 & 91128.0779882681 & 1165.8220117319 \tabularnewline
43 & 89060 & 88444.5776701432 & 615.422329856781 \tabularnewline
44 & 97281.6 & 96300.8018443891 & 980.798155610901 \tabularnewline
45 & 91812 & 92053.6784931916 & -241.678493191561 \tabularnewline
46 & 95980.4 & 96070.9897940233 & -90.5897940233262 \tabularnewline
47 & 92043.7 & 91981.9713598822 & 61.7286401177844 \tabularnewline
48 & 100079.2 & 99528.412083977 & 550.78791602295 \tabularnewline
49 & 94384.8 & 94678.3918040098 & -293.591804009833 \tabularnewline
50 & 97900.5 & 98751.6156523403 & -851.115652340261 \tabularnewline
51 & 93630.8 & 93812.7537004801 & -181.953700480095 \tabularnewline
52 & 102255.2 & 101229.977216133 & 1025.22278386701 \tabularnewline
53 & 95251.8 & 96703.4940310131 & -1451.69403101306 \tabularnewline
54 & 100001.8 & 99636.8331727392 & 364.966827260767 \tabularnewline
55 & 95689.8 & 95802.5584463665 & -112.758446366468 \tabularnewline
56 & 104298 & 103452.353835186 & 845.646164813981 \tabularnewline
57 & 97435.1 & 98589.2613166042 & -1154.16131660424 \tabularnewline
58 & 101220.2 & 101923.989190044 & -703.789190044175 \tabularnewline
59 & 97537 & 96951.9127264197 & 585.08727358027 \tabularnewline
60 & 105834.9 & 105432.949061932 & 401.950938067544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287090&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]5[/C][C]64363.7[/C][C]63223.3354415778[/C][C]1140.36455842216[/C][/ROW]
[ROW][C]6[/C][C]67342[/C][C]67471.6781419928[/C][C]-129.678141992845[/C][/ROW]
[ROW][C]7[/C][C]64411.2[/C][C]64582.0572413641[/C][C]-170.857241364094[/C][/ROW]
[ROW][C]8[/C][C]69174.5[/C][C]69777.5176914552[/C][C]-603.017691455156[/C][/ROW]
[ROW][C]9[/C][C]66290.2[/C][C]65530.0284493296[/C][C]760.171550670413[/C][/ROW]
[ROW][C]10[/C][C]69336.8[/C][C]69462.4976946375[/C][C]-125.697694637536[/C][/ROW]
[ROW][C]11[/C][C]66712.2[/C][C]66477.9904332887[/C][C]234.209566711259[/C][/ROW]
[ROW][C]12[/C][C]72225.9[/C][C]72245.4598819664[/C][C]-19.5598819664156[/C][/ROW]
[ROW][C]13[/C][C]68229.5[/C][C]68421.7118147574[/C][C]-192.211814757364[/C][/ROW]
[ROW][C]14[/C][C]71096.3[/C][C]71478.4588700459[/C][C]-382.158870045896[/C][/ROW]
[ROW][C]15[/C][C]68407.9[/C][C]68154.2787285912[/C][C]253.621271408774[/C][/ROW]
[ROW][C]16[/C][C]74522.4[/C][C]74059.1867417554[/C][C]463.213258244548[/C][/ROW]
[ROW][C]17[/C][C]71798.4[/C][C]70575.4248880558[/C][C]1222.97511194424[/C][/ROW]
[ROW][C]18[/C][C]75074.3[/C][C]75194.3787684566[/C][C]-120.078768456631[/C][/ROW]
[ROW][C]19[/C][C]72694.6[/C][C]71972.0442103468[/C][C]722.555789653168[/C][/ROW]
[ROW][C]20[/C][C]78789.4[/C][C]78700.2614152092[/C][C]89.1385847907513[/C][/ROW]
[ROW][C]21[/C][C]74814.5[/C][C]74631.1592790364[/C][C]183.340720963606[/C][/ROW]
[ROW][C]22[/C][C]78303.2[/C][C]78340.3120816755[/C][C]-37.1120816755138[/C][/ROW]
[ROW][C]23[/C][C]75431.6[/C][C]75069.1456296076[/C][C]362.454370392385[/C][/ROW]
[ROW][C]24[/C][C]82600.7[/C][C]81647.9800331925[/C][C]952.719966807534[/C][/ROW]
[ROW][C]25[/C][C]78830.5[/C][C]78228.4036333226[/C][C]602.096366677404[/C][/ROW]
[ROW][C]26[/C][C]82168.1[/C][C]82536.5502578647[/C][C]-368.450257864723[/C][/ROW]
[ROW][C]27[/C][C]79493.2[/C][C]78779.7500004015[/C][C]713.44999959851[/C][/ROW]
[ROW][C]28[/C][C]86876.6[/C][C]86046.2064100812[/C][C]830.393589918793[/C][/ROW]
[ROW][C]29[/C][C]83478.5[/C][C]82274.0043065933[/C][C]1204.49569340669[/C][/ROW]
[ROW][C]30[/C][C]87003.2[/C][C]87385.9105659825[/C][C]-382.710565982488[/C][/ROW]
[ROW][C]31[/C][C]83672.7[/C][C]83431.6349282123[/C][C]241.065071787671[/C][/ROW]
[ROW][C]32[/C][C]90914.2[/C][C]90575.8105522507[/C][C]338.389447749287[/C][/ROW]
[ROW][C]33[/C][C]86448[/C][C]86103.0183050935[/C][C]344.981694906543[/C][/ROW]
[ROW][C]34[/C][C]90577.7[/C][C]90471.3987887822[/C][C]106.301211217826[/C][/ROW]
[ROW][C]35[/C][C]86621.1[/C][C]86852.0939409499[/C][C]-230.99394094992[/C][/ROW]
[ROW][C]36[/C][C]91418.5[/C][C]93760.6499370987[/C][C]-2342.1499370987[/C][/ROW]
[ROW][C]37[/C][C]84275.4[/C][C]86577.2369203655[/C][C]-2301.83692036553[/C][/ROW]
[ROW][C]38[/C][C]87677.9[/C][C]88169.4516922063[/C][C]-491.551692206267[/C][/ROW]
[ROW][C]39[/C][C]85149.6[/C][C]84014.409528768[/C][C]1135.19047123201[/C][/ROW]
[ROW][C]40[/C][C]92600[/C][C]92072.8081123428[/C][C]527.191887657173[/C][/ROW]
[ROW][C]41[/C][C]87111.3[/C][C]87636.2738061318[/C][C]-524.973806131748[/C][/ROW]
[ROW][C]42[/C][C]92293.9[/C][C]91128.0779882681[/C][C]1165.8220117319[/C][/ROW]
[ROW][C]43[/C][C]89060[/C][C]88444.5776701432[/C][C]615.422329856781[/C][/ROW]
[ROW][C]44[/C][C]97281.6[/C][C]96300.8018443891[/C][C]980.798155610901[/C][/ROW]
[ROW][C]45[/C][C]91812[/C][C]92053.6784931916[/C][C]-241.678493191561[/C][/ROW]
[ROW][C]46[/C][C]95980.4[/C][C]96070.9897940233[/C][C]-90.5897940233262[/C][/ROW]
[ROW][C]47[/C][C]92043.7[/C][C]91981.9713598822[/C][C]61.7286401177844[/C][/ROW]
[ROW][C]48[/C][C]100079.2[/C][C]99528.412083977[/C][C]550.78791602295[/C][/ROW]
[ROW][C]49[/C][C]94384.8[/C][C]94678.3918040098[/C][C]-293.591804009833[/C][/ROW]
[ROW][C]50[/C][C]97900.5[/C][C]98751.6156523403[/C][C]-851.115652340261[/C][/ROW]
[ROW][C]51[/C][C]93630.8[/C][C]93812.7537004801[/C][C]-181.953700480095[/C][/ROW]
[ROW][C]52[/C][C]102255.2[/C][C]101229.977216133[/C][C]1025.22278386701[/C][/ROW]
[ROW][C]53[/C][C]95251.8[/C][C]96703.4940310131[/C][C]-1451.69403101306[/C][/ROW]
[ROW][C]54[/C][C]100001.8[/C][C]99636.8331727392[/C][C]364.966827260767[/C][/ROW]
[ROW][C]55[/C][C]95689.8[/C][C]95802.5584463665[/C][C]-112.758446366468[/C][/ROW]
[ROW][C]56[/C][C]104298[/C][C]103452.353835186[/C][C]845.646164813981[/C][/ROW]
[ROW][C]57[/C][C]97435.1[/C][C]98589.2613166042[/C][C]-1154.16131660424[/C][/ROW]
[ROW][C]58[/C][C]101220.2[/C][C]101923.989190044[/C][C]-703.789190044175[/C][/ROW]
[ROW][C]59[/C][C]97537[/C][C]96951.9127264197[/C][C]585.08727358027[/C][/ROW]
[ROW][C]60[/C][C]105834.9[/C][C]105432.949061932[/C][C]401.950938067544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287090&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287090&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
564363.763223.33544157781140.36455842216
66734267471.6781419928-129.678141992845
764411.264582.0572413641-170.857241364094
869174.569777.5176914552-603.017691455156
966290.265530.0284493296760.171550670413
1069336.869462.4976946375-125.697694637536
1166712.266477.9904332887234.209566711259
1272225.972245.4598819664-19.5598819664156
1368229.568421.7118147574-192.211814757364
1471096.371478.4588700459-382.158870045896
1568407.968154.2787285912253.621271408774
1674522.474059.1867417554463.213258244548
1771798.470575.42488805581222.97511194424
1875074.375194.3787684566-120.078768456631
1972694.671972.0442103468722.555789653168
2078789.478700.261415209289.1385847907513
2174814.574631.1592790364183.340720963606
2278303.278340.3120816755-37.1120816755138
2375431.675069.1456296076362.454370392385
2482600.781647.9800331925952.719966807534
2578830.578228.4036333226602.096366677404
2682168.182536.5502578647-368.450257864723
2779493.278779.7500004015713.44999959851
2886876.686046.2064100812830.393589918793
2983478.582274.00430659331204.49569340669
3087003.287385.9105659825-382.710565982488
3183672.783431.6349282123241.065071787671
3290914.290575.8105522507338.389447749287
338644886103.0183050935344.981694906543
3490577.790471.3987887822106.301211217826
3586621.186852.0939409499-230.99394094992
3691418.593760.6499370987-2342.1499370987
3784275.486577.2369203655-2301.83692036553
3887677.988169.4516922063-491.551692206267
3985149.684014.4095287681135.19047123201
409260092072.8081123428527.191887657173
4187111.387636.2738061318-524.973806131748
4292293.991128.07798826811165.8220117319
438906088444.5776701432615.422329856781
4497281.696300.8018443891980.798155610901
459181292053.6784931916-241.678493191561
4695980.496070.9897940233-90.5897940233262
4792043.791981.971359882261.7286401177844
48100079.299528.412083977550.78791602295
4994384.894678.3918040098-293.591804009833
5097900.598751.6156523403-851.115652340261
5193630.893812.7537004801-181.953700480095
52102255.2101229.9772161331025.22278386701
5395251.896703.4940310131-1451.69403101306
54100001.899636.8331727392364.966827260767
5595689.895802.5584463665-112.758446366468
56104298103452.353835186845.646164813981
5797435.198589.2613166042-1154.16131660424
58101220.2101923.989190044-703.789190044175
599753796951.9127264197585.08727358027
60105834.9105432.949061932401.950938067544







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61100001.16336780198502.0295237916101500.297211811
62104588.538477293102421.933308003106755.143646584
63100181.81588770897615.0580931214102748.573682295
64108286.600684523105496.867985599111076.333383448

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 100001.163367801 & 98502.0295237916 & 101500.297211811 \tabularnewline
62 & 104588.538477293 & 102421.933308003 & 106755.143646584 \tabularnewline
63 & 100181.815887708 & 97615.0580931214 & 102748.573682295 \tabularnewline
64 & 108286.600684523 & 105496.867985599 & 111076.333383448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287090&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]61[/C][C]100001.163367801[/C][C]98502.0295237916[/C][C]101500.297211811[/C][/ROW]
[ROW][C]62[/C][C]104588.538477293[/C][C]102421.933308003[/C][C]106755.143646584[/C][/ROW]
[ROW][C]63[/C][C]100181.815887708[/C][C]97615.0580931214[/C][C]102748.573682295[/C][/ROW]
[ROW][C]64[/C][C]108286.600684523[/C][C]105496.867985599[/C][C]111076.333383448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287090&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287090&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
61100001.16336780198502.0295237916101500.297211811
62104588.538477293102421.933308003106755.143646584
63100181.81588770897615.0580931214102748.573682295
64108286.600684523105496.867985599111076.333383448



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')