Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Nov 2012 16:24:16 -0500
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/Nov/23/t1353705882mjbdohyczoa6etq.htm/, Retrieved Tue, 30 Apr 2024 05:09:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192297, Retrieved Tue, 30 Apr 2024 05:09:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [ws8] [2012-11-23 21:24:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R P       [Exponential Smoothing] [ws8] [2012-11-23 21:53:38] [74be16979710d4c4e7c6647856088456]
-             [Exponential Smoothing] [ws8] [2012-11-23 22:00:51] [74be16979710d4c4e7c6647856088456]
-   PD          [Exponential Smoothing] [Deel 4: tijdreeks...] [2012-12-18 19:07:23] [5e6119a0aa181aac6bb71d6b937f8665]
-    D        [Exponential Smoothing] [Deel 4: tijdreeks...] [2012-12-18 19:07:09] [5e6119a0aa181aac6bb71d6b937f8665]
- R  D      [Exponential Smoothing] [Deel 4: tijdreeks...] [2012-12-18 19:06:53] [5e6119a0aa181aac6bb71d6b937f8665]
Feedback Forum

Post a new message
Dataseries X:
88.1
101.7
114.8
103.4
96.4
110
71.1
79.4
119.2
99.1
113.2
103.6
97.5
102.4
120.8
89.5
101.7
112.5
72.4
84.7
117.2
112.8
111.3
102.3
95.2
103
116.4
95.1
100.7
112.4
75.3
93.3
118.6
118.7
110.7
113.3
89.5
106.3
115.1
105.7
95.8
114.7
79.6
80.6
125
127.5
99.5
104.3
90
96
108.9
95.8
87.2
108.4
74.9
80.8
119.1
107.9
106.9
96.8
93.7
95.2
112.7
98.5
91.5
112
76.7
84.7
114.9
108.4
104.6
111.3
90.8
109.1
121
95.2
110.5
102.4
86.7
99.1
126
110.3
104.6
103.1
102




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192297&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192297&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0904208023746893
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0904208023746893 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192297&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]0.0904208023746893[/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=192297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192297&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
alpha0.0904208023746893
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.788.113.6
3114.889.329722912295825.4702770877042
4103.491.632765803271611.7672341967284
596.492.69676856107073.70323143892931
611093.031617719157916.9683822808421
771.194.5659124599921-23.4659124599921
879.492.4441058269054-13.0441058269054
9119.291.264647311776227.9353526882238
1099.193.79058431646545.30941568353464
11113.294.270665942711318.9293340572887
12103.695.98227151658997.6177284834101
1397.596.67107263833240.828927361667638
14102.496.74602491548475.65397508451532
15120.897.257261879233123.5427381207669
1689.599.38601515021-9.88601515020999
17101.798.49211372803973.20788627196033
18112.598.782173378677113.7178266213229
1972.4100.022550268614-27.622550268614
2084.797.5248971096907-12.8248971096907
21117.296.365259622659720.8347403773404
22112.898.249153564847114.5508464351529
23111.399.564852774744511.7351472252555
24102.3100.6259542028371.67404579716276
2595.2100.777322767029-5.57732276702866
26103100.2730167673312.72698323266869
27116.4100.51959277929215.8804072207085
2895.1101.955511942225-6.85551194222482
29100.7101.33563105172-0.635631051719585
30112.4101.27815678200911.1218432179912
3175.3102.283802769665-26.9838027696651
3293.399.8439056721116-6.54390567211161
33118.699.25220047057519.347799529425
34118.7101.0016440282117.6983559717898
35110.7102.6019435758928.09805642410767
36113.3103.3341763354369.96582366456434
3789.5104.23529410751-14.7352941075102
38106.3102.9029169910823.39708300891787
39115.1103.21008396248211.8899160375181
40105.7104.2851797107621.41482028923802
4195.8104.413108896531-8.61310889653087
42114.7103.63430467916611.065695320834
4379.6104.63487372891-25.0348737289096
4480.6102.371200358993-21.7712003589926
45125100.40263095387224.5973690461276
46127.5102.6267447993324.8732552006704
4799.5104.875804492245-5.37580449224461
48104.3104.389719936646-0.0897199366464037
4990104.381607387986-14.3816073879858
5096103.081210908526-7.08121090852639
51108.9102.4409221363936.45907786360698
5295.8103.024957139421-7.22495713942097
5387.2102.371670717752-15.1716707177518
54108.4100.9998360780887.40016392191191
5574.9101.668964837612-26.7689648376116
5680.899.2484935582549-18.4484935582549
57119.197.580365968113221.5196340318868
58107.999.52618854408618.37381145591392
59106.9100.2833552948646.61664470513583
6096.8100.881637618131-4.0816376181308
6193.7100.512572669697-6.81257266969669
6295.299.8965743826668-4.69657438266684
63112.799.471906358573713.2280936414263
6498.5100.668001199519-2.16800119951898
6591.5100.471968791509-8.97196879150918
6611299.660716174500312.3392838254997
6776.7100.776444118731-24.076444118731
6884.798.5994327231859-13.8994327231859
69114.997.342634863802517.5573651361975
70108.498.93018590700289.46981409299717
71104.699.78645409563084.81354590436921
72111.3100.22169877857111.0783012214287
7390.8101.223407663961-10.4234076639613
74109.1100.2809147795078.81908522049252
75121101.07834354135519.9216564586448
7695.2102.879675702979-7.67967570297874
77110.5102.1852732639388.314726736062
78102.4102.937097526939-0.537097526939007
7986.7102.8885327376-16.1885327375997
8099.1101.424752618197-2.32475261819704
81126101.21454662113724.785453378863
82110.3103.4556672028746.84433279712574
83104.6104.074537266110.525462733890237
84103.1104.122050028126-1.02205002812612
85102104.029635444516-2.02963544451588

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.7 & 88.1 & 13.6 \tabularnewline
3 & 114.8 & 89.3297229122958 & 25.4702770877042 \tabularnewline
4 & 103.4 & 91.6327658032716 & 11.7672341967284 \tabularnewline
5 & 96.4 & 92.6967685610707 & 3.70323143892931 \tabularnewline
6 & 110 & 93.0316177191579 & 16.9683822808421 \tabularnewline
7 & 71.1 & 94.5659124599921 & -23.4659124599921 \tabularnewline
8 & 79.4 & 92.4441058269054 & -13.0441058269054 \tabularnewline
9 & 119.2 & 91.2646473117762 & 27.9353526882238 \tabularnewline
10 & 99.1 & 93.7905843164654 & 5.30941568353464 \tabularnewline
11 & 113.2 & 94.2706659427113 & 18.9293340572887 \tabularnewline
12 & 103.6 & 95.9822715165899 & 7.6177284834101 \tabularnewline
13 & 97.5 & 96.6710726383324 & 0.828927361667638 \tabularnewline
14 & 102.4 & 96.7460249154847 & 5.65397508451532 \tabularnewline
15 & 120.8 & 97.2572618792331 & 23.5427381207669 \tabularnewline
16 & 89.5 & 99.38601515021 & -9.88601515020999 \tabularnewline
17 & 101.7 & 98.4921137280397 & 3.20788627196033 \tabularnewline
18 & 112.5 & 98.7821733786771 & 13.7178266213229 \tabularnewline
19 & 72.4 & 100.022550268614 & -27.622550268614 \tabularnewline
20 & 84.7 & 97.5248971096907 & -12.8248971096907 \tabularnewline
21 & 117.2 & 96.3652596226597 & 20.8347403773404 \tabularnewline
22 & 112.8 & 98.2491535648471 & 14.5508464351529 \tabularnewline
23 & 111.3 & 99.5648527747445 & 11.7351472252555 \tabularnewline
24 & 102.3 & 100.625954202837 & 1.67404579716276 \tabularnewline
25 & 95.2 & 100.777322767029 & -5.57732276702866 \tabularnewline
26 & 103 & 100.273016767331 & 2.72698323266869 \tabularnewline
27 & 116.4 & 100.519592779292 & 15.8804072207085 \tabularnewline
28 & 95.1 & 101.955511942225 & -6.85551194222482 \tabularnewline
29 & 100.7 & 101.33563105172 & -0.635631051719585 \tabularnewline
30 & 112.4 & 101.278156782009 & 11.1218432179912 \tabularnewline
31 & 75.3 & 102.283802769665 & -26.9838027696651 \tabularnewline
32 & 93.3 & 99.8439056721116 & -6.54390567211161 \tabularnewline
33 & 118.6 & 99.252200470575 & 19.347799529425 \tabularnewline
34 & 118.7 & 101.00164402821 & 17.6983559717898 \tabularnewline
35 & 110.7 & 102.601943575892 & 8.09805642410767 \tabularnewline
36 & 113.3 & 103.334176335436 & 9.96582366456434 \tabularnewline
37 & 89.5 & 104.23529410751 & -14.7352941075102 \tabularnewline
38 & 106.3 & 102.902916991082 & 3.39708300891787 \tabularnewline
39 & 115.1 & 103.210083962482 & 11.8899160375181 \tabularnewline
40 & 105.7 & 104.285179710762 & 1.41482028923802 \tabularnewline
41 & 95.8 & 104.413108896531 & -8.61310889653087 \tabularnewline
42 & 114.7 & 103.634304679166 & 11.065695320834 \tabularnewline
43 & 79.6 & 104.63487372891 & -25.0348737289096 \tabularnewline
44 & 80.6 & 102.371200358993 & -21.7712003589926 \tabularnewline
45 & 125 & 100.402630953872 & 24.5973690461276 \tabularnewline
46 & 127.5 & 102.62674479933 & 24.8732552006704 \tabularnewline
47 & 99.5 & 104.875804492245 & -5.37580449224461 \tabularnewline
48 & 104.3 & 104.389719936646 & -0.0897199366464037 \tabularnewline
49 & 90 & 104.381607387986 & -14.3816073879858 \tabularnewline
50 & 96 & 103.081210908526 & -7.08121090852639 \tabularnewline
51 & 108.9 & 102.440922136393 & 6.45907786360698 \tabularnewline
52 & 95.8 & 103.024957139421 & -7.22495713942097 \tabularnewline
53 & 87.2 & 102.371670717752 & -15.1716707177518 \tabularnewline
54 & 108.4 & 100.999836078088 & 7.40016392191191 \tabularnewline
55 & 74.9 & 101.668964837612 & -26.7689648376116 \tabularnewline
56 & 80.8 & 99.2484935582549 & -18.4484935582549 \tabularnewline
57 & 119.1 & 97.5803659681132 & 21.5196340318868 \tabularnewline
58 & 107.9 & 99.5261885440861 & 8.37381145591392 \tabularnewline
59 & 106.9 & 100.283355294864 & 6.61664470513583 \tabularnewline
60 & 96.8 & 100.881637618131 & -4.0816376181308 \tabularnewline
61 & 93.7 & 100.512572669697 & -6.81257266969669 \tabularnewline
62 & 95.2 & 99.8965743826668 & -4.69657438266684 \tabularnewline
63 & 112.7 & 99.4719063585737 & 13.2280936414263 \tabularnewline
64 & 98.5 & 100.668001199519 & -2.16800119951898 \tabularnewline
65 & 91.5 & 100.471968791509 & -8.97196879150918 \tabularnewline
66 & 112 & 99.6607161745003 & 12.3392838254997 \tabularnewline
67 & 76.7 & 100.776444118731 & -24.076444118731 \tabularnewline
68 & 84.7 & 98.5994327231859 & -13.8994327231859 \tabularnewline
69 & 114.9 & 97.3426348638025 & 17.5573651361975 \tabularnewline
70 & 108.4 & 98.9301859070028 & 9.46981409299717 \tabularnewline
71 & 104.6 & 99.7864540956308 & 4.81354590436921 \tabularnewline
72 & 111.3 & 100.221698778571 & 11.0783012214287 \tabularnewline
73 & 90.8 & 101.223407663961 & -10.4234076639613 \tabularnewline
74 & 109.1 & 100.280914779507 & 8.81908522049252 \tabularnewline
75 & 121 & 101.078343541355 & 19.9216564586448 \tabularnewline
76 & 95.2 & 102.879675702979 & -7.67967570297874 \tabularnewline
77 & 110.5 & 102.185273263938 & 8.314726736062 \tabularnewline
78 & 102.4 & 102.937097526939 & -0.537097526939007 \tabularnewline
79 & 86.7 & 102.8885327376 & -16.1885327375997 \tabularnewline
80 & 99.1 & 101.424752618197 & -2.32475261819704 \tabularnewline
81 & 126 & 101.214546621137 & 24.785453378863 \tabularnewline
82 & 110.3 & 103.455667202874 & 6.84433279712574 \tabularnewline
83 & 104.6 & 104.07453726611 & 0.525462733890237 \tabularnewline
84 & 103.1 & 104.122050028126 & -1.02205002812612 \tabularnewline
85 & 102 & 104.029635444516 & -2.02963544451588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192297&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]101.7[/C][C]88.1[/C][C]13.6[/C][/ROW]
[ROW][C]3[/C][C]114.8[/C][C]89.3297229122958[/C][C]25.4702770877042[/C][/ROW]
[ROW][C]4[/C][C]103.4[/C][C]91.6327658032716[/C][C]11.7672341967284[/C][/ROW]
[ROW][C]5[/C][C]96.4[/C][C]92.6967685610707[/C][C]3.70323143892931[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]93.0316177191579[/C][C]16.9683822808421[/C][/ROW]
[ROW][C]7[/C][C]71.1[/C][C]94.5659124599921[/C][C]-23.4659124599921[/C][/ROW]
[ROW][C]8[/C][C]79.4[/C][C]92.4441058269054[/C][C]-13.0441058269054[/C][/ROW]
[ROW][C]9[/C][C]119.2[/C][C]91.2646473117762[/C][C]27.9353526882238[/C][/ROW]
[ROW][C]10[/C][C]99.1[/C][C]93.7905843164654[/C][C]5.30941568353464[/C][/ROW]
[ROW][C]11[/C][C]113.2[/C][C]94.2706659427113[/C][C]18.9293340572887[/C][/ROW]
[ROW][C]12[/C][C]103.6[/C][C]95.9822715165899[/C][C]7.6177284834101[/C][/ROW]
[ROW][C]13[/C][C]97.5[/C][C]96.6710726383324[/C][C]0.828927361667638[/C][/ROW]
[ROW][C]14[/C][C]102.4[/C][C]96.7460249154847[/C][C]5.65397508451532[/C][/ROW]
[ROW][C]15[/C][C]120.8[/C][C]97.2572618792331[/C][C]23.5427381207669[/C][/ROW]
[ROW][C]16[/C][C]89.5[/C][C]99.38601515021[/C][C]-9.88601515020999[/C][/ROW]
[ROW][C]17[/C][C]101.7[/C][C]98.4921137280397[/C][C]3.20788627196033[/C][/ROW]
[ROW][C]18[/C][C]112.5[/C][C]98.7821733786771[/C][C]13.7178266213229[/C][/ROW]
[ROW][C]19[/C][C]72.4[/C][C]100.022550268614[/C][C]-27.622550268614[/C][/ROW]
[ROW][C]20[/C][C]84.7[/C][C]97.5248971096907[/C][C]-12.8248971096907[/C][/ROW]
[ROW][C]21[/C][C]117.2[/C][C]96.3652596226597[/C][C]20.8347403773404[/C][/ROW]
[ROW][C]22[/C][C]112.8[/C][C]98.2491535648471[/C][C]14.5508464351529[/C][/ROW]
[ROW][C]23[/C][C]111.3[/C][C]99.5648527747445[/C][C]11.7351472252555[/C][/ROW]
[ROW][C]24[/C][C]102.3[/C][C]100.625954202837[/C][C]1.67404579716276[/C][/ROW]
[ROW][C]25[/C][C]95.2[/C][C]100.777322767029[/C][C]-5.57732276702866[/C][/ROW]
[ROW][C]26[/C][C]103[/C][C]100.273016767331[/C][C]2.72698323266869[/C][/ROW]
[ROW][C]27[/C][C]116.4[/C][C]100.519592779292[/C][C]15.8804072207085[/C][/ROW]
[ROW][C]28[/C][C]95.1[/C][C]101.955511942225[/C][C]-6.85551194222482[/C][/ROW]
[ROW][C]29[/C][C]100.7[/C][C]101.33563105172[/C][C]-0.635631051719585[/C][/ROW]
[ROW][C]30[/C][C]112.4[/C][C]101.278156782009[/C][C]11.1218432179912[/C][/ROW]
[ROW][C]31[/C][C]75.3[/C][C]102.283802769665[/C][C]-26.9838027696651[/C][/ROW]
[ROW][C]32[/C][C]93.3[/C][C]99.8439056721116[/C][C]-6.54390567211161[/C][/ROW]
[ROW][C]33[/C][C]118.6[/C][C]99.252200470575[/C][C]19.347799529425[/C][/ROW]
[ROW][C]34[/C][C]118.7[/C][C]101.00164402821[/C][C]17.6983559717898[/C][/ROW]
[ROW][C]35[/C][C]110.7[/C][C]102.601943575892[/C][C]8.09805642410767[/C][/ROW]
[ROW][C]36[/C][C]113.3[/C][C]103.334176335436[/C][C]9.96582366456434[/C][/ROW]
[ROW][C]37[/C][C]89.5[/C][C]104.23529410751[/C][C]-14.7352941075102[/C][/ROW]
[ROW][C]38[/C][C]106.3[/C][C]102.902916991082[/C][C]3.39708300891787[/C][/ROW]
[ROW][C]39[/C][C]115.1[/C][C]103.210083962482[/C][C]11.8899160375181[/C][/ROW]
[ROW][C]40[/C][C]105.7[/C][C]104.285179710762[/C][C]1.41482028923802[/C][/ROW]
[ROW][C]41[/C][C]95.8[/C][C]104.413108896531[/C][C]-8.61310889653087[/C][/ROW]
[ROW][C]42[/C][C]114.7[/C][C]103.634304679166[/C][C]11.065695320834[/C][/ROW]
[ROW][C]43[/C][C]79.6[/C][C]104.63487372891[/C][C]-25.0348737289096[/C][/ROW]
[ROW][C]44[/C][C]80.6[/C][C]102.371200358993[/C][C]-21.7712003589926[/C][/ROW]
[ROW][C]45[/C][C]125[/C][C]100.402630953872[/C][C]24.5973690461276[/C][/ROW]
[ROW][C]46[/C][C]127.5[/C][C]102.62674479933[/C][C]24.8732552006704[/C][/ROW]
[ROW][C]47[/C][C]99.5[/C][C]104.875804492245[/C][C]-5.37580449224461[/C][/ROW]
[ROW][C]48[/C][C]104.3[/C][C]104.389719936646[/C][C]-0.0897199366464037[/C][/ROW]
[ROW][C]49[/C][C]90[/C][C]104.381607387986[/C][C]-14.3816073879858[/C][/ROW]
[ROW][C]50[/C][C]96[/C][C]103.081210908526[/C][C]-7.08121090852639[/C][/ROW]
[ROW][C]51[/C][C]108.9[/C][C]102.440922136393[/C][C]6.45907786360698[/C][/ROW]
[ROW][C]52[/C][C]95.8[/C][C]103.024957139421[/C][C]-7.22495713942097[/C][/ROW]
[ROW][C]53[/C][C]87.2[/C][C]102.371670717752[/C][C]-15.1716707177518[/C][/ROW]
[ROW][C]54[/C][C]108.4[/C][C]100.999836078088[/C][C]7.40016392191191[/C][/ROW]
[ROW][C]55[/C][C]74.9[/C][C]101.668964837612[/C][C]-26.7689648376116[/C][/ROW]
[ROW][C]56[/C][C]80.8[/C][C]99.2484935582549[/C][C]-18.4484935582549[/C][/ROW]
[ROW][C]57[/C][C]119.1[/C][C]97.5803659681132[/C][C]21.5196340318868[/C][/ROW]
[ROW][C]58[/C][C]107.9[/C][C]99.5261885440861[/C][C]8.37381145591392[/C][/ROW]
[ROW][C]59[/C][C]106.9[/C][C]100.283355294864[/C][C]6.61664470513583[/C][/ROW]
[ROW][C]60[/C][C]96.8[/C][C]100.881637618131[/C][C]-4.0816376181308[/C][/ROW]
[ROW][C]61[/C][C]93.7[/C][C]100.512572669697[/C][C]-6.81257266969669[/C][/ROW]
[ROW][C]62[/C][C]95.2[/C][C]99.8965743826668[/C][C]-4.69657438266684[/C][/ROW]
[ROW][C]63[/C][C]112.7[/C][C]99.4719063585737[/C][C]13.2280936414263[/C][/ROW]
[ROW][C]64[/C][C]98.5[/C][C]100.668001199519[/C][C]-2.16800119951898[/C][/ROW]
[ROW][C]65[/C][C]91.5[/C][C]100.471968791509[/C][C]-8.97196879150918[/C][/ROW]
[ROW][C]66[/C][C]112[/C][C]99.6607161745003[/C][C]12.3392838254997[/C][/ROW]
[ROW][C]67[/C][C]76.7[/C][C]100.776444118731[/C][C]-24.076444118731[/C][/ROW]
[ROW][C]68[/C][C]84.7[/C][C]98.5994327231859[/C][C]-13.8994327231859[/C][/ROW]
[ROW][C]69[/C][C]114.9[/C][C]97.3426348638025[/C][C]17.5573651361975[/C][/ROW]
[ROW][C]70[/C][C]108.4[/C][C]98.9301859070028[/C][C]9.46981409299717[/C][/ROW]
[ROW][C]71[/C][C]104.6[/C][C]99.7864540956308[/C][C]4.81354590436921[/C][/ROW]
[ROW][C]72[/C][C]111.3[/C][C]100.221698778571[/C][C]11.0783012214287[/C][/ROW]
[ROW][C]73[/C][C]90.8[/C][C]101.223407663961[/C][C]-10.4234076639613[/C][/ROW]
[ROW][C]74[/C][C]109.1[/C][C]100.280914779507[/C][C]8.81908522049252[/C][/ROW]
[ROW][C]75[/C][C]121[/C][C]101.078343541355[/C][C]19.9216564586448[/C][/ROW]
[ROW][C]76[/C][C]95.2[/C][C]102.879675702979[/C][C]-7.67967570297874[/C][/ROW]
[ROW][C]77[/C][C]110.5[/C][C]102.185273263938[/C][C]8.314726736062[/C][/ROW]
[ROW][C]78[/C][C]102.4[/C][C]102.937097526939[/C][C]-0.537097526939007[/C][/ROW]
[ROW][C]79[/C][C]86.7[/C][C]102.8885327376[/C][C]-16.1885327375997[/C][/ROW]
[ROW][C]80[/C][C]99.1[/C][C]101.424752618197[/C][C]-2.32475261819704[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]101.214546621137[/C][C]24.785453378863[/C][/ROW]
[ROW][C]82[/C][C]110.3[/C][C]103.455667202874[/C][C]6.84433279712574[/C][/ROW]
[ROW][C]83[/C][C]104.6[/C][C]104.07453726611[/C][C]0.525462733890237[/C][/ROW]
[ROW][C]84[/C][C]103.1[/C][C]104.122050028126[/C][C]-1.02205002812612[/C][/ROW]
[ROW][C]85[/C][C]102[/C][C]104.029635444516[/C][C]-2.02963544451588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192297&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
2101.788.113.6
3114.889.329722912295825.4702770877042
4103.491.632765803271611.7672341967284
596.492.69676856107073.70323143892931
611093.031617719157916.9683822808421
771.194.5659124599921-23.4659124599921
879.492.4441058269054-13.0441058269054
9119.291.264647311776227.9353526882238
1099.193.79058431646545.30941568353464
11113.294.270665942711318.9293340572887
12103.695.98227151658997.6177284834101
1397.596.67107263833240.828927361667638
14102.496.74602491548475.65397508451532
15120.897.257261879233123.5427381207669
1689.599.38601515021-9.88601515020999
17101.798.49211372803973.20788627196033
18112.598.782173378677113.7178266213229
1972.4100.022550268614-27.622550268614
2084.797.5248971096907-12.8248971096907
21117.296.365259622659720.8347403773404
22112.898.249153564847114.5508464351529
23111.399.564852774744511.7351472252555
24102.3100.6259542028371.67404579716276
2595.2100.777322767029-5.57732276702866
26103100.2730167673312.72698323266869
27116.4100.51959277929215.8804072207085
2895.1101.955511942225-6.85551194222482
29100.7101.33563105172-0.635631051719585
30112.4101.27815678200911.1218432179912
3175.3102.283802769665-26.9838027696651
3293.399.8439056721116-6.54390567211161
33118.699.25220047057519.347799529425
34118.7101.0016440282117.6983559717898
35110.7102.6019435758928.09805642410767
36113.3103.3341763354369.96582366456434
3789.5104.23529410751-14.7352941075102
38106.3102.9029169910823.39708300891787
39115.1103.21008396248211.8899160375181
40105.7104.2851797107621.41482028923802
4195.8104.413108896531-8.61310889653087
42114.7103.63430467916611.065695320834
4379.6104.63487372891-25.0348737289096
4480.6102.371200358993-21.7712003589926
45125100.40263095387224.5973690461276
46127.5102.6267447993324.8732552006704
4799.5104.875804492245-5.37580449224461
48104.3104.389719936646-0.0897199366464037
4990104.381607387986-14.3816073879858
5096103.081210908526-7.08121090852639
51108.9102.4409221363936.45907786360698
5295.8103.024957139421-7.22495713942097
5387.2102.371670717752-15.1716707177518
54108.4100.9998360780887.40016392191191
5574.9101.668964837612-26.7689648376116
5680.899.2484935582549-18.4484935582549
57119.197.580365968113221.5196340318868
58107.999.52618854408618.37381145591392
59106.9100.2833552948646.61664470513583
6096.8100.881637618131-4.0816376181308
6193.7100.512572669697-6.81257266969669
6295.299.8965743826668-4.69657438266684
63112.799.471906358573713.2280936414263
6498.5100.668001199519-2.16800119951898
6591.5100.471968791509-8.97196879150918
6611299.660716174500312.3392838254997
6776.7100.776444118731-24.076444118731
6884.798.5994327231859-13.8994327231859
69114.997.342634863802517.5573651361975
70108.498.93018590700289.46981409299717
71104.699.78645409563084.81354590436921
72111.3100.22169877857111.0783012214287
7390.8101.223407663961-10.4234076639613
74109.1100.2809147795078.81908522049252
75121101.07834354135519.9216564586448
7695.2102.879675702979-7.67967570297874
77110.5102.1852732639388.314726736062
78102.4102.937097526939-0.537097526939007
7986.7102.8885327376-16.1885327375997
8099.1101.424752618197-2.32475261819704
81126101.21454662113724.785453378863
82110.3103.4556672028746.84433279712574
83104.6104.074537266110.525462733890237
84103.1104.122050028126-1.02205002812612
85102104.029635444516-2.02963544451588







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86103.84611417909576.4703655258422131.221862832347
87103.84611417909576.3586823533318131.333546004857
88103.84611417909576.2474511240503131.444777234139
89103.84611417909576.1366663954275131.555561962762
90103.84611417909576.0263228332616131.665905524928
91103.84611417909575.9164152087227131.775813149467
92103.84611417909575.8069383954611131.885289962728
93103.84611417909575.6978873668172131.994340991372
94103.84611417909575.5892571931289132.10297116506
95103.84611417909575.4810430391304132.211185319059
96103.84611417909575.3732401614416132.318988196748
97103.84611417909575.2658439061415132.426384452048

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 103.846114179095 & 76.4703655258422 & 131.221862832347 \tabularnewline
87 & 103.846114179095 & 76.3586823533318 & 131.333546004857 \tabularnewline
88 & 103.846114179095 & 76.2474511240503 & 131.444777234139 \tabularnewline
89 & 103.846114179095 & 76.1366663954275 & 131.555561962762 \tabularnewline
90 & 103.846114179095 & 76.0263228332616 & 131.665905524928 \tabularnewline
91 & 103.846114179095 & 75.9164152087227 & 131.775813149467 \tabularnewline
92 & 103.846114179095 & 75.8069383954611 & 131.885289962728 \tabularnewline
93 & 103.846114179095 & 75.6978873668172 & 131.994340991372 \tabularnewline
94 & 103.846114179095 & 75.5892571931289 & 132.10297116506 \tabularnewline
95 & 103.846114179095 & 75.4810430391304 & 132.211185319059 \tabularnewline
96 & 103.846114179095 & 75.3732401614416 & 132.318988196748 \tabularnewline
97 & 103.846114179095 & 75.2658439061415 & 132.426384452048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192297&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]86[/C][C]103.846114179095[/C][C]76.4703655258422[/C][C]131.221862832347[/C][/ROW]
[ROW][C]87[/C][C]103.846114179095[/C][C]76.3586823533318[/C][C]131.333546004857[/C][/ROW]
[ROW][C]88[/C][C]103.846114179095[/C][C]76.2474511240503[/C][C]131.444777234139[/C][/ROW]
[ROW][C]89[/C][C]103.846114179095[/C][C]76.1366663954275[/C][C]131.555561962762[/C][/ROW]
[ROW][C]90[/C][C]103.846114179095[/C][C]76.0263228332616[/C][C]131.665905524928[/C][/ROW]
[ROW][C]91[/C][C]103.846114179095[/C][C]75.9164152087227[/C][C]131.775813149467[/C][/ROW]
[ROW][C]92[/C][C]103.846114179095[/C][C]75.8069383954611[/C][C]131.885289962728[/C][/ROW]
[ROW][C]93[/C][C]103.846114179095[/C][C]75.6978873668172[/C][C]131.994340991372[/C][/ROW]
[ROW][C]94[/C][C]103.846114179095[/C][C]75.5892571931289[/C][C]132.10297116506[/C][/ROW]
[ROW][C]95[/C][C]103.846114179095[/C][C]75.4810430391304[/C][C]132.211185319059[/C][/ROW]
[ROW][C]96[/C][C]103.846114179095[/C][C]75.3732401614416[/C][C]132.318988196748[/C][/ROW]
[ROW][C]97[/C][C]103.846114179095[/C][C]75.2658439061415[/C][C]132.426384452048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192297&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192297&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
86103.84611417909576.4703655258422131.221862832347
87103.84611417909576.3586823533318131.333546004857
88103.84611417909576.2474511240503131.444777234139
89103.84611417909576.1366663954275131.555561962762
90103.84611417909576.0263228332616131.665905524928
91103.84611417909575.9164152087227131.775813149467
92103.84611417909575.8069383954611131.885289962728
93103.84611417909575.6978873668172131.994340991372
94103.84611417909575.5892571931289132.10297116506
95103.84611417909575.4810430391304132.211185319059
96103.84611417909575.3732401614416132.318988196748
97103.84611417909575.2658439061415132.426384452048



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')