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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 May 2013 14:15:47 -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/2013/May/22/t1369246581ujc8gf9k807udsg.htm/, Retrieved Sun, 28 Apr 2024 00:00:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210285, Retrieved Sun, 28 Apr 2024 00:00:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgv 10 oef 2] [2013-05-22 18:15:47] [9bda411d6223d16f0472c7feaae49b5f] [Current]
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Dataseries X:
6,3
6,2
6,2
6,3
6,5
6,5
6,2
6,2
6,2
6,1
6,1
6,2
6,1
6,1
6,2
6,2
6,4
6,2
5,7
5,7
5,7
5,9
6
6,3
6,4
6,5
6,8
7
7,3
7,4
6,9
6,9
7
7,1
7,2
7,1
6,8
6,5
6,4
6,5
6,7
6,6
6,2
6,2
6,5
6,8
6,8
6,5
5,9
5,5
5,6
6
6,3
6,2
5,6
5,4
5,7
5,9
6,2
6,3
6,1
5,9
5,9
5,7
5,9
6,1
6,1
6,5
6,8
6,8
6,9
6,9
6,8
6,6
6,5
6,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210285&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210285&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210285&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]0.999933893038648[/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=210285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210285&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26.26.3-0.0999999999999996
36.26.20000661069614-6.61069613538956e-06
46.36.200000000437010.0999999995629866
56.56.299993389303890.200006610696106
66.56.499986778170721.32218292829833e-05
76.26.49999999912595-0.299999999125945
86.26.20001983208835-1.98320883475489e-05
96.26.20000000131104-1.31103927714094e-09
106.16.20000000000009-0.100000000000088
116.16.10000661069614-6.61069613538956e-06
126.26.100000000437010.0999999995629874
136.16.19999338930389-0.0999933893038945
146.16.10000661025912-6.61025912229718e-06
156.26.100000000436980.0999999995630168
166.26.199993389303896.61069610607967e-06
176.46.199999999562990.200000000437013
186.26.3999867786077-0.199986778607701
195.76.20001322051824-0.500013220518245
205.75.70003305435464-3.30543546445128e-05
215.75.70000000218512-2.18512319349884e-09
225.95.700000000000140.199999999999855
2365.899986778607730.10001322139227
246.35.999993388429840.300006611570161
256.46.299980167474520.100019832525477
266.56.39999338799280.100006612007203
276.86.499993388866770.300006611133234
2876.799980167474550.200019832525448
297.36.999986777296660.300013222703338
307.47.299980167037480.100019832962519
316.97.39999338799277-0.499993387992768
326.96.90003305304358-3.30530435759258e-05
3376.900000002185040.0999999978149635
347.16.999993389304010.10000661069599
357.27.099993388866850.100006611133149
367.17.19999338886682-0.0999933888668236
376.87.10000661025909-0.300006610259093
386.56.80001983252539-0.30001983252539
396.46.50001983339947-0.100019833399474
406.56.400006612007260.0999933879927388
416.76.499993389740960.200006610259035
426.66.69998677817075-0.099986778170746
436.26.60000660982208-0.400006609822079
446.26.2000264432215-2.64432214960308e-05
456.56.200000001748080.299999998251919
466.86.499980167911710.30001983208829
476.86.799980166600561.98333994445576e-05
486.56.79999999868887-0.299999998688874
495.96.50001983208832-0.600019832088319
505.55.90003966548785-0.40003966548785
515.65.500026445406710.0999735545932943
5265.599993391052090.40000660894791
536.35.999973556778560.300026443221438
546.26.29998016616351-0.0999801661635127
555.66.20000660938498-0.600006609384981
565.45.60003966461374-0.200039664613737
575.75.400013224014380.299986775985622
585.95.699980168785790.200019831214206
596.25.899986777296750.300013222703251
606.36.199980167037480.100019832962518
616.16.29999338799277-0.199993387992768
625.96.10001322095517-0.20001322095517
635.95.90001322226627-1.3222266267654e-05
645.75.90000000087408-0.200000000874084
655.95.700013221392330.199986778607672
666.15.899986779481760.200013220518244
676.16.099986777733761.32222662383441e-05
686.56.099999999125920.400000000874084
696.86.49997355721540.300026442784598
706.86.799980166163541.983383645765e-05
716.96.799999998688850.100000001311155
726.96.899993389303786.61069622154287e-06
736.86.89999999956299-0.0999999995629874
746.66.80000661069611-0.200006610696106
756.56.60001322182928-0.100013221829283
766.56.50000661157019-6.61157018999603e-06

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.2 & 6.3 & -0.0999999999999996 \tabularnewline
3 & 6.2 & 6.20000661069614 & -6.61069613538956e-06 \tabularnewline
4 & 6.3 & 6.20000000043701 & 0.0999999995629866 \tabularnewline
5 & 6.5 & 6.29999338930389 & 0.200006610696106 \tabularnewline
6 & 6.5 & 6.49998677817072 & 1.32218292829833e-05 \tabularnewline
7 & 6.2 & 6.49999999912595 & -0.299999999125945 \tabularnewline
8 & 6.2 & 6.20001983208835 & -1.98320883475489e-05 \tabularnewline
9 & 6.2 & 6.20000000131104 & -1.31103927714094e-09 \tabularnewline
10 & 6.1 & 6.20000000000009 & -0.100000000000088 \tabularnewline
11 & 6.1 & 6.10000661069614 & -6.61069613538956e-06 \tabularnewline
12 & 6.2 & 6.10000000043701 & 0.0999999995629874 \tabularnewline
13 & 6.1 & 6.19999338930389 & -0.0999933893038945 \tabularnewline
14 & 6.1 & 6.10000661025912 & -6.61025912229718e-06 \tabularnewline
15 & 6.2 & 6.10000000043698 & 0.0999999995630168 \tabularnewline
16 & 6.2 & 6.19999338930389 & 6.61069610607967e-06 \tabularnewline
17 & 6.4 & 6.19999999956299 & 0.200000000437013 \tabularnewline
18 & 6.2 & 6.3999867786077 & -0.199986778607701 \tabularnewline
19 & 5.7 & 6.20001322051824 & -0.500013220518245 \tabularnewline
20 & 5.7 & 5.70003305435464 & -3.30543546445128e-05 \tabularnewline
21 & 5.7 & 5.70000000218512 & -2.18512319349884e-09 \tabularnewline
22 & 5.9 & 5.70000000000014 & 0.199999999999855 \tabularnewline
23 & 6 & 5.89998677860773 & 0.10001322139227 \tabularnewline
24 & 6.3 & 5.99999338842984 & 0.300006611570161 \tabularnewline
25 & 6.4 & 6.29998016747452 & 0.100019832525477 \tabularnewline
26 & 6.5 & 6.3999933879928 & 0.100006612007203 \tabularnewline
27 & 6.8 & 6.49999338886677 & 0.300006611133234 \tabularnewline
28 & 7 & 6.79998016747455 & 0.200019832525448 \tabularnewline
29 & 7.3 & 6.99998677729666 & 0.300013222703338 \tabularnewline
30 & 7.4 & 7.29998016703748 & 0.100019832962519 \tabularnewline
31 & 6.9 & 7.39999338799277 & -0.499993387992768 \tabularnewline
32 & 6.9 & 6.90003305304358 & -3.30530435759258e-05 \tabularnewline
33 & 7 & 6.90000000218504 & 0.0999999978149635 \tabularnewline
34 & 7.1 & 6.99999338930401 & 0.10000661069599 \tabularnewline
35 & 7.2 & 7.09999338886685 & 0.100006611133149 \tabularnewline
36 & 7.1 & 7.19999338886682 & -0.0999933888668236 \tabularnewline
37 & 6.8 & 7.10000661025909 & -0.300006610259093 \tabularnewline
38 & 6.5 & 6.80001983252539 & -0.30001983252539 \tabularnewline
39 & 6.4 & 6.50001983339947 & -0.100019833399474 \tabularnewline
40 & 6.5 & 6.40000661200726 & 0.0999933879927388 \tabularnewline
41 & 6.7 & 6.49999338974096 & 0.200006610259035 \tabularnewline
42 & 6.6 & 6.69998677817075 & -0.099986778170746 \tabularnewline
43 & 6.2 & 6.60000660982208 & -0.400006609822079 \tabularnewline
44 & 6.2 & 6.2000264432215 & -2.64432214960308e-05 \tabularnewline
45 & 6.5 & 6.20000000174808 & 0.299999998251919 \tabularnewline
46 & 6.8 & 6.49998016791171 & 0.30001983208829 \tabularnewline
47 & 6.8 & 6.79998016660056 & 1.98333994445576e-05 \tabularnewline
48 & 6.5 & 6.79999999868887 & -0.299999998688874 \tabularnewline
49 & 5.9 & 6.50001983208832 & -0.600019832088319 \tabularnewline
50 & 5.5 & 5.90003966548785 & -0.40003966548785 \tabularnewline
51 & 5.6 & 5.50002644540671 & 0.0999735545932943 \tabularnewline
52 & 6 & 5.59999339105209 & 0.40000660894791 \tabularnewline
53 & 6.3 & 5.99997355677856 & 0.300026443221438 \tabularnewline
54 & 6.2 & 6.29998016616351 & -0.0999801661635127 \tabularnewline
55 & 5.6 & 6.20000660938498 & -0.600006609384981 \tabularnewline
56 & 5.4 & 5.60003966461374 & -0.200039664613737 \tabularnewline
57 & 5.7 & 5.40001322401438 & 0.299986775985622 \tabularnewline
58 & 5.9 & 5.69998016878579 & 0.200019831214206 \tabularnewline
59 & 6.2 & 5.89998677729675 & 0.300013222703251 \tabularnewline
60 & 6.3 & 6.19998016703748 & 0.100019832962518 \tabularnewline
61 & 6.1 & 6.29999338799277 & -0.199993387992768 \tabularnewline
62 & 5.9 & 6.10001322095517 & -0.20001322095517 \tabularnewline
63 & 5.9 & 5.90001322226627 & -1.3222266267654e-05 \tabularnewline
64 & 5.7 & 5.90000000087408 & -0.200000000874084 \tabularnewline
65 & 5.9 & 5.70001322139233 & 0.199986778607672 \tabularnewline
66 & 6.1 & 5.89998677948176 & 0.200013220518244 \tabularnewline
67 & 6.1 & 6.09998677773376 & 1.32222662383441e-05 \tabularnewline
68 & 6.5 & 6.09999999912592 & 0.400000000874084 \tabularnewline
69 & 6.8 & 6.4999735572154 & 0.300026442784598 \tabularnewline
70 & 6.8 & 6.79998016616354 & 1.983383645765e-05 \tabularnewline
71 & 6.9 & 6.79999999868885 & 0.100000001311155 \tabularnewline
72 & 6.9 & 6.89999338930378 & 6.61069622154287e-06 \tabularnewline
73 & 6.8 & 6.89999999956299 & -0.0999999995629874 \tabularnewline
74 & 6.6 & 6.80000661069611 & -0.200006610696106 \tabularnewline
75 & 6.5 & 6.60001322182928 & -0.100013221829283 \tabularnewline
76 & 6.5 & 6.50000661157019 & -6.61157018999603e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210285&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]6.2[/C][C]6.3[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]3[/C][C]6.2[/C][C]6.20000661069614[/C][C]-6.61069613538956e-06[/C][/ROW]
[ROW][C]4[/C][C]6.3[/C][C]6.20000000043701[/C][C]0.0999999995629866[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.29999338930389[/C][C]0.200006610696106[/C][/ROW]
[ROW][C]6[/C][C]6.5[/C][C]6.49998677817072[/C][C]1.32218292829833e-05[/C][/ROW]
[ROW][C]7[/C][C]6.2[/C][C]6.49999999912595[/C][C]-0.299999999125945[/C][/ROW]
[ROW][C]8[/C][C]6.2[/C][C]6.20001983208835[/C][C]-1.98320883475489e-05[/C][/ROW]
[ROW][C]9[/C][C]6.2[/C][C]6.20000000131104[/C][C]-1.31103927714094e-09[/C][/ROW]
[ROW][C]10[/C][C]6.1[/C][C]6.20000000000009[/C][C]-0.100000000000088[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.10000661069614[/C][C]-6.61069613538956e-06[/C][/ROW]
[ROW][C]12[/C][C]6.2[/C][C]6.10000000043701[/C][C]0.0999999995629874[/C][/ROW]
[ROW][C]13[/C][C]6.1[/C][C]6.19999338930389[/C][C]-0.0999933893038945[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.10000661025912[/C][C]-6.61025912229718e-06[/C][/ROW]
[ROW][C]15[/C][C]6.2[/C][C]6.10000000043698[/C][C]0.0999999995630168[/C][/ROW]
[ROW][C]16[/C][C]6.2[/C][C]6.19999338930389[/C][C]6.61069610607967e-06[/C][/ROW]
[ROW][C]17[/C][C]6.4[/C][C]6.19999999956299[/C][C]0.200000000437013[/C][/ROW]
[ROW][C]18[/C][C]6.2[/C][C]6.3999867786077[/C][C]-0.199986778607701[/C][/ROW]
[ROW][C]19[/C][C]5.7[/C][C]6.20001322051824[/C][C]-0.500013220518245[/C][/ROW]
[ROW][C]20[/C][C]5.7[/C][C]5.70003305435464[/C][C]-3.30543546445128e-05[/C][/ROW]
[ROW][C]21[/C][C]5.7[/C][C]5.70000000218512[/C][C]-2.18512319349884e-09[/C][/ROW]
[ROW][C]22[/C][C]5.9[/C][C]5.70000000000014[/C][C]0.199999999999855[/C][/ROW]
[ROW][C]23[/C][C]6[/C][C]5.89998677860773[/C][C]0.10001322139227[/C][/ROW]
[ROW][C]24[/C][C]6.3[/C][C]5.99999338842984[/C][C]0.300006611570161[/C][/ROW]
[ROW][C]25[/C][C]6.4[/C][C]6.29998016747452[/C][C]0.100019832525477[/C][/ROW]
[ROW][C]26[/C][C]6.5[/C][C]6.3999933879928[/C][C]0.100006612007203[/C][/ROW]
[ROW][C]27[/C][C]6.8[/C][C]6.49999338886677[/C][C]0.300006611133234[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]6.79998016747455[/C][C]0.200019832525448[/C][/ROW]
[ROW][C]29[/C][C]7.3[/C][C]6.99998677729666[/C][C]0.300013222703338[/C][/ROW]
[ROW][C]30[/C][C]7.4[/C][C]7.29998016703748[/C][C]0.100019832962519[/C][/ROW]
[ROW][C]31[/C][C]6.9[/C][C]7.39999338799277[/C][C]-0.499993387992768[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]6.90003305304358[/C][C]-3.30530435759258e-05[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]6.90000000218504[/C][C]0.0999999978149635[/C][/ROW]
[ROW][C]34[/C][C]7.1[/C][C]6.99999338930401[/C][C]0.10000661069599[/C][/ROW]
[ROW][C]35[/C][C]7.2[/C][C]7.09999338886685[/C][C]0.100006611133149[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.19999338886682[/C][C]-0.0999933888668236[/C][/ROW]
[ROW][C]37[/C][C]6.8[/C][C]7.10000661025909[/C][C]-0.300006610259093[/C][/ROW]
[ROW][C]38[/C][C]6.5[/C][C]6.80001983252539[/C][C]-0.30001983252539[/C][/ROW]
[ROW][C]39[/C][C]6.4[/C][C]6.50001983339947[/C][C]-0.100019833399474[/C][/ROW]
[ROW][C]40[/C][C]6.5[/C][C]6.40000661200726[/C][C]0.0999933879927388[/C][/ROW]
[ROW][C]41[/C][C]6.7[/C][C]6.49999338974096[/C][C]0.200006610259035[/C][/ROW]
[ROW][C]42[/C][C]6.6[/C][C]6.69998677817075[/C][C]-0.099986778170746[/C][/ROW]
[ROW][C]43[/C][C]6.2[/C][C]6.60000660982208[/C][C]-0.400006609822079[/C][/ROW]
[ROW][C]44[/C][C]6.2[/C][C]6.2000264432215[/C][C]-2.64432214960308e-05[/C][/ROW]
[ROW][C]45[/C][C]6.5[/C][C]6.20000000174808[/C][C]0.299999998251919[/C][/ROW]
[ROW][C]46[/C][C]6.8[/C][C]6.49998016791171[/C][C]0.30001983208829[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.79998016660056[/C][C]1.98333994445576e-05[/C][/ROW]
[ROW][C]48[/C][C]6.5[/C][C]6.79999999868887[/C][C]-0.299999998688874[/C][/ROW]
[ROW][C]49[/C][C]5.9[/C][C]6.50001983208832[/C][C]-0.600019832088319[/C][/ROW]
[ROW][C]50[/C][C]5.5[/C][C]5.90003966548785[/C][C]-0.40003966548785[/C][/ROW]
[ROW][C]51[/C][C]5.6[/C][C]5.50002644540671[/C][C]0.0999735545932943[/C][/ROW]
[ROW][C]52[/C][C]6[/C][C]5.59999339105209[/C][C]0.40000660894791[/C][/ROW]
[ROW][C]53[/C][C]6.3[/C][C]5.99997355677856[/C][C]0.300026443221438[/C][/ROW]
[ROW][C]54[/C][C]6.2[/C][C]6.29998016616351[/C][C]-0.0999801661635127[/C][/ROW]
[ROW][C]55[/C][C]5.6[/C][C]6.20000660938498[/C][C]-0.600006609384981[/C][/ROW]
[ROW][C]56[/C][C]5.4[/C][C]5.60003966461374[/C][C]-0.200039664613737[/C][/ROW]
[ROW][C]57[/C][C]5.7[/C][C]5.40001322401438[/C][C]0.299986775985622[/C][/ROW]
[ROW][C]58[/C][C]5.9[/C][C]5.69998016878579[/C][C]0.200019831214206[/C][/ROW]
[ROW][C]59[/C][C]6.2[/C][C]5.89998677729675[/C][C]0.300013222703251[/C][/ROW]
[ROW][C]60[/C][C]6.3[/C][C]6.19998016703748[/C][C]0.100019832962518[/C][/ROW]
[ROW][C]61[/C][C]6.1[/C][C]6.29999338799277[/C][C]-0.199993387992768[/C][/ROW]
[ROW][C]62[/C][C]5.9[/C][C]6.10001322095517[/C][C]-0.20001322095517[/C][/ROW]
[ROW][C]63[/C][C]5.9[/C][C]5.90001322226627[/C][C]-1.3222266267654e-05[/C][/ROW]
[ROW][C]64[/C][C]5.7[/C][C]5.90000000087408[/C][C]-0.200000000874084[/C][/ROW]
[ROW][C]65[/C][C]5.9[/C][C]5.70001322139233[/C][C]0.199986778607672[/C][/ROW]
[ROW][C]66[/C][C]6.1[/C][C]5.89998677948176[/C][C]0.200013220518244[/C][/ROW]
[ROW][C]67[/C][C]6.1[/C][C]6.09998677773376[/C][C]1.32222662383441e-05[/C][/ROW]
[ROW][C]68[/C][C]6.5[/C][C]6.09999999912592[/C][C]0.400000000874084[/C][/ROW]
[ROW][C]69[/C][C]6.8[/C][C]6.4999735572154[/C][C]0.300026442784598[/C][/ROW]
[ROW][C]70[/C][C]6.8[/C][C]6.79998016616354[/C][C]1.983383645765e-05[/C][/ROW]
[ROW][C]71[/C][C]6.9[/C][C]6.79999999868885[/C][C]0.100000001311155[/C][/ROW]
[ROW][C]72[/C][C]6.9[/C][C]6.89999338930378[/C][C]6.61069622154287e-06[/C][/ROW]
[ROW][C]73[/C][C]6.8[/C][C]6.89999999956299[/C][C]-0.0999999995629874[/C][/ROW]
[ROW][C]74[/C][C]6.6[/C][C]6.80000661069611[/C][C]-0.200006610696106[/C][/ROW]
[ROW][C]75[/C][C]6.5[/C][C]6.60001322182928[/C][C]-0.100013221829283[/C][/ROW]
[ROW][C]76[/C][C]6.5[/C][C]6.50000661157019[/C][C]-6.61157018999603e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210285&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
26.26.3-0.0999999999999996
36.26.20000661069614-6.61069613538956e-06
46.36.200000000437010.0999999995629866
56.56.299993389303890.200006610696106
66.56.499986778170721.32218292829833e-05
76.26.49999999912595-0.299999999125945
86.26.20001983208835-1.98320883475489e-05
96.26.20000000131104-1.31103927714094e-09
106.16.20000000000009-0.100000000000088
116.16.10000661069614-6.61069613538956e-06
126.26.100000000437010.0999999995629874
136.16.19999338930389-0.0999933893038945
146.16.10000661025912-6.61025912229718e-06
156.26.100000000436980.0999999995630168
166.26.199993389303896.61069610607967e-06
176.46.199999999562990.200000000437013
186.26.3999867786077-0.199986778607701
195.76.20001322051824-0.500013220518245
205.75.70003305435464-3.30543546445128e-05
215.75.70000000218512-2.18512319349884e-09
225.95.700000000000140.199999999999855
2365.899986778607730.10001322139227
246.35.999993388429840.300006611570161
256.46.299980167474520.100019832525477
266.56.39999338799280.100006612007203
276.86.499993388866770.300006611133234
2876.799980167474550.200019832525448
297.36.999986777296660.300013222703338
307.47.299980167037480.100019832962519
316.97.39999338799277-0.499993387992768
326.96.90003305304358-3.30530435759258e-05
3376.900000002185040.0999999978149635
347.16.999993389304010.10000661069599
357.27.099993388866850.100006611133149
367.17.19999338886682-0.0999933888668236
376.87.10000661025909-0.300006610259093
386.56.80001983252539-0.30001983252539
396.46.50001983339947-0.100019833399474
406.56.400006612007260.0999933879927388
416.76.499993389740960.200006610259035
426.66.69998677817075-0.099986778170746
436.26.60000660982208-0.400006609822079
446.26.2000264432215-2.64432214960308e-05
456.56.200000001748080.299999998251919
466.86.499980167911710.30001983208829
476.86.799980166600561.98333994445576e-05
486.56.79999999868887-0.299999998688874
495.96.50001983208832-0.600019832088319
505.55.90003966548785-0.40003966548785
515.65.500026445406710.0999735545932943
5265.599993391052090.40000660894791
536.35.999973556778560.300026443221438
546.26.29998016616351-0.0999801661635127
555.66.20000660938498-0.600006609384981
565.45.60003966461374-0.200039664613737
575.75.400013224014380.299986775985622
585.95.699980168785790.200019831214206
596.25.899986777296750.300013222703251
606.36.199980167037480.100019832962518
616.16.29999338799277-0.199993387992768
625.96.10001322095517-0.20001322095517
635.95.90001322226627-1.3222266267654e-05
645.75.90000000087408-0.200000000874084
655.95.700013221392330.199986778607672
666.15.899986779481760.200013220518244
676.16.099986777733761.32222662383441e-05
686.56.099999999125920.400000000874084
696.86.49997355721540.300026442784598
706.86.799980166163541.983383645765e-05
716.96.799999998688850.100000001311155
726.96.899993389303786.61069622154287e-06
736.86.89999999956299-0.0999999995629874
746.66.80000661069611-0.200006610696106
756.56.60001322182928-0.100013221829283
766.56.50000661157019-6.61157018999603e-06







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
776.500000000437076.054707798127646.9452922027465
786.500000000437075.870282543409877.12971745746427
796.500000000437075.72876527226937.27123472860484
806.500000000437075.609459750824947.3905402500492
816.500000000437075.504349024227817.49565097664633
826.500000000437075.409321405857687.59067859501646
836.500000000437075.321934328701887.67806567217226
846.500000000437075.240596309332387.75940369154176
856.500000000437075.16420189165897.83579810921524
866.500000000437075.091946195476997.90805380539715
876.500000000437075.023221598675397.97677840219875
886.500000000437074.957556037708778.04244396316537

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 6.50000000043707 & 6.05470779812764 & 6.9452922027465 \tabularnewline
78 & 6.50000000043707 & 5.87028254340987 & 7.12971745746427 \tabularnewline
79 & 6.50000000043707 & 5.7287652722693 & 7.27123472860484 \tabularnewline
80 & 6.50000000043707 & 5.60945975082494 & 7.3905402500492 \tabularnewline
81 & 6.50000000043707 & 5.50434902422781 & 7.49565097664633 \tabularnewline
82 & 6.50000000043707 & 5.40932140585768 & 7.59067859501646 \tabularnewline
83 & 6.50000000043707 & 5.32193432870188 & 7.67806567217226 \tabularnewline
84 & 6.50000000043707 & 5.24059630933238 & 7.75940369154176 \tabularnewline
85 & 6.50000000043707 & 5.1642018916589 & 7.83579810921524 \tabularnewline
86 & 6.50000000043707 & 5.09194619547699 & 7.90805380539715 \tabularnewline
87 & 6.50000000043707 & 5.02322159867539 & 7.97677840219875 \tabularnewline
88 & 6.50000000043707 & 4.95755603770877 & 8.04244396316537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210285&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]77[/C][C]6.50000000043707[/C][C]6.05470779812764[/C][C]6.9452922027465[/C][/ROW]
[ROW][C]78[/C][C]6.50000000043707[/C][C]5.87028254340987[/C][C]7.12971745746427[/C][/ROW]
[ROW][C]79[/C][C]6.50000000043707[/C][C]5.7287652722693[/C][C]7.27123472860484[/C][/ROW]
[ROW][C]80[/C][C]6.50000000043707[/C][C]5.60945975082494[/C][C]7.3905402500492[/C][/ROW]
[ROW][C]81[/C][C]6.50000000043707[/C][C]5.50434902422781[/C][C]7.49565097664633[/C][/ROW]
[ROW][C]82[/C][C]6.50000000043707[/C][C]5.40932140585768[/C][C]7.59067859501646[/C][/ROW]
[ROW][C]83[/C][C]6.50000000043707[/C][C]5.32193432870188[/C][C]7.67806567217226[/C][/ROW]
[ROW][C]84[/C][C]6.50000000043707[/C][C]5.24059630933238[/C][C]7.75940369154176[/C][/ROW]
[ROW][C]85[/C][C]6.50000000043707[/C][C]5.1642018916589[/C][C]7.83579810921524[/C][/ROW]
[ROW][C]86[/C][C]6.50000000043707[/C][C]5.09194619547699[/C][C]7.90805380539715[/C][/ROW]
[ROW][C]87[/C][C]6.50000000043707[/C][C]5.02322159867539[/C][C]7.97677840219875[/C][/ROW]
[ROW][C]88[/C][C]6.50000000043707[/C][C]4.95755603770877[/C][C]8.04244396316537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210285&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210285&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
776.500000000437076.054707798127646.9452922027465
786.500000000437075.870282543409877.12971745746427
796.500000000437075.72876527226937.27123472860484
806.500000000437075.609459750824947.3905402500492
816.500000000437075.504349024227817.49565097664633
826.500000000437075.409321405857687.59067859501646
836.500000000437075.321934328701887.67806567217226
846.500000000437075.240596309332387.75940369154176
856.500000000437075.16420189165897.83579810921524
866.500000000437075.091946195476997.90805380539715
876.500000000437075.023221598675397.97677840219875
886.500000000437074.957556037708778.04244396316537



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')