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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 19:59:55 +0100
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/Apr/02/t1428001241bm8szqef6oomesn.htm/, Retrieved Thu, 09 May 2024 07:36:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278627, Retrieved Thu, 09 May 2024 07:36:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 2] [2015-04-02 18:59:55] [24a1c9f91cd9dd71c8b0e9e460386711] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12,8
12,1
11,4
11,4
10,6
10,4
10,9
11,6
13,3
15,2
17,4
19,1
19,9
19,4
18,2
15,8
13,5
12,1
10,3
8,8
8,2
6,8
5,9
4,9
3,9
3,6
2,8
4
4,2
4,2
4,8
4
3,8
4
3,7
4
4,6
4,6
4,6
4,5
4,1
4,1
4,4
4,2
4,4
3,2
2,8
1,7
-0,2
-2,9
-5,2
-5,3
-4,8
-2,2
-0,8
-1,1
-1,5
-2
-2,8
-3,4
-4,1
-5,5
-8,6
-7,6
-8,6
-8,7
-4,6
-4,3
-1,5
1,2
1,8
0

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278627&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278627&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278627&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278627&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1319.918.05619658119661.84380341880341
1419.419.5067016317016-0.106701631701632
1518.218.4942016317016-0.294201631701629
1615.816.327534965035-0.527534965034963
1713.514.2942016317016-0.794201631701629
1812.113.1358682983683-1.0358682983683
1910.310.1275349650350.172465034965034
208.810.365034965035-1.56503496503496
218.29.87753496503497-1.67753496503497
226.89.59836829836829-2.79836829836829
235.98.6608682983683-2.7608682983683
244.97.3733682983683-2.4733682983683
253.95.61920163170163-1.71920163170163
263.63.506701631701630.0932983682983664
272.82.694201631701630.105798368298365
2840.9275349650349643.07246503496504
294.22.494201631701631.70579836829837
304.23.83586829836830.364131701631702
314.82.227534965034972.57246503496503
3244.86503496503496-0.865034965034964
333.85.07753496503496-1.27753496503496
3445.19836829836829-1.19836829836829
353.75.8608682983683-2.1608682983683
3645.1733682983683-1.1733682983683
374.64.71920163170163-0.119201631701626
384.64.206701631701630.393298368298366
394.63.694201631701630.905798368298365
404.52.727534965034961.77246503496504
414.12.994201631701631.10579836829837
424.13.73586829836830.364131701631702
434.42.127534965034972.27246503496503
444.24.46503496503496-0.265034965034963
454.45.27753496503496-0.877534965034965
463.25.79836829836829-2.59836829836829
472.85.0608682983683-2.2608682983683
481.74.2733682983683-2.5733682983683
49-0.22.41920163170163-2.61920163170163
50-2.9-0.593298368298366-2.30670163170163
51-5.2-3.80579836829837-1.39420163170163
52-5.3-7.072465034965041.77246503496504
53-4.8-6.805798368298372.00579836829837
54-2.2-5.16413170163172.9641317016317
55-0.8-4.172465034965033.37246503496503
56-1.1-0.734965034965037-0.365034965034964
57-1.5-0.0224650349650348-1.47753496503497
58-2-0.101631701631706-1.89836829836829
59-2.8-0.139131701631702-2.6608682983683
60-3.4-1.3266317016317-2.0733682983683
61-4.1-2.68079836829838-1.41920163170162
62-5.5-4.49329836829837-1.00670163170163
63-8.6-6.40579836829837-2.19420163170163
64-7.6-10.4724650349652.87246503496504
65-8.6-9.105798368298370.505798368298374
66-8.7-8.96413170163170.264131701631701
67-4.6-10.6724650349656.07246503496503
68-4.3-4.534965034965040.234965034965037
69-1.5-3.222465034965031.72246503496503
701.2-0.1016317016317061.30163170163171
711.83.0608682983683-1.2608682983683
7203.2733682983683-3.2733682983683

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 19.9 & 18.0561965811966 & 1.84380341880341 \tabularnewline
14 & 19.4 & 19.5067016317016 & -0.106701631701632 \tabularnewline
15 & 18.2 & 18.4942016317016 & -0.294201631701629 \tabularnewline
16 & 15.8 & 16.327534965035 & -0.527534965034963 \tabularnewline
17 & 13.5 & 14.2942016317016 & -0.794201631701629 \tabularnewline
18 & 12.1 & 13.1358682983683 & -1.0358682983683 \tabularnewline
19 & 10.3 & 10.127534965035 & 0.172465034965034 \tabularnewline
20 & 8.8 & 10.365034965035 & -1.56503496503496 \tabularnewline
21 & 8.2 & 9.87753496503497 & -1.67753496503497 \tabularnewline
22 & 6.8 & 9.59836829836829 & -2.79836829836829 \tabularnewline
23 & 5.9 & 8.6608682983683 & -2.7608682983683 \tabularnewline
24 & 4.9 & 7.3733682983683 & -2.4733682983683 \tabularnewline
25 & 3.9 & 5.61920163170163 & -1.71920163170163 \tabularnewline
26 & 3.6 & 3.50670163170163 & 0.0932983682983664 \tabularnewline
27 & 2.8 & 2.69420163170163 & 0.105798368298365 \tabularnewline
28 & 4 & 0.927534965034964 & 3.07246503496504 \tabularnewline
29 & 4.2 & 2.49420163170163 & 1.70579836829837 \tabularnewline
30 & 4.2 & 3.8358682983683 & 0.364131701631702 \tabularnewline
31 & 4.8 & 2.22753496503497 & 2.57246503496503 \tabularnewline
32 & 4 & 4.86503496503496 & -0.865034965034964 \tabularnewline
33 & 3.8 & 5.07753496503496 & -1.27753496503496 \tabularnewline
34 & 4 & 5.19836829836829 & -1.19836829836829 \tabularnewline
35 & 3.7 & 5.8608682983683 & -2.1608682983683 \tabularnewline
36 & 4 & 5.1733682983683 & -1.1733682983683 \tabularnewline
37 & 4.6 & 4.71920163170163 & -0.119201631701626 \tabularnewline
38 & 4.6 & 4.20670163170163 & 0.393298368298366 \tabularnewline
39 & 4.6 & 3.69420163170163 & 0.905798368298365 \tabularnewline
40 & 4.5 & 2.72753496503496 & 1.77246503496504 \tabularnewline
41 & 4.1 & 2.99420163170163 & 1.10579836829837 \tabularnewline
42 & 4.1 & 3.7358682983683 & 0.364131701631702 \tabularnewline
43 & 4.4 & 2.12753496503497 & 2.27246503496503 \tabularnewline
44 & 4.2 & 4.46503496503496 & -0.265034965034963 \tabularnewline
45 & 4.4 & 5.27753496503496 & -0.877534965034965 \tabularnewline
46 & 3.2 & 5.79836829836829 & -2.59836829836829 \tabularnewline
47 & 2.8 & 5.0608682983683 & -2.2608682983683 \tabularnewline
48 & 1.7 & 4.2733682983683 & -2.5733682983683 \tabularnewline
49 & -0.2 & 2.41920163170163 & -2.61920163170163 \tabularnewline
50 & -2.9 & -0.593298368298366 & -2.30670163170163 \tabularnewline
51 & -5.2 & -3.80579836829837 & -1.39420163170163 \tabularnewline
52 & -5.3 & -7.07246503496504 & 1.77246503496504 \tabularnewline
53 & -4.8 & -6.80579836829837 & 2.00579836829837 \tabularnewline
54 & -2.2 & -5.1641317016317 & 2.9641317016317 \tabularnewline
55 & -0.8 & -4.17246503496503 & 3.37246503496503 \tabularnewline
56 & -1.1 & -0.734965034965037 & -0.365034965034964 \tabularnewline
57 & -1.5 & -0.0224650349650348 & -1.47753496503497 \tabularnewline
58 & -2 & -0.101631701631706 & -1.89836829836829 \tabularnewline
59 & -2.8 & -0.139131701631702 & -2.6608682983683 \tabularnewline
60 & -3.4 & -1.3266317016317 & -2.0733682983683 \tabularnewline
61 & -4.1 & -2.68079836829838 & -1.41920163170162 \tabularnewline
62 & -5.5 & -4.49329836829837 & -1.00670163170163 \tabularnewline
63 & -8.6 & -6.40579836829837 & -2.19420163170163 \tabularnewline
64 & -7.6 & -10.472465034965 & 2.87246503496504 \tabularnewline
65 & -8.6 & -9.10579836829837 & 0.505798368298374 \tabularnewline
66 & -8.7 & -8.9641317016317 & 0.264131701631701 \tabularnewline
67 & -4.6 & -10.672465034965 & 6.07246503496503 \tabularnewline
68 & -4.3 & -4.53496503496504 & 0.234965034965037 \tabularnewline
69 & -1.5 & -3.22246503496503 & 1.72246503496503 \tabularnewline
70 & 1.2 & -0.101631701631706 & 1.30163170163171 \tabularnewline
71 & 1.8 & 3.0608682983683 & -1.2608682983683 \tabularnewline
72 & 0 & 3.2733682983683 & -3.2733682983683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278627&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]19.9[/C][C]18.0561965811966[/C][C]1.84380341880341[/C][/ROW]
[ROW][C]14[/C][C]19.4[/C][C]19.5067016317016[/C][C]-0.106701631701632[/C][/ROW]
[ROW][C]15[/C][C]18.2[/C][C]18.4942016317016[/C][C]-0.294201631701629[/C][/ROW]
[ROW][C]16[/C][C]15.8[/C][C]16.327534965035[/C][C]-0.527534965034963[/C][/ROW]
[ROW][C]17[/C][C]13.5[/C][C]14.2942016317016[/C][C]-0.794201631701629[/C][/ROW]
[ROW][C]18[/C][C]12.1[/C][C]13.1358682983683[/C][C]-1.0358682983683[/C][/ROW]
[ROW][C]19[/C][C]10.3[/C][C]10.127534965035[/C][C]0.172465034965034[/C][/ROW]
[ROW][C]20[/C][C]8.8[/C][C]10.365034965035[/C][C]-1.56503496503496[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]9.87753496503497[/C][C]-1.67753496503497[/C][/ROW]
[ROW][C]22[/C][C]6.8[/C][C]9.59836829836829[/C][C]-2.79836829836829[/C][/ROW]
[ROW][C]23[/C][C]5.9[/C][C]8.6608682983683[/C][C]-2.7608682983683[/C][/ROW]
[ROW][C]24[/C][C]4.9[/C][C]7.3733682983683[/C][C]-2.4733682983683[/C][/ROW]
[ROW][C]25[/C][C]3.9[/C][C]5.61920163170163[/C][C]-1.71920163170163[/C][/ROW]
[ROW][C]26[/C][C]3.6[/C][C]3.50670163170163[/C][C]0.0932983682983664[/C][/ROW]
[ROW][C]27[/C][C]2.8[/C][C]2.69420163170163[/C][C]0.105798368298365[/C][/ROW]
[ROW][C]28[/C][C]4[/C][C]0.927534965034964[/C][C]3.07246503496504[/C][/ROW]
[ROW][C]29[/C][C]4.2[/C][C]2.49420163170163[/C][C]1.70579836829837[/C][/ROW]
[ROW][C]30[/C][C]4.2[/C][C]3.8358682983683[/C][C]0.364131701631702[/C][/ROW]
[ROW][C]31[/C][C]4.8[/C][C]2.22753496503497[/C][C]2.57246503496503[/C][/ROW]
[ROW][C]32[/C][C]4[/C][C]4.86503496503496[/C][C]-0.865034965034964[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]5.07753496503496[/C][C]-1.27753496503496[/C][/ROW]
[ROW][C]34[/C][C]4[/C][C]5.19836829836829[/C][C]-1.19836829836829[/C][/ROW]
[ROW][C]35[/C][C]3.7[/C][C]5.8608682983683[/C][C]-2.1608682983683[/C][/ROW]
[ROW][C]36[/C][C]4[/C][C]5.1733682983683[/C][C]-1.1733682983683[/C][/ROW]
[ROW][C]37[/C][C]4.6[/C][C]4.71920163170163[/C][C]-0.119201631701626[/C][/ROW]
[ROW][C]38[/C][C]4.6[/C][C]4.20670163170163[/C][C]0.393298368298366[/C][/ROW]
[ROW][C]39[/C][C]4.6[/C][C]3.69420163170163[/C][C]0.905798368298365[/C][/ROW]
[ROW][C]40[/C][C]4.5[/C][C]2.72753496503496[/C][C]1.77246503496504[/C][/ROW]
[ROW][C]41[/C][C]4.1[/C][C]2.99420163170163[/C][C]1.10579836829837[/C][/ROW]
[ROW][C]42[/C][C]4.1[/C][C]3.7358682983683[/C][C]0.364131701631702[/C][/ROW]
[ROW][C]43[/C][C]4.4[/C][C]2.12753496503497[/C][C]2.27246503496503[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.46503496503496[/C][C]-0.265034965034963[/C][/ROW]
[ROW][C]45[/C][C]4.4[/C][C]5.27753496503496[/C][C]-0.877534965034965[/C][/ROW]
[ROW][C]46[/C][C]3.2[/C][C]5.79836829836829[/C][C]-2.59836829836829[/C][/ROW]
[ROW][C]47[/C][C]2.8[/C][C]5.0608682983683[/C][C]-2.2608682983683[/C][/ROW]
[ROW][C]48[/C][C]1.7[/C][C]4.2733682983683[/C][C]-2.5733682983683[/C][/ROW]
[ROW][C]49[/C][C]-0.2[/C][C]2.41920163170163[/C][C]-2.61920163170163[/C][/ROW]
[ROW][C]50[/C][C]-2.9[/C][C]-0.593298368298366[/C][C]-2.30670163170163[/C][/ROW]
[ROW][C]51[/C][C]-5.2[/C][C]-3.80579836829837[/C][C]-1.39420163170163[/C][/ROW]
[ROW][C]52[/C][C]-5.3[/C][C]-7.07246503496504[/C][C]1.77246503496504[/C][/ROW]
[ROW][C]53[/C][C]-4.8[/C][C]-6.80579836829837[/C][C]2.00579836829837[/C][/ROW]
[ROW][C]54[/C][C]-2.2[/C][C]-5.1641317016317[/C][C]2.9641317016317[/C][/ROW]
[ROW][C]55[/C][C]-0.8[/C][C]-4.17246503496503[/C][C]3.37246503496503[/C][/ROW]
[ROW][C]56[/C][C]-1.1[/C][C]-0.734965034965037[/C][C]-0.365034965034964[/C][/ROW]
[ROW][C]57[/C][C]-1.5[/C][C]-0.0224650349650348[/C][C]-1.47753496503497[/C][/ROW]
[ROW][C]58[/C][C]-2[/C][C]-0.101631701631706[/C][C]-1.89836829836829[/C][/ROW]
[ROW][C]59[/C][C]-2.8[/C][C]-0.139131701631702[/C][C]-2.6608682983683[/C][/ROW]
[ROW][C]60[/C][C]-3.4[/C][C]-1.3266317016317[/C][C]-2.0733682983683[/C][/ROW]
[ROW][C]61[/C][C]-4.1[/C][C]-2.68079836829838[/C][C]-1.41920163170162[/C][/ROW]
[ROW][C]62[/C][C]-5.5[/C][C]-4.49329836829837[/C][C]-1.00670163170163[/C][/ROW]
[ROW][C]63[/C][C]-8.6[/C][C]-6.40579836829837[/C][C]-2.19420163170163[/C][/ROW]
[ROW][C]64[/C][C]-7.6[/C][C]-10.472465034965[/C][C]2.87246503496504[/C][/ROW]
[ROW][C]65[/C][C]-8.6[/C][C]-9.10579836829837[/C][C]0.505798368298374[/C][/ROW]
[ROW][C]66[/C][C]-8.7[/C][C]-8.9641317016317[/C][C]0.264131701631701[/C][/ROW]
[ROW][C]67[/C][C]-4.6[/C][C]-10.672465034965[/C][C]6.07246503496503[/C][/ROW]
[ROW][C]68[/C][C]-4.3[/C][C]-4.53496503496504[/C][C]0.234965034965037[/C][/ROW]
[ROW][C]69[/C][C]-1.5[/C][C]-3.22246503496503[/C][C]1.72246503496503[/C][/ROW]
[ROW][C]70[/C][C]1.2[/C][C]-0.101631701631706[/C][C]1.30163170163171[/C][/ROW]
[ROW][C]71[/C][C]1.8[/C][C]3.0608682983683[/C][C]-1.2608682983683[/C][/ROW]
[ROW][C]72[/C][C]0[/C][C]3.2733682983683[/C][C]-3.2733682983683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278627&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278627&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1319.918.05619658119661.84380341880341
1419.419.5067016317016-0.106701631701632
1518.218.4942016317016-0.294201631701629
1615.816.327534965035-0.527534965034963
1713.514.2942016317016-0.794201631701629
1812.113.1358682983683-1.0358682983683
1910.310.1275349650350.172465034965034
208.810.365034965035-1.56503496503496
218.29.87753496503497-1.67753496503497
226.89.59836829836829-2.79836829836829
235.98.6608682983683-2.7608682983683
244.97.3733682983683-2.4733682983683
253.95.61920163170163-1.71920163170163
263.63.506701631701630.0932983682983664
272.82.694201631701630.105798368298365
2840.9275349650349643.07246503496504
294.22.494201631701631.70579836829837
304.23.83586829836830.364131701631702
314.82.227534965034972.57246503496503
3244.86503496503496-0.865034965034964
333.85.07753496503496-1.27753496503496
3445.19836829836829-1.19836829836829
353.75.8608682983683-2.1608682983683
3645.1733682983683-1.1733682983683
374.64.71920163170163-0.119201631701626
384.64.206701631701630.393298368298366
394.63.694201631701630.905798368298365
404.52.727534965034961.77246503496504
414.12.994201631701631.10579836829837
424.13.73586829836830.364131701631702
434.42.127534965034972.27246503496503
444.24.46503496503496-0.265034965034963
454.45.27753496503496-0.877534965034965
463.25.79836829836829-2.59836829836829
472.85.0608682983683-2.2608682983683
481.74.2733682983683-2.5733682983683
49-0.22.41920163170163-2.61920163170163
50-2.9-0.593298368298366-2.30670163170163
51-5.2-3.80579836829837-1.39420163170163
52-5.3-7.072465034965041.77246503496504
53-4.8-6.805798368298372.00579836829837
54-2.2-5.16413170163172.9641317016317
55-0.8-4.172465034965033.37246503496503
56-1.1-0.734965034965037-0.365034965034964
57-1.5-0.0224650349650348-1.47753496503497
58-2-0.101631701631706-1.89836829836829
59-2.8-0.139131701631702-2.6608682983683
60-3.4-1.3266317016317-2.0733682983683
61-4.1-2.68079836829838-1.41920163170162
62-5.5-4.49329836829837-1.00670163170163
63-8.6-6.40579836829837-2.19420163170163
64-7.6-10.4724650349652.87246503496504
65-8.6-9.105798368298370.505798368298374
66-8.7-8.96413170163170.264131701631701
67-4.6-10.6724650349656.07246503496503
68-4.3-4.534965034965040.234965034965037
69-1.5-3.222465034965031.72246503496503
701.2-0.1016317016317061.30163170163171
711.83.0608682983683-1.2608682983683
7203.2733682983683-3.2733682983683






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.719201631701625-3.060786377388914.49918964079216
740.325903263403259-5.019807044660255.67161357146677
75-0.579895104895107-7.127026388641045.96723617885083
76-2.45236013986014-10.01233615804125.10761587832093
77-3.95815850815851-12.4104686506194.49415163430201
78-4.32229020979022-13.58133206590094.93675164632046
79-6.29475524475525-16.2956634756153.70615298610447
80-6.22972027972029-16.92114089584734.46170033640673
81-5.15218531468532-16.49214934195696.18777871258628
82-3.75381701631703-15.70718865316848.19955462053432
83-1.89294871794873-14.429750656144510.6438532202471
84-0.419580419580426-13.513842987072312.6746821479114

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.719201631701625 & -3.06078637738891 & 4.49918964079216 \tabularnewline
74 & 0.325903263403259 & -5.01980704466025 & 5.67161357146677 \tabularnewline
75 & -0.579895104895107 & -7.12702638864104 & 5.96723617885083 \tabularnewline
76 & -2.45236013986014 & -10.0123361580412 & 5.10761587832093 \tabularnewline
77 & -3.95815850815851 & -12.410468650619 & 4.49415163430201 \tabularnewline
78 & -4.32229020979022 & -13.5813320659009 & 4.93675164632046 \tabularnewline
79 & -6.29475524475525 & -16.295663475615 & 3.70615298610447 \tabularnewline
80 & -6.22972027972029 & -16.9211408958473 & 4.46170033640673 \tabularnewline
81 & -5.15218531468532 & -16.4921493419569 & 6.18777871258628 \tabularnewline
82 & -3.75381701631703 & -15.7071886531684 & 8.19955462053432 \tabularnewline
83 & -1.89294871794873 & -14.4297506561445 & 10.6438532202471 \tabularnewline
84 & -0.419580419580426 & -13.5138429870723 & 12.6746821479114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278627&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]73[/C][C]0.719201631701625[/C][C]-3.06078637738891[/C][C]4.49918964079216[/C][/ROW]
[ROW][C]74[/C][C]0.325903263403259[/C][C]-5.01980704466025[/C][C]5.67161357146677[/C][/ROW]
[ROW][C]75[/C][C]-0.579895104895107[/C][C]-7.12702638864104[/C][C]5.96723617885083[/C][/ROW]
[ROW][C]76[/C][C]-2.45236013986014[/C][C]-10.0123361580412[/C][C]5.10761587832093[/C][/ROW]
[ROW][C]77[/C][C]-3.95815850815851[/C][C]-12.410468650619[/C][C]4.49415163430201[/C][/ROW]
[ROW][C]78[/C][C]-4.32229020979022[/C][C]-13.5813320659009[/C][C]4.93675164632046[/C][/ROW]
[ROW][C]79[/C][C]-6.29475524475525[/C][C]-16.295663475615[/C][C]3.70615298610447[/C][/ROW]
[ROW][C]80[/C][C]-6.22972027972029[/C][C]-16.9211408958473[/C][C]4.46170033640673[/C][/ROW]
[ROW][C]81[/C][C]-5.15218531468532[/C][C]-16.4921493419569[/C][C]6.18777871258628[/C][/ROW]
[ROW][C]82[/C][C]-3.75381701631703[/C][C]-15.7071886531684[/C][C]8.19955462053432[/C][/ROW]
[ROW][C]83[/C][C]-1.89294871794873[/C][C]-14.4297506561445[/C][C]10.6438532202471[/C][/ROW]
[ROW][C]84[/C][C]-0.419580419580426[/C][C]-13.5138429870723[/C][C]12.6746821479114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278627&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278627&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.719201631701625-3.060786377388914.49918964079216
740.325903263403259-5.019807044660255.67161357146677
75-0.579895104895107-7.127026388641045.96723617885083
76-2.45236013986014-10.01233615804125.10761587832093
77-3.95815850815851-12.4104686506194.49415163430201
78-4.32229020979022-13.58133206590094.93675164632046
79-6.29475524475525-16.2956634756153.70615298610447
80-6.22972027972029-16.92114089584734.46170033640673
81-5.15218531468532-16.49214934195696.18777871258628
82-3.75381701631703-15.70718865316848.19955462053432
83-1.89294871794873-14.429750656144510.6438532202471
84-0.419580419580426-13.513842987072312.6746821479114


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')