Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 22:42:16 +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/2016/Dec/16/t1481924568frukkk10r5j3aa0.htm/, Retrieved Fri, 01 Nov 2024 05:23:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300569, Retrieved Fri, 01 Nov 2024 05:23:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [multiple regressi...] [2016-12-16 20:41:06] [15f3778596b3a039df0348fb43372a09]
- RM D    [Exponential Smoothing] [exponential smoot...] [2016-12-16 21:42:16] [ca14e1566745fb922befb698831e7d61] [Current]
Feedback Forum

Post a new message
Dataseries X:
-116.7
-130.2
-99.74
-96.29
-34.84
95.61
52.07
189.5
174
174.4
155.9
192.3
160.8
139.2
117.7
212.1
167.6
98.05
3.502
-26.04
-77.59
-114.1
-117.7
-173.2
-67.78
-271.3
-315.9
-291.4
54.76
279.2
84.67
98.12
112.6
-11.97
28.48
80.93
97.39
-824.2
-366.1
-316.6
-69.17
-93.72
-31.26
-11.81
-89.36
-63.9
-55.45
-41
-48.55
-38.09
-1.64
134.8
73.27
126.7
149.2
69.62
95.08
33.53
46.98
62.44
103.9
141.3
189.8




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300569&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300569&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.563119198627642
beta0
gamma0.198433481205845

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.563119198627642 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.198433481205845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300569&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]0.563119198627642[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.198433481205845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300569&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
alpha0.563119198627642
beta0
gamma0.198433481205845







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13160.876.435487179487284.3645128205128
14139.2112.5839178777426.6160821222604
15117.7124.772348559188-7.07234855918826
16212.1236.930177152277-24.8301771522767
17167.6201.105314871991-33.5053148719914
1898.05138.553649324329-40.5036493243293
193.50258.8612539548051-55.3592539548051
20-26.04141.566549077305-167.606549077305
21-77.5910.6357373223024-88.2257373223024
22-114.1-61.3187986641448-52.7812013358552
23-117.7-131.58883595017513.8888359501753
24-173.2-96.6677786005546-76.5322213994454
25-67.78-162.79217829721295.012178297212
26-271.3-125.654156899057-145.645843100943
27-315.9-213.390233466871-102.509766533129
28-291.4-156.514504941633-134.885495058367
2954.76-255.065692761724309.825692761724
30279.2-124.887774485397404.087774485397
3184.6744.489937654569940.1800623454301
3298.12171.264338387268-73.1443383872681
33112.6100.40867474964612.1913252503543
34-11.9788.073664422924-100.043664422924
3528.48-3.0310291109908431.5110291109908
3680.9333.974661273061446.9553387269386
3797.3952.25996654036145.130033459639
38-824.240.4453226774005-864.645322677401
39-366.1-448.43362145715582.3336214571547
40-316.6-290.275741894443-26.3242581055572
41-69.17-289.141209262809219.971209262809
42-93.72-201.390328237708107.670328237708
43-31.26-230.478777586238199.218777586238
44-11.81-23.970916799341812.1609167993418
45-89.36-39.3916530653948-49.9683469346052
46-63.9-96.459819020815132.5598190208151
47-55.45-101.48823489802846.0382348980283
48-41-54.963101367838913.9631013678389
49-48.55-55.41459732266976.8645973226697
50-38.09-167.647286384624129.557286384624
51-1.64-14.576365362044712.9363653620447
52134.895.082842157102439.7171578428976
5373.27154.75835606438-81.4883560643802
54126.763.016005164386663.6839948356134
55149.217.0945048734626132.105495126537
5669.62169.593209229957-99.9732092299574
5795.0885.64149741863489.43850258136523
5833.5369.1809824211893-35.6509824211893
5946.9826.910222539110520.0697774608895
6062.4456.0313687631356.40863123686503
61103.950.710423703231253.1895762967688
62141.3-24.7993329246295166.099332924629
63189.8138.73904103270351.0609589672971

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 160.8 & 76.4354871794872 & 84.3645128205128 \tabularnewline
14 & 139.2 & 112.58391787774 & 26.6160821222604 \tabularnewline
15 & 117.7 & 124.772348559188 & -7.07234855918826 \tabularnewline
16 & 212.1 & 236.930177152277 & -24.8301771522767 \tabularnewline
17 & 167.6 & 201.105314871991 & -33.5053148719914 \tabularnewline
18 & 98.05 & 138.553649324329 & -40.5036493243293 \tabularnewline
19 & 3.502 & 58.8612539548051 & -55.3592539548051 \tabularnewline
20 & -26.04 & 141.566549077305 & -167.606549077305 \tabularnewline
21 & -77.59 & 10.6357373223024 & -88.2257373223024 \tabularnewline
22 & -114.1 & -61.3187986641448 & -52.7812013358552 \tabularnewline
23 & -117.7 & -131.588835950175 & 13.8888359501753 \tabularnewline
24 & -173.2 & -96.6677786005546 & -76.5322213994454 \tabularnewline
25 & -67.78 & -162.792178297212 & 95.012178297212 \tabularnewline
26 & -271.3 & -125.654156899057 & -145.645843100943 \tabularnewline
27 & -315.9 & -213.390233466871 & -102.509766533129 \tabularnewline
28 & -291.4 & -156.514504941633 & -134.885495058367 \tabularnewline
29 & 54.76 & -255.065692761724 & 309.825692761724 \tabularnewline
30 & 279.2 & -124.887774485397 & 404.087774485397 \tabularnewline
31 & 84.67 & 44.4899376545699 & 40.1800623454301 \tabularnewline
32 & 98.12 & 171.264338387268 & -73.1443383872681 \tabularnewline
33 & 112.6 & 100.408674749646 & 12.1913252503543 \tabularnewline
34 & -11.97 & 88.073664422924 & -100.043664422924 \tabularnewline
35 & 28.48 & -3.03102911099084 & 31.5110291109908 \tabularnewline
36 & 80.93 & 33.9746612730614 & 46.9553387269386 \tabularnewline
37 & 97.39 & 52.259966540361 & 45.130033459639 \tabularnewline
38 & -824.2 & 40.4453226774005 & -864.645322677401 \tabularnewline
39 & -366.1 & -448.433621457155 & 82.3336214571547 \tabularnewline
40 & -316.6 & -290.275741894443 & -26.3242581055572 \tabularnewline
41 & -69.17 & -289.141209262809 & 219.971209262809 \tabularnewline
42 & -93.72 & -201.390328237708 & 107.670328237708 \tabularnewline
43 & -31.26 & -230.478777586238 & 199.218777586238 \tabularnewline
44 & -11.81 & -23.9709167993418 & 12.1609167993418 \tabularnewline
45 & -89.36 & -39.3916530653948 & -49.9683469346052 \tabularnewline
46 & -63.9 & -96.4598190208151 & 32.5598190208151 \tabularnewline
47 & -55.45 & -101.488234898028 & 46.0382348980283 \tabularnewline
48 & -41 & -54.9631013678389 & 13.9631013678389 \tabularnewline
49 & -48.55 & -55.4145973226697 & 6.8645973226697 \tabularnewline
50 & -38.09 & -167.647286384624 & 129.557286384624 \tabularnewline
51 & -1.64 & -14.5763653620447 & 12.9363653620447 \tabularnewline
52 & 134.8 & 95.0828421571024 & 39.7171578428976 \tabularnewline
53 & 73.27 & 154.75835606438 & -81.4883560643802 \tabularnewline
54 & 126.7 & 63.0160051643866 & 63.6839948356134 \tabularnewline
55 & 149.2 & 17.0945048734626 & 132.105495126537 \tabularnewline
56 & 69.62 & 169.593209229957 & -99.9732092299574 \tabularnewline
57 & 95.08 & 85.6414974186348 & 9.43850258136523 \tabularnewline
58 & 33.53 & 69.1809824211893 & -35.6509824211893 \tabularnewline
59 & 46.98 & 26.9102225391105 & 20.0697774608895 \tabularnewline
60 & 62.44 & 56.031368763135 & 6.40863123686503 \tabularnewline
61 & 103.9 & 50.7104237032312 & 53.1895762967688 \tabularnewline
62 & 141.3 & -24.7993329246295 & 166.099332924629 \tabularnewline
63 & 189.8 & 138.739041032703 & 51.0609589672971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300569&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]160.8[/C][C]76.4354871794872[/C][C]84.3645128205128[/C][/ROW]
[ROW][C]14[/C][C]139.2[/C][C]112.58391787774[/C][C]26.6160821222604[/C][/ROW]
[ROW][C]15[/C][C]117.7[/C][C]124.772348559188[/C][C]-7.07234855918826[/C][/ROW]
[ROW][C]16[/C][C]212.1[/C][C]236.930177152277[/C][C]-24.8301771522767[/C][/ROW]
[ROW][C]17[/C][C]167.6[/C][C]201.105314871991[/C][C]-33.5053148719914[/C][/ROW]
[ROW][C]18[/C][C]98.05[/C][C]138.553649324329[/C][C]-40.5036493243293[/C][/ROW]
[ROW][C]19[/C][C]3.502[/C][C]58.8612539548051[/C][C]-55.3592539548051[/C][/ROW]
[ROW][C]20[/C][C]-26.04[/C][C]141.566549077305[/C][C]-167.606549077305[/C][/ROW]
[ROW][C]21[/C][C]-77.59[/C][C]10.6357373223024[/C][C]-88.2257373223024[/C][/ROW]
[ROW][C]22[/C][C]-114.1[/C][C]-61.3187986641448[/C][C]-52.7812013358552[/C][/ROW]
[ROW][C]23[/C][C]-117.7[/C][C]-131.588835950175[/C][C]13.8888359501753[/C][/ROW]
[ROW][C]24[/C][C]-173.2[/C][C]-96.6677786005546[/C][C]-76.5322213994454[/C][/ROW]
[ROW][C]25[/C][C]-67.78[/C][C]-162.792178297212[/C][C]95.012178297212[/C][/ROW]
[ROW][C]26[/C][C]-271.3[/C][C]-125.654156899057[/C][C]-145.645843100943[/C][/ROW]
[ROW][C]27[/C][C]-315.9[/C][C]-213.390233466871[/C][C]-102.509766533129[/C][/ROW]
[ROW][C]28[/C][C]-291.4[/C][C]-156.514504941633[/C][C]-134.885495058367[/C][/ROW]
[ROW][C]29[/C][C]54.76[/C][C]-255.065692761724[/C][C]309.825692761724[/C][/ROW]
[ROW][C]30[/C][C]279.2[/C][C]-124.887774485397[/C][C]404.087774485397[/C][/ROW]
[ROW][C]31[/C][C]84.67[/C][C]44.4899376545699[/C][C]40.1800623454301[/C][/ROW]
[ROW][C]32[/C][C]98.12[/C][C]171.264338387268[/C][C]-73.1443383872681[/C][/ROW]
[ROW][C]33[/C][C]112.6[/C][C]100.408674749646[/C][C]12.1913252503543[/C][/ROW]
[ROW][C]34[/C][C]-11.97[/C][C]88.073664422924[/C][C]-100.043664422924[/C][/ROW]
[ROW][C]35[/C][C]28.48[/C][C]-3.03102911099084[/C][C]31.5110291109908[/C][/ROW]
[ROW][C]36[/C][C]80.93[/C][C]33.9746612730614[/C][C]46.9553387269386[/C][/ROW]
[ROW][C]37[/C][C]97.39[/C][C]52.259966540361[/C][C]45.130033459639[/C][/ROW]
[ROW][C]38[/C][C]-824.2[/C][C]40.4453226774005[/C][C]-864.645322677401[/C][/ROW]
[ROW][C]39[/C][C]-366.1[/C][C]-448.433621457155[/C][C]82.3336214571547[/C][/ROW]
[ROW][C]40[/C][C]-316.6[/C][C]-290.275741894443[/C][C]-26.3242581055572[/C][/ROW]
[ROW][C]41[/C][C]-69.17[/C][C]-289.141209262809[/C][C]219.971209262809[/C][/ROW]
[ROW][C]42[/C][C]-93.72[/C][C]-201.390328237708[/C][C]107.670328237708[/C][/ROW]
[ROW][C]43[/C][C]-31.26[/C][C]-230.478777586238[/C][C]199.218777586238[/C][/ROW]
[ROW][C]44[/C][C]-11.81[/C][C]-23.9709167993418[/C][C]12.1609167993418[/C][/ROW]
[ROW][C]45[/C][C]-89.36[/C][C]-39.3916530653948[/C][C]-49.9683469346052[/C][/ROW]
[ROW][C]46[/C][C]-63.9[/C][C]-96.4598190208151[/C][C]32.5598190208151[/C][/ROW]
[ROW][C]47[/C][C]-55.45[/C][C]-101.488234898028[/C][C]46.0382348980283[/C][/ROW]
[ROW][C]48[/C][C]-41[/C][C]-54.9631013678389[/C][C]13.9631013678389[/C][/ROW]
[ROW][C]49[/C][C]-48.55[/C][C]-55.4145973226697[/C][C]6.8645973226697[/C][/ROW]
[ROW][C]50[/C][C]-38.09[/C][C]-167.647286384624[/C][C]129.557286384624[/C][/ROW]
[ROW][C]51[/C][C]-1.64[/C][C]-14.5763653620447[/C][C]12.9363653620447[/C][/ROW]
[ROW][C]52[/C][C]134.8[/C][C]95.0828421571024[/C][C]39.7171578428976[/C][/ROW]
[ROW][C]53[/C][C]73.27[/C][C]154.75835606438[/C][C]-81.4883560643802[/C][/ROW]
[ROW][C]54[/C][C]126.7[/C][C]63.0160051643866[/C][C]63.6839948356134[/C][/ROW]
[ROW][C]55[/C][C]149.2[/C][C]17.0945048734626[/C][C]132.105495126537[/C][/ROW]
[ROW][C]56[/C][C]69.62[/C][C]169.593209229957[/C][C]-99.9732092299574[/C][/ROW]
[ROW][C]57[/C][C]95.08[/C][C]85.6414974186348[/C][C]9.43850258136523[/C][/ROW]
[ROW][C]58[/C][C]33.53[/C][C]69.1809824211893[/C][C]-35.6509824211893[/C][/ROW]
[ROW][C]59[/C][C]46.98[/C][C]26.9102225391105[/C][C]20.0697774608895[/C][/ROW]
[ROW][C]60[/C][C]62.44[/C][C]56.031368763135[/C][C]6.40863123686503[/C][/ROW]
[ROW][C]61[/C][C]103.9[/C][C]50.7104237032312[/C][C]53.1895762967688[/C][/ROW]
[ROW][C]62[/C][C]141.3[/C][C]-24.7993329246295[/C][C]166.099332924629[/C][/ROW]
[ROW][C]63[/C][C]189.8[/C][C]138.739041032703[/C][C]51.0609589672971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300569&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300569&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
13160.876.435487179487284.3645128205128
14139.2112.5839178777426.6160821222604
15117.7124.772348559188-7.07234855918826
16212.1236.930177152277-24.8301771522767
17167.6201.105314871991-33.5053148719914
1898.05138.553649324329-40.5036493243293
193.50258.8612539548051-55.3592539548051
20-26.04141.566549077305-167.606549077305
21-77.5910.6357373223024-88.2257373223024
22-114.1-61.3187986641448-52.7812013358552
23-117.7-131.58883595017513.8888359501753
24-173.2-96.6677786005546-76.5322213994454
25-67.78-162.79217829721295.012178297212
26-271.3-125.654156899057-145.645843100943
27-315.9-213.390233466871-102.509766533129
28-291.4-156.514504941633-134.885495058367
2954.76-255.065692761724309.825692761724
30279.2-124.887774485397404.087774485397
3184.6744.489937654569940.1800623454301
3298.12171.264338387268-73.1443383872681
33112.6100.40867474964612.1913252503543
34-11.9788.073664422924-100.043664422924
3528.48-3.0310291109908431.5110291109908
3680.9333.974661273061446.9553387269386
3797.3952.25996654036145.130033459639
38-824.240.4453226774005-864.645322677401
39-366.1-448.43362145715582.3336214571547
40-316.6-290.275741894443-26.3242581055572
41-69.17-289.141209262809219.971209262809
42-93.72-201.390328237708107.670328237708
43-31.26-230.478777586238199.218777586238
44-11.81-23.970916799341812.1609167993418
45-89.36-39.3916530653948-49.9683469346052
46-63.9-96.459819020815132.5598190208151
47-55.45-101.48823489802846.0382348980283
48-41-54.963101367838913.9631013678389
49-48.55-55.41459732266976.8645973226697
50-38.09-167.647286384624129.557286384624
51-1.64-14.576365362044712.9363653620447
52134.895.082842157102439.7171578428976
5373.27154.75835606438-81.4883560643802
54126.763.016005164386663.6839948356134
55149.217.0945048734626132.105495126537
5669.62169.593209229957-99.9732092299574
5795.0885.64149741863489.43850258136523
5833.5369.1809824211893-35.6509824211893
5946.9826.910222539110520.0697774608895
6062.4456.0313687631356.40863123686503
61103.950.710423703231253.1895762967688
62141.3-24.7993329246295166.099332924629
63189.8138.73904103270351.0609589672971







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
64272.18861367498-49.9454193174255594.322646667385
65298.991111947026-70.7063912622498668.688615156303
66265.721668069306-146.081868275871677.525204414483
67189.87006917452-260.116665311748639.856803660787
68247.858317397538-237.315847084491733.032481879567
69229.688534914515-288.288181307417747.665251136447
70204.00413027023-344.818051511152752.826312051612
71186.639654801213-391.384303078127764.663612680554
72203.274814965209-402.544963970505809.094593900924
73198.400569936153-433.994491095271830.795630967577
74102.727089316882-555.170639729327760.624818363092
75162.758858815354-519.689183566907845.206901197615

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 272.18861367498 & -49.9454193174255 & 594.322646667385 \tabularnewline
65 & 298.991111947026 & -70.7063912622498 & 668.688615156303 \tabularnewline
66 & 265.721668069306 & -146.081868275871 & 677.525204414483 \tabularnewline
67 & 189.87006917452 & -260.116665311748 & 639.856803660787 \tabularnewline
68 & 247.858317397538 & -237.315847084491 & 733.032481879567 \tabularnewline
69 & 229.688534914515 & -288.288181307417 & 747.665251136447 \tabularnewline
70 & 204.00413027023 & -344.818051511152 & 752.826312051612 \tabularnewline
71 & 186.639654801213 & -391.384303078127 & 764.663612680554 \tabularnewline
72 & 203.274814965209 & -402.544963970505 & 809.094593900924 \tabularnewline
73 & 198.400569936153 & -433.994491095271 & 830.795630967577 \tabularnewline
74 & 102.727089316882 & -555.170639729327 & 760.624818363092 \tabularnewline
75 & 162.758858815354 & -519.689183566907 & 845.206901197615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300569&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]64[/C][C]272.18861367498[/C][C]-49.9454193174255[/C][C]594.322646667385[/C][/ROW]
[ROW][C]65[/C][C]298.991111947026[/C][C]-70.7063912622498[/C][C]668.688615156303[/C][/ROW]
[ROW][C]66[/C][C]265.721668069306[/C][C]-146.081868275871[/C][C]677.525204414483[/C][/ROW]
[ROW][C]67[/C][C]189.87006917452[/C][C]-260.116665311748[/C][C]639.856803660787[/C][/ROW]
[ROW][C]68[/C][C]247.858317397538[/C][C]-237.315847084491[/C][C]733.032481879567[/C][/ROW]
[ROW][C]69[/C][C]229.688534914515[/C][C]-288.288181307417[/C][C]747.665251136447[/C][/ROW]
[ROW][C]70[/C][C]204.00413027023[/C][C]-344.818051511152[/C][C]752.826312051612[/C][/ROW]
[ROW][C]71[/C][C]186.639654801213[/C][C]-391.384303078127[/C][C]764.663612680554[/C][/ROW]
[ROW][C]72[/C][C]203.274814965209[/C][C]-402.544963970505[/C][C]809.094593900924[/C][/ROW]
[ROW][C]73[/C][C]198.400569936153[/C][C]-433.994491095271[/C][C]830.795630967577[/C][/ROW]
[ROW][C]74[/C][C]102.727089316882[/C][C]-555.170639729327[/C][C]760.624818363092[/C][/ROW]
[ROW][C]75[/C][C]162.758858815354[/C][C]-519.689183566907[/C][C]845.206901197615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300569&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300569&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
64272.18861367498-49.9454193174255594.322646667385
65298.991111947026-70.7063912622498668.688615156303
66265.721668069306-146.081868275871677.525204414483
67189.87006917452-260.116665311748639.856803660787
68247.858317397538-237.315847084491733.032481879567
69229.688534914515-288.288181307417747.665251136447
70204.00413027023-344.818051511152752.826312051612
71186.639654801213-391.384303078127764.663612680554
72203.274814965209-402.544963970505809.094593900924
73198.400569936153-433.994491095271830.795630967577
74102.727089316882-555.170639729327760.624818363092
75162.758858815354-519.689183566907845.206901197615



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')