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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 24 Dec 2014 11:55:20 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/24/t1419422179rsakgytfng0dlev.htm/, Retrieved Thu, 16 May 2024 17:20:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271438, Retrieved Thu, 16 May 2024 17:20:45 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

156

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [-] [2014-12-24 11:55:20] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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2.37
2.45
2.53
2.56
2.62
2.67
2.62
2.6
2.53
2.49
2.48
2.44
2.36
2.35
2.44
2.5
2.58
2.55
2.44
2.3
2.24
2.19
2.25
2.28
2.27
2.37
2.47
2.5
2.47
2.61
2.61
2.65
2.43
2.43
2.33
2.27
2.22
2.17
2.28
2.3
2.33
2.44
2.41
2.4
2.34
2.37
2.38
2.3
2.29
2.34
2.35
2.38
2.37
2.45
2.51
2.46
2.42
2.48
2.44
2.43
2.36
2.42
2.42
2.43
2.47
2.54
2.55
2.55
2.49
2.54
2.55
2.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271438&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]2 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=271438&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271438&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.855584728044903
beta	0.0268942887022738
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.855584728044903 \tabularnewline
beta & 0.0268942887022738 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271438&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]0.855584728044903[/C][/ROW]
[ROW][C]beta[/C][C]0.0268942887022738[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271438&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271438&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
Parameter	Value
alpha	0.855584728044903
beta	0.0268942887022738
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.36	2.40069444444445	-0.0406944444444455
14	2.35	2.36107686978582	-0.0110768697858155
15	2.44	2.45112809045052	-0.0111280904505207
16	2.5	2.51087942632204	-0.0108794263220444
17	2.58	2.58809317609641	-0.00809317609641491
18	2.55	2.55167123892362	-0.00167123892362131
19	2.44	2.45487202400666	-0.0148720240066593
20	2.3	2.4106028752723	-0.110602875272296
21	2.24	2.23521619546365	0.00478380453634664
22	2.19	2.18699600703415	0.00300399296585097
23	2.25	2.16523882858036	0.0847611714196352
24	2.28	2.18788222702045	0.0921177729795466
25	2.27	2.17889591700101	0.091104082998994
26	2.37	2.25879277484555	0.111207225154454
27	2.47	2.45874719665203	0.0112528033479689
28	2.5	2.5434843804655	-0.0434843804654994
29	2.47	2.59825514144234	-0.128255141442338
30	2.61	2.46223785457279	0.147762145427206
31	2.61	2.49710964652301	0.112890353476992
32	2.65	2.55699137627486	0.0930086237251375
33	2.43	2.58582469098643	-0.155824690986431
34	2.43	2.40958714488035	0.0204128551196461
35	2.33	2.42458614232157	-0.0945861423215666
36	2.27	2.30077271471776	-0.0307727147177586
37	2.22	2.18959662664762	0.0304033733523768
38	2.17	2.22216517970769	-0.0521651797076892
39	2.28	2.26584956152979	0.0141504384702142
40	2.3	2.34317154759988	-0.0431715475998828
41	2.33	2.38398548467517	-0.0539854846751706
42	2.44	2.35109997727017	0.0889000227298347
43	2.41	2.32894646287754	0.0810535371224592
44	2.4	2.3563575435189	0.0436424564811015
45	2.34	2.30352232637452	0.0364776736254817
46	2.37	2.31819582079156	0.0518041792084443
47	2.38	2.34509615039548	0.0349038496045235
48	2.3	2.34591863107788	-0.0459186310778752
49	2.29	2.23490079220564	0.0550992077943575
50	2.34	2.28152492616096	0.0584750738390407
51	2.35	2.43684463955306	-0.0868446395530591
52	2.38	2.42455090999095	-0.0445509099909511
53	2.37	2.46766354934459	-0.0976635493445928
54	2.45	2.42207812037056	0.0279218796294414
55	2.51	2.34925187177712	0.160748128222882
56	2.46	2.44391188207151	0.0160881179284926
57	2.42	2.37029904081766	0.0497009591823367
58	2.48	2.40263598142782	0.0773640185721827
59	2.44	2.4536888177537	-0.0136888177537022
60	2.43	2.40487058410065	0.0251294158993525
61	2.36	2.37447015803971	-0.0144701580397091
62	2.42	2.36569978689943	0.0543002131005723
63	2.42	2.50000555753464	-0.0800055575346388
64	2.43	2.50337286244156	-0.0733728624415568
65	2.47	2.51719416007028	-0.0471941600702794
66	2.54	2.53712589849507	0.00287410150493184
67	2.55	2.46567480914517	0.084325190854829
68	2.55	2.47592240551451	0.074077594485491
69	2.49	2.4599780390158	0.0300219609841972
70	2.54	2.48221943367185	0.0577805663281468
71	2.55	2.50566346139051	0.0443365386094854
72	2.5	2.5157278797608	-0.0157278797607989

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.36 & 2.40069444444445 & -0.0406944444444455 \tabularnewline
14 & 2.35 & 2.36107686978582 & -0.0110768697858155 \tabularnewline
15 & 2.44 & 2.45112809045052 & -0.0111280904505207 \tabularnewline
16 & 2.5 & 2.51087942632204 & -0.0108794263220444 \tabularnewline
17 & 2.58 & 2.58809317609641 & -0.00809317609641491 \tabularnewline
18 & 2.55 & 2.55167123892362 & -0.00167123892362131 \tabularnewline
19 & 2.44 & 2.45487202400666 & -0.0148720240066593 \tabularnewline
20 & 2.3 & 2.4106028752723 & -0.110602875272296 \tabularnewline
21 & 2.24 & 2.23521619546365 & 0.00478380453634664 \tabularnewline
22 & 2.19 & 2.18699600703415 & 0.00300399296585097 \tabularnewline
23 & 2.25 & 2.16523882858036 & 0.0847611714196352 \tabularnewline
24 & 2.28 & 2.18788222702045 & 0.0921177729795466 \tabularnewline
25 & 2.27 & 2.17889591700101 & 0.091104082998994 \tabularnewline
26 & 2.37 & 2.25879277484555 & 0.111207225154454 \tabularnewline
27 & 2.47 & 2.45874719665203 & 0.0112528033479689 \tabularnewline
28 & 2.5 & 2.5434843804655 & -0.0434843804654994 \tabularnewline
29 & 2.47 & 2.59825514144234 & -0.128255141442338 \tabularnewline
30 & 2.61 & 2.46223785457279 & 0.147762145427206 \tabularnewline
31 & 2.61 & 2.49710964652301 & 0.112890353476992 \tabularnewline
32 & 2.65 & 2.55699137627486 & 0.0930086237251375 \tabularnewline
33 & 2.43 & 2.58582469098643 & -0.155824690986431 \tabularnewline
34 & 2.43 & 2.40958714488035 & 0.0204128551196461 \tabularnewline
35 & 2.33 & 2.42458614232157 & -0.0945861423215666 \tabularnewline
36 & 2.27 & 2.30077271471776 & -0.0307727147177586 \tabularnewline
37 & 2.22 & 2.18959662664762 & 0.0304033733523768 \tabularnewline
38 & 2.17 & 2.22216517970769 & -0.0521651797076892 \tabularnewline
39 & 2.28 & 2.26584956152979 & 0.0141504384702142 \tabularnewline
40 & 2.3 & 2.34317154759988 & -0.0431715475998828 \tabularnewline
41 & 2.33 & 2.38398548467517 & -0.0539854846751706 \tabularnewline
42 & 2.44 & 2.35109997727017 & 0.0889000227298347 \tabularnewline
43 & 2.41 & 2.32894646287754 & 0.0810535371224592 \tabularnewline
44 & 2.4 & 2.3563575435189 & 0.0436424564811015 \tabularnewline
45 & 2.34 & 2.30352232637452 & 0.0364776736254817 \tabularnewline
46 & 2.37 & 2.31819582079156 & 0.0518041792084443 \tabularnewline
47 & 2.38 & 2.34509615039548 & 0.0349038496045235 \tabularnewline
48 & 2.3 & 2.34591863107788 & -0.0459186310778752 \tabularnewline
49 & 2.29 & 2.23490079220564 & 0.0550992077943575 \tabularnewline
50 & 2.34 & 2.28152492616096 & 0.0584750738390407 \tabularnewline
51 & 2.35 & 2.43684463955306 & -0.0868446395530591 \tabularnewline
52 & 2.38 & 2.42455090999095 & -0.0445509099909511 \tabularnewline
53 & 2.37 & 2.46766354934459 & -0.0976635493445928 \tabularnewline
54 & 2.45 & 2.42207812037056 & 0.0279218796294414 \tabularnewline
55 & 2.51 & 2.34925187177712 & 0.160748128222882 \tabularnewline
56 & 2.46 & 2.44391188207151 & 0.0160881179284926 \tabularnewline
57 & 2.42 & 2.37029904081766 & 0.0497009591823367 \tabularnewline
58 & 2.48 & 2.40263598142782 & 0.0773640185721827 \tabularnewline
59 & 2.44 & 2.4536888177537 & -0.0136888177537022 \tabularnewline
60 & 2.43 & 2.40487058410065 & 0.0251294158993525 \tabularnewline
61 & 2.36 & 2.37447015803971 & -0.0144701580397091 \tabularnewline
62 & 2.42 & 2.36569978689943 & 0.0543002131005723 \tabularnewline
63 & 2.42 & 2.50000555753464 & -0.0800055575346388 \tabularnewline
64 & 2.43 & 2.50337286244156 & -0.0733728624415568 \tabularnewline
65 & 2.47 & 2.51719416007028 & -0.0471941600702794 \tabularnewline
66 & 2.54 & 2.53712589849507 & 0.00287410150493184 \tabularnewline
67 & 2.55 & 2.46567480914517 & 0.084325190854829 \tabularnewline
68 & 2.55 & 2.47592240551451 & 0.074077594485491 \tabularnewline
69 & 2.49 & 2.4599780390158 & 0.0300219609841972 \tabularnewline
70 & 2.54 & 2.48221943367185 & 0.0577805663281468 \tabularnewline
71 & 2.55 & 2.50566346139051 & 0.0443365386094854 \tabularnewline
72 & 2.5 & 2.5157278797608 & -0.0157278797607989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271438&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]2.36[/C][C]2.40069444444445[/C][C]-0.0406944444444455[/C][/ROW]
[ROW][C]14[/C][C]2.35[/C][C]2.36107686978582[/C][C]-0.0110768697858155[/C][/ROW]
[ROW][C]15[/C][C]2.44[/C][C]2.45112809045052[/C][C]-0.0111280904505207[/C][/ROW]
[ROW][C]16[/C][C]2.5[/C][C]2.51087942632204[/C][C]-0.0108794263220444[/C][/ROW]
[ROW][C]17[/C][C]2.58[/C][C]2.58809317609641[/C][C]-0.00809317609641491[/C][/ROW]
[ROW][C]18[/C][C]2.55[/C][C]2.55167123892362[/C][C]-0.00167123892362131[/C][/ROW]
[ROW][C]19[/C][C]2.44[/C][C]2.45487202400666[/C][C]-0.0148720240066593[/C][/ROW]
[ROW][C]20[/C][C]2.3[/C][C]2.4106028752723[/C][C]-0.110602875272296[/C][/ROW]
[ROW][C]21[/C][C]2.24[/C][C]2.23521619546365[/C][C]0.00478380453634664[/C][/ROW]
[ROW][C]22[/C][C]2.19[/C][C]2.18699600703415[/C][C]0.00300399296585097[/C][/ROW]
[ROW][C]23[/C][C]2.25[/C][C]2.16523882858036[/C][C]0.0847611714196352[/C][/ROW]
[ROW][C]24[/C][C]2.28[/C][C]2.18788222702045[/C][C]0.0921177729795466[/C][/ROW]
[ROW][C]25[/C][C]2.27[/C][C]2.17889591700101[/C][C]0.091104082998994[/C][/ROW]
[ROW][C]26[/C][C]2.37[/C][C]2.25879277484555[/C][C]0.111207225154454[/C][/ROW]
[ROW][C]27[/C][C]2.47[/C][C]2.45874719665203[/C][C]0.0112528033479689[/C][/ROW]
[ROW][C]28[/C][C]2.5[/C][C]2.5434843804655[/C][C]-0.0434843804654994[/C][/ROW]
[ROW][C]29[/C][C]2.47[/C][C]2.59825514144234[/C][C]-0.128255141442338[/C][/ROW]
[ROW][C]30[/C][C]2.61[/C][C]2.46223785457279[/C][C]0.147762145427206[/C][/ROW]
[ROW][C]31[/C][C]2.61[/C][C]2.49710964652301[/C][C]0.112890353476992[/C][/ROW]
[ROW][C]32[/C][C]2.65[/C][C]2.55699137627486[/C][C]0.0930086237251375[/C][/ROW]
[ROW][C]33[/C][C]2.43[/C][C]2.58582469098643[/C][C]-0.155824690986431[/C][/ROW]
[ROW][C]34[/C][C]2.43[/C][C]2.40958714488035[/C][C]0.0204128551196461[/C][/ROW]
[ROW][C]35[/C][C]2.33[/C][C]2.42458614232157[/C][C]-0.0945861423215666[/C][/ROW]
[ROW][C]36[/C][C]2.27[/C][C]2.30077271471776[/C][C]-0.0307727147177586[/C][/ROW]
[ROW][C]37[/C][C]2.22[/C][C]2.18959662664762[/C][C]0.0304033733523768[/C][/ROW]
[ROW][C]38[/C][C]2.17[/C][C]2.22216517970769[/C][C]-0.0521651797076892[/C][/ROW]
[ROW][C]39[/C][C]2.28[/C][C]2.26584956152979[/C][C]0.0141504384702142[/C][/ROW]
[ROW][C]40[/C][C]2.3[/C][C]2.34317154759988[/C][C]-0.0431715475998828[/C][/ROW]
[ROW][C]41[/C][C]2.33[/C][C]2.38398548467517[/C][C]-0.0539854846751706[/C][/ROW]
[ROW][C]42[/C][C]2.44[/C][C]2.35109997727017[/C][C]0.0889000227298347[/C][/ROW]
[ROW][C]43[/C][C]2.41[/C][C]2.32894646287754[/C][C]0.0810535371224592[/C][/ROW]
[ROW][C]44[/C][C]2.4[/C][C]2.3563575435189[/C][C]0.0436424564811015[/C][/ROW]
[ROW][C]45[/C][C]2.34[/C][C]2.30352232637452[/C][C]0.0364776736254817[/C][/ROW]
[ROW][C]46[/C][C]2.37[/C][C]2.31819582079156[/C][C]0.0518041792084443[/C][/ROW]
[ROW][C]47[/C][C]2.38[/C][C]2.34509615039548[/C][C]0.0349038496045235[/C][/ROW]
[ROW][C]48[/C][C]2.3[/C][C]2.34591863107788[/C][C]-0.0459186310778752[/C][/ROW]
[ROW][C]49[/C][C]2.29[/C][C]2.23490079220564[/C][C]0.0550992077943575[/C][/ROW]
[ROW][C]50[/C][C]2.34[/C][C]2.28152492616096[/C][C]0.0584750738390407[/C][/ROW]
[ROW][C]51[/C][C]2.35[/C][C]2.43684463955306[/C][C]-0.0868446395530591[/C][/ROW]
[ROW][C]52[/C][C]2.38[/C][C]2.42455090999095[/C][C]-0.0445509099909511[/C][/ROW]
[ROW][C]53[/C][C]2.37[/C][C]2.46766354934459[/C][C]-0.0976635493445928[/C][/ROW]
[ROW][C]54[/C][C]2.45[/C][C]2.42207812037056[/C][C]0.0279218796294414[/C][/ROW]
[ROW][C]55[/C][C]2.51[/C][C]2.34925187177712[/C][C]0.160748128222882[/C][/ROW]
[ROW][C]56[/C][C]2.46[/C][C]2.44391188207151[/C][C]0.0160881179284926[/C][/ROW]
[ROW][C]57[/C][C]2.42[/C][C]2.37029904081766[/C][C]0.0497009591823367[/C][/ROW]
[ROW][C]58[/C][C]2.48[/C][C]2.40263598142782[/C][C]0.0773640185721827[/C][/ROW]
[ROW][C]59[/C][C]2.44[/C][C]2.4536888177537[/C][C]-0.0136888177537022[/C][/ROW]
[ROW][C]60[/C][C]2.43[/C][C]2.40487058410065[/C][C]0.0251294158993525[/C][/ROW]
[ROW][C]61[/C][C]2.36[/C][C]2.37447015803971[/C][C]-0.0144701580397091[/C][/ROW]
[ROW][C]62[/C][C]2.42[/C][C]2.36569978689943[/C][C]0.0543002131005723[/C][/ROW]
[ROW][C]63[/C][C]2.42[/C][C]2.50000555753464[/C][C]-0.0800055575346388[/C][/ROW]
[ROW][C]64[/C][C]2.43[/C][C]2.50337286244156[/C][C]-0.0733728624415568[/C][/ROW]
[ROW][C]65[/C][C]2.47[/C][C]2.51719416007028[/C][C]-0.0471941600702794[/C][/ROW]
[ROW][C]66[/C][C]2.54[/C][C]2.53712589849507[/C][C]0.00287410150493184[/C][/ROW]
[ROW][C]67[/C][C]2.55[/C][C]2.46567480914517[/C][C]0.084325190854829[/C][/ROW]
[ROW][C]68[/C][C]2.55[/C][C]2.47592240551451[/C][C]0.074077594485491[/C][/ROW]
[ROW][C]69[/C][C]2.49[/C][C]2.4599780390158[/C][C]0.0300219609841972[/C][/ROW]
[ROW][C]70[/C][C]2.54[/C][C]2.48221943367185[/C][C]0.0577805663281468[/C][/ROW]
[ROW][C]71[/C][C]2.55[/C][C]2.50566346139051[/C][C]0.0443365386094854[/C][/ROW]
[ROW][C]72[/C][C]2.5[/C][C]2.5157278797608[/C][C]-0.0157278797607989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271438&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271438&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
t	Observed	Fitted	Residuals
13	2.36	2.40069444444445	-0.0406944444444455
14	2.35	2.36107686978582	-0.0110768697858155
15	2.44	2.45112809045052	-0.0111280904505207
16	2.5	2.51087942632204	-0.0108794263220444
17	2.58	2.58809317609641	-0.00809317609641491
18	2.55	2.55167123892362	-0.00167123892362131
19	2.44	2.45487202400666	-0.0148720240066593
20	2.3	2.4106028752723	-0.110602875272296
21	2.24	2.23521619546365	0.00478380453634664
22	2.19	2.18699600703415	0.00300399296585097
23	2.25	2.16523882858036	0.0847611714196352
24	2.28	2.18788222702045	0.0921177729795466
25	2.27	2.17889591700101	0.091104082998994
26	2.37	2.25879277484555	0.111207225154454
27	2.47	2.45874719665203	0.0112528033479689
28	2.5	2.5434843804655	-0.0434843804654994
29	2.47	2.59825514144234	-0.128255141442338
30	2.61	2.46223785457279	0.147762145427206
31	2.61	2.49710964652301	0.112890353476992
32	2.65	2.55699137627486	0.0930086237251375
33	2.43	2.58582469098643	-0.155824690986431
34	2.43	2.40958714488035	0.0204128551196461
35	2.33	2.42458614232157	-0.0945861423215666
36	2.27	2.30077271471776	-0.0307727147177586
37	2.22	2.18959662664762	0.0304033733523768
38	2.17	2.22216517970769	-0.0521651797076892
39	2.28	2.26584956152979	0.0141504384702142
40	2.3	2.34317154759988	-0.0431715475998828
41	2.33	2.38398548467517	-0.0539854846751706
42	2.44	2.35109997727017	0.0889000227298347
43	2.41	2.32894646287754	0.0810535371224592
44	2.4	2.3563575435189	0.0436424564811015
45	2.34	2.30352232637452	0.0364776736254817
46	2.37	2.31819582079156	0.0518041792084443
47	2.38	2.34509615039548	0.0349038496045235
48	2.3	2.34591863107788	-0.0459186310778752
49	2.29	2.23490079220564	0.0550992077943575
50	2.34	2.28152492616096	0.0584750738390407
51	2.35	2.43684463955306	-0.0868446395530591
52	2.38	2.42455090999095	-0.0445509099909511
53	2.37	2.46766354934459	-0.0976635493445928
54	2.45	2.42207812037056	0.0279218796294414
55	2.51	2.34925187177712	0.160748128222882
56	2.46	2.44391188207151	0.0160881179284926
57	2.42	2.37029904081766	0.0497009591823367
58	2.48	2.40263598142782	0.0773640185721827
59	2.44	2.4536888177537	-0.0136888177537022
60	2.43	2.40487058410065	0.0251294158993525
61	2.36	2.37447015803971	-0.0144701580397091
62	2.42	2.36569978689943	0.0543002131005723
63	2.42	2.50000555753464	-0.0800055575346388
64	2.43	2.50337286244156	-0.0733728624415568
65	2.47	2.51719416007028	-0.0471941600702794
66	2.54	2.53712589849507	0.00287410150493184
67	2.55	2.46567480914517	0.084325190854829
68	2.55	2.47592240551451	0.074077594485491
69	2.49	2.4599780390158	0.0300219609841972
70	2.54	2.48221943367185	0.0577805663281468
71	2.55	2.50566346139051	0.0443365386094854
72	2.5	2.5157278797608	-0.0157278797607989

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	2.44734274939958	2.31460952258435	2.58007597621481
74	2.46390823677183	2.28722194866407	2.64059452487958
75	2.53413422387653	2.32073396535318	2.74753448239988
76	2.61052633364942	2.36435232197044	2.85670034532839
77	2.69620868018199	2.41976226186935	2.97265509849463
78	2.77013934054701	2.46514546916455	3.07513321192947
79	2.7143155587211	2.38202619852013	3.04660491892207
80	2.65531911230939	2.29667423099732	3.01396399362146
81	2.57231144227132	2.18803326923215	2.95658961531049
82	2.57486311781881	2.16551538571391	2.9842108499237
83	2.54758774753403	2.11361498095257	2.9815605141155
84	2.51068237735889	2.05243707179985	2.96892768291793

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.44734274939958 & 2.31460952258435 & 2.58007597621481 \tabularnewline
74 & 2.46390823677183 & 2.28722194866407 & 2.64059452487958 \tabularnewline
75 & 2.53413422387653 & 2.32073396535318 & 2.74753448239988 \tabularnewline
76 & 2.61052633364942 & 2.36435232197044 & 2.85670034532839 \tabularnewline
77 & 2.69620868018199 & 2.41976226186935 & 2.97265509849463 \tabularnewline
78 & 2.77013934054701 & 2.46514546916455 & 3.07513321192947 \tabularnewline
79 & 2.7143155587211 & 2.38202619852013 & 3.04660491892207 \tabularnewline
80 & 2.65531911230939 & 2.29667423099732 & 3.01396399362146 \tabularnewline
81 & 2.57231144227132 & 2.18803326923215 & 2.95658961531049 \tabularnewline
82 & 2.57486311781881 & 2.16551538571391 & 2.9842108499237 \tabularnewline
83 & 2.54758774753403 & 2.11361498095257 & 2.9815605141155 \tabularnewline
84 & 2.51068237735889 & 2.05243707179985 & 2.96892768291793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271438&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]2.44734274939958[/C][C]2.31460952258435[/C][C]2.58007597621481[/C][/ROW]
[ROW][C]74[/C][C]2.46390823677183[/C][C]2.28722194866407[/C][C]2.64059452487958[/C][/ROW]
[ROW][C]75[/C][C]2.53413422387653[/C][C]2.32073396535318[/C][C]2.74753448239988[/C][/ROW]
[ROW][C]76[/C][C]2.61052633364942[/C][C]2.36435232197044[/C][C]2.85670034532839[/C][/ROW]
[ROW][C]77[/C][C]2.69620868018199[/C][C]2.41976226186935[/C][C]2.97265509849463[/C][/ROW]
[ROW][C]78[/C][C]2.77013934054701[/C][C]2.46514546916455[/C][C]3.07513321192947[/C][/ROW]
[ROW][C]79[/C][C]2.7143155587211[/C][C]2.38202619852013[/C][C]3.04660491892207[/C][/ROW]
[ROW][C]80[/C][C]2.65531911230939[/C][C]2.29667423099732[/C][C]3.01396399362146[/C][/ROW]
[ROW][C]81[/C][C]2.57231144227132[/C][C]2.18803326923215[/C][C]2.95658961531049[/C][/ROW]
[ROW][C]82[/C][C]2.57486311781881[/C][C]2.16551538571391[/C][C]2.9842108499237[/C][/ROW]
[ROW][C]83[/C][C]2.54758774753403[/C][C]2.11361498095257[/C][C]2.9815605141155[/C][/ROW]
[ROW][C]84[/C][C]2.51068237735889[/C][C]2.05243707179985[/C][C]2.96892768291793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271438&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271438&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	2.44734274939958	2.31460952258435	2.58007597621481
74	2.46390823677183	2.28722194866407	2.64059452487958
75	2.53413422387653	2.32073396535318	2.74753448239988
76	2.61052633364942	2.36435232197044	2.85670034532839
77	2.69620868018199	2.41976226186935	2.97265509849463
78	2.77013934054701	2.46514546916455	3.07513321192947
79	2.7143155587211	2.38202619852013	3.04660491892207
80	2.65531911230939	2.29667423099732	3.01396399362146
81	2.57231144227132	2.18803326923215	2.95658961531049
82	2.57486311781881	2.16551538571391	2.9842108499237
83	2.54758774753403	2.11361498095257	2.9815605141155
84	2.51068237735889	2.05243707179985	2.96892768291793

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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):

par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code