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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 22 May 2015 15:27:25 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/22/t1432305095vx6e1fyuvvv5ff1.htm/, Retrieved Fri, 03 May 2024 04:50:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279231, Retrieved Fri, 03 May 2024 04:50:36 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-05-22 14:27:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279231&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279231&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999937226073122
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999937226073122 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279231&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]0.999937226073122[/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=279231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279231&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	0.999937226073122
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	96.89	96.86	0.0300000000000011
3	96.9	96.8899981167822	0.0100018832178108
4	96.94	96.8999993721425	0.0400006278574807
5	96.88	96.9399974890035	-0.0599974890035071
6	96.89	96.880003766278	0.00999623372202052
7	96.89	96.8899993724971	6.27502856787032e-07
8	96.95	96.8899999999606	0.0600000000393948
9	97.03	96.9499962335644	0.0800037664356239
10	97.29	97.0299949778494	0.260005022150594
11	97.37	97.2899836784638	0.0800163215362488
12	97.41	97.3699949770613	0.0400050229387006
13	97.41	97.4099974887276	2.51127238470872e-06
14	97.32	97.4099999998424	-0.0899999998423624
15	97.33	97.3200056496534	0.00999435034658802
16	97.38	97.3299993726154	0.0500006273846054
17	97.47	97.3799968612643	0.0900031387357245
18	97.5	97.4699943501496	0.0300056498504375
19	97.5	97.4999981164275	1.88357246599935e-06
20	97.58	97.4999999998818	0.0800000001182326
21	97.7	97.5799949780858	0.120005021914167
22	97.9	97.6999924668135	0.200007533186479
23	97.98	97.8999874447417	0.0800125552582642
24	98.03	97.9799949772977	0.0500050227022939
25	98.03	98.0299968609884	3.13901163906394e-06
26	97.94	98.029999999803	-0.0899999998029557
27	98.12	97.9400056496534	0.179994350346604
28	98.19	98.1199887010478	0.0700112989521813
29	98.34	98.1899956051158	0.150004394884178
30	98.42	98.3399905836351	0.0800094163649163
31	98.43	98.4199949774948	0.0100050225052541
32	98.45	98.4299993719455	0.0200006280545466
33	98.77	98.449998744482	0.320001255517951
34	99.24	98.7699799122646	0.470020087735406
35	99.46	99.2399704949934	0.220029505006622
36	99.54	99.4599861878839	0.0800138121160643
37	99.55	99.5399949772188	0.0100050227811863
38	99.24	99.5499993719454	-0.309999371945423
39	99.43	99.2400194598779	0.189980540122107
40	99.47	99.4299880741755	0.0400119258245155
41	99.57	99.4699974882943	0.100002511705696
42	99.62	99.5699937224496	0.0500062775503807
43	99.64	99.6199968609096	0.0200031390904059
44	99.75	99.6399987443244	0.110001255675598
45	99.85	99.7499930947892	0.100006905210776
46	100.28	99.8499937221738	0.430006277826166
47	100.52	100.279973006817	0.240026993182639
48	100.57	100.519984932563	0.0500150674369166
49	100.57	100.569996860358	3.13964218889851e-06
50	100.27	100.569999999803	-0.299999999802907
51	100.27	100.270018832178	-1.88321780427714e-05
52	100.18	100.270000001182	-0.0900000011821476
53	100.16	100.180005649654	-0.0200056496535126
54	100.18	100.160001255833	0.0199987441668128
55	100.18	100.1799987446	1.25539969531019e-06
56	100.59	100.179999999921	0.410000000078796
57	100.69	100.58997426269	0.10002573731002
58	101.06	100.689993720992	0.370006279008322
59	101.15	101.059976773253	0.0900232267471068
60	101.16	101.149994348889	0.0100056511114417
61	101.16	101.159999371906	6.2809401413233e-07
62	100.81	101.159999999961	-0.349999999960559
63	100.94	100.810021970874	0.129978029125581
64	101.13	100.939991840769	0.190008159231297
65	101.29	101.129988072442	0.160011927558301
66	101.34	101.289989955423	0.0500100445770357
67	101.35	101.339996860673	0.0100031393268694
68	101.7	101.349999372064	0.350000627936339
69	102.05	101.699978029086	0.350021970913829
70	102.48	102.049978027746	0.430021972253613
71	102.66	102.479973005832	0.180026994167832
72	102.72	102.659988698999	0.0600113010013672
73	102.73	102.719996232855	0.0100037671450224
74	102.18	102.729999372024	-0.54999937202426
75	102.22	102.18003452562	0.0399654743796276
76	102.37	102.21999749121	0.150002508789782
77	102.53	102.369990583753	0.160009416246524
78	102.61	102.529989955581	0.0800100444193959
79	102.62	102.609994977455	0.0100050225446751
80	103	102.619999371945	0.380000628054546
81	103.17	102.999976145868	0.170023854131642
82	103.52	103.169989326935	0.350010673064986
83	103.69	103.519978028456	0.170021971544386
84	103.73	103.689989327053	0.0400106729468206
85	99.57	103.729997488373	-4.15999748837295
86	99.09	99.5702611393781	-0.480261139378129
87	99.14	99.0900301478776	0.0499698521223593
88	99.36	99.1399968631962	0.22000313680384
89	99.6	99.3599861895392	0.240013810460809
90	99.65	99.5999849333906	0.0500150666094044
91	99.8	99.6499968603579	0.150003139642124
92	100.15	99.7999905837139	0.350009416286127
93	100.45	100.149978028535	0.300021971465497
94	100.89	100.449981166443	0.440018833557303
95	101.13	100.88997237829	0.240027621710084
96	101.17	101.129984932524	0.0400150674763751

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 96.89 & 96.86 & 0.0300000000000011 \tabularnewline
3 & 96.9 & 96.8899981167822 & 0.0100018832178108 \tabularnewline
4 & 96.94 & 96.8999993721425 & 0.0400006278574807 \tabularnewline
5 & 96.88 & 96.9399974890035 & -0.0599974890035071 \tabularnewline
6 & 96.89 & 96.880003766278 & 0.00999623372202052 \tabularnewline
7 & 96.89 & 96.8899993724971 & 6.27502856787032e-07 \tabularnewline
8 & 96.95 & 96.8899999999606 & 0.0600000000393948 \tabularnewline
9 & 97.03 & 96.9499962335644 & 0.0800037664356239 \tabularnewline
10 & 97.29 & 97.0299949778494 & 0.260005022150594 \tabularnewline
11 & 97.37 & 97.2899836784638 & 0.0800163215362488 \tabularnewline
12 & 97.41 & 97.3699949770613 & 0.0400050229387006 \tabularnewline
13 & 97.41 & 97.4099974887276 & 2.51127238470872e-06 \tabularnewline
14 & 97.32 & 97.4099999998424 & -0.0899999998423624 \tabularnewline
15 & 97.33 & 97.3200056496534 & 0.00999435034658802 \tabularnewline
16 & 97.38 & 97.3299993726154 & 0.0500006273846054 \tabularnewline
17 & 97.47 & 97.3799968612643 & 0.0900031387357245 \tabularnewline
18 & 97.5 & 97.4699943501496 & 0.0300056498504375 \tabularnewline
19 & 97.5 & 97.4999981164275 & 1.88357246599935e-06 \tabularnewline
20 & 97.58 & 97.4999999998818 & 0.0800000001182326 \tabularnewline
21 & 97.7 & 97.5799949780858 & 0.120005021914167 \tabularnewline
22 & 97.9 & 97.6999924668135 & 0.200007533186479 \tabularnewline
23 & 97.98 & 97.8999874447417 & 0.0800125552582642 \tabularnewline
24 & 98.03 & 97.9799949772977 & 0.0500050227022939 \tabularnewline
25 & 98.03 & 98.0299968609884 & 3.13901163906394e-06 \tabularnewline
26 & 97.94 & 98.029999999803 & -0.0899999998029557 \tabularnewline
27 & 98.12 & 97.9400056496534 & 0.179994350346604 \tabularnewline
28 & 98.19 & 98.1199887010478 & 0.0700112989521813 \tabularnewline
29 & 98.34 & 98.1899956051158 & 0.150004394884178 \tabularnewline
30 & 98.42 & 98.3399905836351 & 0.0800094163649163 \tabularnewline
31 & 98.43 & 98.4199949774948 & 0.0100050225052541 \tabularnewline
32 & 98.45 & 98.4299993719455 & 0.0200006280545466 \tabularnewline
33 & 98.77 & 98.449998744482 & 0.320001255517951 \tabularnewline
34 & 99.24 & 98.7699799122646 & 0.470020087735406 \tabularnewline
35 & 99.46 & 99.2399704949934 & 0.220029505006622 \tabularnewline
36 & 99.54 & 99.4599861878839 & 0.0800138121160643 \tabularnewline
37 & 99.55 & 99.5399949772188 & 0.0100050227811863 \tabularnewline
38 & 99.24 & 99.5499993719454 & -0.309999371945423 \tabularnewline
39 & 99.43 & 99.2400194598779 & 0.189980540122107 \tabularnewline
40 & 99.47 & 99.4299880741755 & 0.0400119258245155 \tabularnewline
41 & 99.57 & 99.4699974882943 & 0.100002511705696 \tabularnewline
42 & 99.62 & 99.5699937224496 & 0.0500062775503807 \tabularnewline
43 & 99.64 & 99.6199968609096 & 0.0200031390904059 \tabularnewline
44 & 99.75 & 99.6399987443244 & 0.110001255675598 \tabularnewline
45 & 99.85 & 99.7499930947892 & 0.100006905210776 \tabularnewline
46 & 100.28 & 99.8499937221738 & 0.430006277826166 \tabularnewline
47 & 100.52 & 100.279973006817 & 0.240026993182639 \tabularnewline
48 & 100.57 & 100.519984932563 & 0.0500150674369166 \tabularnewline
49 & 100.57 & 100.569996860358 & 3.13964218889851e-06 \tabularnewline
50 & 100.27 & 100.569999999803 & -0.299999999802907 \tabularnewline
51 & 100.27 & 100.270018832178 & -1.88321780427714e-05 \tabularnewline
52 & 100.18 & 100.270000001182 & -0.0900000011821476 \tabularnewline
53 & 100.16 & 100.180005649654 & -0.0200056496535126 \tabularnewline
54 & 100.18 & 100.160001255833 & 0.0199987441668128 \tabularnewline
55 & 100.18 & 100.1799987446 & 1.25539969531019e-06 \tabularnewline
56 & 100.59 & 100.179999999921 & 0.410000000078796 \tabularnewline
57 & 100.69 & 100.58997426269 & 0.10002573731002 \tabularnewline
58 & 101.06 & 100.689993720992 & 0.370006279008322 \tabularnewline
59 & 101.15 & 101.059976773253 & 0.0900232267471068 \tabularnewline
60 & 101.16 & 101.149994348889 & 0.0100056511114417 \tabularnewline
61 & 101.16 & 101.159999371906 & 6.2809401413233e-07 \tabularnewline
62 & 100.81 & 101.159999999961 & -0.349999999960559 \tabularnewline
63 & 100.94 & 100.810021970874 & 0.129978029125581 \tabularnewline
64 & 101.13 & 100.939991840769 & 0.190008159231297 \tabularnewline
65 & 101.29 & 101.129988072442 & 0.160011927558301 \tabularnewline
66 & 101.34 & 101.289989955423 & 0.0500100445770357 \tabularnewline
67 & 101.35 & 101.339996860673 & 0.0100031393268694 \tabularnewline
68 & 101.7 & 101.349999372064 & 0.350000627936339 \tabularnewline
69 & 102.05 & 101.699978029086 & 0.350021970913829 \tabularnewline
70 & 102.48 & 102.049978027746 & 0.430021972253613 \tabularnewline
71 & 102.66 & 102.479973005832 & 0.180026994167832 \tabularnewline
72 & 102.72 & 102.659988698999 & 0.0600113010013672 \tabularnewline
73 & 102.73 & 102.719996232855 & 0.0100037671450224 \tabularnewline
74 & 102.18 & 102.729999372024 & -0.54999937202426 \tabularnewline
75 & 102.22 & 102.18003452562 & 0.0399654743796276 \tabularnewline
76 & 102.37 & 102.21999749121 & 0.150002508789782 \tabularnewline
77 & 102.53 & 102.369990583753 & 0.160009416246524 \tabularnewline
78 & 102.61 & 102.529989955581 & 0.0800100444193959 \tabularnewline
79 & 102.62 & 102.609994977455 & 0.0100050225446751 \tabularnewline
80 & 103 & 102.619999371945 & 0.380000628054546 \tabularnewline
81 & 103.17 & 102.999976145868 & 0.170023854131642 \tabularnewline
82 & 103.52 & 103.169989326935 & 0.350010673064986 \tabularnewline
83 & 103.69 & 103.519978028456 & 0.170021971544386 \tabularnewline
84 & 103.73 & 103.689989327053 & 0.0400106729468206 \tabularnewline
85 & 99.57 & 103.729997488373 & -4.15999748837295 \tabularnewline
86 & 99.09 & 99.5702611393781 & -0.480261139378129 \tabularnewline
87 & 99.14 & 99.0900301478776 & 0.0499698521223593 \tabularnewline
88 & 99.36 & 99.1399968631962 & 0.22000313680384 \tabularnewline
89 & 99.6 & 99.3599861895392 & 0.240013810460809 \tabularnewline
90 & 99.65 & 99.5999849333906 & 0.0500150666094044 \tabularnewline
91 & 99.8 & 99.6499968603579 & 0.150003139642124 \tabularnewline
92 & 100.15 & 99.7999905837139 & 0.350009416286127 \tabularnewline
93 & 100.45 & 100.149978028535 & 0.300021971465497 \tabularnewline
94 & 100.89 & 100.449981166443 & 0.440018833557303 \tabularnewline
95 & 101.13 & 100.88997237829 & 0.240027621710084 \tabularnewline
96 & 101.17 & 101.129984932524 & 0.0400150674763751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279231&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]96.89[/C][C]96.86[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]3[/C][C]96.9[/C][C]96.8899981167822[/C][C]0.0100018832178108[/C][/ROW]
[ROW][C]4[/C][C]96.94[/C][C]96.8999993721425[/C][C]0.0400006278574807[/C][/ROW]
[ROW][C]5[/C][C]96.88[/C][C]96.9399974890035[/C][C]-0.0599974890035071[/C][/ROW]
[ROW][C]6[/C][C]96.89[/C][C]96.880003766278[/C][C]0.00999623372202052[/C][/ROW]
[ROW][C]7[/C][C]96.89[/C][C]96.8899993724971[/C][C]6.27502856787032e-07[/C][/ROW]
[ROW][C]8[/C][C]96.95[/C][C]96.8899999999606[/C][C]0.0600000000393948[/C][/ROW]
[ROW][C]9[/C][C]97.03[/C][C]96.9499962335644[/C][C]0.0800037664356239[/C][/ROW]
[ROW][C]10[/C][C]97.29[/C][C]97.0299949778494[/C][C]0.260005022150594[/C][/ROW]
[ROW][C]11[/C][C]97.37[/C][C]97.2899836784638[/C][C]0.0800163215362488[/C][/ROW]
[ROW][C]12[/C][C]97.41[/C][C]97.3699949770613[/C][C]0.0400050229387006[/C][/ROW]
[ROW][C]13[/C][C]97.41[/C][C]97.4099974887276[/C][C]2.51127238470872e-06[/C][/ROW]
[ROW][C]14[/C][C]97.32[/C][C]97.4099999998424[/C][C]-0.0899999998423624[/C][/ROW]
[ROW][C]15[/C][C]97.33[/C][C]97.3200056496534[/C][C]0.00999435034658802[/C][/ROW]
[ROW][C]16[/C][C]97.38[/C][C]97.3299993726154[/C][C]0.0500006273846054[/C][/ROW]
[ROW][C]17[/C][C]97.47[/C][C]97.3799968612643[/C][C]0.0900031387357245[/C][/ROW]
[ROW][C]18[/C][C]97.5[/C][C]97.4699943501496[/C][C]0.0300056498504375[/C][/ROW]
[ROW][C]19[/C][C]97.5[/C][C]97.4999981164275[/C][C]1.88357246599935e-06[/C][/ROW]
[ROW][C]20[/C][C]97.58[/C][C]97.4999999998818[/C][C]0.0800000001182326[/C][/ROW]
[ROW][C]21[/C][C]97.7[/C][C]97.5799949780858[/C][C]0.120005021914167[/C][/ROW]
[ROW][C]22[/C][C]97.9[/C][C]97.6999924668135[/C][C]0.200007533186479[/C][/ROW]
[ROW][C]23[/C][C]97.98[/C][C]97.8999874447417[/C][C]0.0800125552582642[/C][/ROW]
[ROW][C]24[/C][C]98.03[/C][C]97.9799949772977[/C][C]0.0500050227022939[/C][/ROW]
[ROW][C]25[/C][C]98.03[/C][C]98.0299968609884[/C][C]3.13901163906394e-06[/C][/ROW]
[ROW][C]26[/C][C]97.94[/C][C]98.029999999803[/C][C]-0.0899999998029557[/C][/ROW]
[ROW][C]27[/C][C]98.12[/C][C]97.9400056496534[/C][C]0.179994350346604[/C][/ROW]
[ROW][C]28[/C][C]98.19[/C][C]98.1199887010478[/C][C]0.0700112989521813[/C][/ROW]
[ROW][C]29[/C][C]98.34[/C][C]98.1899956051158[/C][C]0.150004394884178[/C][/ROW]
[ROW][C]30[/C][C]98.42[/C][C]98.3399905836351[/C][C]0.0800094163649163[/C][/ROW]
[ROW][C]31[/C][C]98.43[/C][C]98.4199949774948[/C][C]0.0100050225052541[/C][/ROW]
[ROW][C]32[/C][C]98.45[/C][C]98.4299993719455[/C][C]0.0200006280545466[/C][/ROW]
[ROW][C]33[/C][C]98.77[/C][C]98.449998744482[/C][C]0.320001255517951[/C][/ROW]
[ROW][C]34[/C][C]99.24[/C][C]98.7699799122646[/C][C]0.470020087735406[/C][/ROW]
[ROW][C]35[/C][C]99.46[/C][C]99.2399704949934[/C][C]0.220029505006622[/C][/ROW]
[ROW][C]36[/C][C]99.54[/C][C]99.4599861878839[/C][C]0.0800138121160643[/C][/ROW]
[ROW][C]37[/C][C]99.55[/C][C]99.5399949772188[/C][C]0.0100050227811863[/C][/ROW]
[ROW][C]38[/C][C]99.24[/C][C]99.5499993719454[/C][C]-0.309999371945423[/C][/ROW]
[ROW][C]39[/C][C]99.43[/C][C]99.2400194598779[/C][C]0.189980540122107[/C][/ROW]
[ROW][C]40[/C][C]99.47[/C][C]99.4299880741755[/C][C]0.0400119258245155[/C][/ROW]
[ROW][C]41[/C][C]99.57[/C][C]99.4699974882943[/C][C]0.100002511705696[/C][/ROW]
[ROW][C]42[/C][C]99.62[/C][C]99.5699937224496[/C][C]0.0500062775503807[/C][/ROW]
[ROW][C]43[/C][C]99.64[/C][C]99.6199968609096[/C][C]0.0200031390904059[/C][/ROW]
[ROW][C]44[/C][C]99.75[/C][C]99.6399987443244[/C][C]0.110001255675598[/C][/ROW]
[ROW][C]45[/C][C]99.85[/C][C]99.7499930947892[/C][C]0.100006905210776[/C][/ROW]
[ROW][C]46[/C][C]100.28[/C][C]99.8499937221738[/C][C]0.430006277826166[/C][/ROW]
[ROW][C]47[/C][C]100.52[/C][C]100.279973006817[/C][C]0.240026993182639[/C][/ROW]
[ROW][C]48[/C][C]100.57[/C][C]100.519984932563[/C][C]0.0500150674369166[/C][/ROW]
[ROW][C]49[/C][C]100.57[/C][C]100.569996860358[/C][C]3.13964218889851e-06[/C][/ROW]
[ROW][C]50[/C][C]100.27[/C][C]100.569999999803[/C][C]-0.299999999802907[/C][/ROW]
[ROW][C]51[/C][C]100.27[/C][C]100.270018832178[/C][C]-1.88321780427714e-05[/C][/ROW]
[ROW][C]52[/C][C]100.18[/C][C]100.270000001182[/C][C]-0.0900000011821476[/C][/ROW]
[ROW][C]53[/C][C]100.16[/C][C]100.180005649654[/C][C]-0.0200056496535126[/C][/ROW]
[ROW][C]54[/C][C]100.18[/C][C]100.160001255833[/C][C]0.0199987441668128[/C][/ROW]
[ROW][C]55[/C][C]100.18[/C][C]100.1799987446[/C][C]1.25539969531019e-06[/C][/ROW]
[ROW][C]56[/C][C]100.59[/C][C]100.179999999921[/C][C]0.410000000078796[/C][/ROW]
[ROW][C]57[/C][C]100.69[/C][C]100.58997426269[/C][C]0.10002573731002[/C][/ROW]
[ROW][C]58[/C][C]101.06[/C][C]100.689993720992[/C][C]0.370006279008322[/C][/ROW]
[ROW][C]59[/C][C]101.15[/C][C]101.059976773253[/C][C]0.0900232267471068[/C][/ROW]
[ROW][C]60[/C][C]101.16[/C][C]101.149994348889[/C][C]0.0100056511114417[/C][/ROW]
[ROW][C]61[/C][C]101.16[/C][C]101.159999371906[/C][C]6.2809401413233e-07[/C][/ROW]
[ROW][C]62[/C][C]100.81[/C][C]101.159999999961[/C][C]-0.349999999960559[/C][/ROW]
[ROW][C]63[/C][C]100.94[/C][C]100.810021970874[/C][C]0.129978029125581[/C][/ROW]
[ROW][C]64[/C][C]101.13[/C][C]100.939991840769[/C][C]0.190008159231297[/C][/ROW]
[ROW][C]65[/C][C]101.29[/C][C]101.129988072442[/C][C]0.160011927558301[/C][/ROW]
[ROW][C]66[/C][C]101.34[/C][C]101.289989955423[/C][C]0.0500100445770357[/C][/ROW]
[ROW][C]67[/C][C]101.35[/C][C]101.339996860673[/C][C]0.0100031393268694[/C][/ROW]
[ROW][C]68[/C][C]101.7[/C][C]101.349999372064[/C][C]0.350000627936339[/C][/ROW]
[ROW][C]69[/C][C]102.05[/C][C]101.699978029086[/C][C]0.350021970913829[/C][/ROW]
[ROW][C]70[/C][C]102.48[/C][C]102.049978027746[/C][C]0.430021972253613[/C][/ROW]
[ROW][C]71[/C][C]102.66[/C][C]102.479973005832[/C][C]0.180026994167832[/C][/ROW]
[ROW][C]72[/C][C]102.72[/C][C]102.659988698999[/C][C]0.0600113010013672[/C][/ROW]
[ROW][C]73[/C][C]102.73[/C][C]102.719996232855[/C][C]0.0100037671450224[/C][/ROW]
[ROW][C]74[/C][C]102.18[/C][C]102.729999372024[/C][C]-0.54999937202426[/C][/ROW]
[ROW][C]75[/C][C]102.22[/C][C]102.18003452562[/C][C]0.0399654743796276[/C][/ROW]
[ROW][C]76[/C][C]102.37[/C][C]102.21999749121[/C][C]0.150002508789782[/C][/ROW]
[ROW][C]77[/C][C]102.53[/C][C]102.369990583753[/C][C]0.160009416246524[/C][/ROW]
[ROW][C]78[/C][C]102.61[/C][C]102.529989955581[/C][C]0.0800100444193959[/C][/ROW]
[ROW][C]79[/C][C]102.62[/C][C]102.609994977455[/C][C]0.0100050225446751[/C][/ROW]
[ROW][C]80[/C][C]103[/C][C]102.619999371945[/C][C]0.380000628054546[/C][/ROW]
[ROW][C]81[/C][C]103.17[/C][C]102.999976145868[/C][C]0.170023854131642[/C][/ROW]
[ROW][C]82[/C][C]103.52[/C][C]103.169989326935[/C][C]0.350010673064986[/C][/ROW]
[ROW][C]83[/C][C]103.69[/C][C]103.519978028456[/C][C]0.170021971544386[/C][/ROW]
[ROW][C]84[/C][C]103.73[/C][C]103.689989327053[/C][C]0.0400106729468206[/C][/ROW]
[ROW][C]85[/C][C]99.57[/C][C]103.729997488373[/C][C]-4.15999748837295[/C][/ROW]
[ROW][C]86[/C][C]99.09[/C][C]99.5702611393781[/C][C]-0.480261139378129[/C][/ROW]
[ROW][C]87[/C][C]99.14[/C][C]99.0900301478776[/C][C]0.0499698521223593[/C][/ROW]
[ROW][C]88[/C][C]99.36[/C][C]99.1399968631962[/C][C]0.22000313680384[/C][/ROW]
[ROW][C]89[/C][C]99.6[/C][C]99.3599861895392[/C][C]0.240013810460809[/C][/ROW]
[ROW][C]90[/C][C]99.65[/C][C]99.5999849333906[/C][C]0.0500150666094044[/C][/ROW]
[ROW][C]91[/C][C]99.8[/C][C]99.6499968603579[/C][C]0.150003139642124[/C][/ROW]
[ROW][C]92[/C][C]100.15[/C][C]99.7999905837139[/C][C]0.350009416286127[/C][/ROW]
[ROW][C]93[/C][C]100.45[/C][C]100.149978028535[/C][C]0.300021971465497[/C][/ROW]
[ROW][C]94[/C][C]100.89[/C][C]100.449981166443[/C][C]0.440018833557303[/C][/ROW]
[ROW][C]95[/C][C]101.13[/C][C]100.88997237829[/C][C]0.240027621710084[/C][/ROW]
[ROW][C]96[/C][C]101.17[/C][C]101.129984932524[/C][C]0.0400150674763751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279231&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279231&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
2	96.89	96.86	0.0300000000000011
3	96.9	96.8899981167822	0.0100018832178108
4	96.94	96.8999993721425	0.0400006278574807
5	96.88	96.9399974890035	-0.0599974890035071
6	96.89	96.880003766278	0.00999623372202052
7	96.89	96.8899993724971	6.27502856787032e-07
8	96.95	96.8899999999606	0.0600000000393948
9	97.03	96.9499962335644	0.0800037664356239
10	97.29	97.0299949778494	0.260005022150594
11	97.37	97.2899836784638	0.0800163215362488
12	97.41	97.3699949770613	0.0400050229387006
13	97.41	97.4099974887276	2.51127238470872e-06
14	97.32	97.4099999998424	-0.0899999998423624
15	97.33	97.3200056496534	0.00999435034658802
16	97.38	97.3299993726154	0.0500006273846054
17	97.47	97.3799968612643	0.0900031387357245
18	97.5	97.4699943501496	0.0300056498504375
19	97.5	97.4999981164275	1.88357246599935e-06
20	97.58	97.4999999998818	0.0800000001182326
21	97.7	97.5799949780858	0.120005021914167
22	97.9	97.6999924668135	0.200007533186479
23	97.98	97.8999874447417	0.0800125552582642
24	98.03	97.9799949772977	0.0500050227022939
25	98.03	98.0299968609884	3.13901163906394e-06
26	97.94	98.029999999803	-0.0899999998029557
27	98.12	97.9400056496534	0.179994350346604
28	98.19	98.1199887010478	0.0700112989521813
29	98.34	98.1899956051158	0.150004394884178
30	98.42	98.3399905836351	0.0800094163649163
31	98.43	98.4199949774948	0.0100050225052541
32	98.45	98.4299993719455	0.0200006280545466
33	98.77	98.449998744482	0.320001255517951
34	99.24	98.7699799122646	0.470020087735406
35	99.46	99.2399704949934	0.220029505006622
36	99.54	99.4599861878839	0.0800138121160643
37	99.55	99.5399949772188	0.0100050227811863
38	99.24	99.5499993719454	-0.309999371945423
39	99.43	99.2400194598779	0.189980540122107
40	99.47	99.4299880741755	0.0400119258245155
41	99.57	99.4699974882943	0.100002511705696
42	99.62	99.5699937224496	0.0500062775503807
43	99.64	99.6199968609096	0.0200031390904059
44	99.75	99.6399987443244	0.110001255675598
45	99.85	99.7499930947892	0.100006905210776
46	100.28	99.8499937221738	0.430006277826166
47	100.52	100.279973006817	0.240026993182639
48	100.57	100.519984932563	0.0500150674369166
49	100.57	100.569996860358	3.13964218889851e-06
50	100.27	100.569999999803	-0.299999999802907
51	100.27	100.270018832178	-1.88321780427714e-05
52	100.18	100.270000001182	-0.0900000011821476
53	100.16	100.180005649654	-0.0200056496535126
54	100.18	100.160001255833	0.0199987441668128
55	100.18	100.1799987446	1.25539969531019e-06
56	100.59	100.179999999921	0.410000000078796
57	100.69	100.58997426269	0.10002573731002
58	101.06	100.689993720992	0.370006279008322
59	101.15	101.059976773253	0.0900232267471068
60	101.16	101.149994348889	0.0100056511114417
61	101.16	101.159999371906	6.2809401413233e-07
62	100.81	101.159999999961	-0.349999999960559
63	100.94	100.810021970874	0.129978029125581
64	101.13	100.939991840769	0.190008159231297
65	101.29	101.129988072442	0.160011927558301
66	101.34	101.289989955423	0.0500100445770357
67	101.35	101.339996860673	0.0100031393268694
68	101.7	101.349999372064	0.350000627936339
69	102.05	101.699978029086	0.350021970913829
70	102.48	102.049978027746	0.430021972253613
71	102.66	102.479973005832	0.180026994167832
72	102.72	102.659988698999	0.0600113010013672
73	102.73	102.719996232855	0.0100037671450224
74	102.18	102.729999372024	-0.54999937202426
75	102.22	102.18003452562	0.0399654743796276
76	102.37	102.21999749121	0.150002508789782
77	102.53	102.369990583753	0.160009416246524
78	102.61	102.529989955581	0.0800100444193959
79	102.62	102.609994977455	0.0100050225446751
80	103	102.619999371945	0.380000628054546
81	103.17	102.999976145868	0.170023854131642
82	103.52	103.169989326935	0.350010673064986
83	103.69	103.519978028456	0.170021971544386
84	103.73	103.689989327053	0.0400106729468206
85	99.57	103.729997488373	-4.15999748837295
86	99.09	99.5702611393781	-0.480261139378129
87	99.14	99.0900301478776	0.0499698521223593
88	99.36	99.1399968631962	0.22000313680384
89	99.6	99.3599861895392	0.240013810460809
90	99.65	99.5999849333906	0.0500150666094044
91	99.8	99.6499968603579	0.150003139642124
92	100.15	99.7999905837139	0.350009416286127
93	100.45	100.149978028535	0.300021971465497
94	100.89	100.449981166443	0.440018833557303
95	101.13	100.88997237829	0.240027621710084
96	101.17	101.129984932524	0.0400150674763751

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	101.169997488097	100.248814822076	102.091180154118
98	101.169997488097	99.8672893570812	102.472705619113
99	101.169997488097	99.5745290788041	102.76546589739
100	101.169997488097	99.3277188947543	103.01227608144
101	101.169997488097	99.1102738692768	103.229721106917
102	101.169997488097	98.9136880331766	103.426306943018
103	101.169997488097	98.73290837877	103.607086597424
104	101.169997488097	98.5646425607911	103.775352415403
105	101.169997488097	98.4066036928383	103.933391283356
106	101.169997488097	98.2571266982899	104.082868277904
107	101.169997488097	98.1149545737423	104.225040402452
108	101.169997488097	97.9791107494324	104.360884226762

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 101.169997488097 & 100.248814822076 & 102.091180154118 \tabularnewline
98 & 101.169997488097 & 99.8672893570812 & 102.472705619113 \tabularnewline
99 & 101.169997488097 & 99.5745290788041 & 102.76546589739 \tabularnewline
100 & 101.169997488097 & 99.3277188947543 & 103.01227608144 \tabularnewline
101 & 101.169997488097 & 99.1102738692768 & 103.229721106917 \tabularnewline
102 & 101.169997488097 & 98.9136880331766 & 103.426306943018 \tabularnewline
103 & 101.169997488097 & 98.73290837877 & 103.607086597424 \tabularnewline
104 & 101.169997488097 & 98.5646425607911 & 103.775352415403 \tabularnewline
105 & 101.169997488097 & 98.4066036928383 & 103.933391283356 \tabularnewline
106 & 101.169997488097 & 98.2571266982899 & 104.082868277904 \tabularnewline
107 & 101.169997488097 & 98.1149545737423 & 104.225040402452 \tabularnewline
108 & 101.169997488097 & 97.9791107494324 & 104.360884226762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279231&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]97[/C][C]101.169997488097[/C][C]100.248814822076[/C][C]102.091180154118[/C][/ROW]
[ROW][C]98[/C][C]101.169997488097[/C][C]99.8672893570812[/C][C]102.472705619113[/C][/ROW]
[ROW][C]99[/C][C]101.169997488097[/C][C]99.5745290788041[/C][C]102.76546589739[/C][/ROW]
[ROW][C]100[/C][C]101.169997488097[/C][C]99.3277188947543[/C][C]103.01227608144[/C][/ROW]
[ROW][C]101[/C][C]101.169997488097[/C][C]99.1102738692768[/C][C]103.229721106917[/C][/ROW]
[ROW][C]102[/C][C]101.169997488097[/C][C]98.9136880331766[/C][C]103.426306943018[/C][/ROW]
[ROW][C]103[/C][C]101.169997488097[/C][C]98.73290837877[/C][C]103.607086597424[/C][/ROW]
[ROW][C]104[/C][C]101.169997488097[/C][C]98.5646425607911[/C][C]103.775352415403[/C][/ROW]
[ROW][C]105[/C][C]101.169997488097[/C][C]98.4066036928383[/C][C]103.933391283356[/C][/ROW]
[ROW][C]106[/C][C]101.169997488097[/C][C]98.2571266982899[/C][C]104.082868277904[/C][/ROW]
[ROW][C]107[/C][C]101.169997488097[/C][C]98.1149545737423[/C][C]104.225040402452[/C][/ROW]
[ROW][C]108[/C][C]101.169997488097[/C][C]97.9791107494324[/C][C]104.360884226762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279231&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279231&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
97	101.169997488097	100.248814822076	102.091180154118
98	101.169997488097	99.8672893570812	102.472705619113
99	101.169997488097	99.5745290788041	102.76546589739
100	101.169997488097	99.3277188947543	103.01227608144
101	101.169997488097	99.1102738692768	103.229721106917
102	101.169997488097	98.9136880331766	103.426306943018
103	101.169997488097	98.73290837877	103.607086597424
104	101.169997488097	98.5646425607911	103.775352415403
105	101.169997488097	98.4066036928383	103.933391283356
106	101.169997488097	98.2571266982899	104.082868277904
107	101.169997488097	98.1149545737423	104.225040402452
108	101.169997488097	97.9791107494324	104.360884226762

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code