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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Dec 2011 07:35:38 -0500

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/2011/Dec/24/t13247302222dijvxv9z2elp36.htm/, Retrieved Fri, 03 May 2024 02:20:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160750, Retrieved Fri, 03 May 2024 02:20:01 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

151

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

-       [Exponential Smoothing] [Opgave 10 - oefen...] [2011-12-24 12:35:38] [1dca9aa876cba4edc5cb0d742d3acdc5] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160750&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160750&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160750&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160750&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160750&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160750&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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	50	49.2	0.800000000000004
4	49.3	50.3	-1
5	51	49.6	1.40000000000001
6	47.7	51.3	-3.59999999999999
7	43.4	48	-4.6
8	42.6	43.7	-1.09999999999999
9	44.1	42.9	1.2
10	46.8	44.4	2.4
11	47.9	47.1	0.800000000000004
12	48.5	48.2	0.300000000000004
13	49.7	48.8	0.900000000000006
14	48	50	-2
15	48.2	48.3	-0.0999999999999943
16	47.3	48.5	-1.2
17	46.6	47.6	-0.999999999999993
18	45.6	46.9	-1.3
19	47.7	45.9	1.8
20	48.1	48	0.100000000000001
21	47.6	48.4	-0.799999999999997
22	46.3	47.9	-1.6
23	46.1	46.6	-0.499999999999993
24	46.7	46.4	0.300000000000004
25	47.1	47	0.100000000000001
26	46.7	47.4	-0.699999999999996
27	46.3	47	-0.700000000000003
28	45.9	46.6	-0.699999999999996
29	46.6	46.2	0.400000000000006
30	49	46.9	2.1
31	54.1	49.3	4.8
32	59.2	54.4	4.8
33	63.8	59.5	4.3
34	62.5	64.1	-1.59999999999999
35	59.5	62.8	-3.3
36	56.9	59.8	-2.9
37	54.4	57.2	-2.8
38	54.7	54.7	7.105427357601e-15
39	53.3	55	-1.7
40	52.9	53.6	-0.699999999999996
41	54.8	53.2	1.6
42	52.6	55.1	-2.49999999999999
43	49.1	52.9	-3.8
44	52.6	49.4	3.2
45	53.6	52.9	0.700000000000003
46	52.7	53.9	-1.2
47	55.8	53	2.8
48	57.9	56.1	1.8
49	60.6	58.2	2.40000000000001
50	61.9	60.9	1
51	65.5	62.2	3.3
52	67.5	65.8	1.7
53	65.5	67.8	-2.3
54	62.2	65.8	-3.59999999999999
55	55.5	62.5	-7
56	52.3	55.8	-3.5
57	52.5	52.6	-0.0999999999999943
58	50.8	52.8	-2
59	50.9	51.1	-0.199999999999996
60	51.5	51.2	0.300000000000004
61	51.1	51.8	-0.699999999999996
62	51.1	51.4	-0.299999999999997
63	54.3	51.4	2.9
64	51.9	54.6	-2.7
65	52.4	52.2	0.200000000000003
66	53.4	52.7	0.700000000000003
67	56	53.7	2.3
68	53.4	56.3	-2.9
69	53.8	53.7	0.100000000000001
70	53.8	54.1	-0.299999999999997
71	51.6	54.1	-2.49999999999999
72	54.2	51.9	2.3
73	55.7	54.5	1.2
74	59.2	56	3.2
75	59.8	59.5	0.299999999999997
76	61.6	60.1	1.50000000000001
77	65.8	61.9	3.9
78	64.2	66.1	-1.89999999999999
79	67	64.5	2.5
80	62.8	67.3	-4.5
81	65.5	63.1	2.40000000000001
82	75.2	65.8	9.40000000000001
83	80.9	75.5	5.40000000000001
84	83.2	81.2	2
85	83.7	83.5	0.200000000000003
86	86.4	84	2.40000000000001
87	85.9	86.7	-0.799999999999997
88	80.4	86.2	-5.8
89	81.8	80.7	1.09999999999999
90	87.5	82.1	5.40000000000001
91	83.7	87.8	-4.09999999999999
92	87	84	3
93	99.7	87.3	12.4
94	101.4	100	1.40000000000001
95	101.9	101.7	0.200000000000003
96	115.7	102.2	13.5
97	123.2	116	7.2
98	136.9	123.5	13.4
99	146.8	137.2	9.60000000000002
100	149.6	147.1	2.49999999999997
101	146.5	149.9	-3.39999999999998
102	157	146.8	10.2
103	147.9	157.3	-9.40000000000001
104	133.6	148.2	-14.6
105	128.7	133.9	-5.19999999999999
106	100.8	129	-28.2
107	91.8	101.1	-9.3
108	89.3	92.1	-2.8
109	96.7	89.6	7.10000000000001
110	91.6	97	-5.40000000000001
111	93.3	91.9	1.40000000000001
112	93.3	93.6	-0.299999999999997
113	101	93.6	7.40000000000001
114	100.4	101.3	-0.899999999999991
115	86.9	100.7	-13.8
116	83.9	87.2	-3.3
117	80.3	84.2	-3.90000000000001
118	87.7	80.6	7.10000000000001
119	92.7	88	4.7
120	95.5	93	2.5
121	92	95.8	-3.8
122	87.4	92.3	-4.89999999999999
123	86.8	87.7	-0.900000000000006
124	83.7	87.1	-3.39999999999999
125	85	84	1
126	81.7	85.3	-3.59999999999999
127	90.9	82	8.90000000000001
128	101.5	91.2	10.3
129	113.8	101.8	12
130	120.1	114.1	6
131	122.1	120.4	1.7
132	132.5	122.4	10.1

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 50 & 49.2 & 0.800000000000004 \tabularnewline
4 & 49.3 & 50.3 & -1 \tabularnewline
5 & 51 & 49.6 & 1.40000000000001 \tabularnewline
6 & 47.7 & 51.3 & -3.59999999999999 \tabularnewline
7 & 43.4 & 48 & -4.6 \tabularnewline
8 & 42.6 & 43.7 & -1.09999999999999 \tabularnewline
9 & 44.1 & 42.9 & 1.2 \tabularnewline
10 & 46.8 & 44.4 & 2.4 \tabularnewline
11 & 47.9 & 47.1 & 0.800000000000004 \tabularnewline
12 & 48.5 & 48.2 & 0.300000000000004 \tabularnewline
13 & 49.7 & 48.8 & 0.900000000000006 \tabularnewline
14 & 48 & 50 & -2 \tabularnewline
15 & 48.2 & 48.3 & -0.0999999999999943 \tabularnewline
16 & 47.3 & 48.5 & -1.2 \tabularnewline
17 & 46.6 & 47.6 & -0.999999999999993 \tabularnewline
18 & 45.6 & 46.9 & -1.3 \tabularnewline
19 & 47.7 & 45.9 & 1.8 \tabularnewline
20 & 48.1 & 48 & 0.100000000000001 \tabularnewline
21 & 47.6 & 48.4 & -0.799999999999997 \tabularnewline
22 & 46.3 & 47.9 & -1.6 \tabularnewline
23 & 46.1 & 46.6 & -0.499999999999993 \tabularnewline
24 & 46.7 & 46.4 & 0.300000000000004 \tabularnewline
25 & 47.1 & 47 & 0.100000000000001 \tabularnewline
26 & 46.7 & 47.4 & -0.699999999999996 \tabularnewline
27 & 46.3 & 47 & -0.700000000000003 \tabularnewline
28 & 45.9 & 46.6 & -0.699999999999996 \tabularnewline
29 & 46.6 & 46.2 & 0.400000000000006 \tabularnewline
30 & 49 & 46.9 & 2.1 \tabularnewline
31 & 54.1 & 49.3 & 4.8 \tabularnewline
32 & 59.2 & 54.4 & 4.8 \tabularnewline
33 & 63.8 & 59.5 & 4.3 \tabularnewline
34 & 62.5 & 64.1 & -1.59999999999999 \tabularnewline
35 & 59.5 & 62.8 & -3.3 \tabularnewline
36 & 56.9 & 59.8 & -2.9 \tabularnewline
37 & 54.4 & 57.2 & -2.8 \tabularnewline
38 & 54.7 & 54.7 & 7.105427357601e-15 \tabularnewline
39 & 53.3 & 55 & -1.7 \tabularnewline
40 & 52.9 & 53.6 & -0.699999999999996 \tabularnewline
41 & 54.8 & 53.2 & 1.6 \tabularnewline
42 & 52.6 & 55.1 & -2.49999999999999 \tabularnewline
43 & 49.1 & 52.9 & -3.8 \tabularnewline
44 & 52.6 & 49.4 & 3.2 \tabularnewline
45 & 53.6 & 52.9 & 0.700000000000003 \tabularnewline
46 & 52.7 & 53.9 & -1.2 \tabularnewline
47 & 55.8 & 53 & 2.8 \tabularnewline
48 & 57.9 & 56.1 & 1.8 \tabularnewline
49 & 60.6 & 58.2 & 2.40000000000001 \tabularnewline
50 & 61.9 & 60.9 & 1 \tabularnewline
51 & 65.5 & 62.2 & 3.3 \tabularnewline
52 & 67.5 & 65.8 & 1.7 \tabularnewline
53 & 65.5 & 67.8 & -2.3 \tabularnewline
54 & 62.2 & 65.8 & -3.59999999999999 \tabularnewline
55 & 55.5 & 62.5 & -7 \tabularnewline
56 & 52.3 & 55.8 & -3.5 \tabularnewline
57 & 52.5 & 52.6 & -0.0999999999999943 \tabularnewline
58 & 50.8 & 52.8 & -2 \tabularnewline
59 & 50.9 & 51.1 & -0.199999999999996 \tabularnewline
60 & 51.5 & 51.2 & 0.300000000000004 \tabularnewline
61 & 51.1 & 51.8 & -0.699999999999996 \tabularnewline
62 & 51.1 & 51.4 & -0.299999999999997 \tabularnewline
63 & 54.3 & 51.4 & 2.9 \tabularnewline
64 & 51.9 & 54.6 & -2.7 \tabularnewline
65 & 52.4 & 52.2 & 0.200000000000003 \tabularnewline
66 & 53.4 & 52.7 & 0.700000000000003 \tabularnewline
67 & 56 & 53.7 & 2.3 \tabularnewline
68 & 53.4 & 56.3 & -2.9 \tabularnewline
69 & 53.8 & 53.7 & 0.100000000000001 \tabularnewline
70 & 53.8 & 54.1 & -0.299999999999997 \tabularnewline
71 & 51.6 & 54.1 & -2.49999999999999 \tabularnewline
72 & 54.2 & 51.9 & 2.3 \tabularnewline
73 & 55.7 & 54.5 & 1.2 \tabularnewline
74 & 59.2 & 56 & 3.2 \tabularnewline
75 & 59.8 & 59.5 & 0.299999999999997 \tabularnewline
76 & 61.6 & 60.1 & 1.50000000000001 \tabularnewline
77 & 65.8 & 61.9 & 3.9 \tabularnewline
78 & 64.2 & 66.1 & -1.89999999999999 \tabularnewline
79 & 67 & 64.5 & 2.5 \tabularnewline
80 & 62.8 & 67.3 & -4.5 \tabularnewline
81 & 65.5 & 63.1 & 2.40000000000001 \tabularnewline
82 & 75.2 & 65.8 & 9.40000000000001 \tabularnewline
83 & 80.9 & 75.5 & 5.40000000000001 \tabularnewline
84 & 83.2 & 81.2 & 2 \tabularnewline
85 & 83.7 & 83.5 & 0.200000000000003 \tabularnewline
86 & 86.4 & 84 & 2.40000000000001 \tabularnewline
87 & 85.9 & 86.7 & -0.799999999999997 \tabularnewline
88 & 80.4 & 86.2 & -5.8 \tabularnewline
89 & 81.8 & 80.7 & 1.09999999999999 \tabularnewline
90 & 87.5 & 82.1 & 5.40000000000001 \tabularnewline
91 & 83.7 & 87.8 & -4.09999999999999 \tabularnewline
92 & 87 & 84 & 3 \tabularnewline
93 & 99.7 & 87.3 & 12.4 \tabularnewline
94 & 101.4 & 100 & 1.40000000000001 \tabularnewline
95 & 101.9 & 101.7 & 0.200000000000003 \tabularnewline
96 & 115.7 & 102.2 & 13.5 \tabularnewline
97 & 123.2 & 116 & 7.2 \tabularnewline
98 & 136.9 & 123.5 & 13.4 \tabularnewline
99 & 146.8 & 137.2 & 9.60000000000002 \tabularnewline
100 & 149.6 & 147.1 & 2.49999999999997 \tabularnewline
101 & 146.5 & 149.9 & -3.39999999999998 \tabularnewline
102 & 157 & 146.8 & 10.2 \tabularnewline
103 & 147.9 & 157.3 & -9.40000000000001 \tabularnewline
104 & 133.6 & 148.2 & -14.6 \tabularnewline
105 & 128.7 & 133.9 & -5.19999999999999 \tabularnewline
106 & 100.8 & 129 & -28.2 \tabularnewline
107 & 91.8 & 101.1 & -9.3 \tabularnewline
108 & 89.3 & 92.1 & -2.8 \tabularnewline
109 & 96.7 & 89.6 & 7.10000000000001 \tabularnewline
110 & 91.6 & 97 & -5.40000000000001 \tabularnewline
111 & 93.3 & 91.9 & 1.40000000000001 \tabularnewline
112 & 93.3 & 93.6 & -0.299999999999997 \tabularnewline
113 & 101 & 93.6 & 7.40000000000001 \tabularnewline
114 & 100.4 & 101.3 & -0.899999999999991 \tabularnewline
115 & 86.9 & 100.7 & -13.8 \tabularnewline
116 & 83.9 & 87.2 & -3.3 \tabularnewline
117 & 80.3 & 84.2 & -3.90000000000001 \tabularnewline
118 & 87.7 & 80.6 & 7.10000000000001 \tabularnewline
119 & 92.7 & 88 & 4.7 \tabularnewline
120 & 95.5 & 93 & 2.5 \tabularnewline
121 & 92 & 95.8 & -3.8 \tabularnewline
122 & 87.4 & 92.3 & -4.89999999999999 \tabularnewline
123 & 86.8 & 87.7 & -0.900000000000006 \tabularnewline
124 & 83.7 & 87.1 & -3.39999999999999 \tabularnewline
125 & 85 & 84 & 1 \tabularnewline
126 & 81.7 & 85.3 & -3.59999999999999 \tabularnewline
127 & 90.9 & 82 & 8.90000000000001 \tabularnewline
128 & 101.5 & 91.2 & 10.3 \tabularnewline
129 & 113.8 & 101.8 & 12 \tabularnewline
130 & 120.1 & 114.1 & 6 \tabularnewline
131 & 122.1 & 120.4 & 1.7 \tabularnewline
132 & 132.5 & 122.4 & 10.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160750&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]3[/C][C]50[/C][C]49.2[/C][C]0.800000000000004[/C][/ROW]
[ROW][C]4[/C][C]49.3[/C][C]50.3[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]51[/C][C]49.6[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]6[/C][C]47.7[/C][C]51.3[/C][C]-3.59999999999999[/C][/ROW]
[ROW][C]7[/C][C]43.4[/C][C]48[/C][C]-4.6[/C][/ROW]
[ROW][C]8[/C][C]42.6[/C][C]43.7[/C][C]-1.09999999999999[/C][/ROW]
[ROW][C]9[/C][C]44.1[/C][C]42.9[/C][C]1.2[/C][/ROW]
[ROW][C]10[/C][C]46.8[/C][C]44.4[/C][C]2.4[/C][/ROW]
[ROW][C]11[/C][C]47.9[/C][C]47.1[/C][C]0.800000000000004[/C][/ROW]
[ROW][C]12[/C][C]48.5[/C][C]48.2[/C][C]0.300000000000004[/C][/ROW]
[ROW][C]13[/C][C]49.7[/C][C]48.8[/C][C]0.900000000000006[/C][/ROW]
[ROW][C]14[/C][C]48[/C][C]50[/C][C]-2[/C][/ROW]
[ROW][C]15[/C][C]48.2[/C][C]48.3[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]16[/C][C]47.3[/C][C]48.5[/C][C]-1.2[/C][/ROW]
[ROW][C]17[/C][C]46.6[/C][C]47.6[/C][C]-0.999999999999993[/C][/ROW]
[ROW][C]18[/C][C]45.6[/C][C]46.9[/C][C]-1.3[/C][/ROW]
[ROW][C]19[/C][C]47.7[/C][C]45.9[/C][C]1.8[/C][/ROW]
[ROW][C]20[/C][C]48.1[/C][C]48[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]21[/C][C]47.6[/C][C]48.4[/C][C]-0.799999999999997[/C][/ROW]
[ROW][C]22[/C][C]46.3[/C][C]47.9[/C][C]-1.6[/C][/ROW]
[ROW][C]23[/C][C]46.1[/C][C]46.6[/C][C]-0.499999999999993[/C][/ROW]
[ROW][C]24[/C][C]46.7[/C][C]46.4[/C][C]0.300000000000004[/C][/ROW]
[ROW][C]25[/C][C]47.1[/C][C]47[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]26[/C][C]46.7[/C][C]47.4[/C][C]-0.699999999999996[/C][/ROW]
[ROW][C]27[/C][C]46.3[/C][C]47[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]28[/C][C]45.9[/C][C]46.6[/C][C]-0.699999999999996[/C][/ROW]
[ROW][C]29[/C][C]46.6[/C][C]46.2[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]30[/C][C]49[/C][C]46.9[/C][C]2.1[/C][/ROW]
[ROW][C]31[/C][C]54.1[/C][C]49.3[/C][C]4.8[/C][/ROW]
[ROW][C]32[/C][C]59.2[/C][C]54.4[/C][C]4.8[/C][/ROW]
[ROW][C]33[/C][C]63.8[/C][C]59.5[/C][C]4.3[/C][/ROW]
[ROW][C]34[/C][C]62.5[/C][C]64.1[/C][C]-1.59999999999999[/C][/ROW]
[ROW][C]35[/C][C]59.5[/C][C]62.8[/C][C]-3.3[/C][/ROW]
[ROW][C]36[/C][C]56.9[/C][C]59.8[/C][C]-2.9[/C][/ROW]
[ROW][C]37[/C][C]54.4[/C][C]57.2[/C][C]-2.8[/C][/ROW]
[ROW][C]38[/C][C]54.7[/C][C]54.7[/C][C]7.105427357601e-15[/C][/ROW]
[ROW][C]39[/C][C]53.3[/C][C]55[/C][C]-1.7[/C][/ROW]
[ROW][C]40[/C][C]52.9[/C][C]53.6[/C][C]-0.699999999999996[/C][/ROW]
[ROW][C]41[/C][C]54.8[/C][C]53.2[/C][C]1.6[/C][/ROW]
[ROW][C]42[/C][C]52.6[/C][C]55.1[/C][C]-2.49999999999999[/C][/ROW]
[ROW][C]43[/C][C]49.1[/C][C]52.9[/C][C]-3.8[/C][/ROW]
[ROW][C]44[/C][C]52.6[/C][C]49.4[/C][C]3.2[/C][/ROW]
[ROW][C]45[/C][C]53.6[/C][C]52.9[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]46[/C][C]52.7[/C][C]53.9[/C][C]-1.2[/C][/ROW]
[ROW][C]47[/C][C]55.8[/C][C]53[/C][C]2.8[/C][/ROW]
[ROW][C]48[/C][C]57.9[/C][C]56.1[/C][C]1.8[/C][/ROW]
[ROW][C]49[/C][C]60.6[/C][C]58.2[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]50[/C][C]61.9[/C][C]60.9[/C][C]1[/C][/ROW]
[ROW][C]51[/C][C]65.5[/C][C]62.2[/C][C]3.3[/C][/ROW]
[ROW][C]52[/C][C]67.5[/C][C]65.8[/C][C]1.7[/C][/ROW]
[ROW][C]53[/C][C]65.5[/C][C]67.8[/C][C]-2.3[/C][/ROW]
[ROW][C]54[/C][C]62.2[/C][C]65.8[/C][C]-3.59999999999999[/C][/ROW]
[ROW][C]55[/C][C]55.5[/C][C]62.5[/C][C]-7[/C][/ROW]
[ROW][C]56[/C][C]52.3[/C][C]55.8[/C][C]-3.5[/C][/ROW]
[ROW][C]57[/C][C]52.5[/C][C]52.6[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]58[/C][C]50.8[/C][C]52.8[/C][C]-2[/C][/ROW]
[ROW][C]59[/C][C]50.9[/C][C]51.1[/C][C]-0.199999999999996[/C][/ROW]
[ROW][C]60[/C][C]51.5[/C][C]51.2[/C][C]0.300000000000004[/C][/ROW]
[ROW][C]61[/C][C]51.1[/C][C]51.8[/C][C]-0.699999999999996[/C][/ROW]
[ROW][C]62[/C][C]51.1[/C][C]51.4[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]63[/C][C]54.3[/C][C]51.4[/C][C]2.9[/C][/ROW]
[ROW][C]64[/C][C]51.9[/C][C]54.6[/C][C]-2.7[/C][/ROW]
[ROW][C]65[/C][C]52.4[/C][C]52.2[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]66[/C][C]53.4[/C][C]52.7[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]67[/C][C]56[/C][C]53.7[/C][C]2.3[/C][/ROW]
[ROW][C]68[/C][C]53.4[/C][C]56.3[/C][C]-2.9[/C][/ROW]
[ROW][C]69[/C][C]53.8[/C][C]53.7[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]70[/C][C]53.8[/C][C]54.1[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]71[/C][C]51.6[/C][C]54.1[/C][C]-2.49999999999999[/C][/ROW]
[ROW][C]72[/C][C]54.2[/C][C]51.9[/C][C]2.3[/C][/ROW]
[ROW][C]73[/C][C]55.7[/C][C]54.5[/C][C]1.2[/C][/ROW]
[ROW][C]74[/C][C]59.2[/C][C]56[/C][C]3.2[/C][/ROW]
[ROW][C]75[/C][C]59.8[/C][C]59.5[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]76[/C][C]61.6[/C][C]60.1[/C][C]1.50000000000001[/C][/ROW]
[ROW][C]77[/C][C]65.8[/C][C]61.9[/C][C]3.9[/C][/ROW]
[ROW][C]78[/C][C]64.2[/C][C]66.1[/C][C]-1.89999999999999[/C][/ROW]
[ROW][C]79[/C][C]67[/C][C]64.5[/C][C]2.5[/C][/ROW]
[ROW][C]80[/C][C]62.8[/C][C]67.3[/C][C]-4.5[/C][/ROW]
[ROW][C]81[/C][C]65.5[/C][C]63.1[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]82[/C][C]75.2[/C][C]65.8[/C][C]9.40000000000001[/C][/ROW]
[ROW][C]83[/C][C]80.9[/C][C]75.5[/C][C]5.40000000000001[/C][/ROW]
[ROW][C]84[/C][C]83.2[/C][C]81.2[/C][C]2[/C][/ROW]
[ROW][C]85[/C][C]83.7[/C][C]83.5[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]86[/C][C]86.4[/C][C]84[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]87[/C][C]85.9[/C][C]86.7[/C][C]-0.799999999999997[/C][/ROW]
[ROW][C]88[/C][C]80.4[/C][C]86.2[/C][C]-5.8[/C][/ROW]
[ROW][C]89[/C][C]81.8[/C][C]80.7[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]90[/C][C]87.5[/C][C]82.1[/C][C]5.40000000000001[/C][/ROW]
[ROW][C]91[/C][C]83.7[/C][C]87.8[/C][C]-4.09999999999999[/C][/ROW]
[ROW][C]92[/C][C]87[/C][C]84[/C][C]3[/C][/ROW]
[ROW][C]93[/C][C]99.7[/C][C]87.3[/C][C]12.4[/C][/ROW]
[ROW][C]94[/C][C]101.4[/C][C]100[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]95[/C][C]101.9[/C][C]101.7[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]96[/C][C]115.7[/C][C]102.2[/C][C]13.5[/C][/ROW]
[ROW][C]97[/C][C]123.2[/C][C]116[/C][C]7.2[/C][/ROW]
[ROW][C]98[/C][C]136.9[/C][C]123.5[/C][C]13.4[/C][/ROW]
[ROW][C]99[/C][C]146.8[/C][C]137.2[/C][C]9.60000000000002[/C][/ROW]
[ROW][C]100[/C][C]149.6[/C][C]147.1[/C][C]2.49999999999997[/C][/ROW]
[ROW][C]101[/C][C]146.5[/C][C]149.9[/C][C]-3.39999999999998[/C][/ROW]
[ROW][C]102[/C][C]157[/C][C]146.8[/C][C]10.2[/C][/ROW]
[ROW][C]103[/C][C]147.9[/C][C]157.3[/C][C]-9.40000000000001[/C][/ROW]
[ROW][C]104[/C][C]133.6[/C][C]148.2[/C][C]-14.6[/C][/ROW]
[ROW][C]105[/C][C]128.7[/C][C]133.9[/C][C]-5.19999999999999[/C][/ROW]
[ROW][C]106[/C][C]100.8[/C][C]129[/C][C]-28.2[/C][/ROW]
[ROW][C]107[/C][C]91.8[/C][C]101.1[/C][C]-9.3[/C][/ROW]
[ROW][C]108[/C][C]89.3[/C][C]92.1[/C][C]-2.8[/C][/ROW]
[ROW][C]109[/C][C]96.7[/C][C]89.6[/C][C]7.10000000000001[/C][/ROW]
[ROW][C]110[/C][C]91.6[/C][C]97[/C][C]-5.40000000000001[/C][/ROW]
[ROW][C]111[/C][C]93.3[/C][C]91.9[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]112[/C][C]93.3[/C][C]93.6[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]113[/C][C]101[/C][C]93.6[/C][C]7.40000000000001[/C][/ROW]
[ROW][C]114[/C][C]100.4[/C][C]101.3[/C][C]-0.899999999999991[/C][/ROW]
[ROW][C]115[/C][C]86.9[/C][C]100.7[/C][C]-13.8[/C][/ROW]
[ROW][C]116[/C][C]83.9[/C][C]87.2[/C][C]-3.3[/C][/ROW]
[ROW][C]117[/C][C]80.3[/C][C]84.2[/C][C]-3.90000000000001[/C][/ROW]
[ROW][C]118[/C][C]87.7[/C][C]80.6[/C][C]7.10000000000001[/C][/ROW]
[ROW][C]119[/C][C]92.7[/C][C]88[/C][C]4.7[/C][/ROW]
[ROW][C]120[/C][C]95.5[/C][C]93[/C][C]2.5[/C][/ROW]
[ROW][C]121[/C][C]92[/C][C]95.8[/C][C]-3.8[/C][/ROW]
[ROW][C]122[/C][C]87.4[/C][C]92.3[/C][C]-4.89999999999999[/C][/ROW]
[ROW][C]123[/C][C]86.8[/C][C]87.7[/C][C]-0.900000000000006[/C][/ROW]
[ROW][C]124[/C][C]83.7[/C][C]87.1[/C][C]-3.39999999999999[/C][/ROW]
[ROW][C]125[/C][C]85[/C][C]84[/C][C]1[/C][/ROW]
[ROW][C]126[/C][C]81.7[/C][C]85.3[/C][C]-3.59999999999999[/C][/ROW]
[ROW][C]127[/C][C]90.9[/C][C]82[/C][C]8.90000000000001[/C][/ROW]
[ROW][C]128[/C][C]101.5[/C][C]91.2[/C][C]10.3[/C][/ROW]
[ROW][C]129[/C][C]113.8[/C][C]101.8[/C][C]12[/C][/ROW]
[ROW][C]130[/C][C]120.1[/C][C]114.1[/C][C]6[/C][/ROW]
[ROW][C]131[/C][C]122.1[/C][C]120.4[/C][C]1.7[/C][/ROW]
[ROW][C]132[/C][C]132.5[/C][C]122.4[/C][C]10.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160750&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160750&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
3	50	49.2	0.800000000000004
4	49.3	50.3	-1
5	51	49.6	1.40000000000001
6	47.7	51.3	-3.59999999999999
7	43.4	48	-4.6
8	42.6	43.7	-1.09999999999999
9	44.1	42.9	1.2
10	46.8	44.4	2.4
11	47.9	47.1	0.800000000000004
12	48.5	48.2	0.300000000000004
13	49.7	48.8	0.900000000000006
14	48	50	-2
15	48.2	48.3	-0.0999999999999943
16	47.3	48.5	-1.2
17	46.6	47.6	-0.999999999999993
18	45.6	46.9	-1.3
19	47.7	45.9	1.8
20	48.1	48	0.100000000000001
21	47.6	48.4	-0.799999999999997
22	46.3	47.9	-1.6
23	46.1	46.6	-0.499999999999993
24	46.7	46.4	0.300000000000004
25	47.1	47	0.100000000000001
26	46.7	47.4	-0.699999999999996
27	46.3	47	-0.700000000000003
28	45.9	46.6	-0.699999999999996
29	46.6	46.2	0.400000000000006
30	49	46.9	2.1
31	54.1	49.3	4.8
32	59.2	54.4	4.8
33	63.8	59.5	4.3
34	62.5	64.1	-1.59999999999999
35	59.5	62.8	-3.3
36	56.9	59.8	-2.9
37	54.4	57.2	-2.8
38	54.7	54.7	7.105427357601e-15
39	53.3	55	-1.7
40	52.9	53.6	-0.699999999999996
41	54.8	53.2	1.6
42	52.6	55.1	-2.49999999999999
43	49.1	52.9	-3.8
44	52.6	49.4	3.2
45	53.6	52.9	0.700000000000003
46	52.7	53.9	-1.2
47	55.8	53	2.8
48	57.9	56.1	1.8
49	60.6	58.2	2.40000000000001
50	61.9	60.9	1
51	65.5	62.2	3.3
52	67.5	65.8	1.7
53	65.5	67.8	-2.3
54	62.2	65.8	-3.59999999999999
55	55.5	62.5	-7
56	52.3	55.8	-3.5
57	52.5	52.6	-0.0999999999999943
58	50.8	52.8	-2
59	50.9	51.1	-0.199999999999996
60	51.5	51.2	0.300000000000004
61	51.1	51.8	-0.699999999999996
62	51.1	51.4	-0.299999999999997
63	54.3	51.4	2.9
64	51.9	54.6	-2.7
65	52.4	52.2	0.200000000000003
66	53.4	52.7	0.700000000000003
67	56	53.7	2.3
68	53.4	56.3	-2.9
69	53.8	53.7	0.100000000000001
70	53.8	54.1	-0.299999999999997
71	51.6	54.1	-2.49999999999999
72	54.2	51.9	2.3
73	55.7	54.5	1.2
74	59.2	56	3.2
75	59.8	59.5	0.299999999999997
76	61.6	60.1	1.50000000000001
77	65.8	61.9	3.9
78	64.2	66.1	-1.89999999999999
79	67	64.5	2.5
80	62.8	67.3	-4.5
81	65.5	63.1	2.40000000000001
82	75.2	65.8	9.40000000000001
83	80.9	75.5	5.40000000000001
84	83.2	81.2	2
85	83.7	83.5	0.200000000000003
86	86.4	84	2.40000000000001
87	85.9	86.7	-0.799999999999997
88	80.4	86.2	-5.8
89	81.8	80.7	1.09999999999999
90	87.5	82.1	5.40000000000001
91	83.7	87.8	-4.09999999999999
92	87	84	3
93	99.7	87.3	12.4
94	101.4	100	1.40000000000001
95	101.9	101.7	0.200000000000003
96	115.7	102.2	13.5
97	123.2	116	7.2
98	136.9	123.5	13.4
99	146.8	137.2	9.60000000000002
100	149.6	147.1	2.49999999999997
101	146.5	149.9	-3.39999999999998
102	157	146.8	10.2
103	147.9	157.3	-9.40000000000001
104	133.6	148.2	-14.6
105	128.7	133.9	-5.19999999999999
106	100.8	129	-28.2
107	91.8	101.1	-9.3
108	89.3	92.1	-2.8
109	96.7	89.6	7.10000000000001
110	91.6	97	-5.40000000000001
111	93.3	91.9	1.40000000000001
112	93.3	93.6	-0.299999999999997
113	101	93.6	7.40000000000001
114	100.4	101.3	-0.899999999999991
115	86.9	100.7	-13.8
116	83.9	87.2	-3.3
117	80.3	84.2	-3.90000000000001
118	87.7	80.6	7.10000000000001
119	92.7	88	4.7
120	95.5	93	2.5
121	92	95.8	-3.8
122	87.4	92.3	-4.89999999999999
123	86.8	87.7	-0.900000000000006
124	83.7	87.1	-3.39999999999999
125	85	84	1
126	81.7	85.3	-3.59999999999999
127	90.9	82	8.90000000000001
128	101.5	91.2	10.3
129	113.8	101.8	12
130	120.1	114.1	6
131	122.1	120.4	1.7
132	132.5	122.4	10.1

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	132.8	122.452246027773	143.147753972227
134	133.1	118.466065992376	147.733934007624
135	133.4	115.47716437588	151.32283562412
136	133.7	113.004492055546	154.395507944454
137	134	110.861718703657	157.138281296344
138	134.3	108.953282784186	159.646717215814
139	134.6	107.222416361406	161.977583638594
140	134.9	105.632131984752	164.167868015248
141	135.2	104.156738083318	166.243261916682
142	135.5	102.777528780707	168.222471219293
143	135.8	101.480382651213	170.119617348787
144	136.1	100.25432875176	171.94567124824

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 132.8 & 122.452246027773 & 143.147753972227 \tabularnewline
134 & 133.1 & 118.466065992376 & 147.733934007624 \tabularnewline
135 & 133.4 & 115.47716437588 & 151.32283562412 \tabularnewline
136 & 133.7 & 113.004492055546 & 154.395507944454 \tabularnewline
137 & 134 & 110.861718703657 & 157.138281296344 \tabularnewline
138 & 134.3 & 108.953282784186 & 159.646717215814 \tabularnewline
139 & 134.6 & 107.222416361406 & 161.977583638594 \tabularnewline
140 & 134.9 & 105.632131984752 & 164.167868015248 \tabularnewline
141 & 135.2 & 104.156738083318 & 166.243261916682 \tabularnewline
142 & 135.5 & 102.777528780707 & 168.222471219293 \tabularnewline
143 & 135.8 & 101.480382651213 & 170.119617348787 \tabularnewline
144 & 136.1 & 100.25432875176 & 171.94567124824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160750&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]133[/C][C]132.8[/C][C]122.452246027773[/C][C]143.147753972227[/C][/ROW]
[ROW][C]134[/C][C]133.1[/C][C]118.466065992376[/C][C]147.733934007624[/C][/ROW]
[ROW][C]135[/C][C]133.4[/C][C]115.47716437588[/C][C]151.32283562412[/C][/ROW]
[ROW][C]136[/C][C]133.7[/C][C]113.004492055546[/C][C]154.395507944454[/C][/ROW]
[ROW][C]137[/C][C]134[/C][C]110.861718703657[/C][C]157.138281296344[/C][/ROW]
[ROW][C]138[/C][C]134.3[/C][C]108.953282784186[/C][C]159.646717215814[/C][/ROW]
[ROW][C]139[/C][C]134.6[/C][C]107.222416361406[/C][C]161.977583638594[/C][/ROW]
[ROW][C]140[/C][C]134.9[/C][C]105.632131984752[/C][C]164.167868015248[/C][/ROW]
[ROW][C]141[/C][C]135.2[/C][C]104.156738083318[/C][C]166.243261916682[/C][/ROW]
[ROW][C]142[/C][C]135.5[/C][C]102.777528780707[/C][C]168.222471219293[/C][/ROW]
[ROW][C]143[/C][C]135.8[/C][C]101.480382651213[/C][C]170.119617348787[/C][/ROW]
[ROW][C]144[/C][C]136.1[/C][C]100.25432875176[/C][C]171.94567124824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160750&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160750&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
133	132.8	122.452246027773	143.147753972227
134	133.1	118.466065992376	147.733934007624
135	133.4	115.47716437588	151.32283562412
136	133.7	113.004492055546	154.395507944454
137	134	110.861718703657	157.138281296344
138	134.3	108.953282784186	159.646717215814
139	134.6	107.222416361406	161.977583638594
140	134.9	105.632131984752	164.167868015248
141	135.2	104.156738083318	166.243261916682
142	135.5	102.777528780707	168.222471219293
143	135.8	101.480382651213	170.119617348787
144	136.1	100.25432875176	171.94567124824

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 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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