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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Thu, 11 Dec 2014 15:03:57 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/11/t14183105146c3zyivoq8fbrw2.htm/, Retrieved Thu, 16 May 2024 19:59:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266089, Retrieved Thu, 16 May 2024 19:59:38 +0000

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-       [Multiple Regression] [] [2014-12-11 15:03:57] [58179e1d3a5a39b9daf58e365d8a3352] [Current]

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12.9 149 96 86 7.5 1.8 2.1 1.5
12.8 148 88 71 6.5 2.2 2 2.1
7.4 158 114 108 1 2.3 2.1 1.9
6.7 128 69 64 1 2.1 2 1.6
12.6 224 176 119 5.5 2.7 2.3 2.1
14.8 159 114 97 8.5 2.1 2.1 2.1
13.3 105 121 129 6.5 2.4 2.1 2.2
11.1 159 110 153 4.5 2.9 2.2 1.5
8.2 167 158 78 2 2.2 2.1 1.9
11.4 165 116 80 5 2.1 2.1 2.2
6.4 159 181 99 0.5 2.2 2.1 1.6
12 176 141 147 5 2.7 2.3 1.9
6.3 54 35 40 2.5 1.9 1.8 0.1
11.3 91 80 57 5 2 2 2.2
11.9 163 152 120 5.5 2.5 2.2 1.8
9.3 124 97 71 3.5 2.2 2 1.6
10 121 84 68 4 1.9 2 2.1
13.8 148 101 137 6.5 3.5 2.2 1.6
10.8 221 107 79 4.5 2.1 2.2 1.9
11.7 149 112 101 5.5 2.3 2.1 1.8
10.9 244 171 111 4 2.2 2.3 2.4
16.1 148 137 189 7.5 3.5 2.7 2.4
9.9 150 66 81 4 1.9 2 1.9
11.5 153 93 63 5.5 1.9 2 2.1
8.3 94 105 69 2.5 1.9 1.9 1.9
11.7 156 131 71 5.5 2.1 2 2.1
9 132 102 64 3.5 2 2 1.5
10.8 105 120 85 4.5 2.3 2 2.1
10.4 151 77 55 4.5 1.8 2 2.1
12.7 131 108 69 6 2.4 2.2 2.1
11.8 157 168 96 5 2.3 2.1 2.4
13 162 75 100 6.5 2.3 2.1 2.1
10.8 163 107 68 5 1.8 2 1.9
12.3 59 62 57 6 1.9 1.9 2.4
11.3 187 121 105 4.5 2.6 2.2 2.1
11.6 116 97 69 5 2.1 2.2 2.4
10.9 148 126 49 5 1.8 2 2.1
12.1 155 104 50 6.5 1.9 2.2 1.5
13.3 125 148 93 7 2.4 2 1.9
10.1 116 146 58 4.5 1.9 1.9 1.8
14.3 138 97 74 8.5 2.1 2 1.6
9.3 164 118 107 3.5 2.1 2.1 1.5
12.5 162 58 65 6 2.4 2 2.1
7.6 99 63 58 1.5 1.8 1.9 2.4
9.2 186 50 70 3.5 2.1 2.1 1.5
14.5 188 94 95 7.5 2.7 2.2 2.1
12.3 177 127 136 5 2.9 2.2 2.1
12.6 139 128 82 6.5 2.1 2 1.9
13 162 146 102 6.5 2.3 2.1 2.1
12.6 108 69 65 6.5 2.2 2.1 1.8
13.2 159 186 90 7 2 2.1 2.1
7.7 110 85 83 1.5 2.1 2 2.1
10.5 96 54 70 4 2.1 2.1 2.2
10.9 87 106 77 4.5 2 2.1 2.2
4.3 97 34 37 0 1.7 1 1.6
10.3 127 60 81 3.5 2.2 2.2 2.4
11.4 74 62 71 4.5 2.4 2 2.4
5.6 114 64 40 0 1.8 2 1.8
8.8 95 98 43 3 1.9 2 1.9
9 121 35 32 3.5 1.7 2 1.8
9.6 130 55 76 3 2.1 2.2 2.2
6.4 52 54 30 1 1.7 1.8 1.9
11.6 118 51 51 5.5 1.9 2.1 2.1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&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	6 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Multiple Linear Regression - Estimated Regression Equation
TOT[t] = + 0.159974 -0.000200027LFM[t] -0.000410877BLOG[t] + 0.00139442HOURS[t] + 1.00136Ex[t] + 0.910273PR[t] + 0.99492PE[t] + 1.00838PA[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TOT[t] =  +  0.159974 -0.000200027LFM[t] -0.000410877BLOG[t] +  0.00139442HOURS[t] +  1.00136Ex[t] +  0.910273PR[t] +  0.99492PE[t] +  1.00838PA[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TOT[t] =  +  0.159974 -0.000200027LFM[t] -0.000410877BLOG[t] +  0.00139442HOURS[t] +  1.00136Ex[t] +  0.910273PR[t] +  0.99492PE[t] +  1.00838PA[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
TOT[t] = + 0.159974 -0.000200027LFM[t] -0.000410877BLOG[t] + 0.00139442HOURS[t] + 1.00136Ex[t] + 0.910273PR[t] + 0.99492PE[t] + 1.00838PA[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	0.159974	0.095171	1.681	0.0984506	0.0492253
LFM	-0.000200027	0.000229734	-0.8707	0.387707	0.193853
BLOG	-0.000410877	0.000242352	-1.695	0.0956599	0.04783
HOURS	0.00139442	0.000513137	2.717	0.00878005	0.00439003
Ex	1.00136	0.00378567	264.5	4.42561e-87	2.21281e-87
PR	0.910273	0.0373982	24.34	3.98491e-31	1.99246e-31
PE	0.99492	0.0517882	19.21	4.61452e-26	2.30726e-26
PA	1.00838	0.0200236	50.36	1.05577e-47	5.27885e-48

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.159974 & 0.095171 & 1.681 & 0.0984506 & 0.0492253 \tabularnewline
LFM & -0.000200027 & 0.000229734 & -0.8707 & 0.387707 & 0.193853 \tabularnewline
BLOG & -0.000410877 & 0.000242352 & -1.695 & 0.0956599 & 0.04783 \tabularnewline
HOURS & 0.00139442 & 0.000513137 & 2.717 & 0.00878005 & 0.00439003 \tabularnewline
Ex & 1.00136 & 0.00378567 & 264.5 & 4.42561e-87 & 2.21281e-87 \tabularnewline
PR & 0.910273 & 0.0373982 & 24.34 & 3.98491e-31 & 1.99246e-31 \tabularnewline
PE & 0.99492 & 0.0517882 & 19.21 & 4.61452e-26 & 2.30726e-26 \tabularnewline
PA & 1.00838 & 0.0200236 & 50.36 & 1.05577e-47 & 5.27885e-48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.159974[/C][C]0.095171[/C][C]1.681[/C][C]0.0984506[/C][C]0.0492253[/C][/ROW]
[ROW][C]LFM[/C][C]-0.000200027[/C][C]0.000229734[/C][C]-0.8707[/C][C]0.387707[/C][C]0.193853[/C][/ROW]
[ROW][C]BLOG[/C][C]-0.000410877[/C][C]0.000242352[/C][C]-1.695[/C][C]0.0956599[/C][C]0.04783[/C][/ROW]
[ROW][C]HOURS[/C][C]0.00139442[/C][C]0.000513137[/C][C]2.717[/C][C]0.00878005[/C][C]0.00439003[/C][/ROW]
[ROW][C]Ex[/C][C]1.00136[/C][C]0.00378567[/C][C]264.5[/C][C]4.42561e-87[/C][C]2.21281e-87[/C][/ROW]
[ROW][C]PR[/C][C]0.910273[/C][C]0.0373982[/C][C]24.34[/C][C]3.98491e-31[/C][C]1.99246e-31[/C][/ROW]
[ROW][C]PE[/C][C]0.99492[/C][C]0.0517882[/C][C]19.21[/C][C]4.61452e-26[/C][C]2.30726e-26[/C][/ROW]
[ROW][C]PA[/C][C]1.00838[/C][C]0.0200236[/C][C]50.36[/C][C]1.05577e-47[/C][C]5.27885e-48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	0.159974	0.095171	1.681	0.0984506	0.0492253
LFM	-0.000200027	0.000229734	-0.8707	0.387707	0.193853
BLOG	-0.000410877	0.000242352	-1.695	0.0956599	0.04783
HOURS	0.00139442	0.000513137	2.717	0.00878005	0.00439003
Ex	1.00136	0.00378567	264.5	4.42561e-87	2.21281e-87
PR	0.910273	0.0373982	24.34	3.98491e-31	1.99246e-31
PE	0.99492	0.0517882	19.21	4.61452e-26	2.30726e-26
PA	1.00838	0.0200236	50.36	1.05577e-47	5.27885e-48

Multiple Linear Regression - Regression Statistics
Multiple R	0.99978
R-squared	0.999561
Adjusted R-squared	0.999505
F-TEST (value)	17888.7
F-TEST (DF numerator)	7
F-TEST (DF denominator)	55
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0533886
Sum Squared Residuals	0.156769

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99978 \tabularnewline
R-squared & 0.999561 \tabularnewline
Adjusted R-squared & 0.999505 \tabularnewline
F-TEST (value) & 17888.7 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 55 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0533886 \tabularnewline
Sum Squared Residuals & 0.156769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99978[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999561[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.999505[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17888.7[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]55[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0533886[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.156769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.99978
R-squared	0.999561
Adjusted R-squared	0.999505
F-TEST (value)	17888.7
F-TEST (DF numerator)	7
F-TEST (DF denominator)	55
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0533886
Sum Squared Residuals	0.156769

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.9	12.9612	-0.0612249
2	12.8	12.8121	-0.0120788
3	7.4	7.33236	0.0676422
4	6.7	6.71143	-0.0114346
5	12.6	12.5799	0.0200954
6	14.8	14.8466	-0.0466337
7	13.3	13.2704	0.0296187
8	11.1	11.1436	-0.0436127
9	8.2	8.18098	0.0190216
10	11.4	11.417	-0.016987
11	6.4	6.39786	0.0021402
12	12	11.9406	0.0594243
13	6.3	6.31518	-0.0151777
14	11.3	11.224	0.0760102
15	11.9	12.0193	-0.119303
16	9.3	9.30492	-0.00491635
17	10	10.0385	-0.0384601
18	13.8	13.7769	0.0230803
19	10.8	10.7044	0.0956113
20	11.7	11.7305	-0.0304977
21	10.9	10.9121	-0.0121406
22	16.1	16.1402	-0.0401571
23	9.9	9.85651	0.0434926
24	11.5	11.5234	-0.023428
25	8.3	8.23342	0.066579
26	11.7	11.7004	-0.000424449
27	9	9.00861	-0.00860874
28	10.8	10.9154	-0.115363
29	10.4	10.4269	-0.0268603
30	12.7	12.6848	0.0151682
31	11.8	11.8033	-0.00326193
32	13	13.0456	-0.0455772
33	10.8	10.7293	0.0707344
34	12.3	12.2503	0.0496985
35	11.3	11.3985	-0.0985036
36	11.6	11.7204	-0.120423
37	10.9	10.8996	0.00035953
38	12.1	12.0957	0.00430129
39	13.3	13.3038	-0.00376308
40	10.1	10.0987	0.00128333
41	14.3	14.2221	0.0779321
42	9.3	9.24611	0.053887
43	12.5	12.4946	0.0053868
44	7.6	7.64614	-0.0461403
45	9.2	9.21806	-0.0180586
46	14.5	14.4906	0.00944207
47	12.3	12.215	0.084973
48	12.6	12.5201	0.0799197
49	13	13.0192	-0.0191938
50	12.6	12.6165	-0.0164994
51	13.2	13.2142	-0.0142235
52	7.7	7.73982	-0.0398223
53	10.5	10.441	0.0590401
54	10.9	10.8408	0.0591922
55	4.3	4.33398	-0.0339791
56	10.3	10.3391	-0.0391471
57	11.4	11.3194	0.0805875
58	5.6	5.61006	-0.0100575
59	8.8	8.80001	-1.37924e-05
60	9	9.02315	-0.0231473
61	9.6	9.54025	0.0597526
62	6.4	6.42481	-0.0248093
63	11.6	11.6304	-0.0304447

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.9 & 12.9612 & -0.0612249 \tabularnewline
2 & 12.8 & 12.8121 & -0.0120788 \tabularnewline
3 & 7.4 & 7.33236 & 0.0676422 \tabularnewline
4 & 6.7 & 6.71143 & -0.0114346 \tabularnewline
5 & 12.6 & 12.5799 & 0.0200954 \tabularnewline
6 & 14.8 & 14.8466 & -0.0466337 \tabularnewline
7 & 13.3 & 13.2704 & 0.0296187 \tabularnewline
8 & 11.1 & 11.1436 & -0.0436127 \tabularnewline
9 & 8.2 & 8.18098 & 0.0190216 \tabularnewline
10 & 11.4 & 11.417 & -0.016987 \tabularnewline
11 & 6.4 & 6.39786 & 0.0021402 \tabularnewline
12 & 12 & 11.9406 & 0.0594243 \tabularnewline
13 & 6.3 & 6.31518 & -0.0151777 \tabularnewline
14 & 11.3 & 11.224 & 0.0760102 \tabularnewline
15 & 11.9 & 12.0193 & -0.119303 \tabularnewline
16 & 9.3 & 9.30492 & -0.00491635 \tabularnewline
17 & 10 & 10.0385 & -0.0384601 \tabularnewline
18 & 13.8 & 13.7769 & 0.0230803 \tabularnewline
19 & 10.8 & 10.7044 & 0.0956113 \tabularnewline
20 & 11.7 & 11.7305 & -0.0304977 \tabularnewline
21 & 10.9 & 10.9121 & -0.0121406 \tabularnewline
22 & 16.1 & 16.1402 & -0.0401571 \tabularnewline
23 & 9.9 & 9.85651 & 0.0434926 \tabularnewline
24 & 11.5 & 11.5234 & -0.023428 \tabularnewline
25 & 8.3 & 8.23342 & 0.066579 \tabularnewline
26 & 11.7 & 11.7004 & -0.000424449 \tabularnewline
27 & 9 & 9.00861 & -0.00860874 \tabularnewline
28 & 10.8 & 10.9154 & -0.115363 \tabularnewline
29 & 10.4 & 10.4269 & -0.0268603 \tabularnewline
30 & 12.7 & 12.6848 & 0.0151682 \tabularnewline
31 & 11.8 & 11.8033 & -0.00326193 \tabularnewline
32 & 13 & 13.0456 & -0.0455772 \tabularnewline
33 & 10.8 & 10.7293 & 0.0707344 \tabularnewline
34 & 12.3 & 12.2503 & 0.0496985 \tabularnewline
35 & 11.3 & 11.3985 & -0.0985036 \tabularnewline
36 & 11.6 & 11.7204 & -0.120423 \tabularnewline
37 & 10.9 & 10.8996 & 0.00035953 \tabularnewline
38 & 12.1 & 12.0957 & 0.00430129 \tabularnewline
39 & 13.3 & 13.3038 & -0.00376308 \tabularnewline
40 & 10.1 & 10.0987 & 0.00128333 \tabularnewline
41 & 14.3 & 14.2221 & 0.0779321 \tabularnewline
42 & 9.3 & 9.24611 & 0.053887 \tabularnewline
43 & 12.5 & 12.4946 & 0.0053868 \tabularnewline
44 & 7.6 & 7.64614 & -0.0461403 \tabularnewline
45 & 9.2 & 9.21806 & -0.0180586 \tabularnewline
46 & 14.5 & 14.4906 & 0.00944207 \tabularnewline
47 & 12.3 & 12.215 & 0.084973 \tabularnewline
48 & 12.6 & 12.5201 & 0.0799197 \tabularnewline
49 & 13 & 13.0192 & -0.0191938 \tabularnewline
50 & 12.6 & 12.6165 & -0.0164994 \tabularnewline
51 & 13.2 & 13.2142 & -0.0142235 \tabularnewline
52 & 7.7 & 7.73982 & -0.0398223 \tabularnewline
53 & 10.5 & 10.441 & 0.0590401 \tabularnewline
54 & 10.9 & 10.8408 & 0.0591922 \tabularnewline
55 & 4.3 & 4.33398 & -0.0339791 \tabularnewline
56 & 10.3 & 10.3391 & -0.0391471 \tabularnewline
57 & 11.4 & 11.3194 & 0.0805875 \tabularnewline
58 & 5.6 & 5.61006 & -0.0100575 \tabularnewline
59 & 8.8 & 8.80001 & -1.37924e-05 \tabularnewline
60 & 9 & 9.02315 & -0.0231473 \tabularnewline
61 & 9.6 & 9.54025 & 0.0597526 \tabularnewline
62 & 6.4 & 6.42481 & -0.0248093 \tabularnewline
63 & 11.6 & 11.6304 & -0.0304447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]12.9[/C][C]12.9612[/C][C]-0.0612249[/C][/ROW]
[ROW][C]2[/C][C]12.8[/C][C]12.8121[/C][C]-0.0120788[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]7.33236[/C][C]0.0676422[/C][/ROW]
[ROW][C]4[/C][C]6.7[/C][C]6.71143[/C][C]-0.0114346[/C][/ROW]
[ROW][C]5[/C][C]12.6[/C][C]12.5799[/C][C]0.0200954[/C][/ROW]
[ROW][C]6[/C][C]14.8[/C][C]14.8466[/C][C]-0.0466337[/C][/ROW]
[ROW][C]7[/C][C]13.3[/C][C]13.2704[/C][C]0.0296187[/C][/ROW]
[ROW][C]8[/C][C]11.1[/C][C]11.1436[/C][C]-0.0436127[/C][/ROW]
[ROW][C]9[/C][C]8.2[/C][C]8.18098[/C][C]0.0190216[/C][/ROW]
[ROW][C]10[/C][C]11.4[/C][C]11.417[/C][C]-0.016987[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]6.39786[/C][C]0.0021402[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]11.9406[/C][C]0.0594243[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]6.31518[/C][C]-0.0151777[/C][/ROW]
[ROW][C]14[/C][C]11.3[/C][C]11.224[/C][C]0.0760102[/C][/ROW]
[ROW][C]15[/C][C]11.9[/C][C]12.0193[/C][C]-0.119303[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.30492[/C][C]-0.00491635[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]10.0385[/C][C]-0.0384601[/C][/ROW]
[ROW][C]18[/C][C]13.8[/C][C]13.7769[/C][C]0.0230803[/C][/ROW]
[ROW][C]19[/C][C]10.8[/C][C]10.7044[/C][C]0.0956113[/C][/ROW]
[ROW][C]20[/C][C]11.7[/C][C]11.7305[/C][C]-0.0304977[/C][/ROW]
[ROW][C]21[/C][C]10.9[/C][C]10.9121[/C][C]-0.0121406[/C][/ROW]
[ROW][C]22[/C][C]16.1[/C][C]16.1402[/C][C]-0.0401571[/C][/ROW]
[ROW][C]23[/C][C]9.9[/C][C]9.85651[/C][C]0.0434926[/C][/ROW]
[ROW][C]24[/C][C]11.5[/C][C]11.5234[/C][C]-0.023428[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.23342[/C][C]0.066579[/C][/ROW]
[ROW][C]26[/C][C]11.7[/C][C]11.7004[/C][C]-0.000424449[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]9.00861[/C][C]-0.00860874[/C][/ROW]
[ROW][C]28[/C][C]10.8[/C][C]10.9154[/C][C]-0.115363[/C][/ROW]
[ROW][C]29[/C][C]10.4[/C][C]10.4269[/C][C]-0.0268603[/C][/ROW]
[ROW][C]30[/C][C]12.7[/C][C]12.6848[/C][C]0.0151682[/C][/ROW]
[ROW][C]31[/C][C]11.8[/C][C]11.8033[/C][C]-0.00326193[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]13.0456[/C][C]-0.0455772[/C][/ROW]
[ROW][C]33[/C][C]10.8[/C][C]10.7293[/C][C]0.0707344[/C][/ROW]
[ROW][C]34[/C][C]12.3[/C][C]12.2503[/C][C]0.0496985[/C][/ROW]
[ROW][C]35[/C][C]11.3[/C][C]11.3985[/C][C]-0.0985036[/C][/ROW]
[ROW][C]36[/C][C]11.6[/C][C]11.7204[/C][C]-0.120423[/C][/ROW]
[ROW][C]37[/C][C]10.9[/C][C]10.8996[/C][C]0.00035953[/C][/ROW]
[ROW][C]38[/C][C]12.1[/C][C]12.0957[/C][C]0.00430129[/C][/ROW]
[ROW][C]39[/C][C]13.3[/C][C]13.3038[/C][C]-0.00376308[/C][/ROW]
[ROW][C]40[/C][C]10.1[/C][C]10.0987[/C][C]0.00128333[/C][/ROW]
[ROW][C]41[/C][C]14.3[/C][C]14.2221[/C][C]0.0779321[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]9.24611[/C][C]0.053887[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]12.4946[/C][C]0.0053868[/C][/ROW]
[ROW][C]44[/C][C]7.6[/C][C]7.64614[/C][C]-0.0461403[/C][/ROW]
[ROW][C]45[/C][C]9.2[/C][C]9.21806[/C][C]-0.0180586[/C][/ROW]
[ROW][C]46[/C][C]14.5[/C][C]14.4906[/C][C]0.00944207[/C][/ROW]
[ROW][C]47[/C][C]12.3[/C][C]12.215[/C][C]0.084973[/C][/ROW]
[ROW][C]48[/C][C]12.6[/C][C]12.5201[/C][C]0.0799197[/C][/ROW]
[ROW][C]49[/C][C]13[/C][C]13.0192[/C][C]-0.0191938[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]12.6165[/C][C]-0.0164994[/C][/ROW]
[ROW][C]51[/C][C]13.2[/C][C]13.2142[/C][C]-0.0142235[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.73982[/C][C]-0.0398223[/C][/ROW]
[ROW][C]53[/C][C]10.5[/C][C]10.441[/C][C]0.0590401[/C][/ROW]
[ROW][C]54[/C][C]10.9[/C][C]10.8408[/C][C]0.0591922[/C][/ROW]
[ROW][C]55[/C][C]4.3[/C][C]4.33398[/C][C]-0.0339791[/C][/ROW]
[ROW][C]56[/C][C]10.3[/C][C]10.3391[/C][C]-0.0391471[/C][/ROW]
[ROW][C]57[/C][C]11.4[/C][C]11.3194[/C][C]0.0805875[/C][/ROW]
[ROW][C]58[/C][C]5.6[/C][C]5.61006[/C][C]-0.0100575[/C][/ROW]
[ROW][C]59[/C][C]8.8[/C][C]8.80001[/C][C]-1.37924e-05[/C][/ROW]
[ROW][C]60[/C][C]9[/C][C]9.02315[/C][C]-0.0231473[/C][/ROW]
[ROW][C]61[/C][C]9.6[/C][C]9.54025[/C][C]0.0597526[/C][/ROW]
[ROW][C]62[/C][C]6.4[/C][C]6.42481[/C][C]-0.0248093[/C][/ROW]
[ROW][C]63[/C][C]11.6[/C][C]11.6304[/C][C]-0.0304447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.9	12.9612	-0.0612249
2	12.8	12.8121	-0.0120788
3	7.4	7.33236	0.0676422
4	6.7	6.71143	-0.0114346
5	12.6	12.5799	0.0200954
6	14.8	14.8466	-0.0466337
7	13.3	13.2704	0.0296187
8	11.1	11.1436	-0.0436127
9	8.2	8.18098	0.0190216
10	11.4	11.417	-0.016987
11	6.4	6.39786	0.0021402
12	12	11.9406	0.0594243
13	6.3	6.31518	-0.0151777
14	11.3	11.224	0.0760102
15	11.9	12.0193	-0.119303
16	9.3	9.30492	-0.00491635
17	10	10.0385	-0.0384601
18	13.8	13.7769	0.0230803
19	10.8	10.7044	0.0956113
20	11.7	11.7305	-0.0304977
21	10.9	10.9121	-0.0121406
22	16.1	16.1402	-0.0401571
23	9.9	9.85651	0.0434926
24	11.5	11.5234	-0.023428
25	8.3	8.23342	0.066579
26	11.7	11.7004	-0.000424449
27	9	9.00861	-0.00860874
28	10.8	10.9154	-0.115363
29	10.4	10.4269	-0.0268603
30	12.7	12.6848	0.0151682
31	11.8	11.8033	-0.00326193
32	13	13.0456	-0.0455772
33	10.8	10.7293	0.0707344
34	12.3	12.2503	0.0496985
35	11.3	11.3985	-0.0985036
36	11.6	11.7204	-0.120423
37	10.9	10.8996	0.00035953
38	12.1	12.0957	0.00430129
39	13.3	13.3038	-0.00376308
40	10.1	10.0987	0.00128333
41	14.3	14.2221	0.0779321
42	9.3	9.24611	0.053887
43	12.5	12.4946	0.0053868
44	7.6	7.64614	-0.0461403
45	9.2	9.21806	-0.0180586
46	14.5	14.4906	0.00944207
47	12.3	12.215	0.084973
48	12.6	12.5201	0.0799197
49	13	13.0192	-0.0191938
50	12.6	12.6165	-0.0164994
51	13.2	13.2142	-0.0142235
52	7.7	7.73982	-0.0398223
53	10.5	10.441	0.0590401
54	10.9	10.8408	0.0591922
55	4.3	4.33398	-0.0339791
56	10.3	10.3391	-0.0391471
57	11.4	11.3194	0.0805875
58	5.6	5.61006	-0.0100575
59	8.8	8.80001	-1.37924e-05
60	9	9.02315	-0.0231473
61	9.6	9.54025	0.0597526
62	6.4	6.42481	-0.0248093
63	11.6	11.6304	-0.0304447

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.184284	0.368568	0.815716
12	0.122953	0.245907	0.877047
13	0.237729	0.475459	0.762271
14	0.154485	0.30897	0.845515
15	0.641791	0.716419	0.358209
16	0.532114	0.935773	0.467886
17	0.539165	0.92167	0.460835
18	0.43811	0.87622	0.56189
19	0.627213	0.745573	0.372787
20	0.556741	0.886517	0.443259
21	0.496232	0.992464	0.503768
22	0.58488	0.830239	0.41512
23	0.508616	0.982768	0.491384
24	0.442538	0.885076	0.557462
25	0.447628	0.895256	0.552372
26	0.367296	0.734592	0.632704
27	0.292537	0.585075	0.707463
28	0.646331	0.707338	0.353669
29	0.600698	0.798604	0.399302
30	0.537297	0.925406	0.462703
31	0.465983	0.931967	0.534017
32	0.512097	0.975805	0.487903
33	0.631204	0.737592	0.368796
34	0.587743	0.824514	0.412257
35	0.778951	0.442098	0.221049
36	0.956218	0.0875636	0.0437818
37	0.950197	0.0996059	0.0498029
38	0.928792	0.142417	0.0712083
39	0.937238	0.125524	0.0627622
40	0.903034	0.193932	0.0969662
41	0.90424	0.191519	0.0957597
42	0.871799	0.256402	0.128201
43	0.815926	0.368147	0.184074
44	0.766235	0.467529	0.233765
45	0.682993	0.634014	0.317007
46	0.58887	0.822259	0.41113
47	0.545859	0.908282	0.454141
48	0.695965	0.608071	0.304035
49	0.581996	0.836008	0.418004
50	0.651284	0.697433	0.348716
51	0.510018	0.979964	0.489982
52	0.938853	0.122293	0.0611467

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.184284 & 0.368568 & 0.815716 \tabularnewline
12 & 0.122953 & 0.245907 & 0.877047 \tabularnewline
13 & 0.237729 & 0.475459 & 0.762271 \tabularnewline
14 & 0.154485 & 0.30897 & 0.845515 \tabularnewline
15 & 0.641791 & 0.716419 & 0.358209 \tabularnewline
16 & 0.532114 & 0.935773 & 0.467886 \tabularnewline
17 & 0.539165 & 0.92167 & 0.460835 \tabularnewline
18 & 0.43811 & 0.87622 & 0.56189 \tabularnewline
19 & 0.627213 & 0.745573 & 0.372787 \tabularnewline
20 & 0.556741 & 0.886517 & 0.443259 \tabularnewline
21 & 0.496232 & 0.992464 & 0.503768 \tabularnewline
22 & 0.58488 & 0.830239 & 0.41512 \tabularnewline
23 & 0.508616 & 0.982768 & 0.491384 \tabularnewline
24 & 0.442538 & 0.885076 & 0.557462 \tabularnewline
25 & 0.447628 & 0.895256 & 0.552372 \tabularnewline
26 & 0.367296 & 0.734592 & 0.632704 \tabularnewline
27 & 0.292537 & 0.585075 & 0.707463 \tabularnewline
28 & 0.646331 & 0.707338 & 0.353669 \tabularnewline
29 & 0.600698 & 0.798604 & 0.399302 \tabularnewline
30 & 0.537297 & 0.925406 & 0.462703 \tabularnewline
31 & 0.465983 & 0.931967 & 0.534017 \tabularnewline
32 & 0.512097 & 0.975805 & 0.487903 \tabularnewline
33 & 0.631204 & 0.737592 & 0.368796 \tabularnewline
34 & 0.587743 & 0.824514 & 0.412257 \tabularnewline
35 & 0.778951 & 0.442098 & 0.221049 \tabularnewline
36 & 0.956218 & 0.0875636 & 0.0437818 \tabularnewline
37 & 0.950197 & 0.0996059 & 0.0498029 \tabularnewline
38 & 0.928792 & 0.142417 & 0.0712083 \tabularnewline
39 & 0.937238 & 0.125524 & 0.0627622 \tabularnewline
40 & 0.903034 & 0.193932 & 0.0969662 \tabularnewline
41 & 0.90424 & 0.191519 & 0.0957597 \tabularnewline
42 & 0.871799 & 0.256402 & 0.128201 \tabularnewline
43 & 0.815926 & 0.368147 & 0.184074 \tabularnewline
44 & 0.766235 & 0.467529 & 0.233765 \tabularnewline
45 & 0.682993 & 0.634014 & 0.317007 \tabularnewline
46 & 0.58887 & 0.822259 & 0.41113 \tabularnewline
47 & 0.545859 & 0.908282 & 0.454141 \tabularnewline
48 & 0.695965 & 0.608071 & 0.304035 \tabularnewline
49 & 0.581996 & 0.836008 & 0.418004 \tabularnewline
50 & 0.651284 & 0.697433 & 0.348716 \tabularnewline
51 & 0.510018 & 0.979964 & 0.489982 \tabularnewline
52 & 0.938853 & 0.122293 & 0.0611467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]11[/C][C]0.184284[/C][C]0.368568[/C][C]0.815716[/C][/ROW]
[ROW][C]12[/C][C]0.122953[/C][C]0.245907[/C][C]0.877047[/C][/ROW]
[ROW][C]13[/C][C]0.237729[/C][C]0.475459[/C][C]0.762271[/C][/ROW]
[ROW][C]14[/C][C]0.154485[/C][C]0.30897[/C][C]0.845515[/C][/ROW]
[ROW][C]15[/C][C]0.641791[/C][C]0.716419[/C][C]0.358209[/C][/ROW]
[ROW][C]16[/C][C]0.532114[/C][C]0.935773[/C][C]0.467886[/C][/ROW]
[ROW][C]17[/C][C]0.539165[/C][C]0.92167[/C][C]0.460835[/C][/ROW]
[ROW][C]18[/C][C]0.43811[/C][C]0.87622[/C][C]0.56189[/C][/ROW]
[ROW][C]19[/C][C]0.627213[/C][C]0.745573[/C][C]0.372787[/C][/ROW]
[ROW][C]20[/C][C]0.556741[/C][C]0.886517[/C][C]0.443259[/C][/ROW]
[ROW][C]21[/C][C]0.496232[/C][C]0.992464[/C][C]0.503768[/C][/ROW]
[ROW][C]22[/C][C]0.58488[/C][C]0.830239[/C][C]0.41512[/C][/ROW]
[ROW][C]23[/C][C]0.508616[/C][C]0.982768[/C][C]0.491384[/C][/ROW]
[ROW][C]24[/C][C]0.442538[/C][C]0.885076[/C][C]0.557462[/C][/ROW]
[ROW][C]25[/C][C]0.447628[/C][C]0.895256[/C][C]0.552372[/C][/ROW]
[ROW][C]26[/C][C]0.367296[/C][C]0.734592[/C][C]0.632704[/C][/ROW]
[ROW][C]27[/C][C]0.292537[/C][C]0.585075[/C][C]0.707463[/C][/ROW]
[ROW][C]28[/C][C]0.646331[/C][C]0.707338[/C][C]0.353669[/C][/ROW]
[ROW][C]29[/C][C]0.600698[/C][C]0.798604[/C][C]0.399302[/C][/ROW]
[ROW][C]30[/C][C]0.537297[/C][C]0.925406[/C][C]0.462703[/C][/ROW]
[ROW][C]31[/C][C]0.465983[/C][C]0.931967[/C][C]0.534017[/C][/ROW]
[ROW][C]32[/C][C]0.512097[/C][C]0.975805[/C][C]0.487903[/C][/ROW]
[ROW][C]33[/C][C]0.631204[/C][C]0.737592[/C][C]0.368796[/C][/ROW]
[ROW][C]34[/C][C]0.587743[/C][C]0.824514[/C][C]0.412257[/C][/ROW]
[ROW][C]35[/C][C]0.778951[/C][C]0.442098[/C][C]0.221049[/C][/ROW]
[ROW][C]36[/C][C]0.956218[/C][C]0.0875636[/C][C]0.0437818[/C][/ROW]
[ROW][C]37[/C][C]0.950197[/C][C]0.0996059[/C][C]0.0498029[/C][/ROW]
[ROW][C]38[/C][C]0.928792[/C][C]0.142417[/C][C]0.0712083[/C][/ROW]
[ROW][C]39[/C][C]0.937238[/C][C]0.125524[/C][C]0.0627622[/C][/ROW]
[ROW][C]40[/C][C]0.903034[/C][C]0.193932[/C][C]0.0969662[/C][/ROW]
[ROW][C]41[/C][C]0.90424[/C][C]0.191519[/C][C]0.0957597[/C][/ROW]
[ROW][C]42[/C][C]0.871799[/C][C]0.256402[/C][C]0.128201[/C][/ROW]
[ROW][C]43[/C][C]0.815926[/C][C]0.368147[/C][C]0.184074[/C][/ROW]
[ROW][C]44[/C][C]0.766235[/C][C]0.467529[/C][C]0.233765[/C][/ROW]
[ROW][C]45[/C][C]0.682993[/C][C]0.634014[/C][C]0.317007[/C][/ROW]
[ROW][C]46[/C][C]0.58887[/C][C]0.822259[/C][C]0.41113[/C][/ROW]
[ROW][C]47[/C][C]0.545859[/C][C]0.908282[/C][C]0.454141[/C][/ROW]
[ROW][C]48[/C][C]0.695965[/C][C]0.608071[/C][C]0.304035[/C][/ROW]
[ROW][C]49[/C][C]0.581996[/C][C]0.836008[/C][C]0.418004[/C][/ROW]
[ROW][C]50[/C][C]0.651284[/C][C]0.697433[/C][C]0.348716[/C][/ROW]
[ROW][C]51[/C][C]0.510018[/C][C]0.979964[/C][C]0.489982[/C][/ROW]
[ROW][C]52[/C][C]0.938853[/C][C]0.122293[/C][C]0.0611467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.184284	0.368568	0.815716
12	0.122953	0.245907	0.877047
13	0.237729	0.475459	0.762271
14	0.154485	0.30897	0.845515
15	0.641791	0.716419	0.358209
16	0.532114	0.935773	0.467886
17	0.539165	0.92167	0.460835
18	0.43811	0.87622	0.56189
19	0.627213	0.745573	0.372787
20	0.556741	0.886517	0.443259
21	0.496232	0.992464	0.503768
22	0.58488	0.830239	0.41512
23	0.508616	0.982768	0.491384
24	0.442538	0.885076	0.557462
25	0.447628	0.895256	0.552372
26	0.367296	0.734592	0.632704
27	0.292537	0.585075	0.707463
28	0.646331	0.707338	0.353669
29	0.600698	0.798604	0.399302
30	0.537297	0.925406	0.462703
31	0.465983	0.931967	0.534017
32	0.512097	0.975805	0.487903
33	0.631204	0.737592	0.368796
34	0.587743	0.824514	0.412257
35	0.778951	0.442098	0.221049
36	0.956218	0.0875636	0.0437818
37	0.950197	0.0996059	0.0498029
38	0.928792	0.142417	0.0712083
39	0.937238	0.125524	0.0627622
40	0.903034	0.193932	0.0969662
41	0.90424	0.191519	0.0957597
42	0.871799	0.256402	0.128201
43	0.815926	0.368147	0.184074
44	0.766235	0.467529	0.233765
45	0.682993	0.634014	0.317007
46	0.58887	0.822259	0.41113
47	0.545859	0.908282	0.454141
48	0.695965	0.608071	0.304035
49	0.581996	0.836008	0.418004
50	0.651284	0.697433	0.348716
51	0.510018	0.979964	0.489982
52	0.938853	0.122293	0.0611467

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	2	0.047619	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 2 & 0.047619 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266089&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.047619[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266089&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266089&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	2	0.047619	OK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant1,6))
a<-table.element(a,signif(numsignificant1/numgqtests,6))
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code