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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 08 Dec 2014 11:05:34 +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/08/t141803683076zlzb9l60i8rvx.htm/, Retrieved Sun, 19 May 2024 10:21:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263933, Retrieved Sun, 19 May 2024 10:21:17 +0000

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119

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-       [Multiple Regression] [paper] [2014-12-08 11:05:34] [58179e1d3a5a39b9daf58e365d8a3352] [Current]

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149 7.5 1.8 2.1 1.5 12.9
148 6.5 2.2 2 2.1 12.8
158 1 2.3 2.1 1.9 7.4
128 1 2.1 2 1.6 6.7
224 5.5 2.7 2.3 2.1 12.6
159 8.5 2.1 2.1 2.1 14.8
105 6.5 2.4 2.1 2.2 13.3
159 4.5 2.9 2.2 1.5 11.1
167 2 2.2 2.1 1.9 8.2
165 5 2.1 2.1 2.2 11.4
159 0.5 2.2 2.1 1.6 6.4
176 5 2.7 2.3 1.9 12
54 2.5 1.9 1.8 0.1 6.3
91 5 2 2 2.2 11.3
163 5.5 2.5 2.2 1.8 11.9
124 3.5 2.2 2 1.6 9.3
121 4 1.9 2 2.1 10
148 6.5 3.5 2.2 1.6 13.8
221 4.5 2.1 2.2 1.9 10.8
149 5.5 2.3 2.1 1.8 11.7
244 4 2.2 2.3 2.4 10.9
148 7.5 3.5 2.7 2.4 16.1
150 4 1.9 2 1.9 9.9
153 5.5 1.9 2 2.1 11.5
94 2.5 1.9 1.9 1.9 8.3
156 5.5 2.1 2 2.1 11.7
132 3.5 2 2 1.5 9
105 4.5 2.3 2 2.1 10.8
151 4.5 1.8 2 2.1 10.4
131 6 2.4 2.2 2.1 12.7
157 5 2.3 2.1 2.4 11.8
162 6.5 2.3 2.1 2.1 13
163 5 1.8 2 1.9 10.8
59 6 1.9 1.9 2.4 12.3
187 4.5 2.6 2.2 2.1 11.3
116 5 2.1 2.2 2.4 11.6
148 5 1.8 2 2.1 10.9
155 6.5 1.9 2.2 1.5 12.1
125 7 2.4 2 1.9 13.3
116 4.5 1.9 1.9 1.8 10.1
138 8.5 2.1 2 1.6 14.3
164 3.5 2.1 2.1 1.5 9.3
162 6 2.4 2 2.1 12.5
99 1.5 1.8 1.9 2.4 7.6
186 3.5 2.1 2.1 1.5 9.2
188 7.5 2.7 2.2 2.1 14.5
177 5 2.9 2.2 2.1 12.3
139 6.5 2.1 2 1.9 12.6
162 6.5 2.3 2.1 2.1 13
108 6.5 2.2 2.1 1.8 12.6
159 7 2 2.1 2.1 13.2
110 1.5 2.1 2 2.1 7.7
96 4 2.1 2.1 2.2 10.5
87 4.5 2 2.1 2.2 10.9
97 0 1.7 1 1.6 4.3
127 3.5 2.2 2.2 2.4 10.3
74 4.5 2.4 2 2.4 11.4
114 0 1.8 2 1.8 5.6
95 3 1.9 2 1.9 8.8
121 3.5 1.7 2 1.8 9
130 3 2.1 2.2 2.2 9.6
52 1 1.7 1.8 1.9 6.4
118 5.5 1.9 2.1 2.1 11.6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&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]5 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=263933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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	5 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Multiple Linear Regression - Estimated Regression Equation
TOT[t] = + 0.023147 -0.000175379LFM[t] + 1.00081Ex[t] + 0.987089PR[t] + 1.01512PE[t] + 1.00772PA[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TOT[t] =  +  0.023147 -0.000175379LFM[t] +  1.00081Ex[t] +  0.987089PR[t] +  1.01512PE[t] +  1.00772PA[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TOT[t] =  +  0.023147 -0.000175379LFM[t] +  1.00081Ex[t] +  0.987089PR[t] +  1.01512PE[t] +  1.00772PA[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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] = + 0.023147 -0.000175379LFM[t] + 1.00081Ex[t] + 0.987089PR[t] + 1.01512PE[t] + 1.00772PA[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)	0.023147	0.0824072	0.2809	0.779815	0.389908
LFM	-0.000175379	0.000217168	-0.8076	0.422694	0.211347
Ex	1.00081	0.00396506	252.4	1.36113e-88	6.80563e-89
PR	0.987089	0.0246649	40.02	2.03806e-43	1.01903e-43
PE	1.01512	0.0534352	19	2.48243e-26	1.24122e-26
PA	1.00772	0.0209385	48.13	7.45259e-48	3.72629e-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) & 0.023147 & 0.0824072 & 0.2809 & 0.779815 & 0.389908 \tabularnewline
LFM & -0.000175379 & 0.000217168 & -0.8076 & 0.422694 & 0.211347 \tabularnewline
Ex & 1.00081 & 0.00396506 & 252.4 & 1.36113e-88 & 6.80563e-89 \tabularnewline
PR & 0.987089 & 0.0246649 & 40.02 & 2.03806e-43 & 1.01903e-43 \tabularnewline
PE & 1.01512 & 0.0534352 & 19 & 2.48243e-26 & 1.24122e-26 \tabularnewline
PA & 1.00772 & 0.0209385 & 48.13 & 7.45259e-48 & 3.72629e-48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&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]0.023147[/C][C]0.0824072[/C][C]0.2809[/C][C]0.779815[/C][C]0.389908[/C][/ROW]
[ROW][C]LFM[/C][C]-0.000175379[/C][C]0.000217168[/C][C]-0.8076[/C][C]0.422694[/C][C]0.211347[/C][/ROW]
[ROW][C]Ex[/C][C]1.00081[/C][C]0.00396506[/C][C]252.4[/C][C]1.36113e-88[/C][C]6.80563e-89[/C][/ROW]
[ROW][C]PR[/C][C]0.987089[/C][C]0.0246649[/C][C]40.02[/C][C]2.03806e-43[/C][C]1.01903e-43[/C][/ROW]
[ROW][C]PE[/C][C]1.01512[/C][C]0.0534352[/C][C]19[/C][C]2.48243e-26[/C][C]1.24122e-26[/C][/ROW]
[ROW][C]PA[/C][C]1.00772[/C][C]0.0209385[/C][C]48.13[/C][C]7.45259e-48[/C][C]3.72629e-48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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)	0.023147	0.0824072	0.2809	0.779815	0.389908
LFM	-0.000175379	0.000217168	-0.8076	0.422694	0.211347
Ex	1.00081	0.00396506	252.4	1.36113e-88	6.80563e-89
PR	0.987089	0.0246649	40.02	2.03806e-43	1.01903e-43
PE	1.01512	0.0534352	19	2.48243e-26	1.24122e-26
PA	1.00772	0.0209385	48.13	7.45259e-48	3.72629e-48

Multiple Linear Regression - Regression Statistics
Multiple R	0.999749
R-squared	0.999498
Adjusted R-squared	0.999454
F-TEST (value)	22716.5
F-TEST (DF numerator)	5
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0560555
Sum Squared Residuals	0.179106

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999749 \tabularnewline
R-squared & 0.999498 \tabularnewline
Adjusted R-squared & 0.999454 \tabularnewline
F-TEST (value) & 22716.5 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0560555 \tabularnewline
Sum Squared Residuals & 0.179106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999749[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999498[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.999454[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]22716.5[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/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]0.0560555[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.179106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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	0.999749
R-squared	0.999498
Adjusted R-squared	0.999454
F-TEST (value)	22716.5
F-TEST (DF numerator)	5
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0560555
Sum Squared Residuals	0.179106

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.9	12.9232	-0.0231529
2	12.8	12.8205	-0.0204756
3	7.4	7.31296	0.0870394
4	6.7	6.71698	-0.016977
5	12.6	12.6044	-0.00441991
6	14.8	14.823	-0.0229633
7	13.3	13.2277	0.0722817
8	11.1	11.1063	-0.00628825
9	8.2	8.21348	-0.0134802
10	11.4	11.4199	-0.0198582
11	6.4	6.41136	-0.0113575
12	12	11.9109	0.0891089
13	6.3	6.31915	-0.0191482
14	11.3	11.2326	0.0673845
15	11.9	12.0139	-0.113873
16	9.3	9.31841	-0.018405
17	10	10.0271	-0.0270665
18	13.8	13.8029	-0.00285683
19	10.8	10.7088	0.0911699
20	11.7	11.7174	-0.0173988
21	10.9	10.9085	-0.00847229
22	16.1	16.1174	-0.0173967
23	9.9	9.82044	0.079563
24	11.5	11.5227	-0.0226649
25	8.3	8.22754	0.0724641
26	11.7	11.7196	-0.0195566
27	9	9.01881	-0.0188124
28	10.8	10.9251	-0.125112
29	10.4	10.4235	-0.0234997
30	12.7	12.7235	-0.023495
31	11.8	11.8202	-0.0202226
32	13	13.0182	-0.018241
33	10.8	10.7203	0.0797448
34	12.3	12.2404	0.0596426
35	11.3	11.4099	-0.109881
36	11.6	11.7315	-0.131507
37	10.9	10.9244	-0.0244293
38	12.1	12.1215	-0.0215143
39	13.3	13.3208	-0.0207872
40	10.1	10.1245	-0.0245199
41	14.3	14.2213	0.0787242
42	9.3	9.21342	0.086579
43	12.5	12.515	-0.0150347
44	7.6	7.631	-0.0310018
45	9.2	9.20956	-0.00956265
46	14.5	14.5108	-0.0108358
47	12.3	12.2082	0.0918347
48	12.6	12.5218	0.0781984
49	13	13.0182	-0.018241
50	12.6	12.6267	-0.0266874
51	13.2	13.223	-0.0230438
52	7.7	7.7244	-0.024396
53	10.5	10.4312	0.0688476
54	10.9	10.8344	0.0655746
55	4.3	4.31165	-0.011653
56	10.3	10.3271	-0.0270763
57	11.4	11.3316	0.0684273
58	5.6	5.62404	-0.024042
59	8.8	8.82928	-0.0292759
60	9	9.02693	-0.0269299
61	9.6	9.52589	0.0741057
62	6.4	6.43476	-0.0347617
63	11.6	11.6303	-0.0303149

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.9 & 12.9232 & -0.0231529 \tabularnewline
2 & 12.8 & 12.8205 & -0.0204756 \tabularnewline
3 & 7.4 & 7.31296 & 0.0870394 \tabularnewline
4 & 6.7 & 6.71698 & -0.016977 \tabularnewline
5 & 12.6 & 12.6044 & -0.00441991 \tabularnewline
6 & 14.8 & 14.823 & -0.0229633 \tabularnewline
7 & 13.3 & 13.2277 & 0.0722817 \tabularnewline
8 & 11.1 & 11.1063 & -0.00628825 \tabularnewline
9 & 8.2 & 8.21348 & -0.0134802 \tabularnewline
10 & 11.4 & 11.4199 & -0.0198582 \tabularnewline
11 & 6.4 & 6.41136 & -0.0113575 \tabularnewline
12 & 12 & 11.9109 & 0.0891089 \tabularnewline
13 & 6.3 & 6.31915 & -0.0191482 \tabularnewline
14 & 11.3 & 11.2326 & 0.0673845 \tabularnewline
15 & 11.9 & 12.0139 & -0.113873 \tabularnewline
16 & 9.3 & 9.31841 & -0.018405 \tabularnewline
17 & 10 & 10.0271 & -0.0270665 \tabularnewline
18 & 13.8 & 13.8029 & -0.00285683 \tabularnewline
19 & 10.8 & 10.7088 & 0.0911699 \tabularnewline
20 & 11.7 & 11.7174 & -0.0173988 \tabularnewline
21 & 10.9 & 10.9085 & -0.00847229 \tabularnewline
22 & 16.1 & 16.1174 & -0.0173967 \tabularnewline
23 & 9.9 & 9.82044 & 0.079563 \tabularnewline
24 & 11.5 & 11.5227 & -0.0226649 \tabularnewline
25 & 8.3 & 8.22754 & 0.0724641 \tabularnewline
26 & 11.7 & 11.7196 & -0.0195566 \tabularnewline
27 & 9 & 9.01881 & -0.0188124 \tabularnewline
28 & 10.8 & 10.9251 & -0.125112 \tabularnewline
29 & 10.4 & 10.4235 & -0.0234997 \tabularnewline
30 & 12.7 & 12.7235 & -0.023495 \tabularnewline
31 & 11.8 & 11.8202 & -0.0202226 \tabularnewline
32 & 13 & 13.0182 & -0.018241 \tabularnewline
33 & 10.8 & 10.7203 & 0.0797448 \tabularnewline
34 & 12.3 & 12.2404 & 0.0596426 \tabularnewline
35 & 11.3 & 11.4099 & -0.109881 \tabularnewline
36 & 11.6 & 11.7315 & -0.131507 \tabularnewline
37 & 10.9 & 10.9244 & -0.0244293 \tabularnewline
38 & 12.1 & 12.1215 & -0.0215143 \tabularnewline
39 & 13.3 & 13.3208 & -0.0207872 \tabularnewline
40 & 10.1 & 10.1245 & -0.0245199 \tabularnewline
41 & 14.3 & 14.2213 & 0.0787242 \tabularnewline
42 & 9.3 & 9.21342 & 0.086579 \tabularnewline
43 & 12.5 & 12.515 & -0.0150347 \tabularnewline
44 & 7.6 & 7.631 & -0.0310018 \tabularnewline
45 & 9.2 & 9.20956 & -0.00956265 \tabularnewline
46 & 14.5 & 14.5108 & -0.0108358 \tabularnewline
47 & 12.3 & 12.2082 & 0.0918347 \tabularnewline
48 & 12.6 & 12.5218 & 0.0781984 \tabularnewline
49 & 13 & 13.0182 & -0.018241 \tabularnewline
50 & 12.6 & 12.6267 & -0.0266874 \tabularnewline
51 & 13.2 & 13.223 & -0.0230438 \tabularnewline
52 & 7.7 & 7.7244 & -0.024396 \tabularnewline
53 & 10.5 & 10.4312 & 0.0688476 \tabularnewline
54 & 10.9 & 10.8344 & 0.0655746 \tabularnewline
55 & 4.3 & 4.31165 & -0.011653 \tabularnewline
56 & 10.3 & 10.3271 & -0.0270763 \tabularnewline
57 & 11.4 & 11.3316 & 0.0684273 \tabularnewline
58 & 5.6 & 5.62404 & -0.024042 \tabularnewline
59 & 8.8 & 8.82928 & -0.0292759 \tabularnewline
60 & 9 & 9.02693 & -0.0269299 \tabularnewline
61 & 9.6 & 9.52589 & 0.0741057 \tabularnewline
62 & 6.4 & 6.43476 & -0.0347617 \tabularnewline
63 & 11.6 & 11.6303 & -0.0303149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&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]12.9232[/C][C]-0.0231529[/C][/ROW]
[ROW][C]2[/C][C]12.8[/C][C]12.8205[/C][C]-0.0204756[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]7.31296[/C][C]0.0870394[/C][/ROW]
[ROW][C]4[/C][C]6.7[/C][C]6.71698[/C][C]-0.016977[/C][/ROW]
[ROW][C]5[/C][C]12.6[/C][C]12.6044[/C][C]-0.00441991[/C][/ROW]
[ROW][C]6[/C][C]14.8[/C][C]14.823[/C][C]-0.0229633[/C][/ROW]
[ROW][C]7[/C][C]13.3[/C][C]13.2277[/C][C]0.0722817[/C][/ROW]
[ROW][C]8[/C][C]11.1[/C][C]11.1063[/C][C]-0.00628825[/C][/ROW]
[ROW][C]9[/C][C]8.2[/C][C]8.21348[/C][C]-0.0134802[/C][/ROW]
[ROW][C]10[/C][C]11.4[/C][C]11.4199[/C][C]-0.0198582[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]6.41136[/C][C]-0.0113575[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]11.9109[/C][C]0.0891089[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]6.31915[/C][C]-0.0191482[/C][/ROW]
[ROW][C]14[/C][C]11.3[/C][C]11.2326[/C][C]0.0673845[/C][/ROW]
[ROW][C]15[/C][C]11.9[/C][C]12.0139[/C][C]-0.113873[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.31841[/C][C]-0.018405[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]10.0271[/C][C]-0.0270665[/C][/ROW]
[ROW][C]18[/C][C]13.8[/C][C]13.8029[/C][C]-0.00285683[/C][/ROW]
[ROW][C]19[/C][C]10.8[/C][C]10.7088[/C][C]0.0911699[/C][/ROW]
[ROW][C]20[/C][C]11.7[/C][C]11.7174[/C][C]-0.0173988[/C][/ROW]
[ROW][C]21[/C][C]10.9[/C][C]10.9085[/C][C]-0.00847229[/C][/ROW]
[ROW][C]22[/C][C]16.1[/C][C]16.1174[/C][C]-0.0173967[/C][/ROW]
[ROW][C]23[/C][C]9.9[/C][C]9.82044[/C][C]0.079563[/C][/ROW]
[ROW][C]24[/C][C]11.5[/C][C]11.5227[/C][C]-0.0226649[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.22754[/C][C]0.0724641[/C][/ROW]
[ROW][C]26[/C][C]11.7[/C][C]11.7196[/C][C]-0.0195566[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]9.01881[/C][C]-0.0188124[/C][/ROW]
[ROW][C]28[/C][C]10.8[/C][C]10.9251[/C][C]-0.125112[/C][/ROW]
[ROW][C]29[/C][C]10.4[/C][C]10.4235[/C][C]-0.0234997[/C][/ROW]
[ROW][C]30[/C][C]12.7[/C][C]12.7235[/C][C]-0.023495[/C][/ROW]
[ROW][C]31[/C][C]11.8[/C][C]11.8202[/C][C]-0.0202226[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]13.0182[/C][C]-0.018241[/C][/ROW]
[ROW][C]33[/C][C]10.8[/C][C]10.7203[/C][C]0.0797448[/C][/ROW]
[ROW][C]34[/C][C]12.3[/C][C]12.2404[/C][C]0.0596426[/C][/ROW]
[ROW][C]35[/C][C]11.3[/C][C]11.4099[/C][C]-0.109881[/C][/ROW]
[ROW][C]36[/C][C]11.6[/C][C]11.7315[/C][C]-0.131507[/C][/ROW]
[ROW][C]37[/C][C]10.9[/C][C]10.9244[/C][C]-0.0244293[/C][/ROW]
[ROW][C]38[/C][C]12.1[/C][C]12.1215[/C][C]-0.0215143[/C][/ROW]
[ROW][C]39[/C][C]13.3[/C][C]13.3208[/C][C]-0.0207872[/C][/ROW]
[ROW][C]40[/C][C]10.1[/C][C]10.1245[/C][C]-0.0245199[/C][/ROW]
[ROW][C]41[/C][C]14.3[/C][C]14.2213[/C][C]0.0787242[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]9.21342[/C][C]0.086579[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]12.515[/C][C]-0.0150347[/C][/ROW]
[ROW][C]44[/C][C]7.6[/C][C]7.631[/C][C]-0.0310018[/C][/ROW]
[ROW][C]45[/C][C]9.2[/C][C]9.20956[/C][C]-0.00956265[/C][/ROW]
[ROW][C]46[/C][C]14.5[/C][C]14.5108[/C][C]-0.0108358[/C][/ROW]
[ROW][C]47[/C][C]12.3[/C][C]12.2082[/C][C]0.0918347[/C][/ROW]
[ROW][C]48[/C][C]12.6[/C][C]12.5218[/C][C]0.0781984[/C][/ROW]
[ROW][C]49[/C][C]13[/C][C]13.0182[/C][C]-0.018241[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]12.6267[/C][C]-0.0266874[/C][/ROW]
[ROW][C]51[/C][C]13.2[/C][C]13.223[/C][C]-0.0230438[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.7244[/C][C]-0.024396[/C][/ROW]
[ROW][C]53[/C][C]10.5[/C][C]10.4312[/C][C]0.0688476[/C][/ROW]
[ROW][C]54[/C][C]10.9[/C][C]10.8344[/C][C]0.0655746[/C][/ROW]
[ROW][C]55[/C][C]4.3[/C][C]4.31165[/C][C]-0.011653[/C][/ROW]
[ROW][C]56[/C][C]10.3[/C][C]10.3271[/C][C]-0.0270763[/C][/ROW]
[ROW][C]57[/C][C]11.4[/C][C]11.3316[/C][C]0.0684273[/C][/ROW]
[ROW][C]58[/C][C]5.6[/C][C]5.62404[/C][C]-0.024042[/C][/ROW]
[ROW][C]59[/C][C]8.8[/C][C]8.82928[/C][C]-0.0292759[/C][/ROW]
[ROW][C]60[/C][C]9[/C][C]9.02693[/C][C]-0.0269299[/C][/ROW]
[ROW][C]61[/C][C]9.6[/C][C]9.52589[/C][C]0.0741057[/C][/ROW]
[ROW][C]62[/C][C]6.4[/C][C]6.43476[/C][C]-0.0347617[/C][/ROW]
[ROW][C]63[/C][C]11.6[/C][C]11.6303[/C][C]-0.0303149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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	12.9232	-0.0231529
2	12.8	12.8205	-0.0204756
3	7.4	7.31296	0.0870394
4	6.7	6.71698	-0.016977
5	12.6	12.6044	-0.00441991
6	14.8	14.823	-0.0229633
7	13.3	13.2277	0.0722817
8	11.1	11.1063	-0.00628825
9	8.2	8.21348	-0.0134802
10	11.4	11.4199	-0.0198582
11	6.4	6.41136	-0.0113575
12	12	11.9109	0.0891089
13	6.3	6.31915	-0.0191482
14	11.3	11.2326	0.0673845
15	11.9	12.0139	-0.113873
16	9.3	9.31841	-0.018405
17	10	10.0271	-0.0270665
18	13.8	13.8029	-0.00285683
19	10.8	10.7088	0.0911699
20	11.7	11.7174	-0.0173988
21	10.9	10.9085	-0.00847229
22	16.1	16.1174	-0.0173967
23	9.9	9.82044	0.079563
24	11.5	11.5227	-0.0226649
25	8.3	8.22754	0.0724641
26	11.7	11.7196	-0.0195566
27	9	9.01881	-0.0188124
28	10.8	10.9251	-0.125112
29	10.4	10.4235	-0.0234997
30	12.7	12.7235	-0.023495
31	11.8	11.8202	-0.0202226
32	13	13.0182	-0.018241
33	10.8	10.7203	0.0797448
34	12.3	12.2404	0.0596426
35	11.3	11.4099	-0.109881
36	11.6	11.7315	-0.131507
37	10.9	10.9244	-0.0244293
38	12.1	12.1215	-0.0215143
39	13.3	13.3208	-0.0207872
40	10.1	10.1245	-0.0245199
41	14.3	14.2213	0.0787242
42	9.3	9.21342	0.086579
43	12.5	12.515	-0.0150347
44	7.6	7.631	-0.0310018
45	9.2	9.20956	-0.00956265
46	14.5	14.5108	-0.0108358
47	12.3	12.2082	0.0918347
48	12.6	12.5218	0.0781984
49	13	13.0182	-0.018241
50	12.6	12.6267	-0.0266874
51	13.2	13.223	-0.0230438
52	7.7	7.7244	-0.024396
53	10.5	10.4312	0.0688476
54	10.9	10.8344	0.0655746
55	4.3	4.31165	-0.011653
56	10.3	10.3271	-0.0270763
57	11.4	11.3316	0.0684273
58	5.6	5.62404	-0.024042
59	8.8	8.82928	-0.0292759
60	9	9.02693	-0.0269299
61	9.6	9.52589	0.0741057
62	6.4	6.43476	-0.0347617
63	11.6	11.6303	-0.0303149

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.282732	0.565464	0.717268
10	0.204118	0.408237	0.795882
11	0.120058	0.240117	0.879942
12	0.0893824	0.178765	0.910618
13	0.0780056	0.156011	0.921994
14	0.0440059	0.0880119	0.955994
15	0.455004	0.910008	0.544996
16	0.362756	0.725513	0.637244
17	0.326259	0.652517	0.673741
18	0.244288	0.488577	0.755712
19	0.523262	0.953476	0.476738
20	0.439658	0.879316	0.560342
21	0.37187	0.743741	0.62813
22	0.367119	0.734237	0.632881
23	0.427711	0.855421	0.572289
24	0.363526	0.727051	0.636474
25	0.357766	0.715532	0.642234
26	0.295489	0.590979	0.704511
27	0.239217	0.478434	0.760783
28	0.584229	0.831543	0.415771
29	0.514939	0.970123	0.485061
30	0.455152	0.910305	0.544848
31	0.382529	0.765058	0.617471
32	0.312105	0.624211	0.687895
33	0.443619	0.887238	0.556381
34	0.440647	0.881294	0.559353
35	0.679324	0.641352	0.320676
36	0.914669	0.170663	0.0853313
37	0.880261	0.239478	0.119739
38	0.841669	0.316661	0.158331
39	0.844153	0.311694	0.155847
40	0.803785	0.392429	0.196215
41	0.823948	0.352105	0.176052
42	0.895569	0.208861	0.104431
43	0.864487	0.271025	0.135513
44	0.820148	0.359703	0.179852
45	0.76181	0.47638	0.23819
46	0.753788	0.492424	0.246212
47	0.731593	0.536814	0.268407
48	0.859871	0.280259	0.140129
49	0.790549	0.418902	0.209451
50	0.726106	0.547789	0.273894
51	0.635926	0.728149	0.364074
52	0.574524	0.850953	0.425476
53	0.518606	0.962788	0.481394
54	0.579217	0.841566	0.420783

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.282732 & 0.565464 & 0.717268 \tabularnewline
10 & 0.204118 & 0.408237 & 0.795882 \tabularnewline
11 & 0.120058 & 0.240117 & 0.879942 \tabularnewline
12 & 0.0893824 & 0.178765 & 0.910618 \tabularnewline
13 & 0.0780056 & 0.156011 & 0.921994 \tabularnewline
14 & 0.0440059 & 0.0880119 & 0.955994 \tabularnewline
15 & 0.455004 & 0.910008 & 0.544996 \tabularnewline
16 & 0.362756 & 0.725513 & 0.637244 \tabularnewline
17 & 0.326259 & 0.652517 & 0.673741 \tabularnewline
18 & 0.244288 & 0.488577 & 0.755712 \tabularnewline
19 & 0.523262 & 0.953476 & 0.476738 \tabularnewline
20 & 0.439658 & 0.879316 & 0.560342 \tabularnewline
21 & 0.37187 & 0.743741 & 0.62813 \tabularnewline
22 & 0.367119 & 0.734237 & 0.632881 \tabularnewline
23 & 0.427711 & 0.855421 & 0.572289 \tabularnewline
24 & 0.363526 & 0.727051 & 0.636474 \tabularnewline
25 & 0.357766 & 0.715532 & 0.642234 \tabularnewline
26 & 0.295489 & 0.590979 & 0.704511 \tabularnewline
27 & 0.239217 & 0.478434 & 0.760783 \tabularnewline
28 & 0.584229 & 0.831543 & 0.415771 \tabularnewline
29 & 0.514939 & 0.970123 & 0.485061 \tabularnewline
30 & 0.455152 & 0.910305 & 0.544848 \tabularnewline
31 & 0.382529 & 0.765058 & 0.617471 \tabularnewline
32 & 0.312105 & 0.624211 & 0.687895 \tabularnewline
33 & 0.443619 & 0.887238 & 0.556381 \tabularnewline
34 & 0.440647 & 0.881294 & 0.559353 \tabularnewline
35 & 0.679324 & 0.641352 & 0.320676 \tabularnewline
36 & 0.914669 & 0.170663 & 0.0853313 \tabularnewline
37 & 0.880261 & 0.239478 & 0.119739 \tabularnewline
38 & 0.841669 & 0.316661 & 0.158331 \tabularnewline
39 & 0.844153 & 0.311694 & 0.155847 \tabularnewline
40 & 0.803785 & 0.392429 & 0.196215 \tabularnewline
41 & 0.823948 & 0.352105 & 0.176052 \tabularnewline
42 & 0.895569 & 0.208861 & 0.104431 \tabularnewline
43 & 0.864487 & 0.271025 & 0.135513 \tabularnewline
44 & 0.820148 & 0.359703 & 0.179852 \tabularnewline
45 & 0.76181 & 0.47638 & 0.23819 \tabularnewline
46 & 0.753788 & 0.492424 & 0.246212 \tabularnewline
47 & 0.731593 & 0.536814 & 0.268407 \tabularnewline
48 & 0.859871 & 0.280259 & 0.140129 \tabularnewline
49 & 0.790549 & 0.418902 & 0.209451 \tabularnewline
50 & 0.726106 & 0.547789 & 0.273894 \tabularnewline
51 & 0.635926 & 0.728149 & 0.364074 \tabularnewline
52 & 0.574524 & 0.850953 & 0.425476 \tabularnewline
53 & 0.518606 & 0.962788 & 0.481394 \tabularnewline
54 & 0.579217 & 0.841566 & 0.420783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&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]9[/C][C]0.282732[/C][C]0.565464[/C][C]0.717268[/C][/ROW]
[ROW][C]10[/C][C]0.204118[/C][C]0.408237[/C][C]0.795882[/C][/ROW]
[ROW][C]11[/C][C]0.120058[/C][C]0.240117[/C][C]0.879942[/C][/ROW]
[ROW][C]12[/C][C]0.0893824[/C][C]0.178765[/C][C]0.910618[/C][/ROW]
[ROW][C]13[/C][C]0.0780056[/C][C]0.156011[/C][C]0.921994[/C][/ROW]
[ROW][C]14[/C][C]0.0440059[/C][C]0.0880119[/C][C]0.955994[/C][/ROW]
[ROW][C]15[/C][C]0.455004[/C][C]0.910008[/C][C]0.544996[/C][/ROW]
[ROW][C]16[/C][C]0.362756[/C][C]0.725513[/C][C]0.637244[/C][/ROW]
[ROW][C]17[/C][C]0.326259[/C][C]0.652517[/C][C]0.673741[/C][/ROW]
[ROW][C]18[/C][C]0.244288[/C][C]0.488577[/C][C]0.755712[/C][/ROW]
[ROW][C]19[/C][C]0.523262[/C][C]0.953476[/C][C]0.476738[/C][/ROW]
[ROW][C]20[/C][C]0.439658[/C][C]0.879316[/C][C]0.560342[/C][/ROW]
[ROW][C]21[/C][C]0.37187[/C][C]0.743741[/C][C]0.62813[/C][/ROW]
[ROW][C]22[/C][C]0.367119[/C][C]0.734237[/C][C]0.632881[/C][/ROW]
[ROW][C]23[/C][C]0.427711[/C][C]0.855421[/C][C]0.572289[/C][/ROW]
[ROW][C]24[/C][C]0.363526[/C][C]0.727051[/C][C]0.636474[/C][/ROW]
[ROW][C]25[/C][C]0.357766[/C][C]0.715532[/C][C]0.642234[/C][/ROW]
[ROW][C]26[/C][C]0.295489[/C][C]0.590979[/C][C]0.704511[/C][/ROW]
[ROW][C]27[/C][C]0.239217[/C][C]0.478434[/C][C]0.760783[/C][/ROW]
[ROW][C]28[/C][C]0.584229[/C][C]0.831543[/C][C]0.415771[/C][/ROW]
[ROW][C]29[/C][C]0.514939[/C][C]0.970123[/C][C]0.485061[/C][/ROW]
[ROW][C]30[/C][C]0.455152[/C][C]0.910305[/C][C]0.544848[/C][/ROW]
[ROW][C]31[/C][C]0.382529[/C][C]0.765058[/C][C]0.617471[/C][/ROW]
[ROW][C]32[/C][C]0.312105[/C][C]0.624211[/C][C]0.687895[/C][/ROW]
[ROW][C]33[/C][C]0.443619[/C][C]0.887238[/C][C]0.556381[/C][/ROW]
[ROW][C]34[/C][C]0.440647[/C][C]0.881294[/C][C]0.559353[/C][/ROW]
[ROW][C]35[/C][C]0.679324[/C][C]0.641352[/C][C]0.320676[/C][/ROW]
[ROW][C]36[/C][C]0.914669[/C][C]0.170663[/C][C]0.0853313[/C][/ROW]
[ROW][C]37[/C][C]0.880261[/C][C]0.239478[/C][C]0.119739[/C][/ROW]
[ROW][C]38[/C][C]0.841669[/C][C]0.316661[/C][C]0.158331[/C][/ROW]
[ROW][C]39[/C][C]0.844153[/C][C]0.311694[/C][C]0.155847[/C][/ROW]
[ROW][C]40[/C][C]0.803785[/C][C]0.392429[/C][C]0.196215[/C][/ROW]
[ROW][C]41[/C][C]0.823948[/C][C]0.352105[/C][C]0.176052[/C][/ROW]
[ROW][C]42[/C][C]0.895569[/C][C]0.208861[/C][C]0.104431[/C][/ROW]
[ROW][C]43[/C][C]0.864487[/C][C]0.271025[/C][C]0.135513[/C][/ROW]
[ROW][C]44[/C][C]0.820148[/C][C]0.359703[/C][C]0.179852[/C][/ROW]
[ROW][C]45[/C][C]0.76181[/C][C]0.47638[/C][C]0.23819[/C][/ROW]
[ROW][C]46[/C][C]0.753788[/C][C]0.492424[/C][C]0.246212[/C][/ROW]
[ROW][C]47[/C][C]0.731593[/C][C]0.536814[/C][C]0.268407[/C][/ROW]
[ROW][C]48[/C][C]0.859871[/C][C]0.280259[/C][C]0.140129[/C][/ROW]
[ROW][C]49[/C][C]0.790549[/C][C]0.418902[/C][C]0.209451[/C][/ROW]
[ROW][C]50[/C][C]0.726106[/C][C]0.547789[/C][C]0.273894[/C][/ROW]
[ROW][C]51[/C][C]0.635926[/C][C]0.728149[/C][C]0.364074[/C][/ROW]
[ROW][C]52[/C][C]0.574524[/C][C]0.850953[/C][C]0.425476[/C][/ROW]
[ROW][C]53[/C][C]0.518606[/C][C]0.962788[/C][C]0.481394[/C][/ROW]
[ROW][C]54[/C][C]0.579217[/C][C]0.841566[/C][C]0.420783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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
9	0.282732	0.565464	0.717268
10	0.204118	0.408237	0.795882
11	0.120058	0.240117	0.879942
12	0.0893824	0.178765	0.910618
13	0.0780056	0.156011	0.921994
14	0.0440059	0.0880119	0.955994
15	0.455004	0.910008	0.544996
16	0.362756	0.725513	0.637244
17	0.326259	0.652517	0.673741
18	0.244288	0.488577	0.755712
19	0.523262	0.953476	0.476738
20	0.439658	0.879316	0.560342
21	0.37187	0.743741	0.62813
22	0.367119	0.734237	0.632881
23	0.427711	0.855421	0.572289
24	0.363526	0.727051	0.636474
25	0.357766	0.715532	0.642234
26	0.295489	0.590979	0.704511
27	0.239217	0.478434	0.760783
28	0.584229	0.831543	0.415771
29	0.514939	0.970123	0.485061
30	0.455152	0.910305	0.544848
31	0.382529	0.765058	0.617471
32	0.312105	0.624211	0.687895
33	0.443619	0.887238	0.556381
34	0.440647	0.881294	0.559353
35	0.679324	0.641352	0.320676
36	0.914669	0.170663	0.0853313
37	0.880261	0.239478	0.119739
38	0.841669	0.316661	0.158331
39	0.844153	0.311694	0.155847
40	0.803785	0.392429	0.196215
41	0.823948	0.352105	0.176052
42	0.895569	0.208861	0.104431
43	0.864487	0.271025	0.135513
44	0.820148	0.359703	0.179852
45	0.76181	0.47638	0.23819
46	0.753788	0.492424	0.246212
47	0.731593	0.536814	0.268407
48	0.859871	0.280259	0.140129
49	0.790549	0.418902	0.209451
50	0.726106	0.547789	0.273894
51	0.635926	0.728149	0.364074
52	0.574524	0.850953	0.425476
53	0.518606	0.962788	0.481394
54	0.579217	0.841566	0.420783

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	1	0.0217391	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 & 1 & 0.0217391 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263933&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]1[/C][C]0.0217391[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263933&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263933&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	1	0.0217391	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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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