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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 18 Dec 2010 16:50:17 +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/2010/Dec/18/t1292690990x84uebrndon348c.htm/, Retrieved Tue, 30 Apr 2024 00:12:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112103, Retrieved Tue, 30 Apr 2024 00:12:33 +0000

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142

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

-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-   PD  [Multiple Regression] [Ws 7 - multiple r...] [2010-11-21 14:34:41] [603e2f5305d3a2a4e062624458fa1155]
-    D    [Multiple Regression] [PAPER - Multiple ...] [2010-12-18 15:51:20] [603e2f5305d3a2a4e062624458fa1155]
-    D        [Multiple Regression] [PAPER - Multiple ...] [2010-12-18 16:50:17] [0829c729852d8a4b1b0c41cf0848af95] [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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Brood[t] = + 106.911785714286 -0.463380952380941M1[t] -0.426404761904755M2[t] -0.619428571428571M3[t] -0.700452380952378M4[t] -0.78147619047619M5[t] -1.02450000000000M6[t] -1.31552380952381M7[t] -1.36854761904761M8[t] -1.22357142857143M9[t] + 0.130547619047621M10[t] + 0.124023809523815M11[t] + 0.309023809523809t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Brood[t] =  +  106.911785714286 -0.463380952380941M1[t] -0.426404761904755M2[t] -0.619428571428571M3[t] -0.700452380952378M4[t] -0.78147619047619M5[t] -1.02450000000000M6[t] -1.31552380952381M7[t] -1.36854761904761M8[t] -1.22357142857143M9[t] +  0.130547619047621M10[t] +  0.124023809523815M11[t] +  0.309023809523809t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Brood[t] =  +  106.911785714286 -0.463380952380941M1[t] -0.426404761904755M2[t] -0.619428571428571M3[t] -0.700452380952378M4[t] -0.78147619047619M5[t] -1.02450000000000M6[t] -1.31552380952381M7[t] -1.36854761904761M8[t] -1.22357142857143M9[t] +  0.130547619047621M10[t] +  0.124023809523815M11[t] +  0.309023809523809t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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
Brood[t] = + 106.911785714286 -0.463380952380941M1[t] -0.426404761904755M2[t] -0.619428571428571M3[t] -0.700452380952378M4[t] -0.78147619047619M5[t] -1.02450000000000M6[t] -1.31552380952381M7[t] -1.36854761904761M8[t] -1.22357142857143M9[t] + 0.130547619047621M10[t] + 0.124023809523815M11[t] + 0.309023809523809t + 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)	106.911785714286	1.486722	71.9111	0	0
M1	-0.463380952380941	1.795913	-0.258	0.797595	0.398797
M2	-0.426404761904755	1.79473	-0.2376	0.813304	0.406652
M3	-0.619428571428571	1.793808	-0.3453	0.731503	0.365752
M4	-0.700452380952378	1.79315	-0.3906	0.697958	0.348979
M5	-0.78147619047619	1.792755	-0.4359	0.665035	0.332517
M6	-1.02450000000000	1.792623	-0.5715	0.570563	0.285281
M7	-1.31552380952381	1.792755	-0.7338	0.466963	0.233481
M8	-1.36854761904761	1.79315	-0.7632	0.449412	0.224706
M9	-1.22357142857143	1.793808	-0.6821	0.498746	0.249373
M10	0.130547619047621	1.890091	0.0691	0.945247	0.472624
M11	0.124023809523815	1.889716	0.0656	0.947969	0.473984
t	0.309023809523809	0.021732	14.2195	0	0

\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) & 106.911785714286 & 1.486722 & 71.9111 & 0 & 0 \tabularnewline
M1 & -0.463380952380941 & 1.795913 & -0.258 & 0.797595 & 0.398797 \tabularnewline
M2 & -0.426404761904755 & 1.79473 & -0.2376 & 0.813304 & 0.406652 \tabularnewline
M3 & -0.619428571428571 & 1.793808 & -0.3453 & 0.731503 & 0.365752 \tabularnewline
M4 & -0.700452380952378 & 1.79315 & -0.3906 & 0.697958 & 0.348979 \tabularnewline
M5 & -0.78147619047619 & 1.792755 & -0.4359 & 0.665035 & 0.332517 \tabularnewline
M6 & -1.02450000000000 & 1.792623 & -0.5715 & 0.570563 & 0.285281 \tabularnewline
M7 & -1.31552380952381 & 1.792755 & -0.7338 & 0.466963 & 0.233481 \tabularnewline
M8 & -1.36854761904761 & 1.79315 & -0.7632 & 0.449412 & 0.224706 \tabularnewline
M9 & -1.22357142857143 & 1.793808 & -0.6821 & 0.498746 & 0.249373 \tabularnewline
M10 & 0.130547619047621 & 1.890091 & 0.0691 & 0.945247 & 0.472624 \tabularnewline
M11 & 0.124023809523815 & 1.889716 & 0.0656 & 0.947969 & 0.473984 \tabularnewline
t & 0.309023809523809 & 0.021732 & 14.2195 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&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]106.911785714286[/C][C]1.486722[/C][C]71.9111[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.463380952380941[/C][C]1.795913[/C][C]-0.258[/C][C]0.797595[/C][C]0.398797[/C][/ROW]
[ROW][C]M2[/C][C]-0.426404761904755[/C][C]1.79473[/C][C]-0.2376[/C][C]0.813304[/C][C]0.406652[/C][/ROW]
[ROW][C]M3[/C][C]-0.619428571428571[/C][C]1.793808[/C][C]-0.3453[/C][C]0.731503[/C][C]0.365752[/C][/ROW]
[ROW][C]M4[/C][C]-0.700452380952378[/C][C]1.79315[/C][C]-0.3906[/C][C]0.697958[/C][C]0.348979[/C][/ROW]
[ROW][C]M5[/C][C]-0.78147619047619[/C][C]1.792755[/C][C]-0.4359[/C][C]0.665035[/C][C]0.332517[/C][/ROW]
[ROW][C]M6[/C][C]-1.02450000000000[/C][C]1.792623[/C][C]-0.5715[/C][C]0.570563[/C][C]0.285281[/C][/ROW]
[ROW][C]M7[/C][C]-1.31552380952381[/C][C]1.792755[/C][C]-0.7338[/C][C]0.466963[/C][C]0.233481[/C][/ROW]
[ROW][C]M8[/C][C]-1.36854761904761[/C][C]1.79315[/C][C]-0.7632[/C][C]0.449412[/C][C]0.224706[/C][/ROW]
[ROW][C]M9[/C][C]-1.22357142857143[/C][C]1.793808[/C][C]-0.6821[/C][C]0.498746[/C][C]0.249373[/C][/ROW]
[ROW][C]M10[/C][C]0.130547619047621[/C][C]1.890091[/C][C]0.0691[/C][C]0.945247[/C][C]0.472624[/C][/ROW]
[ROW][C]M11[/C][C]0.124023809523815[/C][C]1.889716[/C][C]0.0656[/C][C]0.947969[/C][C]0.473984[/C][/ROW]
[ROW][C]t[/C][C]0.309023809523809[/C][C]0.021732[/C][C]14.2195[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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)	106.911785714286	1.486722	71.9111	0	0
M1	-0.463380952380941	1.795913	-0.258	0.797595	0.398797
M2	-0.426404761904755	1.79473	-0.2376	0.813304	0.406652
M3	-0.619428571428571	1.793808	-0.3453	0.731503	0.365752
M4	-0.700452380952378	1.79315	-0.3906	0.697958	0.348979
M5	-0.78147619047619	1.792755	-0.4359	0.665035	0.332517
M6	-1.02450000000000	1.792623	-0.5715	0.570563	0.285281
M7	-1.31552380952381	1.792755	-0.7338	0.466963	0.233481
M8	-1.36854761904761	1.79315	-0.7632	0.449412	0.224706
M9	-1.22357142857143	1.793808	-0.6821	0.498746	0.249373
M10	0.130547619047621	1.890091	0.0691	0.945247	0.472624
M11	0.124023809523815	1.889716	0.0656	0.947969	0.473984
t	0.309023809523809	0.021732	14.2195	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.907342742855159
R-squared	0.823270853011923
Adjusted R-squared	0.775071994742447
F-TEST (value)	17.0807127506857
F-TEST (DF numerator)	12
F-TEST (DF denominator)	44
p-value	8.83182416089312e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.67228486432564
Sum Squared Residuals	314.208681428571

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.907342742855159 \tabularnewline
R-squared & 0.823270853011923 \tabularnewline
Adjusted R-squared & 0.775071994742447 \tabularnewline
F-TEST (value) & 17.0807127506857 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 44 \tabularnewline
p-value & 8.83182416089312e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.67228486432564 \tabularnewline
Sum Squared Residuals & 314.208681428571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.907342742855159[/C][/ROW]
[ROW][C]R-squared[/C][C]0.823270853011923[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.775071994742447[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17.0807127506857[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]44[/C][/ROW]
[ROW][C]p-value[/C][C]8.83182416089312e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.67228486432564[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]314.208681428571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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	0.907342742855159
R-squared	0.823270853011923
Adjusted R-squared	0.775071994742447
F-TEST (value)	17.0807127506857
F-TEST (DF numerator)	12
F-TEST (DF denominator)	44
p-value	8.83182416089312e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.67228486432564
Sum Squared Residuals	314.208681428571

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	104.37	106.757428571429	-2.38742857142851
2	104.89	107.103428571429	-2.21342857142857
3	105.15	107.219428571429	-2.06942857142857
4	105.72	107.447428571429	-1.72742857142858
5	106.38	107.675428571429	-1.29542857142858
6	106.4	107.741428571429	-1.34142857142857
7	106.47	107.759428571429	-1.28942857142858
8	106.59	108.015428571429	-1.42542857142858
9	106.76	108.469428571429	-1.70942857142857
10	107.35	110.132571428571	-2.78257142857144
11	107.81	110.435071428571	-2.62507142857143
12	108.03	110.620071428571	-2.59007142857143
13	109.08	110.465714285714	-1.38571428571429
14	109.86	110.811714285714	-0.951714285714292
15	110.29	110.927714285714	-0.637714285714282
16	110.34	111.155714285714	-0.815714285714287
17	110.59	111.383714285714	-0.793714285714284
18	110.64	111.449714285714	-0.80971428571429
19	110.83	111.467714285714	-0.637714285714289
20	111.51	111.723714285714	-0.213714285714284
21	113.32	112.177714285714	1.14228571428571
22	115.89	113.840857142857	2.04914285714286
23	116.51	114.143357142857	2.36664285714286
24	117.44	114.328357142857	3.11164285714286
25	118.25	114.174	4.07599999999998
26	118.65	114.52	4.13
27	118.52	114.636	3.88399999999999
28	119.07	114.864	4.20599999999999
29	119.12	115.092	4.02800000000000
30	119.28	115.158	4.122
31	119.3	115.176	4.124
32	119.44	115.432	4.008
33	119.57	115.886	3.68400000000000
34	119.93	117.549142857143	2.38085714285715
35	120.03	117.851642857143	2.17835714285714
36	119.66	118.036642857143	1.62335714285714
37	119.46	117.882285714286	1.57771428571427
38	119.48	118.228285714286	1.25171428571429
39	119.56	118.344285714286	1.21571428571429
40	119.43	118.572285714286	0.857714285714295
41	119.57	118.800285714286	0.769714285714281
42	119.59	118.866285714286	0.72371428571429
43	119.5	118.884285714286	0.61571428571429
44	119.54	119.140285714286	0.399714285714294
45	119.56	119.594285714286	-0.0342857142857081
46	119.61	121.257428571429	-1.64742857142857
47	119.64	121.559928571429	-1.91992857142857
48	119.6	121.744928571429	-2.14492857142857
49	119.71	121.590571428571	-1.88057142857145
50	119.72	121.936571428571	-2.21657142857143
51	119.66	122.052571428571	-2.39257142857143
52	119.76	122.280571428571	-2.52057142857142
53	119.8	122.508571428571	-2.70857142857143
54	119.88	122.574571428571	-2.69457142857143
55	119.78	122.592571428571	-2.81257142857142
56	120.08	122.848571428571	-2.76857142857143
57	120.22	123.302571428571	-3.08257142857142

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 104.37 & 106.757428571429 & -2.38742857142851 \tabularnewline
2 & 104.89 & 107.103428571429 & -2.21342857142857 \tabularnewline
3 & 105.15 & 107.219428571429 & -2.06942857142857 \tabularnewline
4 & 105.72 & 107.447428571429 & -1.72742857142858 \tabularnewline
5 & 106.38 & 107.675428571429 & -1.29542857142858 \tabularnewline
6 & 106.4 & 107.741428571429 & -1.34142857142857 \tabularnewline
7 & 106.47 & 107.759428571429 & -1.28942857142858 \tabularnewline
8 & 106.59 & 108.015428571429 & -1.42542857142858 \tabularnewline
9 & 106.76 & 108.469428571429 & -1.70942857142857 \tabularnewline
10 & 107.35 & 110.132571428571 & -2.78257142857144 \tabularnewline
11 & 107.81 & 110.435071428571 & -2.62507142857143 \tabularnewline
12 & 108.03 & 110.620071428571 & -2.59007142857143 \tabularnewline
13 & 109.08 & 110.465714285714 & -1.38571428571429 \tabularnewline
14 & 109.86 & 110.811714285714 & -0.951714285714292 \tabularnewline
15 & 110.29 & 110.927714285714 & -0.637714285714282 \tabularnewline
16 & 110.34 & 111.155714285714 & -0.815714285714287 \tabularnewline
17 & 110.59 & 111.383714285714 & -0.793714285714284 \tabularnewline
18 & 110.64 & 111.449714285714 & -0.80971428571429 \tabularnewline
19 & 110.83 & 111.467714285714 & -0.637714285714289 \tabularnewline
20 & 111.51 & 111.723714285714 & -0.213714285714284 \tabularnewline
21 & 113.32 & 112.177714285714 & 1.14228571428571 \tabularnewline
22 & 115.89 & 113.840857142857 & 2.04914285714286 \tabularnewline
23 & 116.51 & 114.143357142857 & 2.36664285714286 \tabularnewline
24 & 117.44 & 114.328357142857 & 3.11164285714286 \tabularnewline
25 & 118.25 & 114.174 & 4.07599999999998 \tabularnewline
26 & 118.65 & 114.52 & 4.13 \tabularnewline
27 & 118.52 & 114.636 & 3.88399999999999 \tabularnewline
28 & 119.07 & 114.864 & 4.20599999999999 \tabularnewline
29 & 119.12 & 115.092 & 4.02800000000000 \tabularnewline
30 & 119.28 & 115.158 & 4.122 \tabularnewline
31 & 119.3 & 115.176 & 4.124 \tabularnewline
32 & 119.44 & 115.432 & 4.008 \tabularnewline
33 & 119.57 & 115.886 & 3.68400000000000 \tabularnewline
34 & 119.93 & 117.549142857143 & 2.38085714285715 \tabularnewline
35 & 120.03 & 117.851642857143 & 2.17835714285714 \tabularnewline
36 & 119.66 & 118.036642857143 & 1.62335714285714 \tabularnewline
37 & 119.46 & 117.882285714286 & 1.57771428571427 \tabularnewline
38 & 119.48 & 118.228285714286 & 1.25171428571429 \tabularnewline
39 & 119.56 & 118.344285714286 & 1.21571428571429 \tabularnewline
40 & 119.43 & 118.572285714286 & 0.857714285714295 \tabularnewline
41 & 119.57 & 118.800285714286 & 0.769714285714281 \tabularnewline
42 & 119.59 & 118.866285714286 & 0.72371428571429 \tabularnewline
43 & 119.5 & 118.884285714286 & 0.61571428571429 \tabularnewline
44 & 119.54 & 119.140285714286 & 0.399714285714294 \tabularnewline
45 & 119.56 & 119.594285714286 & -0.0342857142857081 \tabularnewline
46 & 119.61 & 121.257428571429 & -1.64742857142857 \tabularnewline
47 & 119.64 & 121.559928571429 & -1.91992857142857 \tabularnewline
48 & 119.6 & 121.744928571429 & -2.14492857142857 \tabularnewline
49 & 119.71 & 121.590571428571 & -1.88057142857145 \tabularnewline
50 & 119.72 & 121.936571428571 & -2.21657142857143 \tabularnewline
51 & 119.66 & 122.052571428571 & -2.39257142857143 \tabularnewline
52 & 119.76 & 122.280571428571 & -2.52057142857142 \tabularnewline
53 & 119.8 & 122.508571428571 & -2.70857142857143 \tabularnewline
54 & 119.88 & 122.574571428571 & -2.69457142857143 \tabularnewline
55 & 119.78 & 122.592571428571 & -2.81257142857142 \tabularnewline
56 & 120.08 & 122.848571428571 & -2.76857142857143 \tabularnewline
57 & 120.22 & 123.302571428571 & -3.08257142857142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&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]104.37[/C][C]106.757428571429[/C][C]-2.38742857142851[/C][/ROW]
[ROW][C]2[/C][C]104.89[/C][C]107.103428571429[/C][C]-2.21342857142857[/C][/ROW]
[ROW][C]3[/C][C]105.15[/C][C]107.219428571429[/C][C]-2.06942857142857[/C][/ROW]
[ROW][C]4[/C][C]105.72[/C][C]107.447428571429[/C][C]-1.72742857142858[/C][/ROW]
[ROW][C]5[/C][C]106.38[/C][C]107.675428571429[/C][C]-1.29542857142858[/C][/ROW]
[ROW][C]6[/C][C]106.4[/C][C]107.741428571429[/C][C]-1.34142857142857[/C][/ROW]
[ROW][C]7[/C][C]106.47[/C][C]107.759428571429[/C][C]-1.28942857142858[/C][/ROW]
[ROW][C]8[/C][C]106.59[/C][C]108.015428571429[/C][C]-1.42542857142858[/C][/ROW]
[ROW][C]9[/C][C]106.76[/C][C]108.469428571429[/C][C]-1.70942857142857[/C][/ROW]
[ROW][C]10[/C][C]107.35[/C][C]110.132571428571[/C][C]-2.78257142857144[/C][/ROW]
[ROW][C]11[/C][C]107.81[/C][C]110.435071428571[/C][C]-2.62507142857143[/C][/ROW]
[ROW][C]12[/C][C]108.03[/C][C]110.620071428571[/C][C]-2.59007142857143[/C][/ROW]
[ROW][C]13[/C][C]109.08[/C][C]110.465714285714[/C][C]-1.38571428571429[/C][/ROW]
[ROW][C]14[/C][C]109.86[/C][C]110.811714285714[/C][C]-0.951714285714292[/C][/ROW]
[ROW][C]15[/C][C]110.29[/C][C]110.927714285714[/C][C]-0.637714285714282[/C][/ROW]
[ROW][C]16[/C][C]110.34[/C][C]111.155714285714[/C][C]-0.815714285714287[/C][/ROW]
[ROW][C]17[/C][C]110.59[/C][C]111.383714285714[/C][C]-0.793714285714284[/C][/ROW]
[ROW][C]18[/C][C]110.64[/C][C]111.449714285714[/C][C]-0.80971428571429[/C][/ROW]
[ROW][C]19[/C][C]110.83[/C][C]111.467714285714[/C][C]-0.637714285714289[/C][/ROW]
[ROW][C]20[/C][C]111.51[/C][C]111.723714285714[/C][C]-0.213714285714284[/C][/ROW]
[ROW][C]21[/C][C]113.32[/C][C]112.177714285714[/C][C]1.14228571428571[/C][/ROW]
[ROW][C]22[/C][C]115.89[/C][C]113.840857142857[/C][C]2.04914285714286[/C][/ROW]
[ROW][C]23[/C][C]116.51[/C][C]114.143357142857[/C][C]2.36664285714286[/C][/ROW]
[ROW][C]24[/C][C]117.44[/C][C]114.328357142857[/C][C]3.11164285714286[/C][/ROW]
[ROW][C]25[/C][C]118.25[/C][C]114.174[/C][C]4.07599999999998[/C][/ROW]
[ROW][C]26[/C][C]118.65[/C][C]114.52[/C][C]4.13[/C][/ROW]
[ROW][C]27[/C][C]118.52[/C][C]114.636[/C][C]3.88399999999999[/C][/ROW]
[ROW][C]28[/C][C]119.07[/C][C]114.864[/C][C]4.20599999999999[/C][/ROW]
[ROW][C]29[/C][C]119.12[/C][C]115.092[/C][C]4.02800000000000[/C][/ROW]
[ROW][C]30[/C][C]119.28[/C][C]115.158[/C][C]4.122[/C][/ROW]
[ROW][C]31[/C][C]119.3[/C][C]115.176[/C][C]4.124[/C][/ROW]
[ROW][C]32[/C][C]119.44[/C][C]115.432[/C][C]4.008[/C][/ROW]
[ROW][C]33[/C][C]119.57[/C][C]115.886[/C][C]3.68400000000000[/C][/ROW]
[ROW][C]34[/C][C]119.93[/C][C]117.549142857143[/C][C]2.38085714285715[/C][/ROW]
[ROW][C]35[/C][C]120.03[/C][C]117.851642857143[/C][C]2.17835714285714[/C][/ROW]
[ROW][C]36[/C][C]119.66[/C][C]118.036642857143[/C][C]1.62335714285714[/C][/ROW]
[ROW][C]37[/C][C]119.46[/C][C]117.882285714286[/C][C]1.57771428571427[/C][/ROW]
[ROW][C]38[/C][C]119.48[/C][C]118.228285714286[/C][C]1.25171428571429[/C][/ROW]
[ROW][C]39[/C][C]119.56[/C][C]118.344285714286[/C][C]1.21571428571429[/C][/ROW]
[ROW][C]40[/C][C]119.43[/C][C]118.572285714286[/C][C]0.857714285714295[/C][/ROW]
[ROW][C]41[/C][C]119.57[/C][C]118.800285714286[/C][C]0.769714285714281[/C][/ROW]
[ROW][C]42[/C][C]119.59[/C][C]118.866285714286[/C][C]0.72371428571429[/C][/ROW]
[ROW][C]43[/C][C]119.5[/C][C]118.884285714286[/C][C]0.61571428571429[/C][/ROW]
[ROW][C]44[/C][C]119.54[/C][C]119.140285714286[/C][C]0.399714285714294[/C][/ROW]
[ROW][C]45[/C][C]119.56[/C][C]119.594285714286[/C][C]-0.0342857142857081[/C][/ROW]
[ROW][C]46[/C][C]119.61[/C][C]121.257428571429[/C][C]-1.64742857142857[/C][/ROW]
[ROW][C]47[/C][C]119.64[/C][C]121.559928571429[/C][C]-1.91992857142857[/C][/ROW]
[ROW][C]48[/C][C]119.6[/C][C]121.744928571429[/C][C]-2.14492857142857[/C][/ROW]
[ROW][C]49[/C][C]119.71[/C][C]121.590571428571[/C][C]-1.88057142857145[/C][/ROW]
[ROW][C]50[/C][C]119.72[/C][C]121.936571428571[/C][C]-2.21657142857143[/C][/ROW]
[ROW][C]51[/C][C]119.66[/C][C]122.052571428571[/C][C]-2.39257142857143[/C][/ROW]
[ROW][C]52[/C][C]119.76[/C][C]122.280571428571[/C][C]-2.52057142857142[/C][/ROW]
[ROW][C]53[/C][C]119.8[/C][C]122.508571428571[/C][C]-2.70857142857143[/C][/ROW]
[ROW][C]54[/C][C]119.88[/C][C]122.574571428571[/C][C]-2.69457142857143[/C][/ROW]
[ROW][C]55[/C][C]119.78[/C][C]122.592571428571[/C][C]-2.81257142857142[/C][/ROW]
[ROW][C]56[/C][C]120.08[/C][C]122.848571428571[/C][C]-2.76857142857143[/C][/ROW]
[ROW][C]57[/C][C]120.22[/C][C]123.302571428571[/C][C]-3.08257142857142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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	104.37	106.757428571429	-2.38742857142851
2	104.89	107.103428571429	-2.21342857142857
3	105.15	107.219428571429	-2.06942857142857
4	105.72	107.447428571429	-1.72742857142858
5	106.38	107.675428571429	-1.29542857142858
6	106.4	107.741428571429	-1.34142857142857
7	106.47	107.759428571429	-1.28942857142858
8	106.59	108.015428571429	-1.42542857142858
9	106.76	108.469428571429	-1.70942857142857
10	107.35	110.132571428571	-2.78257142857144
11	107.81	110.435071428571	-2.62507142857143
12	108.03	110.620071428571	-2.59007142857143
13	109.08	110.465714285714	-1.38571428571429
14	109.86	110.811714285714	-0.951714285714292
15	110.29	110.927714285714	-0.637714285714282
16	110.34	111.155714285714	-0.815714285714287
17	110.59	111.383714285714	-0.793714285714284
18	110.64	111.449714285714	-0.80971428571429
19	110.83	111.467714285714	-0.637714285714289
20	111.51	111.723714285714	-0.213714285714284
21	113.32	112.177714285714	1.14228571428571
22	115.89	113.840857142857	2.04914285714286
23	116.51	114.143357142857	2.36664285714286
24	117.44	114.328357142857	3.11164285714286
25	118.25	114.174	4.07599999999998
26	118.65	114.52	4.13
27	118.52	114.636	3.88399999999999
28	119.07	114.864	4.20599999999999
29	119.12	115.092	4.02800000000000
30	119.28	115.158	4.122
31	119.3	115.176	4.124
32	119.44	115.432	4.008
33	119.57	115.886	3.68400000000000
34	119.93	117.549142857143	2.38085714285715
35	120.03	117.851642857143	2.17835714285714
36	119.66	118.036642857143	1.62335714285714
37	119.46	117.882285714286	1.57771428571427
38	119.48	118.228285714286	1.25171428571429
39	119.56	118.344285714286	1.21571428571429
40	119.43	118.572285714286	0.857714285714295
41	119.57	118.800285714286	0.769714285714281
42	119.59	118.866285714286	0.72371428571429
43	119.5	118.884285714286	0.61571428571429
44	119.54	119.140285714286	0.399714285714294
45	119.56	119.594285714286	-0.0342857142857081
46	119.61	121.257428571429	-1.64742857142857
47	119.64	121.559928571429	-1.91992857142857
48	119.6	121.744928571429	-2.14492857142857
49	119.71	121.590571428571	-1.88057142857145
50	119.72	121.936571428571	-2.21657142857143
51	119.66	122.052571428571	-2.39257142857143
52	119.76	122.280571428571	-2.52057142857142
53	119.8	122.508571428571	-2.70857142857143
54	119.88	122.574571428571	-2.69457142857143
55	119.78	122.592571428571	-2.81257142857142
56	120.08	122.848571428571	-2.76857142857143
57	120.22	123.302571428571	-3.08257142857142

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.000711758411078018	0.00142351682215604	0.999288241588922
17	0.000548751110497066	0.00109750222099413	0.999451248889503
18	0.00024082349950649	0.00048164699901298	0.999759176500494
19	0.000120351888149118	0.000240703776298235	0.99987964811185
20	0.000201679518095747	0.000403359036191494	0.999798320481904
21	0.115964327761146	0.231928655522292	0.884035672238854
22	0.967739156888554	0.0645216862228915	0.0322608431114457
23	0.99998435332589	3.12933482197734e-05	1.56466741098867e-05
24	0.999999996306932	7.38613661568576e-09	3.69306830784288e-09
25	0.99999999981083	3.78337779341133e-10	1.89168889670566e-10
26	0.999999999853872	2.92255241606575e-10	1.46127620803288e-10
27	0.999999999975598	4.88048978936672e-11	2.44024489468336e-11
28	0.999999999884767	2.30465525303569e-10	1.15232762651784e-10
29	0.999999999491633	1.01673375893903e-09	5.08366879469517e-10
30	0.999999997128625	5.74274934984942e-09	2.87137467492471e-09
31	0.99999998120785	3.75842996495553e-08	1.87921498247776e-08
32	0.999999884838874	2.30322251359141e-07	1.15161125679571e-07
33	0.999999340400447	1.31919910594486e-06	6.59599552972431e-07
34	0.999999351312276	1.29737544724931e-06	6.48687723624653e-07
35	0.999999897923116	2.04153767742508e-07	1.02076883871254e-07
36	0.999999912374499	1.75251002715106e-07	8.76255013575532e-08
37	0.999999608809729	7.82380542561824e-07	3.91190271280912e-07
38	0.999997793185787	4.41362842620912e-06	2.20681421310456e-06
39	0.999993003271502	1.39934569956719e-05	6.99672849783594e-06
40	0.99992747611316	0.000145047773679456	7.25238868397279e-05
41	0.999445611800604	0.00110877639879158	0.000554388199395789

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.000711758411078018 & 0.00142351682215604 & 0.999288241588922 \tabularnewline
17 & 0.000548751110497066 & 0.00109750222099413 & 0.999451248889503 \tabularnewline
18 & 0.00024082349950649 & 0.00048164699901298 & 0.999759176500494 \tabularnewline
19 & 0.000120351888149118 & 0.000240703776298235 & 0.99987964811185 \tabularnewline
20 & 0.000201679518095747 & 0.000403359036191494 & 0.999798320481904 \tabularnewline
21 & 0.115964327761146 & 0.231928655522292 & 0.884035672238854 \tabularnewline
22 & 0.967739156888554 & 0.0645216862228915 & 0.0322608431114457 \tabularnewline
23 & 0.99998435332589 & 3.12933482197734e-05 & 1.56466741098867e-05 \tabularnewline
24 & 0.999999996306932 & 7.38613661568576e-09 & 3.69306830784288e-09 \tabularnewline
25 & 0.99999999981083 & 3.78337779341133e-10 & 1.89168889670566e-10 \tabularnewline
26 & 0.999999999853872 & 2.92255241606575e-10 & 1.46127620803288e-10 \tabularnewline
27 & 0.999999999975598 & 4.88048978936672e-11 & 2.44024489468336e-11 \tabularnewline
28 & 0.999999999884767 & 2.30465525303569e-10 & 1.15232762651784e-10 \tabularnewline
29 & 0.999999999491633 & 1.01673375893903e-09 & 5.08366879469517e-10 \tabularnewline
30 & 0.999999997128625 & 5.74274934984942e-09 & 2.87137467492471e-09 \tabularnewline
31 & 0.99999998120785 & 3.75842996495553e-08 & 1.87921498247776e-08 \tabularnewline
32 & 0.999999884838874 & 2.30322251359141e-07 & 1.15161125679571e-07 \tabularnewline
33 & 0.999999340400447 & 1.31919910594486e-06 & 6.59599552972431e-07 \tabularnewline
34 & 0.999999351312276 & 1.29737544724931e-06 & 6.48687723624653e-07 \tabularnewline
35 & 0.999999897923116 & 2.04153767742508e-07 & 1.02076883871254e-07 \tabularnewline
36 & 0.999999912374499 & 1.75251002715106e-07 & 8.76255013575532e-08 \tabularnewline
37 & 0.999999608809729 & 7.82380542561824e-07 & 3.91190271280912e-07 \tabularnewline
38 & 0.999997793185787 & 4.41362842620912e-06 & 2.20681421310456e-06 \tabularnewline
39 & 0.999993003271502 & 1.39934569956719e-05 & 6.99672849783594e-06 \tabularnewline
40 & 0.99992747611316 & 0.000145047773679456 & 7.25238868397279e-05 \tabularnewline
41 & 0.999445611800604 & 0.00110877639879158 & 0.000554388199395789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&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]16[/C][C]0.000711758411078018[/C][C]0.00142351682215604[/C][C]0.999288241588922[/C][/ROW]
[ROW][C]17[/C][C]0.000548751110497066[/C][C]0.00109750222099413[/C][C]0.999451248889503[/C][/ROW]
[ROW][C]18[/C][C]0.00024082349950649[/C][C]0.00048164699901298[/C][C]0.999759176500494[/C][/ROW]
[ROW][C]19[/C][C]0.000120351888149118[/C][C]0.000240703776298235[/C][C]0.99987964811185[/C][/ROW]
[ROW][C]20[/C][C]0.000201679518095747[/C][C]0.000403359036191494[/C][C]0.999798320481904[/C][/ROW]
[ROW][C]21[/C][C]0.115964327761146[/C][C]0.231928655522292[/C][C]0.884035672238854[/C][/ROW]
[ROW][C]22[/C][C]0.967739156888554[/C][C]0.0645216862228915[/C][C]0.0322608431114457[/C][/ROW]
[ROW][C]23[/C][C]0.99998435332589[/C][C]3.12933482197734e-05[/C][C]1.56466741098867e-05[/C][/ROW]
[ROW][C]24[/C][C]0.999999996306932[/C][C]7.38613661568576e-09[/C][C]3.69306830784288e-09[/C][/ROW]
[ROW][C]25[/C][C]0.99999999981083[/C][C]3.78337779341133e-10[/C][C]1.89168889670566e-10[/C][/ROW]
[ROW][C]26[/C][C]0.999999999853872[/C][C]2.92255241606575e-10[/C][C]1.46127620803288e-10[/C][/ROW]
[ROW][C]27[/C][C]0.999999999975598[/C][C]4.88048978936672e-11[/C][C]2.44024489468336e-11[/C][/ROW]
[ROW][C]28[/C][C]0.999999999884767[/C][C]2.30465525303569e-10[/C][C]1.15232762651784e-10[/C][/ROW]
[ROW][C]29[/C][C]0.999999999491633[/C][C]1.01673375893903e-09[/C][C]5.08366879469517e-10[/C][/ROW]
[ROW][C]30[/C][C]0.999999997128625[/C][C]5.74274934984942e-09[/C][C]2.87137467492471e-09[/C][/ROW]
[ROW][C]31[/C][C]0.99999998120785[/C][C]3.75842996495553e-08[/C][C]1.87921498247776e-08[/C][/ROW]
[ROW][C]32[/C][C]0.999999884838874[/C][C]2.30322251359141e-07[/C][C]1.15161125679571e-07[/C][/ROW]
[ROW][C]33[/C][C]0.999999340400447[/C][C]1.31919910594486e-06[/C][C]6.59599552972431e-07[/C][/ROW]
[ROW][C]34[/C][C]0.999999351312276[/C][C]1.29737544724931e-06[/C][C]6.48687723624653e-07[/C][/ROW]
[ROW][C]35[/C][C]0.999999897923116[/C][C]2.04153767742508e-07[/C][C]1.02076883871254e-07[/C][/ROW]
[ROW][C]36[/C][C]0.999999912374499[/C][C]1.75251002715106e-07[/C][C]8.76255013575532e-08[/C][/ROW]
[ROW][C]37[/C][C]0.999999608809729[/C][C]7.82380542561824e-07[/C][C]3.91190271280912e-07[/C][/ROW]
[ROW][C]38[/C][C]0.999997793185787[/C][C]4.41362842620912e-06[/C][C]2.20681421310456e-06[/C][/ROW]
[ROW][C]39[/C][C]0.999993003271502[/C][C]1.39934569956719e-05[/C][C]6.99672849783594e-06[/C][/ROW]
[ROW][C]40[/C][C]0.99992747611316[/C][C]0.000145047773679456[/C][C]7.25238868397279e-05[/C][/ROW]
[ROW][C]41[/C][C]0.999445611800604[/C][C]0.00110877639879158[/C][C]0.000554388199395789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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
16	0.000711758411078018	0.00142351682215604	0.999288241588922
17	0.000548751110497066	0.00109750222099413	0.999451248889503
18	0.00024082349950649	0.00048164699901298	0.999759176500494
19	0.000120351888149118	0.000240703776298235	0.99987964811185
20	0.000201679518095747	0.000403359036191494	0.999798320481904
21	0.115964327761146	0.231928655522292	0.884035672238854
22	0.967739156888554	0.0645216862228915	0.0322608431114457
23	0.99998435332589	3.12933482197734e-05	1.56466741098867e-05
24	0.999999996306932	7.38613661568576e-09	3.69306830784288e-09
25	0.99999999981083	3.78337779341133e-10	1.89168889670566e-10
26	0.999999999853872	2.92255241606575e-10	1.46127620803288e-10
27	0.999999999975598	4.88048978936672e-11	2.44024489468336e-11
28	0.999999999884767	2.30465525303569e-10	1.15232762651784e-10
29	0.999999999491633	1.01673375893903e-09	5.08366879469517e-10
30	0.999999997128625	5.74274934984942e-09	2.87137467492471e-09
31	0.99999998120785	3.75842996495553e-08	1.87921498247776e-08
32	0.999999884838874	2.30322251359141e-07	1.15161125679571e-07
33	0.999999340400447	1.31919910594486e-06	6.59599552972431e-07
34	0.999999351312276	1.29737544724931e-06	6.48687723624653e-07
35	0.999999897923116	2.04153767742508e-07	1.02076883871254e-07
36	0.999999912374499	1.75251002715106e-07	8.76255013575532e-08
37	0.999999608809729	7.82380542561824e-07	3.91190271280912e-07
38	0.999997793185787	4.41362842620912e-06	2.20681421310456e-06
39	0.999993003271502	1.39934569956719e-05	6.99672849783594e-06
40	0.99992747611316	0.000145047773679456	7.25238868397279e-05
41	0.999445611800604	0.00110877639879158	0.000554388199395789

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	24	0.923076923076923	NOK
5% type I error level	24	0.923076923076923	NOK
10% type I error level	25	0.961538461538462	NOK

\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 & 24 & 0.923076923076923 & NOK \tabularnewline
5% type I error level & 24 & 0.923076923076923 & NOK \tabularnewline
10% type I error level & 25 & 0.961538461538462 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112103&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]24[/C][C]0.923076923076923[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]24[/C][C]0.923076923076923[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]25[/C][C]0.961538461538462[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112103&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112103&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	24	0.923076923076923	NOK
5% type I error level	24	0.923076923076923	NOK
10% type I error level	25	0.961538461538462	NOK

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 = Include Monthly Dummies ; par3 = 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], 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,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
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, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
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,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
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,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
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,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
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,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
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