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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 10:30:56 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258738527l5se3b3c6jzz9oc.htm/, Retrieved Fri, 29 Mar 2024 05:57:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58357, Retrieved Fri, 29 Mar 2024 05:57:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Icons vs. Inprod] [2009-11-18 16:53:03] [8b10896fd8c0913ff1dc4e6dd35f743c]
- R  D    [Multiple Regression] [] [2009-11-20 17:30:56] [18c0746232b29e9668aa6bedcb8dd698] [Current]
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Dataseries X:
12,6	18
15,7	16
13,2	19
20,3	18
12,8	23
8	20
0,9	20
3,6	15
14,1	17
21,7	16
24,5	15
18,9	10
13,9	13
11	10
5,8	19
15,5	21
22,4	17
31,7	16
30,3	17
31,4	14
20,2	18
19,7	17
10,8	14
13,2	15
15,1	16
15,6	11
15,5	15
12,7	13
10,9	17
10	16
9,1	9
10,3	17
16,9	15
22	12
27,6	12
28,9	12
31	12
32,9	4
38,1	7
28,8	4
29	3
21,8	3
28,8	0
25,6	5
28,2	3
20,2	4
17,9	3
16,3	10
13,2	4
8,1	1
4,5	1
-0,1	8
0	5
2,3	4
2,8	0
2,9	2
0,1	7
3,5	6
8,6	9
13,8	10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&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]3 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=58357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 16.3381031035382 -0.0223985047378945X[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  16.3381031035382 -0.0223985047378945X[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  16.3381031035382 -0.0223985047378945X[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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
Y[t] = + 16.3381031035382 -0.0223985047378945X[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)16.33810310353822.6259546.221800
X-0.02239850473789450.203793-0.10990.9128620.456431

\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) & 16.3381031035382 & 2.625954 & 6.2218 & 0 & 0 \tabularnewline
X & -0.0223985047378945 & 0.203793 & -0.1099 & 0.912862 & 0.456431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&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]16.3381031035382[/C][C]2.625954[/C][C]6.2218[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.0223985047378945[/C][C]0.203793[/C][C]-0.1099[/C][C]0.912862[/C][C]0.456431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)16.33810310353822.6259546.221800
X-0.02239850473789450.203793-0.10990.9128620.456431







Multiple Linear Regression - Regression Statistics
Multiple R0.0144301357461699
R-squared0.000208228817652892
Adjusted R-squared-0.0170295603406634
F-TEST (value)0.0120797867835872
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.91286168172439
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.77484659466084
Sum Squared Residuals5541.76230505086

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.0144301357461699 \tabularnewline
R-squared & 0.000208228817652892 \tabularnewline
Adjusted R-squared & -0.0170295603406634 \tabularnewline
F-TEST (value) & 0.0120797867835872 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0.91286168172439 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.77484659466084 \tabularnewline
Sum Squared Residuals & 5541.76230505086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.0144301357461699[/C][/ROW]
[ROW][C]R-squared[/C][C]0.000208228817652892[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.0170295603406634[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.0120797867835872[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/C][/ROW]
[ROW][C]p-value[/C][C]0.91286168172439[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.77484659466084[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5541.76230505086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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 R0.0144301357461699
R-squared0.000208228817652892
Adjusted R-squared-0.0170295603406634
F-TEST (value)0.0120797867835872
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.91286168172439
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.77484659466084
Sum Squared Residuals5541.76230505086







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
112.615.9349300182561-3.33493001825614
215.715.9797270277319-0.27972702773189
313.215.9125315135182-2.71253151351821
420.315.93493001825614.36506998174390
512.815.8229374945666-3.02293749456663
6815.8901330087803-7.89013300878032
70.915.8901330087803-14.9901330087803
83.616.0021255324698-12.4021255324698
914.115.957328522994-1.857328522994
1021.715.97972702773195.7202729722681
1124.516.00212553246988.49787446753021
1218.916.11411805615932.78588194384074
1313.916.0469225419456-2.14692254194558
141116.1141180561593-5.11411805615926
155.815.9125315135182-10.1125315135182
1615.515.8677345040424-0.367734504042422
1722.415.9573285229946.442671477006
1831.715.979727027731915.7202729722681
1930.315.95732852299414.342671477006
2031.416.024524037207715.3754759627923
2120.215.93493001825614.26506998174389
2219.715.9573285229943.742671477006
2310.816.0245240372077-5.22452403720768
2413.216.0021255324698-2.80212553246979
2515.115.9797270277319-0.879727027731895
2615.616.0917195514214-0.491719551421368
2715.516.0021255324698-0.502125532469789
2812.716.0469225419456-3.34692254194558
2910.915.957328522994-5.057328522994
301015.9797270277319-5.9797270277319
319.116.1365165608972-7.03651656089716
3210.315.957328522994-5.657328522994
3316.916.00212553246980.897874467530209
342216.06932104668355.93067895331653
3527.616.069321046683511.5306789533165
3628.916.069321046683512.8306789533165
373116.069321046683514.9306789533165
3832.916.248509084586616.6514909154134
3938.116.181313570372921.9186864296271
4028.816.248509084586612.5514909154134
412916.270907589324512.7290924106755
4221.816.27090758932455.52909241067548
4328.816.338103103538212.4618968964618
4425.616.22611057984879.37388942015127
4528.216.270907589324511.9290924106755
4620.216.24850908458663.95149091541337
4717.916.27090758932451.62909241067547
4816.316.11411805615930.185881943840738
4913.216.2485090845866-3.04850908458663
508.116.3157045988003-8.21570459880031
514.516.3157045988003-11.8157045988003
52-0.116.1589150656350-16.2589150656351
53016.2261105798487-16.2261105798487
542.316.2485090845866-13.9485090845866
552.816.3381031035382-13.5381031035382
562.916.2933060940624-13.3933060940624
570.116.1813135703729-16.0813135703729
583.516.2037120751108-12.7037120751108
598.616.1365165608972-7.53651656089716
6013.816.1141180561593-2.31411805615926

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.6 & 15.9349300182561 & -3.33493001825614 \tabularnewline
2 & 15.7 & 15.9797270277319 & -0.27972702773189 \tabularnewline
3 & 13.2 & 15.9125315135182 & -2.71253151351821 \tabularnewline
4 & 20.3 & 15.9349300182561 & 4.36506998174390 \tabularnewline
5 & 12.8 & 15.8229374945666 & -3.02293749456663 \tabularnewline
6 & 8 & 15.8901330087803 & -7.89013300878032 \tabularnewline
7 & 0.9 & 15.8901330087803 & -14.9901330087803 \tabularnewline
8 & 3.6 & 16.0021255324698 & -12.4021255324698 \tabularnewline
9 & 14.1 & 15.957328522994 & -1.857328522994 \tabularnewline
10 & 21.7 & 15.9797270277319 & 5.7202729722681 \tabularnewline
11 & 24.5 & 16.0021255324698 & 8.49787446753021 \tabularnewline
12 & 18.9 & 16.1141180561593 & 2.78588194384074 \tabularnewline
13 & 13.9 & 16.0469225419456 & -2.14692254194558 \tabularnewline
14 & 11 & 16.1141180561593 & -5.11411805615926 \tabularnewline
15 & 5.8 & 15.9125315135182 & -10.1125315135182 \tabularnewline
16 & 15.5 & 15.8677345040424 & -0.367734504042422 \tabularnewline
17 & 22.4 & 15.957328522994 & 6.442671477006 \tabularnewline
18 & 31.7 & 15.9797270277319 & 15.7202729722681 \tabularnewline
19 & 30.3 & 15.957328522994 & 14.342671477006 \tabularnewline
20 & 31.4 & 16.0245240372077 & 15.3754759627923 \tabularnewline
21 & 20.2 & 15.9349300182561 & 4.26506998174389 \tabularnewline
22 & 19.7 & 15.957328522994 & 3.742671477006 \tabularnewline
23 & 10.8 & 16.0245240372077 & -5.22452403720768 \tabularnewline
24 & 13.2 & 16.0021255324698 & -2.80212553246979 \tabularnewline
25 & 15.1 & 15.9797270277319 & -0.879727027731895 \tabularnewline
26 & 15.6 & 16.0917195514214 & -0.491719551421368 \tabularnewline
27 & 15.5 & 16.0021255324698 & -0.502125532469789 \tabularnewline
28 & 12.7 & 16.0469225419456 & -3.34692254194558 \tabularnewline
29 & 10.9 & 15.957328522994 & -5.057328522994 \tabularnewline
30 & 10 & 15.9797270277319 & -5.9797270277319 \tabularnewline
31 & 9.1 & 16.1365165608972 & -7.03651656089716 \tabularnewline
32 & 10.3 & 15.957328522994 & -5.657328522994 \tabularnewline
33 & 16.9 & 16.0021255324698 & 0.897874467530209 \tabularnewline
34 & 22 & 16.0693210466835 & 5.93067895331653 \tabularnewline
35 & 27.6 & 16.0693210466835 & 11.5306789533165 \tabularnewline
36 & 28.9 & 16.0693210466835 & 12.8306789533165 \tabularnewline
37 & 31 & 16.0693210466835 & 14.9306789533165 \tabularnewline
38 & 32.9 & 16.2485090845866 & 16.6514909154134 \tabularnewline
39 & 38.1 & 16.1813135703729 & 21.9186864296271 \tabularnewline
40 & 28.8 & 16.2485090845866 & 12.5514909154134 \tabularnewline
41 & 29 & 16.2709075893245 & 12.7290924106755 \tabularnewline
42 & 21.8 & 16.2709075893245 & 5.52909241067548 \tabularnewline
43 & 28.8 & 16.3381031035382 & 12.4618968964618 \tabularnewline
44 & 25.6 & 16.2261105798487 & 9.37388942015127 \tabularnewline
45 & 28.2 & 16.2709075893245 & 11.9290924106755 \tabularnewline
46 & 20.2 & 16.2485090845866 & 3.95149091541337 \tabularnewline
47 & 17.9 & 16.2709075893245 & 1.62909241067547 \tabularnewline
48 & 16.3 & 16.1141180561593 & 0.185881943840738 \tabularnewline
49 & 13.2 & 16.2485090845866 & -3.04850908458663 \tabularnewline
50 & 8.1 & 16.3157045988003 & -8.21570459880031 \tabularnewline
51 & 4.5 & 16.3157045988003 & -11.8157045988003 \tabularnewline
52 & -0.1 & 16.1589150656350 & -16.2589150656351 \tabularnewline
53 & 0 & 16.2261105798487 & -16.2261105798487 \tabularnewline
54 & 2.3 & 16.2485090845866 & -13.9485090845866 \tabularnewline
55 & 2.8 & 16.3381031035382 & -13.5381031035382 \tabularnewline
56 & 2.9 & 16.2933060940624 & -13.3933060940624 \tabularnewline
57 & 0.1 & 16.1813135703729 & -16.0813135703729 \tabularnewline
58 & 3.5 & 16.2037120751108 & -12.7037120751108 \tabularnewline
59 & 8.6 & 16.1365165608972 & -7.53651656089716 \tabularnewline
60 & 13.8 & 16.1141180561593 & -2.31411805615926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&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]12.6[/C][C]15.9349300182561[/C][C]-3.33493001825614[/C][/ROW]
[ROW][C]2[/C][C]15.7[/C][C]15.9797270277319[/C][C]-0.27972702773189[/C][/ROW]
[ROW][C]3[/C][C]13.2[/C][C]15.9125315135182[/C][C]-2.71253151351821[/C][/ROW]
[ROW][C]4[/C][C]20.3[/C][C]15.9349300182561[/C][C]4.36506998174390[/C][/ROW]
[ROW][C]5[/C][C]12.8[/C][C]15.8229374945666[/C][C]-3.02293749456663[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]15.8901330087803[/C][C]-7.89013300878032[/C][/ROW]
[ROW][C]7[/C][C]0.9[/C][C]15.8901330087803[/C][C]-14.9901330087803[/C][/ROW]
[ROW][C]8[/C][C]3.6[/C][C]16.0021255324698[/C][C]-12.4021255324698[/C][/ROW]
[ROW][C]9[/C][C]14.1[/C][C]15.957328522994[/C][C]-1.857328522994[/C][/ROW]
[ROW][C]10[/C][C]21.7[/C][C]15.9797270277319[/C][C]5.7202729722681[/C][/ROW]
[ROW][C]11[/C][C]24.5[/C][C]16.0021255324698[/C][C]8.49787446753021[/C][/ROW]
[ROW][C]12[/C][C]18.9[/C][C]16.1141180561593[/C][C]2.78588194384074[/C][/ROW]
[ROW][C]13[/C][C]13.9[/C][C]16.0469225419456[/C][C]-2.14692254194558[/C][/ROW]
[ROW][C]14[/C][C]11[/C][C]16.1141180561593[/C][C]-5.11411805615926[/C][/ROW]
[ROW][C]15[/C][C]5.8[/C][C]15.9125315135182[/C][C]-10.1125315135182[/C][/ROW]
[ROW][C]16[/C][C]15.5[/C][C]15.8677345040424[/C][C]-0.367734504042422[/C][/ROW]
[ROW][C]17[/C][C]22.4[/C][C]15.957328522994[/C][C]6.442671477006[/C][/ROW]
[ROW][C]18[/C][C]31.7[/C][C]15.9797270277319[/C][C]15.7202729722681[/C][/ROW]
[ROW][C]19[/C][C]30.3[/C][C]15.957328522994[/C][C]14.342671477006[/C][/ROW]
[ROW][C]20[/C][C]31.4[/C][C]16.0245240372077[/C][C]15.3754759627923[/C][/ROW]
[ROW][C]21[/C][C]20.2[/C][C]15.9349300182561[/C][C]4.26506998174389[/C][/ROW]
[ROW][C]22[/C][C]19.7[/C][C]15.957328522994[/C][C]3.742671477006[/C][/ROW]
[ROW][C]23[/C][C]10.8[/C][C]16.0245240372077[/C][C]-5.22452403720768[/C][/ROW]
[ROW][C]24[/C][C]13.2[/C][C]16.0021255324698[/C][C]-2.80212553246979[/C][/ROW]
[ROW][C]25[/C][C]15.1[/C][C]15.9797270277319[/C][C]-0.879727027731895[/C][/ROW]
[ROW][C]26[/C][C]15.6[/C][C]16.0917195514214[/C][C]-0.491719551421368[/C][/ROW]
[ROW][C]27[/C][C]15.5[/C][C]16.0021255324698[/C][C]-0.502125532469789[/C][/ROW]
[ROW][C]28[/C][C]12.7[/C][C]16.0469225419456[/C][C]-3.34692254194558[/C][/ROW]
[ROW][C]29[/C][C]10.9[/C][C]15.957328522994[/C][C]-5.057328522994[/C][/ROW]
[ROW][C]30[/C][C]10[/C][C]15.9797270277319[/C][C]-5.9797270277319[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]16.1365165608972[/C][C]-7.03651656089716[/C][/ROW]
[ROW][C]32[/C][C]10.3[/C][C]15.957328522994[/C][C]-5.657328522994[/C][/ROW]
[ROW][C]33[/C][C]16.9[/C][C]16.0021255324698[/C][C]0.897874467530209[/C][/ROW]
[ROW][C]34[/C][C]22[/C][C]16.0693210466835[/C][C]5.93067895331653[/C][/ROW]
[ROW][C]35[/C][C]27.6[/C][C]16.0693210466835[/C][C]11.5306789533165[/C][/ROW]
[ROW][C]36[/C][C]28.9[/C][C]16.0693210466835[/C][C]12.8306789533165[/C][/ROW]
[ROW][C]37[/C][C]31[/C][C]16.0693210466835[/C][C]14.9306789533165[/C][/ROW]
[ROW][C]38[/C][C]32.9[/C][C]16.2485090845866[/C][C]16.6514909154134[/C][/ROW]
[ROW][C]39[/C][C]38.1[/C][C]16.1813135703729[/C][C]21.9186864296271[/C][/ROW]
[ROW][C]40[/C][C]28.8[/C][C]16.2485090845866[/C][C]12.5514909154134[/C][/ROW]
[ROW][C]41[/C][C]29[/C][C]16.2709075893245[/C][C]12.7290924106755[/C][/ROW]
[ROW][C]42[/C][C]21.8[/C][C]16.2709075893245[/C][C]5.52909241067548[/C][/ROW]
[ROW][C]43[/C][C]28.8[/C][C]16.3381031035382[/C][C]12.4618968964618[/C][/ROW]
[ROW][C]44[/C][C]25.6[/C][C]16.2261105798487[/C][C]9.37388942015127[/C][/ROW]
[ROW][C]45[/C][C]28.2[/C][C]16.2709075893245[/C][C]11.9290924106755[/C][/ROW]
[ROW][C]46[/C][C]20.2[/C][C]16.2485090845866[/C][C]3.95149091541337[/C][/ROW]
[ROW][C]47[/C][C]17.9[/C][C]16.2709075893245[/C][C]1.62909241067547[/C][/ROW]
[ROW][C]48[/C][C]16.3[/C][C]16.1141180561593[/C][C]0.185881943840738[/C][/ROW]
[ROW][C]49[/C][C]13.2[/C][C]16.2485090845866[/C][C]-3.04850908458663[/C][/ROW]
[ROW][C]50[/C][C]8.1[/C][C]16.3157045988003[/C][C]-8.21570459880031[/C][/ROW]
[ROW][C]51[/C][C]4.5[/C][C]16.3157045988003[/C][C]-11.8157045988003[/C][/ROW]
[ROW][C]52[/C][C]-0.1[/C][C]16.1589150656350[/C][C]-16.2589150656351[/C][/ROW]
[ROW][C]53[/C][C]0[/C][C]16.2261105798487[/C][C]-16.2261105798487[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]16.2485090845866[/C][C]-13.9485090845866[/C][/ROW]
[ROW][C]55[/C][C]2.8[/C][C]16.3381031035382[/C][C]-13.5381031035382[/C][/ROW]
[ROW][C]56[/C][C]2.9[/C][C]16.2933060940624[/C][C]-13.3933060940624[/C][/ROW]
[ROW][C]57[/C][C]0.1[/C][C]16.1813135703729[/C][C]-16.0813135703729[/C][/ROW]
[ROW][C]58[/C][C]3.5[/C][C]16.2037120751108[/C][C]-12.7037120751108[/C][/ROW]
[ROW][C]59[/C][C]8.6[/C][C]16.1365165608972[/C][C]-7.53651656089716[/C][/ROW]
[ROW][C]60[/C][C]13.8[/C][C]16.1141180561593[/C][C]-2.31411805615926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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 IndexActualsInterpolationForecastResidualsPrediction Error
112.615.9349300182561-3.33493001825614
215.715.9797270277319-0.27972702773189
313.215.9125315135182-2.71253151351821
420.315.93493001825614.36506998174390
512.815.8229374945666-3.02293749456663
6815.8901330087803-7.89013300878032
70.915.8901330087803-14.9901330087803
83.616.0021255324698-12.4021255324698
914.115.957328522994-1.857328522994
1021.715.97972702773195.7202729722681
1124.516.00212553246988.49787446753021
1218.916.11411805615932.78588194384074
1313.916.0469225419456-2.14692254194558
141116.1141180561593-5.11411805615926
155.815.9125315135182-10.1125315135182
1615.515.8677345040424-0.367734504042422
1722.415.9573285229946.442671477006
1831.715.979727027731915.7202729722681
1930.315.95732852299414.342671477006
2031.416.024524037207715.3754759627923
2120.215.93493001825614.26506998174389
2219.715.9573285229943.742671477006
2310.816.0245240372077-5.22452403720768
2413.216.0021255324698-2.80212553246979
2515.115.9797270277319-0.879727027731895
2615.616.0917195514214-0.491719551421368
2715.516.0021255324698-0.502125532469789
2812.716.0469225419456-3.34692254194558
2910.915.957328522994-5.057328522994
301015.9797270277319-5.9797270277319
319.116.1365165608972-7.03651656089716
3210.315.957328522994-5.657328522994
3316.916.00212553246980.897874467530209
342216.06932104668355.93067895331653
3527.616.069321046683511.5306789533165
3628.916.069321046683512.8306789533165
373116.069321046683514.9306789533165
3832.916.248509084586616.6514909154134
3938.116.181313570372921.9186864296271
4028.816.248509084586612.5514909154134
412916.270907589324512.7290924106755
4221.816.27090758932455.52909241067548
4328.816.338103103538212.4618968964618
4425.616.22611057984879.37388942015127
4528.216.270907589324511.9290924106755
4620.216.24850908458663.95149091541337
4717.916.27090758932451.62909241067547
4816.316.11411805615930.185881943840738
4913.216.2485090845866-3.04850908458663
508.116.3157045988003-8.21570459880031
514.516.3157045988003-11.8157045988003
52-0.116.1589150656350-16.2589150656351
53016.2261105798487-16.2261105798487
542.316.2485090845866-13.9485090845866
552.816.3381031035382-13.5381031035382
562.916.2933060940624-13.3933060940624
570.116.1813135703729-16.0813135703729
583.516.2037120751108-12.7037120751108
598.616.1365165608972-7.53651656089716
6013.816.1141180561593-2.31411805615926







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.04799692436287980.09599384872575970.95200307563712
60.04258295291053710.08516590582107420.957417047089463
70.1361657405848320.2723314811696650.863834259415168
80.1791095845715820.3582191691431640.820890415428418
90.1118957212873030.2237914425746060.888104278712697
100.1205692956256760.2411385912513520.879430704374324
110.1269914419587390.2539828839174780.873008558041261
120.07957118528481760.1591423705696350.920428814715182
130.05073908523573710.1014781704714740.949260914764263
140.04231795865928310.08463591731856630.957682041340717
150.03727811516765960.07455623033531920.96272188483234
160.02520873202136320.05041746404272650.974791267978637
170.02575227481877630.05150454963755270.974247725181224
180.0869772465411680.1739544930823360.913022753458832
190.1529645135201190.3059290270402380.847035486479881
200.2184772469018370.4369544938036750.781522753098163
210.1733254123883860.3466508247767720.826674587611614
220.1311194013365480.2622388026730970.868880598663452
230.1117737116346450.2235474232692910.888226288365355
240.08268797778590960.1653759555718190.91731202221409
250.05662293983693350.1132458796738670.943377060163066
260.03887916284745260.07775832569490520.961120837152547
270.02506010489827520.05012020979655040.974939895101725
280.01745243518667970.03490487037335950.98254756481332
290.01242384288553490.02484768577106980.987576157114465
300.00966396730653420.01932793461306840.990336032693466
310.008838319732269550.01767663946453910.99116168026773
320.007204386116314190.01440877223262840.992795613883686
330.004438369472337360.008876738944674730.995561630527663
340.00285835164661270.00571670329322540.997141648353387
350.002904950342775390.005809900685550780.997095049657225
360.003417267158439910.006834534316879820.99658273284156
370.006113638620899390.01222727724179880.9938863613791
380.009259273128189020.01851854625637800.99074072687181
390.04525211095466970.09050422190933940.95474788904533
400.05588564226205790.1117712845241160.944114357737942
410.07639569399431170.1527913879886230.923604306005688
420.07661202170544940.1532240434108990.92338797829455
430.1337660365921750.267532073184350.866233963407825
440.2127485383003100.4254970766006190.78725146169969
450.5320595779225750.935880844154850.467940422077425
460.7064370719557350.587125856088530.293562928044265
470.8693231399412920.2613537201174150.130676860058708
480.9075457535642050.184908492871590.092454246435795
490.9564827957433480.08703440851330330.0435172042566517
500.9685484272220660.06290314555586830.0314515727779342
510.963316651774520.07336669645095910.0366833482254796
520.9733933005728180.05321339885436360.0266066994271818
530.9673012390189850.06539752196202930.0326987609810146
540.930295520246890.1394089595062210.0697044797531104
550.8744538945066650.2510922109866700.125546105493335

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.0479969243628798 & 0.0959938487257597 & 0.95200307563712 \tabularnewline
6 & 0.0425829529105371 & 0.0851659058210742 & 0.957417047089463 \tabularnewline
7 & 0.136165740584832 & 0.272331481169665 & 0.863834259415168 \tabularnewline
8 & 0.179109584571582 & 0.358219169143164 & 0.820890415428418 \tabularnewline
9 & 0.111895721287303 & 0.223791442574606 & 0.888104278712697 \tabularnewline
10 & 0.120569295625676 & 0.241138591251352 & 0.879430704374324 \tabularnewline
11 & 0.126991441958739 & 0.253982883917478 & 0.873008558041261 \tabularnewline
12 & 0.0795711852848176 & 0.159142370569635 & 0.920428814715182 \tabularnewline
13 & 0.0507390852357371 & 0.101478170471474 & 0.949260914764263 \tabularnewline
14 & 0.0423179586592831 & 0.0846359173185663 & 0.957682041340717 \tabularnewline
15 & 0.0372781151676596 & 0.0745562303353192 & 0.96272188483234 \tabularnewline
16 & 0.0252087320213632 & 0.0504174640427265 & 0.974791267978637 \tabularnewline
17 & 0.0257522748187763 & 0.0515045496375527 & 0.974247725181224 \tabularnewline
18 & 0.086977246541168 & 0.173954493082336 & 0.913022753458832 \tabularnewline
19 & 0.152964513520119 & 0.305929027040238 & 0.847035486479881 \tabularnewline
20 & 0.218477246901837 & 0.436954493803675 & 0.781522753098163 \tabularnewline
21 & 0.173325412388386 & 0.346650824776772 & 0.826674587611614 \tabularnewline
22 & 0.131119401336548 & 0.262238802673097 & 0.868880598663452 \tabularnewline
23 & 0.111773711634645 & 0.223547423269291 & 0.888226288365355 \tabularnewline
24 & 0.0826879777859096 & 0.165375955571819 & 0.91731202221409 \tabularnewline
25 & 0.0566229398369335 & 0.113245879673867 & 0.943377060163066 \tabularnewline
26 & 0.0388791628474526 & 0.0777583256949052 & 0.961120837152547 \tabularnewline
27 & 0.0250601048982752 & 0.0501202097965504 & 0.974939895101725 \tabularnewline
28 & 0.0174524351866797 & 0.0349048703733595 & 0.98254756481332 \tabularnewline
29 & 0.0124238428855349 & 0.0248476857710698 & 0.987576157114465 \tabularnewline
30 & 0.0096639673065342 & 0.0193279346130684 & 0.990336032693466 \tabularnewline
31 & 0.00883831973226955 & 0.0176766394645391 & 0.99116168026773 \tabularnewline
32 & 0.00720438611631419 & 0.0144087722326284 & 0.992795613883686 \tabularnewline
33 & 0.00443836947233736 & 0.00887673894467473 & 0.995561630527663 \tabularnewline
34 & 0.0028583516466127 & 0.0057167032932254 & 0.997141648353387 \tabularnewline
35 & 0.00290495034277539 & 0.00580990068555078 & 0.997095049657225 \tabularnewline
36 & 0.00341726715843991 & 0.00683453431687982 & 0.99658273284156 \tabularnewline
37 & 0.00611363862089939 & 0.0122272772417988 & 0.9938863613791 \tabularnewline
38 & 0.00925927312818902 & 0.0185185462563780 & 0.99074072687181 \tabularnewline
39 & 0.0452521109546697 & 0.0905042219093394 & 0.95474788904533 \tabularnewline
40 & 0.0558856422620579 & 0.111771284524116 & 0.944114357737942 \tabularnewline
41 & 0.0763956939943117 & 0.152791387988623 & 0.923604306005688 \tabularnewline
42 & 0.0766120217054494 & 0.153224043410899 & 0.92338797829455 \tabularnewline
43 & 0.133766036592175 & 0.26753207318435 & 0.866233963407825 \tabularnewline
44 & 0.212748538300310 & 0.425497076600619 & 0.78725146169969 \tabularnewline
45 & 0.532059577922575 & 0.93588084415485 & 0.467940422077425 \tabularnewline
46 & 0.706437071955735 & 0.58712585608853 & 0.293562928044265 \tabularnewline
47 & 0.869323139941292 & 0.261353720117415 & 0.130676860058708 \tabularnewline
48 & 0.907545753564205 & 0.18490849287159 & 0.092454246435795 \tabularnewline
49 & 0.956482795743348 & 0.0870344085133033 & 0.0435172042566517 \tabularnewline
50 & 0.968548427222066 & 0.0629031455558683 & 0.0314515727779342 \tabularnewline
51 & 0.96331665177452 & 0.0733666964509591 & 0.0366833482254796 \tabularnewline
52 & 0.973393300572818 & 0.0532133988543636 & 0.0266066994271818 \tabularnewline
53 & 0.967301239018985 & 0.0653975219620293 & 0.0326987609810146 \tabularnewline
54 & 0.93029552024689 & 0.139408959506221 & 0.0697044797531104 \tabularnewline
55 & 0.874453894506665 & 0.251092210986670 & 0.125546105493335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&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]5[/C][C]0.0479969243628798[/C][C]0.0959938487257597[/C][C]0.95200307563712[/C][/ROW]
[ROW][C]6[/C][C]0.0425829529105371[/C][C]0.0851659058210742[/C][C]0.957417047089463[/C][/ROW]
[ROW][C]7[/C][C]0.136165740584832[/C][C]0.272331481169665[/C][C]0.863834259415168[/C][/ROW]
[ROW][C]8[/C][C]0.179109584571582[/C][C]0.358219169143164[/C][C]0.820890415428418[/C][/ROW]
[ROW][C]9[/C][C]0.111895721287303[/C][C]0.223791442574606[/C][C]0.888104278712697[/C][/ROW]
[ROW][C]10[/C][C]0.120569295625676[/C][C]0.241138591251352[/C][C]0.879430704374324[/C][/ROW]
[ROW][C]11[/C][C]0.126991441958739[/C][C]0.253982883917478[/C][C]0.873008558041261[/C][/ROW]
[ROW][C]12[/C][C]0.0795711852848176[/C][C]0.159142370569635[/C][C]0.920428814715182[/C][/ROW]
[ROW][C]13[/C][C]0.0507390852357371[/C][C]0.101478170471474[/C][C]0.949260914764263[/C][/ROW]
[ROW][C]14[/C][C]0.0423179586592831[/C][C]0.0846359173185663[/C][C]0.957682041340717[/C][/ROW]
[ROW][C]15[/C][C]0.0372781151676596[/C][C]0.0745562303353192[/C][C]0.96272188483234[/C][/ROW]
[ROW][C]16[/C][C]0.0252087320213632[/C][C]0.0504174640427265[/C][C]0.974791267978637[/C][/ROW]
[ROW][C]17[/C][C]0.0257522748187763[/C][C]0.0515045496375527[/C][C]0.974247725181224[/C][/ROW]
[ROW][C]18[/C][C]0.086977246541168[/C][C]0.173954493082336[/C][C]0.913022753458832[/C][/ROW]
[ROW][C]19[/C][C]0.152964513520119[/C][C]0.305929027040238[/C][C]0.847035486479881[/C][/ROW]
[ROW][C]20[/C][C]0.218477246901837[/C][C]0.436954493803675[/C][C]0.781522753098163[/C][/ROW]
[ROW][C]21[/C][C]0.173325412388386[/C][C]0.346650824776772[/C][C]0.826674587611614[/C][/ROW]
[ROW][C]22[/C][C]0.131119401336548[/C][C]0.262238802673097[/C][C]0.868880598663452[/C][/ROW]
[ROW][C]23[/C][C]0.111773711634645[/C][C]0.223547423269291[/C][C]0.888226288365355[/C][/ROW]
[ROW][C]24[/C][C]0.0826879777859096[/C][C]0.165375955571819[/C][C]0.91731202221409[/C][/ROW]
[ROW][C]25[/C][C]0.0566229398369335[/C][C]0.113245879673867[/C][C]0.943377060163066[/C][/ROW]
[ROW][C]26[/C][C]0.0388791628474526[/C][C]0.0777583256949052[/C][C]0.961120837152547[/C][/ROW]
[ROW][C]27[/C][C]0.0250601048982752[/C][C]0.0501202097965504[/C][C]0.974939895101725[/C][/ROW]
[ROW][C]28[/C][C]0.0174524351866797[/C][C]0.0349048703733595[/C][C]0.98254756481332[/C][/ROW]
[ROW][C]29[/C][C]0.0124238428855349[/C][C]0.0248476857710698[/C][C]0.987576157114465[/C][/ROW]
[ROW][C]30[/C][C]0.0096639673065342[/C][C]0.0193279346130684[/C][C]0.990336032693466[/C][/ROW]
[ROW][C]31[/C][C]0.00883831973226955[/C][C]0.0176766394645391[/C][C]0.99116168026773[/C][/ROW]
[ROW][C]32[/C][C]0.00720438611631419[/C][C]0.0144087722326284[/C][C]0.992795613883686[/C][/ROW]
[ROW][C]33[/C][C]0.00443836947233736[/C][C]0.00887673894467473[/C][C]0.995561630527663[/C][/ROW]
[ROW][C]34[/C][C]0.0028583516466127[/C][C]0.0057167032932254[/C][C]0.997141648353387[/C][/ROW]
[ROW][C]35[/C][C]0.00290495034277539[/C][C]0.00580990068555078[/C][C]0.997095049657225[/C][/ROW]
[ROW][C]36[/C][C]0.00341726715843991[/C][C]0.00683453431687982[/C][C]0.99658273284156[/C][/ROW]
[ROW][C]37[/C][C]0.00611363862089939[/C][C]0.0122272772417988[/C][C]0.9938863613791[/C][/ROW]
[ROW][C]38[/C][C]0.00925927312818902[/C][C]0.0185185462563780[/C][C]0.99074072687181[/C][/ROW]
[ROW][C]39[/C][C]0.0452521109546697[/C][C]0.0905042219093394[/C][C]0.95474788904533[/C][/ROW]
[ROW][C]40[/C][C]0.0558856422620579[/C][C]0.111771284524116[/C][C]0.944114357737942[/C][/ROW]
[ROW][C]41[/C][C]0.0763956939943117[/C][C]0.152791387988623[/C][C]0.923604306005688[/C][/ROW]
[ROW][C]42[/C][C]0.0766120217054494[/C][C]0.153224043410899[/C][C]0.92338797829455[/C][/ROW]
[ROW][C]43[/C][C]0.133766036592175[/C][C]0.26753207318435[/C][C]0.866233963407825[/C][/ROW]
[ROW][C]44[/C][C]0.212748538300310[/C][C]0.425497076600619[/C][C]0.78725146169969[/C][/ROW]
[ROW][C]45[/C][C]0.532059577922575[/C][C]0.93588084415485[/C][C]0.467940422077425[/C][/ROW]
[ROW][C]46[/C][C]0.706437071955735[/C][C]0.58712585608853[/C][C]0.293562928044265[/C][/ROW]
[ROW][C]47[/C][C]0.869323139941292[/C][C]0.261353720117415[/C][C]0.130676860058708[/C][/ROW]
[ROW][C]48[/C][C]0.907545753564205[/C][C]0.18490849287159[/C][C]0.092454246435795[/C][/ROW]
[ROW][C]49[/C][C]0.956482795743348[/C][C]0.0870344085133033[/C][C]0.0435172042566517[/C][/ROW]
[ROW][C]50[/C][C]0.968548427222066[/C][C]0.0629031455558683[/C][C]0.0314515727779342[/C][/ROW]
[ROW][C]51[/C][C]0.96331665177452[/C][C]0.0733666964509591[/C][C]0.0366833482254796[/C][/ROW]
[ROW][C]52[/C][C]0.973393300572818[/C][C]0.0532133988543636[/C][C]0.0266066994271818[/C][/ROW]
[ROW][C]53[/C][C]0.967301239018985[/C][C]0.0653975219620293[/C][C]0.0326987609810146[/C][/ROW]
[ROW][C]54[/C][C]0.93029552024689[/C][C]0.139408959506221[/C][C]0.0697044797531104[/C][/ROW]
[ROW][C]55[/C][C]0.874453894506665[/C][C]0.251092210986670[/C][C]0.125546105493335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.04799692436287980.09599384872575970.95200307563712
60.04258295291053710.08516590582107420.957417047089463
70.1361657405848320.2723314811696650.863834259415168
80.1791095845715820.3582191691431640.820890415428418
90.1118957212873030.2237914425746060.888104278712697
100.1205692956256760.2411385912513520.879430704374324
110.1269914419587390.2539828839174780.873008558041261
120.07957118528481760.1591423705696350.920428814715182
130.05073908523573710.1014781704714740.949260914764263
140.04231795865928310.08463591731856630.957682041340717
150.03727811516765960.07455623033531920.96272188483234
160.02520873202136320.05041746404272650.974791267978637
170.02575227481877630.05150454963755270.974247725181224
180.0869772465411680.1739544930823360.913022753458832
190.1529645135201190.3059290270402380.847035486479881
200.2184772469018370.4369544938036750.781522753098163
210.1733254123883860.3466508247767720.826674587611614
220.1311194013365480.2622388026730970.868880598663452
230.1117737116346450.2235474232692910.888226288365355
240.08268797778590960.1653759555718190.91731202221409
250.05662293983693350.1132458796738670.943377060163066
260.03887916284745260.07775832569490520.961120837152547
270.02506010489827520.05012020979655040.974939895101725
280.01745243518667970.03490487037335950.98254756481332
290.01242384288553490.02484768577106980.987576157114465
300.00966396730653420.01932793461306840.990336032693466
310.008838319732269550.01767663946453910.99116168026773
320.007204386116314190.01440877223262840.992795613883686
330.004438369472337360.008876738944674730.995561630527663
340.00285835164661270.00571670329322540.997141648353387
350.002904950342775390.005809900685550780.997095049657225
360.003417267158439910.006834534316879820.99658273284156
370.006113638620899390.01222727724179880.9938863613791
380.009259273128189020.01851854625637800.99074072687181
390.04525211095466970.09050422190933940.95474788904533
400.05588564226205790.1117712845241160.944114357737942
410.07639569399431170.1527913879886230.923604306005688
420.07661202170544940.1532240434108990.92338797829455
430.1337660365921750.267532073184350.866233963407825
440.2127485383003100.4254970766006190.78725146169969
450.5320595779225750.935880844154850.467940422077425
460.7064370719557350.587125856088530.293562928044265
470.8693231399412920.2613537201174150.130676860058708
480.9075457535642050.184908492871590.092454246435795
490.9564827957433480.08703440851330330.0435172042566517
500.9685484272220660.06290314555586830.0314515727779342
510.963316651774520.07336669645095910.0366833482254796
520.9733933005728180.05321339885436360.0266066994271818
530.9673012390189850.06539752196202930.0326987609810146
540.930295520246890.1394089595062210.0697044797531104
550.8744538945066650.2510922109866700.125546105493335







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.0784313725490196NOK
5% type I error level110.215686274509804NOK
10% type I error level250.490196078431373NOK

\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 & 4 & 0.0784313725490196 & NOK \tabularnewline
5% type I error level & 11 & 0.215686274509804 & NOK \tabularnewline
10% type I error level & 25 & 0.490196078431373 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58357&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]4[/C][C]0.0784313725490196[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]11[/C][C]0.215686274509804[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]25[/C][C]0.490196078431373[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58357&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58357&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 testsOK/NOK
1% type I error level40.0784313725490196NOK
5% type I error level110.215686274509804NOK
10% type I error level250.490196078431373NOK



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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$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')
}