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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, 26 Mar 2010 10:01:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/26/t12695980552yd4c8av2ljk4az.htm/, Retrieved Tue, 18 Jan 2022 13:50:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74579, Retrieved Tue, 18 Jan 2022 13:50:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
6.3	0
2.1	3.41
9.1	1.02
15.8	-1.7
5.2	2.2
10.9	0.52
8.3	1.72
11	-0.37
3.2	2.67
6.3	-1.1
6.6	-0.1
9.5	-0.7
3.3	1.44
11	-0.92
4.7	1.93
10.4	-1
7.4	0.02
2.1	2.72
17.9	-2
6.1	1.79
11.9	-1.7
13.8	0.23
14.3	0.54
15.2	-0.32
10	1
11.9	0.21
6.5	2.28
7.5	0.4
10.6	-0.55
7.4	0.63
8.4	0.83
5.7	-0.12
4.9	0.56
3.2	1.74
11	-0.05
4.9	0.3
13.2	-1
9.7	0.62
12.8	0.54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time92 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 & 92 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&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]92 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=74579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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 time92 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
SWS[t] = + 9.71704929682466 -2.19699958033701logWb[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
SWS[t] =  +  9.71704929682466 -2.19699958033701logWb[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]SWS[t] =  +  9.71704929682466 -2.19699958033701logWb[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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
SWS[t] = + 9.71704929682466 -2.19699958033701logWb[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9.717049296824660.47917520.278700
logWb-2.196999580337010.354881-6.190800

\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) & 9.71704929682466 & 0.479175 & 20.2787 & 0 & 0 \tabularnewline
logWb & -2.19699958033701 & 0.354881 & -6.1908 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&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]9.71704929682466[/C][C]0.479175[/C][C]20.2787[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]logWb[/C][C]-2.19699958033701[/C][C]0.354881[/C][C]-6.1908[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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)9.717049296824660.47917520.278700
logWb-2.196999580337010.354881-6.190800







Multiple Linear Regression - Regression Statistics
Multiple R0.713303306547448
R-squared0.508801607131523
Adjusted R-squared0.495525974891835
F-TEST (value)38.3259793541448
F-TEST (DF numerator)1
F-TEST (DF denominator)37
p-value3.46497637471188e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.8185432386865
Sum Squared Residuals293.934881568779

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.713303306547448 \tabularnewline
R-squared & 0.508801607131523 \tabularnewline
Adjusted R-squared & 0.495525974891835 \tabularnewline
F-TEST (value) & 38.3259793541448 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 37 \tabularnewline
p-value & 3.46497637471188e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.8185432386865 \tabularnewline
Sum Squared Residuals & 293.934881568779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.713303306547448[/C][/ROW]
[ROW][C]R-squared[/C][C]0.508801607131523[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.495525974891835[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]38.3259793541448[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]37[/C][/ROW]
[ROW][C]p-value[/C][C]3.46497637471188e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.8185432386865[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]293.934881568779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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 R0.713303306547448
R-squared0.508801607131523
Adjusted R-squared0.495525974891835
F-TEST (value)38.3259793541448
F-TEST (DF numerator)1
F-TEST (DF denominator)37
p-value3.46497637471188e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.8185432386865
Sum Squared Residuals293.934881568779







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.39.71704929682467-3.41704929682467
22.12.22528072787545-0.125280727875454
39.17.476109724880911.62389027511909
415.813.45194858339762.34805141660243
55.24.883650220083240.316349779916759
610.98.574609515049412.32539048495059
78.35.9382100186452.36178998135500
81110.52993914154940.470060858450649
93.23.85106041732485-0.651060417324847
106.312.1337488351954-5.83374883519537
116.69.93674925485836-3.33674925485836
129.511.2549490030606-1.75494900306056
133.36.55336990113937-3.25336990113937
141111.7382889107347-0.738288910734705
154.75.47684010677423-0.776840106774233
1610.411.9140488771617-1.51404887716167
177.49.67310930521792-2.27310930521792
182.13.741210438308-1.64121043830800
1917.914.11104845749873.78895154250133
206.15.784420048021410.315579951978585
2111.913.4519485833976-1.55194858339757
2213.89.211739393347154.58826060665285
2314.38.530669523442685.76933047655733
2415.210.42008916253254.7799108374675
25107.520049716487652.47995028351235
2611.99.255679384953892.64432061504611
276.54.707890253656281.79210974634372
287.58.83824946468986-1.33824946468985
2910.610.9253990660100-0.325399066010013
307.48.33293956121234-0.932939561212343
318.47.893539645144940.506460354855059
325.79.9806892464651-4.2806892464651
334.98.48672953183593-3.58672953183593
343.25.89427002703826-2.69427002703826
35119.82689927584151.17310072415849
364.99.05794942272356-4.15794942272356
3713.211.91404887716171.28595112283833
389.78.354909557015711.34509044298429
3912.88.530669523442684.26933047655733

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.3 & 9.71704929682467 & -3.41704929682467 \tabularnewline
2 & 2.1 & 2.22528072787545 & -0.125280727875454 \tabularnewline
3 & 9.1 & 7.47610972488091 & 1.62389027511909 \tabularnewline
4 & 15.8 & 13.4519485833976 & 2.34805141660243 \tabularnewline
5 & 5.2 & 4.88365022008324 & 0.316349779916759 \tabularnewline
6 & 10.9 & 8.57460951504941 & 2.32539048495059 \tabularnewline
7 & 8.3 & 5.938210018645 & 2.36178998135500 \tabularnewline
8 & 11 & 10.5299391415494 & 0.470060858450649 \tabularnewline
9 & 3.2 & 3.85106041732485 & -0.651060417324847 \tabularnewline
10 & 6.3 & 12.1337488351954 & -5.83374883519537 \tabularnewline
11 & 6.6 & 9.93674925485836 & -3.33674925485836 \tabularnewline
12 & 9.5 & 11.2549490030606 & -1.75494900306056 \tabularnewline
13 & 3.3 & 6.55336990113937 & -3.25336990113937 \tabularnewline
14 & 11 & 11.7382889107347 & -0.738288910734705 \tabularnewline
15 & 4.7 & 5.47684010677423 & -0.776840106774233 \tabularnewline
16 & 10.4 & 11.9140488771617 & -1.51404887716167 \tabularnewline
17 & 7.4 & 9.67310930521792 & -2.27310930521792 \tabularnewline
18 & 2.1 & 3.741210438308 & -1.64121043830800 \tabularnewline
19 & 17.9 & 14.1110484574987 & 3.78895154250133 \tabularnewline
20 & 6.1 & 5.78442004802141 & 0.315579951978585 \tabularnewline
21 & 11.9 & 13.4519485833976 & -1.55194858339757 \tabularnewline
22 & 13.8 & 9.21173939334715 & 4.58826060665285 \tabularnewline
23 & 14.3 & 8.53066952344268 & 5.76933047655733 \tabularnewline
24 & 15.2 & 10.4200891625325 & 4.7799108374675 \tabularnewline
25 & 10 & 7.52004971648765 & 2.47995028351235 \tabularnewline
26 & 11.9 & 9.25567938495389 & 2.64432061504611 \tabularnewline
27 & 6.5 & 4.70789025365628 & 1.79210974634372 \tabularnewline
28 & 7.5 & 8.83824946468986 & -1.33824946468985 \tabularnewline
29 & 10.6 & 10.9253990660100 & -0.325399066010013 \tabularnewline
30 & 7.4 & 8.33293956121234 & -0.932939561212343 \tabularnewline
31 & 8.4 & 7.89353964514494 & 0.506460354855059 \tabularnewline
32 & 5.7 & 9.9806892464651 & -4.2806892464651 \tabularnewline
33 & 4.9 & 8.48672953183593 & -3.58672953183593 \tabularnewline
34 & 3.2 & 5.89427002703826 & -2.69427002703826 \tabularnewline
35 & 11 & 9.8268992758415 & 1.17310072415849 \tabularnewline
36 & 4.9 & 9.05794942272356 & -4.15794942272356 \tabularnewline
37 & 13.2 & 11.9140488771617 & 1.28595112283833 \tabularnewline
38 & 9.7 & 8.35490955701571 & 1.34509044298429 \tabularnewline
39 & 12.8 & 8.53066952344268 & 4.26933047655733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&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]6.3[/C][C]9.71704929682467[/C][C]-3.41704929682467[/C][/ROW]
[ROW][C]2[/C][C]2.1[/C][C]2.22528072787545[/C][C]-0.125280727875454[/C][/ROW]
[ROW][C]3[/C][C]9.1[/C][C]7.47610972488091[/C][C]1.62389027511909[/C][/ROW]
[ROW][C]4[/C][C]15.8[/C][C]13.4519485833976[/C][C]2.34805141660243[/C][/ROW]
[ROW][C]5[/C][C]5.2[/C][C]4.88365022008324[/C][C]0.316349779916759[/C][/ROW]
[ROW][C]6[/C][C]10.9[/C][C]8.57460951504941[/C][C]2.32539048495059[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]5.938210018645[/C][C]2.36178998135500[/C][/ROW]
[ROW][C]8[/C][C]11[/C][C]10.5299391415494[/C][C]0.470060858450649[/C][/ROW]
[ROW][C]9[/C][C]3.2[/C][C]3.85106041732485[/C][C]-0.651060417324847[/C][/ROW]
[ROW][C]10[/C][C]6.3[/C][C]12.1337488351954[/C][C]-5.83374883519537[/C][/ROW]
[ROW][C]11[/C][C]6.6[/C][C]9.93674925485836[/C][C]-3.33674925485836[/C][/ROW]
[ROW][C]12[/C][C]9.5[/C][C]11.2549490030606[/C][C]-1.75494900306056[/C][/ROW]
[ROW][C]13[/C][C]3.3[/C][C]6.55336990113937[/C][C]-3.25336990113937[/C][/ROW]
[ROW][C]14[/C][C]11[/C][C]11.7382889107347[/C][C]-0.738288910734705[/C][/ROW]
[ROW][C]15[/C][C]4.7[/C][C]5.47684010677423[/C][C]-0.776840106774233[/C][/ROW]
[ROW][C]16[/C][C]10.4[/C][C]11.9140488771617[/C][C]-1.51404887716167[/C][/ROW]
[ROW][C]17[/C][C]7.4[/C][C]9.67310930521792[/C][C]-2.27310930521792[/C][/ROW]
[ROW][C]18[/C][C]2.1[/C][C]3.741210438308[/C][C]-1.64121043830800[/C][/ROW]
[ROW][C]19[/C][C]17.9[/C][C]14.1110484574987[/C][C]3.78895154250133[/C][/ROW]
[ROW][C]20[/C][C]6.1[/C][C]5.78442004802141[/C][C]0.315579951978585[/C][/ROW]
[ROW][C]21[/C][C]11.9[/C][C]13.4519485833976[/C][C]-1.55194858339757[/C][/ROW]
[ROW][C]22[/C][C]13.8[/C][C]9.21173939334715[/C][C]4.58826060665285[/C][/ROW]
[ROW][C]23[/C][C]14.3[/C][C]8.53066952344268[/C][C]5.76933047655733[/C][/ROW]
[ROW][C]24[/C][C]15.2[/C][C]10.4200891625325[/C][C]4.7799108374675[/C][/ROW]
[ROW][C]25[/C][C]10[/C][C]7.52004971648765[/C][C]2.47995028351235[/C][/ROW]
[ROW][C]26[/C][C]11.9[/C][C]9.25567938495389[/C][C]2.64432061504611[/C][/ROW]
[ROW][C]27[/C][C]6.5[/C][C]4.70789025365628[/C][C]1.79210974634372[/C][/ROW]
[ROW][C]28[/C][C]7.5[/C][C]8.83824946468986[/C][C]-1.33824946468985[/C][/ROW]
[ROW][C]29[/C][C]10.6[/C][C]10.9253990660100[/C][C]-0.325399066010013[/C][/ROW]
[ROW][C]30[/C][C]7.4[/C][C]8.33293956121234[/C][C]-0.932939561212343[/C][/ROW]
[ROW][C]31[/C][C]8.4[/C][C]7.89353964514494[/C][C]0.506460354855059[/C][/ROW]
[ROW][C]32[/C][C]5.7[/C][C]9.9806892464651[/C][C]-4.2806892464651[/C][/ROW]
[ROW][C]33[/C][C]4.9[/C][C]8.48672953183593[/C][C]-3.58672953183593[/C][/ROW]
[ROW][C]34[/C][C]3.2[/C][C]5.89427002703826[/C][C]-2.69427002703826[/C][/ROW]
[ROW][C]35[/C][C]11[/C][C]9.8268992758415[/C][C]1.17310072415849[/C][/ROW]
[ROW][C]36[/C][C]4.9[/C][C]9.05794942272356[/C][C]-4.15794942272356[/C][/ROW]
[ROW][C]37[/C][C]13.2[/C][C]11.9140488771617[/C][C]1.28595112283833[/C][/ROW]
[ROW][C]38[/C][C]9.7[/C][C]8.35490955701571[/C][C]1.34509044298429[/C][/ROW]
[ROW][C]39[/C][C]12.8[/C][C]8.53066952344268[/C][C]4.26933047655733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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
16.39.71704929682467-3.41704929682467
22.12.22528072787545-0.125280727875454
39.17.476109724880911.62389027511909
415.813.45194858339762.34805141660243
55.24.883650220083240.316349779916759
610.98.574609515049412.32539048495059
78.35.9382100186452.36178998135500
81110.52993914154940.470060858450649
93.23.85106041732485-0.651060417324847
106.312.1337488351954-5.83374883519537
116.69.93674925485836-3.33674925485836
129.511.2549490030606-1.75494900306056
133.36.55336990113937-3.25336990113937
141111.7382889107347-0.738288910734705
154.75.47684010677423-0.776840106774233
1610.411.9140488771617-1.51404887716167
177.49.67310930521792-2.27310930521792
182.13.741210438308-1.64121043830800
1917.914.11104845749873.78895154250133
206.15.784420048021410.315579951978585
2111.913.4519485833976-1.55194858339757
2213.89.211739393347154.58826060665285
2314.38.530669523442685.76933047655733
2415.210.42008916253254.7799108374675
25107.520049716487652.47995028351235
2611.99.255679384953892.64432061504611
276.54.707890253656281.79210974634372
287.58.83824946468986-1.33824946468985
2910.610.9253990660100-0.325399066010013
307.48.33293956121234-0.932939561212343
318.47.893539645144940.506460354855059
325.79.9806892464651-4.2806892464651
334.98.48672953183593-3.58672953183593
343.25.89427002703826-2.69427002703826
35119.82689927584151.17310072415849
364.99.05794942272356-4.15794942272356
3713.211.91404887716171.28595112283833
389.78.354909557015711.34509044298429
3912.88.530669523442684.26933047655733







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.471108200669190.942216401338380.52889179933081
60.3773113798765290.7546227597530570.622688620123471
70.3025534294477380.6051068588954760.697446570552262
80.1902679583356460.3805359166712920.809732041664354
90.120421230424590.240842460849180.87957876957541
100.4967773048067650.993554609613530.503222695193235
110.501420379277820.997159241444360.49857962072218
120.4127565161274990.8255130322549970.587243483872501
130.4295070125086030.8590140250172060.570492987491397
140.3384861338104870.6769722676209750.661513866189513
150.2531681131287930.5063362262575860.746831886871207
160.1941596657986290.3883193315972590.80584033420137
170.1630882801161250.326176560232250.836911719883875
180.1240609409287680.2481218818575370.875939059071231
190.2102748526192820.4205497052385650.789725147380718
200.1510046714742400.3020093429484810.84899532852576
210.1146949718279250.2293899436558500.885305028172075
220.2094532650580630.4189065301161260.790546734941937
230.451642612660060.903285225320120.54835738733994
240.6145971096822010.7708057806355970.385402890317799
250.5910798305676640.8178403388646730.408920169432336
260.5915677896034790.8168644207930410.408432210396521
270.5654848263118850.8690303473762290.434515173688114
280.4669806160603750.933961232120750.533019383939625
290.3570000302332870.7140000604665740.642999969766713
300.2572710233099650.514542046619930.742728976690035
310.1845364055652410.3690728111304810.81546359443476
320.2655892592554820.5311785185109640.734410740744518
330.2812846340502150.5625692681004310.718715365949784
340.2157265578690630.4314531157381260.784273442130937

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.47110820066919 & 0.94221640133838 & 0.52889179933081 \tabularnewline
6 & 0.377311379876529 & 0.754622759753057 & 0.622688620123471 \tabularnewline
7 & 0.302553429447738 & 0.605106858895476 & 0.697446570552262 \tabularnewline
8 & 0.190267958335646 & 0.380535916671292 & 0.809732041664354 \tabularnewline
9 & 0.12042123042459 & 0.24084246084918 & 0.87957876957541 \tabularnewline
10 & 0.496777304806765 & 0.99355460961353 & 0.503222695193235 \tabularnewline
11 & 0.50142037927782 & 0.99715924144436 & 0.49857962072218 \tabularnewline
12 & 0.412756516127499 & 0.825513032254997 & 0.587243483872501 \tabularnewline
13 & 0.429507012508603 & 0.859014025017206 & 0.570492987491397 \tabularnewline
14 & 0.338486133810487 & 0.676972267620975 & 0.661513866189513 \tabularnewline
15 & 0.253168113128793 & 0.506336226257586 & 0.746831886871207 \tabularnewline
16 & 0.194159665798629 & 0.388319331597259 & 0.80584033420137 \tabularnewline
17 & 0.163088280116125 & 0.32617656023225 & 0.836911719883875 \tabularnewline
18 & 0.124060940928768 & 0.248121881857537 & 0.875939059071231 \tabularnewline
19 & 0.210274852619282 & 0.420549705238565 & 0.789725147380718 \tabularnewline
20 & 0.151004671474240 & 0.302009342948481 & 0.84899532852576 \tabularnewline
21 & 0.114694971827925 & 0.229389943655850 & 0.885305028172075 \tabularnewline
22 & 0.209453265058063 & 0.418906530116126 & 0.790546734941937 \tabularnewline
23 & 0.45164261266006 & 0.90328522532012 & 0.54835738733994 \tabularnewline
24 & 0.614597109682201 & 0.770805780635597 & 0.385402890317799 \tabularnewline
25 & 0.591079830567664 & 0.817840338864673 & 0.408920169432336 \tabularnewline
26 & 0.591567789603479 & 0.816864420793041 & 0.408432210396521 \tabularnewline
27 & 0.565484826311885 & 0.869030347376229 & 0.434515173688114 \tabularnewline
28 & 0.466980616060375 & 0.93396123212075 & 0.533019383939625 \tabularnewline
29 & 0.357000030233287 & 0.714000060466574 & 0.642999969766713 \tabularnewline
30 & 0.257271023309965 & 0.51454204661993 & 0.742728976690035 \tabularnewline
31 & 0.184536405565241 & 0.369072811130481 & 0.81546359443476 \tabularnewline
32 & 0.265589259255482 & 0.531178518510964 & 0.734410740744518 \tabularnewline
33 & 0.281284634050215 & 0.562569268100431 & 0.718715365949784 \tabularnewline
34 & 0.215726557869063 & 0.431453115738126 & 0.784273442130937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&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]0.47110820066919[/C][C]0.94221640133838[/C][C]0.52889179933081[/C][/ROW]
[ROW][C]6[/C][C]0.377311379876529[/C][C]0.754622759753057[/C][C]0.622688620123471[/C][/ROW]
[ROW][C]7[/C][C]0.302553429447738[/C][C]0.605106858895476[/C][C]0.697446570552262[/C][/ROW]
[ROW][C]8[/C][C]0.190267958335646[/C][C]0.380535916671292[/C][C]0.809732041664354[/C][/ROW]
[ROW][C]9[/C][C]0.12042123042459[/C][C]0.24084246084918[/C][C]0.87957876957541[/C][/ROW]
[ROW][C]10[/C][C]0.496777304806765[/C][C]0.99355460961353[/C][C]0.503222695193235[/C][/ROW]
[ROW][C]11[/C][C]0.50142037927782[/C][C]0.99715924144436[/C][C]0.49857962072218[/C][/ROW]
[ROW][C]12[/C][C]0.412756516127499[/C][C]0.825513032254997[/C][C]0.587243483872501[/C][/ROW]
[ROW][C]13[/C][C]0.429507012508603[/C][C]0.859014025017206[/C][C]0.570492987491397[/C][/ROW]
[ROW][C]14[/C][C]0.338486133810487[/C][C]0.676972267620975[/C][C]0.661513866189513[/C][/ROW]
[ROW][C]15[/C][C]0.253168113128793[/C][C]0.506336226257586[/C][C]0.746831886871207[/C][/ROW]
[ROW][C]16[/C][C]0.194159665798629[/C][C]0.388319331597259[/C][C]0.80584033420137[/C][/ROW]
[ROW][C]17[/C][C]0.163088280116125[/C][C]0.32617656023225[/C][C]0.836911719883875[/C][/ROW]
[ROW][C]18[/C][C]0.124060940928768[/C][C]0.248121881857537[/C][C]0.875939059071231[/C][/ROW]
[ROW][C]19[/C][C]0.210274852619282[/C][C]0.420549705238565[/C][C]0.789725147380718[/C][/ROW]
[ROW][C]20[/C][C]0.151004671474240[/C][C]0.302009342948481[/C][C]0.84899532852576[/C][/ROW]
[ROW][C]21[/C][C]0.114694971827925[/C][C]0.229389943655850[/C][C]0.885305028172075[/C][/ROW]
[ROW][C]22[/C][C]0.209453265058063[/C][C]0.418906530116126[/C][C]0.790546734941937[/C][/ROW]
[ROW][C]23[/C][C]0.45164261266006[/C][C]0.90328522532012[/C][C]0.54835738733994[/C][/ROW]
[ROW][C]24[/C][C]0.614597109682201[/C][C]0.770805780635597[/C][C]0.385402890317799[/C][/ROW]
[ROW][C]25[/C][C]0.591079830567664[/C][C]0.817840338864673[/C][C]0.408920169432336[/C][/ROW]
[ROW][C]26[/C][C]0.591567789603479[/C][C]0.816864420793041[/C][C]0.408432210396521[/C][/ROW]
[ROW][C]27[/C][C]0.565484826311885[/C][C]0.869030347376229[/C][C]0.434515173688114[/C][/ROW]
[ROW][C]28[/C][C]0.466980616060375[/C][C]0.93396123212075[/C][C]0.533019383939625[/C][/ROW]
[ROW][C]29[/C][C]0.357000030233287[/C][C]0.714000060466574[/C][C]0.642999969766713[/C][/ROW]
[ROW][C]30[/C][C]0.257271023309965[/C][C]0.51454204661993[/C][C]0.742728976690035[/C][/ROW]
[ROW][C]31[/C][C]0.184536405565241[/C][C]0.369072811130481[/C][C]0.81546359443476[/C][/ROW]
[ROW][C]32[/C][C]0.265589259255482[/C][C]0.531178518510964[/C][C]0.734410740744518[/C][/ROW]
[ROW][C]33[/C][C]0.281284634050215[/C][C]0.562569268100431[/C][C]0.718715365949784[/C][/ROW]
[ROW][C]34[/C][C]0.215726557869063[/C][C]0.431453115738126[/C][C]0.784273442130937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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
50.471108200669190.942216401338380.52889179933081
60.3773113798765290.7546227597530570.622688620123471
70.3025534294477380.6051068588954760.697446570552262
80.1902679583356460.3805359166712920.809732041664354
90.120421230424590.240842460849180.87957876957541
100.4967773048067650.993554609613530.503222695193235
110.501420379277820.997159241444360.49857962072218
120.4127565161274990.8255130322549970.587243483872501
130.4295070125086030.8590140250172060.570492987491397
140.3384861338104870.6769722676209750.661513866189513
150.2531681131287930.5063362262575860.746831886871207
160.1941596657986290.3883193315972590.80584033420137
170.1630882801161250.326176560232250.836911719883875
180.1240609409287680.2481218818575370.875939059071231
190.2102748526192820.4205497052385650.789725147380718
200.1510046714742400.3020093429484810.84899532852576
210.1146949718279250.2293899436558500.885305028172075
220.2094532650580630.4189065301161260.790546734941937
230.451642612660060.903285225320120.54835738733994
240.6145971096822010.7708057806355970.385402890317799
250.5910798305676640.8178403388646730.408920169432336
260.5915677896034790.8168644207930410.408432210396521
270.5654848263118850.8690303473762290.434515173688114
280.4669806160603750.933961232120750.533019383939625
290.3570000302332870.7140000604665740.642999969766713
300.2572710233099650.514542046619930.742728976690035
310.1845364055652410.3690728111304810.81546359443476
320.2655892592554820.5311785185109640.734410740744518
330.2812846340502150.5625692681004310.718715365949784
340.2157265578690630.4314531157381260.784273442130937







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74579&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74579&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74579&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 level00OK
5% type I error level00OK
10% type I error level00OK



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')
}