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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 15:35:54 -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/t1258756602qqfy2og8whzgo7i.htm/, Retrieved Fri, 29 Mar 2024 12:11:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58478, Retrieved Fri, 29 Mar 2024 12:11:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Seatbelt Law part 1] [2009-11-20 22:35:54] [befe6dd6a614b6d3a2a74a47a0a4f514] [Current]
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Dataseries X:
8.9	1,6
8.8	1,3
8.3	1,1
7.5	1,6
7.2	1,9
7.4	1,6
8.8	1,7
9.3	1,6
9.3	1,4
8.7	2,1
8.2	1,9
8.3	1,7
8.5	1,8
8.6	2
8.5	2,5
8.2	2,1
8.1	2,1
7.9	2,3
8.6	2,4
8.7	2,4
8.7	2,3
8.5	1,7
8.4	2
8.5	2,3
8.7	2
8.7	2
8.6	1,3
8.5	1,7
8.3	1,9
8	1,7
8.2	1,6
8.1	1,7
8.1	1,8
8	1,9
7.9	1,9
7.9	1,9
8	2
8	2,1
7.9	1,9
8	1,9
7.7	1,3
7.2	1,3
7.5	1,4
7.3	1,2
7	1,3
7	1,8
7	2,2
7.2	2,6
7.3	2,8
7.1	3,1
6.8	3,9
6.4	3,7
6.1	4,6
6.5	5,1
7.7	5,2
7.9	4,9
7.5	5,1
6.9	4,8
6.6	3,9
6.9	3,5




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=58478&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=58478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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
TWIB[t] = + 8.74315783324895 -0.362640679154173GI[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TWIB[t] =  +  8.74315783324895 -0.362640679154173GI[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58478&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TWIB[t] =  +  8.74315783324895 -0.362640679154173GI[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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
TWIB[t] = + 8.74315783324895 -0.362640679154173GI[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.743157833248950.1959244.626200
GI-0.3626406791541730.077072-4.70521.6e-058e-06

\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) & 8.74315783324895 & 0.19592 & 44.6262 & 0 & 0 \tabularnewline
GI & -0.362640679154173 & 0.077072 & -4.7052 & 1.6e-05 & 8e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58478&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]8.74315783324895[/C][C]0.19592[/C][C]44.6262[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]GI[/C][C]-0.362640679154173[/C][C]0.077072[/C][C]-4.7052[/C][C]1.6e-05[/C][C]8e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58478&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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)8.743157833248950.1959244.626200
GI-0.3626406791541730.077072-4.70521.6e-058e-06







Multiple Linear Regression - Regression Statistics
Multiple R0.525604291373647
R-squared0.276259871110393
Adjusted R-squared0.26378159302609
F-TEST (value)22.1392622639097
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value1.61549115280657e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.637776285338418
Sum Squared Residuals23.5919982281241

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.525604291373647 \tabularnewline
R-squared & 0.276259871110393 \tabularnewline
Adjusted R-squared & 0.26378159302609 \tabularnewline
F-TEST (value) & 22.1392622639097 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 1.61549115280657e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.637776285338418 \tabularnewline
Sum Squared Residuals & 23.5919982281241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58478&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.525604291373647[/C][/ROW]
[ROW][C]R-squared[/C][C]0.276259871110393[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.26378159302609[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]22.1392622639097[/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]1.61549115280657e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.637776285338418[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]23.5919982281241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58478&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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 R0.525604291373647
R-squared0.276259871110393
Adjusted R-squared0.26378159302609
F-TEST (value)22.1392622639097
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value1.61549115280657e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.637776285338418
Sum Squared Residuals23.5919982281241







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.98.162932746602310.737067253397693
28.88.271724950348530.528275049651468
38.38.34425308617937-0.0442530861793669
47.58.16293274660228-0.662932746602281
57.28.05414054285603-0.85414054285603
67.48.16293274660228-0.762932746602281
78.88.126668678686860.673331321313136
89.38.162932746602281.13706725339772
99.38.235460882433121.06453911756688
108.77.98161240702520.718387592974804
118.28.054140542856030.145859457143970
128.38.126668678686860.173331321313136
138.58.090404610771450.409595389228553
148.68.017876474940610.582123525059387
158.57.836556135363530.663443864636474
168.27.98161240702520.218387592974804
178.17.98161240702520.118387592974804
187.97.90908427119436-0.0090842711943604
198.67.872820203278940.727179796721056
208.77.872820203278940.827179796721056
218.77.909084271194360.790915728805639
228.58.126668678686860.373331321313136
238.48.017876474940610.382123525059388
248.57.909084271194360.590915728805639
258.78.017876474940610.682123525059387
268.78.017876474940610.682123525059387
278.68.271724950348530.328275049651466
288.58.126668678686860.373331321313136
298.38.054140542856030.245859457143971
3088.12666867868686-0.126668678686864
318.28.162932746602280.0370672533977179
328.18.12666867868686-0.0266686786868646
338.18.090404610771450.00959538922855273
3488.05414054285603-0.0541405428560297
357.98.05414054285603-0.154140542856029
367.98.05414054285603-0.154140542856029
3788.01787647494061-0.0178764749406124
3887.98161240702520.0183875929748048
397.98.05414054285603-0.154140542856029
4088.05414054285603-0.0541405428560297
417.78.27172495034853-0.571724950348533
427.28.27172495034853-1.07172495034853
437.58.23546088243312-0.735460882433116
447.38.30798901826395-1.00798901826395
4578.27172495034853-1.27172495034853
4678.09040461077145-1.09040461077145
4777.94534833910978-0.945348339109778
487.27.80029206744811-0.600292067448109
497.37.72776393161727-0.427763931617275
507.17.61897172787102-0.518971727871023
516.87.32885918454769-0.528859184547685
526.47.40138732037852-1.00138732037852
536.17.07501070913976-0.975010709139765
546.56.89369036956268-0.393690369562678
557.76.857426301647260.84257369835274
567.96.966218505393510.933781494606488
577.56.893690369562680.606309630437322
586.97.00248257330893-0.102482573308929
596.67.32885918454769-0.728859184547685
606.97.47391545620935-0.573915456209353

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 8.16293274660231 & 0.737067253397693 \tabularnewline
2 & 8.8 & 8.27172495034853 & 0.528275049651468 \tabularnewline
3 & 8.3 & 8.34425308617937 & -0.0442530861793669 \tabularnewline
4 & 7.5 & 8.16293274660228 & -0.662932746602281 \tabularnewline
5 & 7.2 & 8.05414054285603 & -0.85414054285603 \tabularnewline
6 & 7.4 & 8.16293274660228 & -0.762932746602281 \tabularnewline
7 & 8.8 & 8.12666867868686 & 0.673331321313136 \tabularnewline
8 & 9.3 & 8.16293274660228 & 1.13706725339772 \tabularnewline
9 & 9.3 & 8.23546088243312 & 1.06453911756688 \tabularnewline
10 & 8.7 & 7.9816124070252 & 0.718387592974804 \tabularnewline
11 & 8.2 & 8.05414054285603 & 0.145859457143970 \tabularnewline
12 & 8.3 & 8.12666867868686 & 0.173331321313136 \tabularnewline
13 & 8.5 & 8.09040461077145 & 0.409595389228553 \tabularnewline
14 & 8.6 & 8.01787647494061 & 0.582123525059387 \tabularnewline
15 & 8.5 & 7.83655613536353 & 0.663443864636474 \tabularnewline
16 & 8.2 & 7.9816124070252 & 0.218387592974804 \tabularnewline
17 & 8.1 & 7.9816124070252 & 0.118387592974804 \tabularnewline
18 & 7.9 & 7.90908427119436 & -0.0090842711943604 \tabularnewline
19 & 8.6 & 7.87282020327894 & 0.727179796721056 \tabularnewline
20 & 8.7 & 7.87282020327894 & 0.827179796721056 \tabularnewline
21 & 8.7 & 7.90908427119436 & 0.790915728805639 \tabularnewline
22 & 8.5 & 8.12666867868686 & 0.373331321313136 \tabularnewline
23 & 8.4 & 8.01787647494061 & 0.382123525059388 \tabularnewline
24 & 8.5 & 7.90908427119436 & 0.590915728805639 \tabularnewline
25 & 8.7 & 8.01787647494061 & 0.682123525059387 \tabularnewline
26 & 8.7 & 8.01787647494061 & 0.682123525059387 \tabularnewline
27 & 8.6 & 8.27172495034853 & 0.328275049651466 \tabularnewline
28 & 8.5 & 8.12666867868686 & 0.373331321313136 \tabularnewline
29 & 8.3 & 8.05414054285603 & 0.245859457143971 \tabularnewline
30 & 8 & 8.12666867868686 & -0.126668678686864 \tabularnewline
31 & 8.2 & 8.16293274660228 & 0.0370672533977179 \tabularnewline
32 & 8.1 & 8.12666867868686 & -0.0266686786868646 \tabularnewline
33 & 8.1 & 8.09040461077145 & 0.00959538922855273 \tabularnewline
34 & 8 & 8.05414054285603 & -0.0541405428560297 \tabularnewline
35 & 7.9 & 8.05414054285603 & -0.154140542856029 \tabularnewline
36 & 7.9 & 8.05414054285603 & -0.154140542856029 \tabularnewline
37 & 8 & 8.01787647494061 & -0.0178764749406124 \tabularnewline
38 & 8 & 7.9816124070252 & 0.0183875929748048 \tabularnewline
39 & 7.9 & 8.05414054285603 & -0.154140542856029 \tabularnewline
40 & 8 & 8.05414054285603 & -0.0541405428560297 \tabularnewline
41 & 7.7 & 8.27172495034853 & -0.571724950348533 \tabularnewline
42 & 7.2 & 8.27172495034853 & -1.07172495034853 \tabularnewline
43 & 7.5 & 8.23546088243312 & -0.735460882433116 \tabularnewline
44 & 7.3 & 8.30798901826395 & -1.00798901826395 \tabularnewline
45 & 7 & 8.27172495034853 & -1.27172495034853 \tabularnewline
46 & 7 & 8.09040461077145 & -1.09040461077145 \tabularnewline
47 & 7 & 7.94534833910978 & -0.945348339109778 \tabularnewline
48 & 7.2 & 7.80029206744811 & -0.600292067448109 \tabularnewline
49 & 7.3 & 7.72776393161727 & -0.427763931617275 \tabularnewline
50 & 7.1 & 7.61897172787102 & -0.518971727871023 \tabularnewline
51 & 6.8 & 7.32885918454769 & -0.528859184547685 \tabularnewline
52 & 6.4 & 7.40138732037852 & -1.00138732037852 \tabularnewline
53 & 6.1 & 7.07501070913976 & -0.975010709139765 \tabularnewline
54 & 6.5 & 6.89369036956268 & -0.393690369562678 \tabularnewline
55 & 7.7 & 6.85742630164726 & 0.84257369835274 \tabularnewline
56 & 7.9 & 6.96621850539351 & 0.933781494606488 \tabularnewline
57 & 7.5 & 6.89369036956268 & 0.606309630437322 \tabularnewline
58 & 6.9 & 7.00248257330893 & -0.102482573308929 \tabularnewline
59 & 6.6 & 7.32885918454769 & -0.728859184547685 \tabularnewline
60 & 6.9 & 7.47391545620935 & -0.573915456209353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58478&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]8.9[/C][C]8.16293274660231[/C][C]0.737067253397693[/C][/ROW]
[ROW][C]2[/C][C]8.8[/C][C]8.27172495034853[/C][C]0.528275049651468[/C][/ROW]
[ROW][C]3[/C][C]8.3[/C][C]8.34425308617937[/C][C]-0.0442530861793669[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]8.16293274660228[/C][C]-0.662932746602281[/C][/ROW]
[ROW][C]5[/C][C]7.2[/C][C]8.05414054285603[/C][C]-0.85414054285603[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]8.16293274660228[/C][C]-0.762932746602281[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.12666867868686[/C][C]0.673331321313136[/C][/ROW]
[ROW][C]8[/C][C]9.3[/C][C]8.16293274660228[/C][C]1.13706725339772[/C][/ROW]
[ROW][C]9[/C][C]9.3[/C][C]8.23546088243312[/C][C]1.06453911756688[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]7.9816124070252[/C][C]0.718387592974804[/C][/ROW]
[ROW][C]11[/C][C]8.2[/C][C]8.05414054285603[/C][C]0.145859457143970[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.12666867868686[/C][C]0.173331321313136[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.09040461077145[/C][C]0.409595389228553[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]8.01787647494061[/C][C]0.582123525059387[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]7.83655613536353[/C][C]0.663443864636474[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]7.9816124070252[/C][C]0.218387592974804[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]7.9816124070252[/C][C]0.118387592974804[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.90908427119436[/C][C]-0.0090842711943604[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]7.87282020327894[/C][C]0.727179796721056[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]7.87282020327894[/C][C]0.827179796721056[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]7.90908427119436[/C][C]0.790915728805639[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.12666867868686[/C][C]0.373331321313136[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]8.01787647494061[/C][C]0.382123525059388[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]7.90908427119436[/C][C]0.590915728805639[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.01787647494061[/C][C]0.682123525059387[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.01787647494061[/C][C]0.682123525059387[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.27172495034853[/C][C]0.328275049651466[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.12666867868686[/C][C]0.373331321313136[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]8.05414054285603[/C][C]0.245859457143971[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.12666867868686[/C][C]-0.126668678686864[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.16293274660228[/C][C]0.0370672533977179[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.12666867868686[/C][C]-0.0266686786868646[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.09040461077145[/C][C]0.00959538922855273[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.05414054285603[/C][C]-0.0541405428560297[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]8.05414054285603[/C][C]-0.154140542856029[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.05414054285603[/C][C]-0.154140542856029[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.01787647494061[/C][C]-0.0178764749406124[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.9816124070252[/C][C]0.0183875929748048[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]8.05414054285603[/C][C]-0.154140542856029[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]8.05414054285603[/C][C]-0.0541405428560297[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]8.27172495034853[/C][C]-0.571724950348533[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]8.27172495034853[/C][C]-1.07172495034853[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]8.23546088243312[/C][C]-0.735460882433116[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]8.30798901826395[/C][C]-1.00798901826395[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]8.27172495034853[/C][C]-1.27172495034853[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]8.09040461077145[/C][C]-1.09040461077145[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]7.94534833910978[/C][C]-0.945348339109778[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.80029206744811[/C][C]-0.600292067448109[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.72776393161727[/C][C]-0.427763931617275[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.61897172787102[/C][C]-0.518971727871023[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.32885918454769[/C][C]-0.528859184547685[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]7.40138732037852[/C][C]-1.00138732037852[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]7.07501070913976[/C][C]-0.975010709139765[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.89369036956268[/C][C]-0.393690369562678[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]6.85742630164726[/C][C]0.84257369835274[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]6.96621850539351[/C][C]0.933781494606488[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]6.89369036956268[/C][C]0.606309630437322[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]7.00248257330893[/C][C]-0.102482573308929[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]7.32885918454769[/C][C]-0.728859184547685[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]7.47391545620935[/C][C]-0.573915456209353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58478&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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
18.98.162932746602310.737067253397693
28.88.271724950348530.528275049651468
38.38.34425308617937-0.0442530861793669
47.58.16293274660228-0.662932746602281
57.28.05414054285603-0.85414054285603
67.48.16293274660228-0.762932746602281
78.88.126668678686860.673331321313136
89.38.162932746602281.13706725339772
99.38.235460882433121.06453911756688
108.77.98161240702520.718387592974804
118.28.054140542856030.145859457143970
128.38.126668678686860.173331321313136
138.58.090404610771450.409595389228553
148.68.017876474940610.582123525059387
158.57.836556135363530.663443864636474
168.27.98161240702520.218387592974804
178.17.98161240702520.118387592974804
187.97.90908427119436-0.0090842711943604
198.67.872820203278940.727179796721056
208.77.872820203278940.827179796721056
218.77.909084271194360.790915728805639
228.58.126668678686860.373331321313136
238.48.017876474940610.382123525059388
248.57.909084271194360.590915728805639
258.78.017876474940610.682123525059387
268.78.017876474940610.682123525059387
278.68.271724950348530.328275049651466
288.58.126668678686860.373331321313136
298.38.054140542856030.245859457143971
3088.12666867868686-0.126668678686864
318.28.162932746602280.0370672533977179
328.18.12666867868686-0.0266686786868646
338.18.090404610771450.00959538922855273
3488.05414054285603-0.0541405428560297
357.98.05414054285603-0.154140542856029
367.98.05414054285603-0.154140542856029
3788.01787647494061-0.0178764749406124
3887.98161240702520.0183875929748048
397.98.05414054285603-0.154140542856029
4088.05414054285603-0.0541405428560297
417.78.27172495034853-0.571724950348533
427.28.27172495034853-1.07172495034853
437.58.23546088243312-0.735460882433116
447.38.30798901826395-1.00798901826395
4578.27172495034853-1.27172495034853
4678.09040461077145-1.09040461077145
4777.94534833910978-0.945348339109778
487.27.80029206744811-0.600292067448109
497.37.72776393161727-0.427763931617275
507.17.61897172787102-0.518971727871023
516.87.32885918454769-0.528859184547685
526.47.40138732037852-1.00138732037852
536.17.07501070913976-0.975010709139765
546.56.89369036956268-0.393690369562678
557.76.857426301647260.84257369835274
567.96.966218505393510.933781494606488
577.56.893690369562680.606309630437322
586.97.00248257330893-0.102482573308929
596.67.32885918454769-0.728859184547685
606.97.47391545620935-0.573915456209353







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.6929324366076640.6141351267846730.307067563392336
60.6384005657619580.7231988684760840.361599434238042
70.7407400368575160.5185199262849680.259259963142484
80.8723378560349760.2553242879300480.127662143965024
90.8964633792635410.2070732414729190.103536620736459
100.9048003310569350.1903993378861290.0951996689430645
110.8552994510823320.2894010978353370.144700548917668
120.7940064630193670.4119870739612660.205993536980633
130.7348193664854550.5303612670290910.265180633514545
140.6938683884388180.6122632231223640.306131611561182
150.6550709812809990.6898580374380020.344929018719001
160.5789033520116140.8421932959767710.421096647988386
170.5024490914365240.9951018171269510.497550908563476
180.4328643577693860.8657287155387730.567135642230614
190.4204229061017120.8408458122034240.579577093898288
200.4301572409994140.8603144819988270.569842759000586
210.437046519022740.874093038045480.56295348097726
220.3880349814984370.7760699629968740.611965018501563
230.3425130231705810.6850260463411610.65748697682942
240.3264271999210610.6528543998421220.673572800078939
250.3477946682626910.6955893365253830.652205331737309
260.3853761332683750.7707522665367510.614623866731625
270.3784427634797870.7568855269595730.621557236520213
280.3825265167964480.7650530335928960.617473483203552
290.3728646804825230.7457293609650450.627135319517477
300.3494031443720790.6988062887441570.650596855627921
310.3320396631067530.6640793262135060.667960336893247
320.3162726022418690.6325452044837380.683727397758131
330.3088791643418330.6177583286836670.691120835658167
340.3031533492623210.6063066985246430.696846650737678
350.2974580103308390.5949160206616780.702541989669161
360.2945970203631540.5891940407263080.705402979636846
370.3091473182258180.6182946364516360.690852681774182
380.3410018496738950.682003699347790.658998150326105
390.3705867938087790.7411735876175570.629413206191221
400.4512693075969740.9025386151939480.548730692403026
410.4913482184652640.9826964369305280.508651781534736
420.5273678560678240.9452642878643520.472632143932176
430.537031826287970.925936347424060.46296817371203
440.5311991363570690.9376017272858620.468800863642931
450.5284271602849450.943145679430110.471572839715055
460.5355005031237510.92899899375250.46449949687625
470.5428967049069380.9142065901861240.457103295093062
480.5385408745314730.9229182509370530.461459125468527
490.5673191079418260.8653617841163490.432680892058174
500.5920979893322260.8158040213355470.407902010667773
510.5070682095124380.9858635809751230.492931790487562
520.4304672756369820.8609345512739650.569532724363017
530.5986610579855310.8026778840289380.401338942014469
540.8180661104077170.3638677791845660.181933889592283
550.6974740492500680.6050519014998650.302525950749932

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.692932436607664 & 0.614135126784673 & 0.307067563392336 \tabularnewline
6 & 0.638400565761958 & 0.723198868476084 & 0.361599434238042 \tabularnewline
7 & 0.740740036857516 & 0.518519926284968 & 0.259259963142484 \tabularnewline
8 & 0.872337856034976 & 0.255324287930048 & 0.127662143965024 \tabularnewline
9 & 0.896463379263541 & 0.207073241472919 & 0.103536620736459 \tabularnewline
10 & 0.904800331056935 & 0.190399337886129 & 0.0951996689430645 \tabularnewline
11 & 0.855299451082332 & 0.289401097835337 & 0.144700548917668 \tabularnewline
12 & 0.794006463019367 & 0.411987073961266 & 0.205993536980633 \tabularnewline
13 & 0.734819366485455 & 0.530361267029091 & 0.265180633514545 \tabularnewline
14 & 0.693868388438818 & 0.612263223122364 & 0.306131611561182 \tabularnewline
15 & 0.655070981280999 & 0.689858037438002 & 0.344929018719001 \tabularnewline
16 & 0.578903352011614 & 0.842193295976771 & 0.421096647988386 \tabularnewline
17 & 0.502449091436524 & 0.995101817126951 & 0.497550908563476 \tabularnewline
18 & 0.432864357769386 & 0.865728715538773 & 0.567135642230614 \tabularnewline
19 & 0.420422906101712 & 0.840845812203424 & 0.579577093898288 \tabularnewline
20 & 0.430157240999414 & 0.860314481998827 & 0.569842759000586 \tabularnewline
21 & 0.43704651902274 & 0.87409303804548 & 0.56295348097726 \tabularnewline
22 & 0.388034981498437 & 0.776069962996874 & 0.611965018501563 \tabularnewline
23 & 0.342513023170581 & 0.685026046341161 & 0.65748697682942 \tabularnewline
24 & 0.326427199921061 & 0.652854399842122 & 0.673572800078939 \tabularnewline
25 & 0.347794668262691 & 0.695589336525383 & 0.652205331737309 \tabularnewline
26 & 0.385376133268375 & 0.770752266536751 & 0.614623866731625 \tabularnewline
27 & 0.378442763479787 & 0.756885526959573 & 0.621557236520213 \tabularnewline
28 & 0.382526516796448 & 0.765053033592896 & 0.617473483203552 \tabularnewline
29 & 0.372864680482523 & 0.745729360965045 & 0.627135319517477 \tabularnewline
30 & 0.349403144372079 & 0.698806288744157 & 0.650596855627921 \tabularnewline
31 & 0.332039663106753 & 0.664079326213506 & 0.667960336893247 \tabularnewline
32 & 0.316272602241869 & 0.632545204483738 & 0.683727397758131 \tabularnewline
33 & 0.308879164341833 & 0.617758328683667 & 0.691120835658167 \tabularnewline
34 & 0.303153349262321 & 0.606306698524643 & 0.696846650737678 \tabularnewline
35 & 0.297458010330839 & 0.594916020661678 & 0.702541989669161 \tabularnewline
36 & 0.294597020363154 & 0.589194040726308 & 0.705402979636846 \tabularnewline
37 & 0.309147318225818 & 0.618294636451636 & 0.690852681774182 \tabularnewline
38 & 0.341001849673895 & 0.68200369934779 & 0.658998150326105 \tabularnewline
39 & 0.370586793808779 & 0.741173587617557 & 0.629413206191221 \tabularnewline
40 & 0.451269307596974 & 0.902538615193948 & 0.548730692403026 \tabularnewline
41 & 0.491348218465264 & 0.982696436930528 & 0.508651781534736 \tabularnewline
42 & 0.527367856067824 & 0.945264287864352 & 0.472632143932176 \tabularnewline
43 & 0.53703182628797 & 0.92593634742406 & 0.46296817371203 \tabularnewline
44 & 0.531199136357069 & 0.937601727285862 & 0.468800863642931 \tabularnewline
45 & 0.528427160284945 & 0.94314567943011 & 0.471572839715055 \tabularnewline
46 & 0.535500503123751 & 0.9289989937525 & 0.46449949687625 \tabularnewline
47 & 0.542896704906938 & 0.914206590186124 & 0.457103295093062 \tabularnewline
48 & 0.538540874531473 & 0.922918250937053 & 0.461459125468527 \tabularnewline
49 & 0.567319107941826 & 0.865361784116349 & 0.432680892058174 \tabularnewline
50 & 0.592097989332226 & 0.815804021335547 & 0.407902010667773 \tabularnewline
51 & 0.507068209512438 & 0.985863580975123 & 0.492931790487562 \tabularnewline
52 & 0.430467275636982 & 0.860934551273965 & 0.569532724363017 \tabularnewline
53 & 0.598661057985531 & 0.802677884028938 & 0.401338942014469 \tabularnewline
54 & 0.818066110407717 & 0.363867779184566 & 0.181933889592283 \tabularnewline
55 & 0.697474049250068 & 0.605051901499865 & 0.302525950749932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58478&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]0.692932436607664[/C][C]0.614135126784673[/C][C]0.307067563392336[/C][/ROW]
[ROW][C]6[/C][C]0.638400565761958[/C][C]0.723198868476084[/C][C]0.361599434238042[/C][/ROW]
[ROW][C]7[/C][C]0.740740036857516[/C][C]0.518519926284968[/C][C]0.259259963142484[/C][/ROW]
[ROW][C]8[/C][C]0.872337856034976[/C][C]0.255324287930048[/C][C]0.127662143965024[/C][/ROW]
[ROW][C]9[/C][C]0.896463379263541[/C][C]0.207073241472919[/C][C]0.103536620736459[/C][/ROW]
[ROW][C]10[/C][C]0.904800331056935[/C][C]0.190399337886129[/C][C]0.0951996689430645[/C][/ROW]
[ROW][C]11[/C][C]0.855299451082332[/C][C]0.289401097835337[/C][C]0.144700548917668[/C][/ROW]
[ROW][C]12[/C][C]0.794006463019367[/C][C]0.411987073961266[/C][C]0.205993536980633[/C][/ROW]
[ROW][C]13[/C][C]0.734819366485455[/C][C]0.530361267029091[/C][C]0.265180633514545[/C][/ROW]
[ROW][C]14[/C][C]0.693868388438818[/C][C]0.612263223122364[/C][C]0.306131611561182[/C][/ROW]
[ROW][C]15[/C][C]0.655070981280999[/C][C]0.689858037438002[/C][C]0.344929018719001[/C][/ROW]
[ROW][C]16[/C][C]0.578903352011614[/C][C]0.842193295976771[/C][C]0.421096647988386[/C][/ROW]
[ROW][C]17[/C][C]0.502449091436524[/C][C]0.995101817126951[/C][C]0.497550908563476[/C][/ROW]
[ROW][C]18[/C][C]0.432864357769386[/C][C]0.865728715538773[/C][C]0.567135642230614[/C][/ROW]
[ROW][C]19[/C][C]0.420422906101712[/C][C]0.840845812203424[/C][C]0.579577093898288[/C][/ROW]
[ROW][C]20[/C][C]0.430157240999414[/C][C]0.860314481998827[/C][C]0.569842759000586[/C][/ROW]
[ROW][C]21[/C][C]0.43704651902274[/C][C]0.87409303804548[/C][C]0.56295348097726[/C][/ROW]
[ROW][C]22[/C][C]0.388034981498437[/C][C]0.776069962996874[/C][C]0.611965018501563[/C][/ROW]
[ROW][C]23[/C][C]0.342513023170581[/C][C]0.685026046341161[/C][C]0.65748697682942[/C][/ROW]
[ROW][C]24[/C][C]0.326427199921061[/C][C]0.652854399842122[/C][C]0.673572800078939[/C][/ROW]
[ROW][C]25[/C][C]0.347794668262691[/C][C]0.695589336525383[/C][C]0.652205331737309[/C][/ROW]
[ROW][C]26[/C][C]0.385376133268375[/C][C]0.770752266536751[/C][C]0.614623866731625[/C][/ROW]
[ROW][C]27[/C][C]0.378442763479787[/C][C]0.756885526959573[/C][C]0.621557236520213[/C][/ROW]
[ROW][C]28[/C][C]0.382526516796448[/C][C]0.765053033592896[/C][C]0.617473483203552[/C][/ROW]
[ROW][C]29[/C][C]0.372864680482523[/C][C]0.745729360965045[/C][C]0.627135319517477[/C][/ROW]
[ROW][C]30[/C][C]0.349403144372079[/C][C]0.698806288744157[/C][C]0.650596855627921[/C][/ROW]
[ROW][C]31[/C][C]0.332039663106753[/C][C]0.664079326213506[/C][C]0.667960336893247[/C][/ROW]
[ROW][C]32[/C][C]0.316272602241869[/C][C]0.632545204483738[/C][C]0.683727397758131[/C][/ROW]
[ROW][C]33[/C][C]0.308879164341833[/C][C]0.617758328683667[/C][C]0.691120835658167[/C][/ROW]
[ROW][C]34[/C][C]0.303153349262321[/C][C]0.606306698524643[/C][C]0.696846650737678[/C][/ROW]
[ROW][C]35[/C][C]0.297458010330839[/C][C]0.594916020661678[/C][C]0.702541989669161[/C][/ROW]
[ROW][C]36[/C][C]0.294597020363154[/C][C]0.589194040726308[/C][C]0.705402979636846[/C][/ROW]
[ROW][C]37[/C][C]0.309147318225818[/C][C]0.618294636451636[/C][C]0.690852681774182[/C][/ROW]
[ROW][C]38[/C][C]0.341001849673895[/C][C]0.68200369934779[/C][C]0.658998150326105[/C][/ROW]
[ROW][C]39[/C][C]0.370586793808779[/C][C]0.741173587617557[/C][C]0.629413206191221[/C][/ROW]
[ROW][C]40[/C][C]0.451269307596974[/C][C]0.902538615193948[/C][C]0.548730692403026[/C][/ROW]
[ROW][C]41[/C][C]0.491348218465264[/C][C]0.982696436930528[/C][C]0.508651781534736[/C][/ROW]
[ROW][C]42[/C][C]0.527367856067824[/C][C]0.945264287864352[/C][C]0.472632143932176[/C][/ROW]
[ROW][C]43[/C][C]0.53703182628797[/C][C]0.92593634742406[/C][C]0.46296817371203[/C][/ROW]
[ROW][C]44[/C][C]0.531199136357069[/C][C]0.937601727285862[/C][C]0.468800863642931[/C][/ROW]
[ROW][C]45[/C][C]0.528427160284945[/C][C]0.94314567943011[/C][C]0.471572839715055[/C][/ROW]
[ROW][C]46[/C][C]0.535500503123751[/C][C]0.9289989937525[/C][C]0.46449949687625[/C][/ROW]
[ROW][C]47[/C][C]0.542896704906938[/C][C]0.914206590186124[/C][C]0.457103295093062[/C][/ROW]
[ROW][C]48[/C][C]0.538540874531473[/C][C]0.922918250937053[/C][C]0.461459125468527[/C][/ROW]
[ROW][C]49[/C][C]0.567319107941826[/C][C]0.865361784116349[/C][C]0.432680892058174[/C][/ROW]
[ROW][C]50[/C][C]0.592097989332226[/C][C]0.815804021335547[/C][C]0.407902010667773[/C][/ROW]
[ROW][C]51[/C][C]0.507068209512438[/C][C]0.985863580975123[/C][C]0.492931790487562[/C][/ROW]
[ROW][C]52[/C][C]0.430467275636982[/C][C]0.860934551273965[/C][C]0.569532724363017[/C][/ROW]
[ROW][C]53[/C][C]0.598661057985531[/C][C]0.802677884028938[/C][C]0.401338942014469[/C][/ROW]
[ROW][C]54[/C][C]0.818066110407717[/C][C]0.363867779184566[/C][C]0.181933889592283[/C][/ROW]
[ROW][C]55[/C][C]0.697474049250068[/C][C]0.605051901499865[/C][C]0.302525950749932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58478&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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
50.6929324366076640.6141351267846730.307067563392336
60.6384005657619580.7231988684760840.361599434238042
70.7407400368575160.5185199262849680.259259963142484
80.8723378560349760.2553242879300480.127662143965024
90.8964633792635410.2070732414729190.103536620736459
100.9048003310569350.1903993378861290.0951996689430645
110.8552994510823320.2894010978353370.144700548917668
120.7940064630193670.4119870739612660.205993536980633
130.7348193664854550.5303612670290910.265180633514545
140.6938683884388180.6122632231223640.306131611561182
150.6550709812809990.6898580374380020.344929018719001
160.5789033520116140.8421932959767710.421096647988386
170.5024490914365240.9951018171269510.497550908563476
180.4328643577693860.8657287155387730.567135642230614
190.4204229061017120.8408458122034240.579577093898288
200.4301572409994140.8603144819988270.569842759000586
210.437046519022740.874093038045480.56295348097726
220.3880349814984370.7760699629968740.611965018501563
230.3425130231705810.6850260463411610.65748697682942
240.3264271999210610.6528543998421220.673572800078939
250.3477946682626910.6955893365253830.652205331737309
260.3853761332683750.7707522665367510.614623866731625
270.3784427634797870.7568855269595730.621557236520213
280.3825265167964480.7650530335928960.617473483203552
290.3728646804825230.7457293609650450.627135319517477
300.3494031443720790.6988062887441570.650596855627921
310.3320396631067530.6640793262135060.667960336893247
320.3162726022418690.6325452044837380.683727397758131
330.3088791643418330.6177583286836670.691120835658167
340.3031533492623210.6063066985246430.696846650737678
350.2974580103308390.5949160206616780.702541989669161
360.2945970203631540.5891940407263080.705402979636846
370.3091473182258180.6182946364516360.690852681774182
380.3410018496738950.682003699347790.658998150326105
390.3705867938087790.7411735876175570.629413206191221
400.4512693075969740.9025386151939480.548730692403026
410.4913482184652640.9826964369305280.508651781534736
420.5273678560678240.9452642878643520.472632143932176
430.537031826287970.925936347424060.46296817371203
440.5311991363570690.9376017272858620.468800863642931
450.5284271602849450.943145679430110.471572839715055
460.5355005031237510.92899899375250.46449949687625
470.5428967049069380.9142065901861240.457103295093062
480.5385408745314730.9229182509370530.461459125468527
490.5673191079418260.8653617841163490.432680892058174
500.5920979893322260.8158040213355470.407902010667773
510.5070682095124380.9858635809751230.492931790487562
520.4304672756369820.8609345512739650.569532724363017
530.5986610579855310.8026778840289380.401338942014469
540.8180661104077170.3638677791845660.181933889592283
550.6974740492500680.6050519014998650.302525950749932







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=58478&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=58478&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58478&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')
}