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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 18 Nov 2009 10:25:36 -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/18/t1258565553xz6u50qdxmlbmwb.htm/, Retrieved Wed, 01 May 2024 22:24:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57547, Retrieved Wed, 01 May 2024 22:24:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

Tree of Dependent Computations

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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [] [2009-11-18 17:25:36] [508aab72d879399b4187e5fcd8f7c773] [Current]
-   P         [Multiple Regression] [] [2009-11-19 18:27:34] [96d96f181930b548ce74f8c3116c4873]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.2	2.4	7.5	8.3	8.8	8.9
7.4	2	7.2	7.5	8.3	8.8
8.8	2.1	7.4	7.2	7.5	8.3
9.3	2	8.8	7.4	7.2	7.5
9.3	1.8	9.3	8.8	7.4	7.2
8.7	2.7	9.3	9.3	8.8	7.4
8.2	2.3	8.7	9.3	9.3	8.8
8.3	1.9	8.2	8.7	9.3	9.3
8.5	2	8.3	8.2	8.7	9.3
8.6	2.3	8.5	8.3	8.2	8.7
8.5	2.8	8.6	8.5	8.3	8.2
8.2	2.4	8.5	8.6	8.5	8.3
8.1	2.3	8.2	8.5	8.6	8.5
7.9	2.7	8.1	8.2	8.5	8.6
8.6	2.7	7.9	8.1	8.2	8.5
8.7	2.9	8.6	7.9	8.1	8.2
8.7	3	8.7	8.6	7.9	8.1
8.5	2.2	8.7	8.7	8.6	7.9
8.4	2.3	8.5	8.7	8.7	8.6
8.5	2.8	8.4	8.5	8.7	8.7
8.7	2.8	8.5	8.4	8.5	8.7
8.7	2.8	8.7	8.5	8.4	8.5
8.6	2.2	8.7	8.7	8.5	8.4
8.5	2.6	8.6	8.7	8.7	8.5
8.3	2.8	8.5	8.6	8.7	8.7
8	2.5	8.3	8.5	8.6	8.7
8.2	2.4	8	8.3	8.5	8.6
8.1	2.3	8.2	8	8.3	8.5
8.1	1.9	8.1	8.2	8	8.3
8	1.7	8.1	8.1	8.2	8
7.9	2	8	8.1	8.1	8.2
7.9	2.1	7.9	8	8.1	8.1
8	1.7	7.9	7.9	8	8.1
8	1.8	8	7.9	7.9	8
7.9	1.8	8	8	7.9	7.9
8	1.8	7.9	8	8	7.9
7.7	1.3	8	7.9	8	8
7.2	1.3	7.7	8	7.9	8
7.5	1.3	7.2	7.7	8	7.9
7.3	1.2	7.5	7.2	7.7	8
7	1.4	7.3	7.5	7.2	7.7
7	2.2	7	7.3	7.5	7.2
7	2.9	7	7	7.3	7.5
7.2	3.1	7	7	7	7.3
7.3	3.5	7.2	7	7	7
7.1	3.6	7.3	7.2	7	7
6.8	4.4	7.1	7.3	7.2	7
6.4	4.1	6.8	7.1	7.3	7.2
6.1	5.1	6.4	6.8	7.1	7.3
6.5	5.8	6.1	6.4	6.8	7.1
7.7	5.9	6.5	6.1	6.4	6.8
7.9	5.4	7.7	6.5	6.1	6.4
7.5	5.5	7.9	7.7	6.5	6.1
6.9	4.8	7.5	7.9	7.7	6.5
6.6	3.2	6.9	7.5	7.9	7.7
6.9	2.7	6.6	6.9	7.5	7.9

Tables (Output of Computation)





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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&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]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=0

As an alternative you can also use a QR Code:  
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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 2.20711870010436 + 0.0300708114127846`X(t)`[t] + 1.14109921130441`Y(t-1)`[t] -0.46973056134648`Y(t-2)`[t] -0.244934881684172`Y(t-3)`[t] + 0.321061204660699`Y(t-4) `[t] -0.0107759424689206t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  2.20711870010436 +  0.0300708114127846`X(t)`[t] +  1.14109921130441`Y(t-1)`[t] -0.46973056134648`Y(t-2)`[t] -0.244934881684172`Y(t-3)`[t] +  0.321061204660699`Y(t-4)
`[t] -0.0107759424689206t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  2.20711870010436 +  0.0300708114127846`X(t)`[t] +  1.14109921130441`Y(t-1)`[t] -0.46973056134648`Y(t-2)`[t] -0.244934881684172`Y(t-3)`[t] +  0.321061204660699`Y(t-4)
`[t] -0.0107759424689206t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 2.20711870010436 + 0.0300708114127846`X(t)`[t] + 1.14109921130441`Y(t-1)`[t] -0.46973056134648`Y(t-2)`[t] -0.244934881684172`Y(t-3)`[t] + 0.321061204660699`Y(t-4) `[t] -0.0107759424689206t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.207118700104361.0583262.08550.0422560.021128
`X(t)`0.03007081141278460.0411080.73150.4679550.233977
`Y(t-1)`1.141099211304410.1282348.898600
`Y(t-2)`-0.469730561346480.201695-2.32890.0240310.012016
`Y(t-3)`-0.2449348816841720.201658-1.21460.2303370.115169
`Y(t-4) `0.3210612046606990.1348892.38020.0212380.010619
t-0.01077594246892060.003909-2.75660.0081820.004091

\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) & 2.20711870010436 & 1.058326 & 2.0855 & 0.042256 & 0.021128 \tabularnewline
`X(t)` & 0.0300708114127846 & 0.041108 & 0.7315 & 0.467955 & 0.233977 \tabularnewline
`Y(t-1)` & 1.14109921130441 & 0.128234 & 8.8986 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.46973056134648 & 0.201695 & -2.3289 & 0.024031 & 0.012016 \tabularnewline
`Y(t-3)` & -0.244934881684172 & 0.201658 & -1.2146 & 0.230337 & 0.115169 \tabularnewline
`Y(t-4)
` & 0.321061204660699 & 0.134889 & 2.3802 & 0.021238 & 0.010619 \tabularnewline
t & -0.0107759424689206 & 0.003909 & -2.7566 & 0.008182 & 0.004091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&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]2.20711870010436[/C][C]1.058326[/C][C]2.0855[/C][C]0.042256[/C][C]0.021128[/C][/ROW]
[ROW][C]`X(t)`[/C][C]0.0300708114127846[/C][C]0.041108[/C][C]0.7315[/C][C]0.467955[/C][C]0.233977[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.14109921130441[/C][C]0.128234[/C][C]8.8986[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.46973056134648[/C][C]0.201695[/C][C]-2.3289[/C][C]0.024031[/C][C]0.012016[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.244934881684172[/C][C]0.201658[/C][C]-1.2146[/C][C]0.230337[/C][C]0.115169[/C][/ROW]
[ROW][C]`Y(t-4)
`[/C][C]0.321061204660699[/C][C]0.134889[/C][C]2.3802[/C][C]0.021238[/C][C]0.010619[/C][/ROW]
[ROW][C]t[/C][C]-0.0107759424689206[/C][C]0.003909[/C][C]-2.7566[/C][C]0.008182[/C][C]0.004091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=2

As an alternative you can also use a QR Code:  
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)2.207118700104361.0583262.08550.0422560.021128
`X(t)`0.03007081141278460.0411080.73150.4679550.233977
`Y(t-1)`1.141099211304410.1282348.898600
`Y(t-2)`-0.469730561346480.201695-2.32890.0240310.012016
`Y(t-3)`-0.2449348816841720.201658-1.21460.2303370.115169
`Y(t-4) `0.3210612046606990.1348892.38020.0212380.010619
t-0.01077594246892060.003909-2.75660.0081820.004091






Multiple Linear Regression - Regression Statistics
Multiple R0.942705450612171
R-squared0.888693566613897
Adjusted R-squared0.875064207423762
F-TEST (value)65.2043543805884
F-TEST (DF numerator)6
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.262912839277478
Sum Squared Residuals3.3870348917903

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.942705450612171 \tabularnewline
R-squared & 0.888693566613897 \tabularnewline
Adjusted R-squared & 0.875064207423762 \tabularnewline
F-TEST (value) & 65.2043543805884 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 49 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.262912839277478 \tabularnewline
Sum Squared Residuals & 3.3870348917903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.942705450612171[/C][/ROW]
[ROW][C]R-squared[/C][C]0.888693566613897[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.875064207423762[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]65.2043543805884[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]49[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.262912839277478[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.3870348917903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R0.942705450612171
R-squared0.888693566613897
Adjusted R-squared0.875064207423762
F-TEST (value)65.2043543805884
F-TEST (DF numerator)6
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.262912839277478
Sum Squared Residuals3.3870348917903






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.63001089329295-0.430010893292947
27.47.7310226323208-0.331022632320797
38.88.127810084674970.672189915325033
49.39.43425134539835-0.134251345398347
59.39.185082722678960.114917277321039
68.78.68780863638260.0121913636173924
78.28.30736308824881-0.107363088248815
88.38.156378154700810.143621845299190
98.58.64454542418735-0.144545424187355
108.68.75386822931417-0.15386822931417
118.58.59326741091402-0.0932674109140198
128.28.39249931074413-0.192499310744133
138.18.12307833264098-0.0230783326409790
147.98.20773957064516-0.307739570645162
158.68.057091186089190.542908813910811
168.78.87322009285542-0.173220092855418
178.78.667630615586440.0323693844135539
188.58.350158309741590.149841690258411
198.48.314418961247140.0855810387528632
208.58.330620736089530.169379263910467
218.78.529914747222540.170085252777464
228.78.660666838116130.0393331618838724
238.68.481302687895750.118697312104247
248.58.351564292990740.148435707009259
258.38.34387788874072-0.0438778887407227
2688.16732740489015-0.167327404890150
278.27.897548097860270.302451902139730
288.18.26978494078566-0.169784940785661
298.18.0481928639250.0518071360749982
3087.933070477573130.0669295224268723
317.97.90591158649816-0.00591158649815773
327.97.798899739708650.101100260291347
3387.847562016977680.152437983022317
3487.946290444482830.0537095555171705
357.97.856435325413190.043564674586809
3687.707055973645410.292944026354587
377.77.87443372320126-0.174433723201258
387.27.49884844937478-0.298848449374782
397.57.001842461023110.498157538976888
407.37.6708410664488-0.370841066448798
4177.32308935504148-0.323089355041484
4276.853975343745160.146024656254838
4377.15047347540418-0.150473475404178
447.27.154979918790930.0450200812090737
457.37.28813378174980.0118662182502067
467.17.3005287292833-0.200528729283296
476.86.98962956121224-0.189629561212238
486.46.76116747696118-0.361167476961176
496.16.54603492659012-0.446034926590124
506.56.411139236830530.0888607631694698
517.77.002384819704060.697615180295943
527.98.10305628319642-0.203056283196422
537.57.56553827644201-0.0655382764420088
546.96.817829593036350.0821704069636503
556.66.598459519318920.00154048068107764
566.96.674342938165980.22565706183402

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.63001089329295 & -0.430010893292947 \tabularnewline
2 & 7.4 & 7.7310226323208 & -0.331022632320797 \tabularnewline
3 & 8.8 & 8.12781008467497 & 0.672189915325033 \tabularnewline
4 & 9.3 & 9.43425134539835 & -0.134251345398347 \tabularnewline
5 & 9.3 & 9.18508272267896 & 0.114917277321039 \tabularnewline
6 & 8.7 & 8.6878086363826 & 0.0121913636173924 \tabularnewline
7 & 8.2 & 8.30736308824881 & -0.107363088248815 \tabularnewline
8 & 8.3 & 8.15637815470081 & 0.143621845299190 \tabularnewline
9 & 8.5 & 8.64454542418735 & -0.144545424187355 \tabularnewline
10 & 8.6 & 8.75386822931417 & -0.15386822931417 \tabularnewline
11 & 8.5 & 8.59326741091402 & -0.0932674109140198 \tabularnewline
12 & 8.2 & 8.39249931074413 & -0.192499310744133 \tabularnewline
13 & 8.1 & 8.12307833264098 & -0.0230783326409790 \tabularnewline
14 & 7.9 & 8.20773957064516 & -0.307739570645162 \tabularnewline
15 & 8.6 & 8.05709118608919 & 0.542908813910811 \tabularnewline
16 & 8.7 & 8.87322009285542 & -0.173220092855418 \tabularnewline
17 & 8.7 & 8.66763061558644 & 0.0323693844135539 \tabularnewline
18 & 8.5 & 8.35015830974159 & 0.149841690258411 \tabularnewline
19 & 8.4 & 8.31441896124714 & 0.0855810387528632 \tabularnewline
20 & 8.5 & 8.33062073608953 & 0.169379263910467 \tabularnewline
21 & 8.7 & 8.52991474722254 & 0.170085252777464 \tabularnewline
22 & 8.7 & 8.66066683811613 & 0.0393331618838724 \tabularnewline
23 & 8.6 & 8.48130268789575 & 0.118697312104247 \tabularnewline
24 & 8.5 & 8.35156429299074 & 0.148435707009259 \tabularnewline
25 & 8.3 & 8.34387788874072 & -0.0438778887407227 \tabularnewline
26 & 8 & 8.16732740489015 & -0.167327404890150 \tabularnewline
27 & 8.2 & 7.89754809786027 & 0.302451902139730 \tabularnewline
28 & 8.1 & 8.26978494078566 & -0.169784940785661 \tabularnewline
29 & 8.1 & 8.048192863925 & 0.0518071360749982 \tabularnewline
30 & 8 & 7.93307047757313 & 0.0669295224268723 \tabularnewline
31 & 7.9 & 7.90591158649816 & -0.00591158649815773 \tabularnewline
32 & 7.9 & 7.79889973970865 & 0.101100260291347 \tabularnewline
33 & 8 & 7.84756201697768 & 0.152437983022317 \tabularnewline
34 & 8 & 7.94629044448283 & 0.0537095555171705 \tabularnewline
35 & 7.9 & 7.85643532541319 & 0.043564674586809 \tabularnewline
36 & 8 & 7.70705597364541 & 0.292944026354587 \tabularnewline
37 & 7.7 & 7.87443372320126 & -0.174433723201258 \tabularnewline
38 & 7.2 & 7.49884844937478 & -0.298848449374782 \tabularnewline
39 & 7.5 & 7.00184246102311 & 0.498157538976888 \tabularnewline
40 & 7.3 & 7.6708410664488 & -0.370841066448798 \tabularnewline
41 & 7 & 7.32308935504148 & -0.323089355041484 \tabularnewline
42 & 7 & 6.85397534374516 & 0.146024656254838 \tabularnewline
43 & 7 & 7.15047347540418 & -0.150473475404178 \tabularnewline
44 & 7.2 & 7.15497991879093 & 0.0450200812090737 \tabularnewline
45 & 7.3 & 7.2881337817498 & 0.0118662182502067 \tabularnewline
46 & 7.1 & 7.3005287292833 & -0.200528729283296 \tabularnewline
47 & 6.8 & 6.98962956121224 & -0.189629561212238 \tabularnewline
48 & 6.4 & 6.76116747696118 & -0.361167476961176 \tabularnewline
49 & 6.1 & 6.54603492659012 & -0.446034926590124 \tabularnewline
50 & 6.5 & 6.41113923683053 & 0.0888607631694698 \tabularnewline
51 & 7.7 & 7.00238481970406 & 0.697615180295943 \tabularnewline
52 & 7.9 & 8.10305628319642 & -0.203056283196422 \tabularnewline
53 & 7.5 & 7.56553827644201 & -0.0655382764420088 \tabularnewline
54 & 6.9 & 6.81782959303635 & 0.0821704069636503 \tabularnewline
55 & 6.6 & 6.59845951931892 & 0.00154048068107764 \tabularnewline
56 & 6.9 & 6.67434293816598 & 0.22565706183402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&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]7.2[/C][C]7.63001089329295[/C][C]-0.430010893292947[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.7310226323208[/C][C]-0.331022632320797[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.12781008467497[/C][C]0.672189915325033[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.43425134539835[/C][C]-0.134251345398347[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.18508272267896[/C][C]0.114917277321039[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.6878086363826[/C][C]0.0121913636173924[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.30736308824881[/C][C]-0.107363088248815[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.15637815470081[/C][C]0.143621845299190[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.64454542418735[/C][C]-0.144545424187355[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.75386822931417[/C][C]-0.15386822931417[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.59326741091402[/C][C]-0.0932674109140198[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.39249931074413[/C][C]-0.192499310744133[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]8.12307833264098[/C][C]-0.0230783326409790[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.20773957064516[/C][C]-0.307739570645162[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.05709118608919[/C][C]0.542908813910811[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.87322009285542[/C][C]-0.173220092855418[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.66763061558644[/C][C]0.0323693844135539[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.35015830974159[/C][C]0.149841690258411[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.31441896124714[/C][C]0.0855810387528632[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.33062073608953[/C][C]0.169379263910467[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.52991474722254[/C][C]0.170085252777464[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.66066683811613[/C][C]0.0393331618838724[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.48130268789575[/C][C]0.118697312104247[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.35156429299074[/C][C]0.148435707009259[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.34387788874072[/C][C]-0.0438778887407227[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.16732740489015[/C][C]-0.167327404890150[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]7.89754809786027[/C][C]0.302451902139730[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]8.26978494078566[/C][C]-0.169784940785661[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.048192863925[/C][C]0.0518071360749982[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.93307047757313[/C][C]0.0669295224268723[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.90591158649816[/C][C]-0.00591158649815773[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.79889973970865[/C][C]0.101100260291347[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.84756201697768[/C][C]0.152437983022317[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.94629044448283[/C][C]0.0537095555171705[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.85643532541319[/C][C]0.043564674586809[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.70705597364541[/C][C]0.292944026354587[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.87443372320126[/C][C]-0.174433723201258[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.49884844937478[/C][C]-0.298848449374782[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.00184246102311[/C][C]0.498157538976888[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.6708410664488[/C][C]-0.370841066448798[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.32308935504148[/C][C]-0.323089355041484[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.85397534374516[/C][C]0.146024656254838[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.15047347540418[/C][C]-0.150473475404178[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.15497991879093[/C][C]0.0450200812090737[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.2881337817498[/C][C]0.0118662182502067[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.3005287292833[/C][C]-0.200528729283296[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.98962956121224[/C][C]-0.189629561212238[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.76116747696118[/C][C]-0.361167476961176[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.54603492659012[/C][C]-0.446034926590124[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.41113923683053[/C][C]0.0888607631694698[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.00238481970406[/C][C]0.697615180295943[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]8.10305628319642[/C][C]-0.203056283196422[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.56553827644201[/C][C]-0.0655382764420088[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.81782959303635[/C][C]0.0821704069636503[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.59845951931892[/C][C]0.00154048068107764[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.67434293816598[/C][C]0.22565706183402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.27.63001089329295-0.430010893292947
27.47.7310226323208-0.331022632320797
38.88.127810084674970.672189915325033
49.39.43425134539835-0.134251345398347
59.39.185082722678960.114917277321039
68.78.68780863638260.0121913636173924
78.28.30736308824881-0.107363088248815
88.38.156378154700810.143621845299190
98.58.64454542418735-0.144545424187355
108.68.75386822931417-0.15386822931417
118.58.59326741091402-0.0932674109140198
128.28.39249931074413-0.192499310744133
138.18.12307833264098-0.0230783326409790
147.98.20773957064516-0.307739570645162
158.68.057091186089190.542908813910811
168.78.87322009285542-0.173220092855418
178.78.667630615586440.0323693844135539
188.58.350158309741590.149841690258411
198.48.314418961247140.0855810387528632
208.58.330620736089530.169379263910467
218.78.529914747222540.170085252777464
228.78.660666838116130.0393331618838724
238.68.481302687895750.118697312104247
248.58.351564292990740.148435707009259
258.38.34387788874072-0.0438778887407227
2688.16732740489015-0.167327404890150
278.27.897548097860270.302451902139730
288.18.26978494078566-0.169784940785661
298.18.0481928639250.0518071360749982
3087.933070477573130.0669295224268723
317.97.90591158649816-0.00591158649815773
327.97.798899739708650.101100260291347
3387.847562016977680.152437983022317
3487.946290444482830.0537095555171705
357.97.856435325413190.043564674586809
3687.707055973645410.292944026354587
377.77.87443372320126-0.174433723201258
387.27.49884844937478-0.298848449374782
397.57.001842461023110.498157538976888
407.37.6708410664488-0.370841066448798
4177.32308935504148-0.323089355041484
4276.853975343745160.146024656254838
4377.15047347540418-0.150473475404178
447.27.154979918790930.0450200812090737
457.37.28813378174980.0118662182502067
467.17.3005287292833-0.200528729283296
476.86.98962956121224-0.189629561212238
486.46.76116747696118-0.361167476961176
496.16.54603492659012-0.446034926590124
506.56.411139236830530.0888607631694698
517.77.002384819704060.697615180295943
527.98.10305628319642-0.203056283196422
537.57.56553827644201-0.0655382764420088
546.96.817829593036350.0821704069636503
556.66.598459519318920.00154048068107764
566.96.674342938165980.22565706183402






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.9209393380022780.1581213239954450.0790606619977223
110.8954972703032370.2090054593935260.104502729696763
120.9256395701022560.1487208597954880.0743604298977441
130.8815752464733730.2368495070532540.118424753526627
140.8834387986308770.2331224027382450.116561201369123
150.9449982527365880.1100034945268250.0550017472634124
160.926905301347840.1461893973043210.0730946986521606
170.8859461882661660.2281076234676670.114053811733834
180.8356039921800460.3287920156399090.164396007819954
190.7695068375627870.4609863248744260.230493162437213
200.7098960693326570.5802078613346870.290103930667343
210.6390706002280550.721858799543890.360929399771945
220.5511228523099850.897754295380030.448877147690015
230.4799296435958550.959859287191710.520070356404145
240.3944275612589920.7888551225179850.605572438741008
250.3294297110781840.6588594221563680.670570288921816
260.3571079111859360.7142158223718720.642892088814064
270.3042811356861850.608562271372370.695718864313815
280.3292246528768950.658449305753790.670775347123105
290.2863361166634010.5726722333268030.713663883336599
300.2198478578494080.4396957156988160.780152142150592
310.1709490840448290.3418981680896590.829050915955171
320.1213965476228800.2427930952457600.87860345237712
330.08785718509529970.1757143701905990.9121428149047
340.06128853712757360.1225770742551470.938711462872426
350.04395507254702550.0879101450940510.956044927452975
360.0736848785072980.1473697570145960.926315121492702
370.06603760637262570.1320752127452510.933962393627374
380.07422895447689960.1484579089537990.9257710455231
390.5713392845475320.8573214309049360.428660715452468
400.5844599960505520.8310800078988960.415540003949448
410.559352926237420.881294147525160.44064707376258
420.4978744926665880.9957489853331750.502125507333412
430.4609408491380190.9218816982760370.539059150861981
440.3896834386643930.7793668773287870.610316561335607
450.2658458766958980.5316917533917960.734154123304102
460.1680991528239990.3361983056479980.831900847176001

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.920939338002278 & 0.158121323995445 & 0.0790606619977223 \tabularnewline
11 & 0.895497270303237 & 0.209005459393526 & 0.104502729696763 \tabularnewline
12 & 0.925639570102256 & 0.148720859795488 & 0.0743604298977441 \tabularnewline
13 & 0.881575246473373 & 0.236849507053254 & 0.118424753526627 \tabularnewline
14 & 0.883438798630877 & 0.233122402738245 & 0.116561201369123 \tabularnewline
15 & 0.944998252736588 & 0.110003494526825 & 0.0550017472634124 \tabularnewline
16 & 0.92690530134784 & 0.146189397304321 & 0.0730946986521606 \tabularnewline
17 & 0.885946188266166 & 0.228107623467667 & 0.114053811733834 \tabularnewline
18 & 0.835603992180046 & 0.328792015639909 & 0.164396007819954 \tabularnewline
19 & 0.769506837562787 & 0.460986324874426 & 0.230493162437213 \tabularnewline
20 & 0.709896069332657 & 0.580207861334687 & 0.290103930667343 \tabularnewline
21 & 0.639070600228055 & 0.72185879954389 & 0.360929399771945 \tabularnewline
22 & 0.551122852309985 & 0.89775429538003 & 0.448877147690015 \tabularnewline
23 & 0.479929643595855 & 0.95985928719171 & 0.520070356404145 \tabularnewline
24 & 0.394427561258992 & 0.788855122517985 & 0.605572438741008 \tabularnewline
25 & 0.329429711078184 & 0.658859422156368 & 0.670570288921816 \tabularnewline
26 & 0.357107911185936 & 0.714215822371872 & 0.642892088814064 \tabularnewline
27 & 0.304281135686185 & 0.60856227137237 & 0.695718864313815 \tabularnewline
28 & 0.329224652876895 & 0.65844930575379 & 0.670775347123105 \tabularnewline
29 & 0.286336116663401 & 0.572672233326803 & 0.713663883336599 \tabularnewline
30 & 0.219847857849408 & 0.439695715698816 & 0.780152142150592 \tabularnewline
31 & 0.170949084044829 & 0.341898168089659 & 0.829050915955171 \tabularnewline
32 & 0.121396547622880 & 0.242793095245760 & 0.87860345237712 \tabularnewline
33 & 0.0878571850952997 & 0.175714370190599 & 0.9121428149047 \tabularnewline
34 & 0.0612885371275736 & 0.122577074255147 & 0.938711462872426 \tabularnewline
35 & 0.0439550725470255 & 0.087910145094051 & 0.956044927452975 \tabularnewline
36 & 0.073684878507298 & 0.147369757014596 & 0.926315121492702 \tabularnewline
37 & 0.0660376063726257 & 0.132075212745251 & 0.933962393627374 \tabularnewline
38 & 0.0742289544768996 & 0.148457908953799 & 0.9257710455231 \tabularnewline
39 & 0.571339284547532 & 0.857321430904936 & 0.428660715452468 \tabularnewline
40 & 0.584459996050552 & 0.831080007898896 & 0.415540003949448 \tabularnewline
41 & 0.55935292623742 & 0.88129414752516 & 0.44064707376258 \tabularnewline
42 & 0.497874492666588 & 0.995748985333175 & 0.502125507333412 \tabularnewline
43 & 0.460940849138019 & 0.921881698276037 & 0.539059150861981 \tabularnewline
44 & 0.389683438664393 & 0.779366877328787 & 0.610316561335607 \tabularnewline
45 & 0.265845876695898 & 0.531691753391796 & 0.734154123304102 \tabularnewline
46 & 0.168099152823999 & 0.336198305647998 & 0.831900847176001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&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]10[/C][C]0.920939338002278[/C][C]0.158121323995445[/C][C]0.0790606619977223[/C][/ROW]
[ROW][C]11[/C][C]0.895497270303237[/C][C]0.209005459393526[/C][C]0.104502729696763[/C][/ROW]
[ROW][C]12[/C][C]0.925639570102256[/C][C]0.148720859795488[/C][C]0.0743604298977441[/C][/ROW]
[ROW][C]13[/C][C]0.881575246473373[/C][C]0.236849507053254[/C][C]0.118424753526627[/C][/ROW]
[ROW][C]14[/C][C]0.883438798630877[/C][C]0.233122402738245[/C][C]0.116561201369123[/C][/ROW]
[ROW][C]15[/C][C]0.944998252736588[/C][C]0.110003494526825[/C][C]0.0550017472634124[/C][/ROW]
[ROW][C]16[/C][C]0.92690530134784[/C][C]0.146189397304321[/C][C]0.0730946986521606[/C][/ROW]
[ROW][C]17[/C][C]0.885946188266166[/C][C]0.228107623467667[/C][C]0.114053811733834[/C][/ROW]
[ROW][C]18[/C][C]0.835603992180046[/C][C]0.328792015639909[/C][C]0.164396007819954[/C][/ROW]
[ROW][C]19[/C][C]0.769506837562787[/C][C]0.460986324874426[/C][C]0.230493162437213[/C][/ROW]
[ROW][C]20[/C][C]0.709896069332657[/C][C]0.580207861334687[/C][C]0.290103930667343[/C][/ROW]
[ROW][C]21[/C][C]0.639070600228055[/C][C]0.72185879954389[/C][C]0.360929399771945[/C][/ROW]
[ROW][C]22[/C][C]0.551122852309985[/C][C]0.89775429538003[/C][C]0.448877147690015[/C][/ROW]
[ROW][C]23[/C][C]0.479929643595855[/C][C]0.95985928719171[/C][C]0.520070356404145[/C][/ROW]
[ROW][C]24[/C][C]0.394427561258992[/C][C]0.788855122517985[/C][C]0.605572438741008[/C][/ROW]
[ROW][C]25[/C][C]0.329429711078184[/C][C]0.658859422156368[/C][C]0.670570288921816[/C][/ROW]
[ROW][C]26[/C][C]0.357107911185936[/C][C]0.714215822371872[/C][C]0.642892088814064[/C][/ROW]
[ROW][C]27[/C][C]0.304281135686185[/C][C]0.60856227137237[/C][C]0.695718864313815[/C][/ROW]
[ROW][C]28[/C][C]0.329224652876895[/C][C]0.65844930575379[/C][C]0.670775347123105[/C][/ROW]
[ROW][C]29[/C][C]0.286336116663401[/C][C]0.572672233326803[/C][C]0.713663883336599[/C][/ROW]
[ROW][C]30[/C][C]0.219847857849408[/C][C]0.439695715698816[/C][C]0.780152142150592[/C][/ROW]
[ROW][C]31[/C][C]0.170949084044829[/C][C]0.341898168089659[/C][C]0.829050915955171[/C][/ROW]
[ROW][C]32[/C][C]0.121396547622880[/C][C]0.242793095245760[/C][C]0.87860345237712[/C][/ROW]
[ROW][C]33[/C][C]0.0878571850952997[/C][C]0.175714370190599[/C][C]0.9121428149047[/C][/ROW]
[ROW][C]34[/C][C]0.0612885371275736[/C][C]0.122577074255147[/C][C]0.938711462872426[/C][/ROW]
[ROW][C]35[/C][C]0.0439550725470255[/C][C]0.087910145094051[/C][C]0.956044927452975[/C][/ROW]
[ROW][C]36[/C][C]0.073684878507298[/C][C]0.147369757014596[/C][C]0.926315121492702[/C][/ROW]
[ROW][C]37[/C][C]0.0660376063726257[/C][C]0.132075212745251[/C][C]0.933962393627374[/C][/ROW]
[ROW][C]38[/C][C]0.0742289544768996[/C][C]0.148457908953799[/C][C]0.9257710455231[/C][/ROW]
[ROW][C]39[/C][C]0.571339284547532[/C][C]0.857321430904936[/C][C]0.428660715452468[/C][/ROW]
[ROW][C]40[/C][C]0.584459996050552[/C][C]0.831080007898896[/C][C]0.415540003949448[/C][/ROW]
[ROW][C]41[/C][C]0.55935292623742[/C][C]0.88129414752516[/C][C]0.44064707376258[/C][/ROW]
[ROW][C]42[/C][C]0.497874492666588[/C][C]0.995748985333175[/C][C]0.502125507333412[/C][/ROW]
[ROW][C]43[/C][C]0.460940849138019[/C][C]0.921881698276037[/C][C]0.539059150861981[/C][/ROW]
[ROW][C]44[/C][C]0.389683438664393[/C][C]0.779366877328787[/C][C]0.610316561335607[/C][/ROW]
[ROW][C]45[/C][C]0.265845876695898[/C][C]0.531691753391796[/C][C]0.734154123304102[/C][/ROW]
[ROW][C]46[/C][C]0.168099152823999[/C][C]0.336198305647998[/C][C]0.831900847176001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=5

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.9209393380022780.1581213239954450.0790606619977223
110.8954972703032370.2090054593935260.104502729696763
120.9256395701022560.1487208597954880.0743604298977441
130.8815752464733730.2368495070532540.118424753526627
140.8834387986308770.2331224027382450.116561201369123
150.9449982527365880.1100034945268250.0550017472634124
160.926905301347840.1461893973043210.0730946986521606
170.8859461882661660.2281076234676670.114053811733834
180.8356039921800460.3287920156399090.164396007819954
190.7695068375627870.4609863248744260.230493162437213
200.7098960693326570.5802078613346870.290103930667343
210.6390706002280550.721858799543890.360929399771945
220.5511228523099850.897754295380030.448877147690015
230.4799296435958550.959859287191710.520070356404145
240.3944275612589920.7888551225179850.605572438741008
250.3294297110781840.6588594221563680.670570288921816
260.3571079111859360.7142158223718720.642892088814064
270.3042811356861850.608562271372370.695718864313815
280.3292246528768950.658449305753790.670775347123105
290.2863361166634010.5726722333268030.713663883336599
300.2198478578494080.4396957156988160.780152142150592
310.1709490840448290.3418981680896590.829050915955171
320.1213965476228800.2427930952457600.87860345237712
330.08785718509529970.1757143701905990.9121428149047
340.06128853712757360.1225770742551470.938711462872426
350.04395507254702550.0879101450940510.956044927452975
360.0736848785072980.1473697570145960.926315121492702
370.06603760637262570.1320752127452510.933962393627374
380.07422895447689960.1484579089537990.9257710455231
390.5713392845475320.8573214309049360.428660715452468
400.5844599960505520.8310800078988960.415540003949448
410.559352926237420.881294147525160.44064707376258
420.4978744926665880.9957489853331750.502125507333412
430.4609408491380190.9218816982760370.539059150861981
440.3896834386643930.7793668773287870.610316561335607
450.2658458766958980.5316917533917960.734154123304102
460.1680991528239990.3361983056479980.831900847176001






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 level10.0270270270270270OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 1 & 0.0270270270270270 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57547&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]1[/C][C]0.0270270270270270[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57547&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57547&T=6

As an alternative you can also use a QR Code:  
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 level10.0270270270270270OK


Figures (Output of Computation)

Figure 1
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Figure 9
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}