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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 15 Nov 2011 06:23:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321356288wwf6ry0olfz1xf7.htm/, Retrieved Thu, 31 Oct 2024 23:47:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142740, Retrieved Thu, 31 Oct 2024 23:47:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD    [Multiple Regression] [brandverzekering2] [2011-11-15 11:23:56] [89a94f030b332f6008ade04d76806a4c] [Current]
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Dataseries X:
4.1	24.3
1.7	19
8	37.2
5	27.3
6	21.5
4.8	19.2
3.8	16.8
2.7	14.9
1	18.2
8.4	34.8
6.1	29.6
4.8	25.3
2.2	17.5
0.6	13.7
2.8	17.9
7.4	24.8
6.3	25.3
2.3	21.7
1.1	13.8
3.4	17.2
6.1	26.7
2.9	17.9
1.9	15.8
0.6	16.3
7.2	26.8
1.6	17.8
2.5	17.2
3.5	18.3
4	16.9
0.9	11.9
1.7	13.8
8.9	27.9
5.2	21.4
3.6	18.6
0.7	12.6
1.4	14.2
3.7	19.6
4.8	18.9
5.6	26.4
6.2	31.1
1.4	16.2
1.8	18.9
8.6	35.8
7.2	24.2
2.7	18.2
2.9	19.6
3.6	22.8
1.7	12
0.5	9
0.4	11
7.4	34.3
6.2	27.3
5.8	24.8
4.1	21
3.6	17.2
8.4	30
2.8	14
9	38.9
2.9	14.1
4.1	19.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
afstand[t] = -2.71600231617741 + 0.320463860057686schadebedrag[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
afstand[t] =  -2.71600231617741 +  0.320463860057686schadebedrag[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]afstand[t] =  -2.71600231617741 +  0.320463860057686schadebedrag[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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
afstand[t] = -2.71600231617741 + 0.320463860057686schadebedrag[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.716002316177410.456516-5.949400
schadebedrag0.3204638600576860.02068415.493200

\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) & -2.71600231617741 & 0.456516 & -5.9494 & 0 & 0 \tabularnewline
schadebedrag & 0.320463860057686 & 0.020684 & 15.4932 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&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]-2.71600231617741[/C][C]0.456516[/C][C]-5.9494[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]schadebedrag[/C][C]0.320463860057686[/C][C]0.020684[/C][C]15.4932[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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)-2.716002316177410.456516-5.949400
schadebedrag0.3204638600576860.02068415.493200







Multiple Linear Regression - Regression Statistics
Multiple R0.897437591050394
R-squared0.805394229830334
Adjusted R-squared0.802038957930858
F-TEST (value)240.0384391965
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.09383263240868
Sum Squared Residuals69.3952500078817

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.897437591050394 \tabularnewline
R-squared & 0.805394229830334 \tabularnewline
Adjusted R-squared & 0.802038957930858 \tabularnewline
F-TEST (value) & 240.0384391965 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.09383263240868 \tabularnewline
Sum Squared Residuals & 69.3952500078817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.897437591050394[/C][/ROW]
[ROW][C]R-squared[/C][C]0.805394229830334[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.802038957930858[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]240.0384391965[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.09383263240868[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]69.3952500078817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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 R0.897437591050394
R-squared0.805394229830334
Adjusted R-squared0.802038957930858
F-TEST (value)240.0384391965
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.09383263240868
Sum Squared Residuals69.3952500078817







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
14.15.07126948322438-0.97126948322438
21.73.37281102491863-1.67281102491863
389.20525327796853-1.20525327796852
456.03266106339743-1.03266106339743
564.173970675062851.82602932493715
64.83.436903796930171.36309620306983
73.82.667790532791721.13220946720828
82.72.058909198682120.64109080131788
913.11643993687248-2.11643993687248
108.48.43614001383008-0.036140013830076
116.16.76972794153011-0.669727941530109
124.85.39173334328206-0.591733343282058
132.22.8921152348321-0.692115234832104
140.61.6743525666129-1.0743525666129
152.83.02030077885518-0.220300778855178
167.45.231501413253212.16849858674679
176.35.391733343282060.908266656717942
182.34.23806344707439-1.93806344707439
191.11.70639895261867-0.606398952618665
203.42.79597607681480.604023923185202
216.15.840382747362820.259617252637182
222.93.02030077885518-0.120300778855178
231.92.34732667273404-0.447326672734038
240.62.50755860276288-1.90755860276288
257.25.872429133368591.32757086663141
261.62.98825439284941-1.38825439284941
272.52.7959760768148-0.295976076814798
283.53.148486322878250.351513677121746
2942.699836918797491.30016308120251
300.91.09751761850906-0.197517618509061
311.71.70639895261867-0.00639895261866516
328.96.224939379432042.67506062056796
335.24.141924289057081.05807571094292
343.63.244625480895560.35537451910444
350.71.32184232054944-0.621842320549441
361.41.83458449664174-0.434584496641739
373.73.565089340953250.134910659046754
384.83.340764638912861.45923536108714
395.65.74424358934551-0.144243589345512
406.27.25042373161664-1.05042373161664
411.42.47551221675711-1.07551221675711
421.83.34076463891286-1.54076463891286
438.68.75660387388776-0.156603873887763
447.25.03922309721862.1607769027814
452.73.11643993687248-0.416439936872484
462.93.56508934095325-0.665089340953246
473.64.59057369313784-0.990573693137842
481.71.129564004514830.570435995485171
490.50.1681724243417710.331827575658229
500.40.809100144457143-0.409100144457143
517.48.27590808380123-0.875908083801233
526.26.032661063397430.16733893660257
535.85.231501413253210.568498586746785
544.14.013738745034010.0862612549659934
553.62.79597607681480.804023923185202
568.46.897913485553181.50208651444682
572.81.77049172463021.0295082753698
5899.75004184006659-0.75004184006659
592.91.802538110635971.09746188936403
604.13.661228498970550.438771501029449

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 4.1 & 5.07126948322438 & -0.97126948322438 \tabularnewline
2 & 1.7 & 3.37281102491863 & -1.67281102491863 \tabularnewline
3 & 8 & 9.20525327796853 & -1.20525327796852 \tabularnewline
4 & 5 & 6.03266106339743 & -1.03266106339743 \tabularnewline
5 & 6 & 4.17397067506285 & 1.82602932493715 \tabularnewline
6 & 4.8 & 3.43690379693017 & 1.36309620306983 \tabularnewline
7 & 3.8 & 2.66779053279172 & 1.13220946720828 \tabularnewline
8 & 2.7 & 2.05890919868212 & 0.64109080131788 \tabularnewline
9 & 1 & 3.11643993687248 & -2.11643993687248 \tabularnewline
10 & 8.4 & 8.43614001383008 & -0.036140013830076 \tabularnewline
11 & 6.1 & 6.76972794153011 & -0.669727941530109 \tabularnewline
12 & 4.8 & 5.39173334328206 & -0.591733343282058 \tabularnewline
13 & 2.2 & 2.8921152348321 & -0.692115234832104 \tabularnewline
14 & 0.6 & 1.6743525666129 & -1.0743525666129 \tabularnewline
15 & 2.8 & 3.02030077885518 & -0.220300778855178 \tabularnewline
16 & 7.4 & 5.23150141325321 & 2.16849858674679 \tabularnewline
17 & 6.3 & 5.39173334328206 & 0.908266656717942 \tabularnewline
18 & 2.3 & 4.23806344707439 & -1.93806344707439 \tabularnewline
19 & 1.1 & 1.70639895261867 & -0.606398952618665 \tabularnewline
20 & 3.4 & 2.7959760768148 & 0.604023923185202 \tabularnewline
21 & 6.1 & 5.84038274736282 & 0.259617252637182 \tabularnewline
22 & 2.9 & 3.02030077885518 & -0.120300778855178 \tabularnewline
23 & 1.9 & 2.34732667273404 & -0.447326672734038 \tabularnewline
24 & 0.6 & 2.50755860276288 & -1.90755860276288 \tabularnewline
25 & 7.2 & 5.87242913336859 & 1.32757086663141 \tabularnewline
26 & 1.6 & 2.98825439284941 & -1.38825439284941 \tabularnewline
27 & 2.5 & 2.7959760768148 & -0.295976076814798 \tabularnewline
28 & 3.5 & 3.14848632287825 & 0.351513677121746 \tabularnewline
29 & 4 & 2.69983691879749 & 1.30016308120251 \tabularnewline
30 & 0.9 & 1.09751761850906 & -0.197517618509061 \tabularnewline
31 & 1.7 & 1.70639895261867 & -0.00639895261866516 \tabularnewline
32 & 8.9 & 6.22493937943204 & 2.67506062056796 \tabularnewline
33 & 5.2 & 4.14192428905708 & 1.05807571094292 \tabularnewline
34 & 3.6 & 3.24462548089556 & 0.35537451910444 \tabularnewline
35 & 0.7 & 1.32184232054944 & -0.621842320549441 \tabularnewline
36 & 1.4 & 1.83458449664174 & -0.434584496641739 \tabularnewline
37 & 3.7 & 3.56508934095325 & 0.134910659046754 \tabularnewline
38 & 4.8 & 3.34076463891286 & 1.45923536108714 \tabularnewline
39 & 5.6 & 5.74424358934551 & -0.144243589345512 \tabularnewline
40 & 6.2 & 7.25042373161664 & -1.05042373161664 \tabularnewline
41 & 1.4 & 2.47551221675711 & -1.07551221675711 \tabularnewline
42 & 1.8 & 3.34076463891286 & -1.54076463891286 \tabularnewline
43 & 8.6 & 8.75660387388776 & -0.156603873887763 \tabularnewline
44 & 7.2 & 5.0392230972186 & 2.1607769027814 \tabularnewline
45 & 2.7 & 3.11643993687248 & -0.416439936872484 \tabularnewline
46 & 2.9 & 3.56508934095325 & -0.665089340953246 \tabularnewline
47 & 3.6 & 4.59057369313784 & -0.990573693137842 \tabularnewline
48 & 1.7 & 1.12956400451483 & 0.570435995485171 \tabularnewline
49 & 0.5 & 0.168172424341771 & 0.331827575658229 \tabularnewline
50 & 0.4 & 0.809100144457143 & -0.409100144457143 \tabularnewline
51 & 7.4 & 8.27590808380123 & -0.875908083801233 \tabularnewline
52 & 6.2 & 6.03266106339743 & 0.16733893660257 \tabularnewline
53 & 5.8 & 5.23150141325321 & 0.568498586746785 \tabularnewline
54 & 4.1 & 4.01373874503401 & 0.0862612549659934 \tabularnewline
55 & 3.6 & 2.7959760768148 & 0.804023923185202 \tabularnewline
56 & 8.4 & 6.89791348555318 & 1.50208651444682 \tabularnewline
57 & 2.8 & 1.7704917246302 & 1.0295082753698 \tabularnewline
58 & 9 & 9.75004184006659 & -0.75004184006659 \tabularnewline
59 & 2.9 & 1.80253811063597 & 1.09746188936403 \tabularnewline
60 & 4.1 & 3.66122849897055 & 0.438771501029449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&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]4.1[/C][C]5.07126948322438[/C][C]-0.97126948322438[/C][/ROW]
[ROW][C]2[/C][C]1.7[/C][C]3.37281102491863[/C][C]-1.67281102491863[/C][/ROW]
[ROW][C]3[/C][C]8[/C][C]9.20525327796853[/C][C]-1.20525327796852[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]6.03266106339743[/C][C]-1.03266106339743[/C][/ROW]
[ROW][C]5[/C][C]6[/C][C]4.17397067506285[/C][C]1.82602932493715[/C][/ROW]
[ROW][C]6[/C][C]4.8[/C][C]3.43690379693017[/C][C]1.36309620306983[/C][/ROW]
[ROW][C]7[/C][C]3.8[/C][C]2.66779053279172[/C][C]1.13220946720828[/C][/ROW]
[ROW][C]8[/C][C]2.7[/C][C]2.05890919868212[/C][C]0.64109080131788[/C][/ROW]
[ROW][C]9[/C][C]1[/C][C]3.11643993687248[/C][C]-2.11643993687248[/C][/ROW]
[ROW][C]10[/C][C]8.4[/C][C]8.43614001383008[/C][C]-0.036140013830076[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.76972794153011[/C][C]-0.669727941530109[/C][/ROW]
[ROW][C]12[/C][C]4.8[/C][C]5.39173334328206[/C][C]-0.591733343282058[/C][/ROW]
[ROW][C]13[/C][C]2.2[/C][C]2.8921152348321[/C][C]-0.692115234832104[/C][/ROW]
[ROW][C]14[/C][C]0.6[/C][C]1.6743525666129[/C][C]-1.0743525666129[/C][/ROW]
[ROW][C]15[/C][C]2.8[/C][C]3.02030077885518[/C][C]-0.220300778855178[/C][/ROW]
[ROW][C]16[/C][C]7.4[/C][C]5.23150141325321[/C][C]2.16849858674679[/C][/ROW]
[ROW][C]17[/C][C]6.3[/C][C]5.39173334328206[/C][C]0.908266656717942[/C][/ROW]
[ROW][C]18[/C][C]2.3[/C][C]4.23806344707439[/C][C]-1.93806344707439[/C][/ROW]
[ROW][C]19[/C][C]1.1[/C][C]1.70639895261867[/C][C]-0.606398952618665[/C][/ROW]
[ROW][C]20[/C][C]3.4[/C][C]2.7959760768148[/C][C]0.604023923185202[/C][/ROW]
[ROW][C]21[/C][C]6.1[/C][C]5.84038274736282[/C][C]0.259617252637182[/C][/ROW]
[ROW][C]22[/C][C]2.9[/C][C]3.02030077885518[/C][C]-0.120300778855178[/C][/ROW]
[ROW][C]23[/C][C]1.9[/C][C]2.34732667273404[/C][C]-0.447326672734038[/C][/ROW]
[ROW][C]24[/C][C]0.6[/C][C]2.50755860276288[/C][C]-1.90755860276288[/C][/ROW]
[ROW][C]25[/C][C]7.2[/C][C]5.87242913336859[/C][C]1.32757086663141[/C][/ROW]
[ROW][C]26[/C][C]1.6[/C][C]2.98825439284941[/C][C]-1.38825439284941[/C][/ROW]
[ROW][C]27[/C][C]2.5[/C][C]2.7959760768148[/C][C]-0.295976076814798[/C][/ROW]
[ROW][C]28[/C][C]3.5[/C][C]3.14848632287825[/C][C]0.351513677121746[/C][/ROW]
[ROW][C]29[/C][C]4[/C][C]2.69983691879749[/C][C]1.30016308120251[/C][/ROW]
[ROW][C]30[/C][C]0.9[/C][C]1.09751761850906[/C][C]-0.197517618509061[/C][/ROW]
[ROW][C]31[/C][C]1.7[/C][C]1.70639895261867[/C][C]-0.00639895261866516[/C][/ROW]
[ROW][C]32[/C][C]8.9[/C][C]6.22493937943204[/C][C]2.67506062056796[/C][/ROW]
[ROW][C]33[/C][C]5.2[/C][C]4.14192428905708[/C][C]1.05807571094292[/C][/ROW]
[ROW][C]34[/C][C]3.6[/C][C]3.24462548089556[/C][C]0.35537451910444[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]1.32184232054944[/C][C]-0.621842320549441[/C][/ROW]
[ROW][C]36[/C][C]1.4[/C][C]1.83458449664174[/C][C]-0.434584496641739[/C][/ROW]
[ROW][C]37[/C][C]3.7[/C][C]3.56508934095325[/C][C]0.134910659046754[/C][/ROW]
[ROW][C]38[/C][C]4.8[/C][C]3.34076463891286[/C][C]1.45923536108714[/C][/ROW]
[ROW][C]39[/C][C]5.6[/C][C]5.74424358934551[/C][C]-0.144243589345512[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]7.25042373161664[/C][C]-1.05042373161664[/C][/ROW]
[ROW][C]41[/C][C]1.4[/C][C]2.47551221675711[/C][C]-1.07551221675711[/C][/ROW]
[ROW][C]42[/C][C]1.8[/C][C]3.34076463891286[/C][C]-1.54076463891286[/C][/ROW]
[ROW][C]43[/C][C]8.6[/C][C]8.75660387388776[/C][C]-0.156603873887763[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]5.0392230972186[/C][C]2.1607769027814[/C][/ROW]
[ROW][C]45[/C][C]2.7[/C][C]3.11643993687248[/C][C]-0.416439936872484[/C][/ROW]
[ROW][C]46[/C][C]2.9[/C][C]3.56508934095325[/C][C]-0.665089340953246[/C][/ROW]
[ROW][C]47[/C][C]3.6[/C][C]4.59057369313784[/C][C]-0.990573693137842[/C][/ROW]
[ROW][C]48[/C][C]1.7[/C][C]1.12956400451483[/C][C]0.570435995485171[/C][/ROW]
[ROW][C]49[/C][C]0.5[/C][C]0.168172424341771[/C][C]0.331827575658229[/C][/ROW]
[ROW][C]50[/C][C]0.4[/C][C]0.809100144457143[/C][C]-0.409100144457143[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]8.27590808380123[/C][C]-0.875908083801233[/C][/ROW]
[ROW][C]52[/C][C]6.2[/C][C]6.03266106339743[/C][C]0.16733893660257[/C][/ROW]
[ROW][C]53[/C][C]5.8[/C][C]5.23150141325321[/C][C]0.568498586746785[/C][/ROW]
[ROW][C]54[/C][C]4.1[/C][C]4.01373874503401[/C][C]0.0862612549659934[/C][/ROW]
[ROW][C]55[/C][C]3.6[/C][C]2.7959760768148[/C][C]0.804023923185202[/C][/ROW]
[ROW][C]56[/C][C]8.4[/C][C]6.89791348555318[/C][C]1.50208651444682[/C][/ROW]
[ROW][C]57[/C][C]2.8[/C][C]1.7704917246302[/C][C]1.0295082753698[/C][/ROW]
[ROW][C]58[/C][C]9[/C][C]9.75004184006659[/C][C]-0.75004184006659[/C][/ROW]
[ROW][C]59[/C][C]2.9[/C][C]1.80253811063597[/C][C]1.09746188936403[/C][/ROW]
[ROW][C]60[/C][C]4.1[/C][C]3.66122849897055[/C][C]0.438771501029449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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
14.15.07126948322438-0.97126948322438
21.73.37281102491863-1.67281102491863
389.20525327796853-1.20525327796852
456.03266106339743-1.03266106339743
564.173970675062851.82602932493715
64.83.436903796930171.36309620306983
73.82.667790532791721.13220946720828
82.72.058909198682120.64109080131788
913.11643993687248-2.11643993687248
108.48.43614001383008-0.036140013830076
116.16.76972794153011-0.669727941530109
124.85.39173334328206-0.591733343282058
132.22.8921152348321-0.692115234832104
140.61.6743525666129-1.0743525666129
152.83.02030077885518-0.220300778855178
167.45.231501413253212.16849858674679
176.35.391733343282060.908266656717942
182.34.23806344707439-1.93806344707439
191.11.70639895261867-0.606398952618665
203.42.79597607681480.604023923185202
216.15.840382747362820.259617252637182
222.93.02030077885518-0.120300778855178
231.92.34732667273404-0.447326672734038
240.62.50755860276288-1.90755860276288
257.25.872429133368591.32757086663141
261.62.98825439284941-1.38825439284941
272.52.7959760768148-0.295976076814798
283.53.148486322878250.351513677121746
2942.699836918797491.30016308120251
300.91.09751761850906-0.197517618509061
311.71.70639895261867-0.00639895261866516
328.96.224939379432042.67506062056796
335.24.141924289057081.05807571094292
343.63.244625480895560.35537451910444
350.71.32184232054944-0.621842320549441
361.41.83458449664174-0.434584496641739
373.73.565089340953250.134910659046754
384.83.340764638912861.45923536108714
395.65.74424358934551-0.144243589345512
406.27.25042373161664-1.05042373161664
411.42.47551221675711-1.07551221675711
421.83.34076463891286-1.54076463891286
438.68.75660387388776-0.156603873887763
447.25.03922309721862.1607769027814
452.73.11643993687248-0.416439936872484
462.93.56508934095325-0.665089340953246
473.64.59057369313784-0.990573693137842
481.71.129564004514830.570435995485171
490.50.1681724243417710.331827575658229
500.40.809100144457143-0.409100144457143
517.48.27590808380123-0.875908083801233
526.26.032661063397430.16733893660257
535.85.231501413253210.568498586746785
544.14.013738745034010.0862612549659934
553.62.79597607681480.804023923185202
568.46.897913485553181.50208651444682
572.81.77049172463021.0295082753698
5899.75004184006659-0.75004184006659
592.91.802538110635971.09746188936403
604.13.661228498970550.438771501029449







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.8947777223693250.2104445552613490.105222277630675
60.8996085186639720.2007829626720550.100391481336028
70.851409847693240.297180304613520.14859015230676
80.7729482942460780.4541034115078440.227051705753922
90.9333375381182990.1333249237634010.0666624618817007
100.9118209291970710.1763581416058570.0881790708029287
110.8708013541739340.2583972916521320.129198645826066
120.8200901889249340.3598196221501320.179909811075066
130.7774994513554650.4450010972890710.222500548644535
140.7685786514234360.4628426971531280.231421348576564
150.6952907134466070.6094185731067860.304709286553393
160.8876956597454140.2246086805091710.112304340254586
170.8775094414214390.2449811171571220.122490558578561
180.9327018067644570.1345963864710860.0672981932355431
190.9096493023400150.180701395319970.0903506976599851
200.8865025093976440.2269949812047110.113497490602356
210.84887545391950.3022490921610.1511245460805
220.7983648073336280.4032703853327430.201635192666372
230.7472373490381010.5055253019237990.252762650961899
240.843549035815680.3129019283686410.15645096418432
250.8652090551885310.2695818896229370.134790944811469
260.8860225589438170.2279548821123670.113977441056183
270.849802398937820.300395202124360.15019760106218
280.8089600635613280.3820798728773440.191039936438672
290.8304018880603480.3391962238793050.169598111939652
300.781734872436430.4365302551271390.21826512756357
310.7234065904489870.5531868191020260.276593409551013
320.9382458229039480.1235083541921050.0617541770960523
330.9363627640036670.1272744719926660.0636372359963332
340.9109319984145190.1781360031709620.0890680015854808
350.8929445688262670.2141108623474650.107055431173733
360.8650984245684710.2698031508630570.134901575431529
370.8171720066768330.3656559866463340.182827993323167
380.8513514677798810.2972970644402380.148648532220119
390.7995156262023870.4009687475952250.200484373797613
400.7932736426001790.4134527147996430.206726357399822
410.8112183792704310.3775632414591380.188781620729569
420.8987737395761930.2024525208476140.101226260423807
430.8540006207028010.2919987585943980.145999379297199
440.9662226456970490.0675547086059020.033777354302951
450.9549755239666080.09004895206678310.0450244760333916
460.9531858809247380.09362823815052330.0468141190752617
470.9704201343423830.05915973131523450.0295798656576173
480.9481624887591690.1036750224816630.0518375112408315
490.92086916802620.15826166394760.0791308319737999
500.9661960805175330.06760783896493490.0338039194824675
510.9637667654619190.0724664690761620.036233234538081
520.9274123565232350.1451752869535310.0725876434767653
530.860660897021810.2786782059563810.13933910297819
540.8039632026788450.3920735946423110.196036797321155
550.6581967931376240.6836064137247520.341803206862376

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.894777722369325 & 0.210444555261349 & 0.105222277630675 \tabularnewline
6 & 0.899608518663972 & 0.200782962672055 & 0.100391481336028 \tabularnewline
7 & 0.85140984769324 & 0.29718030461352 & 0.14859015230676 \tabularnewline
8 & 0.772948294246078 & 0.454103411507844 & 0.227051705753922 \tabularnewline
9 & 0.933337538118299 & 0.133324923763401 & 0.0666624618817007 \tabularnewline
10 & 0.911820929197071 & 0.176358141605857 & 0.0881790708029287 \tabularnewline
11 & 0.870801354173934 & 0.258397291652132 & 0.129198645826066 \tabularnewline
12 & 0.820090188924934 & 0.359819622150132 & 0.179909811075066 \tabularnewline
13 & 0.777499451355465 & 0.445001097289071 & 0.222500548644535 \tabularnewline
14 & 0.768578651423436 & 0.462842697153128 & 0.231421348576564 \tabularnewline
15 & 0.695290713446607 & 0.609418573106786 & 0.304709286553393 \tabularnewline
16 & 0.887695659745414 & 0.224608680509171 & 0.112304340254586 \tabularnewline
17 & 0.877509441421439 & 0.244981117157122 & 0.122490558578561 \tabularnewline
18 & 0.932701806764457 & 0.134596386471086 & 0.0672981932355431 \tabularnewline
19 & 0.909649302340015 & 0.18070139531997 & 0.0903506976599851 \tabularnewline
20 & 0.886502509397644 & 0.226994981204711 & 0.113497490602356 \tabularnewline
21 & 0.8488754539195 & 0.302249092161 & 0.1511245460805 \tabularnewline
22 & 0.798364807333628 & 0.403270385332743 & 0.201635192666372 \tabularnewline
23 & 0.747237349038101 & 0.505525301923799 & 0.252762650961899 \tabularnewline
24 & 0.84354903581568 & 0.312901928368641 & 0.15645096418432 \tabularnewline
25 & 0.865209055188531 & 0.269581889622937 & 0.134790944811469 \tabularnewline
26 & 0.886022558943817 & 0.227954882112367 & 0.113977441056183 \tabularnewline
27 & 0.84980239893782 & 0.30039520212436 & 0.15019760106218 \tabularnewline
28 & 0.808960063561328 & 0.382079872877344 & 0.191039936438672 \tabularnewline
29 & 0.830401888060348 & 0.339196223879305 & 0.169598111939652 \tabularnewline
30 & 0.78173487243643 & 0.436530255127139 & 0.21826512756357 \tabularnewline
31 & 0.723406590448987 & 0.553186819102026 & 0.276593409551013 \tabularnewline
32 & 0.938245822903948 & 0.123508354192105 & 0.0617541770960523 \tabularnewline
33 & 0.936362764003667 & 0.127274471992666 & 0.0636372359963332 \tabularnewline
34 & 0.910931998414519 & 0.178136003170962 & 0.0890680015854808 \tabularnewline
35 & 0.892944568826267 & 0.214110862347465 & 0.107055431173733 \tabularnewline
36 & 0.865098424568471 & 0.269803150863057 & 0.134901575431529 \tabularnewline
37 & 0.817172006676833 & 0.365655986646334 & 0.182827993323167 \tabularnewline
38 & 0.851351467779881 & 0.297297064440238 & 0.148648532220119 \tabularnewline
39 & 0.799515626202387 & 0.400968747595225 & 0.200484373797613 \tabularnewline
40 & 0.793273642600179 & 0.413452714799643 & 0.206726357399822 \tabularnewline
41 & 0.811218379270431 & 0.377563241459138 & 0.188781620729569 \tabularnewline
42 & 0.898773739576193 & 0.202452520847614 & 0.101226260423807 \tabularnewline
43 & 0.854000620702801 & 0.291998758594398 & 0.145999379297199 \tabularnewline
44 & 0.966222645697049 & 0.067554708605902 & 0.033777354302951 \tabularnewline
45 & 0.954975523966608 & 0.0900489520667831 & 0.0450244760333916 \tabularnewline
46 & 0.953185880924738 & 0.0936282381505233 & 0.0468141190752617 \tabularnewline
47 & 0.970420134342383 & 0.0591597313152345 & 0.0295798656576173 \tabularnewline
48 & 0.948162488759169 & 0.103675022481663 & 0.0518375112408315 \tabularnewline
49 & 0.9208691680262 & 0.1582616639476 & 0.0791308319737999 \tabularnewline
50 & 0.966196080517533 & 0.0676078389649349 & 0.0338039194824675 \tabularnewline
51 & 0.963766765461919 & 0.072466469076162 & 0.036233234538081 \tabularnewline
52 & 0.927412356523235 & 0.145175286953531 & 0.0725876434767653 \tabularnewline
53 & 0.86066089702181 & 0.278678205956381 & 0.13933910297819 \tabularnewline
54 & 0.803963202678845 & 0.392073594642311 & 0.196036797321155 \tabularnewline
55 & 0.658196793137624 & 0.683606413724752 & 0.341803206862376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&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]0.894777722369325[/C][C]0.210444555261349[/C][C]0.105222277630675[/C][/ROW]
[ROW][C]6[/C][C]0.899608518663972[/C][C]0.200782962672055[/C][C]0.100391481336028[/C][/ROW]
[ROW][C]7[/C][C]0.85140984769324[/C][C]0.29718030461352[/C][C]0.14859015230676[/C][/ROW]
[ROW][C]8[/C][C]0.772948294246078[/C][C]0.454103411507844[/C][C]0.227051705753922[/C][/ROW]
[ROW][C]9[/C][C]0.933337538118299[/C][C]0.133324923763401[/C][C]0.0666624618817007[/C][/ROW]
[ROW][C]10[/C][C]0.911820929197071[/C][C]0.176358141605857[/C][C]0.0881790708029287[/C][/ROW]
[ROW][C]11[/C][C]0.870801354173934[/C][C]0.258397291652132[/C][C]0.129198645826066[/C][/ROW]
[ROW][C]12[/C][C]0.820090188924934[/C][C]0.359819622150132[/C][C]0.179909811075066[/C][/ROW]
[ROW][C]13[/C][C]0.777499451355465[/C][C]0.445001097289071[/C][C]0.222500548644535[/C][/ROW]
[ROW][C]14[/C][C]0.768578651423436[/C][C]0.462842697153128[/C][C]0.231421348576564[/C][/ROW]
[ROW][C]15[/C][C]0.695290713446607[/C][C]0.609418573106786[/C][C]0.304709286553393[/C][/ROW]
[ROW][C]16[/C][C]0.887695659745414[/C][C]0.224608680509171[/C][C]0.112304340254586[/C][/ROW]
[ROW][C]17[/C][C]0.877509441421439[/C][C]0.244981117157122[/C][C]0.122490558578561[/C][/ROW]
[ROW][C]18[/C][C]0.932701806764457[/C][C]0.134596386471086[/C][C]0.0672981932355431[/C][/ROW]
[ROW][C]19[/C][C]0.909649302340015[/C][C]0.18070139531997[/C][C]0.0903506976599851[/C][/ROW]
[ROW][C]20[/C][C]0.886502509397644[/C][C]0.226994981204711[/C][C]0.113497490602356[/C][/ROW]
[ROW][C]21[/C][C]0.8488754539195[/C][C]0.302249092161[/C][C]0.1511245460805[/C][/ROW]
[ROW][C]22[/C][C]0.798364807333628[/C][C]0.403270385332743[/C][C]0.201635192666372[/C][/ROW]
[ROW][C]23[/C][C]0.747237349038101[/C][C]0.505525301923799[/C][C]0.252762650961899[/C][/ROW]
[ROW][C]24[/C][C]0.84354903581568[/C][C]0.312901928368641[/C][C]0.15645096418432[/C][/ROW]
[ROW][C]25[/C][C]0.865209055188531[/C][C]0.269581889622937[/C][C]0.134790944811469[/C][/ROW]
[ROW][C]26[/C][C]0.886022558943817[/C][C]0.227954882112367[/C][C]0.113977441056183[/C][/ROW]
[ROW][C]27[/C][C]0.84980239893782[/C][C]0.30039520212436[/C][C]0.15019760106218[/C][/ROW]
[ROW][C]28[/C][C]0.808960063561328[/C][C]0.382079872877344[/C][C]0.191039936438672[/C][/ROW]
[ROW][C]29[/C][C]0.830401888060348[/C][C]0.339196223879305[/C][C]0.169598111939652[/C][/ROW]
[ROW][C]30[/C][C]0.78173487243643[/C][C]0.436530255127139[/C][C]0.21826512756357[/C][/ROW]
[ROW][C]31[/C][C]0.723406590448987[/C][C]0.553186819102026[/C][C]0.276593409551013[/C][/ROW]
[ROW][C]32[/C][C]0.938245822903948[/C][C]0.123508354192105[/C][C]0.0617541770960523[/C][/ROW]
[ROW][C]33[/C][C]0.936362764003667[/C][C]0.127274471992666[/C][C]0.0636372359963332[/C][/ROW]
[ROW][C]34[/C][C]0.910931998414519[/C][C]0.178136003170962[/C][C]0.0890680015854808[/C][/ROW]
[ROW][C]35[/C][C]0.892944568826267[/C][C]0.214110862347465[/C][C]0.107055431173733[/C][/ROW]
[ROW][C]36[/C][C]0.865098424568471[/C][C]0.269803150863057[/C][C]0.134901575431529[/C][/ROW]
[ROW][C]37[/C][C]0.817172006676833[/C][C]0.365655986646334[/C][C]0.182827993323167[/C][/ROW]
[ROW][C]38[/C][C]0.851351467779881[/C][C]0.297297064440238[/C][C]0.148648532220119[/C][/ROW]
[ROW][C]39[/C][C]0.799515626202387[/C][C]0.400968747595225[/C][C]0.200484373797613[/C][/ROW]
[ROW][C]40[/C][C]0.793273642600179[/C][C]0.413452714799643[/C][C]0.206726357399822[/C][/ROW]
[ROW][C]41[/C][C]0.811218379270431[/C][C]0.377563241459138[/C][C]0.188781620729569[/C][/ROW]
[ROW][C]42[/C][C]0.898773739576193[/C][C]0.202452520847614[/C][C]0.101226260423807[/C][/ROW]
[ROW][C]43[/C][C]0.854000620702801[/C][C]0.291998758594398[/C][C]0.145999379297199[/C][/ROW]
[ROW][C]44[/C][C]0.966222645697049[/C][C]0.067554708605902[/C][C]0.033777354302951[/C][/ROW]
[ROW][C]45[/C][C]0.954975523966608[/C][C]0.0900489520667831[/C][C]0.0450244760333916[/C][/ROW]
[ROW][C]46[/C][C]0.953185880924738[/C][C]0.0936282381505233[/C][C]0.0468141190752617[/C][/ROW]
[ROW][C]47[/C][C]0.970420134342383[/C][C]0.0591597313152345[/C][C]0.0295798656576173[/C][/ROW]
[ROW][C]48[/C][C]0.948162488759169[/C][C]0.103675022481663[/C][C]0.0518375112408315[/C][/ROW]
[ROW][C]49[/C][C]0.9208691680262[/C][C]0.1582616639476[/C][C]0.0791308319737999[/C][/ROW]
[ROW][C]50[/C][C]0.966196080517533[/C][C]0.0676078389649349[/C][C]0.0338039194824675[/C][/ROW]
[ROW][C]51[/C][C]0.963766765461919[/C][C]0.072466469076162[/C][C]0.036233234538081[/C][/ROW]
[ROW][C]52[/C][C]0.927412356523235[/C][C]0.145175286953531[/C][C]0.0725876434767653[/C][/ROW]
[ROW][C]53[/C][C]0.86066089702181[/C][C]0.278678205956381[/C][C]0.13933910297819[/C][/ROW]
[ROW][C]54[/C][C]0.803963202678845[/C][C]0.392073594642311[/C][C]0.196036797321155[/C][/ROW]
[ROW][C]55[/C][C]0.658196793137624[/C][C]0.683606413724752[/C][C]0.341803206862376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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
50.8947777223693250.2104445552613490.105222277630675
60.8996085186639720.2007829626720550.100391481336028
70.851409847693240.297180304613520.14859015230676
80.7729482942460780.4541034115078440.227051705753922
90.9333375381182990.1333249237634010.0666624618817007
100.9118209291970710.1763581416058570.0881790708029287
110.8708013541739340.2583972916521320.129198645826066
120.8200901889249340.3598196221501320.179909811075066
130.7774994513554650.4450010972890710.222500548644535
140.7685786514234360.4628426971531280.231421348576564
150.6952907134466070.6094185731067860.304709286553393
160.8876956597454140.2246086805091710.112304340254586
170.8775094414214390.2449811171571220.122490558578561
180.9327018067644570.1345963864710860.0672981932355431
190.9096493023400150.180701395319970.0903506976599851
200.8865025093976440.2269949812047110.113497490602356
210.84887545391950.3022490921610.1511245460805
220.7983648073336280.4032703853327430.201635192666372
230.7472373490381010.5055253019237990.252762650961899
240.843549035815680.3129019283686410.15645096418432
250.8652090551885310.2695818896229370.134790944811469
260.8860225589438170.2279548821123670.113977441056183
270.849802398937820.300395202124360.15019760106218
280.8089600635613280.3820798728773440.191039936438672
290.8304018880603480.3391962238793050.169598111939652
300.781734872436430.4365302551271390.21826512756357
310.7234065904489870.5531868191020260.276593409551013
320.9382458229039480.1235083541921050.0617541770960523
330.9363627640036670.1272744719926660.0636372359963332
340.9109319984145190.1781360031709620.0890680015854808
350.8929445688262670.2141108623474650.107055431173733
360.8650984245684710.2698031508630570.134901575431529
370.8171720066768330.3656559866463340.182827993323167
380.8513514677798810.2972970644402380.148648532220119
390.7995156262023870.4009687475952250.200484373797613
400.7932736426001790.4134527147996430.206726357399822
410.8112183792704310.3775632414591380.188781620729569
420.8987737395761930.2024525208476140.101226260423807
430.8540006207028010.2919987585943980.145999379297199
440.9662226456970490.0675547086059020.033777354302951
450.9549755239666080.09004895206678310.0450244760333916
460.9531858809247380.09362823815052330.0468141190752617
470.9704201343423830.05915973131523450.0295798656576173
480.9481624887591690.1036750224816630.0518375112408315
490.92086916802620.15826166394760.0791308319737999
500.9661960805175330.06760783896493490.0338039194824675
510.9637667654619190.0724664690761620.036233234538081
520.9274123565232350.1451752869535310.0725876434767653
530.860660897021810.2786782059563810.13933910297819
540.8039632026788450.3920735946423110.196036797321155
550.6581967931376240.6836064137247520.341803206862376







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 level60.117647058823529NOK

\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 & 6 & 0.117647058823529 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142740&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]6[/C][C]0.117647058823529[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142740&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142740&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 level60.117647058823529NOK



Parameters (Session):
par1 = 3 ; par2 = 4 ; par3 = Pearson Chi-Squared ;
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')
}