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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 05:58:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258722016z1pofjj4yg1fjys.htm/, Retrieved Fri, 29 Mar 2024 14:10:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58105, Retrieved Fri, 29 Mar 2024 14:10:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 12:58:41] [2f6049721194fa571920c3539d7b729e] [Current]
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Dataseries X:
2.155	22.782
2.172	19.169
2.15	13.807
2.533	29.743
2.058	25.591
2.16	29.096
2.26	26.482
2.498	22.405
2.695	27.044
2.799	17.97
2.947	18.73
2.93	19.684
2.318	19.785
2.54	18.479
2.57	10.698
2.669	31.956
2.45	29.506
2.842	34.506
3.44	27.165
2.678	26.736
2.981	23.691
2.26	18.157
2.844	17.328
2.546	18.205
2.456	20.995
2.295	17.382
2.379	9.367
2.479	31.124
2.057	26.551
2.28	30.651
2.351	25.859
2.276	25.1
2.548	25.778
2.311	20.418
2.201	18.688
2.725	20.424
2.408	24.776
2.139	19.814
1.898	12.738
2.537	31.566
2.069	30.111
2.063	30.019
2.524	31.934
2.437	25.826
2.189	26.835
2.793	20.205
2.074	17.789
2.622	20.52
2.278	22.518
2.144	15.572
2.427	11.509
2.139	25.447
1.828	24.09
2.072	27.786
1.8	26.195
1.758	20.516
2.246	22.759
1.987	19.028
1.868	16.971
2.514	20.036
2.121	22.485




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
geb[t] = + 1.65564518708982 + 0.0511664330027703aut[t] -0.503409077593554M1[t] -0.322898028365517M2[t] + 0.0344064289725780M3[t] -0.71755991817044M4[t] -0.95342693848849M5[t] -0.92829828099687M6[t] -0.589103588357079M7[t] -0.560205585244431M8[t] -0.414334260425892M9[t] -0.205768911117688M10[t] -0.184785737559013M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
geb[t] =  +  1.65564518708982 +  0.0511664330027703aut[t] -0.503409077593554M1[t] -0.322898028365517M2[t] +  0.0344064289725780M3[t] -0.71755991817044M4[t] -0.95342693848849M5[t] -0.92829828099687M6[t] -0.589103588357079M7[t] -0.560205585244431M8[t] -0.414334260425892M9[t] -0.205768911117688M10[t] -0.184785737559013M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]geb[t] =  +  1.65564518708982 +  0.0511664330027703aut[t] -0.503409077593554M1[t] -0.322898028365517M2[t] +  0.0344064289725780M3[t] -0.71755991817044M4[t] -0.95342693848849M5[t] -0.92829828099687M6[t] -0.589103588357079M7[t] -0.560205585244431M8[t] -0.414334260425892M9[t] -0.205768911117688M10[t] -0.184785737559013M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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
geb[t] = + 1.65564518708982 + 0.0511664330027703aut[t] -0.503409077593554M1[t] -0.322898028365517M2[t] + 0.0344064289725780M3[t] -0.71755991817044M4[t] -0.95342693848849M5[t] -0.92829828099687M6[t] -0.589103588357079M7[t] -0.560205585244431M8[t] -0.414334260425892M9[t] -0.205768911117688M10[t] -0.184785737559013M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.655645187089820.4622593.58160.0007950.000397
aut0.05116643300277030.0222892.29560.0261110.013056
M1-0.5034090775935540.196486-2.56210.0135990.0068
M2-0.3228980283655170.200708-1.60880.114220.05711
M30.03440642897257800.2680730.12830.898410.449205
M4-0.717559918170440.300806-2.38550.0210530.010527
M5-0.953426938488490.256982-3.71010.0005380.000269
M6-0.928298280996870.308356-3.01050.004150.002075
M7-0.5891035883570790.26216-2.24710.0292670.014633
M8-0.5602055852444310.219622-2.55080.0139920.006996
M9-0.4143342604258920.231532-1.78950.0798390.03992
M10-0.2057689111176880.19762-1.04120.3029840.151492
M11-0.1847857375590130.201509-0.9170.3637230.181862

\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) & 1.65564518708982 & 0.462259 & 3.5816 & 0.000795 & 0.000397 \tabularnewline
aut & 0.0511664330027703 & 0.022289 & 2.2956 & 0.026111 & 0.013056 \tabularnewline
M1 & -0.503409077593554 & 0.196486 & -2.5621 & 0.013599 & 0.0068 \tabularnewline
M2 & -0.322898028365517 & 0.200708 & -1.6088 & 0.11422 & 0.05711 \tabularnewline
M3 & 0.0344064289725780 & 0.268073 & 0.1283 & 0.89841 & 0.449205 \tabularnewline
M4 & -0.71755991817044 & 0.300806 & -2.3855 & 0.021053 & 0.010527 \tabularnewline
M5 & -0.95342693848849 & 0.256982 & -3.7101 & 0.000538 & 0.000269 \tabularnewline
M6 & -0.92829828099687 & 0.308356 & -3.0105 & 0.00415 & 0.002075 \tabularnewline
M7 & -0.589103588357079 & 0.26216 & -2.2471 & 0.029267 & 0.014633 \tabularnewline
M8 & -0.560205585244431 & 0.219622 & -2.5508 & 0.013992 & 0.006996 \tabularnewline
M9 & -0.414334260425892 & 0.231532 & -1.7895 & 0.079839 & 0.03992 \tabularnewline
M10 & -0.205768911117688 & 0.19762 & -1.0412 & 0.302984 & 0.151492 \tabularnewline
M11 & -0.184785737559013 & 0.201509 & -0.917 & 0.363723 & 0.181862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&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]1.65564518708982[/C][C]0.462259[/C][C]3.5816[/C][C]0.000795[/C][C]0.000397[/C][/ROW]
[ROW][C]aut[/C][C]0.0511664330027703[/C][C]0.022289[/C][C]2.2956[/C][C]0.026111[/C][C]0.013056[/C][/ROW]
[ROW][C]M1[/C][C]-0.503409077593554[/C][C]0.196486[/C][C]-2.5621[/C][C]0.013599[/C][C]0.0068[/C][/ROW]
[ROW][C]M2[/C][C]-0.322898028365517[/C][C]0.200708[/C][C]-1.6088[/C][C]0.11422[/C][C]0.05711[/C][/ROW]
[ROW][C]M3[/C][C]0.0344064289725780[/C][C]0.268073[/C][C]0.1283[/C][C]0.89841[/C][C]0.449205[/C][/ROW]
[ROW][C]M4[/C][C]-0.71755991817044[/C][C]0.300806[/C][C]-2.3855[/C][C]0.021053[/C][C]0.010527[/C][/ROW]
[ROW][C]M5[/C][C]-0.95342693848849[/C][C]0.256982[/C][C]-3.7101[/C][C]0.000538[/C][C]0.000269[/C][/ROW]
[ROW][C]M6[/C][C]-0.92829828099687[/C][C]0.308356[/C][C]-3.0105[/C][C]0.00415[/C][C]0.002075[/C][/ROW]
[ROW][C]M7[/C][C]-0.589103588357079[/C][C]0.26216[/C][C]-2.2471[/C][C]0.029267[/C][C]0.014633[/C][/ROW]
[ROW][C]M8[/C][C]-0.560205585244431[/C][C]0.219622[/C][C]-2.5508[/C][C]0.013992[/C][C]0.006996[/C][/ROW]
[ROW][C]M9[/C][C]-0.414334260425892[/C][C]0.231532[/C][C]-1.7895[/C][C]0.079839[/C][C]0.03992[/C][/ROW]
[ROW][C]M10[/C][C]-0.205768911117688[/C][C]0.19762[/C][C]-1.0412[/C][C]0.302984[/C][C]0.151492[/C][/ROW]
[ROW][C]M11[/C][C]-0.184785737559013[/C][C]0.201509[/C][C]-0.917[/C][C]0.363723[/C][C]0.181862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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)1.655645187089820.4622593.58160.0007950.000397
aut0.05116643300277030.0222892.29560.0261110.013056
M1-0.5034090775935540.196486-2.56210.0135990.0068
M2-0.3228980283655170.200708-1.60880.114220.05711
M30.03440642897257800.2680730.12830.898410.449205
M4-0.717559918170440.300806-2.38550.0210530.010527
M5-0.953426938488490.256982-3.71010.0005380.000269
M6-0.928298280996870.308356-3.01050.004150.002075
M7-0.5891035883570790.26216-2.24710.0292670.014633
M8-0.5602055852444310.219622-2.55080.0139920.006996
M9-0.4143342604258920.231532-1.78950.0798390.03992
M10-0.2057689111176880.19762-1.04120.3029840.151492
M11-0.1847857375590130.201509-0.9170.3637230.181862







Multiple Linear Regression - Regression Statistics
Multiple R0.525521854351598
R-squared0.276173219401143
Adjusted R-squared0.0952165242514282
F-TEST (value)1.52618403631129
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.147702482386852
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.311704757154909
Sum Squared Residuals4.66367307038404

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.525521854351598 \tabularnewline
R-squared & 0.276173219401143 \tabularnewline
Adjusted R-squared & 0.0952165242514282 \tabularnewline
F-TEST (value) & 1.52618403631129 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.147702482386852 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.311704757154909 \tabularnewline
Sum Squared Residuals & 4.66367307038404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.525521854351598[/C][/ROW]
[ROW][C]R-squared[/C][C]0.276173219401143[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.0952165242514282[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.52618403631129[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.147702482386852[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.311704757154909[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4.66367307038404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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 R0.525521854351598
R-squared0.276173219401143
Adjusted R-squared0.0952165242514282
F-TEST (value)1.52618403631129
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.147702482386852
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.311704757154909
Sum Squared Residuals4.66367307038404







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.1552.31790978616538-0.162909786165381
22.1722.31355651295441-0.141556512954408
32.152.39650655653165-0.246506556531648
42.5332.459928485720780.0730715142792209
52.0582.011618435575230.0463815644247737
62.162.21608544074156-0.0560854407415554
72.262.42153107751210-0.161531077512105
82.4982.241823533272460.256176466727542
92.6952.625055940790850.0699440592091503
102.7992.369337077031920.429662922968084
112.9472.429206739672700.517793260327304
122.932.662805254316350.267194745683649
132.3182.164563986456080.153436013543922
142.542.278251674182500.261748325817503
152.572.237430116326040.332569883673965
162.6692.573159801955910.0958401980440905
172.452.211935020781070.238064979218928
182.8422.492895843286540.349104156713457
193.442.4564777512530.983522248747003
202.6782.463425354607460.214574645392543
212.9812.453494890932560.52750510906744
222.262.37890520000343-0.118905200003434
232.8442.357471400602810.486528599397188
242.5462.58713009990525-0.041130099905254
252.4562.226475370389430.22952462961057
262.2952.222122097178460.0728779028215425
272.3792.169327593999350.209672406000652
282.4792.53058932969760-0.0515893296976046
292.0572.06073821125789-0.00373821125788589
302.282.29564924406086-0.0156492440608636
312.3512.38965438975138-0.0386543897513792
322.2762.37971707021492-0.103717070214925
332.5482.56027923660934-0.0122792366093418
342.3112.49459250502270-0.183592505022697
352.2012.42705774948658-0.226057749486580
362.7252.70066841473840.0243315852615988
372.4082.41993565357290-0.0119356535729049
382.1392.34655886224119-0.207558862241195
391.8982.34180963965169-0.443809639651687
402.5372.55320489308483-0.0162048930848292
412.0692.24289071274775-0.173890712747748
422.0632.26331205840311-0.200312058403112
432.5242.70049047024321-0.176490470243209
442.4372.416863900574940.0201360994250641
452.1892.61436215629327-0.42536215629327
462.7932.483694054793110.309305945206893
472.0742.38105912621709-0.307059126217089
482.6222.70558039230667-0.0835803923066674
492.2782.30440184785265-0.0264018478526492
502.1442.129510853443440.0144891465565571
512.4272.278926093491280.148073906508718
522.1392.24011748954088-0.101117489540877
531.8281.93481761963807-0.106817619638068
542.0722.14905741350793-0.0770574135079261
551.82.40684631124031-0.60684631124031
561.7582.14517014133022-0.387170141330225
572.2462.40580777537398-0.159807775373978
581.9872.42347116314885-0.436471163148846
591.8682.33920498402082-0.471204984020823
602.5142.68081583873333-0.166815838733327
612.1212.30271335556356-0.181713355563558

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.155 & 2.31790978616538 & -0.162909786165381 \tabularnewline
2 & 2.172 & 2.31355651295441 & -0.141556512954408 \tabularnewline
3 & 2.15 & 2.39650655653165 & -0.246506556531648 \tabularnewline
4 & 2.533 & 2.45992848572078 & 0.0730715142792209 \tabularnewline
5 & 2.058 & 2.01161843557523 & 0.0463815644247737 \tabularnewline
6 & 2.16 & 2.21608544074156 & -0.0560854407415554 \tabularnewline
7 & 2.26 & 2.42153107751210 & -0.161531077512105 \tabularnewline
8 & 2.498 & 2.24182353327246 & 0.256176466727542 \tabularnewline
9 & 2.695 & 2.62505594079085 & 0.0699440592091503 \tabularnewline
10 & 2.799 & 2.36933707703192 & 0.429662922968084 \tabularnewline
11 & 2.947 & 2.42920673967270 & 0.517793260327304 \tabularnewline
12 & 2.93 & 2.66280525431635 & 0.267194745683649 \tabularnewline
13 & 2.318 & 2.16456398645608 & 0.153436013543922 \tabularnewline
14 & 2.54 & 2.27825167418250 & 0.261748325817503 \tabularnewline
15 & 2.57 & 2.23743011632604 & 0.332569883673965 \tabularnewline
16 & 2.669 & 2.57315980195591 & 0.0958401980440905 \tabularnewline
17 & 2.45 & 2.21193502078107 & 0.238064979218928 \tabularnewline
18 & 2.842 & 2.49289584328654 & 0.349104156713457 \tabularnewline
19 & 3.44 & 2.456477751253 & 0.983522248747003 \tabularnewline
20 & 2.678 & 2.46342535460746 & 0.214574645392543 \tabularnewline
21 & 2.981 & 2.45349489093256 & 0.52750510906744 \tabularnewline
22 & 2.26 & 2.37890520000343 & -0.118905200003434 \tabularnewline
23 & 2.844 & 2.35747140060281 & 0.486528599397188 \tabularnewline
24 & 2.546 & 2.58713009990525 & -0.041130099905254 \tabularnewline
25 & 2.456 & 2.22647537038943 & 0.22952462961057 \tabularnewline
26 & 2.295 & 2.22212209717846 & 0.0728779028215425 \tabularnewline
27 & 2.379 & 2.16932759399935 & 0.209672406000652 \tabularnewline
28 & 2.479 & 2.53058932969760 & -0.0515893296976046 \tabularnewline
29 & 2.057 & 2.06073821125789 & -0.00373821125788589 \tabularnewline
30 & 2.28 & 2.29564924406086 & -0.0156492440608636 \tabularnewline
31 & 2.351 & 2.38965438975138 & -0.0386543897513792 \tabularnewline
32 & 2.276 & 2.37971707021492 & -0.103717070214925 \tabularnewline
33 & 2.548 & 2.56027923660934 & -0.0122792366093418 \tabularnewline
34 & 2.311 & 2.49459250502270 & -0.183592505022697 \tabularnewline
35 & 2.201 & 2.42705774948658 & -0.226057749486580 \tabularnewline
36 & 2.725 & 2.7006684147384 & 0.0243315852615988 \tabularnewline
37 & 2.408 & 2.41993565357290 & -0.0119356535729049 \tabularnewline
38 & 2.139 & 2.34655886224119 & -0.207558862241195 \tabularnewline
39 & 1.898 & 2.34180963965169 & -0.443809639651687 \tabularnewline
40 & 2.537 & 2.55320489308483 & -0.0162048930848292 \tabularnewline
41 & 2.069 & 2.24289071274775 & -0.173890712747748 \tabularnewline
42 & 2.063 & 2.26331205840311 & -0.200312058403112 \tabularnewline
43 & 2.524 & 2.70049047024321 & -0.176490470243209 \tabularnewline
44 & 2.437 & 2.41686390057494 & 0.0201360994250641 \tabularnewline
45 & 2.189 & 2.61436215629327 & -0.42536215629327 \tabularnewline
46 & 2.793 & 2.48369405479311 & 0.309305945206893 \tabularnewline
47 & 2.074 & 2.38105912621709 & -0.307059126217089 \tabularnewline
48 & 2.622 & 2.70558039230667 & -0.0835803923066674 \tabularnewline
49 & 2.278 & 2.30440184785265 & -0.0264018478526492 \tabularnewline
50 & 2.144 & 2.12951085344344 & 0.0144891465565571 \tabularnewline
51 & 2.427 & 2.27892609349128 & 0.148073906508718 \tabularnewline
52 & 2.139 & 2.24011748954088 & -0.101117489540877 \tabularnewline
53 & 1.828 & 1.93481761963807 & -0.106817619638068 \tabularnewline
54 & 2.072 & 2.14905741350793 & -0.0770574135079261 \tabularnewline
55 & 1.8 & 2.40684631124031 & -0.60684631124031 \tabularnewline
56 & 1.758 & 2.14517014133022 & -0.387170141330225 \tabularnewline
57 & 2.246 & 2.40580777537398 & -0.159807775373978 \tabularnewline
58 & 1.987 & 2.42347116314885 & -0.436471163148846 \tabularnewline
59 & 1.868 & 2.33920498402082 & -0.471204984020823 \tabularnewline
60 & 2.514 & 2.68081583873333 & -0.166815838733327 \tabularnewline
61 & 2.121 & 2.30271335556356 & -0.181713355563558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&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]2.155[/C][C]2.31790978616538[/C][C]-0.162909786165381[/C][/ROW]
[ROW][C]2[/C][C]2.172[/C][C]2.31355651295441[/C][C]-0.141556512954408[/C][/ROW]
[ROW][C]3[/C][C]2.15[/C][C]2.39650655653165[/C][C]-0.246506556531648[/C][/ROW]
[ROW][C]4[/C][C]2.533[/C][C]2.45992848572078[/C][C]0.0730715142792209[/C][/ROW]
[ROW][C]5[/C][C]2.058[/C][C]2.01161843557523[/C][C]0.0463815644247737[/C][/ROW]
[ROW][C]6[/C][C]2.16[/C][C]2.21608544074156[/C][C]-0.0560854407415554[/C][/ROW]
[ROW][C]7[/C][C]2.26[/C][C]2.42153107751210[/C][C]-0.161531077512105[/C][/ROW]
[ROW][C]8[/C][C]2.498[/C][C]2.24182353327246[/C][C]0.256176466727542[/C][/ROW]
[ROW][C]9[/C][C]2.695[/C][C]2.62505594079085[/C][C]0.0699440592091503[/C][/ROW]
[ROW][C]10[/C][C]2.799[/C][C]2.36933707703192[/C][C]0.429662922968084[/C][/ROW]
[ROW][C]11[/C][C]2.947[/C][C]2.42920673967270[/C][C]0.517793260327304[/C][/ROW]
[ROW][C]12[/C][C]2.93[/C][C]2.66280525431635[/C][C]0.267194745683649[/C][/ROW]
[ROW][C]13[/C][C]2.318[/C][C]2.16456398645608[/C][C]0.153436013543922[/C][/ROW]
[ROW][C]14[/C][C]2.54[/C][C]2.27825167418250[/C][C]0.261748325817503[/C][/ROW]
[ROW][C]15[/C][C]2.57[/C][C]2.23743011632604[/C][C]0.332569883673965[/C][/ROW]
[ROW][C]16[/C][C]2.669[/C][C]2.57315980195591[/C][C]0.0958401980440905[/C][/ROW]
[ROW][C]17[/C][C]2.45[/C][C]2.21193502078107[/C][C]0.238064979218928[/C][/ROW]
[ROW][C]18[/C][C]2.842[/C][C]2.49289584328654[/C][C]0.349104156713457[/C][/ROW]
[ROW][C]19[/C][C]3.44[/C][C]2.456477751253[/C][C]0.983522248747003[/C][/ROW]
[ROW][C]20[/C][C]2.678[/C][C]2.46342535460746[/C][C]0.214574645392543[/C][/ROW]
[ROW][C]21[/C][C]2.981[/C][C]2.45349489093256[/C][C]0.52750510906744[/C][/ROW]
[ROW][C]22[/C][C]2.26[/C][C]2.37890520000343[/C][C]-0.118905200003434[/C][/ROW]
[ROW][C]23[/C][C]2.844[/C][C]2.35747140060281[/C][C]0.486528599397188[/C][/ROW]
[ROW][C]24[/C][C]2.546[/C][C]2.58713009990525[/C][C]-0.041130099905254[/C][/ROW]
[ROW][C]25[/C][C]2.456[/C][C]2.22647537038943[/C][C]0.22952462961057[/C][/ROW]
[ROW][C]26[/C][C]2.295[/C][C]2.22212209717846[/C][C]0.0728779028215425[/C][/ROW]
[ROW][C]27[/C][C]2.379[/C][C]2.16932759399935[/C][C]0.209672406000652[/C][/ROW]
[ROW][C]28[/C][C]2.479[/C][C]2.53058932969760[/C][C]-0.0515893296976046[/C][/ROW]
[ROW][C]29[/C][C]2.057[/C][C]2.06073821125789[/C][C]-0.00373821125788589[/C][/ROW]
[ROW][C]30[/C][C]2.28[/C][C]2.29564924406086[/C][C]-0.0156492440608636[/C][/ROW]
[ROW][C]31[/C][C]2.351[/C][C]2.38965438975138[/C][C]-0.0386543897513792[/C][/ROW]
[ROW][C]32[/C][C]2.276[/C][C]2.37971707021492[/C][C]-0.103717070214925[/C][/ROW]
[ROW][C]33[/C][C]2.548[/C][C]2.56027923660934[/C][C]-0.0122792366093418[/C][/ROW]
[ROW][C]34[/C][C]2.311[/C][C]2.49459250502270[/C][C]-0.183592505022697[/C][/ROW]
[ROW][C]35[/C][C]2.201[/C][C]2.42705774948658[/C][C]-0.226057749486580[/C][/ROW]
[ROW][C]36[/C][C]2.725[/C][C]2.7006684147384[/C][C]0.0243315852615988[/C][/ROW]
[ROW][C]37[/C][C]2.408[/C][C]2.41993565357290[/C][C]-0.0119356535729049[/C][/ROW]
[ROW][C]38[/C][C]2.139[/C][C]2.34655886224119[/C][C]-0.207558862241195[/C][/ROW]
[ROW][C]39[/C][C]1.898[/C][C]2.34180963965169[/C][C]-0.443809639651687[/C][/ROW]
[ROW][C]40[/C][C]2.537[/C][C]2.55320489308483[/C][C]-0.0162048930848292[/C][/ROW]
[ROW][C]41[/C][C]2.069[/C][C]2.24289071274775[/C][C]-0.173890712747748[/C][/ROW]
[ROW][C]42[/C][C]2.063[/C][C]2.26331205840311[/C][C]-0.200312058403112[/C][/ROW]
[ROW][C]43[/C][C]2.524[/C][C]2.70049047024321[/C][C]-0.176490470243209[/C][/ROW]
[ROW][C]44[/C][C]2.437[/C][C]2.41686390057494[/C][C]0.0201360994250641[/C][/ROW]
[ROW][C]45[/C][C]2.189[/C][C]2.61436215629327[/C][C]-0.42536215629327[/C][/ROW]
[ROW][C]46[/C][C]2.793[/C][C]2.48369405479311[/C][C]0.309305945206893[/C][/ROW]
[ROW][C]47[/C][C]2.074[/C][C]2.38105912621709[/C][C]-0.307059126217089[/C][/ROW]
[ROW][C]48[/C][C]2.622[/C][C]2.70558039230667[/C][C]-0.0835803923066674[/C][/ROW]
[ROW][C]49[/C][C]2.278[/C][C]2.30440184785265[/C][C]-0.0264018478526492[/C][/ROW]
[ROW][C]50[/C][C]2.144[/C][C]2.12951085344344[/C][C]0.0144891465565571[/C][/ROW]
[ROW][C]51[/C][C]2.427[/C][C]2.27892609349128[/C][C]0.148073906508718[/C][/ROW]
[ROW][C]52[/C][C]2.139[/C][C]2.24011748954088[/C][C]-0.101117489540877[/C][/ROW]
[ROW][C]53[/C][C]1.828[/C][C]1.93481761963807[/C][C]-0.106817619638068[/C][/ROW]
[ROW][C]54[/C][C]2.072[/C][C]2.14905741350793[/C][C]-0.0770574135079261[/C][/ROW]
[ROW][C]55[/C][C]1.8[/C][C]2.40684631124031[/C][C]-0.60684631124031[/C][/ROW]
[ROW][C]56[/C][C]1.758[/C][C]2.14517014133022[/C][C]-0.387170141330225[/C][/ROW]
[ROW][C]57[/C][C]2.246[/C][C]2.40580777537398[/C][C]-0.159807775373978[/C][/ROW]
[ROW][C]58[/C][C]1.987[/C][C]2.42347116314885[/C][C]-0.436471163148846[/C][/ROW]
[ROW][C]59[/C][C]1.868[/C][C]2.33920498402082[/C][C]-0.471204984020823[/C][/ROW]
[ROW][C]60[/C][C]2.514[/C][C]2.68081583873333[/C][C]-0.166815838733327[/C][/ROW]
[ROW][C]61[/C][C]2.121[/C][C]2.30271335556356[/C][C]-0.181713355563558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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
12.1552.31790978616538-0.162909786165381
22.1722.31355651295441-0.141556512954408
32.152.39650655653165-0.246506556531648
42.5332.459928485720780.0730715142792209
52.0582.011618435575230.0463815644247737
62.162.21608544074156-0.0560854407415554
72.262.42153107751210-0.161531077512105
82.4982.241823533272460.256176466727542
92.6952.625055940790850.0699440592091503
102.7992.369337077031920.429662922968084
112.9472.429206739672700.517793260327304
122.932.662805254316350.267194745683649
132.3182.164563986456080.153436013543922
142.542.278251674182500.261748325817503
152.572.237430116326040.332569883673965
162.6692.573159801955910.0958401980440905
172.452.211935020781070.238064979218928
182.8422.492895843286540.349104156713457
193.442.4564777512530.983522248747003
202.6782.463425354607460.214574645392543
212.9812.453494890932560.52750510906744
222.262.37890520000343-0.118905200003434
232.8442.357471400602810.486528599397188
242.5462.58713009990525-0.041130099905254
252.4562.226475370389430.22952462961057
262.2952.222122097178460.0728779028215425
272.3792.169327593999350.209672406000652
282.4792.53058932969760-0.0515893296976046
292.0572.06073821125789-0.00373821125788589
302.282.29564924406086-0.0156492440608636
312.3512.38965438975138-0.0386543897513792
322.2762.37971707021492-0.103717070214925
332.5482.56027923660934-0.0122792366093418
342.3112.49459250502270-0.183592505022697
352.2012.42705774948658-0.226057749486580
362.7252.70066841473840.0243315852615988
372.4082.41993565357290-0.0119356535729049
382.1392.34655886224119-0.207558862241195
391.8982.34180963965169-0.443809639651687
402.5372.55320489308483-0.0162048930848292
412.0692.24289071274775-0.173890712747748
422.0632.26331205840311-0.200312058403112
432.5242.70049047024321-0.176490470243209
442.4372.416863900574940.0201360994250641
452.1892.61436215629327-0.42536215629327
462.7932.483694054793110.309305945206893
472.0742.38105912621709-0.307059126217089
482.6222.70558039230667-0.0835803923066674
492.2782.30440184785265-0.0264018478526492
502.1442.129510853443440.0144891465565571
512.4272.278926093491280.148073906508718
522.1392.24011748954088-0.101117489540877
531.8281.93481761963807-0.106817619638068
542.0722.14905741350793-0.0770574135079261
551.82.40684631124031-0.60684631124031
561.7582.14517014133022-0.387170141330225
572.2462.40580777537398-0.159807775373978
581.9872.42347116314885-0.436471163148846
591.8682.33920498402082-0.471204984020823
602.5142.68081583873333-0.166815838733327
612.1212.30271335556356-0.181713355563558







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.2086661187931570.4173322375863140.791333881206843
170.3147250670503770.6294501341007530.685274932949623
180.3913726593980830.7827453187961660.608627340601917
190.9471082915576840.1057834168846320.0528917084423161
200.9230303721955440.1539392556089120.0769696278044561
210.9581295916799920.08374081664001530.0418704083200077
220.955292477641340.08941504471731830.0447075223586592
230.9857880494990150.02842390100196980.0142119505009849
240.9780902827607480.0438194344785030.0219097172392515
250.9746070499945550.05078590001088970.0253929500054448
260.9593063425025970.08138731499480640.0406936574974032
270.9570490883273460.0859018233453070.0429509116726535
280.9317610962589870.1364778074820260.0682389037410129
290.9027250364070690.1945499271858620.097274963592931
300.8633168091179940.2733663817640120.136683190882006
310.9009998808070410.1980002383859170.0990001191929587
320.8716779709845430.2566440580309140.128322029015457
330.85863223324490.28273553351020.1413677667551
340.822390182474180.3552196350516390.177609817525820
350.849045972569870.3019080548602600.150954027430130
360.7904943223580920.4190113552838160.209505677641908
370.7072028737811670.5855942524376670.292797126218833
380.6656757648159870.6686484703680260.334324235184013
390.8088708043458090.3822583913083820.191129195654191
400.7221562376327760.5556875247344480.277843762367224
410.6780882195834290.6438235608331410.321911780416570
420.6151070146758540.7697859706482920.384892985324146
430.4976486202528990.9952972405057980.502351379747101
440.3985250913256210.7970501826512420.601474908674379
450.8660588988987520.2678822022024960.133941101101248

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.208666118793157 & 0.417332237586314 & 0.791333881206843 \tabularnewline
17 & 0.314725067050377 & 0.629450134100753 & 0.685274932949623 \tabularnewline
18 & 0.391372659398083 & 0.782745318796166 & 0.608627340601917 \tabularnewline
19 & 0.947108291557684 & 0.105783416884632 & 0.0528917084423161 \tabularnewline
20 & 0.923030372195544 & 0.153939255608912 & 0.0769696278044561 \tabularnewline
21 & 0.958129591679992 & 0.0837408166400153 & 0.0418704083200077 \tabularnewline
22 & 0.95529247764134 & 0.0894150447173183 & 0.0447075223586592 \tabularnewline
23 & 0.985788049499015 & 0.0284239010019698 & 0.0142119505009849 \tabularnewline
24 & 0.978090282760748 & 0.043819434478503 & 0.0219097172392515 \tabularnewline
25 & 0.974607049994555 & 0.0507859000108897 & 0.0253929500054448 \tabularnewline
26 & 0.959306342502597 & 0.0813873149948064 & 0.0406936574974032 \tabularnewline
27 & 0.957049088327346 & 0.085901823345307 & 0.0429509116726535 \tabularnewline
28 & 0.931761096258987 & 0.136477807482026 & 0.0682389037410129 \tabularnewline
29 & 0.902725036407069 & 0.194549927185862 & 0.097274963592931 \tabularnewline
30 & 0.863316809117994 & 0.273366381764012 & 0.136683190882006 \tabularnewline
31 & 0.900999880807041 & 0.198000238385917 & 0.0990001191929587 \tabularnewline
32 & 0.871677970984543 & 0.256644058030914 & 0.128322029015457 \tabularnewline
33 & 0.8586322332449 & 0.2827355335102 & 0.1413677667551 \tabularnewline
34 & 0.82239018247418 & 0.355219635051639 & 0.177609817525820 \tabularnewline
35 & 0.84904597256987 & 0.301908054860260 & 0.150954027430130 \tabularnewline
36 & 0.790494322358092 & 0.419011355283816 & 0.209505677641908 \tabularnewline
37 & 0.707202873781167 & 0.585594252437667 & 0.292797126218833 \tabularnewline
38 & 0.665675764815987 & 0.668648470368026 & 0.334324235184013 \tabularnewline
39 & 0.808870804345809 & 0.382258391308382 & 0.191129195654191 \tabularnewline
40 & 0.722156237632776 & 0.555687524734448 & 0.277843762367224 \tabularnewline
41 & 0.678088219583429 & 0.643823560833141 & 0.321911780416570 \tabularnewline
42 & 0.615107014675854 & 0.769785970648292 & 0.384892985324146 \tabularnewline
43 & 0.497648620252899 & 0.995297240505798 & 0.502351379747101 \tabularnewline
44 & 0.398525091325621 & 0.797050182651242 & 0.601474908674379 \tabularnewline
45 & 0.866058898898752 & 0.267882202202496 & 0.133941101101248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&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]16[/C][C]0.208666118793157[/C][C]0.417332237586314[/C][C]0.791333881206843[/C][/ROW]
[ROW][C]17[/C][C]0.314725067050377[/C][C]0.629450134100753[/C][C]0.685274932949623[/C][/ROW]
[ROW][C]18[/C][C]0.391372659398083[/C][C]0.782745318796166[/C][C]0.608627340601917[/C][/ROW]
[ROW][C]19[/C][C]0.947108291557684[/C][C]0.105783416884632[/C][C]0.0528917084423161[/C][/ROW]
[ROW][C]20[/C][C]0.923030372195544[/C][C]0.153939255608912[/C][C]0.0769696278044561[/C][/ROW]
[ROW][C]21[/C][C]0.958129591679992[/C][C]0.0837408166400153[/C][C]0.0418704083200077[/C][/ROW]
[ROW][C]22[/C][C]0.95529247764134[/C][C]0.0894150447173183[/C][C]0.0447075223586592[/C][/ROW]
[ROW][C]23[/C][C]0.985788049499015[/C][C]0.0284239010019698[/C][C]0.0142119505009849[/C][/ROW]
[ROW][C]24[/C][C]0.978090282760748[/C][C]0.043819434478503[/C][C]0.0219097172392515[/C][/ROW]
[ROW][C]25[/C][C]0.974607049994555[/C][C]0.0507859000108897[/C][C]0.0253929500054448[/C][/ROW]
[ROW][C]26[/C][C]0.959306342502597[/C][C]0.0813873149948064[/C][C]0.0406936574974032[/C][/ROW]
[ROW][C]27[/C][C]0.957049088327346[/C][C]0.085901823345307[/C][C]0.0429509116726535[/C][/ROW]
[ROW][C]28[/C][C]0.931761096258987[/C][C]0.136477807482026[/C][C]0.0682389037410129[/C][/ROW]
[ROW][C]29[/C][C]0.902725036407069[/C][C]0.194549927185862[/C][C]0.097274963592931[/C][/ROW]
[ROW][C]30[/C][C]0.863316809117994[/C][C]0.273366381764012[/C][C]0.136683190882006[/C][/ROW]
[ROW][C]31[/C][C]0.900999880807041[/C][C]0.198000238385917[/C][C]0.0990001191929587[/C][/ROW]
[ROW][C]32[/C][C]0.871677970984543[/C][C]0.256644058030914[/C][C]0.128322029015457[/C][/ROW]
[ROW][C]33[/C][C]0.8586322332449[/C][C]0.2827355335102[/C][C]0.1413677667551[/C][/ROW]
[ROW][C]34[/C][C]0.82239018247418[/C][C]0.355219635051639[/C][C]0.177609817525820[/C][/ROW]
[ROW][C]35[/C][C]0.84904597256987[/C][C]0.301908054860260[/C][C]0.150954027430130[/C][/ROW]
[ROW][C]36[/C][C]0.790494322358092[/C][C]0.419011355283816[/C][C]0.209505677641908[/C][/ROW]
[ROW][C]37[/C][C]0.707202873781167[/C][C]0.585594252437667[/C][C]0.292797126218833[/C][/ROW]
[ROW][C]38[/C][C]0.665675764815987[/C][C]0.668648470368026[/C][C]0.334324235184013[/C][/ROW]
[ROW][C]39[/C][C]0.808870804345809[/C][C]0.382258391308382[/C][C]0.191129195654191[/C][/ROW]
[ROW][C]40[/C][C]0.722156237632776[/C][C]0.555687524734448[/C][C]0.277843762367224[/C][/ROW]
[ROW][C]41[/C][C]0.678088219583429[/C][C]0.643823560833141[/C][C]0.321911780416570[/C][/ROW]
[ROW][C]42[/C][C]0.615107014675854[/C][C]0.769785970648292[/C][C]0.384892985324146[/C][/ROW]
[ROW][C]43[/C][C]0.497648620252899[/C][C]0.995297240505798[/C][C]0.502351379747101[/C][/ROW]
[ROW][C]44[/C][C]0.398525091325621[/C][C]0.797050182651242[/C][C]0.601474908674379[/C][/ROW]
[ROW][C]45[/C][C]0.866058898898752[/C][C]0.267882202202496[/C][C]0.133941101101248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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
160.2086661187931570.4173322375863140.791333881206843
170.3147250670503770.6294501341007530.685274932949623
180.3913726593980830.7827453187961660.608627340601917
190.9471082915576840.1057834168846320.0528917084423161
200.9230303721955440.1539392556089120.0769696278044561
210.9581295916799920.08374081664001530.0418704083200077
220.955292477641340.08941504471731830.0447075223586592
230.9857880494990150.02842390100196980.0142119505009849
240.9780902827607480.0438194344785030.0219097172392515
250.9746070499945550.05078590001088970.0253929500054448
260.9593063425025970.08138731499480640.0406936574974032
270.9570490883273460.0859018233453070.0429509116726535
280.9317610962589870.1364778074820260.0682389037410129
290.9027250364070690.1945499271858620.097274963592931
300.8633168091179940.2733663817640120.136683190882006
310.9009998808070410.1980002383859170.0990001191929587
320.8716779709845430.2566440580309140.128322029015457
330.85863223324490.28273553351020.1413677667551
340.822390182474180.3552196350516390.177609817525820
350.849045972569870.3019080548602600.150954027430130
360.7904943223580920.4190113552838160.209505677641908
370.7072028737811670.5855942524376670.292797126218833
380.6656757648159870.6686484703680260.334324235184013
390.8088708043458090.3822583913083820.191129195654191
400.7221562376327760.5556875247344480.277843762367224
410.6780882195834290.6438235608331410.321911780416570
420.6151070146758540.7697859706482920.384892985324146
430.4976486202528990.9952972405057980.502351379747101
440.3985250913256210.7970501826512420.601474908674379
450.8660588988987520.2678822022024960.133941101101248







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0666666666666667NOK
10% type I error level70.233333333333333NOK

\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 & 2 & 0.0666666666666667 & NOK \tabularnewline
10% type I error level & 7 & 0.233333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58105&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]2[/C][C]0.0666666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.233333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58105&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58105&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 level20.0666666666666667NOK
10% type I error level70.233333333333333NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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')
}