Free Statistics

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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 computationThu, 24 Nov 2011 10:46:39 -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/24/t1322150084qjc9kdoxu9hrtmd.htm/, Retrieved Thu, 31 Oct 2024 23:14:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147013, Retrieved Thu, 31 Oct 2024 23:14:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2011-11-24 15:46:39] [a478c561bf1feb1bdaba97497ca665e7] [Current]
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Dataseries X:
12	408	187
-3	5	2
-24	2	1
-11	250	133
1	16	10
17	159	55
10	336	70
28	138	46
-16	97	105
1	1272	321
5	88	17
5	201	104
9	102	35
11	127	76
7	209	103
7	247	178
47	145	31
10	3517	1347
21	27	14
9	101	91
10	2	1
101	5	2
45	100	65
11	34	9
38	1418	418
39	206	82
44	130	117
14	865	137
-5	229	162
-24	1	1
6	229	87
0	17	3
-3	92	16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'AstonUniversity' @ aston.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=147013&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=147013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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 time5 seconds
R Server'AstonUniversity' @ aston.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.







Multiple Linear Regression - Estimated Regression Equation
nr[t] = + 12.8460138674093 + 0.0135641352768076omzet[t] -0.0367789406935189`Personeel `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
nr[t] =  +  12.8460138674093 +  0.0135641352768076omzet[t] -0.0367789406935189`Personeel
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]nr[t] =  +  12.8460138674093 +  0.0135641352768076omzet[t] -0.0367789406935189`Personeel
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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
nr[t] = + 12.8460138674093 + 0.0135641352768076omzet[t] -0.0367789406935189`Personeel `[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)12.84601386740934.8200752.66510.012270.006135
omzet0.01356413527680760.0279970.48450.6315580.315779
`Personeel `-0.03677894069351890.077655-0.47360.63920.3196

\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) & 12.8460138674093 & 4.820075 & 2.6651 & 0.01227 & 0.006135 \tabularnewline
omzet & 0.0135641352768076 & 0.027997 & 0.4845 & 0.631558 & 0.315779 \tabularnewline
`Personeel
` & -0.0367789406935189 & 0.077655 & -0.4736 & 0.6392 & 0.3196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&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]12.8460138674093[/C][C]4.820075[/C][C]2.6651[/C][C]0.01227[/C][C]0.006135[/C][/ROW]
[ROW][C]omzet[/C][C]0.0135641352768076[/C][C]0.027997[/C][C]0.4845[/C][C]0.631558[/C][C]0.315779[/C][/ROW]
[ROW][C]`Personeel
`[/C][C]-0.0367789406935189[/C][C]0.077655[/C][C]-0.4736[/C][C]0.6392[/C][C]0.3196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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)12.84601386740934.8200752.66510.012270.006135
omzet0.01356413527680760.0279970.48450.6315580.315779
`Personeel `-0.03677894069351890.077655-0.47360.63920.3196







Multiple Linear Regression - Regression Statistics
Multiple R0.088134518701946
R-squared0.00776769338682365
Adjusted R-squared-0.0583811270540546
F-TEST (value)0.117427541943339
F-TEST (DF numerator)2
F-TEST (DF denominator)30
p-value0.889611626785825
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation24.5721467704117
Sum Squared Residuals18113.7119071997

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.088134518701946 \tabularnewline
R-squared & 0.00776769338682365 \tabularnewline
Adjusted R-squared & -0.0583811270540546 \tabularnewline
F-TEST (value) & 0.117427541943339 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 30 \tabularnewline
p-value & 0.889611626785825 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 24.5721467704117 \tabularnewline
Sum Squared Residuals & 18113.7119071997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.088134518701946[/C][/ROW]
[ROW][C]R-squared[/C][C]0.00776769338682365[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.0583811270540546[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.117427541943339[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]30[/C][/ROW]
[ROW][C]p-value[/C][C]0.889611626785825[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]24.5721467704117[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]18113.7119071997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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 R0.088134518701946
R-squared0.00776769338682365
Adjusted R-squared-0.0583811270540546
F-TEST (value)0.117427541943339
F-TEST (DF numerator)2
F-TEST (DF denominator)30
p-value0.889611626785825
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation24.5721467704117
Sum Squared Residuals18113.7119071997







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11211.50251915065870.497480849341304
2-312.8402766624063-15.8402766624063
3-2412.8363631972693-36.8363631972693
4-1111.3454485743731-22.3454485743731
5112.695250624903-11.695250624903
61712.97986963827814.02013036172188
71014.8290374718703-4.82903747187028
82813.026033263706814.9739667362932
9-1610.2999462164401-26.2999462164401
10118.2935539768889-17.2935539768889
11513.4144157799785-8.4144157799785
12511.7473952259216-6.74739522592161
13912.9422927413705-3.94229274137047
141111.7734595548564-0.773459554856383
15711.8926872488296-4.89268724882959
1679.64970383733436-2.64970383733436
174713.672666321047333.3273336789527
181011.0098445217716-1.00984452177155
192112.69734035017388.3026596498262
20910.8691079272566-1.8691079272566
211012.8363631972694-2.83636319726935
2210112.840276662406388.1597233375937
234511.811796250011333.1882037499887
241112.976184000579-1.97618400057904
253816.706360480031521.2936395199685
263912.624352597563126.3756474024369
274410.306215392252533.6937846077475
281419.5402760068357-5.54027600683572
29-59.99401245344813-14.9940124534481
30-2412.8227990619925-36.8227990619925
31612.752433005462-6.75243300546205
32012.9662673450344-12.9662673450344
33-313.5054512617792-16.5054512617792

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12 & 11.5025191506587 & 0.497480849341304 \tabularnewline
2 & -3 & 12.8402766624063 & -15.8402766624063 \tabularnewline
3 & -24 & 12.8363631972693 & -36.8363631972693 \tabularnewline
4 & -11 & 11.3454485743731 & -22.3454485743731 \tabularnewline
5 & 1 & 12.695250624903 & -11.695250624903 \tabularnewline
6 & 17 & 12.9798696382781 & 4.02013036172188 \tabularnewline
7 & 10 & 14.8290374718703 & -4.82903747187028 \tabularnewline
8 & 28 & 13.0260332637068 & 14.9739667362932 \tabularnewline
9 & -16 & 10.2999462164401 & -26.2999462164401 \tabularnewline
10 & 1 & 18.2935539768889 & -17.2935539768889 \tabularnewline
11 & 5 & 13.4144157799785 & -8.4144157799785 \tabularnewline
12 & 5 & 11.7473952259216 & -6.74739522592161 \tabularnewline
13 & 9 & 12.9422927413705 & -3.94229274137047 \tabularnewline
14 & 11 & 11.7734595548564 & -0.773459554856383 \tabularnewline
15 & 7 & 11.8926872488296 & -4.89268724882959 \tabularnewline
16 & 7 & 9.64970383733436 & -2.64970383733436 \tabularnewline
17 & 47 & 13.6726663210473 & 33.3273336789527 \tabularnewline
18 & 10 & 11.0098445217716 & -1.00984452177155 \tabularnewline
19 & 21 & 12.6973403501738 & 8.3026596498262 \tabularnewline
20 & 9 & 10.8691079272566 & -1.8691079272566 \tabularnewline
21 & 10 & 12.8363631972694 & -2.83636319726935 \tabularnewline
22 & 101 & 12.8402766624063 & 88.1597233375937 \tabularnewline
23 & 45 & 11.8117962500113 & 33.1882037499887 \tabularnewline
24 & 11 & 12.976184000579 & -1.97618400057904 \tabularnewline
25 & 38 & 16.7063604800315 & 21.2936395199685 \tabularnewline
26 & 39 & 12.6243525975631 & 26.3756474024369 \tabularnewline
27 & 44 & 10.3062153922525 & 33.6937846077475 \tabularnewline
28 & 14 & 19.5402760068357 & -5.54027600683572 \tabularnewline
29 & -5 & 9.99401245344813 & -14.9940124534481 \tabularnewline
30 & -24 & 12.8227990619925 & -36.8227990619925 \tabularnewline
31 & 6 & 12.752433005462 & -6.75243300546205 \tabularnewline
32 & 0 & 12.9662673450344 & -12.9662673450344 \tabularnewline
33 & -3 & 13.5054512617792 & -16.5054512617792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&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]12[/C][C]11.5025191506587[/C][C]0.497480849341304[/C][/ROW]
[ROW][C]2[/C][C]-3[/C][C]12.8402766624063[/C][C]-15.8402766624063[/C][/ROW]
[ROW][C]3[/C][C]-24[/C][C]12.8363631972693[/C][C]-36.8363631972693[/C][/ROW]
[ROW][C]4[/C][C]-11[/C][C]11.3454485743731[/C][C]-22.3454485743731[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]12.695250624903[/C][C]-11.695250624903[/C][/ROW]
[ROW][C]6[/C][C]17[/C][C]12.9798696382781[/C][C]4.02013036172188[/C][/ROW]
[ROW][C]7[/C][C]10[/C][C]14.8290374718703[/C][C]-4.82903747187028[/C][/ROW]
[ROW][C]8[/C][C]28[/C][C]13.0260332637068[/C][C]14.9739667362932[/C][/ROW]
[ROW][C]9[/C][C]-16[/C][C]10.2999462164401[/C][C]-26.2999462164401[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]18.2935539768889[/C][C]-17.2935539768889[/C][/ROW]
[ROW][C]11[/C][C]5[/C][C]13.4144157799785[/C][C]-8.4144157799785[/C][/ROW]
[ROW][C]12[/C][C]5[/C][C]11.7473952259216[/C][C]-6.74739522592161[/C][/ROW]
[ROW][C]13[/C][C]9[/C][C]12.9422927413705[/C][C]-3.94229274137047[/C][/ROW]
[ROW][C]14[/C][C]11[/C][C]11.7734595548564[/C][C]-0.773459554856383[/C][/ROW]
[ROW][C]15[/C][C]7[/C][C]11.8926872488296[/C][C]-4.89268724882959[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]9.64970383733436[/C][C]-2.64970383733436[/C][/ROW]
[ROW][C]17[/C][C]47[/C][C]13.6726663210473[/C][C]33.3273336789527[/C][/ROW]
[ROW][C]18[/C][C]10[/C][C]11.0098445217716[/C][C]-1.00984452177155[/C][/ROW]
[ROW][C]19[/C][C]21[/C][C]12.6973403501738[/C][C]8.3026596498262[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]10.8691079272566[/C][C]-1.8691079272566[/C][/ROW]
[ROW][C]21[/C][C]10[/C][C]12.8363631972694[/C][C]-2.83636319726935[/C][/ROW]
[ROW][C]22[/C][C]101[/C][C]12.8402766624063[/C][C]88.1597233375937[/C][/ROW]
[ROW][C]23[/C][C]45[/C][C]11.8117962500113[/C][C]33.1882037499887[/C][/ROW]
[ROW][C]24[/C][C]11[/C][C]12.976184000579[/C][C]-1.97618400057904[/C][/ROW]
[ROW][C]25[/C][C]38[/C][C]16.7063604800315[/C][C]21.2936395199685[/C][/ROW]
[ROW][C]26[/C][C]39[/C][C]12.6243525975631[/C][C]26.3756474024369[/C][/ROW]
[ROW][C]27[/C][C]44[/C][C]10.3062153922525[/C][C]33.6937846077475[/C][/ROW]
[ROW][C]28[/C][C]14[/C][C]19.5402760068357[/C][C]-5.54027600683572[/C][/ROW]
[ROW][C]29[/C][C]-5[/C][C]9.99401245344813[/C][C]-14.9940124534481[/C][/ROW]
[ROW][C]30[/C][C]-24[/C][C]12.8227990619925[/C][C]-36.8227990619925[/C][/ROW]
[ROW][C]31[/C][C]6[/C][C]12.752433005462[/C][C]-6.75243300546205[/C][/ROW]
[ROW][C]32[/C][C]0[/C][C]12.9662673450344[/C][C]-12.9662673450344[/C][/ROW]
[ROW][C]33[/C][C]-3[/C][C]13.5054512617792[/C][C]-16.5054512617792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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
11211.50251915065870.497480849341304
2-312.8402766624063-15.8402766624063
3-2412.8363631972693-36.8363631972693
4-1111.3454485743731-22.3454485743731
5112.695250624903-11.695250624903
61712.97986963827814.02013036172188
71014.8290374718703-4.82903747187028
82813.026033263706814.9739667362932
9-1610.2999462164401-26.2999462164401
10118.2935539768889-17.2935539768889
11513.4144157799785-8.4144157799785
12511.7473952259216-6.74739522592161
13912.9422927413705-3.94229274137047
141111.7734595548564-0.773459554856383
15711.8926872488296-4.89268724882959
1679.64970383733436-2.64970383733436
174713.672666321047333.3273336789527
181011.0098445217716-1.00984452177155
192112.69734035017388.3026596498262
20910.8691079272566-1.8691079272566
211012.8363631972694-2.83636319726935
2210112.840276662406388.1597233375937
234511.811796250011333.1882037499887
241112.976184000579-1.97618400057904
253816.706360480031521.2936395199685
263912.624352597563126.3756474024369
274410.306215392252533.6937846077475
281419.5402760068357-5.54027600683572
29-59.99401245344813-14.9940124534481
30-2412.8227990619925-36.8227990619925
31612.752433005462-6.75243300546205
32012.9662673450344-12.9662673450344
33-313.5054512617792-16.5054512617792







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.1049850277573650.209970055514730.895014972242635
70.1199183481832080.2398366963664160.880081651816792
80.170652321258560.3413046425171210.82934767874144
90.1053255072564690.2106510145129390.89467449274353
100.1320015828810150.2640031657620290.867998417118985
110.0754231177578270.1508462355156540.924576882242173
120.04178616989613650.0835723397922730.958213830103864
130.02208519753243770.04417039506487530.977914802467562
140.01209743776721740.02419487553443470.987902562232783
150.005802121591896920.01160424318379380.994197878408103
160.002718235936915040.005436471873830090.997281764063085
170.01549457294617310.03098914589234610.984505427053827
180.008850608931424940.01770121786284990.991149391068575
190.005066182555935390.01013236511187080.994933817444065
200.002373470712649730.004746941425299460.99762652928735
210.0009759063463060460.001951812692612090.999024093653694
220.6097782283649020.7804435432701960.390221771635098
230.7098933433682490.5802133132635020.290106656631751
240.598118808414340.803762383171320.40188119158566
250.490473681001840.980947362003680.50952631899816
260.5569168007864930.8861663984270150.443083199213507
270.8957134302019860.2085731395960270.104286569798013

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
6 & 0.104985027757365 & 0.20997005551473 & 0.895014972242635 \tabularnewline
7 & 0.119918348183208 & 0.239836696366416 & 0.880081651816792 \tabularnewline
8 & 0.17065232125856 & 0.341304642517121 & 0.82934767874144 \tabularnewline
9 & 0.105325507256469 & 0.210651014512939 & 0.89467449274353 \tabularnewline
10 & 0.132001582881015 & 0.264003165762029 & 0.867998417118985 \tabularnewline
11 & 0.075423117757827 & 0.150846235515654 & 0.924576882242173 \tabularnewline
12 & 0.0417861698961365 & 0.083572339792273 & 0.958213830103864 \tabularnewline
13 & 0.0220851975324377 & 0.0441703950648753 & 0.977914802467562 \tabularnewline
14 & 0.0120974377672174 & 0.0241948755344347 & 0.987902562232783 \tabularnewline
15 & 0.00580212159189692 & 0.0116042431837938 & 0.994197878408103 \tabularnewline
16 & 0.00271823593691504 & 0.00543647187383009 & 0.997281764063085 \tabularnewline
17 & 0.0154945729461731 & 0.0309891458923461 & 0.984505427053827 \tabularnewline
18 & 0.00885060893142494 & 0.0177012178628499 & 0.991149391068575 \tabularnewline
19 & 0.00506618255593539 & 0.0101323651118708 & 0.994933817444065 \tabularnewline
20 & 0.00237347071264973 & 0.00474694142529946 & 0.99762652928735 \tabularnewline
21 & 0.000975906346306046 & 0.00195181269261209 & 0.999024093653694 \tabularnewline
22 & 0.609778228364902 & 0.780443543270196 & 0.390221771635098 \tabularnewline
23 & 0.709893343368249 & 0.580213313263502 & 0.290106656631751 \tabularnewline
24 & 0.59811880841434 & 0.80376238317132 & 0.40188119158566 \tabularnewline
25 & 0.49047368100184 & 0.98094736200368 & 0.50952631899816 \tabularnewline
26 & 0.556916800786493 & 0.886166398427015 & 0.443083199213507 \tabularnewline
27 & 0.895713430201986 & 0.208573139596027 & 0.104286569798013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&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]6[/C][C]0.104985027757365[/C][C]0.20997005551473[/C][C]0.895014972242635[/C][/ROW]
[ROW][C]7[/C][C]0.119918348183208[/C][C]0.239836696366416[/C][C]0.880081651816792[/C][/ROW]
[ROW][C]8[/C][C]0.17065232125856[/C][C]0.341304642517121[/C][C]0.82934767874144[/C][/ROW]
[ROW][C]9[/C][C]0.105325507256469[/C][C]0.210651014512939[/C][C]0.89467449274353[/C][/ROW]
[ROW][C]10[/C][C]0.132001582881015[/C][C]0.264003165762029[/C][C]0.867998417118985[/C][/ROW]
[ROW][C]11[/C][C]0.075423117757827[/C][C]0.150846235515654[/C][C]0.924576882242173[/C][/ROW]
[ROW][C]12[/C][C]0.0417861698961365[/C][C]0.083572339792273[/C][C]0.958213830103864[/C][/ROW]
[ROW][C]13[/C][C]0.0220851975324377[/C][C]0.0441703950648753[/C][C]0.977914802467562[/C][/ROW]
[ROW][C]14[/C][C]0.0120974377672174[/C][C]0.0241948755344347[/C][C]0.987902562232783[/C][/ROW]
[ROW][C]15[/C][C]0.00580212159189692[/C][C]0.0116042431837938[/C][C]0.994197878408103[/C][/ROW]
[ROW][C]16[/C][C]0.00271823593691504[/C][C]0.00543647187383009[/C][C]0.997281764063085[/C][/ROW]
[ROW][C]17[/C][C]0.0154945729461731[/C][C]0.0309891458923461[/C][C]0.984505427053827[/C][/ROW]
[ROW][C]18[/C][C]0.00885060893142494[/C][C]0.0177012178628499[/C][C]0.991149391068575[/C][/ROW]
[ROW][C]19[/C][C]0.00506618255593539[/C][C]0.0101323651118708[/C][C]0.994933817444065[/C][/ROW]
[ROW][C]20[/C][C]0.00237347071264973[/C][C]0.00474694142529946[/C][C]0.99762652928735[/C][/ROW]
[ROW][C]21[/C][C]0.000975906346306046[/C][C]0.00195181269261209[/C][C]0.999024093653694[/C][/ROW]
[ROW][C]22[/C][C]0.609778228364902[/C][C]0.780443543270196[/C][C]0.390221771635098[/C][/ROW]
[ROW][C]23[/C][C]0.709893343368249[/C][C]0.580213313263502[/C][C]0.290106656631751[/C][/ROW]
[ROW][C]24[/C][C]0.59811880841434[/C][C]0.80376238317132[/C][C]0.40188119158566[/C][/ROW]
[ROW][C]25[/C][C]0.49047368100184[/C][C]0.98094736200368[/C][C]0.50952631899816[/C][/ROW]
[ROW][C]26[/C][C]0.556916800786493[/C][C]0.886166398427015[/C][C]0.443083199213507[/C][/ROW]
[ROW][C]27[/C][C]0.895713430201986[/C][C]0.208573139596027[/C][C]0.104286569798013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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
60.1049850277573650.209970055514730.895014972242635
70.1199183481832080.2398366963664160.880081651816792
80.170652321258560.3413046425171210.82934767874144
90.1053255072564690.2106510145129390.89467449274353
100.1320015828810150.2640031657620290.867998417118985
110.0754231177578270.1508462355156540.924576882242173
120.04178616989613650.0835723397922730.958213830103864
130.02208519753243770.04417039506487530.977914802467562
140.01209743776721740.02419487553443470.987902562232783
150.005802121591896920.01160424318379380.994197878408103
160.002718235936915040.005436471873830090.997281764063085
170.01549457294617310.03098914589234610.984505427053827
180.008850608931424940.01770121786284990.991149391068575
190.005066182555935390.01013236511187080.994933817444065
200.002373470712649730.004746941425299460.99762652928735
210.0009759063463060460.001951812692612090.999024093653694
220.6097782283649020.7804435432701960.390221771635098
230.7098933433682490.5802133132635020.290106656631751
240.598118808414340.803762383171320.40188119158566
250.490473681001840.980947362003680.50952631899816
260.5569168007864930.8861663984270150.443083199213507
270.8957134302019860.2085731395960270.104286569798013







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.136363636363636NOK
5% type I error level90.409090909090909NOK
10% type I error level100.454545454545455NOK

\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 & 3 & 0.136363636363636 & NOK \tabularnewline
5% type I error level & 9 & 0.409090909090909 & NOK \tabularnewline
10% type I error level & 10 & 0.454545454545455 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147013&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]3[/C][C]0.136363636363636[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]9[/C][C]0.409090909090909[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]10[/C][C]0.454545454545455[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147013&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147013&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 level30.136363636363636NOK
5% type I error level90.409090909090909NOK
10% type I error level100.454545454545455NOK



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}