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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 27 Nov 2008 06:33:01 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/27/t12277928152xlln9gs9n9p69g.htm/, Retrieved Sun, 19 May 2024 11:12:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25805, Retrieved Sun, 19 May 2024 11:12:36 +0000

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User-defined keywords

kleuter

Estimated Impact

155

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Multiple Regression] [] [2008-11-18 09:23:14] [488d9a19d3c63b747ac6ad96017e55c8]
F    D    [Multiple Regression] [] [2008-11-27 13:33:01] [b5c0979bf79a38ace87e0d3abace1ca1] [Current]

Feedback Forum

2008-11-30 10:45:23 [Gert-Jan Geudens] [reply] 
De berekeningen van de student(e) zijn correct al hebben we hier wel enkele vragen bij de gebruikte cijfergegevens. De omzet in de referentiemaand is 115. Is dit een percentage of een getal? aangezien de student over percentages spreekt. Indien dit inderdaad een percentage is, welk is dan het basisjaar? 
Deze onduidelijkheid maakt de interpretatie nogal onduidelijk, al lijkt de conclusie van de student wel correct (indien het effectief om percentages gaat).
2008-11-30 11:00:57 [Gert-Jan Geudens] [reply] 
We moeten hier nog even het volgende rechtzetten : De student(e) heeft jaarcijfers gebruikt en dus is deze berekening met seasonal dummies helemaal niet van toepassing. In de vraag staat echter wel dat we gebruik moeten maken van deze seasonal dummies en dus kunnen we besluiten dat de student(e) foutieve tijdreeksen heeft gebruikt.
2008-11-30 15:15:14 [6066575aa30c0611e452e930b1dff53d] [reply] 
Bij deze vraag heeft men redelijk weinig uitleg gegeven. Men had ook nog kunnen vermelden dat de p-waarden in de tabel van multiple linear regression - ordinary least squares bij sommige maanden redelijk hoog zijn. Dus als we een alfa fout van 5% nemen, kunnen we stellen dat er geen significant verschil is en dat we het effect van onze gebeurtenis aan het toeval kunnen toeschrijven. De adjusted r-squared bedraagt 92%, dit houdt in dat we 92% van de schommelingen die ontstaan door de gebeurtenis kunnen verklaren. Verder werden de grafieken niet besproken.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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=25805&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=25805&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
x[t] = + 114.799616724739 + 2.59224738675958y[t] -11.7605884630275M1[t] -6.56836043360433M2[t] + 3.92432055749128M3[t] + 2.25700154858691M4[t] -11.8703174603174M5[t] -2.19763646922184M6[t] -24.3834049554781M7[t] -24.6907239643825M8[t] -8.73804297328687M9[t] -8.60536198219127M10[t] -1.91268099109563M11[t] + 0.427319008904374t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
x[t] =  +  114.799616724739 +  2.59224738675958y[t] -11.7605884630275M1[t] -6.56836043360433M2[t] +  3.92432055749128M3[t] +  2.25700154858691M4[t] -11.8703174603174M5[t] -2.19763646922184M6[t] -24.3834049554781M7[t] -24.6907239643825M8[t] -8.73804297328687M9[t] -8.60536198219127M10[t] -1.91268099109563M11[t] +  0.427319008904374t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]x[t] =  +  114.799616724739 +  2.59224738675958y[t] -11.7605884630275M1[t] -6.56836043360433M2[t] +  3.92432055749128M3[t] +  2.25700154858691M4[t] -11.8703174603174M5[t] -2.19763646922184M6[t] -24.3834049554781M7[t] -24.6907239643825M8[t] -8.73804297328687M9[t] -8.60536198219127M10[t] -1.91268099109563M11[t] +  0.427319008904374t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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
x[t] = + 114.799616724739 + 2.59224738675958y[t] -11.7605884630275M1[t] -6.56836043360433M2[t] + 3.92432055749128M3[t] + 2.25700154858691M4[t] -11.8703174603174M5[t] -2.19763646922184M6[t] -24.3834049554781M7[t] -24.6907239643825M8[t] -8.73804297328687M9[t] -8.60536198219127M10[t] -1.91268099109563M11[t] + 0.427319008904374t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	114.799616724739	1.883033	60.9653	0	0
y	2.59224738675958	1.625029	1.5952	0.117371	0.058685
M1	-11.7605884630275	2.092623	-5.62	1e-06	1e-06
M2	-6.56836043360433	2.195527	-2.9917	0.004408	0.002204
M3	3.92432055749128	2.192757	1.7897	0.07995	0.039975
M4	2.25700154858691	2.190805	1.0302	0.308181	0.154091
M5	-11.8703174603174	2.189676	-5.421	2e-06	1e-06
M6	-2.19763646922184	2.189369	-1.0038	0.320627	0.160313
M7	-24.3834049554781	2.190989	-11.1289	0	0
M8	-24.6907239643825	2.187284	-11.2883	0	0
M9	-8.73804297328687	2.184397	-4.0002	0.000223	0.000111
M10	-8.60536198219127	2.182333	-3.9432	0.000266	0.000133
M11	-1.91268099109563	2.181094	-0.8769	0.384982	0.192491
t	0.427319008904374	0.042458	10.0645	0	0

\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) & 114.799616724739 & 1.883033 & 60.9653 & 0 & 0 \tabularnewline
y & 2.59224738675958 & 1.625029 & 1.5952 & 0.117371 & 0.058685 \tabularnewline
M1 & -11.7605884630275 & 2.092623 & -5.62 & 1e-06 & 1e-06 \tabularnewline
M2 & -6.56836043360433 & 2.195527 & -2.9917 & 0.004408 & 0.002204 \tabularnewline
M3 & 3.92432055749128 & 2.192757 & 1.7897 & 0.07995 & 0.039975 \tabularnewline
M4 & 2.25700154858691 & 2.190805 & 1.0302 & 0.308181 & 0.154091 \tabularnewline
M5 & -11.8703174603174 & 2.189676 & -5.421 & 2e-06 & 1e-06 \tabularnewline
M6 & -2.19763646922184 & 2.189369 & -1.0038 & 0.320627 & 0.160313 \tabularnewline
M7 & -24.3834049554781 & 2.190989 & -11.1289 & 0 & 0 \tabularnewline
M8 & -24.6907239643825 & 2.187284 & -11.2883 & 0 & 0 \tabularnewline
M9 & -8.73804297328687 & 2.184397 & -4.0002 & 0.000223 & 0.000111 \tabularnewline
M10 & -8.60536198219127 & 2.182333 & -3.9432 & 0.000266 & 0.000133 \tabularnewline
M11 & -1.91268099109563 & 2.181094 & -0.8769 & 0.384982 & 0.192491 \tabularnewline
t & 0.427319008904374 & 0.042458 & 10.0645 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&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]114.799616724739[/C][C]1.883033[/C][C]60.9653[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]y[/C][C]2.59224738675958[/C][C]1.625029[/C][C]1.5952[/C][C]0.117371[/C][C]0.058685[/C][/ROW]
[ROW][C]M1[/C][C]-11.7605884630275[/C][C]2.092623[/C][C]-5.62[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M2[/C][C]-6.56836043360433[/C][C]2.195527[/C][C]-2.9917[/C][C]0.004408[/C][C]0.002204[/C][/ROW]
[ROW][C]M3[/C][C]3.92432055749128[/C][C]2.192757[/C][C]1.7897[/C][C]0.07995[/C][C]0.039975[/C][/ROW]
[ROW][C]M4[/C][C]2.25700154858691[/C][C]2.190805[/C][C]1.0302[/C][C]0.308181[/C][C]0.154091[/C][/ROW]
[ROW][C]M5[/C][C]-11.8703174603174[/C][C]2.189676[/C][C]-5.421[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M6[/C][C]-2.19763646922184[/C][C]2.189369[/C][C]-1.0038[/C][C]0.320627[/C][C]0.160313[/C][/ROW]
[ROW][C]M7[/C][C]-24.3834049554781[/C][C]2.190989[/C][C]-11.1289[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-24.6907239643825[/C][C]2.187284[/C][C]-11.2883[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-8.73804297328687[/C][C]2.184397[/C][C]-4.0002[/C][C]0.000223[/C][C]0.000111[/C][/ROW]
[ROW][C]M10[/C][C]-8.60536198219127[/C][C]2.182333[/C][C]-3.9432[/C][C]0.000266[/C][C]0.000133[/C][/ROW]
[ROW][C]M11[/C][C]-1.91268099109563[/C][C]2.181094[/C][C]-0.8769[/C][C]0.384982[/C][C]0.192491[/C][/ROW]
[ROW][C]t[/C][C]0.427319008904374[/C][C]0.042458[/C][C]10.0645[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	114.799616724739	1.883033	60.9653	0	0
y	2.59224738675958	1.625029	1.5952	0.117371	0.058685
M1	-11.7605884630275	2.092623	-5.62	1e-06	1e-06
M2	-6.56836043360433	2.195527	-2.9917	0.004408	0.002204
M3	3.92432055749128	2.192757	1.7897	0.07995	0.039975
M4	2.25700154858691	2.190805	1.0302	0.308181	0.154091
M5	-11.8703174603174	2.189676	-5.421	2e-06	1e-06
M6	-2.19763646922184	2.189369	-1.0038	0.320627	0.160313
M7	-24.3834049554781	2.190989	-11.1289	0	0
M8	-24.6907239643825	2.187284	-11.2883	0	0
M9	-8.73804297328687	2.184397	-4.0002	0.000223	0.000111
M10	-8.60536198219127	2.182333	-3.9432	0.000266	0.000133
M11	-1.91268099109563	2.181094	-0.8769	0.384982	0.192491
t	0.427319008904374	0.042458	10.0645	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.970185957751532
R-squared	0.941260792618257
Adjusted R-squared	0.92501377781054
F-TEST (value)	57.934383870397
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.44795854182024
Sum Squared Residuals	558.755650987225

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.970185957751532 \tabularnewline
R-squared & 0.941260792618257 \tabularnewline
Adjusted R-squared & 0.92501377781054 \tabularnewline
F-TEST (value) & 57.934383870397 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.44795854182024 \tabularnewline
Sum Squared Residuals & 558.755650987225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.970185957751532[/C][/ROW]
[ROW][C]R-squared[/C][C]0.941260792618257[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.92501377781054[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]57.934383870397[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/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]3.44795854182024[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]558.755650987225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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 R	0.970185957751532
R-squared	0.941260792618257
Adjusted R-squared	0.92501377781054
F-TEST (value)	57.934383870397
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.44795854182024
Sum Squared Residuals	558.755650987225

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	104.3	103.466347270615	0.833652729384565
2	119.8	109.085894308943	10.7141056910569
3	116.8	120.005894308943	-3.20589430894311
4	118.2	118.765894308943	-0.565894308943107
5	107.4	105.065894308943	2.33410569105691
6	110.8	115.165894308943	-4.3658943089431
7	94.8	93.4074448315912	1.3925551684088
8	96.5	93.5274448315912	2.97255516840881
9	113.4	109.907444831591	3.49255516840883
10	109.8	110.467444831591	-0.6674448315912
11	118.7	117.587444831591	1.11255516840882
12	117.2	119.927444831591	-2.72744483159118
13	110.3	108.594175377468	1.7058246225319
14	111.6	114.213722415796	-2.61372241579561
15	128.1	125.133722415796	2.96627758420440
16	121.3	123.893722415796	-2.59372241579559
17	107.3	110.193722415796	-2.8937224157956
18	120.5	120.293722415796	0.206277584204412
19	98.5	98.5352729384437	-0.0352729384436661
20	97.7	98.6552729384437	-0.955272938443672
21	113.2	115.035272938444	-1.83527293844367
22	114.6	115.595272938444	-0.995272938443663
23	118.3	122.715272938444	-4.41527293844368
24	123.9	125.055272938444	-1.15527293844367
25	113.6	113.722003484321	-0.122003484320589
26	117.5	119.341550522648	-1.84155052264808
27	130.1	130.261550522648	-0.161550522648086
28	124.7	129.021550522648	-4.32155052264808
29	114.2	115.321550522648	-1.12155052264808
30	127.3	125.421550522648	1.87844947735192
31	105.9	103.663101045296	2.23689895470385
32	101.5	103.783101045296	-2.28310104529616
33	120.2	120.163101045296	0.0368989547038367
34	117.1	120.723101045296	-3.62310104529615
35	131.1	127.843101045296	3.25689895470383
36	130	130.183101045296	-0.183101045296158
37	120.6	118.849831591173	1.75016840882692
38	123.1	124.469378629501	-1.36937862950058
39	135.3	135.389378629501	-0.089378629500551
40	134.1	134.149378629501	-0.0493786295005712
41	123.7	120.449378629501	3.25062137049943
42	134.6	130.549378629501	4.05062137049943
43	108.3	111.383176538908	-3.08317653890825
44	110.4	111.503176538908	-1.10317653890824
45	127.8	127.883176538908	-0.0831765389082544
46	126.6	128.443176538908	-1.84317653890824
47	131.4	135.563176538908	-4.16317653890824
48	141.1	137.903176538908	3.19682346109174
49	127	126.569907084785	0.430092915214842
50	127.3	132.189454123113	-4.88945412311267
51	143.6	143.109454123113	0.490545876887339
52	149.4	141.869454123113	7.53054587688735
53	126.6	128.169454123113	-1.56945412311267
54	136.5	138.269454123113	-1.76945412311265
55	116	116.511004645761	-0.511004645760733
56	118	116.631004645761	1.36899535423927
57	131.4	133.011004645761	-1.61100464576074
58	140.7	133.571004645761	7.12899535423926
59	144.9	140.691004645761	4.20899535423927
60	143.9	143.031004645761	0.868995354239274
61	127.1	131.697735191638	-4.59773519163766

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 104.3 & 103.466347270615 & 0.833652729384565 \tabularnewline
2 & 119.8 & 109.085894308943 & 10.7141056910569 \tabularnewline
3 & 116.8 & 120.005894308943 & -3.20589430894311 \tabularnewline
4 & 118.2 & 118.765894308943 & -0.565894308943107 \tabularnewline
5 & 107.4 & 105.065894308943 & 2.33410569105691 \tabularnewline
6 & 110.8 & 115.165894308943 & -4.3658943089431 \tabularnewline
7 & 94.8 & 93.4074448315912 & 1.3925551684088 \tabularnewline
8 & 96.5 & 93.5274448315912 & 2.97255516840881 \tabularnewline
9 & 113.4 & 109.907444831591 & 3.49255516840883 \tabularnewline
10 & 109.8 & 110.467444831591 & -0.6674448315912 \tabularnewline
11 & 118.7 & 117.587444831591 & 1.11255516840882 \tabularnewline
12 & 117.2 & 119.927444831591 & -2.72744483159118 \tabularnewline
13 & 110.3 & 108.594175377468 & 1.7058246225319 \tabularnewline
14 & 111.6 & 114.213722415796 & -2.61372241579561 \tabularnewline
15 & 128.1 & 125.133722415796 & 2.96627758420440 \tabularnewline
16 & 121.3 & 123.893722415796 & -2.59372241579559 \tabularnewline
17 & 107.3 & 110.193722415796 & -2.8937224157956 \tabularnewline
18 & 120.5 & 120.293722415796 & 0.206277584204412 \tabularnewline
19 & 98.5 & 98.5352729384437 & -0.0352729384436661 \tabularnewline
20 & 97.7 & 98.6552729384437 & -0.955272938443672 \tabularnewline
21 & 113.2 & 115.035272938444 & -1.83527293844367 \tabularnewline
22 & 114.6 & 115.595272938444 & -0.995272938443663 \tabularnewline
23 & 118.3 & 122.715272938444 & -4.41527293844368 \tabularnewline
24 & 123.9 & 125.055272938444 & -1.15527293844367 \tabularnewline
25 & 113.6 & 113.722003484321 & -0.122003484320589 \tabularnewline
26 & 117.5 & 119.341550522648 & -1.84155052264808 \tabularnewline
27 & 130.1 & 130.261550522648 & -0.161550522648086 \tabularnewline
28 & 124.7 & 129.021550522648 & -4.32155052264808 \tabularnewline
29 & 114.2 & 115.321550522648 & -1.12155052264808 \tabularnewline
30 & 127.3 & 125.421550522648 & 1.87844947735192 \tabularnewline
31 & 105.9 & 103.663101045296 & 2.23689895470385 \tabularnewline
32 & 101.5 & 103.783101045296 & -2.28310104529616 \tabularnewline
33 & 120.2 & 120.163101045296 & 0.0368989547038367 \tabularnewline
34 & 117.1 & 120.723101045296 & -3.62310104529615 \tabularnewline
35 & 131.1 & 127.843101045296 & 3.25689895470383 \tabularnewline
36 & 130 & 130.183101045296 & -0.183101045296158 \tabularnewline
37 & 120.6 & 118.849831591173 & 1.75016840882692 \tabularnewline
38 & 123.1 & 124.469378629501 & -1.36937862950058 \tabularnewline
39 & 135.3 & 135.389378629501 & -0.089378629500551 \tabularnewline
40 & 134.1 & 134.149378629501 & -0.0493786295005712 \tabularnewline
41 & 123.7 & 120.449378629501 & 3.25062137049943 \tabularnewline
42 & 134.6 & 130.549378629501 & 4.05062137049943 \tabularnewline
43 & 108.3 & 111.383176538908 & -3.08317653890825 \tabularnewline
44 & 110.4 & 111.503176538908 & -1.10317653890824 \tabularnewline
45 & 127.8 & 127.883176538908 & -0.0831765389082544 \tabularnewline
46 & 126.6 & 128.443176538908 & -1.84317653890824 \tabularnewline
47 & 131.4 & 135.563176538908 & -4.16317653890824 \tabularnewline
48 & 141.1 & 137.903176538908 & 3.19682346109174 \tabularnewline
49 & 127 & 126.569907084785 & 0.430092915214842 \tabularnewline
50 & 127.3 & 132.189454123113 & -4.88945412311267 \tabularnewline
51 & 143.6 & 143.109454123113 & 0.490545876887339 \tabularnewline
52 & 149.4 & 141.869454123113 & 7.53054587688735 \tabularnewline
53 & 126.6 & 128.169454123113 & -1.56945412311267 \tabularnewline
54 & 136.5 & 138.269454123113 & -1.76945412311265 \tabularnewline
55 & 116 & 116.511004645761 & -0.511004645760733 \tabularnewline
56 & 118 & 116.631004645761 & 1.36899535423927 \tabularnewline
57 & 131.4 & 133.011004645761 & -1.61100464576074 \tabularnewline
58 & 140.7 & 133.571004645761 & 7.12899535423926 \tabularnewline
59 & 144.9 & 140.691004645761 & 4.20899535423927 \tabularnewline
60 & 143.9 & 143.031004645761 & 0.868995354239274 \tabularnewline
61 & 127.1 & 131.697735191638 & -4.59773519163766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&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]104.3[/C][C]103.466347270615[/C][C]0.833652729384565[/C][/ROW]
[ROW][C]2[/C][C]119.8[/C][C]109.085894308943[/C][C]10.7141056910569[/C][/ROW]
[ROW][C]3[/C][C]116.8[/C][C]120.005894308943[/C][C]-3.20589430894311[/C][/ROW]
[ROW][C]4[/C][C]118.2[/C][C]118.765894308943[/C][C]-0.565894308943107[/C][/ROW]
[ROW][C]5[/C][C]107.4[/C][C]105.065894308943[/C][C]2.33410569105691[/C][/ROW]
[ROW][C]6[/C][C]110.8[/C][C]115.165894308943[/C][C]-4.3658943089431[/C][/ROW]
[ROW][C]7[/C][C]94.8[/C][C]93.4074448315912[/C][C]1.3925551684088[/C][/ROW]
[ROW][C]8[/C][C]96.5[/C][C]93.5274448315912[/C][C]2.97255516840881[/C][/ROW]
[ROW][C]9[/C][C]113.4[/C][C]109.907444831591[/C][C]3.49255516840883[/C][/ROW]
[ROW][C]10[/C][C]109.8[/C][C]110.467444831591[/C][C]-0.6674448315912[/C][/ROW]
[ROW][C]11[/C][C]118.7[/C][C]117.587444831591[/C][C]1.11255516840882[/C][/ROW]
[ROW][C]12[/C][C]117.2[/C][C]119.927444831591[/C][C]-2.72744483159118[/C][/ROW]
[ROW][C]13[/C][C]110.3[/C][C]108.594175377468[/C][C]1.7058246225319[/C][/ROW]
[ROW][C]14[/C][C]111.6[/C][C]114.213722415796[/C][C]-2.61372241579561[/C][/ROW]
[ROW][C]15[/C][C]128.1[/C][C]125.133722415796[/C][C]2.96627758420440[/C][/ROW]
[ROW][C]16[/C][C]121.3[/C][C]123.893722415796[/C][C]-2.59372241579559[/C][/ROW]
[ROW][C]17[/C][C]107.3[/C][C]110.193722415796[/C][C]-2.8937224157956[/C][/ROW]
[ROW][C]18[/C][C]120.5[/C][C]120.293722415796[/C][C]0.206277584204412[/C][/ROW]
[ROW][C]19[/C][C]98.5[/C][C]98.5352729384437[/C][C]-0.0352729384436661[/C][/ROW]
[ROW][C]20[/C][C]97.7[/C][C]98.6552729384437[/C][C]-0.955272938443672[/C][/ROW]
[ROW][C]21[/C][C]113.2[/C][C]115.035272938444[/C][C]-1.83527293844367[/C][/ROW]
[ROW][C]22[/C][C]114.6[/C][C]115.595272938444[/C][C]-0.995272938443663[/C][/ROW]
[ROW][C]23[/C][C]118.3[/C][C]122.715272938444[/C][C]-4.41527293844368[/C][/ROW]
[ROW][C]24[/C][C]123.9[/C][C]125.055272938444[/C][C]-1.15527293844367[/C][/ROW]
[ROW][C]25[/C][C]113.6[/C][C]113.722003484321[/C][C]-0.122003484320589[/C][/ROW]
[ROW][C]26[/C][C]117.5[/C][C]119.341550522648[/C][C]-1.84155052264808[/C][/ROW]
[ROW][C]27[/C][C]130.1[/C][C]130.261550522648[/C][C]-0.161550522648086[/C][/ROW]
[ROW][C]28[/C][C]124.7[/C][C]129.021550522648[/C][C]-4.32155052264808[/C][/ROW]
[ROW][C]29[/C][C]114.2[/C][C]115.321550522648[/C][C]-1.12155052264808[/C][/ROW]
[ROW][C]30[/C][C]127.3[/C][C]125.421550522648[/C][C]1.87844947735192[/C][/ROW]
[ROW][C]31[/C][C]105.9[/C][C]103.663101045296[/C][C]2.23689895470385[/C][/ROW]
[ROW][C]32[/C][C]101.5[/C][C]103.783101045296[/C][C]-2.28310104529616[/C][/ROW]
[ROW][C]33[/C][C]120.2[/C][C]120.163101045296[/C][C]0.0368989547038367[/C][/ROW]
[ROW][C]34[/C][C]117.1[/C][C]120.723101045296[/C][C]-3.62310104529615[/C][/ROW]
[ROW][C]35[/C][C]131.1[/C][C]127.843101045296[/C][C]3.25689895470383[/C][/ROW]
[ROW][C]36[/C][C]130[/C][C]130.183101045296[/C][C]-0.183101045296158[/C][/ROW]
[ROW][C]37[/C][C]120.6[/C][C]118.849831591173[/C][C]1.75016840882692[/C][/ROW]
[ROW][C]38[/C][C]123.1[/C][C]124.469378629501[/C][C]-1.36937862950058[/C][/ROW]
[ROW][C]39[/C][C]135.3[/C][C]135.389378629501[/C][C]-0.089378629500551[/C][/ROW]
[ROW][C]40[/C][C]134.1[/C][C]134.149378629501[/C][C]-0.0493786295005712[/C][/ROW]
[ROW][C]41[/C][C]123.7[/C][C]120.449378629501[/C][C]3.25062137049943[/C][/ROW]
[ROW][C]42[/C][C]134.6[/C][C]130.549378629501[/C][C]4.05062137049943[/C][/ROW]
[ROW][C]43[/C][C]108.3[/C][C]111.383176538908[/C][C]-3.08317653890825[/C][/ROW]
[ROW][C]44[/C][C]110.4[/C][C]111.503176538908[/C][C]-1.10317653890824[/C][/ROW]
[ROW][C]45[/C][C]127.8[/C][C]127.883176538908[/C][C]-0.0831765389082544[/C][/ROW]
[ROW][C]46[/C][C]126.6[/C][C]128.443176538908[/C][C]-1.84317653890824[/C][/ROW]
[ROW][C]47[/C][C]131.4[/C][C]135.563176538908[/C][C]-4.16317653890824[/C][/ROW]
[ROW][C]48[/C][C]141.1[/C][C]137.903176538908[/C][C]3.19682346109174[/C][/ROW]
[ROW][C]49[/C][C]127[/C][C]126.569907084785[/C][C]0.430092915214842[/C][/ROW]
[ROW][C]50[/C][C]127.3[/C][C]132.189454123113[/C][C]-4.88945412311267[/C][/ROW]
[ROW][C]51[/C][C]143.6[/C][C]143.109454123113[/C][C]0.490545876887339[/C][/ROW]
[ROW][C]52[/C][C]149.4[/C][C]141.869454123113[/C][C]7.53054587688735[/C][/ROW]
[ROW][C]53[/C][C]126.6[/C][C]128.169454123113[/C][C]-1.56945412311267[/C][/ROW]
[ROW][C]54[/C][C]136.5[/C][C]138.269454123113[/C][C]-1.76945412311265[/C][/ROW]
[ROW][C]55[/C][C]116[/C][C]116.511004645761[/C][C]-0.511004645760733[/C][/ROW]
[ROW][C]56[/C][C]118[/C][C]116.631004645761[/C][C]1.36899535423927[/C][/ROW]
[ROW][C]57[/C][C]131.4[/C][C]133.011004645761[/C][C]-1.61100464576074[/C][/ROW]
[ROW][C]58[/C][C]140.7[/C][C]133.571004645761[/C][C]7.12899535423926[/C][/ROW]
[ROW][C]59[/C][C]144.9[/C][C]140.691004645761[/C][C]4.20899535423927[/C][/ROW]
[ROW][C]60[/C][C]143.9[/C][C]143.031004645761[/C][C]0.868995354239274[/C][/ROW]
[ROW][C]61[/C][C]127.1[/C][C]131.697735191638[/C][C]-4.59773519163766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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 Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	104.3	103.466347270615	0.833652729384565
2	119.8	109.085894308943	10.7141056910569
3	116.8	120.005894308943	-3.20589430894311
4	118.2	118.765894308943	-0.565894308943107
5	107.4	105.065894308943	2.33410569105691
6	110.8	115.165894308943	-4.3658943089431
7	94.8	93.4074448315912	1.3925551684088
8	96.5	93.5274448315912	2.97255516840881
9	113.4	109.907444831591	3.49255516840883
10	109.8	110.467444831591	-0.6674448315912
11	118.7	117.587444831591	1.11255516840882
12	117.2	119.927444831591	-2.72744483159118
13	110.3	108.594175377468	1.7058246225319
14	111.6	114.213722415796	-2.61372241579561
15	128.1	125.133722415796	2.96627758420440
16	121.3	123.893722415796	-2.59372241579559
17	107.3	110.193722415796	-2.8937224157956
18	120.5	120.293722415796	0.206277584204412
19	98.5	98.5352729384437	-0.0352729384436661
20	97.7	98.6552729384437	-0.955272938443672
21	113.2	115.035272938444	-1.83527293844367
22	114.6	115.595272938444	-0.995272938443663
23	118.3	122.715272938444	-4.41527293844368
24	123.9	125.055272938444	-1.15527293844367
25	113.6	113.722003484321	-0.122003484320589
26	117.5	119.341550522648	-1.84155052264808
27	130.1	130.261550522648	-0.161550522648086
28	124.7	129.021550522648	-4.32155052264808
29	114.2	115.321550522648	-1.12155052264808
30	127.3	125.421550522648	1.87844947735192
31	105.9	103.663101045296	2.23689895470385
32	101.5	103.783101045296	-2.28310104529616
33	120.2	120.163101045296	0.0368989547038367
34	117.1	120.723101045296	-3.62310104529615
35	131.1	127.843101045296	3.25689895470383
36	130	130.183101045296	-0.183101045296158
37	120.6	118.849831591173	1.75016840882692
38	123.1	124.469378629501	-1.36937862950058
39	135.3	135.389378629501	-0.089378629500551
40	134.1	134.149378629501	-0.0493786295005712
41	123.7	120.449378629501	3.25062137049943
42	134.6	130.549378629501	4.05062137049943
43	108.3	111.383176538908	-3.08317653890825
44	110.4	111.503176538908	-1.10317653890824
45	127.8	127.883176538908	-0.0831765389082544
46	126.6	128.443176538908	-1.84317653890824
47	131.4	135.563176538908	-4.16317653890824
48	141.1	137.903176538908	3.19682346109174
49	127	126.569907084785	0.430092915214842
50	127.3	132.189454123113	-4.88945412311267
51	143.6	143.109454123113	0.490545876887339
52	149.4	141.869454123113	7.53054587688735
53	126.6	128.169454123113	-1.56945412311267
54	136.5	138.269454123113	-1.76945412311265
55	116	116.511004645761	-0.511004645760733
56	118	116.631004645761	1.36899535423927
57	131.4	133.011004645761	-1.61100464576074
58	140.7	133.571004645761	7.12899535423926
59	144.9	140.691004645761	4.20899535423927
60	143.9	143.031004645761	0.868995354239274
61	127.1	131.697735191638	-4.59773519163766

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.98265272004147	0.0346945599170585	0.0173472799585293
18	0.980678326740391	0.0386433465192176	0.0193216732596088
19	0.96042595393575	0.0791480921285006	0.0395740460642503
20	0.931671758525832	0.136656482948336	0.0683282414741679
21	0.89696314492517	0.206073710149660	0.103036855074830
22	0.840334609499383	0.319330781001234	0.159665390500617
23	0.804978975336592	0.390042049326816	0.195021024663408
24	0.751261996492935	0.497476007014131	0.248738003507065
25	0.678360691674782	0.643278616650436	0.321639308325218
26	0.624278471216273	0.751443057567454	0.375721528783727
27	0.555018144495557	0.889963711008886	0.444981855504443
28	0.552091629703333	0.895816740593333	0.447908370296667
29	0.462857633937679	0.925715267875358	0.537142366062321
30	0.485408917555307	0.970817835110614	0.514591082444693
31	0.457972761647405	0.91594552329481	0.542027238352595
32	0.380665734289095	0.76133146857819	0.619334265710905
33	0.292427029138627	0.584854058277255	0.707572970861372
34	0.322375318477102	0.644750636954204	0.677624681522898
35	0.339029931945942	0.678059863891885	0.660970068054058
36	0.289329123441000	0.578658246881999	0.710670876559
37	0.239825256128015	0.47965051225603	0.760174743871985
38	0.181680531531310	0.363361063062619	0.81831946846869
39	0.121884514916035	0.243769029832071	0.878115485083965
40	0.309363089725026	0.618726179450052	0.690636910274974
41	0.240324862678129	0.480649725356257	0.759675137321871
42	0.179154484401181	0.358308968802363	0.820845515598819
43	0.102193074118312	0.204386148236623	0.897806925881688
44	0.0516146736417748	0.103229347283550	0.948385326358225

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.98265272004147 & 0.0346945599170585 & 0.0173472799585293 \tabularnewline
18 & 0.980678326740391 & 0.0386433465192176 & 0.0193216732596088 \tabularnewline
19 & 0.96042595393575 & 0.0791480921285006 & 0.0395740460642503 \tabularnewline
20 & 0.931671758525832 & 0.136656482948336 & 0.0683282414741679 \tabularnewline
21 & 0.89696314492517 & 0.206073710149660 & 0.103036855074830 \tabularnewline
22 & 0.840334609499383 & 0.319330781001234 & 0.159665390500617 \tabularnewline
23 & 0.804978975336592 & 0.390042049326816 & 0.195021024663408 \tabularnewline
24 & 0.751261996492935 & 0.497476007014131 & 0.248738003507065 \tabularnewline
25 & 0.678360691674782 & 0.643278616650436 & 0.321639308325218 \tabularnewline
26 & 0.624278471216273 & 0.751443057567454 & 0.375721528783727 \tabularnewline
27 & 0.555018144495557 & 0.889963711008886 & 0.444981855504443 \tabularnewline
28 & 0.552091629703333 & 0.895816740593333 & 0.447908370296667 \tabularnewline
29 & 0.462857633937679 & 0.925715267875358 & 0.537142366062321 \tabularnewline
30 & 0.485408917555307 & 0.970817835110614 & 0.514591082444693 \tabularnewline
31 & 0.457972761647405 & 0.91594552329481 & 0.542027238352595 \tabularnewline
32 & 0.380665734289095 & 0.76133146857819 & 0.619334265710905 \tabularnewline
33 & 0.292427029138627 & 0.584854058277255 & 0.707572970861372 \tabularnewline
34 & 0.322375318477102 & 0.644750636954204 & 0.677624681522898 \tabularnewline
35 & 0.339029931945942 & 0.678059863891885 & 0.660970068054058 \tabularnewline
36 & 0.289329123441000 & 0.578658246881999 & 0.710670876559 \tabularnewline
37 & 0.239825256128015 & 0.47965051225603 & 0.760174743871985 \tabularnewline
38 & 0.181680531531310 & 0.363361063062619 & 0.81831946846869 \tabularnewline
39 & 0.121884514916035 & 0.243769029832071 & 0.878115485083965 \tabularnewline
40 & 0.309363089725026 & 0.618726179450052 & 0.690636910274974 \tabularnewline
41 & 0.240324862678129 & 0.480649725356257 & 0.759675137321871 \tabularnewline
42 & 0.179154484401181 & 0.358308968802363 & 0.820845515598819 \tabularnewline
43 & 0.102193074118312 & 0.204386148236623 & 0.897806925881688 \tabularnewline
44 & 0.0516146736417748 & 0.103229347283550 & 0.948385326358225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&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]17[/C][C]0.98265272004147[/C][C]0.0346945599170585[/C][C]0.0173472799585293[/C][/ROW]
[ROW][C]18[/C][C]0.980678326740391[/C][C]0.0386433465192176[/C][C]0.0193216732596088[/C][/ROW]
[ROW][C]19[/C][C]0.96042595393575[/C][C]0.0791480921285006[/C][C]0.0395740460642503[/C][/ROW]
[ROW][C]20[/C][C]0.931671758525832[/C][C]0.136656482948336[/C][C]0.0683282414741679[/C][/ROW]
[ROW][C]21[/C][C]0.89696314492517[/C][C]0.206073710149660[/C][C]0.103036855074830[/C][/ROW]
[ROW][C]22[/C][C]0.840334609499383[/C][C]0.319330781001234[/C][C]0.159665390500617[/C][/ROW]
[ROW][C]23[/C][C]0.804978975336592[/C][C]0.390042049326816[/C][C]0.195021024663408[/C][/ROW]
[ROW][C]24[/C][C]0.751261996492935[/C][C]0.497476007014131[/C][C]0.248738003507065[/C][/ROW]
[ROW][C]25[/C][C]0.678360691674782[/C][C]0.643278616650436[/C][C]0.321639308325218[/C][/ROW]
[ROW][C]26[/C][C]0.624278471216273[/C][C]0.751443057567454[/C][C]0.375721528783727[/C][/ROW]
[ROW][C]27[/C][C]0.555018144495557[/C][C]0.889963711008886[/C][C]0.444981855504443[/C][/ROW]
[ROW][C]28[/C][C]0.552091629703333[/C][C]0.895816740593333[/C][C]0.447908370296667[/C][/ROW]
[ROW][C]29[/C][C]0.462857633937679[/C][C]0.925715267875358[/C][C]0.537142366062321[/C][/ROW]
[ROW][C]30[/C][C]0.485408917555307[/C][C]0.970817835110614[/C][C]0.514591082444693[/C][/ROW]
[ROW][C]31[/C][C]0.457972761647405[/C][C]0.91594552329481[/C][C]0.542027238352595[/C][/ROW]
[ROW][C]32[/C][C]0.380665734289095[/C][C]0.76133146857819[/C][C]0.619334265710905[/C][/ROW]
[ROW][C]33[/C][C]0.292427029138627[/C][C]0.584854058277255[/C][C]0.707572970861372[/C][/ROW]
[ROW][C]34[/C][C]0.322375318477102[/C][C]0.644750636954204[/C][C]0.677624681522898[/C][/ROW]
[ROW][C]35[/C][C]0.339029931945942[/C][C]0.678059863891885[/C][C]0.660970068054058[/C][/ROW]
[ROW][C]36[/C][C]0.289329123441000[/C][C]0.578658246881999[/C][C]0.710670876559[/C][/ROW]
[ROW][C]37[/C][C]0.239825256128015[/C][C]0.47965051225603[/C][C]0.760174743871985[/C][/ROW]
[ROW][C]38[/C][C]0.181680531531310[/C][C]0.363361063062619[/C][C]0.81831946846869[/C][/ROW]
[ROW][C]39[/C][C]0.121884514916035[/C][C]0.243769029832071[/C][C]0.878115485083965[/C][/ROW]
[ROW][C]40[/C][C]0.309363089725026[/C][C]0.618726179450052[/C][C]0.690636910274974[/C][/ROW]
[ROW][C]41[/C][C]0.240324862678129[/C][C]0.480649725356257[/C][C]0.759675137321871[/C][/ROW]
[ROW][C]42[/C][C]0.179154484401181[/C][C]0.358308968802363[/C][C]0.820845515598819[/C][/ROW]
[ROW][C]43[/C][C]0.102193074118312[/C][C]0.204386148236623[/C][C]0.897806925881688[/C][/ROW]
[ROW][C]44[/C][C]0.0516146736417748[/C][C]0.103229347283550[/C][C]0.948385326358225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.98265272004147	0.0346945599170585	0.0173472799585293
18	0.980678326740391	0.0386433465192176	0.0193216732596088
19	0.96042595393575	0.0791480921285006	0.0395740460642503
20	0.931671758525832	0.136656482948336	0.0683282414741679
21	0.89696314492517	0.206073710149660	0.103036855074830
22	0.840334609499383	0.319330781001234	0.159665390500617
23	0.804978975336592	0.390042049326816	0.195021024663408
24	0.751261996492935	0.497476007014131	0.248738003507065
25	0.678360691674782	0.643278616650436	0.321639308325218
26	0.624278471216273	0.751443057567454	0.375721528783727
27	0.555018144495557	0.889963711008886	0.444981855504443
28	0.552091629703333	0.895816740593333	0.447908370296667
29	0.462857633937679	0.925715267875358	0.537142366062321
30	0.485408917555307	0.970817835110614	0.514591082444693
31	0.457972761647405	0.91594552329481	0.542027238352595
32	0.380665734289095	0.76133146857819	0.619334265710905
33	0.292427029138627	0.584854058277255	0.707572970861372
34	0.322375318477102	0.644750636954204	0.677624681522898
35	0.339029931945942	0.678059863891885	0.660970068054058
36	0.289329123441000	0.578658246881999	0.710670876559
37	0.239825256128015	0.47965051225603	0.760174743871985
38	0.181680531531310	0.363361063062619	0.81831946846869
39	0.121884514916035	0.243769029832071	0.878115485083965
40	0.309363089725026	0.618726179450052	0.690636910274974
41	0.240324862678129	0.480649725356257	0.759675137321871
42	0.179154484401181	0.358308968802363	0.820845515598819
43	0.102193074118312	0.204386148236623	0.897806925881688
44	0.0516146736417748	0.103229347283550	0.948385326358225

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	2	0.0714285714285714	NOK
10% type I error level	3	0.107142857142857	NOK

\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 & 0.0714285714285714 & NOK \tabularnewline
10% type I error level & 3 & 0.107142857142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25805&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]0.0714285714285714[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.107142857142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25805&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25805&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 tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	2	0.0714285714285714	NOK
10% type I error level	3	0.107142857142857	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code