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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Mon, 24 Nov 2008 13:42:13 -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/24/t1227559651po80z6kq8wai37k.htm/, Retrieved Mon, 13 May 2024 21:02:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25527, Retrieved Mon, 13 May 2024 21:02:08 +0000

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User-defined keywords

Multiple Lineair Regression

Estimated Impact

163

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

-     [Multiple Regression] [Multiple Lineair ...] [2008-11-23 13:54:18] [b635de6fc42b001d22cbe6e730fec936]
F   P   [Multiple Regression] [Multiple Lineair ...] [2008-11-24 10:32:50] [b635de6fc42b001d22cbe6e730fec936]
F    D      [Multiple Regression] [Multiple Lineair ...] [2008-11-24 20:42:13] [f4b2017b314c03698059f43b95818e67] [Current]

Feedback Forum

2008-11-30 16:14:40 [Michael Van Spaandonck] [reply] 
In dit model is rekening gehouden met seasonal dummies en een lineaire trend 
 
Volgens de Adjusted R-square valt 69% van de schommelingen te verklaren door middel van dit model. Aangezien de p-waarde echter 2,76 bedraagt mag gesteld worden dat deze 69% niet significant verschilt van nulhypothese H0 = 0. 
Dit wordt niet behandeld door de student. 
 
Wanneer we de tabel van de ordinary least squares bekijken zien we dat de meeste parameters (maandwaarden) negatief zijn, wat wil zeggen dat er in deze maanden een lager percentage geldt dan in de referentiemaand. Slechts 2 zijn positief, wat duidt op een hoger percentage. 
Wordt niet behandeld in het document. 
 
Zoals gezegd is de parameter voor de nulhypothese 0, wat wil zeggen dat we  ervan uit gaan dat de beurscrash niet van invloed is op de werkloosheid. 
Er wordt terecht gekozen voor een eenzijdige test. 9 maanden hebben daarbij een p-waarde die hoger ligt dan 5%, wat betekent dat deze wijzigingen in het maandelijkse werkloosheidscijfer waarschijnlijk toe te schrijven zijn aan het toeval. 
De student vermeldt slechts dat de p-waarden positief zijn, zonder hieruit verder conclusies te trekken. 
 
De grafiek van Actuals & Interpolation vertoont een aflopend verloop. 
In principe benaderen de voorspellingen (interpolations, de stippen) de actuals (lijn) vrij goed, maar tussen waarnemingen 20 en 34 zijn de afwijkingen vrij groot.  
Wordt niet behandeld in het document. 
 
Er mag gesteld worden dat het gemiddelde van de residuals 0 benadert. Dit betekent in een verdergaande analyse in feite dat er een fixed variation is. 
De student komt ook tot deze conclusie. 
 
Histogram en density plot geven geven een vrij goede normaalverdeling weer. Dit betekent in een verdergaande analyse in feite dat er een fixed distribution is. 
Studnet stelt dat dit het geval is. 
 
Op het Q-Q plot zien we dat de punten vrij dicht bij de rechte liggen. Deze grafiek bevestigt dus de overige twee. 
Wordt niet besproken door de student. 
 
Het residuals lag plot geeft een lage correlatie weer tussen de voorspellingsfout nu en de voorspellingsfout van de voorgaande maand. 
Student stelt dat dit het geval is. 
 
Tot slot de grafiek van de autocorrelatie. 
Bij een lag van 12 zien we dat de autocorrelatie binnen het interval valt, en dat er dus van toeval geen sprake is. 
Wordt ook door de student geconcludeerd.

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Dataseries X:

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
Totaal%werkzoekenden[t] = + 9.19236363636363 + 0.894545454545455stockmarketcrashfollowedbyeconomicdepression[t] -0.125757575757581M1[t] -0.294424242424242M2[t] -0.363090909090908M3[t] -0.191757575757574M4[t] + 0.0395757575757589M5[t] + 0.0509090909090923M6[t] -0.0977575757575742M7[t] -0.326424242424242M8[t] -0.535090909090908M9[t] -0.762666666666665M10[t] -0.131333333333332M11[t] -0.0513333333333333t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Totaal%werkzoekenden[t] =  +  9.19236363636363 +  0.894545454545455stockmarketcrashfollowedbyeconomicdepression[t] -0.125757575757581M1[t] -0.294424242424242M2[t] -0.363090909090908M3[t] -0.191757575757574M4[t] +  0.0395757575757589M5[t] +  0.0509090909090923M6[t] -0.0977575757575742M7[t] -0.326424242424242M8[t] -0.535090909090908M9[t] -0.762666666666665M10[t] -0.131333333333332M11[t] -0.0513333333333333t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Totaal%werkzoekenden[t] =  +  9.19236363636363 +  0.894545454545455stockmarketcrashfollowedbyeconomicdepression[t] -0.125757575757581M1[t] -0.294424242424242M2[t] -0.363090909090908M3[t] -0.191757575757574M4[t] +  0.0395757575757589M5[t] +  0.0509090909090923M6[t] -0.0977575757575742M7[t] -0.326424242424242M8[t] -0.535090909090908M9[t] -0.762666666666665M10[t] -0.131333333333332M11[t] -0.0513333333333333t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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
Totaal%werkzoekenden[t] = + 9.19236363636363 + 0.894545454545455stockmarketcrashfollowedbyeconomicdepression[t] -0.125757575757581M1[t] -0.294424242424242M2[t] -0.363090909090908M3[t] -0.191757575757574M4[t] + 0.0395757575757589M5[t] + 0.0509090909090923M6[t] -0.0977575757575742M7[t] -0.326424242424242M8[t] -0.535090909090908M9[t] -0.762666666666665M10[t] -0.131333333333332M11[t] -0.0513333333333333t + 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)	9.19236363636363	0.214208	42.9132	0	0
stockmarketcrashfollowedbyeconomicdepression	0.894545454545455	0.201066	4.449	5.4e-05	2.7e-05
M1	-0.125757575757581	0.260735	-0.4823	0.631867	0.315933
M2	-0.294424242424242	0.260202	-1.1315	0.263699	0.13185
M3	-0.363090909090908	0.259786	-1.3977	0.168921	0.084461
M4	-0.191757575757574	0.259489	-0.739	0.463672	0.231836
M5	0.0395757575757589	0.25931	0.1526	0.879366	0.439683
M6	0.0509090909090923	0.25925	0.1964	0.845185	0.422593
M7	-0.0977575757575742	0.25931	-0.377	0.707914	0.353957
M8	-0.326424242424242	0.259489	-1.258	0.214757	0.107379
M9	-0.535090909090908	0.259786	-2.0597	0.045108	0.022554
M10	-0.762666666666665	0.258513	-2.9502	0.004981	0.00249
M11	-0.131333333333332	0.258334	-0.5084	0.613612	0.306806
t	-0.0513333333333333	0.005557	-9.2373	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) & 9.19236363636363 & 0.214208 & 42.9132 & 0 & 0 \tabularnewline
stockmarketcrashfollowedbyeconomicdepression & 0.894545454545455 & 0.201066 & 4.449 & 5.4e-05 & 2.7e-05 \tabularnewline
M1 & -0.125757575757581 & 0.260735 & -0.4823 & 0.631867 & 0.315933 \tabularnewline
M2 & -0.294424242424242 & 0.260202 & -1.1315 & 0.263699 & 0.13185 \tabularnewline
M3 & -0.363090909090908 & 0.259786 & -1.3977 & 0.168921 & 0.084461 \tabularnewline
M4 & -0.191757575757574 & 0.259489 & -0.739 & 0.463672 & 0.231836 \tabularnewline
M5 & 0.0395757575757589 & 0.25931 & 0.1526 & 0.879366 & 0.439683 \tabularnewline
M6 & 0.0509090909090923 & 0.25925 & 0.1964 & 0.845185 & 0.422593 \tabularnewline
M7 & -0.0977575757575742 & 0.25931 & -0.377 & 0.707914 & 0.353957 \tabularnewline
M8 & -0.326424242424242 & 0.259489 & -1.258 & 0.214757 & 0.107379 \tabularnewline
M9 & -0.535090909090908 & 0.259786 & -2.0597 & 0.045108 & 0.022554 \tabularnewline
M10 & -0.762666666666665 & 0.258513 & -2.9502 & 0.004981 & 0.00249 \tabularnewline
M11 & -0.131333333333332 & 0.258334 & -0.5084 & 0.613612 & 0.306806 \tabularnewline
t & -0.0513333333333333 & 0.005557 & -9.2373 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&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]9.19236363636363[/C][C]0.214208[/C][C]42.9132[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]stockmarketcrashfollowedbyeconomicdepression[/C][C]0.894545454545455[/C][C]0.201066[/C][C]4.449[/C][C]5.4e-05[/C][C]2.7e-05[/C][/ROW]
[ROW][C]M1[/C][C]-0.125757575757581[/C][C]0.260735[/C][C]-0.4823[/C][C]0.631867[/C][C]0.315933[/C][/ROW]
[ROW][C]M2[/C][C]-0.294424242424242[/C][C]0.260202[/C][C]-1.1315[/C][C]0.263699[/C][C]0.13185[/C][/ROW]
[ROW][C]M3[/C][C]-0.363090909090908[/C][C]0.259786[/C][C]-1.3977[/C][C]0.168921[/C][C]0.084461[/C][/ROW]
[ROW][C]M4[/C][C]-0.191757575757574[/C][C]0.259489[/C][C]-0.739[/C][C]0.463672[/C][C]0.231836[/C][/ROW]
[ROW][C]M5[/C][C]0.0395757575757589[/C][C]0.25931[/C][C]0.1526[/C][C]0.879366[/C][C]0.439683[/C][/ROW]
[ROW][C]M6[/C][C]0.0509090909090923[/C][C]0.25925[/C][C]0.1964[/C][C]0.845185[/C][C]0.422593[/C][/ROW]
[ROW][C]M7[/C][C]-0.0977575757575742[/C][C]0.25931[/C][C]-0.377[/C][C]0.707914[/C][C]0.353957[/C][/ROW]
[ROW][C]M8[/C][C]-0.326424242424242[/C][C]0.259489[/C][C]-1.258[/C][C]0.214757[/C][C]0.107379[/C][/ROW]
[ROW][C]M9[/C][C]-0.535090909090908[/C][C]0.259786[/C][C]-2.0597[/C][C]0.045108[/C][C]0.022554[/C][/ROW]
[ROW][C]M10[/C][C]-0.762666666666665[/C][C]0.258513[/C][C]-2.9502[/C][C]0.004981[/C][C]0.00249[/C][/ROW]
[ROW][C]M11[/C][C]-0.131333333333332[/C][C]0.258334[/C][C]-0.5084[/C][C]0.613612[/C][C]0.306806[/C][/ROW]
[ROW][C]t[/C][C]-0.0513333333333333[/C][C]0.005557[/C][C]-9.2373[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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)	9.19236363636363	0.214208	42.9132	0	0
stockmarketcrashfollowedbyeconomicdepression	0.894545454545455	0.201066	4.449	5.4e-05	2.7e-05
M1	-0.125757575757581	0.260735	-0.4823	0.631867	0.315933
M2	-0.294424242424242	0.260202	-1.1315	0.263699	0.13185
M3	-0.363090909090908	0.259786	-1.3977	0.168921	0.084461
M4	-0.191757575757574	0.259489	-0.739	0.463672	0.231836
M5	0.0395757575757589	0.25931	0.1526	0.879366	0.439683
M6	0.0509090909090923	0.25925	0.1964	0.845185	0.422593
M7	-0.0977575757575742	0.25931	-0.377	0.707914	0.353957
M8	-0.326424242424242	0.259489	-1.258	0.214757	0.107379
M9	-0.535090909090908	0.259786	-2.0597	0.045108	0.022554
M10	-0.762666666666665	0.258513	-2.9502	0.004981	0.00249
M11	-0.131333333333332	0.258334	-0.5084	0.613612	0.306806
t	-0.0513333333333333	0.005557	-9.2373	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.872093262063936
R-squared	0.760546657737317
Adjusted R-squared	0.692875061010907
F-TEST (value)	11.2387869435405
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	2.76699552159698e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.408367036333293
Sum Squared Residuals	7.67112727272732

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.872093262063936 \tabularnewline
R-squared & 0.760546657737317 \tabularnewline
Adjusted R-squared & 0.692875061010907 \tabularnewline
F-TEST (value) & 11.2387869435405 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 2.76699552159698e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.408367036333293 \tabularnewline
Sum Squared Residuals & 7.67112727272732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.872093262063936[/C][/ROW]
[ROW][C]R-squared[/C][C]0.760546657737317[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.692875061010907[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]11.2387869435405[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]2.76699552159698e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.408367036333293[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7.67112727272732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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	0.872093262063936
R-squared	0.760546657737317
Adjusted R-squared	0.692875061010907
F-TEST (value)	11.2387869435405
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	2.76699552159698e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.408367036333293
Sum Squared Residuals	7.67112727272732

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.4	9.01527272727275	-0.615272727272753
2	8.4	8.79527272727273	-0.395272727272731
3	8.4	8.67527272727273	-0.275272727272727
4	8.6	8.79527272727273	-0.195272727272726
5	8.9	8.97527272727273	-0.0752727272727255
6	8.8	8.93527272727273	-0.135272727272725
7	8.3	8.73527272727273	-0.435272727272726
8	7.5	8.45527272727272	-0.955272727272725
9	7.2	8.19527272727273	-0.995272727272727
10	7.5	7.91636363636363	-0.416363636363634
11	8.8	8.49636363636363	0.303636363636366
12	9.3	8.57636363636363	0.723636363636367
13	9.3	8.39927272727272	0.90072727272728
14	8.7	8.17927272727272	0.520727272727274
15	8.2	8.05927272727273	0.140727272727273
16	8.3	8.17927272727273	0.120727272727274
17	8.5	8.35927272727273	0.140727272727273
18	8.6	8.31927272727273	0.280727272727273
19	8.6	8.11927272727273	0.480727272727273
20	8.2	7.83927272727273	0.360727272727273
21	8.1	7.57927272727273	0.520727272727273
22	8	8.1949090909091	-0.194909090909090
23	8.6	8.77490909090909	-0.17490909090909
24	8.7	8.85490909090909	-0.15490909090909
25	8.8	8.67781818181817	0.122181818181826
26	8.5	8.45781818181818	0.0421818181818194
27	8.4	8.33781818181818	0.0621818181818188
28	8.5	8.45781818181818	0.0421818181818181
29	8.7	8.63781818181818	0.0621818181818174
30	8.7	8.59781818181818	0.102181818181817
31	8.6	8.39781818181818	0.202181818181818
32	8.5	8.11781818181818	0.382181818181818
33	8.3	7.85781818181818	0.442181818181819
34	8.1	7.57890909090909	0.521090909090909
35	8.2	8.15890909090909	0.041090909090909
36	8.1	8.23890909090909	-0.13890909090909
37	8.1	8.06181818181818	0.038181818181824
38	7.9	7.84181818181818	0.0581818181818191
39	7.9	7.72181818181818	0.178181818181818
40	7.9	7.84181818181818	0.0581818181818178
41	8	8.02181818181818	-0.0218181818181824
42	8	7.98181818181818	0.0181818181818173
43	7.9	7.78181818181818	0.118181818181818
44	8	7.50181818181818	0.498181818181818
45	7.7	7.24181818181818	0.458181818181817
46	7.2	6.96290909090909	0.237090909090908
47	7.5	7.54290909090909	-0.0429090909090911
48	7.3	7.62290909090909	-0.322909090909091
49	7	7.44581818181818	-0.445818181818176
50	7	7.22581818181818	-0.225818181818182
51	7	7.10581818181818	-0.105818181818183
52	7.2	7.22581818181818	-0.0258181818181832
53	7.3	7.40581818181818	-0.105818181818184
54	7.1	7.36581818181818	-0.265818181818184
55	6.8	7.16581818181818	-0.365818181818184
56	6.6	6.88581818181818	-0.285818181818183
57	6.2	6.62581818181818	-0.425818181818183
58	6.2	6.34690909090909	-0.146909090909092
59	6.8	6.92690909090909	-0.126909090909092
60	6.9	7.00690909090909	-0.106909090909091

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.4 & 9.01527272727275 & -0.615272727272753 \tabularnewline
2 & 8.4 & 8.79527272727273 & -0.395272727272731 \tabularnewline
3 & 8.4 & 8.67527272727273 & -0.275272727272727 \tabularnewline
4 & 8.6 & 8.79527272727273 & -0.195272727272726 \tabularnewline
5 & 8.9 & 8.97527272727273 & -0.0752727272727255 \tabularnewline
6 & 8.8 & 8.93527272727273 & -0.135272727272725 \tabularnewline
7 & 8.3 & 8.73527272727273 & -0.435272727272726 \tabularnewline
8 & 7.5 & 8.45527272727272 & -0.955272727272725 \tabularnewline
9 & 7.2 & 8.19527272727273 & -0.995272727272727 \tabularnewline
10 & 7.5 & 7.91636363636363 & -0.416363636363634 \tabularnewline
11 & 8.8 & 8.49636363636363 & 0.303636363636366 \tabularnewline
12 & 9.3 & 8.57636363636363 & 0.723636363636367 \tabularnewline
13 & 9.3 & 8.39927272727272 & 0.90072727272728 \tabularnewline
14 & 8.7 & 8.17927272727272 & 0.520727272727274 \tabularnewline
15 & 8.2 & 8.05927272727273 & 0.140727272727273 \tabularnewline
16 & 8.3 & 8.17927272727273 & 0.120727272727274 \tabularnewline
17 & 8.5 & 8.35927272727273 & 0.140727272727273 \tabularnewline
18 & 8.6 & 8.31927272727273 & 0.280727272727273 \tabularnewline
19 & 8.6 & 8.11927272727273 & 0.480727272727273 \tabularnewline
20 & 8.2 & 7.83927272727273 & 0.360727272727273 \tabularnewline
21 & 8.1 & 7.57927272727273 & 0.520727272727273 \tabularnewline
22 & 8 & 8.1949090909091 & -0.194909090909090 \tabularnewline
23 & 8.6 & 8.77490909090909 & -0.17490909090909 \tabularnewline
24 & 8.7 & 8.85490909090909 & -0.15490909090909 \tabularnewline
25 & 8.8 & 8.67781818181817 & 0.122181818181826 \tabularnewline
26 & 8.5 & 8.45781818181818 & 0.0421818181818194 \tabularnewline
27 & 8.4 & 8.33781818181818 & 0.0621818181818188 \tabularnewline
28 & 8.5 & 8.45781818181818 & 0.0421818181818181 \tabularnewline
29 & 8.7 & 8.63781818181818 & 0.0621818181818174 \tabularnewline
30 & 8.7 & 8.59781818181818 & 0.102181818181817 \tabularnewline
31 & 8.6 & 8.39781818181818 & 0.202181818181818 \tabularnewline
32 & 8.5 & 8.11781818181818 & 0.382181818181818 \tabularnewline
33 & 8.3 & 7.85781818181818 & 0.442181818181819 \tabularnewline
34 & 8.1 & 7.57890909090909 & 0.521090909090909 \tabularnewline
35 & 8.2 & 8.15890909090909 & 0.041090909090909 \tabularnewline
36 & 8.1 & 8.23890909090909 & -0.13890909090909 \tabularnewline
37 & 8.1 & 8.06181818181818 & 0.038181818181824 \tabularnewline
38 & 7.9 & 7.84181818181818 & 0.0581818181818191 \tabularnewline
39 & 7.9 & 7.72181818181818 & 0.178181818181818 \tabularnewline
40 & 7.9 & 7.84181818181818 & 0.0581818181818178 \tabularnewline
41 & 8 & 8.02181818181818 & -0.0218181818181824 \tabularnewline
42 & 8 & 7.98181818181818 & 0.0181818181818173 \tabularnewline
43 & 7.9 & 7.78181818181818 & 0.118181818181818 \tabularnewline
44 & 8 & 7.50181818181818 & 0.498181818181818 \tabularnewline
45 & 7.7 & 7.24181818181818 & 0.458181818181817 \tabularnewline
46 & 7.2 & 6.96290909090909 & 0.237090909090908 \tabularnewline
47 & 7.5 & 7.54290909090909 & -0.0429090909090911 \tabularnewline
48 & 7.3 & 7.62290909090909 & -0.322909090909091 \tabularnewline
49 & 7 & 7.44581818181818 & -0.445818181818176 \tabularnewline
50 & 7 & 7.22581818181818 & -0.225818181818182 \tabularnewline
51 & 7 & 7.10581818181818 & -0.105818181818183 \tabularnewline
52 & 7.2 & 7.22581818181818 & -0.0258181818181832 \tabularnewline
53 & 7.3 & 7.40581818181818 & -0.105818181818184 \tabularnewline
54 & 7.1 & 7.36581818181818 & -0.265818181818184 \tabularnewline
55 & 6.8 & 7.16581818181818 & -0.365818181818184 \tabularnewline
56 & 6.6 & 6.88581818181818 & -0.285818181818183 \tabularnewline
57 & 6.2 & 6.62581818181818 & -0.425818181818183 \tabularnewline
58 & 6.2 & 6.34690909090909 & -0.146909090909092 \tabularnewline
59 & 6.8 & 6.92690909090909 & -0.126909090909092 \tabularnewline
60 & 6.9 & 7.00690909090909 & -0.106909090909091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&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]8.4[/C][C]9.01527272727275[/C][C]-0.615272727272753[/C][/ROW]
[ROW][C]2[/C][C]8.4[/C][C]8.79527272727273[/C][C]-0.395272727272731[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.67527272727273[/C][C]-0.275272727272727[/C][/ROW]
[ROW][C]4[/C][C]8.6[/C][C]8.79527272727273[/C][C]-0.195272727272726[/C][/ROW]
[ROW][C]5[/C][C]8.9[/C][C]8.97527272727273[/C][C]-0.0752727272727255[/C][/ROW]
[ROW][C]6[/C][C]8.8[/C][C]8.93527272727273[/C][C]-0.135272727272725[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]8.73527272727273[/C][C]-0.435272727272726[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]8.45527272727272[/C][C]-0.955272727272725[/C][/ROW]
[ROW][C]9[/C][C]7.2[/C][C]8.19527272727273[/C][C]-0.995272727272727[/C][/ROW]
[ROW][C]10[/C][C]7.5[/C][C]7.91636363636363[/C][C]-0.416363636363634[/C][/ROW]
[ROW][C]11[/C][C]8.8[/C][C]8.49636363636363[/C][C]0.303636363636366[/C][/ROW]
[ROW][C]12[/C][C]9.3[/C][C]8.57636363636363[/C][C]0.723636363636367[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]8.39927272727272[/C][C]0.90072727272728[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.17927272727272[/C][C]0.520727272727274[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.05927272727273[/C][C]0.140727272727273[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.17927272727273[/C][C]0.120727272727274[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.35927272727273[/C][C]0.140727272727273[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.31927272727273[/C][C]0.280727272727273[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.11927272727273[/C][C]0.480727272727273[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]7.83927272727273[/C][C]0.360727272727273[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.57927272727273[/C][C]0.520727272727273[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]8.1949090909091[/C][C]-0.194909090909090[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.77490909090909[/C][C]-0.17490909090909[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.85490909090909[/C][C]-0.15490909090909[/C][/ROW]
[ROW][C]25[/C][C]8.8[/C][C]8.67781818181817[/C][C]0.122181818181826[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.45781818181818[/C][C]0.0421818181818194[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]8.33781818181818[/C][C]0.0621818181818188[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.45781818181818[/C][C]0.0421818181818181[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.63781818181818[/C][C]0.0621818181818174[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.59781818181818[/C][C]0.102181818181817[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]8.39781818181818[/C][C]0.202181818181818[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]8.11781818181818[/C][C]0.382181818181818[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]7.85781818181818[/C][C]0.442181818181819[/C][/ROW]
[ROW][C]34[/C][C]8.1[/C][C]7.57890909090909[/C][C]0.521090909090909[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]8.15890909090909[/C][C]0.041090909090909[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.23890909090909[/C][C]-0.13890909090909[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.06181818181818[/C][C]0.038181818181824[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]7.84181818181818[/C][C]0.0581818181818191[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.72181818181818[/C][C]0.178181818181818[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.84181818181818[/C][C]0.0581818181818178[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]8.02181818181818[/C][C]-0.0218181818181824[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]7.98181818181818[/C][C]0.0181818181818173[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]7.78181818181818[/C][C]0.118181818181818[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.50181818181818[/C][C]0.498181818181818[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.24181818181818[/C][C]0.458181818181817[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]6.96290909090909[/C][C]0.237090909090908[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]7.54290909090909[/C][C]-0.0429090909090911[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.62290909090909[/C][C]-0.322909090909091[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.44581818181818[/C][C]-0.445818181818176[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]7.22581818181818[/C][C]-0.225818181818182[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]7.10581818181818[/C][C]-0.105818181818183[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.22581818181818[/C][C]-0.0258181818181832[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.40581818181818[/C][C]-0.105818181818184[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.36581818181818[/C][C]-0.265818181818184[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]7.16581818181818[/C][C]-0.365818181818184[/C][/ROW]
[ROW][C]56[/C][C]6.6[/C][C]6.88581818181818[/C][C]-0.285818181818183[/C][/ROW]
[ROW][C]57[/C][C]6.2[/C][C]6.62581818181818[/C][C]-0.425818181818183[/C][/ROW]
[ROW][C]58[/C][C]6.2[/C][C]6.34690909090909[/C][C]-0.146909090909092[/C][/ROW]
[ROW][C]59[/C][C]6.8[/C][C]6.92690909090909[/C][C]-0.126909090909092[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]7.00690909090909[/C][C]-0.106909090909091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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	8.4	9.01527272727275	-0.615272727272753
2	8.4	8.79527272727273	-0.395272727272731
3	8.4	8.67527272727273	-0.275272727272727
4	8.6	8.79527272727273	-0.195272727272726
5	8.9	8.97527272727273	-0.0752727272727255
6	8.8	8.93527272727273	-0.135272727272725
7	8.3	8.73527272727273	-0.435272727272726
8	7.5	8.45527272727272	-0.955272727272725
9	7.2	8.19527272727273	-0.995272727272727
10	7.5	7.91636363636363	-0.416363636363634
11	8.8	8.49636363636363	0.303636363636366
12	9.3	8.57636363636363	0.723636363636367
13	9.3	8.39927272727272	0.90072727272728
14	8.7	8.17927272727272	0.520727272727274
15	8.2	8.05927272727273	0.140727272727273
16	8.3	8.17927272727273	0.120727272727274
17	8.5	8.35927272727273	0.140727272727273
18	8.6	8.31927272727273	0.280727272727273
19	8.6	8.11927272727273	0.480727272727273
20	8.2	7.83927272727273	0.360727272727273
21	8.1	7.57927272727273	0.520727272727273
22	8	8.1949090909091	-0.194909090909090
23	8.6	8.77490909090909	-0.17490909090909
24	8.7	8.85490909090909	-0.15490909090909
25	8.8	8.67781818181817	0.122181818181826
26	8.5	8.45781818181818	0.0421818181818194
27	8.4	8.33781818181818	0.0621818181818188
28	8.5	8.45781818181818	0.0421818181818181
29	8.7	8.63781818181818	0.0621818181818174
30	8.7	8.59781818181818	0.102181818181817
31	8.6	8.39781818181818	0.202181818181818
32	8.5	8.11781818181818	0.382181818181818
33	8.3	7.85781818181818	0.442181818181819
34	8.1	7.57890909090909	0.521090909090909
35	8.2	8.15890909090909	0.041090909090909
36	8.1	8.23890909090909	-0.13890909090909
37	8.1	8.06181818181818	0.038181818181824
38	7.9	7.84181818181818	0.0581818181818191
39	7.9	7.72181818181818	0.178181818181818
40	7.9	7.84181818181818	0.0581818181818178
41	8	8.02181818181818	-0.0218181818181824
42	8	7.98181818181818	0.0181818181818173
43	7.9	7.78181818181818	0.118181818181818
44	8	7.50181818181818	0.498181818181818
45	7.7	7.24181818181818	0.458181818181817
46	7.2	6.96290909090909	0.237090909090908
47	7.5	7.54290909090909	-0.0429090909090911
48	7.3	7.62290909090909	-0.322909090909091
49	7	7.44581818181818	-0.445818181818176
50	7	7.22581818181818	-0.225818181818182
51	7	7.10581818181818	-0.105818181818183
52	7.2	7.22581818181818	-0.0258181818181832
53	7.3	7.40581818181818	-0.105818181818184
54	7.1	7.36581818181818	-0.265818181818184
55	6.8	7.16581818181818	-0.365818181818184
56	6.6	6.88581818181818	-0.285818181818183
57	6.2	6.62581818181818	-0.425818181818183
58	6.2	6.34690909090909	-0.146909090909092
59	6.8	6.92690909090909	-0.126909090909092
60	6.9	7.00690909090909	-0.106909090909091

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.981959688441397	0.0360806231172068	0.0180403115586034
18	0.96408574013091	0.0718285197381804	0.0359142598690902
19	0.94313532732763	0.113729345344740	0.0568646726723701
20	0.956699614607823	0.0866007707843546	0.0433003853921773
21	0.972190128147901	0.0556197437041977	0.0278098718520988
22	0.98350007737318	0.0329998452536408	0.0164999226268204
23	0.990730737193708	0.0185385256125843	0.00926926280629217
24	0.994444174985299	0.0111116500294025	0.00555582501470126
25	0.988740856902454	0.0225182861950914	0.0112591430975457
26	0.98035286735897	0.0392942652820608	0.0196471326410304
27	0.973437665758802	0.0531246684823953	0.0265623342411976
28	0.96625328503873	0.0674934299225407	0.0337467149612703
29	0.951178246679055	0.0976435066418905	0.0488217533209452
30	0.923761976887401	0.152476046225198	0.0762380231125988
31	0.882970581188893	0.234058837622213	0.117029418811107
32	0.891262402705244	0.217475194589512	0.108737597294756
33	0.879544256480426	0.240911487039149	0.120455743519574
34	0.823555738359407	0.352888523281187	0.176444261640593
35	0.859162542221701	0.281674915556598	0.140837457778299
36	0.935598251834033	0.128803496331933	0.0644017481659666
37	0.931618047810787	0.136763904378425	0.0683819521892127
38	0.900264203862807	0.199471592274386	0.0997357961371932
39	0.837946741421896	0.324106517156207	0.162053258578104
40	0.779762898218268	0.440474203563465	0.220237101781732
41	0.716783958085626	0.566432083828748	0.283216041914374
42	0.592178447671983	0.815643104656034	0.407821552328017
43	0.428714320744957	0.857428641489914	0.571285679255043

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.981959688441397 & 0.0360806231172068 & 0.0180403115586034 \tabularnewline
18 & 0.96408574013091 & 0.0718285197381804 & 0.0359142598690902 \tabularnewline
19 & 0.94313532732763 & 0.113729345344740 & 0.0568646726723701 \tabularnewline
20 & 0.956699614607823 & 0.0866007707843546 & 0.0433003853921773 \tabularnewline
21 & 0.972190128147901 & 0.0556197437041977 & 0.0278098718520988 \tabularnewline
22 & 0.98350007737318 & 0.0329998452536408 & 0.0164999226268204 \tabularnewline
23 & 0.990730737193708 & 0.0185385256125843 & 0.00926926280629217 \tabularnewline
24 & 0.994444174985299 & 0.0111116500294025 & 0.00555582501470126 \tabularnewline
25 & 0.988740856902454 & 0.0225182861950914 & 0.0112591430975457 \tabularnewline
26 & 0.98035286735897 & 0.0392942652820608 & 0.0196471326410304 \tabularnewline
27 & 0.973437665758802 & 0.0531246684823953 & 0.0265623342411976 \tabularnewline
28 & 0.96625328503873 & 0.0674934299225407 & 0.0337467149612703 \tabularnewline
29 & 0.951178246679055 & 0.0976435066418905 & 0.0488217533209452 \tabularnewline
30 & 0.923761976887401 & 0.152476046225198 & 0.0762380231125988 \tabularnewline
31 & 0.882970581188893 & 0.234058837622213 & 0.117029418811107 \tabularnewline
32 & 0.891262402705244 & 0.217475194589512 & 0.108737597294756 \tabularnewline
33 & 0.879544256480426 & 0.240911487039149 & 0.120455743519574 \tabularnewline
34 & 0.823555738359407 & 0.352888523281187 & 0.176444261640593 \tabularnewline
35 & 0.859162542221701 & 0.281674915556598 & 0.140837457778299 \tabularnewline
36 & 0.935598251834033 & 0.128803496331933 & 0.0644017481659666 \tabularnewline
37 & 0.931618047810787 & 0.136763904378425 & 0.0683819521892127 \tabularnewline
38 & 0.900264203862807 & 0.199471592274386 & 0.0997357961371932 \tabularnewline
39 & 0.837946741421896 & 0.324106517156207 & 0.162053258578104 \tabularnewline
40 & 0.779762898218268 & 0.440474203563465 & 0.220237101781732 \tabularnewline
41 & 0.716783958085626 & 0.566432083828748 & 0.283216041914374 \tabularnewline
42 & 0.592178447671983 & 0.815643104656034 & 0.407821552328017 \tabularnewline
43 & 0.428714320744957 & 0.857428641489914 & 0.571285679255043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&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]0.981959688441397[/C][C]0.0360806231172068[/C][C]0.0180403115586034[/C][/ROW]
[ROW][C]18[/C][C]0.96408574013091[/C][C]0.0718285197381804[/C][C]0.0359142598690902[/C][/ROW]
[ROW][C]19[/C][C]0.94313532732763[/C][C]0.113729345344740[/C][C]0.0568646726723701[/C][/ROW]
[ROW][C]20[/C][C]0.956699614607823[/C][C]0.0866007707843546[/C][C]0.0433003853921773[/C][/ROW]
[ROW][C]21[/C][C]0.972190128147901[/C][C]0.0556197437041977[/C][C]0.0278098718520988[/C][/ROW]
[ROW][C]22[/C][C]0.98350007737318[/C][C]0.0329998452536408[/C][C]0.0164999226268204[/C][/ROW]
[ROW][C]23[/C][C]0.990730737193708[/C][C]0.0185385256125843[/C][C]0.00926926280629217[/C][/ROW]
[ROW][C]24[/C][C]0.994444174985299[/C][C]0.0111116500294025[/C][C]0.00555582501470126[/C][/ROW]
[ROW][C]25[/C][C]0.988740856902454[/C][C]0.0225182861950914[/C][C]0.0112591430975457[/C][/ROW]
[ROW][C]26[/C][C]0.98035286735897[/C][C]0.0392942652820608[/C][C]0.0196471326410304[/C][/ROW]
[ROW][C]27[/C][C]0.973437665758802[/C][C]0.0531246684823953[/C][C]0.0265623342411976[/C][/ROW]
[ROW][C]28[/C][C]0.96625328503873[/C][C]0.0674934299225407[/C][C]0.0337467149612703[/C][/ROW]
[ROW][C]29[/C][C]0.951178246679055[/C][C]0.0976435066418905[/C][C]0.0488217533209452[/C][/ROW]
[ROW][C]30[/C][C]0.923761976887401[/C][C]0.152476046225198[/C][C]0.0762380231125988[/C][/ROW]
[ROW][C]31[/C][C]0.882970581188893[/C][C]0.234058837622213[/C][C]0.117029418811107[/C][/ROW]
[ROW][C]32[/C][C]0.891262402705244[/C][C]0.217475194589512[/C][C]0.108737597294756[/C][/ROW]
[ROW][C]33[/C][C]0.879544256480426[/C][C]0.240911487039149[/C][C]0.120455743519574[/C][/ROW]
[ROW][C]34[/C][C]0.823555738359407[/C][C]0.352888523281187[/C][C]0.176444261640593[/C][/ROW]
[ROW][C]35[/C][C]0.859162542221701[/C][C]0.281674915556598[/C][C]0.140837457778299[/C][/ROW]
[ROW][C]36[/C][C]0.935598251834033[/C][C]0.128803496331933[/C][C]0.0644017481659666[/C][/ROW]
[ROW][C]37[/C][C]0.931618047810787[/C][C]0.136763904378425[/C][C]0.0683819521892127[/C][/ROW]
[ROW][C]38[/C][C]0.900264203862807[/C][C]0.199471592274386[/C][C]0.0997357961371932[/C][/ROW]
[ROW][C]39[/C][C]0.837946741421896[/C][C]0.324106517156207[/C][C]0.162053258578104[/C][/ROW]
[ROW][C]40[/C][C]0.779762898218268[/C][C]0.440474203563465[/C][C]0.220237101781732[/C][/ROW]
[ROW][C]41[/C][C]0.716783958085626[/C][C]0.566432083828748[/C][C]0.283216041914374[/C][/ROW]
[ROW][C]42[/C][C]0.592178447671983[/C][C]0.815643104656034[/C][C]0.407821552328017[/C][/ROW]
[ROW][C]43[/C][C]0.428714320744957[/C][C]0.857428641489914[/C][C]0.571285679255043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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	0.981959688441397	0.0360806231172068	0.0180403115586034
18	0.96408574013091	0.0718285197381804	0.0359142598690902
19	0.94313532732763	0.113729345344740	0.0568646726723701
20	0.956699614607823	0.0866007707843546	0.0433003853921773
21	0.972190128147901	0.0556197437041977	0.0278098718520988
22	0.98350007737318	0.0329998452536408	0.0164999226268204
23	0.990730737193708	0.0185385256125843	0.00926926280629217
24	0.994444174985299	0.0111116500294025	0.00555582501470126
25	0.988740856902454	0.0225182861950914	0.0112591430975457
26	0.98035286735897	0.0392942652820608	0.0196471326410304
27	0.973437665758802	0.0531246684823953	0.0265623342411976
28	0.96625328503873	0.0674934299225407	0.0337467149612703
29	0.951178246679055	0.0976435066418905	0.0488217533209452
30	0.923761976887401	0.152476046225198	0.0762380231125988
31	0.882970581188893	0.234058837622213	0.117029418811107
32	0.891262402705244	0.217475194589512	0.108737597294756
33	0.879544256480426	0.240911487039149	0.120455743519574
34	0.823555738359407	0.352888523281187	0.176444261640593
35	0.859162542221701	0.281674915556598	0.140837457778299
36	0.935598251834033	0.128803496331933	0.0644017481659666
37	0.931618047810787	0.136763904378425	0.0683819521892127
38	0.900264203862807	0.199471592274386	0.0997357961371932
39	0.837946741421896	0.324106517156207	0.162053258578104
40	0.779762898218268	0.440474203563465	0.220237101781732
41	0.716783958085626	0.566432083828748	0.283216041914374
42	0.592178447671983	0.815643104656034	0.407821552328017
43	0.428714320744957	0.857428641489914	0.571285679255043

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	6	0.222222222222222	NOK
10% type I error level	12	0.444444444444444	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 & 6 & 0.222222222222222 & NOK \tabularnewline
10% type I error level & 12 & 0.444444444444444 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25527&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]6[/C][C]0.222222222222222[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.444444444444444[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25527&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25527&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	6	0.222222222222222	NOK
10% type I error level	12	0.444444444444444	NOK

Figure 1

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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