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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 20 Dec 2009 00:00:57 -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/2009/Dec/20/t1261292727l81wk1o93orxlvk.htm/, Retrieved Sat, 27 Apr 2024 13:02:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69789, Retrieved Sat, 27 Apr 2024 13:02:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

185

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [Seatbelt Law part 3] [2009-11-20 22:41:21] [4b87f7428fbf2a3c94095f0b8c4ae313]
-   PD        [Multiple Regression] [] [2009-12-20 07:00:57] [2b679e8ec54382eeb0ec0b6bb527570a] [Current]

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Dataseries X:

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Boxplots

101.68	0	102.11	102.71	101.09
101.7	0	101.68	102.11	102.71
101.53	0	101.7	101.68	102.11
101.76	0	101.53	101.7	101.68
101.15	0	101.76	101.53	101.7
100.92	0	101.15	101.76	101.53
100.73	0	100.92	101.15	101.76
100.55	0	100.73	100.92	101.15
102.15	0	100.55	100.73	100.92
100.79	0	102.15	100.55	100.73
99.93	0	100.79	102.15	100.55
100.03	0	99.93	100.79	102.15
100.25	0	100.03	99.93	100.79
99.6	0	100.25	100.03	99.93
100.16	0	99.6	100.25	100.03
100.49	0	100.16	99.6	100.25
99.72	0	100.49	100.16	99.6
100.14	0	99.72	100.49	100.16
98.48	0	100.14	99.72	100.49
100.38	0	98.48	100.14	99.72
101.45	0	100.38	98.48	100.14
98.42	0	101.45	100.38	98.48
98.6	0	98.42	101.45	100.38
100.06	0	98.6	98.42	101.45
98.62	0	100.06	98.6	98.42
100.84	0	98.62	100.06	98.6
100.02	0	100.84	98.62	100.06
97.95	0	100.02	100.84	98.62
98.32	0	97.95	100.02	100.84
98.27	0	98.32	97.95	100.02
97.22	0	98.27	98.32	97.95
99.28	0	97.22	98.27	98.32
100.38	0	99.28	97.22	98.27
99.02	0	100.38	99.28	97.22
100.32	0	99.02	100.38	99.28
99.81	0	100.32	99.02	100.38
100.6	0	99.81	100.32	99.02
101.19	0	100.6	99.81	100.32
100.47	0	101.19	100.6	99.81
101.77	0	100.47	101.19	100.6
102.32	0	101.77	100.47	101.19
102.39	0	102.32	101.77	100.47
101.16	0	102.39	102.32	101.77
100.63	0	101.16	102.39	102.32
101.48	0	100.63	101.16	102.39
101.44	1	101.48	100.63	101.16
100.09	1	101.44	101.48	100.63
100.7	1	100.09	101.44	101.48
100.78	1	100.7	100.09	101.44
99.81	1	100.78	100.7	100.09
98.45	1	99.81	100.78	100.7
98.49	1	98.45	99.81	100.78
97.48	1	98.49	98.45	99.81
97.91	1	97.48	98.49	98.45
96.94	1	97.91	97.48	98.49
98.53	1	96.94	97.91	97.48
96.82	1	98.53	96.94	97.91
95.76	1	96.82	98.53	96.94

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9.57163647419904 -0.895777001450823X[t] + 0.510443451262783Y1[t] + 0.069926144750079Y2[t] + 0.32209278622004Y3[t] + 0.184045519935524M1[t] + 0.42493619565798M2[t] -0.266547955685569M3[t] -0.0195626395711653M4[t] -0.347632735869259M5[t] + 0.085924062365643M6[t] -0.976484902148307M7[t] + 0.589330506720091M8[t] + 0.698736392866317M9[t] -0.536921805692414M10[t] -0.228775212256733M11[t] + 0.00858164404031952t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  9.57163647419904 -0.895777001450823X[t] +  0.510443451262783Y1[t] +  0.069926144750079Y2[t] +  0.32209278622004Y3[t] +  0.184045519935524M1[t] +  0.42493619565798M2[t] -0.266547955685569M3[t] -0.0195626395711653M4[t] -0.347632735869259M5[t] +  0.085924062365643M6[t] -0.976484902148307M7[t] +  0.589330506720091M8[t] +  0.698736392866317M9[t] -0.536921805692414M10[t] -0.228775212256733M11[t] +  0.00858164404031952t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  9.57163647419904 -0.895777001450823X[t] +  0.510443451262783Y1[t] +  0.069926144750079Y2[t] +  0.32209278622004Y3[t] +  0.184045519935524M1[t] +  0.42493619565798M2[t] -0.266547955685569M3[t] -0.0195626395711653M4[t] -0.347632735869259M5[t] +  0.085924062365643M6[t] -0.976484902148307M7[t] +  0.589330506720091M8[t] +  0.698736392866317M9[t] -0.536921805692414M10[t] -0.228775212256733M11[t] +  0.00858164404031952t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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
Y[t] = + 9.57163647419904 -0.895777001450823X[t] + 0.510443451262783Y1[t] + 0.069926144750079Y2[t] + 0.32209278622004Y3[t] + 0.184045519935524M1[t] + 0.42493619565798M2[t] -0.266547955685569M3[t] -0.0195626395711653M4[t] -0.347632735869259M5[t] + 0.085924062365643M6[t] -0.976484902148307M7[t] + 0.589330506720091M8[t] + 0.698736392866317M9[t] -0.536921805692414M10[t] -0.228775212256733M11[t] + 0.00858164404031952t + 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)	9.57163647419904	11.290167	0.8478	0.40148	0.20074
X	-0.895777001450823	0.439234	-2.0394	0.04789	0.023945
Y1	0.510443451262783	0.149766	3.4083	0.001478	0.000739
Y2	0.069926144750079	0.171956	0.4067	0.686379	0.343189
Y3	0.32209278622004	0.160887	2.002	0.051932	0.025966
M1	0.184045519935524	0.669672	0.2748	0.784827	0.392414
M2	0.42493619565798	0.659722	0.6441	0.523089	0.261544
M3	-0.266547955685569	0.647923	-0.4114	0.68293	0.341465
M4	-0.0195626395711653	0.653785	-0.0299	0.976274	0.488137
M5	-0.347632735869259	0.624573	-0.5566	0.580831	0.290416
M6	0.085924062365643	0.642128	0.1338	0.894206	0.447103
M7	-0.976484902148307	0.637742	-1.5312	0.13341	0.066705
M8	0.589330506720091	0.652546	0.9031	0.371736	0.185868
M9	0.698736392866317	0.642181	1.0881	0.28292	0.14146
M10	-0.536921805692414	0.752804	-0.7132	0.479744	0.239872
M11	-0.228775212256733	0.74094	-0.3088	0.759065	0.379532
t	0.00858164404031952	0.011222	0.7647	0.448802	0.224401

\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) & 9.57163647419904 & 11.290167 & 0.8478 & 0.40148 & 0.20074 \tabularnewline
X & -0.895777001450823 & 0.439234 & -2.0394 & 0.04789 & 0.023945 \tabularnewline
Y1 & 0.510443451262783 & 0.149766 & 3.4083 & 0.001478 & 0.000739 \tabularnewline
Y2 & 0.069926144750079 & 0.171956 & 0.4067 & 0.686379 & 0.343189 \tabularnewline
Y3 & 0.32209278622004 & 0.160887 & 2.002 & 0.051932 & 0.025966 \tabularnewline
M1 & 0.184045519935524 & 0.669672 & 0.2748 & 0.784827 & 0.392414 \tabularnewline
M2 & 0.42493619565798 & 0.659722 & 0.6441 & 0.523089 & 0.261544 \tabularnewline
M3 & -0.266547955685569 & 0.647923 & -0.4114 & 0.68293 & 0.341465 \tabularnewline
M4 & -0.0195626395711653 & 0.653785 & -0.0299 & 0.976274 & 0.488137 \tabularnewline
M5 & -0.347632735869259 & 0.624573 & -0.5566 & 0.580831 & 0.290416 \tabularnewline
M6 & 0.085924062365643 & 0.642128 & 0.1338 & 0.894206 & 0.447103 \tabularnewline
M7 & -0.976484902148307 & 0.637742 & -1.5312 & 0.13341 & 0.066705 \tabularnewline
M8 & 0.589330506720091 & 0.652546 & 0.9031 & 0.371736 & 0.185868 \tabularnewline
M9 & 0.698736392866317 & 0.642181 & 1.0881 & 0.28292 & 0.14146 \tabularnewline
M10 & -0.536921805692414 & 0.752804 & -0.7132 & 0.479744 & 0.239872 \tabularnewline
M11 & -0.228775212256733 & 0.74094 & -0.3088 & 0.759065 & 0.379532 \tabularnewline
t & 0.00858164404031952 & 0.011222 & 0.7647 & 0.448802 & 0.224401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&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]9.57163647419904[/C][C]11.290167[/C][C]0.8478[/C][C]0.40148[/C][C]0.20074[/C][/ROW]
[ROW][C]X[/C][C]-0.895777001450823[/C][C]0.439234[/C][C]-2.0394[/C][C]0.04789[/C][C]0.023945[/C][/ROW]
[ROW][C]Y1[/C][C]0.510443451262783[/C][C]0.149766[/C][C]3.4083[/C][C]0.001478[/C][C]0.000739[/C][/ROW]
[ROW][C]Y2[/C][C]0.069926144750079[/C][C]0.171956[/C][C]0.4067[/C][C]0.686379[/C][C]0.343189[/C][/ROW]
[ROW][C]Y3[/C][C]0.32209278622004[/C][C]0.160887[/C][C]2.002[/C][C]0.051932[/C][C]0.025966[/C][/ROW]
[ROW][C]M1[/C][C]0.184045519935524[/C][C]0.669672[/C][C]0.2748[/C][C]0.784827[/C][C]0.392414[/C][/ROW]
[ROW][C]M2[/C][C]0.42493619565798[/C][C]0.659722[/C][C]0.6441[/C][C]0.523089[/C][C]0.261544[/C][/ROW]
[ROW][C]M3[/C][C]-0.266547955685569[/C][C]0.647923[/C][C]-0.4114[/C][C]0.68293[/C][C]0.341465[/C][/ROW]
[ROW][C]M4[/C][C]-0.0195626395711653[/C][C]0.653785[/C][C]-0.0299[/C][C]0.976274[/C][C]0.488137[/C][/ROW]
[ROW][C]M5[/C][C]-0.347632735869259[/C][C]0.624573[/C][C]-0.5566[/C][C]0.580831[/C][C]0.290416[/C][/ROW]
[ROW][C]M6[/C][C]0.085924062365643[/C][C]0.642128[/C][C]0.1338[/C][C]0.894206[/C][C]0.447103[/C][/ROW]
[ROW][C]M7[/C][C]-0.976484902148307[/C][C]0.637742[/C][C]-1.5312[/C][C]0.13341[/C][C]0.066705[/C][/ROW]
[ROW][C]M8[/C][C]0.589330506720091[/C][C]0.652546[/C][C]0.9031[/C][C]0.371736[/C][C]0.185868[/C][/ROW]
[ROW][C]M9[/C][C]0.698736392866317[/C][C]0.642181[/C][C]1.0881[/C][C]0.28292[/C][C]0.14146[/C][/ROW]
[ROW][C]M10[/C][C]-0.536921805692414[/C][C]0.752804[/C][C]-0.7132[/C][C]0.479744[/C][C]0.239872[/C][/ROW]
[ROW][C]M11[/C][C]-0.228775212256733[/C][C]0.74094[/C][C]-0.3088[/C][C]0.759065[/C][C]0.379532[/C][/ROW]
[ROW][C]t[/C][C]0.00858164404031952[/C][C]0.011222[/C][C]0.7647[/C][C]0.448802[/C][C]0.224401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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)	9.57163647419904	11.290167	0.8478	0.40148	0.20074
X	-0.895777001450823	0.439234	-2.0394	0.04789	0.023945
Y1	0.510443451262783	0.149766	3.4083	0.001478	0.000739
Y2	0.069926144750079	0.171956	0.4067	0.686379	0.343189
Y3	0.32209278622004	0.160887	2.002	0.051932	0.025966
M1	0.184045519935524	0.669672	0.2748	0.784827	0.392414
M2	0.42493619565798	0.659722	0.6441	0.523089	0.261544
M3	-0.266547955685569	0.647923	-0.4114	0.68293	0.341465
M4	-0.0195626395711653	0.653785	-0.0299	0.976274	0.488137
M5	-0.347632735869259	0.624573	-0.5566	0.580831	0.290416
M6	0.085924062365643	0.642128	0.1338	0.894206	0.447103
M7	-0.976484902148307	0.637742	-1.5312	0.13341	0.066705
M8	0.589330506720091	0.652546	0.9031	0.371736	0.185868
M9	0.698736392866317	0.642181	1.0881	0.28292	0.14146
M10	-0.536921805692414	0.752804	-0.7132	0.479744	0.239872
M11	-0.228775212256733	0.74094	-0.3088	0.759065	0.379532
t	0.00858164404031952	0.011222	0.7647	0.448802	0.224401

Multiple Linear Regression - Regression Statistics
Multiple R	0.861077793082703
R-squared	0.741454965740179
Adjusted R-squared	0.640559342614395
F-TEST (value)	7.3487327078185
F-TEST (DF numerator)	16
F-TEST (DF denominator)	41
p-value	1.28898840601188e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.902740058097228
Sum Squared Residuals	33.4125241122289

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.861077793082703 \tabularnewline
R-squared & 0.741454965740179 \tabularnewline
Adjusted R-squared & 0.640559342614395 \tabularnewline
F-TEST (value) & 7.3487327078185 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 1.28898840601188e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.902740058097228 \tabularnewline
Sum Squared Residuals & 33.4125241122289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.861077793082703[/C][/ROW]
[ROW][C]R-squared[/C][C]0.741454965740179[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.640559342614395[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]7.3487327078185[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/C][/ROW]
[ROW][C]p-value[/C][C]1.28898840601188e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.902740058097228[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]33.4125241122289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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	0.861077793082703
R-squared	0.741454965740179
Adjusted R-squared	0.640559342614395
F-TEST (value)	7.3487327078185
F-TEST (DF numerator)	16
F-TEST (DF denominator)	41
p-value	1.28898840601188e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.902740058097228
Sum Squared Residuals	33.4125241122289

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	101.68	101.628118532882	0.0518814671180148
2	101.7	102.137934795428	-0.437934795428357
3	101.53	101.241917243176	0.288082756824178
4	101.76	101.273607441436	0.486392558563743
5	101.15	101.066075394086	0.0839246059141901
6	100.92	101.158170570726	-0.23817057072585
7	100.73	100.018367648995	0.711632351005163
8	100.55	101.283220833277	-0.733220833276891
9	102.15	101.221961233903	0.928038766097003
10	100.79	100.737809865968	0.0521901340317782
11	99.93	100.414240139807	-0.484240139807354
12	100.03	100.632864529110	-0.602864529110379
13	100.25	100.378353364468	-0.128353364468177
14	99.6	100.470116061835	-0.870116061834543
15	100.16	99.5030183416775	0.656981658322482
16	100.49	100.069842053420	0.420157946579741
17	99.72	99.7485982700962	-0.0285982700962151
18	100.14	100.001142842950	0.138857157050156
19	98.48	99.2141492600016	-0.734149260001632
20	100.38	99.7225677192197	0.657432280780257
21	101.45	100.829599376733	0.62040062326715
22	98.42	99.7468829649655	-1.32688296496551
23	98.6	99.203764813816	-0.60376481381594
24	100.06	99.665764554003	0.394235445997012
25	98.62	99.6402847206308	-1.02028472063079
26	100.84	99.31478734343	1.52521265657012
27	100.02	100.134631117371	-0.114631117371182
28	97.95	99.6630568766787	-1.71305687667873
29	98.32	98.9446570270204	-0.624657027020433
30	98.27	99.1667963419298	-0.896796341929778
31	97.22	97.446587454975	-0.226587454975053
32	99.28	98.6006969077218	0.679303092278244
33	100.38	99.680670856211	0.699329143788943
34	99.02	98.8209325307358	0.199067469264175
35	100.32	99.1838875733328	1.13611242666718
36	99.81	100.344023424253	-0.53402342425341
37	100.6	99.929182227001	0.670817772998906
38	101.19	100.964963161525	0.225036838475027
39	100.47	100.474196623847	-0.00419662384713008
40	101.77	100.657954025609	1.11204597439097
41	102.32	101.141729979643	1.17827002035736
42	102.39	101.723609502209	0.66639049779094
43	101.16	101.162693225022	-0.00269322502242635
44	100.63	102.291290695431	-1.66129069543145
45	101.48	102.075280533442	-0.595280533441516
46	101.44	99.9530689272775	1.48693107272254
47	100.09	100.138107473044	-0.0481074730438910
48	100.7	99.9573474926332	0.742652507366776
49	100.78	100.354061155018	0.425938844982044
50	99.81	100.252198637782	-0.442198637782247
51	98.45	99.2762366739284	-0.82623667392835
52	98.49	98.7955396028557	-0.305539602855722
53	97.48	98.088939329155	-0.6089393291549
54	97.91	97.5802807421855	0.32971925781453
55	96.94	96.688202411006	0.251797588993949
56	98.53	97.4722238443502	1.05777615564984
57	96.82	98.4724879997116	-1.65248799971158
58	95.76	96.171305711053	-0.411305711052982

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.68 & 101.628118532882 & 0.0518814671180148 \tabularnewline
2 & 101.7 & 102.137934795428 & -0.437934795428357 \tabularnewline
3 & 101.53 & 101.241917243176 & 0.288082756824178 \tabularnewline
4 & 101.76 & 101.273607441436 & 0.486392558563743 \tabularnewline
5 & 101.15 & 101.066075394086 & 0.0839246059141901 \tabularnewline
6 & 100.92 & 101.158170570726 & -0.23817057072585 \tabularnewline
7 & 100.73 & 100.018367648995 & 0.711632351005163 \tabularnewline
8 & 100.55 & 101.283220833277 & -0.733220833276891 \tabularnewline
9 & 102.15 & 101.221961233903 & 0.928038766097003 \tabularnewline
10 & 100.79 & 100.737809865968 & 0.0521901340317782 \tabularnewline
11 & 99.93 & 100.414240139807 & -0.484240139807354 \tabularnewline
12 & 100.03 & 100.632864529110 & -0.602864529110379 \tabularnewline
13 & 100.25 & 100.378353364468 & -0.128353364468177 \tabularnewline
14 & 99.6 & 100.470116061835 & -0.870116061834543 \tabularnewline
15 & 100.16 & 99.5030183416775 & 0.656981658322482 \tabularnewline
16 & 100.49 & 100.069842053420 & 0.420157946579741 \tabularnewline
17 & 99.72 & 99.7485982700962 & -0.0285982700962151 \tabularnewline
18 & 100.14 & 100.001142842950 & 0.138857157050156 \tabularnewline
19 & 98.48 & 99.2141492600016 & -0.734149260001632 \tabularnewline
20 & 100.38 & 99.7225677192197 & 0.657432280780257 \tabularnewline
21 & 101.45 & 100.829599376733 & 0.62040062326715 \tabularnewline
22 & 98.42 & 99.7468829649655 & -1.32688296496551 \tabularnewline
23 & 98.6 & 99.203764813816 & -0.60376481381594 \tabularnewline
24 & 100.06 & 99.665764554003 & 0.394235445997012 \tabularnewline
25 & 98.62 & 99.6402847206308 & -1.02028472063079 \tabularnewline
26 & 100.84 & 99.31478734343 & 1.52521265657012 \tabularnewline
27 & 100.02 & 100.134631117371 & -0.114631117371182 \tabularnewline
28 & 97.95 & 99.6630568766787 & -1.71305687667873 \tabularnewline
29 & 98.32 & 98.9446570270204 & -0.624657027020433 \tabularnewline
30 & 98.27 & 99.1667963419298 & -0.896796341929778 \tabularnewline
31 & 97.22 & 97.446587454975 & -0.226587454975053 \tabularnewline
32 & 99.28 & 98.6006969077218 & 0.679303092278244 \tabularnewline
33 & 100.38 & 99.680670856211 & 0.699329143788943 \tabularnewline
34 & 99.02 & 98.8209325307358 & 0.199067469264175 \tabularnewline
35 & 100.32 & 99.1838875733328 & 1.13611242666718 \tabularnewline
36 & 99.81 & 100.344023424253 & -0.53402342425341 \tabularnewline
37 & 100.6 & 99.929182227001 & 0.670817772998906 \tabularnewline
38 & 101.19 & 100.964963161525 & 0.225036838475027 \tabularnewline
39 & 100.47 & 100.474196623847 & -0.00419662384713008 \tabularnewline
40 & 101.77 & 100.657954025609 & 1.11204597439097 \tabularnewline
41 & 102.32 & 101.141729979643 & 1.17827002035736 \tabularnewline
42 & 102.39 & 101.723609502209 & 0.66639049779094 \tabularnewline
43 & 101.16 & 101.162693225022 & -0.00269322502242635 \tabularnewline
44 & 100.63 & 102.291290695431 & -1.66129069543145 \tabularnewline
45 & 101.48 & 102.075280533442 & -0.595280533441516 \tabularnewline
46 & 101.44 & 99.9530689272775 & 1.48693107272254 \tabularnewline
47 & 100.09 & 100.138107473044 & -0.0481074730438910 \tabularnewline
48 & 100.7 & 99.9573474926332 & 0.742652507366776 \tabularnewline
49 & 100.78 & 100.354061155018 & 0.425938844982044 \tabularnewline
50 & 99.81 & 100.252198637782 & -0.442198637782247 \tabularnewline
51 & 98.45 & 99.2762366739284 & -0.82623667392835 \tabularnewline
52 & 98.49 & 98.7955396028557 & -0.305539602855722 \tabularnewline
53 & 97.48 & 98.088939329155 & -0.6089393291549 \tabularnewline
54 & 97.91 & 97.5802807421855 & 0.32971925781453 \tabularnewline
55 & 96.94 & 96.688202411006 & 0.251797588993949 \tabularnewline
56 & 98.53 & 97.4722238443502 & 1.05777615564984 \tabularnewline
57 & 96.82 & 98.4724879997116 & -1.65248799971158 \tabularnewline
58 & 95.76 & 96.171305711053 & -0.411305711052982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&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]101.68[/C][C]101.628118532882[/C][C]0.0518814671180148[/C][/ROW]
[ROW][C]2[/C][C]101.7[/C][C]102.137934795428[/C][C]-0.437934795428357[/C][/ROW]
[ROW][C]3[/C][C]101.53[/C][C]101.241917243176[/C][C]0.288082756824178[/C][/ROW]
[ROW][C]4[/C][C]101.76[/C][C]101.273607441436[/C][C]0.486392558563743[/C][/ROW]
[ROW][C]5[/C][C]101.15[/C][C]101.066075394086[/C][C]0.0839246059141901[/C][/ROW]
[ROW][C]6[/C][C]100.92[/C][C]101.158170570726[/C][C]-0.23817057072585[/C][/ROW]
[ROW][C]7[/C][C]100.73[/C][C]100.018367648995[/C][C]0.711632351005163[/C][/ROW]
[ROW][C]8[/C][C]100.55[/C][C]101.283220833277[/C][C]-0.733220833276891[/C][/ROW]
[ROW][C]9[/C][C]102.15[/C][C]101.221961233903[/C][C]0.928038766097003[/C][/ROW]
[ROW][C]10[/C][C]100.79[/C][C]100.737809865968[/C][C]0.0521901340317782[/C][/ROW]
[ROW][C]11[/C][C]99.93[/C][C]100.414240139807[/C][C]-0.484240139807354[/C][/ROW]
[ROW][C]12[/C][C]100.03[/C][C]100.632864529110[/C][C]-0.602864529110379[/C][/ROW]
[ROW][C]13[/C][C]100.25[/C][C]100.378353364468[/C][C]-0.128353364468177[/C][/ROW]
[ROW][C]14[/C][C]99.6[/C][C]100.470116061835[/C][C]-0.870116061834543[/C][/ROW]
[ROW][C]15[/C][C]100.16[/C][C]99.5030183416775[/C][C]0.656981658322482[/C][/ROW]
[ROW][C]16[/C][C]100.49[/C][C]100.069842053420[/C][C]0.420157946579741[/C][/ROW]
[ROW][C]17[/C][C]99.72[/C][C]99.7485982700962[/C][C]-0.0285982700962151[/C][/ROW]
[ROW][C]18[/C][C]100.14[/C][C]100.001142842950[/C][C]0.138857157050156[/C][/ROW]
[ROW][C]19[/C][C]98.48[/C][C]99.2141492600016[/C][C]-0.734149260001632[/C][/ROW]
[ROW][C]20[/C][C]100.38[/C][C]99.7225677192197[/C][C]0.657432280780257[/C][/ROW]
[ROW][C]21[/C][C]101.45[/C][C]100.829599376733[/C][C]0.62040062326715[/C][/ROW]
[ROW][C]22[/C][C]98.42[/C][C]99.7468829649655[/C][C]-1.32688296496551[/C][/ROW]
[ROW][C]23[/C][C]98.6[/C][C]99.203764813816[/C][C]-0.60376481381594[/C][/ROW]
[ROW][C]24[/C][C]100.06[/C][C]99.665764554003[/C][C]0.394235445997012[/C][/ROW]
[ROW][C]25[/C][C]98.62[/C][C]99.6402847206308[/C][C]-1.02028472063079[/C][/ROW]
[ROW][C]26[/C][C]100.84[/C][C]99.31478734343[/C][C]1.52521265657012[/C][/ROW]
[ROW][C]27[/C][C]100.02[/C][C]100.134631117371[/C][C]-0.114631117371182[/C][/ROW]
[ROW][C]28[/C][C]97.95[/C][C]99.6630568766787[/C][C]-1.71305687667873[/C][/ROW]
[ROW][C]29[/C][C]98.32[/C][C]98.9446570270204[/C][C]-0.624657027020433[/C][/ROW]
[ROW][C]30[/C][C]98.27[/C][C]99.1667963419298[/C][C]-0.896796341929778[/C][/ROW]
[ROW][C]31[/C][C]97.22[/C][C]97.446587454975[/C][C]-0.226587454975053[/C][/ROW]
[ROW][C]32[/C][C]99.28[/C][C]98.6006969077218[/C][C]0.679303092278244[/C][/ROW]
[ROW][C]33[/C][C]100.38[/C][C]99.680670856211[/C][C]0.699329143788943[/C][/ROW]
[ROW][C]34[/C][C]99.02[/C][C]98.8209325307358[/C][C]0.199067469264175[/C][/ROW]
[ROW][C]35[/C][C]100.32[/C][C]99.1838875733328[/C][C]1.13611242666718[/C][/ROW]
[ROW][C]36[/C][C]99.81[/C][C]100.344023424253[/C][C]-0.53402342425341[/C][/ROW]
[ROW][C]37[/C][C]100.6[/C][C]99.929182227001[/C][C]0.670817772998906[/C][/ROW]
[ROW][C]38[/C][C]101.19[/C][C]100.964963161525[/C][C]0.225036838475027[/C][/ROW]
[ROW][C]39[/C][C]100.47[/C][C]100.474196623847[/C][C]-0.00419662384713008[/C][/ROW]
[ROW][C]40[/C][C]101.77[/C][C]100.657954025609[/C][C]1.11204597439097[/C][/ROW]
[ROW][C]41[/C][C]102.32[/C][C]101.141729979643[/C][C]1.17827002035736[/C][/ROW]
[ROW][C]42[/C][C]102.39[/C][C]101.723609502209[/C][C]0.66639049779094[/C][/ROW]
[ROW][C]43[/C][C]101.16[/C][C]101.162693225022[/C][C]-0.00269322502242635[/C][/ROW]
[ROW][C]44[/C][C]100.63[/C][C]102.291290695431[/C][C]-1.66129069543145[/C][/ROW]
[ROW][C]45[/C][C]101.48[/C][C]102.075280533442[/C][C]-0.595280533441516[/C][/ROW]
[ROW][C]46[/C][C]101.44[/C][C]99.9530689272775[/C][C]1.48693107272254[/C][/ROW]
[ROW][C]47[/C][C]100.09[/C][C]100.138107473044[/C][C]-0.0481074730438910[/C][/ROW]
[ROW][C]48[/C][C]100.7[/C][C]99.9573474926332[/C][C]0.742652507366776[/C][/ROW]
[ROW][C]49[/C][C]100.78[/C][C]100.354061155018[/C][C]0.425938844982044[/C][/ROW]
[ROW][C]50[/C][C]99.81[/C][C]100.252198637782[/C][C]-0.442198637782247[/C][/ROW]
[ROW][C]51[/C][C]98.45[/C][C]99.2762366739284[/C][C]-0.82623667392835[/C][/ROW]
[ROW][C]52[/C][C]98.49[/C][C]98.7955396028557[/C][C]-0.305539602855722[/C][/ROW]
[ROW][C]53[/C][C]97.48[/C][C]98.088939329155[/C][C]-0.6089393291549[/C][/ROW]
[ROW][C]54[/C][C]97.91[/C][C]97.5802807421855[/C][C]0.32971925781453[/C][/ROW]
[ROW][C]55[/C][C]96.94[/C][C]96.688202411006[/C][C]0.251797588993949[/C][/ROW]
[ROW][C]56[/C][C]98.53[/C][C]97.4722238443502[/C][C]1.05777615564984[/C][/ROW]
[ROW][C]57[/C][C]96.82[/C][C]98.4724879997116[/C][C]-1.65248799971158[/C][/ROW]
[ROW][C]58[/C][C]95.76[/C][C]96.171305711053[/C][C]-0.411305711052982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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	101.68	101.628118532882	0.0518814671180148
2	101.7	102.137934795428	-0.437934795428357
3	101.53	101.241917243176	0.288082756824178
4	101.76	101.273607441436	0.486392558563743
5	101.15	101.066075394086	0.0839246059141901
6	100.92	101.158170570726	-0.23817057072585
7	100.73	100.018367648995	0.711632351005163
8	100.55	101.283220833277	-0.733220833276891
9	102.15	101.221961233903	0.928038766097003
10	100.79	100.737809865968	0.0521901340317782
11	99.93	100.414240139807	-0.484240139807354
12	100.03	100.632864529110	-0.602864529110379
13	100.25	100.378353364468	-0.128353364468177
14	99.6	100.470116061835	-0.870116061834543
15	100.16	99.5030183416775	0.656981658322482
16	100.49	100.069842053420	0.420157946579741
17	99.72	99.7485982700962	-0.0285982700962151
18	100.14	100.001142842950	0.138857157050156
19	98.48	99.2141492600016	-0.734149260001632
20	100.38	99.7225677192197	0.657432280780257
21	101.45	100.829599376733	0.62040062326715
22	98.42	99.7468829649655	-1.32688296496551
23	98.6	99.203764813816	-0.60376481381594
24	100.06	99.665764554003	0.394235445997012
25	98.62	99.6402847206308	-1.02028472063079
26	100.84	99.31478734343	1.52521265657012
27	100.02	100.134631117371	-0.114631117371182
28	97.95	99.6630568766787	-1.71305687667873
29	98.32	98.9446570270204	-0.624657027020433
30	98.27	99.1667963419298	-0.896796341929778
31	97.22	97.446587454975	-0.226587454975053
32	99.28	98.6006969077218	0.679303092278244
33	100.38	99.680670856211	0.699329143788943
34	99.02	98.8209325307358	0.199067469264175
35	100.32	99.1838875733328	1.13611242666718
36	99.81	100.344023424253	-0.53402342425341
37	100.6	99.929182227001	0.670817772998906
38	101.19	100.964963161525	0.225036838475027
39	100.47	100.474196623847	-0.00419662384713008
40	101.77	100.657954025609	1.11204597439097
41	102.32	101.141729979643	1.17827002035736
42	102.39	101.723609502209	0.66639049779094
43	101.16	101.162693225022	-0.00269322502242635
44	100.63	102.291290695431	-1.66129069543145
45	101.48	102.075280533442	-0.595280533441516
46	101.44	99.9530689272775	1.48693107272254
47	100.09	100.138107473044	-0.0481074730438910
48	100.7	99.9573474926332	0.742652507366776
49	100.78	100.354061155018	0.425938844982044
50	99.81	100.252198637782	-0.442198637782247
51	98.45	99.2762366739284	-0.82623667392835
52	98.49	98.7955396028557	-0.305539602855722
53	97.48	98.088939329155	-0.6089393291549
54	97.91	97.5802807421855	0.32971925781453
55	96.94	96.688202411006	0.251797588993949
56	98.53	97.4722238443502	1.05777615564984
57	96.82	98.4724879997116	-1.65248799971158
58	95.76	96.171305711053	-0.411305711052982

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
20	0.0497432174902092	0.0994864349804184	0.95025678250979
21	0.0769172776722236	0.153834555344447	0.923082722327776
22	0.0693973546435627	0.138794709287125	0.930602645356437
23	0.0459058333298366	0.0918116666596731	0.954094166670163
24	0.0401385862178826	0.0802771724357652	0.959861413782117
25	0.0231356869383544	0.0462713738767088	0.976864313061646
26	0.124936436979262	0.249872873958525	0.875063563020738
27	0.083613121285817	0.167226242571634	0.916386878714183
28	0.195009651661356	0.390019303322713	0.804990348338644
29	0.168209176478803	0.336418352957607	0.831790823521196
30	0.178003992086628	0.356007984173256	0.821996007913372
31	0.173738660072794	0.347477320145588	0.826261339927206
32	0.127453561183697	0.254907122367394	0.872546438816303
33	0.0778284502389225	0.155656900477845	0.922171549761078
34	0.158216087292043	0.316432174584085	0.841783912707957
35	0.226008742511805	0.452017485023609	0.773991257488195
36	0.24010492036141	0.48020984072282	0.75989507963859
37	0.372432775181059	0.744865550362118	0.627567224818941
38	0.228060311071386	0.456120622142773	0.771939688928614

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.0497432174902092 & 0.0994864349804184 & 0.95025678250979 \tabularnewline
21 & 0.0769172776722236 & 0.153834555344447 & 0.923082722327776 \tabularnewline
22 & 0.0693973546435627 & 0.138794709287125 & 0.930602645356437 \tabularnewline
23 & 0.0459058333298366 & 0.0918116666596731 & 0.954094166670163 \tabularnewline
24 & 0.0401385862178826 & 0.0802771724357652 & 0.959861413782117 \tabularnewline
25 & 0.0231356869383544 & 0.0462713738767088 & 0.976864313061646 \tabularnewline
26 & 0.124936436979262 & 0.249872873958525 & 0.875063563020738 \tabularnewline
27 & 0.083613121285817 & 0.167226242571634 & 0.916386878714183 \tabularnewline
28 & 0.195009651661356 & 0.390019303322713 & 0.804990348338644 \tabularnewline
29 & 0.168209176478803 & 0.336418352957607 & 0.831790823521196 \tabularnewline
30 & 0.178003992086628 & 0.356007984173256 & 0.821996007913372 \tabularnewline
31 & 0.173738660072794 & 0.347477320145588 & 0.826261339927206 \tabularnewline
32 & 0.127453561183697 & 0.254907122367394 & 0.872546438816303 \tabularnewline
33 & 0.0778284502389225 & 0.155656900477845 & 0.922171549761078 \tabularnewline
34 & 0.158216087292043 & 0.316432174584085 & 0.841783912707957 \tabularnewline
35 & 0.226008742511805 & 0.452017485023609 & 0.773991257488195 \tabularnewline
36 & 0.24010492036141 & 0.48020984072282 & 0.75989507963859 \tabularnewline
37 & 0.372432775181059 & 0.744865550362118 & 0.627567224818941 \tabularnewline
38 & 0.228060311071386 & 0.456120622142773 & 0.771939688928614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&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]20[/C][C]0.0497432174902092[/C][C]0.0994864349804184[/C][C]0.95025678250979[/C][/ROW]
[ROW][C]21[/C][C]0.0769172776722236[/C][C]0.153834555344447[/C][C]0.923082722327776[/C][/ROW]
[ROW][C]22[/C][C]0.0693973546435627[/C][C]0.138794709287125[/C][C]0.930602645356437[/C][/ROW]
[ROW][C]23[/C][C]0.0459058333298366[/C][C]0.0918116666596731[/C][C]0.954094166670163[/C][/ROW]
[ROW][C]24[/C][C]0.0401385862178826[/C][C]0.0802771724357652[/C][C]0.959861413782117[/C][/ROW]
[ROW][C]25[/C][C]0.0231356869383544[/C][C]0.0462713738767088[/C][C]0.976864313061646[/C][/ROW]
[ROW][C]26[/C][C]0.124936436979262[/C][C]0.249872873958525[/C][C]0.875063563020738[/C][/ROW]
[ROW][C]27[/C][C]0.083613121285817[/C][C]0.167226242571634[/C][C]0.916386878714183[/C][/ROW]
[ROW][C]28[/C][C]0.195009651661356[/C][C]0.390019303322713[/C][C]0.804990348338644[/C][/ROW]
[ROW][C]29[/C][C]0.168209176478803[/C][C]0.336418352957607[/C][C]0.831790823521196[/C][/ROW]
[ROW][C]30[/C][C]0.178003992086628[/C][C]0.356007984173256[/C][C]0.821996007913372[/C][/ROW]
[ROW][C]31[/C][C]0.173738660072794[/C][C]0.347477320145588[/C][C]0.826261339927206[/C][/ROW]
[ROW][C]32[/C][C]0.127453561183697[/C][C]0.254907122367394[/C][C]0.872546438816303[/C][/ROW]
[ROW][C]33[/C][C]0.0778284502389225[/C][C]0.155656900477845[/C][C]0.922171549761078[/C][/ROW]
[ROW][C]34[/C][C]0.158216087292043[/C][C]0.316432174584085[/C][C]0.841783912707957[/C][/ROW]
[ROW][C]35[/C][C]0.226008742511805[/C][C]0.452017485023609[/C][C]0.773991257488195[/C][/ROW]
[ROW][C]36[/C][C]0.24010492036141[/C][C]0.48020984072282[/C][C]0.75989507963859[/C][/ROW]
[ROW][C]37[/C][C]0.372432775181059[/C][C]0.744865550362118[/C][C]0.627567224818941[/C][/ROW]
[ROW][C]38[/C][C]0.228060311071386[/C][C]0.456120622142773[/C][C]0.771939688928614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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
20	0.0497432174902092	0.0994864349804184	0.95025678250979
21	0.0769172776722236	0.153834555344447	0.923082722327776
22	0.0693973546435627	0.138794709287125	0.930602645356437
23	0.0459058333298366	0.0918116666596731	0.954094166670163
24	0.0401385862178826	0.0802771724357652	0.959861413782117
25	0.0231356869383544	0.0462713738767088	0.976864313061646
26	0.124936436979262	0.249872873958525	0.875063563020738
27	0.083613121285817	0.167226242571634	0.916386878714183
28	0.195009651661356	0.390019303322713	0.804990348338644
29	0.168209176478803	0.336418352957607	0.831790823521196
30	0.178003992086628	0.356007984173256	0.821996007913372
31	0.173738660072794	0.347477320145588	0.826261339927206
32	0.127453561183697	0.254907122367394	0.872546438816303
33	0.0778284502389225	0.155656900477845	0.922171549761078
34	0.158216087292043	0.316432174584085	0.841783912707957
35	0.226008742511805	0.452017485023609	0.773991257488195
36	0.24010492036141	0.48020984072282	0.75989507963859
37	0.372432775181059	0.744865550362118	0.627567224818941
38	0.228060311071386	0.456120622142773	0.771939688928614

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	1	0.0526315789473684	NOK
10% type I error level	4	0.210526315789474	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 & 1 & 0.0526315789473684 & NOK \tabularnewline
10% type I error level & 4 & 0.210526315789474 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69789&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]1[/C][C]0.0526315789473684[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.210526315789474[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69789&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69789&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	1	0.0526315789473684	NOK
10% type I error level	4	0.210526315789474	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