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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 12:22:54 -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/Nov/20/t1258745027mhvinry1psiuokx.htm/, Retrieved Fri, 26 Apr 2024 15:00:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58437, Retrieved Fri, 26 Apr 2024 15:00:43 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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 14:10:54] [b98453cac15ba1066b407e146608df68]
- R PD      [Multiple Regression] [Model 4] [2009-11-20 19:22:54] [a25640248f5f3c4d92f02a597edd3aef] [Current]
-    D        [Multiple Regression] [Model 5] [2009-11-20 19:50:08] [2c014794d4323c20be9bea6a55dac7b2] 

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Dataseries X:

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Histogram

Boxplots

95.1	8.9	96.9	98.6	111.7	109.8
97	8.8	95.1	96.9	98.6	111.7
112.7	8.3	97	95.1	96.9	98.6
102.9	7.5	112.7	97	95.1	96.9
97.4	7.2	102.9	112.7	97	95.1
111.4	7.4	97.4	102.9	112.7	97
87.4	8.8	111.4	97.4	102.9	112.7
96.8	9.3	87.4	111.4	97.4	102.9
114.1	9.3	96.8	87.4	111.4	97.4
110.3	8.7	114.1	96.8	87.4	111.4
103.9	8.2	110.3	114.1	96.8	87.4
101.6	8.3	103.9	110.3	114.1	96.8
94.6	8.5	101.6	103.9	110.3	114.1
95.9	8.6	94.6	101.6	103.9	110.3
104.7	8.5	95.9	94.6	101.6	103.9
102.8	8.2	104.7	95.9	94.6	101.6
98.1	8.1	102.8	104.7	95.9	94.6
113.9	7.9	98.1	102.8	104.7	95.9
80.9	8.6	113.9	98.1	102.8	104.7
95.7	8.7	80.9	113.9	98.1	102.8
113.2	8.7	95.7	80.9	113.9	98.1
105.9	8.5	113.2	95.7	80.9	113.9
108.8	8.4	105.9	113.2	95.7	80.9
102.3	8.5	108.8	105.9	113.2	95.7
99	8.7	102.3	108.8	105.9	113.2
100.7	8.7	99	102.3	108.8	105.9
115.5	8.6	100.7	99	102.3	108.8
100.7	8.5	115.5	100.7	99	102.3
109.9	8.3	100.7	115.5	100.7	99
114.6	8	109.9	100.7	115.5	100.7
85.4	8.2	114.6	109.9	100.7	115.5
100.5	8.1	85.4	114.6	109.9	100.7
114.8	8.1	100.5	85.4	114.6	109.9
116.5	8	114.8	100.5	85.4	114.6
112.9	7.9	116.5	114.8	100.5	85.4
102	7.9	112.9	116.5	114.8	100.5
106	8	102	112.9	116.5	114.8
105.3	8	106	102	112.9	116.5
118.8	7.9	105.3	106	102	112.9
106.1	8	118.8	105.3	106	102
109.3	7.7	106.1	118.8	105.3	106
117.2	7.2	109.3	106.1	118.8	105.3
92.5	7.5	117.2	109.3	106.1	118.8
104.2	7.3	92.5	117.2	109.3	106.1
112.5	7	104.2	92.5	117.2	109.3
122.4	7	112.5	104.2	92.5	117.2
113.3	7	122.4	112.5	104.2	92.5
100	7.2	113.3	122.4	112.5	104.2
110.7	7.3	100	113.3	122.4	112.5
112.8	7.1	110.7	100	113.3	122.4
109.8	6.8	112.8	110.7	100	113.3
117.3	6.4	109.8	112.8	110.7	100
109.1	6.1	117.3	109.8	112.8	110.7
115.9	6.5	109.1	117.3	109.8	112.8
96	7.7	115.9	109.1	117.3	109.8
99.8	7.9	96	115.9	109.1	117.3
116.8	7.5	99.8	96	115.9	109.1
115.7	6.9	116.8	99.8	96	115.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&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]8 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=58437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
X[t] = + 18.3307933952183 + 0.00373894172101956Y[t] -0.00994243414329733Y1[t] -0.0286088377747364Y2[t] -0.0351917944930868Y3[t] -0.0205447551967472Y4[t] + 0.246350043357412M1[t] -0.176443499281986M2[t] -0.7592473898286M3[t] -1.01309436201666M4[t] -0.960018480853686M5[t] -0.882068729586974M6[t] + 0.0324099427149764M7[t] -0.0479806478054456M8[t] -0.549765441448620M9[t] -1.09462221361560M10[t] -0.872758620940506M11[t] -0.0116552255662847t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  18.3307933952183 +  0.00373894172101956Y[t] -0.00994243414329733Y1[t] -0.0286088377747364Y2[t] -0.0351917944930868Y3[t] -0.0205447551967472Y4[t] +  0.246350043357412M1[t] -0.176443499281986M2[t] -0.7592473898286M3[t] -1.01309436201666M4[t] -0.960018480853686M5[t] -0.882068729586974M6[t] +  0.0324099427149764M7[t] -0.0479806478054456M8[t] -0.549765441448620M9[t] -1.09462221361560M10[t] -0.872758620940506M11[t] -0.0116552255662847t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  18.3307933952183 +  0.00373894172101956Y[t] -0.00994243414329733Y1[t] -0.0286088377747364Y2[t] -0.0351917944930868Y3[t] -0.0205447551967472Y4[t] +  0.246350043357412M1[t] -0.176443499281986M2[t] -0.7592473898286M3[t] -1.01309436201666M4[t] -0.960018480853686M5[t] -0.882068729586974M6[t] +  0.0324099427149764M7[t] -0.0479806478054456M8[t] -0.549765441448620M9[t] -1.09462221361560M10[t] -0.872758620940506M11[t] -0.0116552255662847t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
X[t] = + 18.3307933952183 + 0.00373894172101956Y[t] -0.00994243414329733Y1[t] -0.0286088377747364Y2[t] -0.0351917944930868Y3[t] -0.0205447551967472Y4[t] + 0.246350043357412M1[t] -0.176443499281986M2[t] -0.7592473898286M3[t] -1.01309436201666M4[t] -0.960018480853686M5[t] -0.882068729586974M6[t] + 0.0324099427149764M7[t] -0.0479806478054456M8[t] -0.549765441448620M9[t] -1.09462221361560M10[t] -0.872758620940506M11[t] -0.0116552255662847t + 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)	18.3307933952183	4.676352	3.9199	0.000338	0.000169
Y	0.00373894172101956	0.021192	0.1764	0.860844	0.430422
Y1	-0.00994243414329733	0.022279	-0.4463	0.65781	0.328905
Y2	-0.0286088377747364	0.020082	-1.4246	0.16202	0.08101
Y3	-0.0351917944930868	0.022778	-1.545	0.130231	0.065116
Y4	-0.0205447551967472	0.021909	-0.9377	0.354017	0.177009
M1	0.246350043357412	0.561956	0.4384	0.663469	0.331735
M2	-0.176443499281986	0.621947	-0.2837	0.778107	0.389054
M3	-0.7592473898286	0.677966	-1.1199	0.26944	0.13472
M4	-1.01309436201666	0.553894	-1.829	0.074856	0.037428
M5	-0.960018480853686	0.433549	-2.2143	0.032568	0.016284
M6	-0.882068729586974	0.488682	-1.805	0.078607	0.039304
M7	0.0324099427149764	0.487602	0.0665	0.947336	0.473668
M8	-0.0479806478054456	0.641393	-0.0748	0.940741	0.470371
M9	-0.549765441448620	0.771893	-0.7122	0.480456	0.240228
M10	-1.09462221361560	0.933406	-1.1727	0.247845	0.123923
M11	-0.872758620940506	0.693778	-1.258	0.215694	0.107847
t	-0.0116552255662847	0.01016	-1.1472	0.25811	0.129055

\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) & 18.3307933952183 & 4.676352 & 3.9199 & 0.000338 & 0.000169 \tabularnewline
Y & 0.00373894172101956 & 0.021192 & 0.1764 & 0.860844 & 0.430422 \tabularnewline
Y1 & -0.00994243414329733 & 0.022279 & -0.4463 & 0.65781 & 0.328905 \tabularnewline
Y2 & -0.0286088377747364 & 0.020082 & -1.4246 & 0.16202 & 0.08101 \tabularnewline
Y3 & -0.0351917944930868 & 0.022778 & -1.545 & 0.130231 & 0.065116 \tabularnewline
Y4 & -0.0205447551967472 & 0.021909 & -0.9377 & 0.354017 & 0.177009 \tabularnewline
M1 & 0.246350043357412 & 0.561956 & 0.4384 & 0.663469 & 0.331735 \tabularnewline
M2 & -0.176443499281986 & 0.621947 & -0.2837 & 0.778107 & 0.389054 \tabularnewline
M3 & -0.7592473898286 & 0.677966 & -1.1199 & 0.26944 & 0.13472 \tabularnewline
M4 & -1.01309436201666 & 0.553894 & -1.829 & 0.074856 & 0.037428 \tabularnewline
M5 & -0.960018480853686 & 0.433549 & -2.2143 & 0.032568 & 0.016284 \tabularnewline
M6 & -0.882068729586974 & 0.488682 & -1.805 & 0.078607 & 0.039304 \tabularnewline
M7 & 0.0324099427149764 & 0.487602 & 0.0665 & 0.947336 & 0.473668 \tabularnewline
M8 & -0.0479806478054456 & 0.641393 & -0.0748 & 0.940741 & 0.470371 \tabularnewline
M9 & -0.549765441448620 & 0.771893 & -0.7122 & 0.480456 & 0.240228 \tabularnewline
M10 & -1.09462221361560 & 0.933406 & -1.1727 & 0.247845 & 0.123923 \tabularnewline
M11 & -0.872758620940506 & 0.693778 & -1.258 & 0.215694 & 0.107847 \tabularnewline
t & -0.0116552255662847 & 0.01016 & -1.1472 & 0.25811 & 0.129055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&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]18.3307933952183[/C][C]4.676352[/C][C]3.9199[/C][C]0.000338[/C][C]0.000169[/C][/ROW]
[ROW][C]Y[/C][C]0.00373894172101956[/C][C]0.021192[/C][C]0.1764[/C][C]0.860844[/C][C]0.430422[/C][/ROW]
[ROW][C]Y1[/C][C]-0.00994243414329733[/C][C]0.022279[/C][C]-0.4463[/C][C]0.65781[/C][C]0.328905[/C][/ROW]
[ROW][C]Y2[/C][C]-0.0286088377747364[/C][C]0.020082[/C][C]-1.4246[/C][C]0.16202[/C][C]0.08101[/C][/ROW]
[ROW][C]Y3[/C][C]-0.0351917944930868[/C][C]0.022778[/C][C]-1.545[/C][C]0.130231[/C][C]0.065116[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0205447551967472[/C][C]0.021909[/C][C]-0.9377[/C][C]0.354017[/C][C]0.177009[/C][/ROW]
[ROW][C]M1[/C][C]0.246350043357412[/C][C]0.561956[/C][C]0.4384[/C][C]0.663469[/C][C]0.331735[/C][/ROW]
[ROW][C]M2[/C][C]-0.176443499281986[/C][C]0.621947[/C][C]-0.2837[/C][C]0.778107[/C][C]0.389054[/C][/ROW]
[ROW][C]M3[/C][C]-0.7592473898286[/C][C]0.677966[/C][C]-1.1199[/C][C]0.26944[/C][C]0.13472[/C][/ROW]
[ROW][C]M4[/C][C]-1.01309436201666[/C][C]0.553894[/C][C]-1.829[/C][C]0.074856[/C][C]0.037428[/C][/ROW]
[ROW][C]M5[/C][C]-0.960018480853686[/C][C]0.433549[/C][C]-2.2143[/C][C]0.032568[/C][C]0.016284[/C][/ROW]
[ROW][C]M6[/C][C]-0.882068729586974[/C][C]0.488682[/C][C]-1.805[/C][C]0.078607[/C][C]0.039304[/C][/ROW]
[ROW][C]M7[/C][C]0.0324099427149764[/C][C]0.487602[/C][C]0.0665[/C][C]0.947336[/C][C]0.473668[/C][/ROW]
[ROW][C]M8[/C][C]-0.0479806478054456[/C][C]0.641393[/C][C]-0.0748[/C][C]0.940741[/C][C]0.470371[/C][/ROW]
[ROW][C]M9[/C][C]-0.549765441448620[/C][C]0.771893[/C][C]-0.7122[/C][C]0.480456[/C][C]0.240228[/C][/ROW]
[ROW][C]M10[/C][C]-1.09462221361560[/C][C]0.933406[/C][C]-1.1727[/C][C]0.247845[/C][C]0.123923[/C][/ROW]
[ROW][C]M11[/C][C]-0.872758620940506[/C][C]0.693778[/C][C]-1.258[/C][C]0.215694[/C][C]0.107847[/C][/ROW]
[ROW][C]t[/C][C]-0.0116552255662847[/C][C]0.01016[/C][C]-1.1472[/C][C]0.25811[/C][C]0.129055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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)	18.3307933952183	4.676352	3.9199	0.000338	0.000169
Y	0.00373894172101956	0.021192	0.1764	0.860844	0.430422
Y1	-0.00994243414329733	0.022279	-0.4463	0.65781	0.328905
Y2	-0.0286088377747364	0.020082	-1.4246	0.16202	0.08101
Y3	-0.0351917944930868	0.022778	-1.545	0.130231	0.065116
Y4	-0.0205447551967472	0.021909	-0.9377	0.354017	0.177009
M1	0.246350043357412	0.561956	0.4384	0.663469	0.331735
M2	-0.176443499281986	0.621947	-0.2837	0.778107	0.389054
M3	-0.7592473898286	0.677966	-1.1199	0.26944	0.13472
M4	-1.01309436201666	0.553894	-1.829	0.074856	0.037428
M5	-0.960018480853686	0.433549	-2.2143	0.032568	0.016284
M6	-0.882068729586974	0.488682	-1.805	0.078607	0.039304
M7	0.0324099427149764	0.487602	0.0665	0.947336	0.473668
M8	-0.0479806478054456	0.641393	-0.0748	0.940741	0.470371
M9	-0.549765441448620	0.771893	-0.7122	0.480456	0.240228
M10	-1.09462221361560	0.933406	-1.1727	0.247845	0.123923
M11	-0.872758620940506	0.693778	-1.258	0.215694	0.107847
t	-0.0116552255662847	0.01016	-1.1472	0.25811	0.129055

Multiple Linear Regression - Regression Statistics
Multiple R	0.83781925068927
R-squared	0.701941096825531
Adjusted R-squared	0.575266062976381
F-TEST (value)	5.54127419978774
F-TEST (DF numerator)	17
F-TEST (DF denominator)	40
p-value	4.24438353996415e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.471101869906799
Sum Squared Residuals	8.87747887318731

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.83781925068927 \tabularnewline
R-squared & 0.701941096825531 \tabularnewline
Adjusted R-squared & 0.575266062976381 \tabularnewline
F-TEST (value) & 5.54127419978774 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 4.24438353996415e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.471101869906799 \tabularnewline
Sum Squared Residuals & 8.87747887318731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.83781925068927[/C][/ROW]
[ROW][C]R-squared[/C][C]0.701941096825531[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.575266062976381[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.54127419978774[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/C][/ROW]
[ROW][C]p-value[/C][C]4.24438353996415e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.471101869906799[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8.87747887318731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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	0.83781925068927
R-squared	0.701941096825531
Adjusted R-squared	0.575266062976381
F-TEST (value)	5.54127419978774
F-TEST (DF numerator)	17
F-TEST (DF denominator)	40
p-value	4.24438353996415e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.471101869906799
Sum Squared Residuals	8.87747887318731

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.9	8.9500707321233	-0.0500707321232941
2	8.8	9.01123483184811	-0.211234831848113
3	8.3	8.83704472759312	-0.537044727593118
4	7.5	8.42271920707304	-0.92271920707304
5	7.2	8.06196893456235	-0.861968934562356
6	7.4	7.92411243392233	-0.524112433922327
7	8.8	8.77768273855173	0.0223172614482707
8	9.3	8.95377113587553	0.346228864124469
9	9.3	8.71847906476528	0.581520935234717
10	8.7	8.2638083978102	0.436191602189792
11	8.2	8.155207150633	0.0447928493670056
12	8.3	8.37811739853015	-0.0781173985301458
13	8.5	8.57090833873204	-0.0709083387320373
14	8.6	8.58001511515205	0.01998488484795
15	8.5	8.41822294681427	0.0817770531857263
16	8.2	8.31452734862594	-0.114527348625942
17	8.1	8.20357178412464	-0.103571784124643
18	7.9	8.09363184796774	-0.193631847967741
19	8.6	8.73651185979242	-0.136511859792415
20	8.7	8.7803195400561	-0.0803195400561012
21	8.7	8.66978461864393	0.0302153813560743
22	8.5	8.32529703593668	0.174702964063322
23	8.4	8.2754118052196	0.124588194780404
24	8.5	8.37230475560633	0.127695244393673
25	8.7	8.47368814195925	0.226311858040754
26	8.7	8.31228356179427	0.387716438205733
27	8.6	8.01983468389998	0.580165316100019
28	8.5	7.75288692974273	0.747113070257266
29	8.3	7.56041471693852	0.739585283061476
30	8	7.42045803134335	0.579541968656647
31	8.2	8.12094981341	0.0790501865899989
32	8.1	8.22151742432917	-0.121517424329170
33	8.1	8.09237839726122	0.00762160273877814
34	8	7.89909239157944	0.100907608420555
35	7.9	7.73834280516965	0.161657194830348
36	7.9	7.73238100976156	0.167618990238445
37	8	7.83977989263602	0.160220107363980
38	8	7.7665448367377	0.233455163262297
39	7.9	7.57263746534287	0.327362534657132
40	8	7.22862468691157	0.771375313088429
41	7.7	6.96451479503463	0.735485204965369
42	7.2	6.93115551379277	0.268844486207234
43	7.5	7.74111518431416	-0.241115184314158
44	7.3	7.86068793990322	-0.560687939903218
45	7	7.62483455741265	-0.624834557412654
46	7	7.39502623528864	-0.395026235288645
47	7	7.33103823897776	-0.331038238977757
48	7.2	7.41719683610197	-0.217196836101970
49	7.3	7.5655528945494	-0.265552894549402
50	7.1	7.52992165446787	-0.429921654467867
51	6.8	7.25226017634976	-0.452260176349760
52	6.4	6.88124182764671	-0.481241827646712
53	6.1	6.60952976933985	-0.509529769339847
54	6.5	6.63064217297381	-0.130642172973813
55	7.7	7.4237404039317	0.276259596068304
56	7.9	7.48370395983598	0.41629604016402
57	7.5	7.49452336191692	0.00547663808308477
58	6.9	7.21677593938503	-0.316775939385026

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 8.9500707321233 & -0.0500707321232941 \tabularnewline
2 & 8.8 & 9.01123483184811 & -0.211234831848113 \tabularnewline
3 & 8.3 & 8.83704472759312 & -0.537044727593118 \tabularnewline
4 & 7.5 & 8.42271920707304 & -0.92271920707304 \tabularnewline
5 & 7.2 & 8.06196893456235 & -0.861968934562356 \tabularnewline
6 & 7.4 & 7.92411243392233 & -0.524112433922327 \tabularnewline
7 & 8.8 & 8.77768273855173 & 0.0223172614482707 \tabularnewline
8 & 9.3 & 8.95377113587553 & 0.346228864124469 \tabularnewline
9 & 9.3 & 8.71847906476528 & 0.581520935234717 \tabularnewline
10 & 8.7 & 8.2638083978102 & 0.436191602189792 \tabularnewline
11 & 8.2 & 8.155207150633 & 0.0447928493670056 \tabularnewline
12 & 8.3 & 8.37811739853015 & -0.0781173985301458 \tabularnewline
13 & 8.5 & 8.57090833873204 & -0.0709083387320373 \tabularnewline
14 & 8.6 & 8.58001511515205 & 0.01998488484795 \tabularnewline
15 & 8.5 & 8.41822294681427 & 0.0817770531857263 \tabularnewline
16 & 8.2 & 8.31452734862594 & -0.114527348625942 \tabularnewline
17 & 8.1 & 8.20357178412464 & -0.103571784124643 \tabularnewline
18 & 7.9 & 8.09363184796774 & -0.193631847967741 \tabularnewline
19 & 8.6 & 8.73651185979242 & -0.136511859792415 \tabularnewline
20 & 8.7 & 8.7803195400561 & -0.0803195400561012 \tabularnewline
21 & 8.7 & 8.66978461864393 & 0.0302153813560743 \tabularnewline
22 & 8.5 & 8.32529703593668 & 0.174702964063322 \tabularnewline
23 & 8.4 & 8.2754118052196 & 0.124588194780404 \tabularnewline
24 & 8.5 & 8.37230475560633 & 0.127695244393673 \tabularnewline
25 & 8.7 & 8.47368814195925 & 0.226311858040754 \tabularnewline
26 & 8.7 & 8.31228356179427 & 0.387716438205733 \tabularnewline
27 & 8.6 & 8.01983468389998 & 0.580165316100019 \tabularnewline
28 & 8.5 & 7.75288692974273 & 0.747113070257266 \tabularnewline
29 & 8.3 & 7.56041471693852 & 0.739585283061476 \tabularnewline
30 & 8 & 7.42045803134335 & 0.579541968656647 \tabularnewline
31 & 8.2 & 8.12094981341 & 0.0790501865899989 \tabularnewline
32 & 8.1 & 8.22151742432917 & -0.121517424329170 \tabularnewline
33 & 8.1 & 8.09237839726122 & 0.00762160273877814 \tabularnewline
34 & 8 & 7.89909239157944 & 0.100907608420555 \tabularnewline
35 & 7.9 & 7.73834280516965 & 0.161657194830348 \tabularnewline
36 & 7.9 & 7.73238100976156 & 0.167618990238445 \tabularnewline
37 & 8 & 7.83977989263602 & 0.160220107363980 \tabularnewline
38 & 8 & 7.7665448367377 & 0.233455163262297 \tabularnewline
39 & 7.9 & 7.57263746534287 & 0.327362534657132 \tabularnewline
40 & 8 & 7.22862468691157 & 0.771375313088429 \tabularnewline
41 & 7.7 & 6.96451479503463 & 0.735485204965369 \tabularnewline
42 & 7.2 & 6.93115551379277 & 0.268844486207234 \tabularnewline
43 & 7.5 & 7.74111518431416 & -0.241115184314158 \tabularnewline
44 & 7.3 & 7.86068793990322 & -0.560687939903218 \tabularnewline
45 & 7 & 7.62483455741265 & -0.624834557412654 \tabularnewline
46 & 7 & 7.39502623528864 & -0.395026235288645 \tabularnewline
47 & 7 & 7.33103823897776 & -0.331038238977757 \tabularnewline
48 & 7.2 & 7.41719683610197 & -0.217196836101970 \tabularnewline
49 & 7.3 & 7.5655528945494 & -0.265552894549402 \tabularnewline
50 & 7.1 & 7.52992165446787 & -0.429921654467867 \tabularnewline
51 & 6.8 & 7.25226017634976 & -0.452260176349760 \tabularnewline
52 & 6.4 & 6.88124182764671 & -0.481241827646712 \tabularnewline
53 & 6.1 & 6.60952976933985 & -0.509529769339847 \tabularnewline
54 & 6.5 & 6.63064217297381 & -0.130642172973813 \tabularnewline
55 & 7.7 & 7.4237404039317 & 0.276259596068304 \tabularnewline
56 & 7.9 & 7.48370395983598 & 0.41629604016402 \tabularnewline
57 & 7.5 & 7.49452336191692 & 0.00547663808308477 \tabularnewline
58 & 6.9 & 7.21677593938503 & -0.316775939385026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&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]8.9[/C][C]8.9500707321233[/C][C]-0.0500707321232941[/C][/ROW]
[ROW][C]2[/C][C]8.8[/C][C]9.01123483184811[/C][C]-0.211234831848113[/C][/ROW]
[ROW][C]3[/C][C]8.3[/C][C]8.83704472759312[/C][C]-0.537044727593118[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]8.42271920707304[/C][C]-0.92271920707304[/C][/ROW]
[ROW][C]5[/C][C]7.2[/C][C]8.06196893456235[/C][C]-0.861968934562356[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]7.92411243392233[/C][C]-0.524112433922327[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.77768273855173[/C][C]0.0223172614482707[/C][/ROW]
[ROW][C]8[/C][C]9.3[/C][C]8.95377113587553[/C][C]0.346228864124469[/C][/ROW]
[ROW][C]9[/C][C]9.3[/C][C]8.71847906476528[/C][C]0.581520935234717[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]8.2638083978102[/C][C]0.436191602189792[/C][/ROW]
[ROW][C]11[/C][C]8.2[/C][C]8.155207150633[/C][C]0.0447928493670056[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.37811739853015[/C][C]-0.0781173985301458[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.57090833873204[/C][C]-0.0709083387320373[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]8.58001511515205[/C][C]0.01998488484795[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.41822294681427[/C][C]0.0817770531857263[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.31452734862594[/C][C]-0.114527348625942[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]8.20357178412464[/C][C]-0.103571784124643[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]8.09363184796774[/C][C]-0.193631847967741[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.73651185979242[/C][C]-0.136511859792415[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]8.7803195400561[/C][C]-0.0803195400561012[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.66978461864393[/C][C]0.0302153813560743[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.32529703593668[/C][C]0.174702964063322[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]8.2754118052196[/C][C]0.124588194780404[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.37230475560633[/C][C]0.127695244393673[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.47368814195925[/C][C]0.226311858040754[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.31228356179427[/C][C]0.387716438205733[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.01983468389998[/C][C]0.580165316100019[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]7.75288692974273[/C][C]0.747113070257266[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]7.56041471693852[/C][C]0.739585283061476[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.42045803134335[/C][C]0.579541968656647[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.12094981341[/C][C]0.0790501865899989[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.22151742432917[/C][C]-0.121517424329170[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.09237839726122[/C][C]0.00762160273877814[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.89909239157944[/C][C]0.100907608420555[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.73834280516965[/C][C]0.161657194830348[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.73238100976156[/C][C]0.167618990238445[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]7.83977989263602[/C][C]0.160220107363980[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.7665448367377[/C][C]0.233455163262297[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.57263746534287[/C][C]0.327362534657132[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.22862468691157[/C][C]0.771375313088429[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]6.96451479503463[/C][C]0.735485204965369[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]6.93115551379277[/C][C]0.268844486207234[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.74111518431416[/C][C]-0.241115184314158[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.86068793990322[/C][C]-0.560687939903218[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.62483455741265[/C][C]-0.624834557412654[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]7.39502623528864[/C][C]-0.395026235288645[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]7.33103823897776[/C][C]-0.331038238977757[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.41719683610197[/C][C]-0.217196836101970[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.5655528945494[/C][C]-0.265552894549402[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.52992165446787[/C][C]-0.429921654467867[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.25226017634976[/C][C]-0.452260176349760[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]6.88124182764671[/C][C]-0.481241827646712[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]6.60952976933985[/C][C]-0.509529769339847[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.63064217297381[/C][C]-0.130642172973813[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.4237404039317[/C][C]0.276259596068304[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.48370395983598[/C][C]0.41629604016402[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.49452336191692[/C][C]0.00547663808308477[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]7.21677593938503[/C][C]-0.316775939385026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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	8.9	8.9500707321233	-0.0500707321232941
2	8.8	9.01123483184811	-0.211234831848113
3	8.3	8.83704472759312	-0.537044727593118
4	7.5	8.42271920707304	-0.92271920707304
5	7.2	8.06196893456235	-0.861968934562356
6	7.4	7.92411243392233	-0.524112433922327
7	8.8	8.77768273855173	0.0223172614482707
8	9.3	8.95377113587553	0.346228864124469
9	9.3	8.71847906476528	0.581520935234717
10	8.7	8.2638083978102	0.436191602189792
11	8.2	8.155207150633	0.0447928493670056
12	8.3	8.37811739853015	-0.0781173985301458
13	8.5	8.57090833873204	-0.0709083387320373
14	8.6	8.58001511515205	0.01998488484795
15	8.5	8.41822294681427	0.0817770531857263
16	8.2	8.31452734862594	-0.114527348625942
17	8.1	8.20357178412464	-0.103571784124643
18	7.9	8.09363184796774	-0.193631847967741
19	8.6	8.73651185979242	-0.136511859792415
20	8.7	8.7803195400561	-0.0803195400561012
21	8.7	8.66978461864393	0.0302153813560743
22	8.5	8.32529703593668	0.174702964063322
23	8.4	8.2754118052196	0.124588194780404
24	8.5	8.37230475560633	0.127695244393673
25	8.7	8.47368814195925	0.226311858040754
26	8.7	8.31228356179427	0.387716438205733
27	8.6	8.01983468389998	0.580165316100019
28	8.5	7.75288692974273	0.747113070257266
29	8.3	7.56041471693852	0.739585283061476
30	8	7.42045803134335	0.579541968656647
31	8.2	8.12094981341	0.0790501865899989
32	8.1	8.22151742432917	-0.121517424329170
33	8.1	8.09237839726122	0.00762160273877814
34	8	7.89909239157944	0.100907608420555
35	7.9	7.73834280516965	0.161657194830348
36	7.9	7.73238100976156	0.167618990238445
37	8	7.83977989263602	0.160220107363980
38	8	7.7665448367377	0.233455163262297
39	7.9	7.57263746534287	0.327362534657132
40	8	7.22862468691157	0.771375313088429
41	7.7	6.96451479503463	0.735485204965369
42	7.2	6.93115551379277	0.268844486207234
43	7.5	7.74111518431416	-0.241115184314158
44	7.3	7.86068793990322	-0.560687939903218
45	7	7.62483455741265	-0.624834557412654
46	7	7.39502623528864	-0.395026235288645
47	7	7.33103823897776	-0.331038238977757
48	7.2	7.41719683610197	-0.217196836101970
49	7.3	7.5655528945494	-0.265552894549402
50	7.1	7.52992165446787	-0.429921654467867
51	6.8	7.25226017634976	-0.452260176349760
52	6.4	6.88124182764671	-0.481241827646712
53	6.1	6.60952976933985	-0.509529769339847
54	6.5	6.63064217297381	-0.130642172973813
55	7.7	7.4237404039317	0.276259596068304
56	7.9	7.48370395983598	0.41629604016402
57	7.5	7.49452336191692	0.00547663808308477
58	6.9	7.21677593938503	-0.316775939385026

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.79271118526718	0.414577629465639	0.207288814732819
22	0.743217970052408	0.513564059895184	0.256782029947592
23	0.638302609545252	0.723394780909496	0.361697390454748
24	0.520061256725813	0.959877486548373	0.479938743274187
25	0.392804188405288	0.785608376810576	0.607195811594712
26	0.283880023102818	0.567760046205637	0.716119976897182
27	0.186291962436433	0.372583924872867	0.813708037563567
28	0.233132772889901	0.466265545779802	0.766867227110099
29	0.168280118171714	0.336560236343429	0.831719881828286
30	0.102982680797510	0.205965361595021	0.89701731920249
31	0.10055854740214	0.20111709480428	0.89944145259786
32	0.274539984765206	0.549079969530411	0.725460015234795
33	0.438212942165467	0.876425884330935	0.561787057834533
34	0.371821268925547	0.743642537851095	0.628178731074453
35	0.268352323723245	0.536704647446489	0.731647676276755
36	0.166577128761237	0.333154257522474	0.833422871238763
37	0.0967359004152693	0.193471800830539	0.90326409958473

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.79271118526718 & 0.414577629465639 & 0.207288814732819 \tabularnewline
22 & 0.743217970052408 & 0.513564059895184 & 0.256782029947592 \tabularnewline
23 & 0.638302609545252 & 0.723394780909496 & 0.361697390454748 \tabularnewline
24 & 0.520061256725813 & 0.959877486548373 & 0.479938743274187 \tabularnewline
25 & 0.392804188405288 & 0.785608376810576 & 0.607195811594712 \tabularnewline
26 & 0.283880023102818 & 0.567760046205637 & 0.716119976897182 \tabularnewline
27 & 0.186291962436433 & 0.372583924872867 & 0.813708037563567 \tabularnewline
28 & 0.233132772889901 & 0.466265545779802 & 0.766867227110099 \tabularnewline
29 & 0.168280118171714 & 0.336560236343429 & 0.831719881828286 \tabularnewline
30 & 0.102982680797510 & 0.205965361595021 & 0.89701731920249 \tabularnewline
31 & 0.10055854740214 & 0.20111709480428 & 0.89944145259786 \tabularnewline
32 & 0.274539984765206 & 0.549079969530411 & 0.725460015234795 \tabularnewline
33 & 0.438212942165467 & 0.876425884330935 & 0.561787057834533 \tabularnewline
34 & 0.371821268925547 & 0.743642537851095 & 0.628178731074453 \tabularnewline
35 & 0.268352323723245 & 0.536704647446489 & 0.731647676276755 \tabularnewline
36 & 0.166577128761237 & 0.333154257522474 & 0.833422871238763 \tabularnewline
37 & 0.0967359004152693 & 0.193471800830539 & 0.90326409958473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&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]21[/C][C]0.79271118526718[/C][C]0.414577629465639[/C][C]0.207288814732819[/C][/ROW]
[ROW][C]22[/C][C]0.743217970052408[/C][C]0.513564059895184[/C][C]0.256782029947592[/C][/ROW]
[ROW][C]23[/C][C]0.638302609545252[/C][C]0.723394780909496[/C][C]0.361697390454748[/C][/ROW]
[ROW][C]24[/C][C]0.520061256725813[/C][C]0.959877486548373[/C][C]0.479938743274187[/C][/ROW]
[ROW][C]25[/C][C]0.392804188405288[/C][C]0.785608376810576[/C][C]0.607195811594712[/C][/ROW]
[ROW][C]26[/C][C]0.283880023102818[/C][C]0.567760046205637[/C][C]0.716119976897182[/C][/ROW]
[ROW][C]27[/C][C]0.186291962436433[/C][C]0.372583924872867[/C][C]0.813708037563567[/C][/ROW]
[ROW][C]28[/C][C]0.233132772889901[/C][C]0.466265545779802[/C][C]0.766867227110099[/C][/ROW]
[ROW][C]29[/C][C]0.168280118171714[/C][C]0.336560236343429[/C][C]0.831719881828286[/C][/ROW]
[ROW][C]30[/C][C]0.102982680797510[/C][C]0.205965361595021[/C][C]0.89701731920249[/C][/ROW]
[ROW][C]31[/C][C]0.10055854740214[/C][C]0.20111709480428[/C][C]0.89944145259786[/C][/ROW]
[ROW][C]32[/C][C]0.274539984765206[/C][C]0.549079969530411[/C][C]0.725460015234795[/C][/ROW]
[ROW][C]33[/C][C]0.438212942165467[/C][C]0.876425884330935[/C][C]0.561787057834533[/C][/ROW]
[ROW][C]34[/C][C]0.371821268925547[/C][C]0.743642537851095[/C][C]0.628178731074453[/C][/ROW]
[ROW][C]35[/C][C]0.268352323723245[/C][C]0.536704647446489[/C][C]0.731647676276755[/C][/ROW]
[ROW][C]36[/C][C]0.166577128761237[/C][C]0.333154257522474[/C][C]0.833422871238763[/C][/ROW]
[ROW][C]37[/C][C]0.0967359004152693[/C][C]0.193471800830539[/C][C]0.90326409958473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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
21	0.79271118526718	0.414577629465639	0.207288814732819
22	0.743217970052408	0.513564059895184	0.256782029947592
23	0.638302609545252	0.723394780909496	0.361697390454748
24	0.520061256725813	0.959877486548373	0.479938743274187
25	0.392804188405288	0.785608376810576	0.607195811594712
26	0.283880023102818	0.567760046205637	0.716119976897182
27	0.186291962436433	0.372583924872867	0.813708037563567
28	0.233132772889901	0.466265545779802	0.766867227110099
29	0.168280118171714	0.336560236343429	0.831719881828286
30	0.102982680797510	0.205965361595021	0.89701731920249
31	0.10055854740214	0.20111709480428	0.89944145259786
32	0.274539984765206	0.549079969530411	0.725460015234795
33	0.438212942165467	0.876425884330935	0.561787057834533
34	0.371821268925547	0.743642537851095	0.628178731074453
35	0.268352323723245	0.536704647446489	0.731647676276755
36	0.166577128761237	0.333154257522474	0.833422871238763
37	0.0967359004152693	0.193471800830539	0.90326409958473

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	0	0	OK
10% type I error level	0	0	OK

\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 & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58437&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58437&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58437&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	0	0	OK
10% type I error level	0	0	OK

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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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