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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 19 Dec 2009 09:39:43 -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/19/t12612409128vejl41tbrhpqac.htm/, Retrieved Fri, 03 May 2024 23:17:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69693, Retrieved Fri, 03 May 2024 23:17:39 +0000

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Estimated Impact

133

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-12-19 16:39:43] [2b679e8ec54382eeb0ec0b6bb527570a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&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]6 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=69693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 100.785684210526 -1.64842105263159X[t] -0.816210526315732M1[t] -0.126M2[t] + 0.0860000000000034M3[t] -0.0699999999999973M4[t] + 0.172000000000002M5[t] -0.330000000000000M6[t] -0.364M7[t] -0.658M8[t] -0.529999999999999M9[t] -1.55000000000000M10[t] -0.582000000000001M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  100.785684210526 -1.64842105263159X[t] -0.816210526315732M1[t] -0.126M2[t] +  0.0860000000000034M3[t] -0.0699999999999973M4[t] +  0.172000000000002M5[t] -0.330000000000000M6[t] -0.364M7[t] -0.658M8[t] -0.529999999999999M9[t] -1.55000000000000M10[t] -0.582000000000001M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  100.785684210526 -1.64842105263159X[t] -0.816210526315732M1[t] -0.126M2[t] +  0.0860000000000034M3[t] -0.0699999999999973M4[t] +  0.172000000000002M5[t] -0.330000000000000M6[t] -0.364M7[t] -0.658M8[t] -0.529999999999999M9[t] -1.55000000000000M10[t] -0.582000000000001M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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] = + 100.785684210526 -1.64842105263159X[t] -0.816210526315732M1[t] -0.126M2[t] + 0.0860000000000034M3[t] -0.0699999999999973M4[t] + 0.172000000000002M5[t] -0.330000000000000M6[t] -0.364M7[t] -0.658M8[t] -0.529999999999999M9[t] -1.55000000000000M10[t] -0.582000000000001M11[t] + 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)	100.785684210526	0.654317	154.0319	0	0
X	-1.64842105263159	0.455148	-3.6217	0.000704	0.000352
M1	-0.816210526315732	0.87943	-0.9281	0.357993	0.178996
M2	-0.126	0.916345	-0.1375	0.891209	0.445604
M3	0.0860000000000034	0.916345	0.0939	0.925618	0.462809
M4	-0.0699999999999973	0.916345	-0.0764	0.939426	0.469713
M5	0.172000000000002	0.916345	0.1877	0.851901	0.425951
M6	-0.330000000000000	0.916345	-0.3601	0.720333	0.360166
M7	-0.364	0.916345	-0.3972	0.692959	0.346479
M8	-0.658	0.916345	-0.7181	0.476195	0.238097
M9	-0.529999999999999	0.916345	-0.5784	0.565708	0.282854
M10	-1.55000000000000	0.916345	-1.6915	0.097224	0.048612
M11	-0.582000000000001	0.916345	-0.6351	0.528359	0.264179

\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) & 100.785684210526 & 0.654317 & 154.0319 & 0 & 0 \tabularnewline
X & -1.64842105263159 & 0.455148 & -3.6217 & 0.000704 & 0.000352 \tabularnewline
M1 & -0.816210526315732 & 0.87943 & -0.9281 & 0.357993 & 0.178996 \tabularnewline
M2 & -0.126 & 0.916345 & -0.1375 & 0.891209 & 0.445604 \tabularnewline
M3 & 0.0860000000000034 & 0.916345 & 0.0939 & 0.925618 & 0.462809 \tabularnewline
M4 & -0.0699999999999973 & 0.916345 & -0.0764 & 0.939426 & 0.469713 \tabularnewline
M5 & 0.172000000000002 & 0.916345 & 0.1877 & 0.851901 & 0.425951 \tabularnewline
M6 & -0.330000000000000 & 0.916345 & -0.3601 & 0.720333 & 0.360166 \tabularnewline
M7 & -0.364 & 0.916345 & -0.3972 & 0.692959 & 0.346479 \tabularnewline
M8 & -0.658 & 0.916345 & -0.7181 & 0.476195 & 0.238097 \tabularnewline
M9 & -0.529999999999999 & 0.916345 & -0.5784 & 0.565708 & 0.282854 \tabularnewline
M10 & -1.55000000000000 & 0.916345 & -1.6915 & 0.097224 & 0.048612 \tabularnewline
M11 & -0.582000000000001 & 0.916345 & -0.6351 & 0.528359 & 0.264179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&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]100.785684210526[/C][C]0.654317[/C][C]154.0319[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-1.64842105263159[/C][C]0.455148[/C][C]-3.6217[/C][C]0.000704[/C][C]0.000352[/C][/ROW]
[ROW][C]M1[/C][C]-0.816210526315732[/C][C]0.87943[/C][C]-0.9281[/C][C]0.357993[/C][C]0.178996[/C][/ROW]
[ROW][C]M2[/C][C]-0.126[/C][C]0.916345[/C][C]-0.1375[/C][C]0.891209[/C][C]0.445604[/C][/ROW]
[ROW][C]M3[/C][C]0.0860000000000034[/C][C]0.916345[/C][C]0.0939[/C][C]0.925618[/C][C]0.462809[/C][/ROW]
[ROW][C]M4[/C][C]-0.0699999999999973[/C][C]0.916345[/C][C]-0.0764[/C][C]0.939426[/C][C]0.469713[/C][/ROW]
[ROW][C]M5[/C][C]0.172000000000002[/C][C]0.916345[/C][C]0.1877[/C][C]0.851901[/C][C]0.425951[/C][/ROW]
[ROW][C]M6[/C][C]-0.330000000000000[/C][C]0.916345[/C][C]-0.3601[/C][C]0.720333[/C][C]0.360166[/C][/ROW]
[ROW][C]M7[/C][C]-0.364[/C][C]0.916345[/C][C]-0.3972[/C][C]0.692959[/C][C]0.346479[/C][/ROW]
[ROW][C]M8[/C][C]-0.658[/C][C]0.916345[/C][C]-0.7181[/C][C]0.476195[/C][C]0.238097[/C][/ROW]
[ROW][C]M9[/C][C]-0.529999999999999[/C][C]0.916345[/C][C]-0.5784[/C][C]0.565708[/C][C]0.282854[/C][/ROW]
[ROW][C]M10[/C][C]-1.55000000000000[/C][C]0.916345[/C][C]-1.6915[/C][C]0.097224[/C][C]0.048612[/C][/ROW]
[ROW][C]M11[/C][C]-0.582000000000001[/C][C]0.916345[/C][C]-0.6351[/C][C]0.528359[/C][C]0.264179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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)	100.785684210526	0.654317	154.0319	0	0
X	-1.64842105263159	0.455148	-3.6217	0.000704	0.000352
M1	-0.816210526315732	0.87943	-0.9281	0.357993	0.178996
M2	-0.126	0.916345	-0.1375	0.891209	0.445604
M3	0.0860000000000034	0.916345	0.0939	0.925618	0.462809
M4	-0.0699999999999973	0.916345	-0.0764	0.939426	0.469713
M5	0.172000000000002	0.916345	0.1877	0.851901	0.425951
M6	-0.330000000000000	0.916345	-0.3601	0.720333	0.360166
M7	-0.364	0.916345	-0.3972	0.692959	0.346479
M8	-0.658	0.916345	-0.7181	0.476195	0.238097
M9	-0.529999999999999	0.916345	-0.5784	0.565708	0.282854
M10	-1.55000000000000	0.916345	-1.6915	0.097224	0.048612
M11	-0.582000000000001	0.916345	-0.6351	0.528359	0.264179

Multiple Linear Regression - Regression Statistics
Multiple R	0.540955008842867
R-squared	0.292632321592186
Adjusted R-squared	0.115790401990232
F-TEST (value)	1.65476784153249
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.107998708785458
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.44886891758740
Sum Squared Residuals	100.762614736843

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.540955008842867 \tabularnewline
R-squared & 0.292632321592186 \tabularnewline
Adjusted R-squared & 0.115790401990232 \tabularnewline
F-TEST (value) & 1.65476784153249 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.107998708785458 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.44886891758740 \tabularnewline
Sum Squared Residuals & 100.762614736843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.540955008842867[/C][/ROW]
[ROW][C]R-squared[/C][C]0.292632321592186[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.115790401990232[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.65476784153249[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.107998708785458[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.44886891758740[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]100.762614736843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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	0.540955008842867
R-squared	0.292632321592186
Adjusted R-squared	0.115790401990232
F-TEST (value)	1.65476784153249
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.107998708785458
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.44886891758740
Sum Squared Residuals	100.762614736843

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	101.09	99.9694736842103	1.12052631578974
2	102.71	100.659684210526	2.05031578947367
3	102.11	100.871684210526	1.23831578947368
4	101.68	100.715684210526	0.964315789473686
5	101.7	100.957684210526	0.742315789473685
6	101.53	100.455684210526	1.07431578947369
7	101.76	100.421684210526	1.33831578947369
8	101.15	100.127684210526	1.02231578947369
9	100.92	100.255684210526	0.664315789473684
10	100.73	99.2356842105263	1.49431578947369
11	100.55	100.203684210526	0.346315789473681
12	102.15	100.785684210526	1.36431578947369
13	100.79	99.9694736842106	0.820526315789422
14	99.93	100.659684210526	-0.72968421052631
15	100.03	100.871684210526	-0.841684210526319
16	100.25	100.715684210526	-0.465684210526320
17	99.6	100.957684210526	-1.35768421052632
18	100.16	100.455684210526	-0.295684210526320
19	100.49	100.421684210526	0.0683157894736786
20	99.72	100.127684210526	-0.407684210526318
21	100.14	100.255684210526	-0.115684210526316
22	98.48	99.2356842105263	-0.755684210526314
23	100.38	100.203684210526	0.17631578947368
24	101.45	100.785684210526	0.664315789473686
25	98.42	99.9694736842106	-1.54947368421058
26	98.6	100.659684210526	-2.05968421052632
27	100.06	100.871684210526	-0.811684210526318
28	98.62	100.715684210526	-2.09568421052631
29	100.84	100.957684210526	-0.117684210526315
30	100.02	100.455684210526	-0.435684210526321
31	97.95	100.421684210526	-2.47168421052631
32	98.32	100.127684210526	-1.80768421052632
33	98.27	100.255684210526	-1.98568421052632
34	97.22	99.2356842105263	-2.01568421052632
35	99.28	100.203684210526	-0.923684210526314
36	100.38	100.785684210526	-0.405684210526321
37	99.02	99.9694736842106	-0.949473684210588
38	100.32	100.659684210526	-0.339684210526323
39	99.81	100.871684210526	-1.06168421052632
40	100.6	100.715684210526	-0.115684210526325
41	101.19	100.957684210526	0.232315789473680
42	100.47	100.455684210526	0.0143157894736818
43	101.77	100.421684210526	1.34831578947368
44	102.32	100.127684210526	2.19231578947368
45	102.39	100.255684210526	2.13431578947368
46	101.16	99.2356842105263	1.92431578947368
47	100.63	100.203684210526	0.42631578947368
48	101.48	100.785684210526	0.694315789473687
49	101.44	98.321052631579	3.11894736842100
50	100.09	99.0112631578947	1.07873684210528
51	100.7	99.2232631578947	1.47673684210527
52	100.78	99.0672631578947	1.71273684210527
53	99.81	99.3092631578947	0.500736842105274
54	98.45	98.8072631578947	-0.357263157894725
55	98.49	98.7732631578947	-0.283263157894732
56	97.48	98.4792631578947	-0.999263157894724
57	97.91	98.6072631578947	-0.697263157894731
58	96.94	97.5872631578947	-0.647263157894732
59	98.53	98.5552631578947	-0.0252631578947256
60	96.82	99.1372631578947	-2.31726315789473
61	95.76	98.321052631579	-2.56105263157899

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.09 & 99.9694736842103 & 1.12052631578974 \tabularnewline
2 & 102.71 & 100.659684210526 & 2.05031578947367 \tabularnewline
3 & 102.11 & 100.871684210526 & 1.23831578947368 \tabularnewline
4 & 101.68 & 100.715684210526 & 0.964315789473686 \tabularnewline
5 & 101.7 & 100.957684210526 & 0.742315789473685 \tabularnewline
6 & 101.53 & 100.455684210526 & 1.07431578947369 \tabularnewline
7 & 101.76 & 100.421684210526 & 1.33831578947369 \tabularnewline
8 & 101.15 & 100.127684210526 & 1.02231578947369 \tabularnewline
9 & 100.92 & 100.255684210526 & 0.664315789473684 \tabularnewline
10 & 100.73 & 99.2356842105263 & 1.49431578947369 \tabularnewline
11 & 100.55 & 100.203684210526 & 0.346315789473681 \tabularnewline
12 & 102.15 & 100.785684210526 & 1.36431578947369 \tabularnewline
13 & 100.79 & 99.9694736842106 & 0.820526315789422 \tabularnewline
14 & 99.93 & 100.659684210526 & -0.72968421052631 \tabularnewline
15 & 100.03 & 100.871684210526 & -0.841684210526319 \tabularnewline
16 & 100.25 & 100.715684210526 & -0.465684210526320 \tabularnewline
17 & 99.6 & 100.957684210526 & -1.35768421052632 \tabularnewline
18 & 100.16 & 100.455684210526 & -0.295684210526320 \tabularnewline
19 & 100.49 & 100.421684210526 & 0.0683157894736786 \tabularnewline
20 & 99.72 & 100.127684210526 & -0.407684210526318 \tabularnewline
21 & 100.14 & 100.255684210526 & -0.115684210526316 \tabularnewline
22 & 98.48 & 99.2356842105263 & -0.755684210526314 \tabularnewline
23 & 100.38 & 100.203684210526 & 0.17631578947368 \tabularnewline
24 & 101.45 & 100.785684210526 & 0.664315789473686 \tabularnewline
25 & 98.42 & 99.9694736842106 & -1.54947368421058 \tabularnewline
26 & 98.6 & 100.659684210526 & -2.05968421052632 \tabularnewline
27 & 100.06 & 100.871684210526 & -0.811684210526318 \tabularnewline
28 & 98.62 & 100.715684210526 & -2.09568421052631 \tabularnewline
29 & 100.84 & 100.957684210526 & -0.117684210526315 \tabularnewline
30 & 100.02 & 100.455684210526 & -0.435684210526321 \tabularnewline
31 & 97.95 & 100.421684210526 & -2.47168421052631 \tabularnewline
32 & 98.32 & 100.127684210526 & -1.80768421052632 \tabularnewline
33 & 98.27 & 100.255684210526 & -1.98568421052632 \tabularnewline
34 & 97.22 & 99.2356842105263 & -2.01568421052632 \tabularnewline
35 & 99.28 & 100.203684210526 & -0.923684210526314 \tabularnewline
36 & 100.38 & 100.785684210526 & -0.405684210526321 \tabularnewline
37 & 99.02 & 99.9694736842106 & -0.949473684210588 \tabularnewline
38 & 100.32 & 100.659684210526 & -0.339684210526323 \tabularnewline
39 & 99.81 & 100.871684210526 & -1.06168421052632 \tabularnewline
40 & 100.6 & 100.715684210526 & -0.115684210526325 \tabularnewline
41 & 101.19 & 100.957684210526 & 0.232315789473680 \tabularnewline
42 & 100.47 & 100.455684210526 & 0.0143157894736818 \tabularnewline
43 & 101.77 & 100.421684210526 & 1.34831578947368 \tabularnewline
44 & 102.32 & 100.127684210526 & 2.19231578947368 \tabularnewline
45 & 102.39 & 100.255684210526 & 2.13431578947368 \tabularnewline
46 & 101.16 & 99.2356842105263 & 1.92431578947368 \tabularnewline
47 & 100.63 & 100.203684210526 & 0.42631578947368 \tabularnewline
48 & 101.48 & 100.785684210526 & 0.694315789473687 \tabularnewline
49 & 101.44 & 98.321052631579 & 3.11894736842100 \tabularnewline
50 & 100.09 & 99.0112631578947 & 1.07873684210528 \tabularnewline
51 & 100.7 & 99.2232631578947 & 1.47673684210527 \tabularnewline
52 & 100.78 & 99.0672631578947 & 1.71273684210527 \tabularnewline
53 & 99.81 & 99.3092631578947 & 0.500736842105274 \tabularnewline
54 & 98.45 & 98.8072631578947 & -0.357263157894725 \tabularnewline
55 & 98.49 & 98.7732631578947 & -0.283263157894732 \tabularnewline
56 & 97.48 & 98.4792631578947 & -0.999263157894724 \tabularnewline
57 & 97.91 & 98.6072631578947 & -0.697263157894731 \tabularnewline
58 & 96.94 & 97.5872631578947 & -0.647263157894732 \tabularnewline
59 & 98.53 & 98.5552631578947 & -0.0252631578947256 \tabularnewline
60 & 96.82 & 99.1372631578947 & -2.31726315789473 \tabularnewline
61 & 95.76 & 98.321052631579 & -2.56105263157899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&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]101.09[/C][C]99.9694736842103[/C][C]1.12052631578974[/C][/ROW]
[ROW][C]2[/C][C]102.71[/C][C]100.659684210526[/C][C]2.05031578947367[/C][/ROW]
[ROW][C]3[/C][C]102.11[/C][C]100.871684210526[/C][C]1.23831578947368[/C][/ROW]
[ROW][C]4[/C][C]101.68[/C][C]100.715684210526[/C][C]0.964315789473686[/C][/ROW]
[ROW][C]5[/C][C]101.7[/C][C]100.957684210526[/C][C]0.742315789473685[/C][/ROW]
[ROW][C]6[/C][C]101.53[/C][C]100.455684210526[/C][C]1.07431578947369[/C][/ROW]
[ROW][C]7[/C][C]101.76[/C][C]100.421684210526[/C][C]1.33831578947369[/C][/ROW]
[ROW][C]8[/C][C]101.15[/C][C]100.127684210526[/C][C]1.02231578947369[/C][/ROW]
[ROW][C]9[/C][C]100.92[/C][C]100.255684210526[/C][C]0.664315789473684[/C][/ROW]
[ROW][C]10[/C][C]100.73[/C][C]99.2356842105263[/C][C]1.49431578947369[/C][/ROW]
[ROW][C]11[/C][C]100.55[/C][C]100.203684210526[/C][C]0.346315789473681[/C][/ROW]
[ROW][C]12[/C][C]102.15[/C][C]100.785684210526[/C][C]1.36431578947369[/C][/ROW]
[ROW][C]13[/C][C]100.79[/C][C]99.9694736842106[/C][C]0.820526315789422[/C][/ROW]
[ROW][C]14[/C][C]99.93[/C][C]100.659684210526[/C][C]-0.72968421052631[/C][/ROW]
[ROW][C]15[/C][C]100.03[/C][C]100.871684210526[/C][C]-0.841684210526319[/C][/ROW]
[ROW][C]16[/C][C]100.25[/C][C]100.715684210526[/C][C]-0.465684210526320[/C][/ROW]
[ROW][C]17[/C][C]99.6[/C][C]100.957684210526[/C][C]-1.35768421052632[/C][/ROW]
[ROW][C]18[/C][C]100.16[/C][C]100.455684210526[/C][C]-0.295684210526320[/C][/ROW]
[ROW][C]19[/C][C]100.49[/C][C]100.421684210526[/C][C]0.0683157894736786[/C][/ROW]
[ROW][C]20[/C][C]99.72[/C][C]100.127684210526[/C][C]-0.407684210526318[/C][/ROW]
[ROW][C]21[/C][C]100.14[/C][C]100.255684210526[/C][C]-0.115684210526316[/C][/ROW]
[ROW][C]22[/C][C]98.48[/C][C]99.2356842105263[/C][C]-0.755684210526314[/C][/ROW]
[ROW][C]23[/C][C]100.38[/C][C]100.203684210526[/C][C]0.17631578947368[/C][/ROW]
[ROW][C]24[/C][C]101.45[/C][C]100.785684210526[/C][C]0.664315789473686[/C][/ROW]
[ROW][C]25[/C][C]98.42[/C][C]99.9694736842106[/C][C]-1.54947368421058[/C][/ROW]
[ROW][C]26[/C][C]98.6[/C][C]100.659684210526[/C][C]-2.05968421052632[/C][/ROW]
[ROW][C]27[/C][C]100.06[/C][C]100.871684210526[/C][C]-0.811684210526318[/C][/ROW]
[ROW][C]28[/C][C]98.62[/C][C]100.715684210526[/C][C]-2.09568421052631[/C][/ROW]
[ROW][C]29[/C][C]100.84[/C][C]100.957684210526[/C][C]-0.117684210526315[/C][/ROW]
[ROW][C]30[/C][C]100.02[/C][C]100.455684210526[/C][C]-0.435684210526321[/C][/ROW]
[ROW][C]31[/C][C]97.95[/C][C]100.421684210526[/C][C]-2.47168421052631[/C][/ROW]
[ROW][C]32[/C][C]98.32[/C][C]100.127684210526[/C][C]-1.80768421052632[/C][/ROW]
[ROW][C]33[/C][C]98.27[/C][C]100.255684210526[/C][C]-1.98568421052632[/C][/ROW]
[ROW][C]34[/C][C]97.22[/C][C]99.2356842105263[/C][C]-2.01568421052632[/C][/ROW]
[ROW][C]35[/C][C]99.28[/C][C]100.203684210526[/C][C]-0.923684210526314[/C][/ROW]
[ROW][C]36[/C][C]100.38[/C][C]100.785684210526[/C][C]-0.405684210526321[/C][/ROW]
[ROW][C]37[/C][C]99.02[/C][C]99.9694736842106[/C][C]-0.949473684210588[/C][/ROW]
[ROW][C]38[/C][C]100.32[/C][C]100.659684210526[/C][C]-0.339684210526323[/C][/ROW]
[ROW][C]39[/C][C]99.81[/C][C]100.871684210526[/C][C]-1.06168421052632[/C][/ROW]
[ROW][C]40[/C][C]100.6[/C][C]100.715684210526[/C][C]-0.115684210526325[/C][/ROW]
[ROW][C]41[/C][C]101.19[/C][C]100.957684210526[/C][C]0.232315789473680[/C][/ROW]
[ROW][C]42[/C][C]100.47[/C][C]100.455684210526[/C][C]0.0143157894736818[/C][/ROW]
[ROW][C]43[/C][C]101.77[/C][C]100.421684210526[/C][C]1.34831578947368[/C][/ROW]
[ROW][C]44[/C][C]102.32[/C][C]100.127684210526[/C][C]2.19231578947368[/C][/ROW]
[ROW][C]45[/C][C]102.39[/C][C]100.255684210526[/C][C]2.13431578947368[/C][/ROW]
[ROW][C]46[/C][C]101.16[/C][C]99.2356842105263[/C][C]1.92431578947368[/C][/ROW]
[ROW][C]47[/C][C]100.63[/C][C]100.203684210526[/C][C]0.42631578947368[/C][/ROW]
[ROW][C]48[/C][C]101.48[/C][C]100.785684210526[/C][C]0.694315789473687[/C][/ROW]
[ROW][C]49[/C][C]101.44[/C][C]98.321052631579[/C][C]3.11894736842100[/C][/ROW]
[ROW][C]50[/C][C]100.09[/C][C]99.0112631578947[/C][C]1.07873684210528[/C][/ROW]
[ROW][C]51[/C][C]100.7[/C][C]99.2232631578947[/C][C]1.47673684210527[/C][/ROW]
[ROW][C]52[/C][C]100.78[/C][C]99.0672631578947[/C][C]1.71273684210527[/C][/ROW]
[ROW][C]53[/C][C]99.81[/C][C]99.3092631578947[/C][C]0.500736842105274[/C][/ROW]
[ROW][C]54[/C][C]98.45[/C][C]98.8072631578947[/C][C]-0.357263157894725[/C][/ROW]
[ROW][C]55[/C][C]98.49[/C][C]98.7732631578947[/C][C]-0.283263157894732[/C][/ROW]
[ROW][C]56[/C][C]97.48[/C][C]98.4792631578947[/C][C]-0.999263157894724[/C][/ROW]
[ROW][C]57[/C][C]97.91[/C][C]98.6072631578947[/C][C]-0.697263157894731[/C][/ROW]
[ROW][C]58[/C][C]96.94[/C][C]97.5872631578947[/C][C]-0.647263157894732[/C][/ROW]
[ROW][C]59[/C][C]98.53[/C][C]98.5552631578947[/C][C]-0.0252631578947256[/C][/ROW]
[ROW][C]60[/C][C]96.82[/C][C]99.1372631578947[/C][C]-2.31726315789473[/C][/ROW]
[ROW][C]61[/C][C]95.76[/C][C]98.321052631579[/C][C]-2.56105263157899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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	101.09	99.9694736842103	1.12052631578974
2	102.71	100.659684210526	2.05031578947367
3	102.11	100.871684210526	1.23831578947368
4	101.68	100.715684210526	0.964315789473686
5	101.7	100.957684210526	0.742315789473685
6	101.53	100.455684210526	1.07431578947369
7	101.76	100.421684210526	1.33831578947369
8	101.15	100.127684210526	1.02231578947369
9	100.92	100.255684210526	0.664315789473684
10	100.73	99.2356842105263	1.49431578947369
11	100.55	100.203684210526	0.346315789473681
12	102.15	100.785684210526	1.36431578947369
13	100.79	99.9694736842106	0.820526315789422
14	99.93	100.659684210526	-0.72968421052631
15	100.03	100.871684210526	-0.841684210526319
16	100.25	100.715684210526	-0.465684210526320
17	99.6	100.957684210526	-1.35768421052632
18	100.16	100.455684210526	-0.295684210526320
19	100.49	100.421684210526	0.0683157894736786
20	99.72	100.127684210526	-0.407684210526318
21	100.14	100.255684210526	-0.115684210526316
22	98.48	99.2356842105263	-0.755684210526314
23	100.38	100.203684210526	0.17631578947368
24	101.45	100.785684210526	0.664315789473686
25	98.42	99.9694736842106	-1.54947368421058
26	98.6	100.659684210526	-2.05968421052632
27	100.06	100.871684210526	-0.811684210526318
28	98.62	100.715684210526	-2.09568421052631
29	100.84	100.957684210526	-0.117684210526315
30	100.02	100.455684210526	-0.435684210526321
31	97.95	100.421684210526	-2.47168421052631
32	98.32	100.127684210526	-1.80768421052632
33	98.27	100.255684210526	-1.98568421052632
34	97.22	99.2356842105263	-2.01568421052632
35	99.28	100.203684210526	-0.923684210526314
36	100.38	100.785684210526	-0.405684210526321
37	99.02	99.9694736842106	-0.949473684210588
38	100.32	100.659684210526	-0.339684210526323
39	99.81	100.871684210526	-1.06168421052632
40	100.6	100.715684210526	-0.115684210526325
41	101.19	100.957684210526	0.232315789473680
42	100.47	100.455684210526	0.0143157894736818
43	101.77	100.421684210526	1.34831578947368
44	102.32	100.127684210526	2.19231578947368
45	102.39	100.255684210526	2.13431578947368
46	101.16	99.2356842105263	1.92431578947368
47	100.63	100.203684210526	0.42631578947368
48	101.48	100.785684210526	0.694315789473687
49	101.44	98.321052631579	3.11894736842100
50	100.09	99.0112631578947	1.07873684210528
51	100.7	99.2232631578947	1.47673684210527
52	100.78	99.0672631578947	1.71273684210527
53	99.81	99.3092631578947	0.500736842105274
54	98.45	98.8072631578947	-0.357263157894725
55	98.49	98.7732631578947	-0.283263157894732
56	97.48	98.4792631578947	-0.999263157894724
57	97.91	98.6072631578947	-0.697263157894731
58	96.94	97.5872631578947	-0.647263157894732
59	98.53	98.5552631578947	-0.0252631578947256
60	96.82	99.1372631578947	-2.31726315789473
61	95.76	98.321052631579	-2.56105263157899

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.59255879106684	0.81488241786632	0.40744120893316
17	0.560863756829613	0.878272486340774	0.439136243170387
18	0.45803912230002	0.91607824460004	0.54196087769998
19	0.363268014783922	0.726536029567844	0.636731985216078
20	0.289604549678118	0.579209099356236	0.710395450321882
21	0.201944009022416	0.403888018044832	0.798055990977584
22	0.200251351583034	0.400502703166067	0.799748648416966
23	0.129759806769463	0.259519613538926	0.870240193230537
24	0.0890528125618273	0.178105625123655	0.910947187438173
25	0.121439802336477	0.242879604672953	0.878560197663523
26	0.177435088965266	0.354870177930531	0.822564911034734
27	0.132064928504199	0.264129857008397	0.867935071495801
28	0.171539903257169	0.343079806514338	0.828460096742831
29	0.116420674902892	0.232841349805785	0.883579325097108
30	0.0793032474405708	0.158606494881142	0.92069675255943
31	0.150787487952337	0.301574975904674	0.849212512047663
32	0.168152856542912	0.336305713085823	0.831847143457088
33	0.208549085640287	0.417098171280575	0.791450914359713
34	0.264837282839322	0.529674565678644	0.735162717160678
35	0.219552695842214	0.439105391684428	0.780447304157786
36	0.166608264982316	0.333216529964632	0.833391735017684
37	0.142655269878261	0.285310539756523	0.857344730121739
38	0.117164884064768	0.234329768129536	0.882835115935232
39	0.155198953314115	0.31039790662823	0.844801046685885
40	0.191936984021553	0.383873968043105	0.808063015978447
41	0.167674617453484	0.335349234906969	0.832325382546516
42	0.129910812003776	0.259821624007552	0.870089187996224
43	0.0882041088964039	0.176408217792808	0.911795891103596
44	0.0654675542858985	0.130935108571797	0.934532445714101
45	0.0415976913344129	0.0831953826688259	0.958402308665587

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.59255879106684 & 0.81488241786632 & 0.40744120893316 \tabularnewline
17 & 0.560863756829613 & 0.878272486340774 & 0.439136243170387 \tabularnewline
18 & 0.45803912230002 & 0.91607824460004 & 0.54196087769998 \tabularnewline
19 & 0.363268014783922 & 0.726536029567844 & 0.636731985216078 \tabularnewline
20 & 0.289604549678118 & 0.579209099356236 & 0.710395450321882 \tabularnewline
21 & 0.201944009022416 & 0.403888018044832 & 0.798055990977584 \tabularnewline
22 & 0.200251351583034 & 0.400502703166067 & 0.799748648416966 \tabularnewline
23 & 0.129759806769463 & 0.259519613538926 & 0.870240193230537 \tabularnewline
24 & 0.0890528125618273 & 0.178105625123655 & 0.910947187438173 \tabularnewline
25 & 0.121439802336477 & 0.242879604672953 & 0.878560197663523 \tabularnewline
26 & 0.177435088965266 & 0.354870177930531 & 0.822564911034734 \tabularnewline
27 & 0.132064928504199 & 0.264129857008397 & 0.867935071495801 \tabularnewline
28 & 0.171539903257169 & 0.343079806514338 & 0.828460096742831 \tabularnewline
29 & 0.116420674902892 & 0.232841349805785 & 0.883579325097108 \tabularnewline
30 & 0.0793032474405708 & 0.158606494881142 & 0.92069675255943 \tabularnewline
31 & 0.150787487952337 & 0.301574975904674 & 0.849212512047663 \tabularnewline
32 & 0.168152856542912 & 0.336305713085823 & 0.831847143457088 \tabularnewline
33 & 0.208549085640287 & 0.417098171280575 & 0.791450914359713 \tabularnewline
34 & 0.264837282839322 & 0.529674565678644 & 0.735162717160678 \tabularnewline
35 & 0.219552695842214 & 0.439105391684428 & 0.780447304157786 \tabularnewline
36 & 0.166608264982316 & 0.333216529964632 & 0.833391735017684 \tabularnewline
37 & 0.142655269878261 & 0.285310539756523 & 0.857344730121739 \tabularnewline
38 & 0.117164884064768 & 0.234329768129536 & 0.882835115935232 \tabularnewline
39 & 0.155198953314115 & 0.31039790662823 & 0.844801046685885 \tabularnewline
40 & 0.191936984021553 & 0.383873968043105 & 0.808063015978447 \tabularnewline
41 & 0.167674617453484 & 0.335349234906969 & 0.832325382546516 \tabularnewline
42 & 0.129910812003776 & 0.259821624007552 & 0.870089187996224 \tabularnewline
43 & 0.0882041088964039 & 0.176408217792808 & 0.911795891103596 \tabularnewline
44 & 0.0654675542858985 & 0.130935108571797 & 0.934532445714101 \tabularnewline
45 & 0.0415976913344129 & 0.0831953826688259 & 0.958402308665587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&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]16[/C][C]0.59255879106684[/C][C]0.81488241786632[/C][C]0.40744120893316[/C][/ROW]
[ROW][C]17[/C][C]0.560863756829613[/C][C]0.878272486340774[/C][C]0.439136243170387[/C][/ROW]
[ROW][C]18[/C][C]0.45803912230002[/C][C]0.91607824460004[/C][C]0.54196087769998[/C][/ROW]
[ROW][C]19[/C][C]0.363268014783922[/C][C]0.726536029567844[/C][C]0.636731985216078[/C][/ROW]
[ROW][C]20[/C][C]0.289604549678118[/C][C]0.579209099356236[/C][C]0.710395450321882[/C][/ROW]
[ROW][C]21[/C][C]0.201944009022416[/C][C]0.403888018044832[/C][C]0.798055990977584[/C][/ROW]
[ROW][C]22[/C][C]0.200251351583034[/C][C]0.400502703166067[/C][C]0.799748648416966[/C][/ROW]
[ROW][C]23[/C][C]0.129759806769463[/C][C]0.259519613538926[/C][C]0.870240193230537[/C][/ROW]
[ROW][C]24[/C][C]0.0890528125618273[/C][C]0.178105625123655[/C][C]0.910947187438173[/C][/ROW]
[ROW][C]25[/C][C]0.121439802336477[/C][C]0.242879604672953[/C][C]0.878560197663523[/C][/ROW]
[ROW][C]26[/C][C]0.177435088965266[/C][C]0.354870177930531[/C][C]0.822564911034734[/C][/ROW]
[ROW][C]27[/C][C]0.132064928504199[/C][C]0.264129857008397[/C][C]0.867935071495801[/C][/ROW]
[ROW][C]28[/C][C]0.171539903257169[/C][C]0.343079806514338[/C][C]0.828460096742831[/C][/ROW]
[ROW][C]29[/C][C]0.116420674902892[/C][C]0.232841349805785[/C][C]0.883579325097108[/C][/ROW]
[ROW][C]30[/C][C]0.0793032474405708[/C][C]0.158606494881142[/C][C]0.92069675255943[/C][/ROW]
[ROW][C]31[/C][C]0.150787487952337[/C][C]0.301574975904674[/C][C]0.849212512047663[/C][/ROW]
[ROW][C]32[/C][C]0.168152856542912[/C][C]0.336305713085823[/C][C]0.831847143457088[/C][/ROW]
[ROW][C]33[/C][C]0.208549085640287[/C][C]0.417098171280575[/C][C]0.791450914359713[/C][/ROW]
[ROW][C]34[/C][C]0.264837282839322[/C][C]0.529674565678644[/C][C]0.735162717160678[/C][/ROW]
[ROW][C]35[/C][C]0.219552695842214[/C][C]0.439105391684428[/C][C]0.780447304157786[/C][/ROW]
[ROW][C]36[/C][C]0.166608264982316[/C][C]0.333216529964632[/C][C]0.833391735017684[/C][/ROW]
[ROW][C]37[/C][C]0.142655269878261[/C][C]0.285310539756523[/C][C]0.857344730121739[/C][/ROW]
[ROW][C]38[/C][C]0.117164884064768[/C][C]0.234329768129536[/C][C]0.882835115935232[/C][/ROW]
[ROW][C]39[/C][C]0.155198953314115[/C][C]0.31039790662823[/C][C]0.844801046685885[/C][/ROW]
[ROW][C]40[/C][C]0.191936984021553[/C][C]0.383873968043105[/C][C]0.808063015978447[/C][/ROW]
[ROW][C]41[/C][C]0.167674617453484[/C][C]0.335349234906969[/C][C]0.832325382546516[/C][/ROW]
[ROW][C]42[/C][C]0.129910812003776[/C][C]0.259821624007552[/C][C]0.870089187996224[/C][/ROW]
[ROW][C]43[/C][C]0.0882041088964039[/C][C]0.176408217792808[/C][C]0.911795891103596[/C][/ROW]
[ROW][C]44[/C][C]0.0654675542858985[/C][C]0.130935108571797[/C][C]0.934532445714101[/C][/ROW]
[ROW][C]45[/C][C]0.0415976913344129[/C][C]0.0831953826688259[/C][C]0.958402308665587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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
16	0.59255879106684	0.81488241786632	0.40744120893316
17	0.560863756829613	0.878272486340774	0.439136243170387
18	0.45803912230002	0.91607824460004	0.54196087769998
19	0.363268014783922	0.726536029567844	0.636731985216078
20	0.289604549678118	0.579209099356236	0.710395450321882
21	0.201944009022416	0.403888018044832	0.798055990977584
22	0.200251351583034	0.400502703166067	0.799748648416966
23	0.129759806769463	0.259519613538926	0.870240193230537
24	0.0890528125618273	0.178105625123655	0.910947187438173
25	0.121439802336477	0.242879604672953	0.878560197663523
26	0.177435088965266	0.354870177930531	0.822564911034734
27	0.132064928504199	0.264129857008397	0.867935071495801
28	0.171539903257169	0.343079806514338	0.828460096742831
29	0.116420674902892	0.232841349805785	0.883579325097108
30	0.0793032474405708	0.158606494881142	0.92069675255943
31	0.150787487952337	0.301574975904674	0.849212512047663
32	0.168152856542912	0.336305713085823	0.831847143457088
33	0.208549085640287	0.417098171280575	0.791450914359713
34	0.264837282839322	0.529674565678644	0.735162717160678
35	0.219552695842214	0.439105391684428	0.780447304157786
36	0.166608264982316	0.333216529964632	0.833391735017684
37	0.142655269878261	0.285310539756523	0.857344730121739
38	0.117164884064768	0.234329768129536	0.882835115935232
39	0.155198953314115	0.31039790662823	0.844801046685885
40	0.191936984021553	0.383873968043105	0.808063015978447
41	0.167674617453484	0.335349234906969	0.832325382546516
42	0.129910812003776	0.259821624007552	0.870089187996224
43	0.0882041088964039	0.176408217792808	0.911795891103596
44	0.0654675542858985	0.130935108571797	0.934532445714101
45	0.0415976913344129	0.0831953826688259	0.958402308665587

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	1	0.0333333333333333	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 & 1 & 0.0333333333333333 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69693&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]1[/C][C]0.0333333333333333[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69693&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69693&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	1	0.0333333333333333	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

PNG link

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code