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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 14 Dec 2010 21:27:06 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292361958306fov635e81a6y.htm/, Retrieved Thu, 02 May 2024 23:27:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110215, Retrieved Thu, 02 May 2024 23:27:00 +0000

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-     [Multiple Regression] [] [2010-12-05 18:56:24] [b98453cac15ba1066b407e146608df68]
-   PD  [Multiple Regression] [Blog 3] [2010-12-14 17:14:39] [1aa8d85d6b335d32b1f6be940e33a166]
-    D      [Multiple Regression] [Multiple regressi...] [2010-12-14 21:27:06] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]

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Dataseries X:

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3.18    0.22    6.62    3.64
3.14    0.22    6.56    3.62
3.02    0.23    6.59    3.61
3.02    0.24    6.56    3.6
3.03    0.25    6.57    3.6
3.04    0.25    6.62    3.63
3.09    0.24    6.69    3.59
3.06    0.24    6.69    3.55
3.06    0.22    6.64    3.54
3.09    0.21    6.6    3.53
3.11    0.21    6.66    3.53
3.1    0.21    6.62    3.53
3.09    0.2    6.64    3.52
3.19    0.2    6.64    3.52
3.22    0.2    6.73    3.48
3.22    0.2    6.73    3.49
3.25    0.2    6.69    3.47
3.25    0.2    6.78    3.46
3.27    0.2    6.77    3.4
3.28    0.2    6.8    3.36
3.24    0.2    6.8    3.3
3.23    0.2    6.74    3.28
3.2    0.2    6.84    3.28
3.19    0.2    6.83    3.24
3.23    0.2    6.89    3.23
3.19    0.2    6.9    3.2
3.16    0.2    6.86    3.15
3.11    0.2    6.78    3.1
3.11    0.2    6.82    3.07
3.07    0.2    6.81    3.03
3.05    0.21    6.81    2.96
3    0.2    6.78    2.88
2.95    0.2    6.79    2.83
2.9    0.19    6.83    2.8
2.88    0.18    6.9    2.8
2.9    0.18    6.79    2.79
2.89    0.17    6.88    2.79
2.89    0.17    6.89    2.78
2.91    0.17    6.91    2.79
2.9    0.17    6.93    2.78
2.9    0.17    6.89    2.78
2.88    0.16    7    2.74
2.83    0.16    7.01    2.71
2.8    0.16    7.15    2.69
2.77    0.16    7.25    2.68
2.78    0.16    7.33    2.68
2.75    0.16    7.39    2.68
2.74    0.15    7.38    2.69
2.73    0.15    7.38    2.68
2.69    0.15    7.35    2.69
2.67    0.15    7.38    2.68
2.66    0.15    7.34    2.68
2.67    0.16    7.25    2.63
2.65    0.15    7.07    2.58
2.64    0.15    6.73    2.52
2.63    0.15    6.56    2.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	10 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 10 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&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]10 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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	10 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
Mayonaise[t] = + 2.47865060894444 -0.465444129700099Eieren[t] -0.0988998564557219Olijfolie[t] + 0.413491668082886Mosterd[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Mayonaise[t] =  +  2.47865060894444 -0.465444129700099Eieren[t] -0.0988998564557219Olijfolie[t] +  0.413491668082886Mosterd[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Mayonaise[t] =  +  2.47865060894444 -0.465444129700099Eieren[t] -0.0988998564557219Olijfolie[t] +  0.413491668082886Mosterd[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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
Mayonaise[t] = + 2.47865060894444 -0.465444129700099Eieren[t] -0.0988998564557219Olijfolie[t] + 0.413491668082886Mosterd[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)	2.47865060894444	0.818087	3.0298	0.003806	0.001903
Eieren	-0.465444129700099	1.326341	-0.3509	0.727064	0.363532
Olijfolie	-0.0988998564557219	0.098111	-1.008	0.318104	0.159052
Mosterd	0.413491668082886	0.091171	4.5354	3.4e-05	1.7e-05

\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) & 2.47865060894444 & 0.818087 & 3.0298 & 0.003806 & 0.001903 \tabularnewline
Eieren & -0.465444129700099 & 1.326341 & -0.3509 & 0.727064 & 0.363532 \tabularnewline
Olijfolie & -0.0988998564557219 & 0.098111 & -1.008 & 0.318104 & 0.159052 \tabularnewline
Mosterd & 0.413491668082886 & 0.091171 & 4.5354 & 3.4e-05 & 1.7e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&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]2.47865060894444[/C][C]0.818087[/C][C]3.0298[/C][C]0.003806[/C][C]0.001903[/C][/ROW]
[ROW][C]Eieren[/C][C]-0.465444129700099[/C][C]1.326341[/C][C]-0.3509[/C][C]0.727064[/C][C]0.363532[/C][/ROW]
[ROW][C]Olijfolie[/C][C]-0.0988998564557219[/C][C]0.098111[/C][C]-1.008[/C][C]0.318104[/C][C]0.159052[/C][/ROW]
[ROW][C]Mosterd[/C][C]0.413491668082886[/C][C]0.091171[/C][C]4.5354[/C][C]3.4e-05[/C][C]1.7e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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)	2.47865060894444	0.818087	3.0298	0.003806	0.001903
Eieren	-0.465444129700099	1.326341	-0.3509	0.727064	0.363532
Olijfolie	-0.0988998564557219	0.098111	-1.008	0.318104	0.159052
Mosterd	0.413491668082886	0.091171	4.5354	3.4e-05	1.7e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.831522318599948
R-squared	0.691429366329834
Adjusted R-squared	0.673627214387324
F-TEST (value)	38.8396508783175
F-TEST (DF numerator)	3
F-TEST (DF denominator)	52
p-value	2.58681964737661e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.112734946676432
Sum Squared Residuals	0.660876746511169

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.831522318599948 \tabularnewline
R-squared & 0.691429366329834 \tabularnewline
Adjusted R-squared & 0.673627214387324 \tabularnewline
F-TEST (value) & 38.8396508783175 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 52 \tabularnewline
p-value & 2.58681964737661e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.112734946676432 \tabularnewline
Sum Squared Residuals & 0.660876746511169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.831522318599948[/C][/ROW]
[ROW][C]R-squared[/C][C]0.691429366329834[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.673627214387324[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]38.8396508783175[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]52[/C][/ROW]
[ROW][C]p-value[/C][C]2.58681964737661e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.112734946676432[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.660876746511169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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	0.831522318599948
R-squared	0.691429366329834
Adjusted R-squared	0.673627214387324
F-TEST (value)	38.8396508783175
F-TEST (DF numerator)	3
F-TEST (DF denominator)	52
p-value	2.58681964737661e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.112734946676432
Sum Squared Residuals	0.660876746511169

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	3.18	3.22664552249524	-0.0466455224952405
2	3.14	3.22430968052093	-0.08430968052093
3	3.02	3.21255332684943	-0.192553326849429
4	3.02	3.20673096456527	-0.186730964565271
5	3.03	3.20108752470371	-0.171087524703713
6	3.04	3.20854728192341	-0.168547281923413
7	3.09	3.1897390665452	-0.099739066545198
8	3.06	3.17319939982188	-0.113199399821882
9	3.06	3.18331835855784	-0.123318358557842
10	3.09	3.18779387743224	-0.0977938774322427
11	3.11	3.1818598860449	-0.0718598860448994
12	3.1	3.18581588030313	-0.085815880303128
13	3.09	3.18435740779019	-0.094357407790186
14	3.19	3.18435740779019	0.00564259220981405
15	3.22	3.15891675398586	0.0610832460141448
16	3.22	3.16305167066668	0.0569483293333158
17	3.25	3.15873783156326	0.0912621684367445
18	3.25	3.14570192780141	0.104298072198588
19	3.27	3.12188142628100	0.148118573719004
20	3.28	3.10237476386401	0.177625236135991
21	3.24	3.07756526377904	0.162434736220965
22	3.23	3.07522942180472	0.154770578195279
23	3.2	3.06533943615915	0.134660563840851
24	3.19	3.04978876800039	0.140211231999609
25	3.23	3.03971985993222	0.190280140067781
26	3.19	3.02632611132517	0.163673888674825
27	3.16	3.00960752217926	0.150392477820741
28	3.11	2.99684492729157	0.113155072708427
29	3.11	2.98048418299086	0.129515817009143
30	3.07	2.9649335148321	0.105066485167901
31	3.05	2.93133465676930	0.118665343230703
32	3	2.90587676031334	0.094123239686662
33	2.95	2.88421317834464	0.0657868216553636
34	2.9	2.87250687534092	0.0274931246590779
35	2.88	2.87023832668602	0.00976167331397747
36	2.9	2.87698239421532	0.0230176057846768
37	2.89	2.87273584843131	0.0172641515686910
38	2.89	2.86761193318592	0.0223880668140772
39	2.91	2.86976885273764	0.0402311472623627
40	2.9	2.86365593892769	0.0363440610723058
41	2.9	2.86761193318592	0.032388066814077
42	2.88	2.84484772354948	0.0351522764505207
43	2.83	2.83145397494244	-0.00145397494243526
44	2.8	2.80933816167698	-0.00933816167697668
45	2.77	2.79531325935058	-0.0253132593505756
46	2.78	2.78740127083412	-0.00740127083411803
47	2.75	2.78146727944677	-0.0314672794467746
48	2.74	2.79124563598916	-0.0512456359891613
49	2.73	2.78711071930833	-0.0571107193083328
50	2.69	2.79421263168283	-0.104212631682833
51	2.67	2.78711071930833	-0.117110719308333
52	2.66	2.79106671356656	-0.131066713566561
53	2.67	2.77463867594643	-0.104638675946431
54	2.65	2.77642050800132	-0.126420508001318
55	2.64	2.78523695911129	-0.14523695911129
56	2.63	2.79378010134711	-0.163780101347105

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.18 & 3.22664552249524 & -0.0466455224952405 \tabularnewline
2 & 3.14 & 3.22430968052093 & -0.08430968052093 \tabularnewline
3 & 3.02 & 3.21255332684943 & -0.192553326849429 \tabularnewline
4 & 3.02 & 3.20673096456527 & -0.186730964565271 \tabularnewline
5 & 3.03 & 3.20108752470371 & -0.171087524703713 \tabularnewline
6 & 3.04 & 3.20854728192341 & -0.168547281923413 \tabularnewline
7 & 3.09 & 3.1897390665452 & -0.099739066545198 \tabularnewline
8 & 3.06 & 3.17319939982188 & -0.113199399821882 \tabularnewline
9 & 3.06 & 3.18331835855784 & -0.123318358557842 \tabularnewline
10 & 3.09 & 3.18779387743224 & -0.0977938774322427 \tabularnewline
11 & 3.11 & 3.1818598860449 & -0.0718598860448994 \tabularnewline
12 & 3.1 & 3.18581588030313 & -0.085815880303128 \tabularnewline
13 & 3.09 & 3.18435740779019 & -0.094357407790186 \tabularnewline
14 & 3.19 & 3.18435740779019 & 0.00564259220981405 \tabularnewline
15 & 3.22 & 3.15891675398586 & 0.0610832460141448 \tabularnewline
16 & 3.22 & 3.16305167066668 & 0.0569483293333158 \tabularnewline
17 & 3.25 & 3.15873783156326 & 0.0912621684367445 \tabularnewline
18 & 3.25 & 3.14570192780141 & 0.104298072198588 \tabularnewline
19 & 3.27 & 3.12188142628100 & 0.148118573719004 \tabularnewline
20 & 3.28 & 3.10237476386401 & 0.177625236135991 \tabularnewline
21 & 3.24 & 3.07756526377904 & 0.162434736220965 \tabularnewline
22 & 3.23 & 3.07522942180472 & 0.154770578195279 \tabularnewline
23 & 3.2 & 3.06533943615915 & 0.134660563840851 \tabularnewline
24 & 3.19 & 3.04978876800039 & 0.140211231999609 \tabularnewline
25 & 3.23 & 3.03971985993222 & 0.190280140067781 \tabularnewline
26 & 3.19 & 3.02632611132517 & 0.163673888674825 \tabularnewline
27 & 3.16 & 3.00960752217926 & 0.150392477820741 \tabularnewline
28 & 3.11 & 2.99684492729157 & 0.113155072708427 \tabularnewline
29 & 3.11 & 2.98048418299086 & 0.129515817009143 \tabularnewline
30 & 3.07 & 2.9649335148321 & 0.105066485167901 \tabularnewline
31 & 3.05 & 2.93133465676930 & 0.118665343230703 \tabularnewline
32 & 3 & 2.90587676031334 & 0.094123239686662 \tabularnewline
33 & 2.95 & 2.88421317834464 & 0.0657868216553636 \tabularnewline
34 & 2.9 & 2.87250687534092 & 0.0274931246590779 \tabularnewline
35 & 2.88 & 2.87023832668602 & 0.00976167331397747 \tabularnewline
36 & 2.9 & 2.87698239421532 & 0.0230176057846768 \tabularnewline
37 & 2.89 & 2.87273584843131 & 0.0172641515686910 \tabularnewline
38 & 2.89 & 2.86761193318592 & 0.0223880668140772 \tabularnewline
39 & 2.91 & 2.86976885273764 & 0.0402311472623627 \tabularnewline
40 & 2.9 & 2.86365593892769 & 0.0363440610723058 \tabularnewline
41 & 2.9 & 2.86761193318592 & 0.032388066814077 \tabularnewline
42 & 2.88 & 2.84484772354948 & 0.0351522764505207 \tabularnewline
43 & 2.83 & 2.83145397494244 & -0.00145397494243526 \tabularnewline
44 & 2.8 & 2.80933816167698 & -0.00933816167697668 \tabularnewline
45 & 2.77 & 2.79531325935058 & -0.0253132593505756 \tabularnewline
46 & 2.78 & 2.78740127083412 & -0.00740127083411803 \tabularnewline
47 & 2.75 & 2.78146727944677 & -0.0314672794467746 \tabularnewline
48 & 2.74 & 2.79124563598916 & -0.0512456359891613 \tabularnewline
49 & 2.73 & 2.78711071930833 & -0.0571107193083328 \tabularnewline
50 & 2.69 & 2.79421263168283 & -0.104212631682833 \tabularnewline
51 & 2.67 & 2.78711071930833 & -0.117110719308333 \tabularnewline
52 & 2.66 & 2.79106671356656 & -0.131066713566561 \tabularnewline
53 & 2.67 & 2.77463867594643 & -0.104638675946431 \tabularnewline
54 & 2.65 & 2.77642050800132 & -0.126420508001318 \tabularnewline
55 & 2.64 & 2.78523695911129 & -0.14523695911129 \tabularnewline
56 & 2.63 & 2.79378010134711 & -0.163780101347105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&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]3.18[/C][C]3.22664552249524[/C][C]-0.0466455224952405[/C][/ROW]
[ROW][C]2[/C][C]3.14[/C][C]3.22430968052093[/C][C]-0.08430968052093[/C][/ROW]
[ROW][C]3[/C][C]3.02[/C][C]3.21255332684943[/C][C]-0.192553326849429[/C][/ROW]
[ROW][C]4[/C][C]3.02[/C][C]3.20673096456527[/C][C]-0.186730964565271[/C][/ROW]
[ROW][C]5[/C][C]3.03[/C][C]3.20108752470371[/C][C]-0.171087524703713[/C][/ROW]
[ROW][C]6[/C][C]3.04[/C][C]3.20854728192341[/C][C]-0.168547281923413[/C][/ROW]
[ROW][C]7[/C][C]3.09[/C][C]3.1897390665452[/C][C]-0.099739066545198[/C][/ROW]
[ROW][C]8[/C][C]3.06[/C][C]3.17319939982188[/C][C]-0.113199399821882[/C][/ROW]
[ROW][C]9[/C][C]3.06[/C][C]3.18331835855784[/C][C]-0.123318358557842[/C][/ROW]
[ROW][C]10[/C][C]3.09[/C][C]3.18779387743224[/C][C]-0.0977938774322427[/C][/ROW]
[ROW][C]11[/C][C]3.11[/C][C]3.1818598860449[/C][C]-0.0718598860448994[/C][/ROW]
[ROW][C]12[/C][C]3.1[/C][C]3.18581588030313[/C][C]-0.085815880303128[/C][/ROW]
[ROW][C]13[/C][C]3.09[/C][C]3.18435740779019[/C][C]-0.094357407790186[/C][/ROW]
[ROW][C]14[/C][C]3.19[/C][C]3.18435740779019[/C][C]0.00564259220981405[/C][/ROW]
[ROW][C]15[/C][C]3.22[/C][C]3.15891675398586[/C][C]0.0610832460141448[/C][/ROW]
[ROW][C]16[/C][C]3.22[/C][C]3.16305167066668[/C][C]0.0569483293333158[/C][/ROW]
[ROW][C]17[/C][C]3.25[/C][C]3.15873783156326[/C][C]0.0912621684367445[/C][/ROW]
[ROW][C]18[/C][C]3.25[/C][C]3.14570192780141[/C][C]0.104298072198588[/C][/ROW]
[ROW][C]19[/C][C]3.27[/C][C]3.12188142628100[/C][C]0.148118573719004[/C][/ROW]
[ROW][C]20[/C][C]3.28[/C][C]3.10237476386401[/C][C]0.177625236135991[/C][/ROW]
[ROW][C]21[/C][C]3.24[/C][C]3.07756526377904[/C][C]0.162434736220965[/C][/ROW]
[ROW][C]22[/C][C]3.23[/C][C]3.07522942180472[/C][C]0.154770578195279[/C][/ROW]
[ROW][C]23[/C][C]3.2[/C][C]3.06533943615915[/C][C]0.134660563840851[/C][/ROW]
[ROW][C]24[/C][C]3.19[/C][C]3.04978876800039[/C][C]0.140211231999609[/C][/ROW]
[ROW][C]25[/C][C]3.23[/C][C]3.03971985993222[/C][C]0.190280140067781[/C][/ROW]
[ROW][C]26[/C][C]3.19[/C][C]3.02632611132517[/C][C]0.163673888674825[/C][/ROW]
[ROW][C]27[/C][C]3.16[/C][C]3.00960752217926[/C][C]0.150392477820741[/C][/ROW]
[ROW][C]28[/C][C]3.11[/C][C]2.99684492729157[/C][C]0.113155072708427[/C][/ROW]
[ROW][C]29[/C][C]3.11[/C][C]2.98048418299086[/C][C]0.129515817009143[/C][/ROW]
[ROW][C]30[/C][C]3.07[/C][C]2.9649335148321[/C][C]0.105066485167901[/C][/ROW]
[ROW][C]31[/C][C]3.05[/C][C]2.93133465676930[/C][C]0.118665343230703[/C][/ROW]
[ROW][C]32[/C][C]3[/C][C]2.90587676031334[/C][C]0.094123239686662[/C][/ROW]
[ROW][C]33[/C][C]2.95[/C][C]2.88421317834464[/C][C]0.0657868216553636[/C][/ROW]
[ROW][C]34[/C][C]2.9[/C][C]2.87250687534092[/C][C]0.0274931246590779[/C][/ROW]
[ROW][C]35[/C][C]2.88[/C][C]2.87023832668602[/C][C]0.00976167331397747[/C][/ROW]
[ROW][C]36[/C][C]2.9[/C][C]2.87698239421532[/C][C]0.0230176057846768[/C][/ROW]
[ROW][C]37[/C][C]2.89[/C][C]2.87273584843131[/C][C]0.0172641515686910[/C][/ROW]
[ROW][C]38[/C][C]2.89[/C][C]2.86761193318592[/C][C]0.0223880668140772[/C][/ROW]
[ROW][C]39[/C][C]2.91[/C][C]2.86976885273764[/C][C]0.0402311472623627[/C][/ROW]
[ROW][C]40[/C][C]2.9[/C][C]2.86365593892769[/C][C]0.0363440610723058[/C][/ROW]
[ROW][C]41[/C][C]2.9[/C][C]2.86761193318592[/C][C]0.032388066814077[/C][/ROW]
[ROW][C]42[/C][C]2.88[/C][C]2.84484772354948[/C][C]0.0351522764505207[/C][/ROW]
[ROW][C]43[/C][C]2.83[/C][C]2.83145397494244[/C][C]-0.00145397494243526[/C][/ROW]
[ROW][C]44[/C][C]2.8[/C][C]2.80933816167698[/C][C]-0.00933816167697668[/C][/ROW]
[ROW][C]45[/C][C]2.77[/C][C]2.79531325935058[/C][C]-0.0253132593505756[/C][/ROW]
[ROW][C]46[/C][C]2.78[/C][C]2.78740127083412[/C][C]-0.00740127083411803[/C][/ROW]
[ROW][C]47[/C][C]2.75[/C][C]2.78146727944677[/C][C]-0.0314672794467746[/C][/ROW]
[ROW][C]48[/C][C]2.74[/C][C]2.79124563598916[/C][C]-0.0512456359891613[/C][/ROW]
[ROW][C]49[/C][C]2.73[/C][C]2.78711071930833[/C][C]-0.0571107193083328[/C][/ROW]
[ROW][C]50[/C][C]2.69[/C][C]2.79421263168283[/C][C]-0.104212631682833[/C][/ROW]
[ROW][C]51[/C][C]2.67[/C][C]2.78711071930833[/C][C]-0.117110719308333[/C][/ROW]
[ROW][C]52[/C][C]2.66[/C][C]2.79106671356656[/C][C]-0.131066713566561[/C][/ROW]
[ROW][C]53[/C][C]2.67[/C][C]2.77463867594643[/C][C]-0.104638675946431[/C][/ROW]
[ROW][C]54[/C][C]2.65[/C][C]2.77642050800132[/C][C]-0.126420508001318[/C][/ROW]
[ROW][C]55[/C][C]2.64[/C][C]2.78523695911129[/C][C]-0.14523695911129[/C][/ROW]
[ROW][C]56[/C][C]2.63[/C][C]2.79378010134711[/C][C]-0.163780101347105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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	3.18	3.22664552249524	-0.0466455224952405
2	3.14	3.22430968052093	-0.08430968052093
3	3.02	3.21255332684943	-0.192553326849429
4	3.02	3.20673096456527	-0.186730964565271
5	3.03	3.20108752470371	-0.171087524703713
6	3.04	3.20854728192341	-0.168547281923413
7	3.09	3.1897390665452	-0.099739066545198
8	3.06	3.17319939982188	-0.113199399821882
9	3.06	3.18331835855784	-0.123318358557842
10	3.09	3.18779387743224	-0.0977938774322427
11	3.11	3.1818598860449	-0.0718598860448994
12	3.1	3.18581588030313	-0.085815880303128
13	3.09	3.18435740779019	-0.094357407790186
14	3.19	3.18435740779019	0.00564259220981405
15	3.22	3.15891675398586	0.0610832460141448
16	3.22	3.16305167066668	0.0569483293333158
17	3.25	3.15873783156326	0.0912621684367445
18	3.25	3.14570192780141	0.104298072198588
19	3.27	3.12188142628100	0.148118573719004
20	3.28	3.10237476386401	0.177625236135991
21	3.24	3.07756526377904	0.162434736220965
22	3.23	3.07522942180472	0.154770578195279
23	3.2	3.06533943615915	0.134660563840851
24	3.19	3.04978876800039	0.140211231999609
25	3.23	3.03971985993222	0.190280140067781
26	3.19	3.02632611132517	0.163673888674825
27	3.16	3.00960752217926	0.150392477820741
28	3.11	2.99684492729157	0.113155072708427
29	3.11	2.98048418299086	0.129515817009143
30	3.07	2.9649335148321	0.105066485167901
31	3.05	2.93133465676930	0.118665343230703
32	3	2.90587676031334	0.094123239686662
33	2.95	2.88421317834464	0.0657868216553636
34	2.9	2.87250687534092	0.0274931246590779
35	2.88	2.87023832668602	0.00976167331397747
36	2.9	2.87698239421532	0.0230176057846768
37	2.89	2.87273584843131	0.0172641515686910
38	2.89	2.86761193318592	0.0223880668140772
39	2.91	2.86976885273764	0.0402311472623627
40	2.9	2.86365593892769	0.0363440610723058
41	2.9	2.86761193318592	0.032388066814077
42	2.88	2.84484772354948	0.0351522764505207
43	2.83	2.83145397494244	-0.00145397494243526
44	2.8	2.80933816167698	-0.00933816167697668
45	2.77	2.79531325935058	-0.0253132593505756
46	2.78	2.78740127083412	-0.00740127083411803
47	2.75	2.78146727944677	-0.0314672794467746
48	2.74	2.79124563598916	-0.0512456359891613
49	2.73	2.78711071930833	-0.0571107193083328
50	2.69	2.79421263168283	-0.104212631682833
51	2.67	2.78711071930833	-0.117110719308333
52	2.66	2.79106671356656	-0.131066713566561
53	2.67	2.77463867594643	-0.104638675946431
54	2.65	2.77642050800132	-0.126420508001318
55	2.64	2.78523695911129	-0.14523695911129
56	2.63	2.79378010134711	-0.163780101347105

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.146002669927434	0.292005339854868	0.853997330072566
8	0.097144699141351	0.194289398282702	0.90285530085865
9	0.0741305099985305	0.148261019997061	0.92586949000147
10	0.0510292958698748	0.102058591739750	0.948970704130125
11	0.038082401495465	0.07616480299093	0.961917598504535
12	0.0468802807533737	0.0937605615067475	0.953119719246626
13	0.110268538791776	0.220537077583553	0.889731461208224
14	0.314506075558127	0.629012151116253	0.685493924441873
15	0.47329071588329	0.94658143176658	0.52670928411671
16	0.564994284914115	0.87001143017177	0.435005715085885
17	0.860726074682	0.278547850636001	0.139273925318000
18	0.894628035440256	0.210743929119487	0.105371964559743
19	0.926734001824748	0.146531996350503	0.0732659981752517
20	0.911928708075615	0.17614258384877	0.088071291924385
21	0.874523131408735	0.250953737182529	0.125476868591265
22	0.844550301916743	0.310899396166513	0.155449698083257
23	0.89589788953775	0.208204220924500	0.104102110462250
24	0.906878235103624	0.186243529792753	0.0931217648963763
25	0.879210853963584	0.241578292072832	0.120789146036416
26	0.879842459540326	0.240315080919347	0.120157540459674
27	0.857803492874558	0.284393014250884	0.142196507125442
28	0.86129523706117	0.277409525877661	0.138704762938831
29	0.850565794663001	0.298868410673998	0.149434205336999
30	0.904574523511161	0.190850952977677	0.0954254764888386
31	0.888559355350757	0.222881289298486	0.111440644649243
32	0.847936142528735	0.304127714942530	0.152063857471265
33	0.818102736782469	0.363794526435062	0.181897263217531
34	0.922076759693822	0.155846480612355	0.0779232403061775
35	0.994173242352802	0.0116535152943963	0.00582675764719816
36	0.996027473743152	0.0079450525136965	0.00397252625684825
37	0.998171139001843	0.00365772199631354	0.00182886099815677
38	0.99853801125671	0.0029239774865818	0.0014619887432909
39	0.998275892840308	0.00344821431938471	0.00172410715969235
40	0.998158748145203	0.0036825037095944	0.0018412518547972
41	0.999234127982965	0.00153174403406991	0.000765872017034953
42	0.998954642482063	0.00209071503587427	0.00104535751793714
43	0.998522776923168	0.00295444615366455	0.00147722307683228
44	0.998148007205653	0.00370398558869442	0.00185199279434721
45	0.99659898908974	0.00680202182052002	0.00340101091026001
46	0.99485843189506	0.0102831362098816	0.00514156810494078
47	0.992097026108705	0.0158059477825902	0.00790297389129508
48	0.990611365310828	0.0187772693783448	0.00938863468917238
49	0.99791908209403	0.00416183581193943	0.00208091790596972

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 & 0.146002669927434 & 0.292005339854868 & 0.853997330072566 \tabularnewline
8 & 0.097144699141351 & 0.194289398282702 & 0.90285530085865 \tabularnewline
9 & 0.0741305099985305 & 0.148261019997061 & 0.92586949000147 \tabularnewline
10 & 0.0510292958698748 & 0.102058591739750 & 0.948970704130125 \tabularnewline
11 & 0.038082401495465 & 0.07616480299093 & 0.961917598504535 \tabularnewline
12 & 0.0468802807533737 & 0.0937605615067475 & 0.953119719246626 \tabularnewline
13 & 0.110268538791776 & 0.220537077583553 & 0.889731461208224 \tabularnewline
14 & 0.314506075558127 & 0.629012151116253 & 0.685493924441873 \tabularnewline
15 & 0.47329071588329 & 0.94658143176658 & 0.52670928411671 \tabularnewline
16 & 0.564994284914115 & 0.87001143017177 & 0.435005715085885 \tabularnewline
17 & 0.860726074682 & 0.278547850636001 & 0.139273925318000 \tabularnewline
18 & 0.894628035440256 & 0.210743929119487 & 0.105371964559743 \tabularnewline
19 & 0.926734001824748 & 0.146531996350503 & 0.0732659981752517 \tabularnewline
20 & 0.911928708075615 & 0.17614258384877 & 0.088071291924385 \tabularnewline
21 & 0.874523131408735 & 0.250953737182529 & 0.125476868591265 \tabularnewline
22 & 0.844550301916743 & 0.310899396166513 & 0.155449698083257 \tabularnewline
23 & 0.89589788953775 & 0.208204220924500 & 0.104102110462250 \tabularnewline
24 & 0.906878235103624 & 0.186243529792753 & 0.0931217648963763 \tabularnewline
25 & 0.879210853963584 & 0.241578292072832 & 0.120789146036416 \tabularnewline
26 & 0.879842459540326 & 0.240315080919347 & 0.120157540459674 \tabularnewline
27 & 0.857803492874558 & 0.284393014250884 & 0.142196507125442 \tabularnewline
28 & 0.86129523706117 & 0.277409525877661 & 0.138704762938831 \tabularnewline
29 & 0.850565794663001 & 0.298868410673998 & 0.149434205336999 \tabularnewline
30 & 0.904574523511161 & 0.190850952977677 & 0.0954254764888386 \tabularnewline
31 & 0.888559355350757 & 0.222881289298486 & 0.111440644649243 \tabularnewline
32 & 0.847936142528735 & 0.304127714942530 & 0.152063857471265 \tabularnewline
33 & 0.818102736782469 & 0.363794526435062 & 0.181897263217531 \tabularnewline
34 & 0.922076759693822 & 0.155846480612355 & 0.0779232403061775 \tabularnewline
35 & 0.994173242352802 & 0.0116535152943963 & 0.00582675764719816 \tabularnewline
36 & 0.996027473743152 & 0.0079450525136965 & 0.00397252625684825 \tabularnewline
37 & 0.998171139001843 & 0.00365772199631354 & 0.00182886099815677 \tabularnewline
38 & 0.99853801125671 & 0.0029239774865818 & 0.0014619887432909 \tabularnewline
39 & 0.998275892840308 & 0.00344821431938471 & 0.00172410715969235 \tabularnewline
40 & 0.998158748145203 & 0.0036825037095944 & 0.0018412518547972 \tabularnewline
41 & 0.999234127982965 & 0.00153174403406991 & 0.000765872017034953 \tabularnewline
42 & 0.998954642482063 & 0.00209071503587427 & 0.00104535751793714 \tabularnewline
43 & 0.998522776923168 & 0.00295444615366455 & 0.00147722307683228 \tabularnewline
44 & 0.998148007205653 & 0.00370398558869442 & 0.00185199279434721 \tabularnewline
45 & 0.99659898908974 & 0.00680202182052002 & 0.00340101091026001 \tabularnewline
46 & 0.99485843189506 & 0.0102831362098816 & 0.00514156810494078 \tabularnewline
47 & 0.992097026108705 & 0.0158059477825902 & 0.00790297389129508 \tabularnewline
48 & 0.990611365310828 & 0.0187772693783448 & 0.00938863468917238 \tabularnewline
49 & 0.99791908209403 & 0.00416183581193943 & 0.00208091790596972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&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]7[/C][C]0.146002669927434[/C][C]0.292005339854868[/C][C]0.853997330072566[/C][/ROW]
[ROW][C]8[/C][C]0.097144699141351[/C][C]0.194289398282702[/C][C]0.90285530085865[/C][/ROW]
[ROW][C]9[/C][C]0.0741305099985305[/C][C]0.148261019997061[/C][C]0.92586949000147[/C][/ROW]
[ROW][C]10[/C][C]0.0510292958698748[/C][C]0.102058591739750[/C][C]0.948970704130125[/C][/ROW]
[ROW][C]11[/C][C]0.038082401495465[/C][C]0.07616480299093[/C][C]0.961917598504535[/C][/ROW]
[ROW][C]12[/C][C]0.0468802807533737[/C][C]0.0937605615067475[/C][C]0.953119719246626[/C][/ROW]
[ROW][C]13[/C][C]0.110268538791776[/C][C]0.220537077583553[/C][C]0.889731461208224[/C][/ROW]
[ROW][C]14[/C][C]0.314506075558127[/C][C]0.629012151116253[/C][C]0.685493924441873[/C][/ROW]
[ROW][C]15[/C][C]0.47329071588329[/C][C]0.94658143176658[/C][C]0.52670928411671[/C][/ROW]
[ROW][C]16[/C][C]0.564994284914115[/C][C]0.87001143017177[/C][C]0.435005715085885[/C][/ROW]
[ROW][C]17[/C][C]0.860726074682[/C][C]0.278547850636001[/C][C]0.139273925318000[/C][/ROW]
[ROW][C]18[/C][C]0.894628035440256[/C][C]0.210743929119487[/C][C]0.105371964559743[/C][/ROW]
[ROW][C]19[/C][C]0.926734001824748[/C][C]0.146531996350503[/C][C]0.0732659981752517[/C][/ROW]
[ROW][C]20[/C][C]0.911928708075615[/C][C]0.17614258384877[/C][C]0.088071291924385[/C][/ROW]
[ROW][C]21[/C][C]0.874523131408735[/C][C]0.250953737182529[/C][C]0.125476868591265[/C][/ROW]
[ROW][C]22[/C][C]0.844550301916743[/C][C]0.310899396166513[/C][C]0.155449698083257[/C][/ROW]
[ROW][C]23[/C][C]0.89589788953775[/C][C]0.208204220924500[/C][C]0.104102110462250[/C][/ROW]
[ROW][C]24[/C][C]0.906878235103624[/C][C]0.186243529792753[/C][C]0.0931217648963763[/C][/ROW]
[ROW][C]25[/C][C]0.879210853963584[/C][C]0.241578292072832[/C][C]0.120789146036416[/C][/ROW]
[ROW][C]26[/C][C]0.879842459540326[/C][C]0.240315080919347[/C][C]0.120157540459674[/C][/ROW]
[ROW][C]27[/C][C]0.857803492874558[/C][C]0.284393014250884[/C][C]0.142196507125442[/C][/ROW]
[ROW][C]28[/C][C]0.86129523706117[/C][C]0.277409525877661[/C][C]0.138704762938831[/C][/ROW]
[ROW][C]29[/C][C]0.850565794663001[/C][C]0.298868410673998[/C][C]0.149434205336999[/C][/ROW]
[ROW][C]30[/C][C]0.904574523511161[/C][C]0.190850952977677[/C][C]0.0954254764888386[/C][/ROW]
[ROW][C]31[/C][C]0.888559355350757[/C][C]0.222881289298486[/C][C]0.111440644649243[/C][/ROW]
[ROW][C]32[/C][C]0.847936142528735[/C][C]0.304127714942530[/C][C]0.152063857471265[/C][/ROW]
[ROW][C]33[/C][C]0.818102736782469[/C][C]0.363794526435062[/C][C]0.181897263217531[/C][/ROW]
[ROW][C]34[/C][C]0.922076759693822[/C][C]0.155846480612355[/C][C]0.0779232403061775[/C][/ROW]
[ROW][C]35[/C][C]0.994173242352802[/C][C]0.0116535152943963[/C][C]0.00582675764719816[/C][/ROW]
[ROW][C]36[/C][C]0.996027473743152[/C][C]0.0079450525136965[/C][C]0.00397252625684825[/C][/ROW]
[ROW][C]37[/C][C]0.998171139001843[/C][C]0.00365772199631354[/C][C]0.00182886099815677[/C][/ROW]
[ROW][C]38[/C][C]0.99853801125671[/C][C]0.0029239774865818[/C][C]0.0014619887432909[/C][/ROW]
[ROW][C]39[/C][C]0.998275892840308[/C][C]0.00344821431938471[/C][C]0.00172410715969235[/C][/ROW]
[ROW][C]40[/C][C]0.998158748145203[/C][C]0.0036825037095944[/C][C]0.0018412518547972[/C][/ROW]
[ROW][C]41[/C][C]0.999234127982965[/C][C]0.00153174403406991[/C][C]0.000765872017034953[/C][/ROW]
[ROW][C]42[/C][C]0.998954642482063[/C][C]0.00209071503587427[/C][C]0.00104535751793714[/C][/ROW]
[ROW][C]43[/C][C]0.998522776923168[/C][C]0.00295444615366455[/C][C]0.00147722307683228[/C][/ROW]
[ROW][C]44[/C][C]0.998148007205653[/C][C]0.00370398558869442[/C][C]0.00185199279434721[/C][/ROW]
[ROW][C]45[/C][C]0.99659898908974[/C][C]0.00680202182052002[/C][C]0.00340101091026001[/C][/ROW]
[ROW][C]46[/C][C]0.99485843189506[/C][C]0.0102831362098816[/C][C]0.00514156810494078[/C][/ROW]
[ROW][C]47[/C][C]0.992097026108705[/C][C]0.0158059477825902[/C][C]0.00790297389129508[/C][/ROW]
[ROW][C]48[/C][C]0.990611365310828[/C][C]0.0187772693783448[/C][C]0.00938863468917238[/C][/ROW]
[ROW][C]49[/C][C]0.99791908209403[/C][C]0.00416183581193943[/C][C]0.00208091790596972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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
7	0.146002669927434	0.292005339854868	0.853997330072566
8	0.097144699141351	0.194289398282702	0.90285530085865
9	0.0741305099985305	0.148261019997061	0.92586949000147
10	0.0510292958698748	0.102058591739750	0.948970704130125
11	0.038082401495465	0.07616480299093	0.961917598504535
12	0.0468802807533737	0.0937605615067475	0.953119719246626
13	0.110268538791776	0.220537077583553	0.889731461208224
14	0.314506075558127	0.629012151116253	0.685493924441873
15	0.47329071588329	0.94658143176658	0.52670928411671
16	0.564994284914115	0.87001143017177	0.435005715085885
17	0.860726074682	0.278547850636001	0.139273925318000
18	0.894628035440256	0.210743929119487	0.105371964559743
19	0.926734001824748	0.146531996350503	0.0732659981752517
20	0.911928708075615	0.17614258384877	0.088071291924385
21	0.874523131408735	0.250953737182529	0.125476868591265
22	0.844550301916743	0.310899396166513	0.155449698083257
23	0.89589788953775	0.208204220924500	0.104102110462250
24	0.906878235103624	0.186243529792753	0.0931217648963763
25	0.879210853963584	0.241578292072832	0.120789146036416
26	0.879842459540326	0.240315080919347	0.120157540459674
27	0.857803492874558	0.284393014250884	0.142196507125442
28	0.86129523706117	0.277409525877661	0.138704762938831
29	0.850565794663001	0.298868410673998	0.149434205336999
30	0.904574523511161	0.190850952977677	0.0954254764888386
31	0.888559355350757	0.222881289298486	0.111440644649243
32	0.847936142528735	0.304127714942530	0.152063857471265
33	0.818102736782469	0.363794526435062	0.181897263217531
34	0.922076759693822	0.155846480612355	0.0779232403061775
35	0.994173242352802	0.0116535152943963	0.00582675764719816
36	0.996027473743152	0.0079450525136965	0.00397252625684825
37	0.998171139001843	0.00365772199631354	0.00182886099815677
38	0.99853801125671	0.0029239774865818	0.0014619887432909
39	0.998275892840308	0.00344821431938471	0.00172410715969235
40	0.998158748145203	0.0036825037095944	0.0018412518547972
41	0.999234127982965	0.00153174403406991	0.000765872017034953
42	0.998954642482063	0.00209071503587427	0.00104535751793714
43	0.998522776923168	0.00295444615366455	0.00147722307683228
44	0.998148007205653	0.00370398558869442	0.00185199279434721
45	0.99659898908974	0.00680202182052002	0.00340101091026001
46	0.99485843189506	0.0102831362098816	0.00514156810494078
47	0.992097026108705	0.0158059477825902	0.00790297389129508
48	0.990611365310828	0.0187772693783448	0.00938863468917238
49	0.99791908209403	0.00416183581193943	0.00208091790596972

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	11	0.255813953488372	NOK
5% type I error level	15	0.348837209302326	NOK
10% type I error level	17	0.395348837209302	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 11 & 0.255813953488372 & NOK \tabularnewline
5% type I error level & 15 & 0.348837209302326 & NOK \tabularnewline
10% type I error level & 17 & 0.395348837209302 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110215&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]11[/C][C]0.255813953488372[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]15[/C][C]0.348837209302326[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]17[/C][C]0.395348837209302[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110215&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110215&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	11	0.255813953488372	NOK
5% type I error level	15	0.348837209302326	NOK
10% type I error level	17	0.395348837209302	NOK

Figure 1

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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