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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 18 Nov 2009 09:26:23 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/18/t1258561638rg49k5jue0r6599.htm/, Retrieved Fri, 01 Aug 2025 17:51:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57514, Retrieved Fri, 01 Aug 2025 17:51:09 +0000

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Estimated Impact

402

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [WS7 Y(t-4)] [2009-11-18 16:26:23] [82f421ff86a0429b20e3ed68bd89f1bd] [Current]

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7,59	43,14	7,59	7,59	7,55	7,55
7,57	43,39	7,59	7,59	7,59	7,55
7,57	43,46	7,57	7,59	7,59	7,59
7,59	43,54	7,57	7,57	7,59	7,59
7,6	43,62	7,59	7,57	7,57	7,59
7,64	44,01	7,6	7,59	7,57	7,57
7,64	44,5	7,64	7,6	7,59	7,57
7,76	44,73	7,64	7,64	7,6	7,59
7,76	44,89	7,76	7,64	7,64	7,6
7,76	45,09	7,76	7,76	7,64	7,64
7,77	45,17	7,76	7,76	7,76	7,64
7,83	45,24	7,77	7,76	7,76	7,76
7,94	45,42	7,83	7,77	7,76	7,76
7,94	45,67	7,94	7,83	7,77	7,76
7,94	45,68	7,94	7,94	7,83	7,77
8,09	46,56	7,94	7,94	7,94	7,83
8,18	46,72	8,09	7,94	7,94	7,94
8,26	47,01	8,18	8,09	7,94	7,94
8,28	47,26	8,26	8,18	8,09	7,94
8,28	47,49	8,28	8,26	8,18	8,09
8,28	47,51	8,28	8,28	8,26	8,18
8,29	47,52	8,28	8,28	8,28	8,26
8,3	47,66	8,29	8,28	8,28	8,28
8,3	47,71	8,3	8,29	8,28	8,28
8,31	47,87	8,3	8,3	8,29	8,28
8,33	48	8,31	8,3	8,3	8,29
8,33	48	8,33	8,31	8,3	8,3
8,34	48,05	8,33	8,33	8,31	8,3
8,48	48,25	8,34	8,33	8,33	8,31
8,59	48,72	8,48	8,34	8,33	8,33
8,67	48,94	8,59	8,48	8,34	8,33
8,67	49,16	8,67	8,59	8,48	8,34
8,67	49,18	8,67	8,67	8,59	8,48
8,71	49,25	8,67	8,67	8,67	8,59
8,72	49,34	8,71	8,67	8,67	8,67
8,72	49,49	8,72	8,71	8,67	8,67
8,72	49,57	8,72	8,72	8,71	8,67
8,74	49,63	8,72	8,72	8,72	8,71
8,74	49,67	8,74	8,72	8,72	8,72
8,74	49,7	8,74	8,74	8,72	8,72
8,74	49,8	8,74	8,74	8,74	8,72
8,79	50,09	8,74	8,74	8,74	8,74
8,85	50,49	8,79	8,74	8,74	8,74
8,86	50,73	8,85	8,79	8,74	8,74
8,87	51,12	8,86	8,85	8,79	8,74
8,92	51,15	8,87	8,86	8,85	8,79
8,96	51,41	8,92	8,87	8,86	8,85
8,97	51,61	8,96	8,92	8,87	8,86
8,99	52,06	8,97	8,96	8,92	8,87
8,98	52,17	8,99	8,97	8,96	8,92
8,98	52,18	8,98	8,99	8,97	8,96
9,01	52,19	8,98	8,98	8,99	8,97
9,01	52,74	9,01	8,98	8,98	8,99
9,03	53,05	9,01	9,01	8,98	8,98
9,05	53,38	9,03	9,01	9,01	8,98
9,05	53,78	9,05	9,03	9,01	9,01

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.0140552377191030 + 0.0139606102770509X[t] + 1.23654257042361Y1[t] -0.419623941627338Y2[t] + 0.222584543954599Y3[t] -0.118384183953442Y4[t] + 0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] + 0.0209832902930584M4[t] + 0.0172570665543621M5[t] + 0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] + 0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.0140552377191030 +  0.0139606102770509X[t] +  1.23654257042361Y1[t] -0.419623941627338Y2[t] +  0.222584543954599Y3[t] -0.118384183953442Y4[t] +  0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] +  0.0209832902930584M4[t] +  0.0172570665543621M5[t] +  0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] +  0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.0140552377191030 +  0.0139606102770509X[t] +  1.23654257042361Y1[t] -0.419623941627338Y2[t] +  0.222584543954599Y3[t] -0.118384183953442Y4[t] +  0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] +  0.0209832902930584M4[t] +  0.0172570665543621M5[t] +  0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] +  0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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] = + 0.0140552377191030 + 0.0139606102770509X[t] + 1.23654257042361Y1[t] -0.419623941627338Y2[t] + 0.222584543954599Y3[t] -0.118384183953442Y4[t] + 0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] + 0.0209832902930584M4[t] + 0.0172570665543621M5[t] + 0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] + 0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t + 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)	0.0140552377191030	0.984515	0.0143	0.988684	0.494342
X	0.0139606102770509	0.019085	0.7315	0.468975	0.234487
Y1	1.23654257042361	0.163712	7.5532	0	0
Y2	-0.419623941627338	0.254319	-1.65	0.107188	0.053594
Y3	0.222584543954599	0.255116	0.8725	0.388425	0.194212
Y4	-0.118384183953442	0.172133	-0.6877	0.495788	0.247894
M1	0.00761324456546221	0.026193	0.2907	0.772893	0.386447
M2	-0.0235156969591707	0.02647	-0.8884	0.379926	0.189963
M3	-0.0147316299733394	0.026501	-0.5559	0.581545	0.290773
M4	0.0209832902930584	0.027171	0.7723	0.444726	0.222363
M5	0.0172570665543621	0.027082	0.6372	0.527802	0.263901
M6	0.0312601726900203	0.026822	1.1655	0.251096	0.125548
M7	-0.000475280260314817	0.028046	-0.0169	0.986568	0.493284
M8	-0.00282851059813795	0.027802	-0.1017	0.919499	0.459749
M9	-0.0261443878669578	0.029397	-0.8894	0.379406	0.189703
M10	0.00808598682866219	0.028024	0.2885	0.774503	0.387252
M11	-0.00838414566602145	0.028244	-0.2968	0.768203	0.384102
t	-0.000382389196704658	0.004024	-0.095	0.924798	0.462399

\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) & 0.0140552377191030 & 0.984515 & 0.0143 & 0.988684 & 0.494342 \tabularnewline
X & 0.0139606102770509 & 0.019085 & 0.7315 & 0.468975 & 0.234487 \tabularnewline
Y1 & 1.23654257042361 & 0.163712 & 7.5532 & 0 & 0 \tabularnewline
Y2 & -0.419623941627338 & 0.254319 & -1.65 & 0.107188 & 0.053594 \tabularnewline
Y3 & 0.222584543954599 & 0.255116 & 0.8725 & 0.388425 & 0.194212 \tabularnewline
Y4 & -0.118384183953442 & 0.172133 & -0.6877 & 0.495788 & 0.247894 \tabularnewline
M1 & 0.00761324456546221 & 0.026193 & 0.2907 & 0.772893 & 0.386447 \tabularnewline
M2 & -0.0235156969591707 & 0.02647 & -0.8884 & 0.379926 & 0.189963 \tabularnewline
M3 & -0.0147316299733394 & 0.026501 & -0.5559 & 0.581545 & 0.290773 \tabularnewline
M4 & 0.0209832902930584 & 0.027171 & 0.7723 & 0.444726 & 0.222363 \tabularnewline
M5 & 0.0172570665543621 & 0.027082 & 0.6372 & 0.527802 & 0.263901 \tabularnewline
M6 & 0.0312601726900203 & 0.026822 & 1.1655 & 0.251096 & 0.125548 \tabularnewline
M7 & -0.000475280260314817 & 0.028046 & -0.0169 & 0.986568 & 0.493284 \tabularnewline
M8 & -0.00282851059813795 & 0.027802 & -0.1017 & 0.919499 & 0.459749 \tabularnewline
M9 & -0.0261443878669578 & 0.029397 & -0.8894 & 0.379406 & 0.189703 \tabularnewline
M10 & 0.00808598682866219 & 0.028024 & 0.2885 & 0.774503 & 0.387252 \tabularnewline
M11 & -0.00838414566602145 & 0.028244 & -0.2968 & 0.768203 & 0.384102 \tabularnewline
t & -0.000382389196704658 & 0.004024 & -0.095 & 0.924798 & 0.462399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]0.0140552377191030[/C][C]0.984515[/C][C]0.0143[/C][C]0.988684[/C][C]0.494342[/C][/ROW]
[ROW][C]X[/C][C]0.0139606102770509[/C][C]0.019085[/C][C]0.7315[/C][C]0.468975[/C][C]0.234487[/C][/ROW]
[ROW][C]Y1[/C][C]1.23654257042361[/C][C]0.163712[/C][C]7.5532[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.419623941627338[/C][C]0.254319[/C][C]-1.65[/C][C]0.107188[/C][C]0.053594[/C][/ROW]
[ROW][C]Y3[/C][C]0.222584543954599[/C][C]0.255116[/C][C]0.8725[/C][C]0.388425[/C][C]0.194212[/C][/ROW]
[ROW][C]Y4[/C][C]-0.118384183953442[/C][C]0.172133[/C][C]-0.6877[/C][C]0.495788[/C][C]0.247894[/C][/ROW]
[ROW][C]M1[/C][C]0.00761324456546221[/C][C]0.026193[/C][C]0.2907[/C][C]0.772893[/C][C]0.386447[/C][/ROW]
[ROW][C]M2[/C][C]-0.0235156969591707[/C][C]0.02647[/C][C]-0.8884[/C][C]0.379926[/C][C]0.189963[/C][/ROW]
[ROW][C]M3[/C][C]-0.0147316299733394[/C][C]0.026501[/C][C]-0.5559[/C][C]0.581545[/C][C]0.290773[/C][/ROW]
[ROW][C]M4[/C][C]0.0209832902930584[/C][C]0.027171[/C][C]0.7723[/C][C]0.444726[/C][C]0.222363[/C][/ROW]
[ROW][C]M5[/C][C]0.0172570665543621[/C][C]0.027082[/C][C]0.6372[/C][C]0.527802[/C][C]0.263901[/C][/ROW]
[ROW][C]M6[/C][C]0.0312601726900203[/C][C]0.026822[/C][C]1.1655[/C][C]0.251096[/C][C]0.125548[/C][/ROW]
[ROW][C]M7[/C][C]-0.000475280260314817[/C][C]0.028046[/C][C]-0.0169[/C][C]0.986568[/C][C]0.493284[/C][/ROW]
[ROW][C]M8[/C][C]-0.00282851059813795[/C][C]0.027802[/C][C]-0.1017[/C][C]0.919499[/C][C]0.459749[/C][/ROW]
[ROW][C]M9[/C][C]-0.0261443878669578[/C][C]0.029397[/C][C]-0.8894[/C][C]0.379406[/C][C]0.189703[/C][/ROW]
[ROW][C]M10[/C][C]0.00808598682866219[/C][C]0.028024[/C][C]0.2885[/C][C]0.774503[/C][C]0.387252[/C][/ROW]
[ROW][C]M11[/C][C]-0.00838414566602145[/C][C]0.028244[/C][C]-0.2968[/C][C]0.768203[/C][C]0.384102[/C][/ROW]
[ROW][C]t[/C][C]-0.000382389196704658[/C][C]0.004024[/C][C]-0.095[/C][C]0.924798[/C][C]0.462399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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)	0.0140552377191030	0.984515	0.0143	0.988684	0.494342
X	0.0139606102770509	0.019085	0.7315	0.468975	0.234487
Y1	1.23654257042361	0.163712	7.5532	0	0
Y2	-0.419623941627338	0.254319	-1.65	0.107188	0.053594
Y3	0.222584543954599	0.255116	0.8725	0.388425	0.194212
Y4	-0.118384183953442	0.172133	-0.6877	0.495788	0.247894
M1	0.00761324456546221	0.026193	0.2907	0.772893	0.386447
M2	-0.0235156969591707	0.02647	-0.8884	0.379926	0.189963
M3	-0.0147316299733394	0.026501	-0.5559	0.581545	0.290773
M4	0.0209832902930584	0.027171	0.7723	0.444726	0.222363
M5	0.0172570665543621	0.027082	0.6372	0.527802	0.263901
M6	0.0312601726900203	0.026822	1.1655	0.251096	0.125548
M7	-0.000475280260314817	0.028046	-0.0169	0.986568	0.493284
M8	-0.00282851059813795	0.027802	-0.1017	0.919499	0.459749
M9	-0.0261443878669578	0.029397	-0.8894	0.379406	0.189703
M10	0.00808598682866219	0.028024	0.2885	0.774503	0.387252
M11	-0.00838414566602145	0.028244	-0.2968	0.768203	0.384102
t	-0.000382389196704658	0.004024	-0.095	0.924798	0.462399

Multiple Linear Regression - Regression Statistics
Multiple R	0.997836985175587
R-squared	0.995678648984306
Adjusted R-squared	0.9937454130036
F-TEST (value)	515.032132094405
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0386849910476448
Sum Squared Residuals	0.0568680842295417

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.997836985175587 \tabularnewline
R-squared & 0.995678648984306 \tabularnewline
Adjusted R-squared & 0.9937454130036 \tabularnewline
F-TEST (value) & 515.032132094405 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0386849910476448 \tabularnewline
Sum Squared Residuals & 0.0568680842295417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.997836985175587[/C][/ROW]
[ROW][C]R-squared[/C][C]0.995678648984306[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.9937454130036[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]515.032132094405[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0386849910476448[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0568680842295417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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	0.997836985175587
R-squared	0.995678648984306
Adjusted R-squared	0.9937454130036
F-TEST (value)	515.032132094405
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0386849910476448
Sum Squared Residuals	0.0568680842295417

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.59	7.61067193101227	-0.0206719310122711
2	7.57	7.59155413461837	-0.0215541346183736
3	7.57	7.57146683636028	-0.00146683636028320
4	7.59	7.61630869508469	-0.0263086950846871
5	7.6	7.63359609150083	-0.0335960915008302
6	7.64	7.65900207699859	-0.0190020769985917
7	7.64	7.68344208816707	-0.0434420881670698
8	7.76	7.66699061309165	0.0930093869083528
9	7.76	7.80163069263993	-0.0416306926399335
10	7.76	7.78318055984084	-0.0231805598408407
11	7.77	7.79415503224617	-0.0241550322461685
12	7.83	7.8012933550647	0.0287066449352988
13	7.94	7.88103343509247	0.0589665649075286
14	7.94	7.9660803486289	-0.0260803486288992
15	7.94	7.94063422973953	-0.000634229739530575
16	8.09	8.00563334665083	0.0843666533491716
17	8.18	8.17621755668842	0.00378244331158241
18	8.26	8.24223209070174	0.0177679092982602
19	8.28	8.30814933360458	-0.0281493336045811
20	8.28	8.30206057187496	-0.0220605718749573
21	8.28	8.27740122574298	0.00259877425701461
22	8.29	8.30636977350749	-0.016369773507488
23	8.3	8.30146947928005	-0.00146947928005223
24	8.3	8.31833845255119	-0.0183384525511864
25	8.31	8.32583261158755	-0.0158326115875441
26	8.33	8.30954358950647	0.0204564104935287
27	8.33	8.33729603744826	-0.00729603744826175
28	8.34	8.3671599656388	-0.0271599656388069
29	8.48	8.38147674950261	0.098523250497391
30	8.59	8.56821099003574	0.0217890099642594
31	8.67	8.61866265850797	0.0513373414920335
32	8.67	8.70174113960338	-0.0317411396033811
33	8.67	8.65266268409473	0.0173373159052656
34	8.71	8.69227241559453	0.0177275844054682
35	8.72	8.71666731692875	0.00333268307125159
36	8.72	8.72234363297876	-0.00234363297876473
37	8.72	8.7353984795116	-0.0153984795115971
38	8.74	8.7022152634883	0.0377847365117088
39	8.74	8.73472237525744	0.00527762474256289
40	8.74	8.7620812458029	-0.0220812458028952
41	8.74	8.7638203847743	-0.0238203847742912
42	8.79	8.77912199501452	0.0108780049854782
43	8.85	8.81441552549948	0.035584474500519
44	8.86	8.8682418095755	-0.00824180957549614
45	8.87	8.84830539752235	0.0216946024776533
46	8.92	8.89817725105714	0.0218227489428605
47	8.96	8.93770817154503	0.0222918284549692
48	8.97	8.97802455940535	-0.00802455940534777
49	8.99	8.99706354279612	-0.00706354279611632
50	8.98	8.99060666375797	-0.0106066637579645
51	8.98	8.97588052119449	0.00411947880551261
52	9.01	9.01881674682278	-0.0088167468227824
53	9.01	9.05488921753385	-0.0448892175338521
54	9.03	9.0614328472494	-0.0314328472494062
55	9.05	9.0653303942209	-0.0153303942209016
56	9.05	9.08096586585452	-0.0309658658545183

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.59 & 7.61067193101227 & -0.0206719310122711 \tabularnewline
2 & 7.57 & 7.59155413461837 & -0.0215541346183736 \tabularnewline
3 & 7.57 & 7.57146683636028 & -0.00146683636028320 \tabularnewline
4 & 7.59 & 7.61630869508469 & -0.0263086950846871 \tabularnewline
5 & 7.6 & 7.63359609150083 & -0.0335960915008302 \tabularnewline
6 & 7.64 & 7.65900207699859 & -0.0190020769985917 \tabularnewline
7 & 7.64 & 7.68344208816707 & -0.0434420881670698 \tabularnewline
8 & 7.76 & 7.66699061309165 & 0.0930093869083528 \tabularnewline
9 & 7.76 & 7.80163069263993 & -0.0416306926399335 \tabularnewline
10 & 7.76 & 7.78318055984084 & -0.0231805598408407 \tabularnewline
11 & 7.77 & 7.79415503224617 & -0.0241550322461685 \tabularnewline
12 & 7.83 & 7.8012933550647 & 0.0287066449352988 \tabularnewline
13 & 7.94 & 7.88103343509247 & 0.0589665649075286 \tabularnewline
14 & 7.94 & 7.9660803486289 & -0.0260803486288992 \tabularnewline
15 & 7.94 & 7.94063422973953 & -0.000634229739530575 \tabularnewline
16 & 8.09 & 8.00563334665083 & 0.0843666533491716 \tabularnewline
17 & 8.18 & 8.17621755668842 & 0.00378244331158241 \tabularnewline
18 & 8.26 & 8.24223209070174 & 0.0177679092982602 \tabularnewline
19 & 8.28 & 8.30814933360458 & -0.0281493336045811 \tabularnewline
20 & 8.28 & 8.30206057187496 & -0.0220605718749573 \tabularnewline
21 & 8.28 & 8.27740122574298 & 0.00259877425701461 \tabularnewline
22 & 8.29 & 8.30636977350749 & -0.016369773507488 \tabularnewline
23 & 8.3 & 8.30146947928005 & -0.00146947928005223 \tabularnewline
24 & 8.3 & 8.31833845255119 & -0.0183384525511864 \tabularnewline
25 & 8.31 & 8.32583261158755 & -0.0158326115875441 \tabularnewline
26 & 8.33 & 8.30954358950647 & 0.0204564104935287 \tabularnewline
27 & 8.33 & 8.33729603744826 & -0.00729603744826175 \tabularnewline
28 & 8.34 & 8.3671599656388 & -0.0271599656388069 \tabularnewline
29 & 8.48 & 8.38147674950261 & 0.098523250497391 \tabularnewline
30 & 8.59 & 8.56821099003574 & 0.0217890099642594 \tabularnewline
31 & 8.67 & 8.61866265850797 & 0.0513373414920335 \tabularnewline
32 & 8.67 & 8.70174113960338 & -0.0317411396033811 \tabularnewline
33 & 8.67 & 8.65266268409473 & 0.0173373159052656 \tabularnewline
34 & 8.71 & 8.69227241559453 & 0.0177275844054682 \tabularnewline
35 & 8.72 & 8.71666731692875 & 0.00333268307125159 \tabularnewline
36 & 8.72 & 8.72234363297876 & -0.00234363297876473 \tabularnewline
37 & 8.72 & 8.7353984795116 & -0.0153984795115971 \tabularnewline
38 & 8.74 & 8.7022152634883 & 0.0377847365117088 \tabularnewline
39 & 8.74 & 8.73472237525744 & 0.00527762474256289 \tabularnewline
40 & 8.74 & 8.7620812458029 & -0.0220812458028952 \tabularnewline
41 & 8.74 & 8.7638203847743 & -0.0238203847742912 \tabularnewline
42 & 8.79 & 8.77912199501452 & 0.0108780049854782 \tabularnewline
43 & 8.85 & 8.81441552549948 & 0.035584474500519 \tabularnewline
44 & 8.86 & 8.8682418095755 & -0.00824180957549614 \tabularnewline
45 & 8.87 & 8.84830539752235 & 0.0216946024776533 \tabularnewline
46 & 8.92 & 8.89817725105714 & 0.0218227489428605 \tabularnewline
47 & 8.96 & 8.93770817154503 & 0.0222918284549692 \tabularnewline
48 & 8.97 & 8.97802455940535 & -0.00802455940534777 \tabularnewline
49 & 8.99 & 8.99706354279612 & -0.00706354279611632 \tabularnewline
50 & 8.98 & 8.99060666375797 & -0.0106066637579645 \tabularnewline
51 & 8.98 & 8.97588052119449 & 0.00411947880551261 \tabularnewline
52 & 9.01 & 9.01881674682278 & -0.0088167468227824 \tabularnewline
53 & 9.01 & 9.05488921753385 & -0.0448892175338521 \tabularnewline
54 & 9.03 & 9.0614328472494 & -0.0314328472494062 \tabularnewline
55 & 9.05 & 9.0653303942209 & -0.0153303942209016 \tabularnewline
56 & 9.05 & 9.08096586585452 & -0.0309658658545183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]7.59[/C][C]7.61067193101227[/C][C]-0.0206719310122711[/C][/ROW]
[ROW][C]2[/C][C]7.57[/C][C]7.59155413461837[/C][C]-0.0215541346183736[/C][/ROW]
[ROW][C]3[/C][C]7.57[/C][C]7.57146683636028[/C][C]-0.00146683636028320[/C][/ROW]
[ROW][C]4[/C][C]7.59[/C][C]7.61630869508469[/C][C]-0.0263086950846871[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.63359609150083[/C][C]-0.0335960915008302[/C][/ROW]
[ROW][C]6[/C][C]7.64[/C][C]7.65900207699859[/C][C]-0.0190020769985917[/C][/ROW]
[ROW][C]7[/C][C]7.64[/C][C]7.68344208816707[/C][C]-0.0434420881670698[/C][/ROW]
[ROW][C]8[/C][C]7.76[/C][C]7.66699061309165[/C][C]0.0930093869083528[/C][/ROW]
[ROW][C]9[/C][C]7.76[/C][C]7.80163069263993[/C][C]-0.0416306926399335[/C][/ROW]
[ROW][C]10[/C][C]7.76[/C][C]7.78318055984084[/C][C]-0.0231805598408407[/C][/ROW]
[ROW][C]11[/C][C]7.77[/C][C]7.79415503224617[/C][C]-0.0241550322461685[/C][/ROW]
[ROW][C]12[/C][C]7.83[/C][C]7.8012933550647[/C][C]0.0287066449352988[/C][/ROW]
[ROW][C]13[/C][C]7.94[/C][C]7.88103343509247[/C][C]0.0589665649075286[/C][/ROW]
[ROW][C]14[/C][C]7.94[/C][C]7.9660803486289[/C][C]-0.0260803486288992[/C][/ROW]
[ROW][C]15[/C][C]7.94[/C][C]7.94063422973953[/C][C]-0.000634229739530575[/C][/ROW]
[ROW][C]16[/C][C]8.09[/C][C]8.00563334665083[/C][C]0.0843666533491716[/C][/ROW]
[ROW][C]17[/C][C]8.18[/C][C]8.17621755668842[/C][C]0.00378244331158241[/C][/ROW]
[ROW][C]18[/C][C]8.26[/C][C]8.24223209070174[/C][C]0.0177679092982602[/C][/ROW]
[ROW][C]19[/C][C]8.28[/C][C]8.30814933360458[/C][C]-0.0281493336045811[/C][/ROW]
[ROW][C]20[/C][C]8.28[/C][C]8.30206057187496[/C][C]-0.0220605718749573[/C][/ROW]
[ROW][C]21[/C][C]8.28[/C][C]8.27740122574298[/C][C]0.00259877425701461[/C][/ROW]
[ROW][C]22[/C][C]8.29[/C][C]8.30636977350749[/C][C]-0.016369773507488[/C][/ROW]
[ROW][C]23[/C][C]8.3[/C][C]8.30146947928005[/C][C]-0.00146947928005223[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.31833845255119[/C][C]-0.0183384525511864[/C][/ROW]
[ROW][C]25[/C][C]8.31[/C][C]8.32583261158755[/C][C]-0.0158326115875441[/C][/ROW]
[ROW][C]26[/C][C]8.33[/C][C]8.30954358950647[/C][C]0.0204564104935287[/C][/ROW]
[ROW][C]27[/C][C]8.33[/C][C]8.33729603744826[/C][C]-0.00729603744826175[/C][/ROW]
[ROW][C]28[/C][C]8.34[/C][C]8.3671599656388[/C][C]-0.0271599656388069[/C][/ROW]
[ROW][C]29[/C][C]8.48[/C][C]8.38147674950261[/C][C]0.098523250497391[/C][/ROW]
[ROW][C]30[/C][C]8.59[/C][C]8.56821099003574[/C][C]0.0217890099642594[/C][/ROW]
[ROW][C]31[/C][C]8.67[/C][C]8.61866265850797[/C][C]0.0513373414920335[/C][/ROW]
[ROW][C]32[/C][C]8.67[/C][C]8.70174113960338[/C][C]-0.0317411396033811[/C][/ROW]
[ROW][C]33[/C][C]8.67[/C][C]8.65266268409473[/C][C]0.0173373159052656[/C][/ROW]
[ROW][C]34[/C][C]8.71[/C][C]8.69227241559453[/C][C]0.0177275844054682[/C][/ROW]
[ROW][C]35[/C][C]8.72[/C][C]8.71666731692875[/C][C]0.00333268307125159[/C][/ROW]
[ROW][C]36[/C][C]8.72[/C][C]8.72234363297876[/C][C]-0.00234363297876473[/C][/ROW]
[ROW][C]37[/C][C]8.72[/C][C]8.7353984795116[/C][C]-0.0153984795115971[/C][/ROW]
[ROW][C]38[/C][C]8.74[/C][C]8.7022152634883[/C][C]0.0377847365117088[/C][/ROW]
[ROW][C]39[/C][C]8.74[/C][C]8.73472237525744[/C][C]0.00527762474256289[/C][/ROW]
[ROW][C]40[/C][C]8.74[/C][C]8.7620812458029[/C][C]-0.0220812458028952[/C][/ROW]
[ROW][C]41[/C][C]8.74[/C][C]8.7638203847743[/C][C]-0.0238203847742912[/C][/ROW]
[ROW][C]42[/C][C]8.79[/C][C]8.77912199501452[/C][C]0.0108780049854782[/C][/ROW]
[ROW][C]43[/C][C]8.85[/C][C]8.81441552549948[/C][C]0.035584474500519[/C][/ROW]
[ROW][C]44[/C][C]8.86[/C][C]8.8682418095755[/C][C]-0.00824180957549614[/C][/ROW]
[ROW][C]45[/C][C]8.87[/C][C]8.84830539752235[/C][C]0.0216946024776533[/C][/ROW]
[ROW][C]46[/C][C]8.92[/C][C]8.89817725105714[/C][C]0.0218227489428605[/C][/ROW]
[ROW][C]47[/C][C]8.96[/C][C]8.93770817154503[/C][C]0.0222918284549692[/C][/ROW]
[ROW][C]48[/C][C]8.97[/C][C]8.97802455940535[/C][C]-0.00802455940534777[/C][/ROW]
[ROW][C]49[/C][C]8.99[/C][C]8.99706354279612[/C][C]-0.00706354279611632[/C][/ROW]
[ROW][C]50[/C][C]8.98[/C][C]8.99060666375797[/C][C]-0.0106066637579645[/C][/ROW]
[ROW][C]51[/C][C]8.98[/C][C]8.97588052119449[/C][C]0.00411947880551261[/C][/ROW]
[ROW][C]52[/C][C]9.01[/C][C]9.01881674682278[/C][C]-0.0088167468227824[/C][/ROW]
[ROW][C]53[/C][C]9.01[/C][C]9.05488921753385[/C][C]-0.0448892175338521[/C][/ROW]
[ROW][C]54[/C][C]9.03[/C][C]9.0614328472494[/C][C]-0.0314328472494062[/C][/ROW]
[ROW][C]55[/C][C]9.05[/C][C]9.0653303942209[/C][C]-0.0153303942209016[/C][/ROW]
[ROW][C]56[/C][C]9.05[/C][C]9.08096586585452[/C][C]-0.0309658658545183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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	7.59	7.61067193101227	-0.0206719310122711
2	7.57	7.59155413461837	-0.0215541346183736
3	7.57	7.57146683636028	-0.00146683636028320
4	7.59	7.61630869508469	-0.0263086950846871
5	7.6	7.63359609150083	-0.0335960915008302
6	7.64	7.65900207699859	-0.0190020769985917
7	7.64	7.68344208816707	-0.0434420881670698
8	7.76	7.66699061309165	0.0930093869083528
9	7.76	7.80163069263993	-0.0416306926399335
10	7.76	7.78318055984084	-0.0231805598408407
11	7.77	7.79415503224617	-0.0241550322461685
12	7.83	7.8012933550647	0.0287066449352988
13	7.94	7.88103343509247	0.0589665649075286
14	7.94	7.9660803486289	-0.0260803486288992
15	7.94	7.94063422973953	-0.000634229739530575
16	8.09	8.00563334665083	0.0843666533491716
17	8.18	8.17621755668842	0.00378244331158241
18	8.26	8.24223209070174	0.0177679092982602
19	8.28	8.30814933360458	-0.0281493336045811
20	8.28	8.30206057187496	-0.0220605718749573
21	8.28	8.27740122574298	0.00259877425701461
22	8.29	8.30636977350749	-0.016369773507488
23	8.3	8.30146947928005	-0.00146947928005223
24	8.3	8.31833845255119	-0.0183384525511864
25	8.31	8.32583261158755	-0.0158326115875441
26	8.33	8.30954358950647	0.0204564104935287
27	8.33	8.33729603744826	-0.00729603744826175
28	8.34	8.3671599656388	-0.0271599656388069
29	8.48	8.38147674950261	0.098523250497391
30	8.59	8.56821099003574	0.0217890099642594
31	8.67	8.61866265850797	0.0513373414920335
32	8.67	8.70174113960338	-0.0317411396033811
33	8.67	8.65266268409473	0.0173373159052656
34	8.71	8.69227241559453	0.0177275844054682
35	8.72	8.71666731692875	0.00333268307125159
36	8.72	8.72234363297876	-0.00234363297876473
37	8.72	8.7353984795116	-0.0153984795115971
38	8.74	8.7022152634883	0.0377847365117088
39	8.74	8.73472237525744	0.00527762474256289
40	8.74	8.7620812458029	-0.0220812458028952
41	8.74	8.7638203847743	-0.0238203847742912
42	8.79	8.77912199501452	0.0108780049854782
43	8.85	8.81441552549948	0.035584474500519
44	8.86	8.8682418095755	-0.00824180957549614
45	8.87	8.84830539752235	0.0216946024776533
46	8.92	8.89817725105714	0.0218227489428605
47	8.96	8.93770817154503	0.0222918284549692
48	8.97	8.97802455940535	-0.00802455940534777
49	8.99	8.99706354279612	-0.00706354279611632
50	8.98	8.99060666375797	-0.0106066637579645
51	8.98	8.97588052119449	0.00411947880551261
52	9.01	9.01881674682278	-0.0088167468227824
53	9.01	9.05488921753385	-0.0448892175338521
54	9.03	9.0614328472494	-0.0314328472494062
55	9.05	9.0653303942209	-0.0153303942209016
56	9.05	9.08096586585452	-0.0309658658545183

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.830045822109994	0.339908355780012	0.169954177890006
22	0.791264967949003	0.417470064101993	0.208735032050997
23	0.680816251234396	0.638367497531208	0.319183748765604
24	0.614677763614583	0.770644472770834	0.385322236385417
25	0.759504530068582	0.480990939862836	0.240495469931418
26	0.674896489328457	0.650207021343086	0.325103510671543
27	0.696827112009139	0.606345775981721	0.303172887990861
28	0.98713153176488	0.0257369364702386	0.0128684682351193
29	0.996898973257942	0.00620205348411592	0.00310102674205796
30	0.993424494642057	0.013151010715886	0.006575505357943
31	0.995039597157284	0.00992080568543284	0.00496040284271642
32	0.985518182266335	0.0289636354673294	0.0144818177336647
33	0.975152698173664	0.0496946036526722	0.0248473018263361
34	0.98151796829719	0.0369640634056189	0.0184820317028095
35	0.937407581104905	0.125184837790189	0.0625924188950947

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.830045822109994 & 0.339908355780012 & 0.169954177890006 \tabularnewline
22 & 0.791264967949003 & 0.417470064101993 & 0.208735032050997 \tabularnewline
23 & 0.680816251234396 & 0.638367497531208 & 0.319183748765604 \tabularnewline
24 & 0.614677763614583 & 0.770644472770834 & 0.385322236385417 \tabularnewline
25 & 0.759504530068582 & 0.480990939862836 & 0.240495469931418 \tabularnewline
26 & 0.674896489328457 & 0.650207021343086 & 0.325103510671543 \tabularnewline
27 & 0.696827112009139 & 0.606345775981721 & 0.303172887990861 \tabularnewline
28 & 0.98713153176488 & 0.0257369364702386 & 0.0128684682351193 \tabularnewline
29 & 0.996898973257942 & 0.00620205348411592 & 0.00310102674205796 \tabularnewline
30 & 0.993424494642057 & 0.013151010715886 & 0.006575505357943 \tabularnewline
31 & 0.995039597157284 & 0.00992080568543284 & 0.00496040284271642 \tabularnewline
32 & 0.985518182266335 & 0.0289636354673294 & 0.0144818177336647 \tabularnewline
33 & 0.975152698173664 & 0.0496946036526722 & 0.0248473018263361 \tabularnewline
34 & 0.98151796829719 & 0.0369640634056189 & 0.0184820317028095 \tabularnewline
35 & 0.937407581104905 & 0.125184837790189 & 0.0625924188950947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.830045822109994[/C][C]0.339908355780012[/C][C]0.169954177890006[/C][/ROW]
[ROW][C]22[/C][C]0.791264967949003[/C][C]0.417470064101993[/C][C]0.208735032050997[/C][/ROW]
[ROW][C]23[/C][C]0.680816251234396[/C][C]0.638367497531208[/C][C]0.319183748765604[/C][/ROW]
[ROW][C]24[/C][C]0.614677763614583[/C][C]0.770644472770834[/C][C]0.385322236385417[/C][/ROW]
[ROW][C]25[/C][C]0.759504530068582[/C][C]0.480990939862836[/C][C]0.240495469931418[/C][/ROW]
[ROW][C]26[/C][C]0.674896489328457[/C][C]0.650207021343086[/C][C]0.325103510671543[/C][/ROW]
[ROW][C]27[/C][C]0.696827112009139[/C][C]0.606345775981721[/C][C]0.303172887990861[/C][/ROW]
[ROW][C]28[/C][C]0.98713153176488[/C][C]0.0257369364702386[/C][C]0.0128684682351193[/C][/ROW]
[ROW][C]29[/C][C]0.996898973257942[/C][C]0.00620205348411592[/C][C]0.00310102674205796[/C][/ROW]
[ROW][C]30[/C][C]0.993424494642057[/C][C]0.013151010715886[/C][C]0.006575505357943[/C][/ROW]
[ROW][C]31[/C][C]0.995039597157284[/C][C]0.00992080568543284[/C][C]0.00496040284271642[/C][/ROW]
[ROW][C]32[/C][C]0.985518182266335[/C][C]0.0289636354673294[/C][C]0.0144818177336647[/C][/ROW]
[ROW][C]33[/C][C]0.975152698173664[/C][C]0.0496946036526722[/C][C]0.0248473018263361[/C][/ROW]
[ROW][C]34[/C][C]0.98151796829719[/C][C]0.0369640634056189[/C][C]0.0184820317028095[/C][/ROW]
[ROW][C]35[/C][C]0.937407581104905[/C][C]0.125184837790189[/C][C]0.0625924188950947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.830045822109994	0.339908355780012	0.169954177890006
22	0.791264967949003	0.417470064101993	0.208735032050997
23	0.680816251234396	0.638367497531208	0.319183748765604
24	0.614677763614583	0.770644472770834	0.385322236385417
25	0.759504530068582	0.480990939862836	0.240495469931418
26	0.674896489328457	0.650207021343086	0.325103510671543
27	0.696827112009139	0.606345775981721	0.303172887990861
28	0.98713153176488	0.0257369364702386	0.0128684682351193
29	0.996898973257942	0.00620205348411592	0.00310102674205796
30	0.993424494642057	0.013151010715886	0.006575505357943
31	0.995039597157284	0.00992080568543284	0.00496040284271642
32	0.985518182266335	0.0289636354673294	0.0144818177336647
33	0.975152698173664	0.0496946036526722	0.0248473018263361
34	0.98151796829719	0.0369640634056189	0.0184820317028095
35	0.937407581104905	0.125184837790189	0.0625924188950947

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	2	0.133333333333333	NOK
5% type I error level	7	0.466666666666667	NOK
10% type I error level	7	0.466666666666667	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 & 2 & 0.133333333333333 & NOK \tabularnewline
5% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
10% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]2[/C][C]0.133333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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	2	0.133333333333333	NOK
5% type I error level	7	0.466666666666667	NOK
10% type I error level	7	0.466666666666667	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code