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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 14 Nov 2009 06:58:56 -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/14/t1258207210ohkxjykpseglkrp.htm/, Retrieved Tue, 04 Nov 2025 01:22:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57224, Retrieved Tue, 04 Nov 2025 01:22:13 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

415

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] [WS 7 4] [2009-11-14 13:58:56] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
-   PD        [Multiple Regression] [ws7 4] [2009-11-18 20:49:31] [6e4e01d7eb22a9f33d58ebb35753a195] 
-    D          [Multiple Regression] [WS 75] [2009-11-18 20:57:24] [6e4e01d7eb22a9f33d58ebb35753a195] 
-    D            [Multiple Regression] [Paper hypothese t...] [2010-12-19 12:54:13] [a9e130f95bad0a0597234e75c6380c5a] 
-    D              [Multiple Regression] [Multiple Regression] [2010-12-22 14:47:15] [a9e130f95bad0a0597234e75c6380c5a] 
-    D              [Multiple Regression] [] [2011-12-20 17:24:43] [06f5daa9a1979410bf169cb7a41fb3eb] 
-    D          [Multiple Regression] [WS7: Correctie] [2009-11-27 15:55:13] [8cf9233b7464ea02e32be3b30fdac052] 

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103,91	100,30	103,88	103,77	103,66	103,64	103,63
103,91	98,50	103,91	103,88	103,77	103,66	103,64
103,92	95,10	103,91	103,91	103,88	103,77	103,66
104,05	93,10	103,92	103,91	103,91	103,88	103,77
104,23	92,20	104,05	103,92	103,91	103,91	103,88
104,30	89,00	104,23	104,05	103,92	103,91	103,91
104,31	86,40	104,30	104,23	104,05	103,92	103,91
104,31	84,50	104,31	104,30	104,23	104,05	103,92
104,34	82,70	104,31	104,31	104,30	104,23	104,05
104,55	80,80	104,34	104,31	104,31	104,30	104,23
104,65	81,80	104,55	104,34	104,31	104,31	104,30
104,73	81,80	104,65	104,55	104,34	104,31	104,31
104,75	82,90	104,73	104,65	104,55	104,34	104,31
104,75	83,80	104,75	104,73	104,65	104,55	104,34
104,76	86,20	104,75	104,75	104,73	104,65	104,55
104,94	86,10	104,76	104,75	104,75	104,73	104,65
105,29	86,20	104,94	104,76	104,75	104,75	104,73
105,38	88,80	105,29	104,94	104,76	104,75	104,75
105,43	89,60	105,38	105,29	104,94	104,76	104,75
105,43	87,80	105,43	105,38	105,29	104,94	104,76
105,42	88,30	105,43	105,43	105,38	105,29	104,94
105,52	88,60	105,42	105,43	105,43	105,38	105,29
105,69	91,00	105,52	105,42	105,43	105,43	105,38
105,72	91,50	105,69	105,52	105,42	105,43	105,43
105,74	95,40	105,72	105,69	105,52	105,42	105,43
105,74	98,70	105,74	105,72	105,69	105,52	105,42
105,74	99,90	105,74	105,74	105,72	105,69	105,52
105,95	98,60	105,74	105,74	105,74	105,72	105,69
106,17	100,30	105,95	105,74	105,74	105,74	105,72
106,34	100,20	106,17	105,95	105,74	105,74	105,74
106,37	100,40	106,34	106,17	105,95	105,74	105,74
106,37	101,40	106,37	106,34	106,17	105,95	105,74
106,36	103,00	106,37	106,37	106,34	106,17	105,95
106,44	109,10	106,36	106,37	106,37	106,34	106,17
106,29	111,40	106,44	106,36	106,37	106,37	106,34
106,23	114,10	106,29	106,44	106,36	106,37	106,37
106,23	121,80	106,23	106,29	106,44	106,36	106,37
106,23	127,60	106,23	106,23	106,29	106,44	106,36
106,23	129,90	106,23	106,23	106,23	106,29	106,44
106,34	128,00	106,23	106,23	106,23	106,23	106,29
106,44	123,50	106,34	106,23	106,23	106,23	106,23
106,44	124,00	106,44	106,34	106,23	106,23	106,23
106,48	127,40	106,44	106,44	106,34	106,23	106,23
106,50	127,60	106,48	106,44	106,44	106,34	106,23
106,57	128,40	106,50	106,48	106,44	106,44	106,34
106,40	131,40	106,57	106,50	106,48	106,44	106,44
106,37	135,10	106,40	106,57	106,50	106,48	106,44
106,25	134,00	106,37	106,40	106,57	106,50	106,48
106,21	144,50	106,25	106,37	106,40	106,57	106,50
106,21	147,30	106,21	106,25	106,37	106,40	106,57
106,24	150,90	106,21	106,21	106,25	106,37	106,40
106,19	148,70	106,24	106,21	106,21	106,25	106,37
106,08	141,40	106,19	106,24	106,21	106,21	106,25
106,13	138,90	106,08	106,19	106,24	106,21	106,21
106,09	139,80	106,13	106,08	106,19	106,24	106,21

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -2.83103972160239 -0.00497969791234237X[t] + 0.932713845855733Y1[t] -0.0849261973825332Y2[t] -0.295020473860288Y3[t] + 0.179390247778269Y4[t] + 0.299672934182992`Y5 `[t] + 0.066291966934211M1[t] + 0.070275643501231M2[t] + 0.0678099255876927M3[t] + 0.155510564164373M4[t] + 0.181984794020036M5[t] + 0.128406954400737M6[t] + 0.123356529101140M7[t] + 0.144114792469188M8[t] + 0.102750256297642M9[t] + 0.080114755808093M10[t] + 0.0357874509842374M11[t] -0.000149240410139286t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -2.83103972160239 -0.00497969791234237X[t] +  0.932713845855733Y1[t] -0.0849261973825332Y2[t] -0.295020473860288Y3[t] +  0.179390247778269Y4[t] +  0.299672934182992`Y5
`[t] +  0.066291966934211M1[t] +  0.070275643501231M2[t] +  0.0678099255876927M3[t] +  0.155510564164373M4[t] +  0.181984794020036M5[t] +  0.128406954400737M6[t] +  0.123356529101140M7[t] +  0.144114792469188M8[t] +  0.102750256297642M9[t] +  0.080114755808093M10[t] +  0.0357874509842374M11[t] -0.000149240410139286t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -2.83103972160239 -0.00497969791234237X[t] +  0.932713845855733Y1[t] -0.0849261973825332Y2[t] -0.295020473860288Y3[t] +  0.179390247778269Y4[t] +  0.299672934182992`Y5
`[t] +  0.066291966934211M1[t] +  0.070275643501231M2[t] +  0.0678099255876927M3[t] +  0.155510564164373M4[t] +  0.181984794020036M5[t] +  0.128406954400737M6[t] +  0.123356529101140M7[t] +  0.144114792469188M8[t] +  0.102750256297642M9[t] +  0.080114755808093M10[t] +  0.0357874509842374M11[t] -0.000149240410139286t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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] = -2.83103972160239 -0.00497969791234237X[t] + 0.932713845855733Y1[t] -0.0849261973825332Y2[t] -0.295020473860288Y3[t] + 0.179390247778269Y4[t] + 0.299672934182992`Y5 `[t] + 0.066291966934211M1[t] + 0.070275643501231M2[t] + 0.0678099255876927M3[t] + 0.155510564164373M4[t] + 0.181984794020036M5[t] + 0.128406954400737M6[t] + 0.123356529101140M7[t] + 0.144114792469188M8[t] + 0.102750256297642M9[t] + 0.080114755808093M10[t] + 0.0357874509842374M11[t] -0.000149240410139286t + 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)	-2.83103972160239	4.34225	-0.652	0.518558	0.259279
X	-0.00497969791234237	0.001643	-3.0301	0.004506	0.002253
Y1	0.932713845855733	0.157745	5.9128	1e-06	0
Y2	-0.0849261973825332	0.224609	-0.3781	0.707572	0.353786
Y3	-0.295020473860288	0.243782	-1.2102	0.234096	0.117048
Y4	0.179390247778269	0.239424	0.7493	0.458569	0.229285
`Y5 `	0.299672934182992	0.185883	1.6122	0.115661	0.057831
M1	0.066291966934211	0.049712	1.3335	0.190735	0.095367
M2	0.070275643501231	0.051292	1.3701	0.179141	0.089571
M3	0.0678099255876927	0.050229	1.35	0.185442	0.092721
M4	0.155510564164373	0.048629	3.1979	0.002883	0.001442
M5	0.181984794020036	0.051174	3.5562	0.001076	0.000538
M6	0.128406954400737	0.053728	2.3899	0.022209	0.011104
M7	0.123356529101140	0.055083	2.2395	0.031396	0.015698
M8	0.144114792469188	0.065772	2.1911	0.034997	0.017499
M9	0.102750256297642	0.061791	1.6629	0.105024	0.052512
M10	0.080114755808093	0.051751	1.5481	0.130347	0.065174
M11	0.0357874509842374	0.050554	0.7079	0.483566	0.241783
t	-0.000149240410139286	0.003603	-0.0414	0.967193	0.483596

\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) & -2.83103972160239 & 4.34225 & -0.652 & 0.518558 & 0.259279 \tabularnewline
X & -0.00497969791234237 & 0.001643 & -3.0301 & 0.004506 & 0.002253 \tabularnewline
Y1 & 0.932713845855733 & 0.157745 & 5.9128 & 1e-06 & 0 \tabularnewline
Y2 & -0.0849261973825332 & 0.224609 & -0.3781 & 0.707572 & 0.353786 \tabularnewline
Y3 & -0.295020473860288 & 0.243782 & -1.2102 & 0.234096 & 0.117048 \tabularnewline
Y4 & 0.179390247778269 & 0.239424 & 0.7493 & 0.458569 & 0.229285 \tabularnewline
`Y5
` & 0.299672934182992 & 0.185883 & 1.6122 & 0.115661 & 0.057831 \tabularnewline
M1 & 0.066291966934211 & 0.049712 & 1.3335 & 0.190735 & 0.095367 \tabularnewline
M2 & 0.070275643501231 & 0.051292 & 1.3701 & 0.179141 & 0.089571 \tabularnewline
M3 & 0.0678099255876927 & 0.050229 & 1.35 & 0.185442 & 0.092721 \tabularnewline
M4 & 0.155510564164373 & 0.048629 & 3.1979 & 0.002883 & 0.001442 \tabularnewline
M5 & 0.181984794020036 & 0.051174 & 3.5562 & 0.001076 & 0.000538 \tabularnewline
M6 & 0.128406954400737 & 0.053728 & 2.3899 & 0.022209 & 0.011104 \tabularnewline
M7 & 0.123356529101140 & 0.055083 & 2.2395 & 0.031396 & 0.015698 \tabularnewline
M8 & 0.144114792469188 & 0.065772 & 2.1911 & 0.034997 & 0.017499 \tabularnewline
M9 & 0.102750256297642 & 0.061791 & 1.6629 & 0.105024 & 0.052512 \tabularnewline
M10 & 0.080114755808093 & 0.051751 & 1.5481 & 0.130347 & 0.065174 \tabularnewline
M11 & 0.0357874509842374 & 0.050554 & 0.7079 & 0.483566 & 0.241783 \tabularnewline
t & -0.000149240410139286 & 0.003603 & -0.0414 & 0.967193 & 0.483596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&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]-2.83103972160239[/C][C]4.34225[/C][C]-0.652[/C][C]0.518558[/C][C]0.259279[/C][/ROW]
[ROW][C]X[/C][C]-0.00497969791234237[/C][C]0.001643[/C][C]-3.0301[/C][C]0.004506[/C][C]0.002253[/C][/ROW]
[ROW][C]Y1[/C][C]0.932713845855733[/C][C]0.157745[/C][C]5.9128[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.0849261973825332[/C][C]0.224609[/C][C]-0.3781[/C][C]0.707572[/C][C]0.353786[/C][/ROW]
[ROW][C]Y3[/C][C]-0.295020473860288[/C][C]0.243782[/C][C]-1.2102[/C][C]0.234096[/C][C]0.117048[/C][/ROW]
[ROW][C]Y4[/C][C]0.179390247778269[/C][C]0.239424[/C][C]0.7493[/C][C]0.458569[/C][C]0.229285[/C][/ROW]
[ROW][C]`Y5
`[/C][C]0.299672934182992[/C][C]0.185883[/C][C]1.6122[/C][C]0.115661[/C][C]0.057831[/C][/ROW]
[ROW][C]M1[/C][C]0.066291966934211[/C][C]0.049712[/C][C]1.3335[/C][C]0.190735[/C][C]0.095367[/C][/ROW]
[ROW][C]M2[/C][C]0.070275643501231[/C][C]0.051292[/C][C]1.3701[/C][C]0.179141[/C][C]0.089571[/C][/ROW]
[ROW][C]M3[/C][C]0.0678099255876927[/C][C]0.050229[/C][C]1.35[/C][C]0.185442[/C][C]0.092721[/C][/ROW]
[ROW][C]M4[/C][C]0.155510564164373[/C][C]0.048629[/C][C]3.1979[/C][C]0.002883[/C][C]0.001442[/C][/ROW]
[ROW][C]M5[/C][C]0.181984794020036[/C][C]0.051174[/C][C]3.5562[/C][C]0.001076[/C][C]0.000538[/C][/ROW]
[ROW][C]M6[/C][C]0.128406954400737[/C][C]0.053728[/C][C]2.3899[/C][C]0.022209[/C][C]0.011104[/C][/ROW]
[ROW][C]M7[/C][C]0.123356529101140[/C][C]0.055083[/C][C]2.2395[/C][C]0.031396[/C][C]0.015698[/C][/ROW]
[ROW][C]M8[/C][C]0.144114792469188[/C][C]0.065772[/C][C]2.1911[/C][C]0.034997[/C][C]0.017499[/C][/ROW]
[ROW][C]M9[/C][C]0.102750256297642[/C][C]0.061791[/C][C]1.6629[/C][C]0.105024[/C][C]0.052512[/C][/ROW]
[ROW][C]M10[/C][C]0.080114755808093[/C][C]0.051751[/C][C]1.5481[/C][C]0.130347[/C][C]0.065174[/C][/ROW]
[ROW][C]M11[/C][C]0.0357874509842374[/C][C]0.050554[/C][C]0.7079[/C][C]0.483566[/C][C]0.241783[/C][/ROW]
[ROW][C]t[/C][C]-0.000149240410139286[/C][C]0.003603[/C][C]-0.0414[/C][C]0.967193[/C][C]0.483596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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)	-2.83103972160239	4.34225	-0.652	0.518558	0.259279
X	-0.00497969791234237	0.001643	-3.0301	0.004506	0.002253
Y1	0.932713845855733	0.157745	5.9128	1e-06	0
Y2	-0.0849261973825332	0.224609	-0.3781	0.707572	0.353786
Y3	-0.295020473860288	0.243782	-1.2102	0.234096	0.117048
Y4	0.179390247778269	0.239424	0.7493	0.458569	0.229285
`Y5 `	0.299672934182992	0.185883	1.6122	0.115661	0.057831
M1	0.066291966934211	0.049712	1.3335	0.190735	0.095367
M2	0.070275643501231	0.051292	1.3701	0.179141	0.089571
M3	0.0678099255876927	0.050229	1.35	0.185442	0.092721
M4	0.155510564164373	0.048629	3.1979	0.002883	0.001442
M5	0.181984794020036	0.051174	3.5562	0.001076	0.000538
M6	0.128406954400737	0.053728	2.3899	0.022209	0.011104
M7	0.123356529101140	0.055083	2.2395	0.031396	0.015698
M8	0.144114792469188	0.065772	2.1911	0.034997	0.017499
M9	0.102750256297642	0.061791	1.6629	0.105024	0.052512
M10	0.080114755808093	0.051751	1.5481	0.130347	0.065174
M11	0.0357874509842374	0.050554	0.7079	0.483566	0.241783
t	-0.000149240410139286	0.003603	-0.0414	0.967193	0.483596

Multiple Linear Regression - Regression Statistics
Multiple R	0.997724269607044
R-squared	0.99545371816291
Adjusted R-squared	0.993180577244363
F-TEST (value)	437.919932742148
F-TEST (DF numerator)	18
F-TEST (DF denominator)	36
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0701871577428226
Sum Squared Residuals	0.177344536032571

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.997724269607044 \tabularnewline
R-squared & 0.99545371816291 \tabularnewline
Adjusted R-squared & 0.993180577244363 \tabularnewline
F-TEST (value) & 437.919932742148 \tabularnewline
F-TEST (DF numerator) & 18 \tabularnewline
F-TEST (DF denominator) & 36 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0701871577428226 \tabularnewline
Sum Squared Residuals & 0.177344536032571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.997724269607044[/C][/ROW]
[ROW][C]R-squared[/C][C]0.99545371816291[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.993180577244363[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]437.919932742148[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]18[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]36[/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]0.0701871577428226[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.177344536032571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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	0.997724269607044
R-squared	0.99545371816291
Adjusted R-squared	0.993180577244363
F-TEST (value)	437.919932742148
F-TEST (DF numerator)	18
F-TEST (DF denominator)	36
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0701871577428226
Sum Squared Residuals	0.177344536032571

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	103.91	103.878451238188	0.0315487618122744
2	103.91	103.884020946423	0.0259790535770017
3	103.92	103.889063308894	0.0309366911055615
4	104.05	104.039747577144	0.0102524228558393
5	104.23	104.229303562892	0.000696437108322132
6	104.3	104.354399586063	-0.0543995860629370
7	104.31	104.375591629482	-0.0655916294822722
8	104.31	104.382258159374	-0.0722581593735686
9	104.34	104.399454869934	-0.0594548699339316
10	104.55	104.477661211202	0.0723387887978133
11	104.65	104.644298097635	0.00570190236534622
12	104.73	104.677944404502	0.0520555954984488
13	104.75	104.748161359175	0.00183864082505709
14	104.75	104.776534341010	-0.0265343410101180
15	104.76	104.817538286797	-0.0575382867965953
16	104.94	104.953332896976	-0.0133328969762984
17	105.29	105.173760786601	0.116239213399018
18	105.38	105.421292876465	-0.0412928764651777
19	105.43	105.415019746652	0.0149802533483907
20	105.43	105.415614368471	0.0143856315290806
21	105.42	105.457540305292	-0.0375403052918494
22	105.52	105.530214142131	-0.0102141421309762
23	105.69	105.603847044932	0.086152955067867
24	105.72	105.733423090087	-0.0134230900865648
25	105.74	105.762393006709	-0.0223930067093367
26	105.74	105.730689745631	0.00931025436913267
27	105.74	105.772013647190	-0.0320136471895232
28	105.95	105.916464349409	0.033535650590646
29	106.17	106.142771753015	0.0272282469853371
30	106.34	106.282898646098	0.0571013539019569
31	106.37	106.354626331666	0.0153736683335060
32	106.37	106.356567066317	0.0134329336831226
33	106.36	106.356781677287	0.00321832271262681
34	106.44	106.381867414091	0.0581325859094093
35	106.29	106.457730039545	-0.167730039544940
36	106.23	106.273587383882	-0.0435873838823813
37	106.23	106.232766994951	-0.00276699495084360
38	106.23	106.268422316619	-0.0384223166185613
39	106.23	106.269120579096	-0.0391205790960142
40	106.34	106.310419048302	0.0295809516981365
41	106.44	106.443770825346	-0.00377082534608349
42	106.44	106.471483399234	-0.0314833992339631
43	106.48	106.408407888759	0.0715921112406273
44	106.5	106.455560405839	0.0444395941613654
45	106.57	106.476223147487	0.0937768525131542
46	106.4	106.520257232576	-0.120257232576246
47	106.37	106.294124817888	0.0758751821117265
48	106.25	106.245045121530	0.00495487847049753
49	106.21	106.218227400977	-0.00822740097715119
50	106.21	106.180332650317	0.0296673496825448
51	106.24	106.142264178023	0.0977358219765712
52	106.19	106.250036128168	-0.0600361281683234
53	106.08	106.220393072147	-0.140393072146593
54	106.13	106.059925492140	0.0700745078601208
55	106.09	106.126354403440	-0.0363544034402519

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 103.91 & 103.878451238188 & 0.0315487618122744 \tabularnewline
2 & 103.91 & 103.884020946423 & 0.0259790535770017 \tabularnewline
3 & 103.92 & 103.889063308894 & 0.0309366911055615 \tabularnewline
4 & 104.05 & 104.039747577144 & 0.0102524228558393 \tabularnewline
5 & 104.23 & 104.229303562892 & 0.000696437108322132 \tabularnewline
6 & 104.3 & 104.354399586063 & -0.0543995860629370 \tabularnewline
7 & 104.31 & 104.375591629482 & -0.0655916294822722 \tabularnewline
8 & 104.31 & 104.382258159374 & -0.0722581593735686 \tabularnewline
9 & 104.34 & 104.399454869934 & -0.0594548699339316 \tabularnewline
10 & 104.55 & 104.477661211202 & 0.0723387887978133 \tabularnewline
11 & 104.65 & 104.644298097635 & 0.00570190236534622 \tabularnewline
12 & 104.73 & 104.677944404502 & 0.0520555954984488 \tabularnewline
13 & 104.75 & 104.748161359175 & 0.00183864082505709 \tabularnewline
14 & 104.75 & 104.776534341010 & -0.0265343410101180 \tabularnewline
15 & 104.76 & 104.817538286797 & -0.0575382867965953 \tabularnewline
16 & 104.94 & 104.953332896976 & -0.0133328969762984 \tabularnewline
17 & 105.29 & 105.173760786601 & 0.116239213399018 \tabularnewline
18 & 105.38 & 105.421292876465 & -0.0412928764651777 \tabularnewline
19 & 105.43 & 105.415019746652 & 0.0149802533483907 \tabularnewline
20 & 105.43 & 105.415614368471 & 0.0143856315290806 \tabularnewline
21 & 105.42 & 105.457540305292 & -0.0375403052918494 \tabularnewline
22 & 105.52 & 105.530214142131 & -0.0102141421309762 \tabularnewline
23 & 105.69 & 105.603847044932 & 0.086152955067867 \tabularnewline
24 & 105.72 & 105.733423090087 & -0.0134230900865648 \tabularnewline
25 & 105.74 & 105.762393006709 & -0.0223930067093367 \tabularnewline
26 & 105.74 & 105.730689745631 & 0.00931025436913267 \tabularnewline
27 & 105.74 & 105.772013647190 & -0.0320136471895232 \tabularnewline
28 & 105.95 & 105.916464349409 & 0.033535650590646 \tabularnewline
29 & 106.17 & 106.142771753015 & 0.0272282469853371 \tabularnewline
30 & 106.34 & 106.282898646098 & 0.0571013539019569 \tabularnewline
31 & 106.37 & 106.354626331666 & 0.0153736683335060 \tabularnewline
32 & 106.37 & 106.356567066317 & 0.0134329336831226 \tabularnewline
33 & 106.36 & 106.356781677287 & 0.00321832271262681 \tabularnewline
34 & 106.44 & 106.381867414091 & 0.0581325859094093 \tabularnewline
35 & 106.29 & 106.457730039545 & -0.167730039544940 \tabularnewline
36 & 106.23 & 106.273587383882 & -0.0435873838823813 \tabularnewline
37 & 106.23 & 106.232766994951 & -0.00276699495084360 \tabularnewline
38 & 106.23 & 106.268422316619 & -0.0384223166185613 \tabularnewline
39 & 106.23 & 106.269120579096 & -0.0391205790960142 \tabularnewline
40 & 106.34 & 106.310419048302 & 0.0295809516981365 \tabularnewline
41 & 106.44 & 106.443770825346 & -0.00377082534608349 \tabularnewline
42 & 106.44 & 106.471483399234 & -0.0314833992339631 \tabularnewline
43 & 106.48 & 106.408407888759 & 0.0715921112406273 \tabularnewline
44 & 106.5 & 106.455560405839 & 0.0444395941613654 \tabularnewline
45 & 106.57 & 106.476223147487 & 0.0937768525131542 \tabularnewline
46 & 106.4 & 106.520257232576 & -0.120257232576246 \tabularnewline
47 & 106.37 & 106.294124817888 & 0.0758751821117265 \tabularnewline
48 & 106.25 & 106.245045121530 & 0.00495487847049753 \tabularnewline
49 & 106.21 & 106.218227400977 & -0.00822740097715119 \tabularnewline
50 & 106.21 & 106.180332650317 & 0.0296673496825448 \tabularnewline
51 & 106.24 & 106.142264178023 & 0.0977358219765712 \tabularnewline
52 & 106.19 & 106.250036128168 & -0.0600361281683234 \tabularnewline
53 & 106.08 & 106.220393072147 & -0.140393072146593 \tabularnewline
54 & 106.13 & 106.059925492140 & 0.0700745078601208 \tabularnewline
55 & 106.09 & 106.126354403440 & -0.0363544034402519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&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]103.91[/C][C]103.878451238188[/C][C]0.0315487618122744[/C][/ROW]
[ROW][C]2[/C][C]103.91[/C][C]103.884020946423[/C][C]0.0259790535770017[/C][/ROW]
[ROW][C]3[/C][C]103.92[/C][C]103.889063308894[/C][C]0.0309366911055615[/C][/ROW]
[ROW][C]4[/C][C]104.05[/C][C]104.039747577144[/C][C]0.0102524228558393[/C][/ROW]
[ROW][C]5[/C][C]104.23[/C][C]104.229303562892[/C][C]0.000696437108322132[/C][/ROW]
[ROW][C]6[/C][C]104.3[/C][C]104.354399586063[/C][C]-0.0543995860629370[/C][/ROW]
[ROW][C]7[/C][C]104.31[/C][C]104.375591629482[/C][C]-0.0655916294822722[/C][/ROW]
[ROW][C]8[/C][C]104.31[/C][C]104.382258159374[/C][C]-0.0722581593735686[/C][/ROW]
[ROW][C]9[/C][C]104.34[/C][C]104.399454869934[/C][C]-0.0594548699339316[/C][/ROW]
[ROW][C]10[/C][C]104.55[/C][C]104.477661211202[/C][C]0.0723387887978133[/C][/ROW]
[ROW][C]11[/C][C]104.65[/C][C]104.644298097635[/C][C]0.00570190236534622[/C][/ROW]
[ROW][C]12[/C][C]104.73[/C][C]104.677944404502[/C][C]0.0520555954984488[/C][/ROW]
[ROW][C]13[/C][C]104.75[/C][C]104.748161359175[/C][C]0.00183864082505709[/C][/ROW]
[ROW][C]14[/C][C]104.75[/C][C]104.776534341010[/C][C]-0.0265343410101180[/C][/ROW]
[ROW][C]15[/C][C]104.76[/C][C]104.817538286797[/C][C]-0.0575382867965953[/C][/ROW]
[ROW][C]16[/C][C]104.94[/C][C]104.953332896976[/C][C]-0.0133328969762984[/C][/ROW]
[ROW][C]17[/C][C]105.29[/C][C]105.173760786601[/C][C]0.116239213399018[/C][/ROW]
[ROW][C]18[/C][C]105.38[/C][C]105.421292876465[/C][C]-0.0412928764651777[/C][/ROW]
[ROW][C]19[/C][C]105.43[/C][C]105.415019746652[/C][C]0.0149802533483907[/C][/ROW]
[ROW][C]20[/C][C]105.43[/C][C]105.415614368471[/C][C]0.0143856315290806[/C][/ROW]
[ROW][C]21[/C][C]105.42[/C][C]105.457540305292[/C][C]-0.0375403052918494[/C][/ROW]
[ROW][C]22[/C][C]105.52[/C][C]105.530214142131[/C][C]-0.0102141421309762[/C][/ROW]
[ROW][C]23[/C][C]105.69[/C][C]105.603847044932[/C][C]0.086152955067867[/C][/ROW]
[ROW][C]24[/C][C]105.72[/C][C]105.733423090087[/C][C]-0.0134230900865648[/C][/ROW]
[ROW][C]25[/C][C]105.74[/C][C]105.762393006709[/C][C]-0.0223930067093367[/C][/ROW]
[ROW][C]26[/C][C]105.74[/C][C]105.730689745631[/C][C]0.00931025436913267[/C][/ROW]
[ROW][C]27[/C][C]105.74[/C][C]105.772013647190[/C][C]-0.0320136471895232[/C][/ROW]
[ROW][C]28[/C][C]105.95[/C][C]105.916464349409[/C][C]0.033535650590646[/C][/ROW]
[ROW][C]29[/C][C]106.17[/C][C]106.142771753015[/C][C]0.0272282469853371[/C][/ROW]
[ROW][C]30[/C][C]106.34[/C][C]106.282898646098[/C][C]0.0571013539019569[/C][/ROW]
[ROW][C]31[/C][C]106.37[/C][C]106.354626331666[/C][C]0.0153736683335060[/C][/ROW]
[ROW][C]32[/C][C]106.37[/C][C]106.356567066317[/C][C]0.0134329336831226[/C][/ROW]
[ROW][C]33[/C][C]106.36[/C][C]106.356781677287[/C][C]0.00321832271262681[/C][/ROW]
[ROW][C]34[/C][C]106.44[/C][C]106.381867414091[/C][C]0.0581325859094093[/C][/ROW]
[ROW][C]35[/C][C]106.29[/C][C]106.457730039545[/C][C]-0.167730039544940[/C][/ROW]
[ROW][C]36[/C][C]106.23[/C][C]106.273587383882[/C][C]-0.0435873838823813[/C][/ROW]
[ROW][C]37[/C][C]106.23[/C][C]106.232766994951[/C][C]-0.00276699495084360[/C][/ROW]
[ROW][C]38[/C][C]106.23[/C][C]106.268422316619[/C][C]-0.0384223166185613[/C][/ROW]
[ROW][C]39[/C][C]106.23[/C][C]106.269120579096[/C][C]-0.0391205790960142[/C][/ROW]
[ROW][C]40[/C][C]106.34[/C][C]106.310419048302[/C][C]0.0295809516981365[/C][/ROW]
[ROW][C]41[/C][C]106.44[/C][C]106.443770825346[/C][C]-0.00377082534608349[/C][/ROW]
[ROW][C]42[/C][C]106.44[/C][C]106.471483399234[/C][C]-0.0314833992339631[/C][/ROW]
[ROW][C]43[/C][C]106.48[/C][C]106.408407888759[/C][C]0.0715921112406273[/C][/ROW]
[ROW][C]44[/C][C]106.5[/C][C]106.455560405839[/C][C]0.0444395941613654[/C][/ROW]
[ROW][C]45[/C][C]106.57[/C][C]106.476223147487[/C][C]0.0937768525131542[/C][/ROW]
[ROW][C]46[/C][C]106.4[/C][C]106.520257232576[/C][C]-0.120257232576246[/C][/ROW]
[ROW][C]47[/C][C]106.37[/C][C]106.294124817888[/C][C]0.0758751821117265[/C][/ROW]
[ROW][C]48[/C][C]106.25[/C][C]106.245045121530[/C][C]0.00495487847049753[/C][/ROW]
[ROW][C]49[/C][C]106.21[/C][C]106.218227400977[/C][C]-0.00822740097715119[/C][/ROW]
[ROW][C]50[/C][C]106.21[/C][C]106.180332650317[/C][C]0.0296673496825448[/C][/ROW]
[ROW][C]51[/C][C]106.24[/C][C]106.142264178023[/C][C]0.0977358219765712[/C][/ROW]
[ROW][C]52[/C][C]106.19[/C][C]106.250036128168[/C][C]-0.0600361281683234[/C][/ROW]
[ROW][C]53[/C][C]106.08[/C][C]106.220393072147[/C][C]-0.140393072146593[/C][/ROW]
[ROW][C]54[/C][C]106.13[/C][C]106.059925492140[/C][C]0.0700745078601208[/C][/ROW]
[ROW][C]55[/C][C]106.09[/C][C]106.126354403440[/C][C]-0.0363544034402519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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	103.91	103.878451238188	0.0315487618122744
2	103.91	103.884020946423	0.0259790535770017
3	103.92	103.889063308894	0.0309366911055615
4	104.05	104.039747577144	0.0102524228558393
5	104.23	104.229303562892	0.000696437108322132
6	104.3	104.354399586063	-0.0543995860629370
7	104.31	104.375591629482	-0.0655916294822722
8	104.31	104.382258159374	-0.0722581593735686
9	104.34	104.399454869934	-0.0594548699339316
10	104.55	104.477661211202	0.0723387887978133
11	104.65	104.644298097635	0.00570190236534622
12	104.73	104.677944404502	0.0520555954984488
13	104.75	104.748161359175	0.00183864082505709
14	104.75	104.776534341010	-0.0265343410101180
15	104.76	104.817538286797	-0.0575382867965953
16	104.94	104.953332896976	-0.0133328969762984
17	105.29	105.173760786601	0.116239213399018
18	105.38	105.421292876465	-0.0412928764651777
19	105.43	105.415019746652	0.0149802533483907
20	105.43	105.415614368471	0.0143856315290806
21	105.42	105.457540305292	-0.0375403052918494
22	105.52	105.530214142131	-0.0102141421309762
23	105.69	105.603847044932	0.086152955067867
24	105.72	105.733423090087	-0.0134230900865648
25	105.74	105.762393006709	-0.0223930067093367
26	105.74	105.730689745631	0.00931025436913267
27	105.74	105.772013647190	-0.0320136471895232
28	105.95	105.916464349409	0.033535650590646
29	106.17	106.142771753015	0.0272282469853371
30	106.34	106.282898646098	0.0571013539019569
31	106.37	106.354626331666	0.0153736683335060
32	106.37	106.356567066317	0.0134329336831226
33	106.36	106.356781677287	0.00321832271262681
34	106.44	106.381867414091	0.0581325859094093
35	106.29	106.457730039545	-0.167730039544940
36	106.23	106.273587383882	-0.0435873838823813
37	106.23	106.232766994951	-0.00276699495084360
38	106.23	106.268422316619	-0.0384223166185613
39	106.23	106.269120579096	-0.0391205790960142
40	106.34	106.310419048302	0.0295809516981365
41	106.44	106.443770825346	-0.00377082534608349
42	106.44	106.471483399234	-0.0314833992339631
43	106.48	106.408407888759	0.0715921112406273
44	106.5	106.455560405839	0.0444395941613654
45	106.57	106.476223147487	0.0937768525131542
46	106.4	106.520257232576	-0.120257232576246
47	106.37	106.294124817888	0.0758751821117265
48	106.25	106.245045121530	0.00495487847049753
49	106.21	106.218227400977	-0.00822740097715119
50	106.21	106.180332650317	0.0296673496825448
51	106.24	106.142264178023	0.0977358219765712
52	106.19	106.250036128168	-0.0600361281683234
53	106.08	106.220393072147	-0.140393072146593
54	106.13	106.059925492140	0.0700745078601208
55	106.09	106.126354403440	-0.0363544034402519

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
22	0.171047795996972	0.342095591993943	0.828952204003028
23	0.0790724928354266	0.158144985670853	0.920927507164573
24	0.0553682055472368	0.110736411094474	0.944631794452763
25	0.0903657768176242	0.180731553635248	0.909634223182376
26	0.204462626340326	0.408925252680652	0.795537373659674
27	0.233771117010724	0.467542234021448	0.766228882989276
28	0.146088471827494	0.292176943654988	0.853911528172506
29	0.158435154434980	0.316870308869960	0.84156484556502
30	0.159355091175182	0.318710182350364	0.840644908824818
31	0.08838058442943	0.17676116885886	0.91161941557057
32	0.306315355309148	0.612630710618297	0.693684644690852
33	0.339060398319434	0.678120796638869	0.660939601680566

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
22 & 0.171047795996972 & 0.342095591993943 & 0.828952204003028 \tabularnewline
23 & 0.0790724928354266 & 0.158144985670853 & 0.920927507164573 \tabularnewline
24 & 0.0553682055472368 & 0.110736411094474 & 0.944631794452763 \tabularnewline
25 & 0.0903657768176242 & 0.180731553635248 & 0.909634223182376 \tabularnewline
26 & 0.204462626340326 & 0.408925252680652 & 0.795537373659674 \tabularnewline
27 & 0.233771117010724 & 0.467542234021448 & 0.766228882989276 \tabularnewline
28 & 0.146088471827494 & 0.292176943654988 & 0.853911528172506 \tabularnewline
29 & 0.158435154434980 & 0.316870308869960 & 0.84156484556502 \tabularnewline
30 & 0.159355091175182 & 0.318710182350364 & 0.840644908824818 \tabularnewline
31 & 0.08838058442943 & 0.17676116885886 & 0.91161941557057 \tabularnewline
32 & 0.306315355309148 & 0.612630710618297 & 0.693684644690852 \tabularnewline
33 & 0.339060398319434 & 0.678120796638869 & 0.660939601680566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&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]22[/C][C]0.171047795996972[/C][C]0.342095591993943[/C][C]0.828952204003028[/C][/ROW]
[ROW][C]23[/C][C]0.0790724928354266[/C][C]0.158144985670853[/C][C]0.920927507164573[/C][/ROW]
[ROW][C]24[/C][C]0.0553682055472368[/C][C]0.110736411094474[/C][C]0.944631794452763[/C][/ROW]
[ROW][C]25[/C][C]0.0903657768176242[/C][C]0.180731553635248[/C][C]0.909634223182376[/C][/ROW]
[ROW][C]26[/C][C]0.204462626340326[/C][C]0.408925252680652[/C][C]0.795537373659674[/C][/ROW]
[ROW][C]27[/C][C]0.233771117010724[/C][C]0.467542234021448[/C][C]0.766228882989276[/C][/ROW]
[ROW][C]28[/C][C]0.146088471827494[/C][C]0.292176943654988[/C][C]0.853911528172506[/C][/ROW]
[ROW][C]29[/C][C]0.158435154434980[/C][C]0.316870308869960[/C][C]0.84156484556502[/C][/ROW]
[ROW][C]30[/C][C]0.159355091175182[/C][C]0.318710182350364[/C][C]0.840644908824818[/C][/ROW]
[ROW][C]31[/C][C]0.08838058442943[/C][C]0.17676116885886[/C][C]0.91161941557057[/C][/ROW]
[ROW][C]32[/C][C]0.306315355309148[/C][C]0.612630710618297[/C][C]0.693684644690852[/C][/ROW]
[ROW][C]33[/C][C]0.339060398319434[/C][C]0.678120796638869[/C][C]0.660939601680566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&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
22	0.171047795996972	0.342095591993943	0.828952204003028
23	0.0790724928354266	0.158144985670853	0.920927507164573
24	0.0553682055472368	0.110736411094474	0.944631794452763
25	0.0903657768176242	0.180731553635248	0.909634223182376
26	0.204462626340326	0.408925252680652	0.795537373659674
27	0.233771117010724	0.467542234021448	0.766228882989276
28	0.146088471827494	0.292176943654988	0.853911528172506
29	0.158435154434980	0.316870308869960	0.84156484556502
30	0.159355091175182	0.318710182350364	0.840644908824818
31	0.08838058442943	0.17676116885886	0.91161941557057
32	0.306315355309148	0.612630710618297	0.693684644690852
33	0.339060398319434	0.678120796638869	0.660939601680566

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57224&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57224&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57224&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 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