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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 14 Dec 2009 12:44:45 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/14/t12608199444vl5odvhkvbjwpc.htm/, Retrieved Sun, 05 May 2024 09:59:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67645, Retrieved Sun, 05 May 2024 09:59:20 +0000

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Estimated Impact

106

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] [Seatbelt Law Model 4] [2009-12-14 19:44:45] [befe6dd6a614b6d3a2a74a47a0a4f514] [Current]

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Dataseries X:

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Histogram

Boxplots

7,2	-6	7,5	8,3	8,8	8,9
7,4	0	7,2	7,5	8,3	8,8
8,8	-4	7,4	7,2	7,5	8,3
9,3	-2	8,8	7,4	7,2	7,5
9,3	-2	9,3	8,8	7,4	7,2
8,7	-6	9,3	9,3	8,8	7,4
8,2	-7	8,7	9,3	9,3	8,8
8,3	-6	8,2	8,7	9,3	9,3
8,5	-6	8,3	8,2	8,7	9,3
8,6	-3	8,5	8,3	8,2	8,7
8,5	-2	8,6	8,5	8,3	8,2
8,2	-5	8,5	8,6	8,5	8,3
8,1	-11	8,2	8,5	8,6	8,5
7,9	-11	8,1	8,2	8,5	8,6
8,6	-11	7,9	8,1	8,2	8,5
8,7	-10	8,6	7,9	8,1	8,2
8,7	-14	8,7	8,6	7,9	8,1
8,5	-8	8,7	8,7	8,6	7,9
8,4	-9	8,5	8,7	8,7	8,6
8,5	-5	8,4	8,5	8,7	8,7
8,7	-1	8,5	8,4	8,5	8,7
8,7	-2	8,7	8,5	8,4	8,5
8,6	-5	8,7	8,7	8,5	8,4
8,5	-4	8,6	8,7	8,7	8,5
8,3	-6	8,5	8,6	8,7	8,7
8	-2	8,3	8,5	8,6	8,7
8,2	-2	8	8,3	8,5	8,6
8,1	-2	8,2	8	8,3	8,5
8,1	-2	8,1	8,2	8	8,3
8	2	8,1	8,1	8,2	8
7,9	1	8	8,1	8,1	8,2
7,9	-8	7,9	8	8,1	8,1
8	-1	7,9	7,9	8	8,1
8	1	8	7,9	7,9	8
7,9	-1	8	8	7,9	7,9
8	2	7,9	8	8	7,9
7,7	2	8	7,9	8	8
7,2	1	7,7	8	7,9	8
7,5	-1	7,2	7,7	8	7,9
7,3	-2	7,5	7,2	7,7	8
7	-2	7,3	7,5	7,2	7,7
7	-1	7	7,3	7,5	7,2
7	-8	7	7	7,3	7,5
7,2	-4	7	7	7	7,3
7,3	-6	7,2	7	7	7
7,1	-3	7,3	7,2	7	7
6,8	-3	7,1	7,3	7,2	7
6,4	-7	6,8	7,1	7,3	7,2
6,1	-9	6,4	6,8	7,1	7,3
6,5	-11	6,1	6,4	6,8	7,1
7,7	-13	6,5	6,1	6,4	6,8
7,9	-11	7,7	6,5	6,1	6,4
7,5	-9	7,9	7,7	6,5	6,1
6,9	-17	7,5	7,9	7,7	6,5
6,6	-22	6,9	7,5	7,9	7,7
6,9	-25	6,6	6,9	7,5	7,9

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	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&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]The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
TW[t] = + 1.35270011267557 -0.00657570862911655CV[t] + 1.46760231982947TW1[t] -0.781349635612117TW2[t] -0.150146906344660TW3[t] + 0.312242286743154`TW4 `[t] -0.149267397052989M1[t] -0.115804029829894M2[t] + 0.594188677576061M3[t] -0.413818723946786M4[t] -0.0394767830123892M5[t] + 0.088878732353515M6[t] -0.0152657568680250M7[t] + 0.134639932667193M8[t] + 0.0116315590137514M9[t] -0.0929071923986117M10[t] -0.0189529698826592M11[t] -0.00698033699299656t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TW[t] =  +  1.35270011267557 -0.00657570862911655CV[t] +  1.46760231982947TW1[t] -0.781349635612117TW2[t] -0.150146906344660TW3[t] +  0.312242286743154`TW4
`[t] -0.149267397052989M1[t] -0.115804029829894M2[t] +  0.594188677576061M3[t] -0.413818723946786M4[t] -0.0394767830123892M5[t] +  0.088878732353515M6[t] -0.0152657568680250M7[t] +  0.134639932667193M8[t] +  0.0116315590137514M9[t] -0.0929071923986117M10[t] -0.0189529698826592M11[t] -0.00698033699299656t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TW[t] =  +  1.35270011267557 -0.00657570862911655CV[t] +  1.46760231982947TW1[t] -0.781349635612117TW2[t] -0.150146906344660TW3[t] +  0.312242286743154`TW4
`[t] -0.149267397052989M1[t] -0.115804029829894M2[t] +  0.594188677576061M3[t] -0.413818723946786M4[t] -0.0394767830123892M5[t] +  0.088878732353515M6[t] -0.0152657568680250M7[t] +  0.134639932667193M8[t] +  0.0116315590137514M9[t] -0.0929071923986117M10[t] -0.0189529698826592M11[t] -0.00698033699299656t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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
TW[t] = + 1.35270011267557 -0.00657570862911655CV[t] + 1.46760231982947TW1[t] -0.781349635612117TW2[t] -0.150146906344660TW3[t] + 0.312242286743154`TW4 `[t] -0.149267397052989M1[t] -0.115804029829894M2[t] + 0.594188677576061M3[t] -0.413818723946786M4[t] -0.0394767830123892M5[t] + 0.088878732353515M6[t] -0.0152657568680250M7[t] + 0.134639932667193M8[t] + 0.0116315590137514M9[t] -0.0929071923986117M10[t] -0.0189529698826592M11[t] -0.00698033699299656t + 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)	1.35270011267557	0.585528	2.3102	0.026401	0.013201
CV	-0.00657570862911655	0.004255	-1.5453	0.130566	0.065283
TW1	1.46760231982947	0.137899	10.6426	0	0
TW2	-0.781349635612117	0.265134	-2.947	0.005458	0.002729
TW3	-0.150146906344660	0.267526	-0.5612	0.577927	0.288964
`TW4 `	0.312242286743154	0.139906	2.2318	0.031603	0.015801
M1	-0.149267397052989	0.103935	-1.4362	0.159137	0.079568
M2	-0.115804029829894	0.106599	-1.0864	0.284165	0.142082
M3	0.594188677576061	0.10943	5.4299	3e-06	2e-06
M4	-0.413818723946786	0.141402	-2.9265	0.005758	0.002879
M5	-0.0394767830123892	0.159351	-0.2477	0.805674	0.402837
M6	0.088878732353515	0.121514	0.7314	0.469005	0.234502
M7	-0.0152657568680250	0.103899	-0.1469	0.883965	0.441982
M8	0.134639932667193	0.107486	1.2526	0.217996	0.108998
M9	0.0116315590137514	0.112751	0.1032	0.918377	0.459189
M10	-0.0929071923986117	0.113715	-0.817	0.41901	0.209505
M11	-0.0189529698826592	0.107729	-0.1759	0.861281	0.430641
t	-0.00698033699299656	0.002418	-2.8862	0.006396	0.003198

\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) & 1.35270011267557 & 0.585528 & 2.3102 & 0.026401 & 0.013201 \tabularnewline
CV & -0.00657570862911655 & 0.004255 & -1.5453 & 0.130566 & 0.065283 \tabularnewline
TW1 & 1.46760231982947 & 0.137899 & 10.6426 & 0 & 0 \tabularnewline
TW2 & -0.781349635612117 & 0.265134 & -2.947 & 0.005458 & 0.002729 \tabularnewline
TW3 & -0.150146906344660 & 0.267526 & -0.5612 & 0.577927 & 0.288964 \tabularnewline
`TW4
` & 0.312242286743154 & 0.139906 & 2.2318 & 0.031603 & 0.015801 \tabularnewline
M1 & -0.149267397052989 & 0.103935 & -1.4362 & 0.159137 & 0.079568 \tabularnewline
M2 & -0.115804029829894 & 0.106599 & -1.0864 & 0.284165 & 0.142082 \tabularnewline
M3 & 0.594188677576061 & 0.10943 & 5.4299 & 3e-06 & 2e-06 \tabularnewline
M4 & -0.413818723946786 & 0.141402 & -2.9265 & 0.005758 & 0.002879 \tabularnewline
M5 & -0.0394767830123892 & 0.159351 & -0.2477 & 0.805674 & 0.402837 \tabularnewline
M6 & 0.088878732353515 & 0.121514 & 0.7314 & 0.469005 & 0.234502 \tabularnewline
M7 & -0.0152657568680250 & 0.103899 & -0.1469 & 0.883965 & 0.441982 \tabularnewline
M8 & 0.134639932667193 & 0.107486 & 1.2526 & 0.217996 & 0.108998 \tabularnewline
M9 & 0.0116315590137514 & 0.112751 & 0.1032 & 0.918377 & 0.459189 \tabularnewline
M10 & -0.0929071923986117 & 0.113715 & -0.817 & 0.41901 & 0.209505 \tabularnewline
M11 & -0.0189529698826592 & 0.107729 & -0.1759 & 0.861281 & 0.430641 \tabularnewline
t & -0.00698033699299656 & 0.002418 & -2.8862 & 0.006396 & 0.003198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&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]1.35270011267557[/C][C]0.585528[/C][C]2.3102[/C][C]0.026401[/C][C]0.013201[/C][/ROW]
[ROW][C]CV[/C][C]-0.00657570862911655[/C][C]0.004255[/C][C]-1.5453[/C][C]0.130566[/C][C]0.065283[/C][/ROW]
[ROW][C]TW1[/C][C]1.46760231982947[/C][C]0.137899[/C][C]10.6426[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]TW2[/C][C]-0.781349635612117[/C][C]0.265134[/C][C]-2.947[/C][C]0.005458[/C][C]0.002729[/C][/ROW]
[ROW][C]TW3[/C][C]-0.150146906344660[/C][C]0.267526[/C][C]-0.5612[/C][C]0.577927[/C][C]0.288964[/C][/ROW]
[ROW][C]`TW4
`[/C][C]0.312242286743154[/C][C]0.139906[/C][C]2.2318[/C][C]0.031603[/C][C]0.015801[/C][/ROW]
[ROW][C]M1[/C][C]-0.149267397052989[/C][C]0.103935[/C][C]-1.4362[/C][C]0.159137[/C][C]0.079568[/C][/ROW]
[ROW][C]M2[/C][C]-0.115804029829894[/C][C]0.106599[/C][C]-1.0864[/C][C]0.284165[/C][C]0.142082[/C][/ROW]
[ROW][C]M3[/C][C]0.594188677576061[/C][C]0.10943[/C][C]5.4299[/C][C]3e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M4[/C][C]-0.413818723946786[/C][C]0.141402[/C][C]-2.9265[/C][C]0.005758[/C][C]0.002879[/C][/ROW]
[ROW][C]M5[/C][C]-0.0394767830123892[/C][C]0.159351[/C][C]-0.2477[/C][C]0.805674[/C][C]0.402837[/C][/ROW]
[ROW][C]M6[/C][C]0.088878732353515[/C][C]0.121514[/C][C]0.7314[/C][C]0.469005[/C][C]0.234502[/C][/ROW]
[ROW][C]M7[/C][C]-0.0152657568680250[/C][C]0.103899[/C][C]-0.1469[/C][C]0.883965[/C][C]0.441982[/C][/ROW]
[ROW][C]M8[/C][C]0.134639932667193[/C][C]0.107486[/C][C]1.2526[/C][C]0.217996[/C][C]0.108998[/C][/ROW]
[ROW][C]M9[/C][C]0.0116315590137514[/C][C]0.112751[/C][C]0.1032[/C][C]0.918377[/C][C]0.459189[/C][/ROW]
[ROW][C]M10[/C][C]-0.0929071923986117[/C][C]0.113715[/C][C]-0.817[/C][C]0.41901[/C][C]0.209505[/C][/ROW]
[ROW][C]M11[/C][C]-0.0189529698826592[/C][C]0.107729[/C][C]-0.1759[/C][C]0.861281[/C][C]0.430641[/C][/ROW]
[ROW][C]t[/C][C]-0.00698033699299656[/C][C]0.002418[/C][C]-2.8862[/C][C]0.006396[/C][C]0.003198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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)	1.35270011267557	0.585528	2.3102	0.026401	0.013201
CV	-0.00657570862911655	0.004255	-1.5453	0.130566	0.065283
TW1	1.46760231982947	0.137899	10.6426	0	0
TW2	-0.781349635612117	0.265134	-2.947	0.005458	0.002729
TW3	-0.150146906344660	0.267526	-0.5612	0.577927	0.288964
`TW4 `	0.312242286743154	0.139906	2.2318	0.031603	0.015801
M1	-0.149267397052989	0.103935	-1.4362	0.159137	0.079568
M2	-0.115804029829894	0.106599	-1.0864	0.284165	0.142082
M3	0.594188677576061	0.10943	5.4299	3e-06	2e-06
M4	-0.413818723946786	0.141402	-2.9265	0.005758	0.002879
M5	-0.0394767830123892	0.159351	-0.2477	0.805674	0.402837
M6	0.088878732353515	0.121514	0.7314	0.469005	0.234502
M7	-0.0152657568680250	0.103899	-0.1469	0.883965	0.441982
M8	0.134639932667193	0.107486	1.2526	0.217996	0.108998
M9	0.0116315590137514	0.112751	0.1032	0.918377	0.459189
M10	-0.0929071923986117	0.113715	-0.817	0.41901	0.209505
M11	-0.0189529698826592	0.107729	-0.1759	0.861281	0.430641
t	-0.00698033699299656	0.002418	-2.8862	0.006396	0.003198

Multiple Linear Regression - Regression Statistics
Multiple R	0.986015428500645
R-squared	0.97222642524131
Adjusted R-squared	0.959801404954528
F-TEST (value)	78.2474718593075
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.149133013777705
Sum Squared Residuals	0.84514492034

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.986015428500645 \tabularnewline
R-squared & 0.97222642524131 \tabularnewline
Adjusted R-squared & 0.959801404954528 \tabularnewline
F-TEST (value) & 78.2474718593075 \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 & 0.149133013777705 \tabularnewline
Sum Squared Residuals & 0.84514492034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.986015428500645[/C][/ROW]
[ROW][C]R-squared[/C][C]0.97222642524131[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.959801404954528[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]78.2474718593075[/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]0.149133013777705[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.84514492034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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	0.986015428500645
R-squared	0.97222642524131
Adjusted R-squared	0.959801404954528
F-TEST (value)	78.2474718593075
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.149133013777705
Sum Squared Residuals	0.84514492034

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.2	7.21538562972578	-0.0153856297257767
2	7.4	7.43106264522006	-0.0310626452200583
3	8.8	8.65229958650316	0.147700413496839
4	9.3	9.3177839938768	-0.0177839938767922
5	9.3	9.20135520058408	0.098644799415917
6	8.7	8.8106011841335	-0.110601184133507
7	8.2	8.18755642291849	0.0124435770815104
8	8.3	8.21503583165571	0.0849641683442926
9	8.5	8.71257031460507	-0.212570314605074
10	8.6	8.68443768184348	-0.0844376818434823
11	8.5	8.5641903295918	-0.0641903295918009
12	8.2	8.37218974023004	-0.172189740230040
13	8.1	7.94068429228529	0.159315707714712
14	7.9	8.10105090052486	-0.201050900524857
15	8.6	8.60249761376222	-0.00249761376221810
16	8.7	8.68586772223183	0.0141322777681728
17	8.7	8.67815280033877	0.0218471996612257
18	8.5	8.51438747158588	-0.0143874715858782
19	8.4	8.31987280012031	0.0801271998796932
20	8.5	8.47722924195985	0.0227707580401458
21	8.7	8.57586227361004	0.124137726389959
22	8.7	8.63887062752431	0.0611293724756861
23	8.6	8.52306279250342	0.076937207496585
24	8.5	8.3828943321864	0.117105667813602
25	8.3	8.23362120432554	0.0663787956744591
26	8	8.03343059026896	-0.0334305902689587
27	8.2	8.43622265381565	-0.23622265381565
28	8.1	7.94796542254395	0.152034577456049
29	8.1	7.99489248193475	0.105107518065251
30	8	8.04439772206052	-0.0443977220605231
31	7.9	7.87055152047525	0.0294484795247471
32	7.9	7.97280875358347	-0.0728087535834725
33	8	7.8899397367289	0.110060263271103
34	8	7.8958199250084	0.104180074991599
35	7.9	7.86658603555406	0.0334139644459371
36	8	7.69705661993896	0.302943380061036
37	7.7	7.79692831011145	-0.0969283101114518
38	7.2	7.32658608009508	-0.126586080095081
39	7.5	7.49711467922639	0.00288532077360756
40	7.3	7.39592646367228	-0.0959264636722778
41	7	7.21676348011353	-0.216763480113532
42	7	6.84638696575593	0.153613034244069
43	7	7.13939905792072	-0.139399057920724
44	7.2	7.23861719050125	-0.0386171905012457
45	7.3	7.32162767505599	-0.0216276750559888
46	7.1	7.1808717656238	-0.0808717656238027
47	6.8	6.84616084235072	-0.0461608423507212
48	6.4	6.6478593076446	-0.247859307644598
49	6.1	6.21338056355194	-0.113380563551942
50	6.5	6.10786978389104	0.392130216108955
51	7.7	7.61186546669258	0.088134533307422
52	7.9	7.95245639767515	-0.0524563976751523
53	7.5	7.50883603702886	-0.00883603702886197
54	6.9	6.88422665646416	0.0157733435358398
55	6.6	6.58262019856523	0.0173798014347733
56	6.9	6.89630898229972	0.00369101770027978

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.2 & 7.21538562972578 & -0.0153856297257767 \tabularnewline
2 & 7.4 & 7.43106264522006 & -0.0310626452200583 \tabularnewline
3 & 8.8 & 8.65229958650316 & 0.147700413496839 \tabularnewline
4 & 9.3 & 9.3177839938768 & -0.0177839938767922 \tabularnewline
5 & 9.3 & 9.20135520058408 & 0.098644799415917 \tabularnewline
6 & 8.7 & 8.8106011841335 & -0.110601184133507 \tabularnewline
7 & 8.2 & 8.18755642291849 & 0.0124435770815104 \tabularnewline
8 & 8.3 & 8.21503583165571 & 0.0849641683442926 \tabularnewline
9 & 8.5 & 8.71257031460507 & -0.212570314605074 \tabularnewline
10 & 8.6 & 8.68443768184348 & -0.0844376818434823 \tabularnewline
11 & 8.5 & 8.5641903295918 & -0.0641903295918009 \tabularnewline
12 & 8.2 & 8.37218974023004 & -0.172189740230040 \tabularnewline
13 & 8.1 & 7.94068429228529 & 0.159315707714712 \tabularnewline
14 & 7.9 & 8.10105090052486 & -0.201050900524857 \tabularnewline
15 & 8.6 & 8.60249761376222 & -0.00249761376221810 \tabularnewline
16 & 8.7 & 8.68586772223183 & 0.0141322777681728 \tabularnewline
17 & 8.7 & 8.67815280033877 & 0.0218471996612257 \tabularnewline
18 & 8.5 & 8.51438747158588 & -0.0143874715858782 \tabularnewline
19 & 8.4 & 8.31987280012031 & 0.0801271998796932 \tabularnewline
20 & 8.5 & 8.47722924195985 & 0.0227707580401458 \tabularnewline
21 & 8.7 & 8.57586227361004 & 0.124137726389959 \tabularnewline
22 & 8.7 & 8.63887062752431 & 0.0611293724756861 \tabularnewline
23 & 8.6 & 8.52306279250342 & 0.076937207496585 \tabularnewline
24 & 8.5 & 8.3828943321864 & 0.117105667813602 \tabularnewline
25 & 8.3 & 8.23362120432554 & 0.0663787956744591 \tabularnewline
26 & 8 & 8.03343059026896 & -0.0334305902689587 \tabularnewline
27 & 8.2 & 8.43622265381565 & -0.23622265381565 \tabularnewline
28 & 8.1 & 7.94796542254395 & 0.152034577456049 \tabularnewline
29 & 8.1 & 7.99489248193475 & 0.105107518065251 \tabularnewline
30 & 8 & 8.04439772206052 & -0.0443977220605231 \tabularnewline
31 & 7.9 & 7.87055152047525 & 0.0294484795247471 \tabularnewline
32 & 7.9 & 7.97280875358347 & -0.0728087535834725 \tabularnewline
33 & 8 & 7.8899397367289 & 0.110060263271103 \tabularnewline
34 & 8 & 7.8958199250084 & 0.104180074991599 \tabularnewline
35 & 7.9 & 7.86658603555406 & 0.0334139644459371 \tabularnewline
36 & 8 & 7.69705661993896 & 0.302943380061036 \tabularnewline
37 & 7.7 & 7.79692831011145 & -0.0969283101114518 \tabularnewline
38 & 7.2 & 7.32658608009508 & -0.126586080095081 \tabularnewline
39 & 7.5 & 7.49711467922639 & 0.00288532077360756 \tabularnewline
40 & 7.3 & 7.39592646367228 & -0.0959264636722778 \tabularnewline
41 & 7 & 7.21676348011353 & -0.216763480113532 \tabularnewline
42 & 7 & 6.84638696575593 & 0.153613034244069 \tabularnewline
43 & 7 & 7.13939905792072 & -0.139399057920724 \tabularnewline
44 & 7.2 & 7.23861719050125 & -0.0386171905012457 \tabularnewline
45 & 7.3 & 7.32162767505599 & -0.0216276750559888 \tabularnewline
46 & 7.1 & 7.1808717656238 & -0.0808717656238027 \tabularnewline
47 & 6.8 & 6.84616084235072 & -0.0461608423507212 \tabularnewline
48 & 6.4 & 6.6478593076446 & -0.247859307644598 \tabularnewline
49 & 6.1 & 6.21338056355194 & -0.113380563551942 \tabularnewline
50 & 6.5 & 6.10786978389104 & 0.392130216108955 \tabularnewline
51 & 7.7 & 7.61186546669258 & 0.088134533307422 \tabularnewline
52 & 7.9 & 7.95245639767515 & -0.0524563976751523 \tabularnewline
53 & 7.5 & 7.50883603702886 & -0.00883603702886197 \tabularnewline
54 & 6.9 & 6.88422665646416 & 0.0157733435358398 \tabularnewline
55 & 6.6 & 6.58262019856523 & 0.0173798014347733 \tabularnewline
56 & 6.9 & 6.89630898229972 & 0.00369101770027978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&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]7.2[/C][C]7.21538562972578[/C][C]-0.0153856297257767[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.43106264522006[/C][C]-0.0310626452200583[/C][/ROW]
[ROW][C]3[/C][C]8.8[/C][C]8.65229958650316[/C][C]0.147700413496839[/C][/ROW]
[ROW][C]4[/C][C]9.3[/C][C]9.3177839938768[/C][C]-0.0177839938767922[/C][/ROW]
[ROW][C]5[/C][C]9.3[/C][C]9.20135520058408[/C][C]0.098644799415917[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.8106011841335[/C][C]-0.110601184133507[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.18755642291849[/C][C]0.0124435770815104[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.21503583165571[/C][C]0.0849641683442926[/C][/ROW]
[ROW][C]9[/C][C]8.5[/C][C]8.71257031460507[/C][C]-0.212570314605074[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.68443768184348[/C][C]-0.0844376818434823[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.5641903295918[/C][C]-0.0641903295918009[/C][/ROW]
[ROW][C]12[/C][C]8.2[/C][C]8.37218974023004[/C][C]-0.172189740230040[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]7.94068429228529[/C][C]0.159315707714712[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.10105090052486[/C][C]-0.201050900524857[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.60249761376222[/C][C]-0.00249761376221810[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.68586772223183[/C][C]0.0141322777681728[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.67815280033877[/C][C]0.0218471996612257[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.51438747158588[/C][C]-0.0143874715858782[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.31987280012031[/C][C]0.0801271998796932[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.47722924195985[/C][C]0.0227707580401458[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.57586227361004[/C][C]0.124137726389959[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.63887062752431[/C][C]0.0611293724756861[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.52306279250342[/C][C]0.076937207496585[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.3828943321864[/C][C]0.117105667813602[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.23362120432554[/C][C]0.0663787956744591[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.03343059026896[/C][C]-0.0334305902689587[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.43622265381565[/C][C]-0.23622265381565[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.94796542254395[/C][C]0.152034577456049[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]7.99489248193475[/C][C]0.105107518065251[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.04439772206052[/C][C]-0.0443977220605231[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.87055152047525[/C][C]0.0294484795247471[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.97280875358347[/C][C]-0.0728087535834725[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.8899397367289[/C][C]0.110060263271103[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.8958199250084[/C][C]0.104180074991599[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.86658603555406[/C][C]0.0334139644459371[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.69705661993896[/C][C]0.302943380061036[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]7.79692831011145[/C][C]-0.0969283101114518[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.32658608009508[/C][C]-0.126586080095081[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.49711467922639[/C][C]0.00288532077360756[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.39592646367228[/C][C]-0.0959264636722778[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.21676348011353[/C][C]-0.216763480113532[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.84638696575593[/C][C]0.153613034244069[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]7.13939905792072[/C][C]-0.139399057920724[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.23861719050125[/C][C]-0.0386171905012457[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.32162767505599[/C][C]-0.0216276750559888[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.1808717656238[/C][C]-0.0808717656238027[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.84616084235072[/C][C]-0.0461608423507212[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.6478593076446[/C][C]-0.247859307644598[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.21338056355194[/C][C]-0.113380563551942[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.10786978389104[/C][C]0.392130216108955[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.61186546669258[/C][C]0.088134533307422[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.95245639767515[/C][C]-0.0524563976751523[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]7.50883603702886[/C][C]-0.00883603702886197[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.88422665646416[/C][C]0.0157733435358398[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.58262019856523[/C][C]0.0173798014347733[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.89630898229972[/C][C]0.00369101770027978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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	7.2	7.21538562972578	-0.0153856297257767
2	7.4	7.43106264522006	-0.0310626452200583
3	8.8	8.65229958650316	0.147700413496839
4	9.3	9.3177839938768	-0.0177839938767922
5	9.3	9.20135520058408	0.098644799415917
6	8.7	8.8106011841335	-0.110601184133507
7	8.2	8.18755642291849	0.0124435770815104
8	8.3	8.21503583165571	0.0849641683442926
9	8.5	8.71257031460507	-0.212570314605074
10	8.6	8.68443768184348	-0.0844376818434823
11	8.5	8.5641903295918	-0.0641903295918009
12	8.2	8.37218974023004	-0.172189740230040
13	8.1	7.94068429228529	0.159315707714712
14	7.9	8.10105090052486	-0.201050900524857
15	8.6	8.60249761376222	-0.00249761376221810
16	8.7	8.68586772223183	0.0141322777681728
17	8.7	8.67815280033877	0.0218471996612257
18	8.5	8.51438747158588	-0.0143874715858782
19	8.4	8.31987280012031	0.0801271998796932
20	8.5	8.47722924195985	0.0227707580401458
21	8.7	8.57586227361004	0.124137726389959
22	8.7	8.63887062752431	0.0611293724756861
23	8.6	8.52306279250342	0.076937207496585
24	8.5	8.3828943321864	0.117105667813602
25	8.3	8.23362120432554	0.0663787956744591
26	8	8.03343059026896	-0.0334305902689587
27	8.2	8.43622265381565	-0.23622265381565
28	8.1	7.94796542254395	0.152034577456049
29	8.1	7.99489248193475	0.105107518065251
30	8	8.04439772206052	-0.0443977220605231
31	7.9	7.87055152047525	0.0294484795247471
32	7.9	7.97280875358347	-0.0728087535834725
33	8	7.8899397367289	0.110060263271103
34	8	7.8958199250084	0.104180074991599
35	7.9	7.86658603555406	0.0334139644459371
36	8	7.69705661993896	0.302943380061036
37	7.7	7.79692831011145	-0.0969283101114518
38	7.2	7.32658608009508	-0.126586080095081
39	7.5	7.49711467922639	0.00288532077360756
40	7.3	7.39592646367228	-0.0959264636722778
41	7	7.21676348011353	-0.216763480113532
42	7	6.84638696575593	0.153613034244069
43	7	7.13939905792072	-0.139399057920724
44	7.2	7.23861719050125	-0.0386171905012457
45	7.3	7.32162767505599	-0.0216276750559888
46	7.1	7.1808717656238	-0.0808717656238027
47	6.8	6.84616084235072	-0.0461608423507212
48	6.4	6.6478593076446	-0.247859307644598
49	6.1	6.21338056355194	-0.113380563551942
50	6.5	6.10786978389104	0.392130216108955
51	7.7	7.61186546669258	0.088134533307422
52	7.9	7.95245639767515	-0.0524563976751523
53	7.5	7.50883603702886	-0.00883603702886197
54	6.9	6.88422665646416	0.0157733435358398
55	6.6	6.58262019856523	0.0173798014347733
56	6.9	6.89630898229972	0.00369101770027978

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.0950031305655785	0.190006261131157	0.904996869434421
22	0.165191891261600	0.330383782523201	0.8348081087384
23	0.08341105832629	0.16682211665258	0.91658894167371
24	0.0354965244777141	0.0709930489554282	0.964503475522286
25	0.0666317042918453	0.133263408583691	0.933368295708155
26	0.0371231151660062	0.0742462303320124	0.962876884833994
27	0.228538783629487	0.457077567258973	0.771461216370513
28	0.159654305078609	0.319308610157218	0.840345694921391
29	0.100178231659854	0.200356463319708	0.899821768340146
30	0.0815446049069758	0.163089209813952	0.918455395093024
31	0.0644747470010004	0.128949494002001	0.935525252999
32	0.0571982513285374	0.114396502657075	0.942801748671463
33	0.0324382665405526	0.0648765330811053	0.967561733459447
34	0.0142519915922420	0.0285039831844839	0.985748008407758
35	0.00506901033022194	0.0101380206604439	0.994930989669778

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0950031305655785 & 0.190006261131157 & 0.904996869434421 \tabularnewline
22 & 0.165191891261600 & 0.330383782523201 & 0.8348081087384 \tabularnewline
23 & 0.08341105832629 & 0.16682211665258 & 0.91658894167371 \tabularnewline
24 & 0.0354965244777141 & 0.0709930489554282 & 0.964503475522286 \tabularnewline
25 & 0.0666317042918453 & 0.133263408583691 & 0.933368295708155 \tabularnewline
26 & 0.0371231151660062 & 0.0742462303320124 & 0.962876884833994 \tabularnewline
27 & 0.228538783629487 & 0.457077567258973 & 0.771461216370513 \tabularnewline
28 & 0.159654305078609 & 0.319308610157218 & 0.840345694921391 \tabularnewline
29 & 0.100178231659854 & 0.200356463319708 & 0.899821768340146 \tabularnewline
30 & 0.0815446049069758 & 0.163089209813952 & 0.918455395093024 \tabularnewline
31 & 0.0644747470010004 & 0.128949494002001 & 0.935525252999 \tabularnewline
32 & 0.0571982513285374 & 0.114396502657075 & 0.942801748671463 \tabularnewline
33 & 0.0324382665405526 & 0.0648765330811053 & 0.967561733459447 \tabularnewline
34 & 0.0142519915922420 & 0.0285039831844839 & 0.985748008407758 \tabularnewline
35 & 0.00506901033022194 & 0.0101380206604439 & 0.994930989669778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&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]0.0950031305655785[/C][C]0.190006261131157[/C][C]0.904996869434421[/C][/ROW]
[ROW][C]22[/C][C]0.165191891261600[/C][C]0.330383782523201[/C][C]0.8348081087384[/C][/ROW]
[ROW][C]23[/C][C]0.08341105832629[/C][C]0.16682211665258[/C][C]0.91658894167371[/C][/ROW]
[ROW][C]24[/C][C]0.0354965244777141[/C][C]0.0709930489554282[/C][C]0.964503475522286[/C][/ROW]
[ROW][C]25[/C][C]0.0666317042918453[/C][C]0.133263408583691[/C][C]0.933368295708155[/C][/ROW]
[ROW][C]26[/C][C]0.0371231151660062[/C][C]0.0742462303320124[/C][C]0.962876884833994[/C][/ROW]
[ROW][C]27[/C][C]0.228538783629487[/C][C]0.457077567258973[/C][C]0.771461216370513[/C][/ROW]
[ROW][C]28[/C][C]0.159654305078609[/C][C]0.319308610157218[/C][C]0.840345694921391[/C][/ROW]
[ROW][C]29[/C][C]0.100178231659854[/C][C]0.200356463319708[/C][C]0.899821768340146[/C][/ROW]
[ROW][C]30[/C][C]0.0815446049069758[/C][C]0.163089209813952[/C][C]0.918455395093024[/C][/ROW]
[ROW][C]31[/C][C]0.0644747470010004[/C][C]0.128949494002001[/C][C]0.935525252999[/C][/ROW]
[ROW][C]32[/C][C]0.0571982513285374[/C][C]0.114396502657075[/C][C]0.942801748671463[/C][/ROW]
[ROW][C]33[/C][C]0.0324382665405526[/C][C]0.0648765330811053[/C][C]0.967561733459447[/C][/ROW]
[ROW][C]34[/C][C]0.0142519915922420[/C][C]0.0285039831844839[/C][C]0.985748008407758[/C][/ROW]
[ROW][C]35[/C][C]0.00506901033022194[/C][C]0.0101380206604439[/C][C]0.994930989669778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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	0.0950031305655785	0.190006261131157	0.904996869434421
22	0.165191891261600	0.330383782523201	0.8348081087384
23	0.08341105832629	0.16682211665258	0.91658894167371
24	0.0354965244777141	0.0709930489554282	0.964503475522286
25	0.0666317042918453	0.133263408583691	0.933368295708155
26	0.0371231151660062	0.0742462303320124	0.962876884833994
27	0.228538783629487	0.457077567258973	0.771461216370513
28	0.159654305078609	0.319308610157218	0.840345694921391
29	0.100178231659854	0.200356463319708	0.899821768340146
30	0.0815446049069758	0.163089209813952	0.918455395093024
31	0.0644747470010004	0.128949494002001	0.935525252999
32	0.0571982513285374	0.114396502657075	0.942801748671463
33	0.0324382665405526	0.0648765330811053	0.967561733459447
34	0.0142519915922420	0.0285039831844839	0.985748008407758
35	0.00506901033022194	0.0101380206604439	0.994930989669778

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	2	0.133333333333333	NOK
10% type I error level	5	0.333333333333333	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 & 0 & 0 & OK \tabularnewline
5% type I error level & 2 & 0.133333333333333 & NOK \tabularnewline
10% type I error level & 5 & 0.333333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67645&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]2[/C][C]0.133333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67645&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67645&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	2	0.133333333333333	NOK
10% type I error level	5	0.333333333333333	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