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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 14 Dec 2010 18:22:33 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292350896y0gat3e713bbpuk.htm/, Retrieved Thu, 02 May 2024 15:14:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109985, Retrieved Thu, 02 May 2024 15:14:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Recursive Partitioning (Regression Trees)] [] [2010-12-05 18:59:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [WS 10 - Multiple ...] [2010-12-11 15:55:17] [033eb2749a430605d9b2be7c4aac4a0c]
-   PD      [Multiple Regression] [SP] [2010-12-14 18:22:33] [cda497ce08bc921f0aec22acd67c882b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1	1	6.3	2.1	3.5	0.075	1.2	42	1
2	2	6.6	4.1	6	0.785	3.5	42	2
2	2	9.5	1.2	10.4	0.2	5	120	2
5	5	3.3	0.5	20	27.66	115	148	5
1	2	11	3.4	3.9	0.12	1	16	3
3	1	4.7	1.5	41	85	325	310	1
1	3	10.4	3.4	9	0.101	4	28	5
3	4	7.4	0.8	7.6	1.04	5.5	68	5
5	5	2.1	0.8	46	521	655	336	5
1	1	17.9	2	24	0.01	0.25	50	1
1	1	6.1	1.9	100	62	1320	267	1
1	3	11.9	1.3	3.2	0.023	0.4	19	4
1	1	13.8	5.6	5	1.7	6.3	12	2
1	1	14.3	3.1	6.5	3.5	10.8	120	2
2	2	15.2	1.8	12	0.48	15.5	140	2
4	4	10	0.9	20.2	10	115	170	4
1	2	11.9	1.8	13	1.62	11.4	17	2
4	4	6.5	1.9	27	192	180	115	4
5	5	7.5	0.9	18	2.5	12.1	31	5
1	3	10.6	2.6	4.7	0.28	1.9	21	3
1	1	7.4	2.4	9.8	4.235	50.4	52	1
3	2	8.4	1.2	29	6.8	179	164	2
2	2	5.7	0.9	7	0.75	12.3	225	2
2	3	4.9	0.5	6	3.6	21	225	3
5	5	3.2	0.6	20	55.5	175	151	5
1	2	11	2.3	4.5	0.9	2.6	60	2
1	3	4.9	0.5	7.5	2	12.3	200	3
2	2	13.2	2.6	2.3	0.104	2.5	46	3
3	4	9.7	0.6	24	4.19	58	210	4
1	1	12.8	6.6	3	3.5	3.9	14	2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
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 & 6 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \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=109985&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/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=109985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
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
S[t] = -0.44848360563522 + 1.01946778957491D[t] -0.0701399164268452SWS[t] + 0.236237232406613PS[t] + 0.0731354251388876L[t] + 0.00206321954317301WB[t] -0.00542342168080034Wbr[t] + 0.00257997006234144Tg[t] -0.272489817386976`P `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
S[t] =  -0.44848360563522 +  1.01946778957491D[t] -0.0701399164268452SWS[t] +  0.236237232406613PS[t] +  0.0731354251388876L[t] +  0.00206321954317301WB[t] -0.00542342168080034Wbr[t] +  0.00257997006234144Tg[t] -0.272489817386976`P
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]S[t] =  -0.44848360563522 +  1.01946778957491D[t] -0.0701399164268452SWS[t] +  0.236237232406613PS[t] +  0.0731354251388876L[t] +  0.00206321954317301WB[t] -0.00542342168080034Wbr[t] +  0.00257997006234144Tg[t] -0.272489817386976`P
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
S[t] = -0.44848360563522 + 1.01946778957491D[t] -0.0701399164268452SWS[t] + 0.236237232406613PS[t] + 0.0731354251388876L[t] + 0.00206321954317301WB[t] -0.00542342168080034Wbr[t] + 0.00257997006234144Tg[t] -0.272489817386976`P `[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.448483605635221.034829-0.43340.6691510.334576
D1.019467789574910.430242.36950.0274690.013735
SWS-0.07013991642684520.056213-1.24780.2258530.112927
PS0.2362372324066130.1650021.43170.166940.08347
L0.07313542513888760.0294312.4850.0214610.010731
WB0.002063219543173010.0020531.00520.3262530.163126
Wbr-0.005423421680800340.002222-2.44130.0235770.011788
Tg0.002579970062341440.0026670.96750.3443040.172152
`P `-0.2724898173869760.348129-0.78270.4425260.221263

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -0.44848360563522 & 1.034829 & -0.4334 & 0.669151 & 0.334576 \tabularnewline
D & 1.01946778957491 & 0.43024 & 2.3695 & 0.027469 & 0.013735 \tabularnewline
SWS & -0.0701399164268452 & 0.056213 & -1.2478 & 0.225853 & 0.112927 \tabularnewline
PS & 0.236237232406613 & 0.165002 & 1.4317 & 0.16694 & 0.08347 \tabularnewline
L & 0.0731354251388876 & 0.029431 & 2.485 & 0.021461 & 0.010731 \tabularnewline
WB & 0.00206321954317301 & 0.002053 & 1.0052 & 0.326253 & 0.163126 \tabularnewline
Wbr & -0.00542342168080034 & 0.002222 & -2.4413 & 0.023577 & 0.011788 \tabularnewline
Tg & 0.00257997006234144 & 0.002667 & 0.9675 & 0.344304 & 0.172152 \tabularnewline
`P
` & -0.272489817386976 & 0.348129 & -0.7827 & 0.442526 & 0.221263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-0.44848360563522[/C][C]1.034829[/C][C]-0.4334[/C][C]0.669151[/C][C]0.334576[/C][/ROW]
[ROW][C]D[/C][C]1.01946778957491[/C][C]0.43024[/C][C]2.3695[/C][C]0.027469[/C][C]0.013735[/C][/ROW]
[ROW][C]SWS[/C][C]-0.0701399164268452[/C][C]0.056213[/C][C]-1.2478[/C][C]0.225853[/C][C]0.112927[/C][/ROW]
[ROW][C]PS[/C][C]0.236237232406613[/C][C]0.165002[/C][C]1.4317[/C][C]0.16694[/C][C]0.08347[/C][/ROW]
[ROW][C]L[/C][C]0.0731354251388876[/C][C]0.029431[/C][C]2.485[/C][C]0.021461[/C][C]0.010731[/C][/ROW]
[ROW][C]WB[/C][C]0.00206321954317301[/C][C]0.002053[/C][C]1.0052[/C][C]0.326253[/C][C]0.163126[/C][/ROW]
[ROW][C]Wbr[/C][C]-0.00542342168080034[/C][C]0.002222[/C][C]-2.4413[/C][C]0.023577[/C][C]0.011788[/C][/ROW]
[ROW][C]Tg[/C][C]0.00257997006234144[/C][C]0.002667[/C][C]0.9675[/C][C]0.344304[/C][C]0.172152[/C][/ROW]
[ROW][C]`P
`[/C][C]-0.272489817386976[/C][C]0.348129[/C][C]-0.7827[/C][C]0.442526[/C][C]0.221263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.448483605635221.034829-0.43340.6691510.334576
D1.019467789574910.430242.36950.0274690.013735
SWS-0.07013991642684520.056213-1.24780.2258530.112927
PS0.2362372324066130.1650021.43170.166940.08347
L0.07313542513888760.0294312.4850.0214610.010731
WB0.002063219543173010.0020531.00520.3262530.163126
Wbr-0.005423421680800340.002222-2.44130.0235770.011788
Tg0.002579970062341440.0026670.96750.3443040.172152
`P `-0.2724898173869760.348129-0.78270.4425260.221263






Multiple Linear Regression - Regression Statistics
Multiple R0.900009031117382
R-squared0.810016256092849
Adjusted R-squared0.737641496509172
F-TEST (value)11.1919716314407
F-TEST (DF numerator)8
F-TEST (DF denominator)21
p-value4.88135444098869e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.7416523261178
Sum Squared Residuals11.5510116295548

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.900009031117382 \tabularnewline
R-squared & 0.810016256092849 \tabularnewline
Adjusted R-squared & 0.737641496509172 \tabularnewline
F-TEST (value) & 11.1919716314407 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 21 \tabularnewline
p-value & 4.88135444098869e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.7416523261178 \tabularnewline
Sum Squared Residuals & 11.5510116295548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.900009031117382[/C][/ROW]
[ROW][C]R-squared[/C][C]0.810016256092849[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.737641496509172[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]11.1919716314407[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C]4.88135444098869e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.7416523261178[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]11.5510116295548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.900009031117382
R-squared0.810016256092849
Adjusted R-squared0.737641496509172
F-TEST (value)11.1919716314407
F-TEST (DF numerator)8
F-TEST (DF denominator)21
p-value4.88135444098869e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.7416523261178
Sum Squared Residuals11.5510116295548






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110.7106904471707030.289309552829297
222.08093048810084-0.0809304881008395
321.706128176003590.293871823996411
454.450982378575570.549017621424427
511.12598187454436-0.125981874544365
632.534297372886290.465702627113708
712.03019482194413-1.03019482194413
832.640476994471430.359523005528566
955.08179789513783-0.0817978951378251
1011.39837781055102-0.398377810551017
1111.29088913147572-0.290889131475716
1211.27333476719684-0.273334767196844
1310.7469788870291970.253021112970803
1410.4889641498545570.511035850145443
1521.560320847107270.439679152892726
1643.363511828557280.636488171442723
1711.57216977795725-0.572169777957252
1844.22364485357897-0.22364485357897
1954.308921762221870.691078237778132
2012.05137307080173-1.05137307080173
2110.9327112344257850.067288765574215
2232.327061550925130.672938449074866
2321.885568892256150.114431107743847
2422.47972488655911-0.47972488655911
2554.221394734879860.778605265120141
2611.28894251066482-0.288942510664816
2712.56881139006279-1.56881139006279
2820.7348985500941461.26510144990585
2933.99194378204456-0.99194378204456
3010.9289751329211950.0710248670788049

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1 & 0.710690447170703 & 0.289309552829297 \tabularnewline
2 & 2 & 2.08093048810084 & -0.0809304881008395 \tabularnewline
3 & 2 & 1.70612817600359 & 0.293871823996411 \tabularnewline
4 & 5 & 4.45098237857557 & 0.549017621424427 \tabularnewline
5 & 1 & 1.12598187454436 & -0.125981874544365 \tabularnewline
6 & 3 & 2.53429737288629 & 0.465702627113708 \tabularnewline
7 & 1 & 2.03019482194413 & -1.03019482194413 \tabularnewline
8 & 3 & 2.64047699447143 & 0.359523005528566 \tabularnewline
9 & 5 & 5.08179789513783 & -0.0817978951378251 \tabularnewline
10 & 1 & 1.39837781055102 & -0.398377810551017 \tabularnewline
11 & 1 & 1.29088913147572 & -0.290889131475716 \tabularnewline
12 & 1 & 1.27333476719684 & -0.273334767196844 \tabularnewline
13 & 1 & 0.746978887029197 & 0.253021112970803 \tabularnewline
14 & 1 & 0.488964149854557 & 0.511035850145443 \tabularnewline
15 & 2 & 1.56032084710727 & 0.439679152892726 \tabularnewline
16 & 4 & 3.36351182855728 & 0.636488171442723 \tabularnewline
17 & 1 & 1.57216977795725 & -0.572169777957252 \tabularnewline
18 & 4 & 4.22364485357897 & -0.22364485357897 \tabularnewline
19 & 5 & 4.30892176222187 & 0.691078237778132 \tabularnewline
20 & 1 & 2.05137307080173 & -1.05137307080173 \tabularnewline
21 & 1 & 0.932711234425785 & 0.067288765574215 \tabularnewline
22 & 3 & 2.32706155092513 & 0.672938449074866 \tabularnewline
23 & 2 & 1.88556889225615 & 0.114431107743847 \tabularnewline
24 & 2 & 2.47972488655911 & -0.47972488655911 \tabularnewline
25 & 5 & 4.22139473487986 & 0.778605265120141 \tabularnewline
26 & 1 & 1.28894251066482 & -0.288942510664816 \tabularnewline
27 & 1 & 2.56881139006279 & -1.56881139006279 \tabularnewline
28 & 2 & 0.734898550094146 & 1.26510144990585 \tabularnewline
29 & 3 & 3.99194378204456 & -0.99194378204456 \tabularnewline
30 & 1 & 0.928975132921195 & 0.0710248670788049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&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]1[/C][C]0.710690447170703[/C][C]0.289309552829297[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]2.08093048810084[/C][C]-0.0809304881008395[/C][/ROW]
[ROW][C]3[/C][C]2[/C][C]1.70612817600359[/C][C]0.293871823996411[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]4.45098237857557[/C][C]0.549017621424427[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]1.12598187454436[/C][C]-0.125981874544365[/C][/ROW]
[ROW][C]6[/C][C]3[/C][C]2.53429737288629[/C][C]0.465702627113708[/C][/ROW]
[ROW][C]7[/C][C]1[/C][C]2.03019482194413[/C][C]-1.03019482194413[/C][/ROW]
[ROW][C]8[/C][C]3[/C][C]2.64047699447143[/C][C]0.359523005528566[/C][/ROW]
[ROW][C]9[/C][C]5[/C][C]5.08179789513783[/C][C]-0.0817978951378251[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]1.39837781055102[/C][C]-0.398377810551017[/C][/ROW]
[ROW][C]11[/C][C]1[/C][C]1.29088913147572[/C][C]-0.290889131475716[/C][/ROW]
[ROW][C]12[/C][C]1[/C][C]1.27333476719684[/C][C]-0.273334767196844[/C][/ROW]
[ROW][C]13[/C][C]1[/C][C]0.746978887029197[/C][C]0.253021112970803[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]0.488964149854557[/C][C]0.511035850145443[/C][/ROW]
[ROW][C]15[/C][C]2[/C][C]1.56032084710727[/C][C]0.439679152892726[/C][/ROW]
[ROW][C]16[/C][C]4[/C][C]3.36351182855728[/C][C]0.636488171442723[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]1.57216977795725[/C][C]-0.572169777957252[/C][/ROW]
[ROW][C]18[/C][C]4[/C][C]4.22364485357897[/C][C]-0.22364485357897[/C][/ROW]
[ROW][C]19[/C][C]5[/C][C]4.30892176222187[/C][C]0.691078237778132[/C][/ROW]
[ROW][C]20[/C][C]1[/C][C]2.05137307080173[/C][C]-1.05137307080173[/C][/ROW]
[ROW][C]21[/C][C]1[/C][C]0.932711234425785[/C][C]0.067288765574215[/C][/ROW]
[ROW][C]22[/C][C]3[/C][C]2.32706155092513[/C][C]0.672938449074866[/C][/ROW]
[ROW][C]23[/C][C]2[/C][C]1.88556889225615[/C][C]0.114431107743847[/C][/ROW]
[ROW][C]24[/C][C]2[/C][C]2.47972488655911[/C][C]-0.47972488655911[/C][/ROW]
[ROW][C]25[/C][C]5[/C][C]4.22139473487986[/C][C]0.778605265120141[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]1.28894251066482[/C][C]-0.288942510664816[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]2.56881139006279[/C][C]-1.56881139006279[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]0.734898550094146[/C][C]1.26510144990585[/C][/ROW]
[ROW][C]29[/C][C]3[/C][C]3.99194378204456[/C][C]-0.99194378204456[/C][/ROW]
[ROW][C]30[/C][C]1[/C][C]0.928975132921195[/C][C]0.0710248670788049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110.7106904471707030.289309552829297
222.08093048810084-0.0809304881008395
321.706128176003590.293871823996411
454.450982378575570.549017621424427
511.12598187454436-0.125981874544365
632.534297372886290.465702627113708
712.03019482194413-1.03019482194413
832.640476994471430.359523005528566
955.08179789513783-0.0817978951378251
1011.39837781055102-0.398377810551017
1111.29088913147572-0.290889131475716
1211.27333476719684-0.273334767196844
1310.7469788870291970.253021112970803
1410.4889641498545570.511035850145443
1521.560320847107270.439679152892726
1643.363511828557280.636488171442723
1711.57216977795725-0.572169777957252
1844.22364485357897-0.22364485357897
1954.308921762221870.691078237778132
2012.05137307080173-1.05137307080173
2110.9327112344257850.067288765574215
2232.327061550925130.672938449074866
2321.885568892256150.114431107743847
2422.47972488655911-0.47972488655911
2554.221394734879860.778605265120141
2611.28894251066482-0.288942510664816
2712.56881139006279-1.56881139006279
2820.7348985500941461.26510144990585
2933.99194378204456-0.99194378204456
3010.9289751329211950.0710248670788049






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.07805881522831140.1561176304566230.921941184771689
130.1187271456620970.2374542913241940.881272854337903
140.04839353251232550.0967870650246510.951606467487675
150.04525206040657560.09050412081315130.954747939593424
160.02511359830291020.05022719660582040.97488640169709
170.01419742319081830.02839484638163660.985802576809182
180.00619567976153970.01239135952307940.99380432023846

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.0780588152283114 & 0.156117630456623 & 0.921941184771689 \tabularnewline
13 & 0.118727145662097 & 0.237454291324194 & 0.881272854337903 \tabularnewline
14 & 0.0483935325123255 & 0.096787065024651 & 0.951606467487675 \tabularnewline
15 & 0.0452520604065756 & 0.0905041208131513 & 0.954747939593424 \tabularnewline
16 & 0.0251135983029102 & 0.0502271966058204 & 0.97488640169709 \tabularnewline
17 & 0.0141974231908183 & 0.0283948463816366 & 0.985802576809182 \tabularnewline
18 & 0.0061956797615397 & 0.0123913595230794 & 0.99380432023846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&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]12[/C][C]0.0780588152283114[/C][C]0.156117630456623[/C][C]0.921941184771689[/C][/ROW]
[ROW][C]13[/C][C]0.118727145662097[/C][C]0.237454291324194[/C][C]0.881272854337903[/C][/ROW]
[ROW][C]14[/C][C]0.0483935325123255[/C][C]0.096787065024651[/C][C]0.951606467487675[/C][/ROW]
[ROW][C]15[/C][C]0.0452520604065756[/C][C]0.0905041208131513[/C][C]0.954747939593424[/C][/ROW]
[ROW][C]16[/C][C]0.0251135983029102[/C][C]0.0502271966058204[/C][C]0.97488640169709[/C][/ROW]
[ROW][C]17[/C][C]0.0141974231908183[/C][C]0.0283948463816366[/C][C]0.985802576809182[/C][/ROW]
[ROW][C]18[/C][C]0.0061956797615397[/C][C]0.0123913595230794[/C][C]0.99380432023846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.07805881522831140.1561176304566230.921941184771689
130.1187271456620970.2374542913241940.881272854337903
140.04839353251232550.0967870650246510.951606467487675
150.04525206040657560.09050412081315130.954747939593424
160.02511359830291020.05022719660582040.97488640169709
170.01419742319081830.02839484638163660.985802576809182
180.00619567976153970.01239135952307940.99380432023846






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.285714285714286NOK
10% type I error level50.714285714285714NOK

\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 & 0.285714285714286 & NOK \tabularnewline
10% type I error level & 5 & 0.714285714285714 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109985&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]0.285714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.714285714285714[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109985&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109985&T=6

As an alternative you can also use a QR Code:  
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 testsOK/NOK
1% type I error level00OK
5% type I error level20.285714285714286NOK
10% type I error level50.714285714285714NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 9
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}