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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, 28 Dec 2010 21:19:23 +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/28/t1293571048fadpkl2l2gexrum.htm/, Retrieved Sun, 28 Apr 2024 20:00:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116557, Retrieved Sun, 28 Apr 2024 20:00:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

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 14:06:21] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [] [2009-11-19 08:06:13] [639dd97b6eeebe46a3c92d62cb04fb95]
-   PD      [Multiple Regression] [] [2009-11-19 08:07:59] [639dd97b6eeebe46a3c92d62cb04fb95]
-   P         [Multiple Regression] [] [2009-11-19 08:09:26] [639dd97b6eeebe46a3c92d62cb04fb95]
-    D          [Multiple Regression] [] [2009-11-19 08:16:57] [639dd97b6eeebe46a3c92d62cb04fb95]
- R  D              [Multiple Regression] [Model 5] [2010-12-28 21:19:23] [e7b77eb06cdf8868fc9cf2043e42b3da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,7	0	3,7	3,93	4,15	4,24	0	0	0
3,65	0	3,7	3,7	3,93	4,15	0	0	0
3,55	0	3,65	3,7	3,7	3,93	0	0	0
3,43	0	3,55	3,65	3,7	3,7	0	0	0
3,47	0	3,43	3,55	3,65	3,7	0	0	0
3,58	0	3,47	3,43	3,55	3,65	0	0	0
3,67	0	3,58	3,47	3,43	3,55	0	0	0
3,72	0	3,67	3,58	3,47	3,43	0	0	0
3,8	0	3,72	3,67	3,58	3,47	0	0	0
3,76	0	3,8	3,72	3,67	3,58	0	0	0
3,63	0	3,76	3,8	3,72	3,67	0	0	0
3,48	0	3,63	3,76	3,8	3,72	0	0	0
3,41	0	3,48	3,63	3,76	3,8	0	0	0
3,43	0	3,41	3,48	3,63	3,76	0	0	0
3,5	0	3,43	3,41	3,48	3,63	0	0	0
3,62	0	3,5	3,43	3,41	3,48	0	0	0
3,58	0	3,62	3,5	3,43	3,41	0	0	0
3,52	0	3,58	3,62	3,5	3,43	0	0	0
3,45	0	3,52	3,58	3,62	3,5	0	0	0
3,36	0	3,45	3,52	3,58	3,62	0	0	0
3,27	0	3,36	3,45	3,52	3,58	0	0	0
3,21	0	3,27	3,36	3,45	3,52	0	0	0
3,19	0	3,21	3,27	3,36	3,45	0	0	0
3,16	0	3,19	3,21	3,27	3,36	0	0	0
3,12	0	3,16	3,19	3,21	3,27	0	0	0
3,06	0	3,12	3,16	3,19	3,21	0	0	0
3,01	0	3,06	3,12	3,16	3,19	0	0	0
2,98	0	3,01	3,06	3,12	3,16	0	0	0
2,97	0	2,98	3,01	3,06	3,12	0	0	0
3,02	0	2,97	2,98	3,01	3,06	0	0	0
3,07	0	3,02	2,97	2,98	3,01	0	0	0
3,18	0	3,07	3,02	2,97	2,98	0	0	0
3,29	1	3,18	3,07	3,02	2,97	0	0	0
3,43	1	3,29	3,18	3,07	3,02	0	0	0
3,61	1	3,43	3,29	3,18	3,07	0	0	0
3,74	1	3,61	3,43	3,29	3,18	0	0	0
3,87	1	3,74	3,61	3,43	3,29	0	0	0
3,88	1	3,87	3,74	3,61	3,43	0	0	0
4,09	1	3,88	3,87	3,74	3,61	0	0	0
4,19	1	4,09	3,88	3,87	3,74	0	0	0
4,2	1	4,19	4,09	3,88	3,87	0	0	0
4,29	1	4,2	4,19	4,09	3,88	0	0	0
4,37	1	4,29	4,2	4,19	4,09	0	0	0
4,47	1	4,37	4,29	4,2	4,19	0	0	0
4,61	1	4,47	4,37	4,29	4,2	0	0	0
4,65	1	4,61	4,47	4,37	4,29	0	0	0
4,69	1	4,65	4,61	4,47	4,37	0	0	0
4,82	1	4,69	4,65	4,61	4,47	0	0	0
4,86	1	4,82	4,69	4,65	4,61	0	0	0
4,87	1	4,86	4,82	4,69	4,65	0	0	0
5,01	1	4,87	4,86	4,82	4,69	0	0	0
5,03	1	5,01	4,87	4,86	4,82	0	0	0
5,13	1	5,03	5,01	4,87	4,86	0	0	0
5,18	1	5,13	5,03	5,01	4,87	0	0	0
5,21	1	5,18	5,13	5,03	5,01	0	0	0
5,26	1	5,21	5,18	5,13	5,03	0	0	0
5,25	1	5,26	5,21	5,18	5,13	0	0	0
5,2	1	5,25	5,26	5,21	5,18	0	0	0
5,16	1	5,2	5,25	5,26	5,21	0	0	0
5,19	1	5,16	5,2	5,25	5,26	0	0	0
5,39	1	5,19	5,16	5,2	5,25	0	0	0
5,58	1	5,39	5,19	5,16	5,2	0	0	0
5,76	1	5,58	5,39	5,19	5,16	0	0	0
5,89	1	5,76	5,58	5,39	5,19	0	0	1
5,98	1	5,89	5,76	5,58	5,39	0	1	0
6,02	1	5,98	5,89	5,76	5,58	1	0	0
5,62	1	6,02	5,98	5,89	5,76	0	0	0
4,87	1	5,62	6,02	5,98	5,89	0	0	0

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'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.205702632696605 + 0.112732044274045X[t] + 2.01139643888264Y1[t] -1.49596877798800Y2[t] + 0.349196496876271Y3[t] + 0.0804553523247682Y4[t] + 0.0525626001017356O1[t] + 0.0942234981695306O2[t] + 0.147369524897714O3[t] + 0.0334034022619562M1[t] -0.0510167264895055M2[t] + 0.0589096577756784M3[t] -0.0626460449796405M4[t] + 0.00665173642907416M5[t] + 0.0244183263253148M6[t] -0.0680214359102388M7[t] -0.0260022922625455M8[t] -0.00904691523431646M9[t] -0.0453841394217003M10[t] -0.000101676244915038M11[t] -0.000797316568880794t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.205702632696605 +  0.112732044274045X[t] +  2.01139643888264Y1[t] -1.49596877798800Y2[t] +  0.349196496876271Y3[t] +  0.0804553523247682Y4[t] +  0.0525626001017356O1[t] +  0.0942234981695306O2[t] +  0.147369524897714O3[t] +  0.0334034022619562M1[t] -0.0510167264895055M2[t] +  0.0589096577756784M3[t] -0.0626460449796405M4[t] +  0.00665173642907416M5[t] +  0.0244183263253148M6[t] -0.0680214359102388M7[t] -0.0260022922625455M8[t] -0.00904691523431646M9[t] -0.0453841394217003M10[t] -0.000101676244915038M11[t] -0.000797316568880794t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.205702632696605 +  0.112732044274045X[t] +  2.01139643888264Y1[t] -1.49596877798800Y2[t] +  0.349196496876271Y3[t] +  0.0804553523247682Y4[t] +  0.0525626001017356O1[t] +  0.0942234981695306O2[t] +  0.147369524897714O3[t] +  0.0334034022619562M1[t] -0.0510167264895055M2[t] +  0.0589096577756784M3[t] -0.0626460449796405M4[t] +  0.00665173642907416M5[t] +  0.0244183263253148M6[t] -0.0680214359102388M7[t] -0.0260022922625455M8[t] -0.00904691523431646M9[t] -0.0453841394217003M10[t] -0.000101676244915038M11[t] -0.000797316568880794t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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
Y[t] = + 0.205702632696605 + 0.112732044274045X[t] + 2.01139643888264Y1[t] -1.49596877798800Y2[t] + 0.349196496876271Y3[t] + 0.0804553523247682Y4[t] + 0.0525626001017356O1[t] + 0.0942234981695306O2[t] + 0.147369524897714O3[t] + 0.0334034022619562M1[t] -0.0510167264895055M2[t] + 0.0589096577756784M3[t] -0.0626460449796405M4[t] + 0.00665173642907416M5[t] + 0.0244183263253148M6[t] -0.0680214359102388M7[t] -0.0260022922625455M8[t] -0.00904691523431646M9[t] -0.0453841394217003M10[t] -0.000101676244915038M11[t] -0.000797316568880794t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.2057026326966050.0911782.25610.028760.01438
X0.1127320442740450.0626111.80050.0781970.039098
Y12.011396438882640.1698611.841500
Y2-1.495968777988000.339394-4.40786e-053e-05
Y30.3491964968762710.3803620.91810.3632730.181637
Y40.08045535232476820.2092980.38440.7024110.351206
O10.05256260010173560.1128680.46570.6435820.321791
O20.09422349816953060.116170.81110.4214050.210703
O30.1473695248977140.1155371.27550.2083940.104197
M10.03340340226195620.0589820.56630.5738640.286932
M2-0.05101672648950550.059973-0.85070.3992710.199636
M30.05890965777567840.0611490.96340.3402890.170144
M4-0.06264604497964050.061892-1.01220.3166350.158318
M50.006651736429074160.0640050.10390.9176710.458835
M60.02441832632531480.0615230.39690.6932390.346619
M7-0.06802143591023880.059775-1.1380.2609040.130452
M8-0.02600229226254550.060628-0.42890.6699660.334983
M9-0.009046915234316460.061209-0.14780.883130.441565
M10-0.04538413942170030.061481-0.73820.4640780.232039
M11-0.0001016762449150380.061539-0.00170.9986890.499344
t-0.0007973165688807940.001463-0.54520.5882220.294111

\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) & 0.205702632696605 & 0.091178 & 2.2561 & 0.02876 & 0.01438 \tabularnewline
X & 0.112732044274045 & 0.062611 & 1.8005 & 0.078197 & 0.039098 \tabularnewline
Y1 & 2.01139643888264 & 0.16986 & 11.8415 & 0 & 0 \tabularnewline
Y2 & -1.49596877798800 & 0.339394 & -4.4078 & 6e-05 & 3e-05 \tabularnewline
Y3 & 0.349196496876271 & 0.380362 & 0.9181 & 0.363273 & 0.181637 \tabularnewline
Y4 & 0.0804553523247682 & 0.209298 & 0.3844 & 0.702411 & 0.351206 \tabularnewline
O1 & 0.0525626001017356 & 0.112868 & 0.4657 & 0.643582 & 0.321791 \tabularnewline
O2 & 0.0942234981695306 & 0.11617 & 0.8111 & 0.421405 & 0.210703 \tabularnewline
O3 & 0.147369524897714 & 0.115537 & 1.2755 & 0.208394 & 0.104197 \tabularnewline
M1 & 0.0334034022619562 & 0.058982 & 0.5663 & 0.573864 & 0.286932 \tabularnewline
M2 & -0.0510167264895055 & 0.059973 & -0.8507 & 0.399271 & 0.199636 \tabularnewline
M3 & 0.0589096577756784 & 0.061149 & 0.9634 & 0.340289 & 0.170144 \tabularnewline
M4 & -0.0626460449796405 & 0.061892 & -1.0122 & 0.316635 & 0.158318 \tabularnewline
M5 & 0.00665173642907416 & 0.064005 & 0.1039 & 0.917671 & 0.458835 \tabularnewline
M6 & 0.0244183263253148 & 0.061523 & 0.3969 & 0.693239 & 0.346619 \tabularnewline
M7 & -0.0680214359102388 & 0.059775 & -1.138 & 0.260904 & 0.130452 \tabularnewline
M8 & -0.0260022922625455 & 0.060628 & -0.4289 & 0.669966 & 0.334983 \tabularnewline
M9 & -0.00904691523431646 & 0.061209 & -0.1478 & 0.88313 & 0.441565 \tabularnewline
M10 & -0.0453841394217003 & 0.061481 & -0.7382 & 0.464078 & 0.232039 \tabularnewline
M11 & -0.000101676244915038 & 0.061539 & -0.0017 & 0.998689 & 0.499344 \tabularnewline
t & -0.000797316568880794 & 0.001463 & -0.5452 & 0.588222 & 0.294111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&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]0.205702632696605[/C][C]0.091178[/C][C]2.2561[/C][C]0.02876[/C][C]0.01438[/C][/ROW]
[ROW][C]X[/C][C]0.112732044274045[/C][C]0.062611[/C][C]1.8005[/C][C]0.078197[/C][C]0.039098[/C][/ROW]
[ROW][C]Y1[/C][C]2.01139643888264[/C][C]0.16986[/C][C]11.8415[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-1.49596877798800[/C][C]0.339394[/C][C]-4.4078[/C][C]6e-05[/C][C]3e-05[/C][/ROW]
[ROW][C]Y3[/C][C]0.349196496876271[/C][C]0.380362[/C][C]0.9181[/C][C]0.363273[/C][C]0.181637[/C][/ROW]
[ROW][C]Y4[/C][C]0.0804553523247682[/C][C]0.209298[/C][C]0.3844[/C][C]0.702411[/C][C]0.351206[/C][/ROW]
[ROW][C]O1[/C][C]0.0525626001017356[/C][C]0.112868[/C][C]0.4657[/C][C]0.643582[/C][C]0.321791[/C][/ROW]
[ROW][C]O2[/C][C]0.0942234981695306[/C][C]0.11617[/C][C]0.8111[/C][C]0.421405[/C][C]0.210703[/C][/ROW]
[ROW][C]O3[/C][C]0.147369524897714[/C][C]0.115537[/C][C]1.2755[/C][C]0.208394[/C][C]0.104197[/C][/ROW]
[ROW][C]M1[/C][C]0.0334034022619562[/C][C]0.058982[/C][C]0.5663[/C][C]0.573864[/C][C]0.286932[/C][/ROW]
[ROW][C]M2[/C][C]-0.0510167264895055[/C][C]0.059973[/C][C]-0.8507[/C][C]0.399271[/C][C]0.199636[/C][/ROW]
[ROW][C]M3[/C][C]0.0589096577756784[/C][C]0.061149[/C][C]0.9634[/C][C]0.340289[/C][C]0.170144[/C][/ROW]
[ROW][C]M4[/C][C]-0.0626460449796405[/C][C]0.061892[/C][C]-1.0122[/C][C]0.316635[/C][C]0.158318[/C][/ROW]
[ROW][C]M5[/C][C]0.00665173642907416[/C][C]0.064005[/C][C]0.1039[/C][C]0.917671[/C][C]0.458835[/C][/ROW]
[ROW][C]M6[/C][C]0.0244183263253148[/C][C]0.061523[/C][C]0.3969[/C][C]0.693239[/C][C]0.346619[/C][/ROW]
[ROW][C]M7[/C][C]-0.0680214359102388[/C][C]0.059775[/C][C]-1.138[/C][C]0.260904[/C][C]0.130452[/C][/ROW]
[ROW][C]M8[/C][C]-0.0260022922625455[/C][C]0.060628[/C][C]-0.4289[/C][C]0.669966[/C][C]0.334983[/C][/ROW]
[ROW][C]M9[/C][C]-0.00904691523431646[/C][C]0.061209[/C][C]-0.1478[/C][C]0.88313[/C][C]0.441565[/C][/ROW]
[ROW][C]M10[/C][C]-0.0453841394217003[/C][C]0.061481[/C][C]-0.7382[/C][C]0.464078[/C][C]0.232039[/C][/ROW]
[ROW][C]M11[/C][C]-0.000101676244915038[/C][C]0.061539[/C][C]-0.0017[/C][C]0.998689[/C][C]0.499344[/C][/ROW]
[ROW][C]t[/C][C]-0.000797316568880794[/C][C]0.001463[/C][C]-0.5452[/C][C]0.588222[/C][C]0.294111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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)0.2057026326966050.0911782.25610.028760.01438
X0.1127320442740450.0626111.80050.0781970.039098
Y12.011396438882640.1698611.841500
Y2-1.495968777988000.339394-4.40786e-053e-05
Y30.3491964968762710.3803620.91810.3632730.181637
Y40.08045535232476820.2092980.38440.7024110.351206
O10.05256260010173560.1128680.46570.6435820.321791
O20.09422349816953060.116170.81110.4214050.210703
O30.1473695248977140.1155371.27550.2083940.104197
M10.03340340226195620.0589820.56630.5738640.286932
M2-0.05101672648950550.059973-0.85070.3992710.199636
M30.05890965777567840.0611490.96340.3402890.170144
M4-0.06264604497964050.061892-1.01220.3166350.158318
M50.006651736429074160.0640050.10390.9176710.458835
M60.02441832632531480.0615230.39690.6932390.346619
M7-0.06802143591023880.059775-1.1380.2609040.130452
M8-0.02600229226254550.060628-0.42890.6699660.334983
M9-0.009046915234316460.061209-0.14780.883130.441565
M10-0.04538413942170030.061481-0.73820.4640780.232039
M11-0.0001016762449150380.061539-0.00170.9986890.499344
t-0.0007973165688807940.001463-0.54520.5882220.294111






Multiple Linear Regression - Regression Statistics
Multiple R0.995945684344728
R-squared0.99190780616489
Adjusted R-squared0.988464319426545
F-TEST (value)288.053325462098
F-TEST (DF numerator)20
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.096133652182226
Sum Squared Residuals0.434358916848981

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.995945684344728 \tabularnewline
R-squared & 0.99190780616489 \tabularnewline
Adjusted R-squared & 0.988464319426545 \tabularnewline
F-TEST (value) & 288.053325462098 \tabularnewline
F-TEST (DF numerator) & 20 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.096133652182226 \tabularnewline
Sum Squared Residuals & 0.434358916848981 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.995945684344728[/C][/ROW]
[ROW][C]R-squared[/C][C]0.99190780616489[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.988464319426545[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]288.053325462098[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]20[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/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]0.096133652182226[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.434358916848981[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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 R0.995945684344728
R-squared0.99190780616489
Adjusted R-squared0.988464319426545
F-TEST (value)288.053325462098
F-TEST (DF numerator)20
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.096133652182226
Sum Squared Residuals0.434358916848981






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.73.591614400656190.108385599343815
23.653.76640556325106-0.116405563251061
33.553.67694943721024-0.126949437210241
43.433.409750481862480.0202495181375195
53.473.369020426991380.100979573008615
63.583.60701939392874-0.0270193939287438
73.673.625248057424250.0447519425757492
83.723.68725221601990.0327477839801003
93.83.710972737153840.0890272628461581
103.763.80022924608338-0.0402292460833767
113.633.66928183944998-0.0392818394499789
123.483.49890190055713-0.0189019005571296
133.413.41674302986718-0.00674302986717874
143.433.366509391836350.0634906081636548
153.53.5577455324358-0.0577455324358003
163.623.509758830643570.110241169356429
173.583.71626110896495-0.136261108964954
183.523.499311133206280.0206888667937171
193.453.392764473476300.0572355265237039
203.363.37863345891653-0.0186334589165254
213.273.29431365043003-0.0243136504300277
223.213.181519544272420.0284804557275791
233.193.20289853518469-0.0128985351846879
243.163.21306442633426-0.0530644263342555
253.123.18705522289881-0.0670552228988065
263.063.054449732285790.00555026771421356
273.013.09064876281587-0.0806487628158677
282.982.941102527782020.0388974722179787
292.972.99988953444921-0.0298895344492094
303.023.019336760744080.00066323925591695
313.073.027130529141130.0428694708588661
323.183.088218113726170.0917818862738275
333.293.38021865915782-0.0902186591578243
343.433.421263753560020.00873624643997809
353.613.62522221830545-0.0152222183054457
363.743.82440401147415-0.0844040114741488
373.873.90695485250253-0.0369548525025316
383.883.96286212186169-0.082862121861689
394.093.957506720820750.132493279179247
404.194.29844200627816-0.108442006278163
414.24.26787983239977-0.0678798323997652
424.294.229502010184420.0604979898155849
434.374.354146196775370.0158538032246329
444.474.433180049147110.0368199508528883
454.614.56303248949780.0469675105022051
464.654.69307327384563-0.043073273845633
474.694.649934726964130.0400652730358689
484.824.726789237871110.0932107621288938
494.864.98626971869992-0.126269718699923
504.874.804218263764490.0657817362355111
515.014.9222363034170.0877636965829957
525.035.09094615343376-0.0609461534337646
535.134.996949097194690.133050902805313
545.185.23483070193647-0.0548307019364752
555.215.110814246540370.0991857534596337
565.265.174108284620380.0858917153796186
575.255.27146246376051-0.0214624637605111
585.25.153914182238550.0460858177614525
595.165.132662680095760.0273373199042435
605.195.126840423763360.0631595762366399
615.395.261362775375370.128637224624625
625.585.515554927000630.0644450729993707
635.765.714913243300330.0450867566996655
645.895.896.41847686111419e-17
655.985.983.98986399474666e-17
666.026.02-2.25514051876985e-17
675.625.87989649664259-0.259896496642586
684.875.09860787756991-0.228607877569909

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.7 & 3.59161440065619 & 0.108385599343815 \tabularnewline
2 & 3.65 & 3.76640556325106 & -0.116405563251061 \tabularnewline
3 & 3.55 & 3.67694943721024 & -0.126949437210241 \tabularnewline
4 & 3.43 & 3.40975048186248 & 0.0202495181375195 \tabularnewline
5 & 3.47 & 3.36902042699138 & 0.100979573008615 \tabularnewline
6 & 3.58 & 3.60701939392874 & -0.0270193939287438 \tabularnewline
7 & 3.67 & 3.62524805742425 & 0.0447519425757492 \tabularnewline
8 & 3.72 & 3.6872522160199 & 0.0327477839801003 \tabularnewline
9 & 3.8 & 3.71097273715384 & 0.0890272628461581 \tabularnewline
10 & 3.76 & 3.80022924608338 & -0.0402292460833767 \tabularnewline
11 & 3.63 & 3.66928183944998 & -0.0392818394499789 \tabularnewline
12 & 3.48 & 3.49890190055713 & -0.0189019005571296 \tabularnewline
13 & 3.41 & 3.41674302986718 & -0.00674302986717874 \tabularnewline
14 & 3.43 & 3.36650939183635 & 0.0634906081636548 \tabularnewline
15 & 3.5 & 3.5577455324358 & -0.0577455324358003 \tabularnewline
16 & 3.62 & 3.50975883064357 & 0.110241169356429 \tabularnewline
17 & 3.58 & 3.71626110896495 & -0.136261108964954 \tabularnewline
18 & 3.52 & 3.49931113320628 & 0.0206888667937171 \tabularnewline
19 & 3.45 & 3.39276447347630 & 0.0572355265237039 \tabularnewline
20 & 3.36 & 3.37863345891653 & -0.0186334589165254 \tabularnewline
21 & 3.27 & 3.29431365043003 & -0.0243136504300277 \tabularnewline
22 & 3.21 & 3.18151954427242 & 0.0284804557275791 \tabularnewline
23 & 3.19 & 3.20289853518469 & -0.0128985351846879 \tabularnewline
24 & 3.16 & 3.21306442633426 & -0.0530644263342555 \tabularnewline
25 & 3.12 & 3.18705522289881 & -0.0670552228988065 \tabularnewline
26 & 3.06 & 3.05444973228579 & 0.00555026771421356 \tabularnewline
27 & 3.01 & 3.09064876281587 & -0.0806487628158677 \tabularnewline
28 & 2.98 & 2.94110252778202 & 0.0388974722179787 \tabularnewline
29 & 2.97 & 2.99988953444921 & -0.0298895344492094 \tabularnewline
30 & 3.02 & 3.01933676074408 & 0.00066323925591695 \tabularnewline
31 & 3.07 & 3.02713052914113 & 0.0428694708588661 \tabularnewline
32 & 3.18 & 3.08821811372617 & 0.0917818862738275 \tabularnewline
33 & 3.29 & 3.38021865915782 & -0.0902186591578243 \tabularnewline
34 & 3.43 & 3.42126375356002 & 0.00873624643997809 \tabularnewline
35 & 3.61 & 3.62522221830545 & -0.0152222183054457 \tabularnewline
36 & 3.74 & 3.82440401147415 & -0.0844040114741488 \tabularnewline
37 & 3.87 & 3.90695485250253 & -0.0369548525025316 \tabularnewline
38 & 3.88 & 3.96286212186169 & -0.082862121861689 \tabularnewline
39 & 4.09 & 3.95750672082075 & 0.132493279179247 \tabularnewline
40 & 4.19 & 4.29844200627816 & -0.108442006278163 \tabularnewline
41 & 4.2 & 4.26787983239977 & -0.0678798323997652 \tabularnewline
42 & 4.29 & 4.22950201018442 & 0.0604979898155849 \tabularnewline
43 & 4.37 & 4.35414619677537 & 0.0158538032246329 \tabularnewline
44 & 4.47 & 4.43318004914711 & 0.0368199508528883 \tabularnewline
45 & 4.61 & 4.5630324894978 & 0.0469675105022051 \tabularnewline
46 & 4.65 & 4.69307327384563 & -0.043073273845633 \tabularnewline
47 & 4.69 & 4.64993472696413 & 0.0400652730358689 \tabularnewline
48 & 4.82 & 4.72678923787111 & 0.0932107621288938 \tabularnewline
49 & 4.86 & 4.98626971869992 & -0.126269718699923 \tabularnewline
50 & 4.87 & 4.80421826376449 & 0.0657817362355111 \tabularnewline
51 & 5.01 & 4.922236303417 & 0.0877636965829957 \tabularnewline
52 & 5.03 & 5.09094615343376 & -0.0609461534337646 \tabularnewline
53 & 5.13 & 4.99694909719469 & 0.133050902805313 \tabularnewline
54 & 5.18 & 5.23483070193647 & -0.0548307019364752 \tabularnewline
55 & 5.21 & 5.11081424654037 & 0.0991857534596337 \tabularnewline
56 & 5.26 & 5.17410828462038 & 0.0858917153796186 \tabularnewline
57 & 5.25 & 5.27146246376051 & -0.0214624637605111 \tabularnewline
58 & 5.2 & 5.15391418223855 & 0.0460858177614525 \tabularnewline
59 & 5.16 & 5.13266268009576 & 0.0273373199042435 \tabularnewline
60 & 5.19 & 5.12684042376336 & 0.0631595762366399 \tabularnewline
61 & 5.39 & 5.26136277537537 & 0.128637224624625 \tabularnewline
62 & 5.58 & 5.51555492700063 & 0.0644450729993707 \tabularnewline
63 & 5.76 & 5.71491324330033 & 0.0450867566996655 \tabularnewline
64 & 5.89 & 5.89 & 6.41847686111419e-17 \tabularnewline
65 & 5.98 & 5.98 & 3.98986399474666e-17 \tabularnewline
66 & 6.02 & 6.02 & -2.25514051876985e-17 \tabularnewline
67 & 5.62 & 5.87989649664259 & -0.259896496642586 \tabularnewline
68 & 4.87 & 5.09860787756991 & -0.228607877569909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]3.7[/C][C]3.59161440065619[/C][C]0.108385599343815[/C][/ROW]
[ROW][C]2[/C][C]3.65[/C][C]3.76640556325106[/C][C]-0.116405563251061[/C][/ROW]
[ROW][C]3[/C][C]3.55[/C][C]3.67694943721024[/C][C]-0.126949437210241[/C][/ROW]
[ROW][C]4[/C][C]3.43[/C][C]3.40975048186248[/C][C]0.0202495181375195[/C][/ROW]
[ROW][C]5[/C][C]3.47[/C][C]3.36902042699138[/C][C]0.100979573008615[/C][/ROW]
[ROW][C]6[/C][C]3.58[/C][C]3.60701939392874[/C][C]-0.0270193939287438[/C][/ROW]
[ROW][C]7[/C][C]3.67[/C][C]3.62524805742425[/C][C]0.0447519425757492[/C][/ROW]
[ROW][C]8[/C][C]3.72[/C][C]3.6872522160199[/C][C]0.0327477839801003[/C][/ROW]
[ROW][C]9[/C][C]3.8[/C][C]3.71097273715384[/C][C]0.0890272628461581[/C][/ROW]
[ROW][C]10[/C][C]3.76[/C][C]3.80022924608338[/C][C]-0.0402292460833767[/C][/ROW]
[ROW][C]11[/C][C]3.63[/C][C]3.66928183944998[/C][C]-0.0392818394499789[/C][/ROW]
[ROW][C]12[/C][C]3.48[/C][C]3.49890190055713[/C][C]-0.0189019005571296[/C][/ROW]
[ROW][C]13[/C][C]3.41[/C][C]3.41674302986718[/C][C]-0.00674302986717874[/C][/ROW]
[ROW][C]14[/C][C]3.43[/C][C]3.36650939183635[/C][C]0.0634906081636548[/C][/ROW]
[ROW][C]15[/C][C]3.5[/C][C]3.5577455324358[/C][C]-0.0577455324358003[/C][/ROW]
[ROW][C]16[/C][C]3.62[/C][C]3.50975883064357[/C][C]0.110241169356429[/C][/ROW]
[ROW][C]17[/C][C]3.58[/C][C]3.71626110896495[/C][C]-0.136261108964954[/C][/ROW]
[ROW][C]18[/C][C]3.52[/C][C]3.49931113320628[/C][C]0.0206888667937171[/C][/ROW]
[ROW][C]19[/C][C]3.45[/C][C]3.39276447347630[/C][C]0.0572355265237039[/C][/ROW]
[ROW][C]20[/C][C]3.36[/C][C]3.37863345891653[/C][C]-0.0186334589165254[/C][/ROW]
[ROW][C]21[/C][C]3.27[/C][C]3.29431365043003[/C][C]-0.0243136504300277[/C][/ROW]
[ROW][C]22[/C][C]3.21[/C][C]3.18151954427242[/C][C]0.0284804557275791[/C][/ROW]
[ROW][C]23[/C][C]3.19[/C][C]3.20289853518469[/C][C]-0.0128985351846879[/C][/ROW]
[ROW][C]24[/C][C]3.16[/C][C]3.21306442633426[/C][C]-0.0530644263342555[/C][/ROW]
[ROW][C]25[/C][C]3.12[/C][C]3.18705522289881[/C][C]-0.0670552228988065[/C][/ROW]
[ROW][C]26[/C][C]3.06[/C][C]3.05444973228579[/C][C]0.00555026771421356[/C][/ROW]
[ROW][C]27[/C][C]3.01[/C][C]3.09064876281587[/C][C]-0.0806487628158677[/C][/ROW]
[ROW][C]28[/C][C]2.98[/C][C]2.94110252778202[/C][C]0.0388974722179787[/C][/ROW]
[ROW][C]29[/C][C]2.97[/C][C]2.99988953444921[/C][C]-0.0298895344492094[/C][/ROW]
[ROW][C]30[/C][C]3.02[/C][C]3.01933676074408[/C][C]0.00066323925591695[/C][/ROW]
[ROW][C]31[/C][C]3.07[/C][C]3.02713052914113[/C][C]0.0428694708588661[/C][/ROW]
[ROW][C]32[/C][C]3.18[/C][C]3.08821811372617[/C][C]0.0917818862738275[/C][/ROW]
[ROW][C]33[/C][C]3.29[/C][C]3.38021865915782[/C][C]-0.0902186591578243[/C][/ROW]
[ROW][C]34[/C][C]3.43[/C][C]3.42126375356002[/C][C]0.00873624643997809[/C][/ROW]
[ROW][C]35[/C][C]3.61[/C][C]3.62522221830545[/C][C]-0.0152222183054457[/C][/ROW]
[ROW][C]36[/C][C]3.74[/C][C]3.82440401147415[/C][C]-0.0844040114741488[/C][/ROW]
[ROW][C]37[/C][C]3.87[/C][C]3.90695485250253[/C][C]-0.0369548525025316[/C][/ROW]
[ROW][C]38[/C][C]3.88[/C][C]3.96286212186169[/C][C]-0.082862121861689[/C][/ROW]
[ROW][C]39[/C][C]4.09[/C][C]3.95750672082075[/C][C]0.132493279179247[/C][/ROW]
[ROW][C]40[/C][C]4.19[/C][C]4.29844200627816[/C][C]-0.108442006278163[/C][/ROW]
[ROW][C]41[/C][C]4.2[/C][C]4.26787983239977[/C][C]-0.0678798323997652[/C][/ROW]
[ROW][C]42[/C][C]4.29[/C][C]4.22950201018442[/C][C]0.0604979898155849[/C][/ROW]
[ROW][C]43[/C][C]4.37[/C][C]4.35414619677537[/C][C]0.0158538032246329[/C][/ROW]
[ROW][C]44[/C][C]4.47[/C][C]4.43318004914711[/C][C]0.0368199508528883[/C][/ROW]
[ROW][C]45[/C][C]4.61[/C][C]4.5630324894978[/C][C]0.0469675105022051[/C][/ROW]
[ROW][C]46[/C][C]4.65[/C][C]4.69307327384563[/C][C]-0.043073273845633[/C][/ROW]
[ROW][C]47[/C][C]4.69[/C][C]4.64993472696413[/C][C]0.0400652730358689[/C][/ROW]
[ROW][C]48[/C][C]4.82[/C][C]4.72678923787111[/C][C]0.0932107621288938[/C][/ROW]
[ROW][C]49[/C][C]4.86[/C][C]4.98626971869992[/C][C]-0.126269718699923[/C][/ROW]
[ROW][C]50[/C][C]4.87[/C][C]4.80421826376449[/C][C]0.0657817362355111[/C][/ROW]
[ROW][C]51[/C][C]5.01[/C][C]4.922236303417[/C][C]0.0877636965829957[/C][/ROW]
[ROW][C]52[/C][C]5.03[/C][C]5.09094615343376[/C][C]-0.0609461534337646[/C][/ROW]
[ROW][C]53[/C][C]5.13[/C][C]4.99694909719469[/C][C]0.133050902805313[/C][/ROW]
[ROW][C]54[/C][C]5.18[/C][C]5.23483070193647[/C][C]-0.0548307019364752[/C][/ROW]
[ROW][C]55[/C][C]5.21[/C][C]5.11081424654037[/C][C]0.0991857534596337[/C][/ROW]
[ROW][C]56[/C][C]5.26[/C][C]5.17410828462038[/C][C]0.0858917153796186[/C][/ROW]
[ROW][C]57[/C][C]5.25[/C][C]5.27146246376051[/C][C]-0.0214624637605111[/C][/ROW]
[ROW][C]58[/C][C]5.2[/C][C]5.15391418223855[/C][C]0.0460858177614525[/C][/ROW]
[ROW][C]59[/C][C]5.16[/C][C]5.13266268009576[/C][C]0.0273373199042435[/C][/ROW]
[ROW][C]60[/C][C]5.19[/C][C]5.12684042376336[/C][C]0.0631595762366399[/C][/ROW]
[ROW][C]61[/C][C]5.39[/C][C]5.26136277537537[/C][C]0.128637224624625[/C][/ROW]
[ROW][C]62[/C][C]5.58[/C][C]5.51555492700063[/C][C]0.0644450729993707[/C][/ROW]
[ROW][C]63[/C][C]5.76[/C][C]5.71491324330033[/C][C]0.0450867566996655[/C][/ROW]
[ROW][C]64[/C][C]5.89[/C][C]5.89[/C][C]6.41847686111419e-17[/C][/ROW]
[ROW][C]65[/C][C]5.98[/C][C]5.98[/C][C]3.98986399474666e-17[/C][/ROW]
[ROW][C]66[/C][C]6.02[/C][C]6.02[/C][C]-2.25514051876985e-17[/C][/ROW]
[ROW][C]67[/C][C]5.62[/C][C]5.87989649664259[/C][C]-0.259896496642586[/C][/ROW]
[ROW][C]68[/C][C]4.87[/C][C]5.09860787756991[/C][C]-0.228607877569909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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
13.73.591614400656190.108385599343815
23.653.76640556325106-0.116405563251061
33.553.67694943721024-0.126949437210241
43.433.409750481862480.0202495181375195
53.473.369020426991380.100979573008615
63.583.60701939392874-0.0270193939287438
73.673.625248057424250.0447519425757492
83.723.68725221601990.0327477839801003
93.83.710972737153840.0890272628461581
103.763.80022924608338-0.0402292460833767
113.633.66928183944998-0.0392818394499789
123.483.49890190055713-0.0189019005571296
133.413.41674302986718-0.00674302986717874
143.433.366509391836350.0634906081636548
153.53.5577455324358-0.0577455324358003
163.623.509758830643570.110241169356429
173.583.71626110896495-0.136261108964954
183.523.499311133206280.0206888667937171
193.453.392764473476300.0572355265237039
203.363.37863345891653-0.0186334589165254
213.273.29431365043003-0.0243136504300277
223.213.181519544272420.0284804557275791
233.193.20289853518469-0.0128985351846879
243.163.21306442633426-0.0530644263342555
253.123.18705522289881-0.0670552228988065
263.063.054449732285790.00555026771421356
273.013.09064876281587-0.0806487628158677
282.982.941102527782020.0388974722179787
292.972.99988953444921-0.0298895344492094
303.023.019336760744080.00066323925591695
313.073.027130529141130.0428694708588661
323.183.088218113726170.0917818862738275
333.293.38021865915782-0.0902186591578243
343.433.421263753560020.00873624643997809
353.613.62522221830545-0.0152222183054457
363.743.82440401147415-0.0844040114741488
373.873.90695485250253-0.0369548525025316
383.883.96286212186169-0.082862121861689
394.093.957506720820750.132493279179247
404.194.29844200627816-0.108442006278163
414.24.26787983239977-0.0678798323997652
424.294.229502010184420.0604979898155849
434.374.354146196775370.0158538032246329
444.474.433180049147110.0368199508528883
454.614.56303248949780.0469675105022051
464.654.69307327384563-0.043073273845633
474.694.649934726964130.0400652730358689
484.824.726789237871110.0932107621288938
494.864.98626971869992-0.126269718699923
504.874.804218263764490.0657817362355111
515.014.9222363034170.0877636965829957
525.035.09094615343376-0.0609461534337646
535.134.996949097194690.133050902805313
545.185.23483070193647-0.0548307019364752
555.215.110814246540370.0991857534596337
565.265.174108284620380.0858917153796186
575.255.27146246376051-0.0214624637605111
585.25.153914182238550.0460858177614525
595.165.132662680095760.0273373199042435
605.195.126840423763360.0631595762366399
615.395.261362775375370.128637224624625
625.585.515554927000630.0644450729993707
635.765.714913243300330.0450867566996655
645.895.896.41847686111419e-17
655.985.983.98986399474666e-17
666.026.02-2.25514051876985e-17
675.625.87989649664259-0.259896496642586
684.875.09860787756991-0.228607877569909






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
240.7221995999778730.5556008000442530.277800400022127
250.6726126106997460.6547747786005090.327387389300254
260.5268459384164210.9463081231671580.473154061583579
270.5234684471080910.9530631057838180.476531552891909
280.4028126837268830.8056253674537670.597187316273117
290.3133241214091570.6266482428183140.686675878590843
300.2685013488739450.5370026977478890.731498651126055
310.1848819889717980.3697639779435960.815118011028202
320.1519950991705750.3039901983411510.848004900829425
330.1129397685534480.2258795371068970.887060231446552
340.08892208296178360.1778441659235670.911077917038216
350.06589214155489640.1317842831097930.934107858445104
360.05619029237491160.1123805847498230.943809707625088
370.03523949036999860.07047898073999720.964760509630001
380.01869530799670730.03739061599341450.981304692003293
390.03660116583359750.0732023316671950.963398834166402
400.02277970430409140.04555940860818270.977220295695909
410.04103896295988730.08207792591977460.958961037040113
420.02794827478200020.05589654956400030.972051725218
430.01333440174747490.02666880349494970.986665598252525
440.0202663814187080.0405327628374160.979733618581292

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
24 & 0.722199599977873 & 0.555600800044253 & 0.277800400022127 \tabularnewline
25 & 0.672612610699746 & 0.654774778600509 & 0.327387389300254 \tabularnewline
26 & 0.526845938416421 & 0.946308123167158 & 0.473154061583579 \tabularnewline
27 & 0.523468447108091 & 0.953063105783818 & 0.476531552891909 \tabularnewline
28 & 0.402812683726883 & 0.805625367453767 & 0.597187316273117 \tabularnewline
29 & 0.313324121409157 & 0.626648242818314 & 0.686675878590843 \tabularnewline
30 & 0.268501348873945 & 0.537002697747889 & 0.731498651126055 \tabularnewline
31 & 0.184881988971798 & 0.369763977943596 & 0.815118011028202 \tabularnewline
32 & 0.151995099170575 & 0.303990198341151 & 0.848004900829425 \tabularnewline
33 & 0.112939768553448 & 0.225879537106897 & 0.887060231446552 \tabularnewline
34 & 0.0889220829617836 & 0.177844165923567 & 0.911077917038216 \tabularnewline
35 & 0.0658921415548964 & 0.131784283109793 & 0.934107858445104 \tabularnewline
36 & 0.0561902923749116 & 0.112380584749823 & 0.943809707625088 \tabularnewline
37 & 0.0352394903699986 & 0.0704789807399972 & 0.964760509630001 \tabularnewline
38 & 0.0186953079967073 & 0.0373906159934145 & 0.981304692003293 \tabularnewline
39 & 0.0366011658335975 & 0.073202331667195 & 0.963398834166402 \tabularnewline
40 & 0.0227797043040914 & 0.0455594086081827 & 0.977220295695909 \tabularnewline
41 & 0.0410389629598873 & 0.0820779259197746 & 0.958961037040113 \tabularnewline
42 & 0.0279482747820002 & 0.0558965495640003 & 0.972051725218 \tabularnewline
43 & 0.0133344017474749 & 0.0266688034949497 & 0.986665598252525 \tabularnewline
44 & 0.020266381418708 & 0.040532762837416 & 0.979733618581292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&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]24[/C][C]0.722199599977873[/C][C]0.555600800044253[/C][C]0.277800400022127[/C][/ROW]
[ROW][C]25[/C][C]0.672612610699746[/C][C]0.654774778600509[/C][C]0.327387389300254[/C][/ROW]
[ROW][C]26[/C][C]0.526845938416421[/C][C]0.946308123167158[/C][C]0.473154061583579[/C][/ROW]
[ROW][C]27[/C][C]0.523468447108091[/C][C]0.953063105783818[/C][C]0.476531552891909[/C][/ROW]
[ROW][C]28[/C][C]0.402812683726883[/C][C]0.805625367453767[/C][C]0.597187316273117[/C][/ROW]
[ROW][C]29[/C][C]0.313324121409157[/C][C]0.626648242818314[/C][C]0.686675878590843[/C][/ROW]
[ROW][C]30[/C][C]0.268501348873945[/C][C]0.537002697747889[/C][C]0.731498651126055[/C][/ROW]
[ROW][C]31[/C][C]0.184881988971798[/C][C]0.369763977943596[/C][C]0.815118011028202[/C][/ROW]
[ROW][C]32[/C][C]0.151995099170575[/C][C]0.303990198341151[/C][C]0.848004900829425[/C][/ROW]
[ROW][C]33[/C][C]0.112939768553448[/C][C]0.225879537106897[/C][C]0.887060231446552[/C][/ROW]
[ROW][C]34[/C][C]0.0889220829617836[/C][C]0.177844165923567[/C][C]0.911077917038216[/C][/ROW]
[ROW][C]35[/C][C]0.0658921415548964[/C][C]0.131784283109793[/C][C]0.934107858445104[/C][/ROW]
[ROW][C]36[/C][C]0.0561902923749116[/C][C]0.112380584749823[/C][C]0.943809707625088[/C][/ROW]
[ROW][C]37[/C][C]0.0352394903699986[/C][C]0.0704789807399972[/C][C]0.964760509630001[/C][/ROW]
[ROW][C]38[/C][C]0.0186953079967073[/C][C]0.0373906159934145[/C][C]0.981304692003293[/C][/ROW]
[ROW][C]39[/C][C]0.0366011658335975[/C][C]0.073202331667195[/C][C]0.963398834166402[/C][/ROW]
[ROW][C]40[/C][C]0.0227797043040914[/C][C]0.0455594086081827[/C][C]0.977220295695909[/C][/ROW]
[ROW][C]41[/C][C]0.0410389629598873[/C][C]0.0820779259197746[/C][C]0.958961037040113[/C][/ROW]
[ROW][C]42[/C][C]0.0279482747820002[/C][C]0.0558965495640003[/C][C]0.972051725218[/C][/ROW]
[ROW][C]43[/C][C]0.0133344017474749[/C][C]0.0266688034949497[/C][C]0.986665598252525[/C][/ROW]
[ROW][C]44[/C][C]0.020266381418708[/C][C]0.040532762837416[/C][C]0.979733618581292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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
240.7221995999778730.5556008000442530.277800400022127
250.6726126106997460.6547747786005090.327387389300254
260.5268459384164210.9463081231671580.473154061583579
270.5234684471080910.9530631057838180.476531552891909
280.4028126837268830.8056253674537670.597187316273117
290.3133241214091570.6266482428183140.686675878590843
300.2685013488739450.5370026977478890.731498651126055
310.1848819889717980.3697639779435960.815118011028202
320.1519950991705750.3039901983411510.848004900829425
330.1129397685534480.2258795371068970.887060231446552
340.08892208296178360.1778441659235670.911077917038216
350.06589214155489640.1317842831097930.934107858445104
360.05619029237491160.1123805847498230.943809707625088
370.03523949036999860.07047898073999720.964760509630001
380.01869530799670730.03739061599341450.981304692003293
390.03660116583359750.0732023316671950.963398834166402
400.02277970430409140.04555940860818270.977220295695909
410.04103896295988730.08207792591977460.958961037040113
420.02794827478200020.05589654956400030.972051725218
430.01333440174747490.02666880349494970.986665598252525
440.0202663814187080.0405327628374160.979733618581292






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.190476190476190NOK
10% type I error level80.380952380952381NOK

\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 & 4 & 0.190476190476190 & NOK \tabularnewline
10% type I error level & 8 & 0.380952380952381 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116557&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]4[/C][C]0.190476190476190[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.380952380952381[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116557&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116557&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 level40.190476190476190NOK
10% type I error level80.380952380952381NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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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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Input Parameters & R Code

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')
}