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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 computationSun, 22 Nov 2009 08:02:10 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/22/t1258902262higlpdy2c87qzyq.htm/, Retrieved Wed, 19 Nov 2025 21:17:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58634, Retrieved Wed, 19 Nov 2025 21:17:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact552

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P           [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D            [Multiple Regression] [model 4] [2009-11-20 08:59:37] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D                [Multiple Regression] [] [2009-11-22 15:02:10] [48076ccf082563ab8a2c81e57fdb5364] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12919,9	12973,9	12919,9	12266,7	12384,6	12476,8
11497,3	12509,8	11497,3	12919,9	12266,7	12384,6
12142	12934,1	12142	11497,3	12919,9	12266,7
13919,4	14908,3	13919,4	12142	11497,3	12919,9
12656,8	13772,1	12656,8	13919,4	12142	11497,3
12034,1	13012,6	12034,1	12656,8	13919,4	12142
13199,7	14049,9	13199,7	12034,1	12656,8	13919,4
10881,3	11816,5	10881,3	13199,7	12034,1	12656,8
11301,2	11593,2	11301,2	10881,3	13199,7	12034,1
13643,9	14466,2	13643,9	11301,2	10881,3	13199,7
12517	13615,9	12517	13643,9	11301,2	10881,3
13981,1	14733,9	13981,1	12517	13643,9	11301,2
14275,7	13880,7	14275,7	13981,1	12517	13643,9
13435	13527,5	13435	14275,7	13981,1	12517
13565,7	13584	13565,7	13435	14275,7	13981,1
16216,3	16170,2	16216,3	13565,7	13435	14275,7
12970	13260,6	12970	16216,3	13565,7	13435
14079,9	14741,9	14079,9	12970	16216,3	13565,7
14235	15486,5	14235	14079,9	12970	16216,3
12213,4	13154,5	12213,4	14235	14079,9	12970
12581	12621,2	12581	12213,4	14235	14079,9
14130,4	15031,6	14130,4	12581	12213,4	14235
14210,8	15452,4	14210,8	14130,4	12581	12213,4
14378,5	15428	14378,5	14210,8	14130,4	12581
13142,8	13105,9	13142,8	14378,5	14210,8	14130,4
13714,7	14716,8	13714,7	13142,8	14378,5	14210,8
13621,9	14180	13621,9	13714,7	13142,8	14378,5
15379,8	16202,2	15379,8	13621,9	13714,7	13142,8
13306,3	14392,4	13306,3	15379,8	13621,9	13714,7
14391,2	15140,6	14391,2	13306,3	15379,8	13621,9
14909,9	15960,1	14909,9	14391,2	13306,3	15379,8
14025,4	14351,3	14025,4	14909,9	14391,2	13306,3
12951,2	13230,2	12951,2	14025,4	14909,9	14391,2
14344,3	15202,1	14344,3	12951,2	14025,4	14909,9
16093,4	17056	16093,4	14344,3	12951,2	14025,4
15413,6	16077,7	15413,6	16093,4	14344,3	12951,2
14705,7	13348,2	14705,7	15413,6	16093,4	14344,3
15972,8	16402,4	15972,8	14705,7	15413,6	16093,4
16241,4	16559,1	16241,4	15972,8	14705,7	15413,6
16626,4	16579	16626,4	16241,4	15972,8	14705,7
17136,2	17561,2	17136,2	16626,4	16241,4	15972,8
15622,9	16129,6	15622,9	17136,2	16626,4	16241,4
18003,9	18484,3	18003,9	15622,9	17136,2	16626,4
16136,1	16402,6	16136,1	18003,9	15622,9	17136,2
14423,7	14032,3	14423,7	16136,1	18003,9	15622,9
16789,4	17109,1	16789,4	14423,7	16136,1	18003,9
16782,2	17157,2	16782,2	16789,4	14423,7	16136,1
14133,8	13879,8	14133,8	16782,2	16789,4	14423,7
12607	12362,4	12607	14133,8	16782,2	16789,4
12004,5	12683,5	12004,5	12607	14133,8	16782,2
12175,4	12608,8	12175,4	12004,5	12607	14133,8
13268	13583,7	13268	12175,4	12004,5	12607
12299,3	12846,3	12299,3	13268	12175,4	12004,5
11800,6	12347,1	11800,6	12299,3	13268	12175,4
13873,3	13967	13873,3	11800,6	12299,3	13268
12269,6	13114,3	12269,6	13873,3	11800,6	12299,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
In_IEU[t] = + 9.33769007937115e-13 + 6.08020428710746e-16Uit_IEU[t] + 1`Yt-1`[t] -3.41313721623565e-17`Yt-2`[t] + 5.63140213847878e-17`Yt-3`[t] -1.54334763119424e-17`Yt-4`[t] -5.14745364092699e-14M1[t] -5.59444995553869e-14M2[t] + 2.95547134569282e-13M3[t] + 3.65302175293353e-14M4[t] + 5.83751278725918e-14M5[t] -9.64817250070245e-14M6[t] + 2.90609718457503e-14M7[t] + 4.92318432510924e-14M8[t] -8.81005101561148e-14M9[t] + 1.13199821482918e-14M10[t] + 4.89132576919884e-14M11[t] -1.69914286080596e-15t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
In_IEU[t] =  +  9.33769007937115e-13 +  6.08020428710746e-16Uit_IEU[t] +  1`Yt-1`[t] -3.41313721623565e-17`Yt-2`[t] +  5.63140213847878e-17`Yt-3`[t] -1.54334763119424e-17`Yt-4`[t] -5.14745364092699e-14M1[t] -5.59444995553869e-14M2[t] +  2.95547134569282e-13M3[t] +  3.65302175293353e-14M4[t] +  5.83751278725918e-14M5[t] -9.64817250070245e-14M6[t] +  2.90609718457503e-14M7[t] +  4.92318432510924e-14M8[t] -8.81005101561148e-14M9[t] +  1.13199821482918e-14M10[t] +  4.89132576919884e-14M11[t] -1.69914286080596e-15t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]In_IEU[t] =  +  9.33769007937115e-13 +  6.08020428710746e-16Uit_IEU[t] +  1`Yt-1`[t] -3.41313721623565e-17`Yt-2`[t] +  5.63140213847878e-17`Yt-3`[t] -1.54334763119424e-17`Yt-4`[t] -5.14745364092699e-14M1[t] -5.59444995553869e-14M2[t] +  2.95547134569282e-13M3[t] +  3.65302175293353e-14M4[t] +  5.83751278725918e-14M5[t] -9.64817250070245e-14M6[t] +  2.90609718457503e-14M7[t] +  4.92318432510924e-14M8[t] -8.81005101561148e-14M9[t] +  1.13199821482918e-14M10[t] +  4.89132576919884e-14M11[t] -1.69914286080596e-15t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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
In_IEU[t] = + 9.33769007937115e-13 + 6.08020428710746e-16Uit_IEU[t] + 1`Yt-1`[t] -3.41313721623565e-17`Yt-2`[t] + 5.63140213847878e-17`Yt-3`[t] -1.54334763119424e-17`Yt-4`[t] -5.14745364092699e-14M1[t] -5.59444995553869e-14M2[t] + 2.95547134569282e-13M3[t] + 3.65302175293353e-14M4[t] + 5.83751278725918e-14M5[t] -9.64817250070245e-14M6[t] + 2.90609718457503e-14M7[t] + 4.92318432510924e-14M8[t] -8.81005101561148e-14M9[t] + 1.13199821482918e-14M10[t] + 4.89132576919884e-14M11[t] -1.69914286080596e-15t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9.33769007937115e-1302.26660.029190.014595
Uit_IEU6.08020428710746e-1605.8211e-061e-06
`Yt-1`10936491626790108000
`Yt-2`-3.41313721623565e-170-0.88850.3798480.189924
`Yt-3`5.63140213847878e-1701.43310.1599980.079999
`Yt-4`-1.54334763119424e-170-0.39780.6929750.346487
M1-5.14745364092699e-140-0.24640.8067250.403363
M2-5.59444995553869e-140-0.32520.7468440.373422
M32.95547134569282e-1301.68310.1005630.050282
M43.65302175293353e-1400.21270.8327230.416362
M55.83751278725918e-1400.38550.7020280.351014
M6-9.64817250070245e-140-0.63150.531520.26576
M72.90609718457503e-1400.15560.8771360.438568
M84.92318432510924e-1400.31210.7566630.378331
M9-8.81005101561148e-140-0.45530.6514810.32574
M101.13199821482918e-1400.05390.9572820.478641
M114.89132576919884e-1400.28890.7742580.387129
t-1.69914286080596e-150-0.7370.4656570.232829

\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) & 9.33769007937115e-13 & 0 & 2.2666 & 0.02919 & 0.014595 \tabularnewline
Uit_IEU & 6.08020428710746e-16 & 0 & 5.821 & 1e-06 & 1e-06 \tabularnewline
`Yt-1` & 1 & 0 & 9364916267901080 & 0 & 0 \tabularnewline
`Yt-2` & -3.41313721623565e-17 & 0 & -0.8885 & 0.379848 & 0.189924 \tabularnewline
`Yt-3` & 5.63140213847878e-17 & 0 & 1.4331 & 0.159998 & 0.079999 \tabularnewline
`Yt-4` & -1.54334763119424e-17 & 0 & -0.3978 & 0.692975 & 0.346487 \tabularnewline
M1 & -5.14745364092699e-14 & 0 & -0.2464 & 0.806725 & 0.403363 \tabularnewline
M2 & -5.59444995553869e-14 & 0 & -0.3252 & 0.746844 & 0.373422 \tabularnewline
M3 & 2.95547134569282e-13 & 0 & 1.6831 & 0.100563 & 0.050282 \tabularnewline
M4 & 3.65302175293353e-14 & 0 & 0.2127 & 0.832723 & 0.416362 \tabularnewline
M5 & 5.83751278725918e-14 & 0 & 0.3855 & 0.702028 & 0.351014 \tabularnewline
M6 & -9.64817250070245e-14 & 0 & -0.6315 & 0.53152 & 0.26576 \tabularnewline
M7 & 2.90609718457503e-14 & 0 & 0.1556 & 0.877136 & 0.438568 \tabularnewline
M8 & 4.92318432510924e-14 & 0 & 0.3121 & 0.756663 & 0.378331 \tabularnewline
M9 & -8.81005101561148e-14 & 0 & -0.4553 & 0.651481 & 0.32574 \tabularnewline
M10 & 1.13199821482918e-14 & 0 & 0.0539 & 0.957282 & 0.478641 \tabularnewline
M11 & 4.89132576919884e-14 & 0 & 0.2889 & 0.774258 & 0.387129 \tabularnewline
t & -1.69914286080596e-15 & 0 & -0.737 & 0.465657 & 0.232829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&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]9.33769007937115e-13[/C][C]0[/C][C]2.2666[/C][C]0.02919[/C][C]0.014595[/C][/ROW]
[ROW][C]Uit_IEU[/C][C]6.08020428710746e-16[/C][C]0[/C][C]5.821[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]1[/C][C]0[/C][C]9364916267901080[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]-3.41313721623565e-17[/C][C]0[/C][C]-0.8885[/C][C]0.379848[/C][C]0.189924[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]5.63140213847878e-17[/C][C]0[/C][C]1.4331[/C][C]0.159998[/C][C]0.079999[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]-1.54334763119424e-17[/C][C]0[/C][C]-0.3978[/C][C]0.692975[/C][C]0.346487[/C][/ROW]
[ROW][C]M1[/C][C]-5.14745364092699e-14[/C][C]0[/C][C]-0.2464[/C][C]0.806725[/C][C]0.403363[/C][/ROW]
[ROW][C]M2[/C][C]-5.59444995553869e-14[/C][C]0[/C][C]-0.3252[/C][C]0.746844[/C][C]0.373422[/C][/ROW]
[ROW][C]M3[/C][C]2.95547134569282e-13[/C][C]0[/C][C]1.6831[/C][C]0.100563[/C][C]0.050282[/C][/ROW]
[ROW][C]M4[/C][C]3.65302175293353e-14[/C][C]0[/C][C]0.2127[/C][C]0.832723[/C][C]0.416362[/C][/ROW]
[ROW][C]M5[/C][C]5.83751278725918e-14[/C][C]0[/C][C]0.3855[/C][C]0.702028[/C][C]0.351014[/C][/ROW]
[ROW][C]M6[/C][C]-9.64817250070245e-14[/C][C]0[/C][C]-0.6315[/C][C]0.53152[/C][C]0.26576[/C][/ROW]
[ROW][C]M7[/C][C]2.90609718457503e-14[/C][C]0[/C][C]0.1556[/C][C]0.877136[/C][C]0.438568[/C][/ROW]
[ROW][C]M8[/C][C]4.92318432510924e-14[/C][C]0[/C][C]0.3121[/C][C]0.756663[/C][C]0.378331[/C][/ROW]
[ROW][C]M9[/C][C]-8.81005101561148e-14[/C][C]0[/C][C]-0.4553[/C][C]0.651481[/C][C]0.32574[/C][/ROW]
[ROW][C]M10[/C][C]1.13199821482918e-14[/C][C]0[/C][C]0.0539[/C][C]0.957282[/C][C]0.478641[/C][/ROW]
[ROW][C]M11[/C][C]4.89132576919884e-14[/C][C]0[/C][C]0.2889[/C][C]0.774258[/C][C]0.387129[/C][/ROW]
[ROW][C]t[/C][C]-1.69914286080596e-15[/C][C]0[/C][C]-0.737[/C][C]0.465657[/C][C]0.232829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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)9.33769007937115e-1302.26660.029190.014595
Uit_IEU6.08020428710746e-1605.8211e-061e-06
`Yt-1`10936491626790108000
`Yt-2`-3.41313721623565e-170-0.88850.3798480.189924
`Yt-3`5.63140213847878e-1701.43310.1599980.079999
`Yt-4`-1.54334763119424e-170-0.39780.6929750.346487
M1-5.14745364092699e-140-0.24640.8067250.403363
M2-5.59444995553869e-140-0.32520.7468440.373422
M32.95547134569282e-1301.68310.1005630.050282
M43.65302175293353e-1400.21270.8327230.416362
M55.83751278725918e-1400.38550.7020280.351014
M6-9.64817250070245e-140-0.63150.531520.26576
M72.90609718457503e-1400.15560.8771360.438568
M84.92318432510924e-1400.31210.7566630.378331
M9-8.81005101561148e-140-0.45530.6514810.32574
M101.13199821482918e-1400.05390.9572820.478641
M114.89132576919884e-1400.28890.7742580.387129
t-1.69914286080596e-150-0.7370.4656570.232829






Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)2.00609417868962e+32
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.06882713278502e-13
Sum Squared Residuals1.62641736803205e-24

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 1 \tabularnewline
R-squared & 1 \tabularnewline
Adjusted R-squared & 1 \tabularnewline
F-TEST (value) & 2.00609417868962e+32 \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 & 2.06882713278502e-13 \tabularnewline
Sum Squared Residuals & 1.62641736803205e-24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]1[/C][/ROW]
[ROW][C]R-squared[/C][C]1[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.00609417868962e+32[/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]2.06882713278502e-13[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.62641736803205e-24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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 R1
R-squared1
Adjusted R-squared1
F-TEST (value)2.00609417868962e+32
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.06882713278502e-13
Sum Squared Residuals1.62641736803205e-24






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
112919.912919.9-1.15687740511203e-13
211497.311497.3-1.11571156397268e-13
312142121421.06359826058060e-12
413919.413919.4-4.05993368457645e-14
512656.812656.8-2.51774014860363e-14
612034.112034.1-6.00121655853554e-14
713199.713199.7-8.46927260993712e-14
810881.310881.3-4.19424696724649e-14
911301.211301.2-6.58784157846455e-14
1013643.913643.9-3.45907733778767e-15
111251712517-9.84696567476705e-14
1213981.113981.1-9.75045326013207e-14
1314275.714275.71.33839947854674e-13
141343513435-4.15601283799536e-15
1513565.713565.7-3.46093314443156e-13
1616216.316216.33.33844272443606e-14
1712970129702.49179536106758e-15
1814079.914079.9-8.97259012924684e-14
1914235142351.45411498973402e-14
2012213.412213.4-7.94746923257248e-14
2112581125817.04527599489535e-15
2214130.414130.43.65401126113927e-14
2314210.814210.8-4.0638454214342e-14
2414378.514378.5-2.51741352550464e-14
2513142.813142.83.06953214359383e-14
2613714.713714.7-1.62655978882567e-14
2713621.913621.9-2.56787644647873e-13
2815379.815379.8-5.98501993942027e-14
2913306.313306.31.26737341014917e-14
3014391.214391.2-5.89634485458661e-14
3114909.914909.95.96286946024191e-14
3214025.414025.4-4.51323340448021e-14
3312951.212951.23.588482180933e-14
3414344.314344.3-3.59044682020389e-14
3516093.416093.42.45345201397967e-14
3615413.615413.66.26302591948495e-14
3714705.714705.71.86638903115609e-14
3815972.815972.87.02227226804949e-14
3916241.416241.4-2.06731654273643e-13
4016626.416626.43.33149325249005e-14
4117136.217136.2-1.23990543922619e-14
4215622.915622.91.27456892173898e-13
4318003.918003.9-5.39988983066923e-14
4416136.116136.11.14635179935757e-13
4514423.714423.72.29483179804199e-14
4616789.416789.42.82343292843405e-15
4716782.216782.21.14573590822216e-13
4814133.814133.86.00484086615178e-14
491260712607-6.75114190909698e-14
5012004.512004.56.17700444430254e-14
5112175.412175.4-2.53985647215925e-13
5213268132683.37501764707062e-14
5312299.312299.32.24109264157388e-14
5411800.611800.68.12446232497919e-14
5513873.313873.36.45217799063042e-14
5612269.612269.65.19143161072346e-14

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12919.9 & 12919.9 & -1.15687740511203e-13 \tabularnewline
2 & 11497.3 & 11497.3 & -1.11571156397268e-13 \tabularnewline
3 & 12142 & 12142 & 1.06359826058060e-12 \tabularnewline
4 & 13919.4 & 13919.4 & -4.05993368457645e-14 \tabularnewline
5 & 12656.8 & 12656.8 & -2.51774014860363e-14 \tabularnewline
6 & 12034.1 & 12034.1 & -6.00121655853554e-14 \tabularnewline
7 & 13199.7 & 13199.7 & -8.46927260993712e-14 \tabularnewline
8 & 10881.3 & 10881.3 & -4.19424696724649e-14 \tabularnewline
9 & 11301.2 & 11301.2 & -6.58784157846455e-14 \tabularnewline
10 & 13643.9 & 13643.9 & -3.45907733778767e-15 \tabularnewline
11 & 12517 & 12517 & -9.84696567476705e-14 \tabularnewline
12 & 13981.1 & 13981.1 & -9.75045326013207e-14 \tabularnewline
13 & 14275.7 & 14275.7 & 1.33839947854674e-13 \tabularnewline
14 & 13435 & 13435 & -4.15601283799536e-15 \tabularnewline
15 & 13565.7 & 13565.7 & -3.46093314443156e-13 \tabularnewline
16 & 16216.3 & 16216.3 & 3.33844272443606e-14 \tabularnewline
17 & 12970 & 12970 & 2.49179536106758e-15 \tabularnewline
18 & 14079.9 & 14079.9 & -8.97259012924684e-14 \tabularnewline
19 & 14235 & 14235 & 1.45411498973402e-14 \tabularnewline
20 & 12213.4 & 12213.4 & -7.94746923257248e-14 \tabularnewline
21 & 12581 & 12581 & 7.04527599489535e-15 \tabularnewline
22 & 14130.4 & 14130.4 & 3.65401126113927e-14 \tabularnewline
23 & 14210.8 & 14210.8 & -4.0638454214342e-14 \tabularnewline
24 & 14378.5 & 14378.5 & -2.51741352550464e-14 \tabularnewline
25 & 13142.8 & 13142.8 & 3.06953214359383e-14 \tabularnewline
26 & 13714.7 & 13714.7 & -1.62655978882567e-14 \tabularnewline
27 & 13621.9 & 13621.9 & -2.56787644647873e-13 \tabularnewline
28 & 15379.8 & 15379.8 & -5.98501993942027e-14 \tabularnewline
29 & 13306.3 & 13306.3 & 1.26737341014917e-14 \tabularnewline
30 & 14391.2 & 14391.2 & -5.89634485458661e-14 \tabularnewline
31 & 14909.9 & 14909.9 & 5.96286946024191e-14 \tabularnewline
32 & 14025.4 & 14025.4 & -4.51323340448021e-14 \tabularnewline
33 & 12951.2 & 12951.2 & 3.588482180933e-14 \tabularnewline
34 & 14344.3 & 14344.3 & -3.59044682020389e-14 \tabularnewline
35 & 16093.4 & 16093.4 & 2.45345201397967e-14 \tabularnewline
36 & 15413.6 & 15413.6 & 6.26302591948495e-14 \tabularnewline
37 & 14705.7 & 14705.7 & 1.86638903115609e-14 \tabularnewline
38 & 15972.8 & 15972.8 & 7.02227226804949e-14 \tabularnewline
39 & 16241.4 & 16241.4 & -2.06731654273643e-13 \tabularnewline
40 & 16626.4 & 16626.4 & 3.33149325249005e-14 \tabularnewline
41 & 17136.2 & 17136.2 & -1.23990543922619e-14 \tabularnewline
42 & 15622.9 & 15622.9 & 1.27456892173898e-13 \tabularnewline
43 & 18003.9 & 18003.9 & -5.39988983066923e-14 \tabularnewline
44 & 16136.1 & 16136.1 & 1.14635179935757e-13 \tabularnewline
45 & 14423.7 & 14423.7 & 2.29483179804199e-14 \tabularnewline
46 & 16789.4 & 16789.4 & 2.82343292843405e-15 \tabularnewline
47 & 16782.2 & 16782.2 & 1.14573590822216e-13 \tabularnewline
48 & 14133.8 & 14133.8 & 6.00484086615178e-14 \tabularnewline
49 & 12607 & 12607 & -6.75114190909698e-14 \tabularnewline
50 & 12004.5 & 12004.5 & 6.17700444430254e-14 \tabularnewline
51 & 12175.4 & 12175.4 & -2.53985647215925e-13 \tabularnewline
52 & 13268 & 13268 & 3.37501764707062e-14 \tabularnewline
53 & 12299.3 & 12299.3 & 2.24109264157388e-14 \tabularnewline
54 & 11800.6 & 11800.6 & 8.12446232497919e-14 \tabularnewline
55 & 13873.3 & 13873.3 & 6.45217799063042e-14 \tabularnewline
56 & 12269.6 & 12269.6 & 5.19143161072346e-14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&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]12919.9[/C][C]12919.9[/C][C]-1.15687740511203e-13[/C][/ROW]
[ROW][C]2[/C][C]11497.3[/C][C]11497.3[/C][C]-1.11571156397268e-13[/C][/ROW]
[ROW][C]3[/C][C]12142[/C][C]12142[/C][C]1.06359826058060e-12[/C][/ROW]
[ROW][C]4[/C][C]13919.4[/C][C]13919.4[/C][C]-4.05993368457645e-14[/C][/ROW]
[ROW][C]5[/C][C]12656.8[/C][C]12656.8[/C][C]-2.51774014860363e-14[/C][/ROW]
[ROW][C]6[/C][C]12034.1[/C][C]12034.1[/C][C]-6.00121655853554e-14[/C][/ROW]
[ROW][C]7[/C][C]13199.7[/C][C]13199.7[/C][C]-8.46927260993712e-14[/C][/ROW]
[ROW][C]8[/C][C]10881.3[/C][C]10881.3[/C][C]-4.19424696724649e-14[/C][/ROW]
[ROW][C]9[/C][C]11301.2[/C][C]11301.2[/C][C]-6.58784157846455e-14[/C][/ROW]
[ROW][C]10[/C][C]13643.9[/C][C]13643.9[/C][C]-3.45907733778767e-15[/C][/ROW]
[ROW][C]11[/C][C]12517[/C][C]12517[/C][C]-9.84696567476705e-14[/C][/ROW]
[ROW][C]12[/C][C]13981.1[/C][C]13981.1[/C][C]-9.75045326013207e-14[/C][/ROW]
[ROW][C]13[/C][C]14275.7[/C][C]14275.7[/C][C]1.33839947854674e-13[/C][/ROW]
[ROW][C]14[/C][C]13435[/C][C]13435[/C][C]-4.15601283799536e-15[/C][/ROW]
[ROW][C]15[/C][C]13565.7[/C][C]13565.7[/C][C]-3.46093314443156e-13[/C][/ROW]
[ROW][C]16[/C][C]16216.3[/C][C]16216.3[/C][C]3.33844272443606e-14[/C][/ROW]
[ROW][C]17[/C][C]12970[/C][C]12970[/C][C]2.49179536106758e-15[/C][/ROW]
[ROW][C]18[/C][C]14079.9[/C][C]14079.9[/C][C]-8.97259012924684e-14[/C][/ROW]
[ROW][C]19[/C][C]14235[/C][C]14235[/C][C]1.45411498973402e-14[/C][/ROW]
[ROW][C]20[/C][C]12213.4[/C][C]12213.4[/C][C]-7.94746923257248e-14[/C][/ROW]
[ROW][C]21[/C][C]12581[/C][C]12581[/C][C]7.04527599489535e-15[/C][/ROW]
[ROW][C]22[/C][C]14130.4[/C][C]14130.4[/C][C]3.65401126113927e-14[/C][/ROW]
[ROW][C]23[/C][C]14210.8[/C][C]14210.8[/C][C]-4.0638454214342e-14[/C][/ROW]
[ROW][C]24[/C][C]14378.5[/C][C]14378.5[/C][C]-2.51741352550464e-14[/C][/ROW]
[ROW][C]25[/C][C]13142.8[/C][C]13142.8[/C][C]3.06953214359383e-14[/C][/ROW]
[ROW][C]26[/C][C]13714.7[/C][C]13714.7[/C][C]-1.62655978882567e-14[/C][/ROW]
[ROW][C]27[/C][C]13621.9[/C][C]13621.9[/C][C]-2.56787644647873e-13[/C][/ROW]
[ROW][C]28[/C][C]15379.8[/C][C]15379.8[/C][C]-5.98501993942027e-14[/C][/ROW]
[ROW][C]29[/C][C]13306.3[/C][C]13306.3[/C][C]1.26737341014917e-14[/C][/ROW]
[ROW][C]30[/C][C]14391.2[/C][C]14391.2[/C][C]-5.89634485458661e-14[/C][/ROW]
[ROW][C]31[/C][C]14909.9[/C][C]14909.9[/C][C]5.96286946024191e-14[/C][/ROW]
[ROW][C]32[/C][C]14025.4[/C][C]14025.4[/C][C]-4.51323340448021e-14[/C][/ROW]
[ROW][C]33[/C][C]12951.2[/C][C]12951.2[/C][C]3.588482180933e-14[/C][/ROW]
[ROW][C]34[/C][C]14344.3[/C][C]14344.3[/C][C]-3.59044682020389e-14[/C][/ROW]
[ROW][C]35[/C][C]16093.4[/C][C]16093.4[/C][C]2.45345201397967e-14[/C][/ROW]
[ROW][C]36[/C][C]15413.6[/C][C]15413.6[/C][C]6.26302591948495e-14[/C][/ROW]
[ROW][C]37[/C][C]14705.7[/C][C]14705.7[/C][C]1.86638903115609e-14[/C][/ROW]
[ROW][C]38[/C][C]15972.8[/C][C]15972.8[/C][C]7.02227226804949e-14[/C][/ROW]
[ROW][C]39[/C][C]16241.4[/C][C]16241.4[/C][C]-2.06731654273643e-13[/C][/ROW]
[ROW][C]40[/C][C]16626.4[/C][C]16626.4[/C][C]3.33149325249005e-14[/C][/ROW]
[ROW][C]41[/C][C]17136.2[/C][C]17136.2[/C][C]-1.23990543922619e-14[/C][/ROW]
[ROW][C]42[/C][C]15622.9[/C][C]15622.9[/C][C]1.27456892173898e-13[/C][/ROW]
[ROW][C]43[/C][C]18003.9[/C][C]18003.9[/C][C]-5.39988983066923e-14[/C][/ROW]
[ROW][C]44[/C][C]16136.1[/C][C]16136.1[/C][C]1.14635179935757e-13[/C][/ROW]
[ROW][C]45[/C][C]14423.7[/C][C]14423.7[/C][C]2.29483179804199e-14[/C][/ROW]
[ROW][C]46[/C][C]16789.4[/C][C]16789.4[/C][C]2.82343292843405e-15[/C][/ROW]
[ROW][C]47[/C][C]16782.2[/C][C]16782.2[/C][C]1.14573590822216e-13[/C][/ROW]
[ROW][C]48[/C][C]14133.8[/C][C]14133.8[/C][C]6.00484086615178e-14[/C][/ROW]
[ROW][C]49[/C][C]12607[/C][C]12607[/C][C]-6.75114190909698e-14[/C][/ROW]
[ROW][C]50[/C][C]12004.5[/C][C]12004.5[/C][C]6.17700444430254e-14[/C][/ROW]
[ROW][C]51[/C][C]12175.4[/C][C]12175.4[/C][C]-2.53985647215925e-13[/C][/ROW]
[ROW][C]52[/C][C]13268[/C][C]13268[/C][C]3.37501764707062e-14[/C][/ROW]
[ROW][C]53[/C][C]12299.3[/C][C]12299.3[/C][C]2.24109264157388e-14[/C][/ROW]
[ROW][C]54[/C][C]11800.6[/C][C]11800.6[/C][C]8.12446232497919e-14[/C][/ROW]
[ROW][C]55[/C][C]13873.3[/C][C]13873.3[/C][C]6.45217799063042e-14[/C][/ROW]
[ROW][C]56[/C][C]12269.6[/C][C]12269.6[/C][C]5.19143161072346e-14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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
112919.912919.9-1.15687740511203e-13
211497.311497.3-1.11571156397268e-13
312142121421.06359826058060e-12
413919.413919.4-4.05993368457645e-14
512656.812656.8-2.51774014860363e-14
612034.112034.1-6.00121655853554e-14
713199.713199.7-8.46927260993712e-14
810881.310881.3-4.19424696724649e-14
911301.211301.2-6.58784157846455e-14
1013643.913643.9-3.45907733778767e-15
111251712517-9.84696567476705e-14
1213981.113981.1-9.75045326013207e-14
1314275.714275.71.33839947854674e-13
141343513435-4.15601283799536e-15
1513565.713565.7-3.46093314443156e-13
1616216.316216.33.33844272443606e-14
1712970129702.49179536106758e-15
1814079.914079.9-8.97259012924684e-14
1914235142351.45411498973402e-14
2012213.412213.4-7.94746923257248e-14
2112581125817.04527599489535e-15
2214130.414130.43.65401126113927e-14
2314210.814210.8-4.0638454214342e-14
2414378.514378.5-2.51741352550464e-14
2513142.813142.83.06953214359383e-14
2613714.713714.7-1.62655978882567e-14
2713621.913621.9-2.56787644647873e-13
2815379.815379.8-5.98501993942027e-14
2913306.313306.31.26737341014917e-14
3014391.214391.2-5.89634485458661e-14
3114909.914909.95.96286946024191e-14
3214025.414025.4-4.51323340448021e-14
3312951.212951.23.588482180933e-14
3414344.314344.3-3.59044682020389e-14
3516093.416093.42.45345201397967e-14
3615413.615413.66.26302591948495e-14
3714705.714705.71.86638903115609e-14
3815972.815972.87.02227226804949e-14
3916241.416241.4-2.06731654273643e-13
4016626.416626.43.33149325249005e-14
4117136.217136.2-1.23990543922619e-14
4215622.915622.91.27456892173898e-13
4318003.918003.9-5.39988983066923e-14
4416136.116136.11.14635179935757e-13
4514423.714423.72.29483179804199e-14
4616789.416789.42.82343292843405e-15
4716782.216782.21.14573590822216e-13
4814133.814133.86.00484086615178e-14
491260712607-6.75114190909698e-14
5012004.512004.56.17700444430254e-14
5112175.412175.4-2.53985647215925e-13
5213268132683.37501764707062e-14
5312299.312299.32.24109264157388e-14
5411800.611800.68.12446232497919e-14
5513873.313873.36.45217799063042e-14
5612269.612269.65.19143161072346e-14






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.9999992446870851.51062582947339e-067.55312914736697e-07
220.4054289538708520.8108579077417040.594571046129148
230.4323071841980120.8646143683960250.567692815801988
240.3240981886648940.6481963773297880.675901811335106
250.99990553731730.0001889253653996889.44626826998439e-05
260.9970672723430840.005865455313832730.00293272765691636
270.9993066478329560.001386704334088230.000693352167044117
280.2131044142508480.4262088285016960.786895585749152
290.6322896330090020.7354207339819950.367710366990998
300.5018924660487360.9962150679025280.498107533951264
310.9649812012716880.0700375974566240.035018798728312
320.02353330891422370.04706661782844740.976466691085776
33100
340.877386026483950.2452279470320980.122613973516049
35100

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.999999244687085 & 1.51062582947339e-06 & 7.55312914736697e-07 \tabularnewline
22 & 0.405428953870852 & 0.810857907741704 & 0.594571046129148 \tabularnewline
23 & 0.432307184198012 & 0.864614368396025 & 0.567692815801988 \tabularnewline
24 & 0.324098188664894 & 0.648196377329788 & 0.675901811335106 \tabularnewline
25 & 0.9999055373173 & 0.000188925365399688 & 9.44626826998439e-05 \tabularnewline
26 & 0.997067272343084 & 0.00586545531383273 & 0.00293272765691636 \tabularnewline
27 & 0.999306647832956 & 0.00138670433408823 & 0.000693352167044117 \tabularnewline
28 & 0.213104414250848 & 0.426208828501696 & 0.786895585749152 \tabularnewline
29 & 0.632289633009002 & 0.735420733981995 & 0.367710366990998 \tabularnewline
30 & 0.501892466048736 & 0.996215067902528 & 0.498107533951264 \tabularnewline
31 & 0.964981201271688 & 0.070037597456624 & 0.035018798728312 \tabularnewline
32 & 0.0235333089142237 & 0.0470666178284474 & 0.976466691085776 \tabularnewline
33 & 1 & 0 & 0 \tabularnewline
34 & 0.87738602648395 & 0.245227947032098 & 0.122613973516049 \tabularnewline
35 & 1 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&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]0.999999244687085[/C][C]1.51062582947339e-06[/C][C]7.55312914736697e-07[/C][/ROW]
[ROW][C]22[/C][C]0.405428953870852[/C][C]0.810857907741704[/C][C]0.594571046129148[/C][/ROW]
[ROW][C]23[/C][C]0.432307184198012[/C][C]0.864614368396025[/C][C]0.567692815801988[/C][/ROW]
[ROW][C]24[/C][C]0.324098188664894[/C][C]0.648196377329788[/C][C]0.675901811335106[/C][/ROW]
[ROW][C]25[/C][C]0.9999055373173[/C][C]0.000188925365399688[/C][C]9.44626826998439e-05[/C][/ROW]
[ROW][C]26[/C][C]0.997067272343084[/C][C]0.00586545531383273[/C][C]0.00293272765691636[/C][/ROW]
[ROW][C]27[/C][C]0.999306647832956[/C][C]0.00138670433408823[/C][C]0.000693352167044117[/C][/ROW]
[ROW][C]28[/C][C]0.213104414250848[/C][C]0.426208828501696[/C][C]0.786895585749152[/C][/ROW]
[ROW][C]29[/C][C]0.632289633009002[/C][C]0.735420733981995[/C][C]0.367710366990998[/C][/ROW]
[ROW][C]30[/C][C]0.501892466048736[/C][C]0.996215067902528[/C][C]0.498107533951264[/C][/ROW]
[ROW][C]31[/C][C]0.964981201271688[/C][C]0.070037597456624[/C][C]0.035018798728312[/C][/ROW]
[ROW][C]32[/C][C]0.0235333089142237[/C][C]0.0470666178284474[/C][C]0.976466691085776[/C][/ROW]
[ROW][C]33[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]0.87738602648395[/C][C]0.245227947032098[/C][C]0.122613973516049[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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
210.9999992446870851.51062582947339e-067.55312914736697e-07
220.4054289538708520.8108579077417040.594571046129148
230.4323071841980120.8646143683960250.567692815801988
240.3240981886648940.6481963773297880.675901811335106
250.99990553731730.0001889253653996889.44626826998439e-05
260.9970672723430840.005865455313832730.00293272765691636
270.9993066478329560.001386704334088230.000693352167044117
280.2131044142508480.4262088285016960.786895585749152
290.6322896330090020.7354207339819950.367710366990998
300.5018924660487360.9962150679025280.498107533951264
310.9649812012716880.0700375974566240.035018798728312
320.02353330891422370.04706661782844740.976466691085776
33100
340.877386026483950.2452279470320980.122613973516049
35100






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level60.4NOK
5% type I error level70.466666666666667NOK
10% type I error level80.533333333333333NOK

\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 & 6 & 0.4 & NOK \tabularnewline
5% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
10% type I error level & 8 & 0.533333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58634&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]6[/C][C]0.4[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.533333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58634&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58634&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 level60.4NOK
5% type I error level70.466666666666667NOK
10% type I error level80.533333333333333NOK


Figures (Output of Computation)

Figure 1
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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')
}