Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 21 Dec 2010 17:22:06 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292952039ox63qwqi3pw7xkt.htm/, Retrieved Wed, 15 May 2024 02:32:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113766, Retrieved Wed, 15 May 2024 02:32:29 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

130

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
-  MPD  [Multiple Regression] [ws8 - Regressie a...] [2010-11-27 11:23:58] [4a7069087cf9e0eda253aeed7d8c30d6]
-    D    [Multiple Regression] [Paper - Regressie...] [2010-11-28 20:30:20] [4a7069087cf9e0eda253aeed7d8c30d6]
-    D      [Multiple Regression] [Paper - Regressie...] [2010-11-29 18:29:27] [4a7069087cf9e0eda253aeed7d8c30d6]
-    D          [Multiple Regression] [Multiple regressi...] [2010-12-21 17:22:06] [039869833c16fe697975601e6b065e0f] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1038,00	0	934,00	988,00	870,00	854,00
934,00	0	988,00	870,00	854,00	834,00
988,00	0	870,00	854,00	834,00	872,00
870,00	0	854,00	834,00	872,00	954,00
854,00	0	834,00	872,00	954,00	870,00
834,00	0	872,00	954,00	870,00	1238,00
872,00	0	954,00	870,00	1238,00	1082,00
954,00	0	870,00	1238,00	1082,00	1053,00
870,00	0	1238,00	1082,00	1053,00	934,00
1238,00	0	1082,00	1053,00	934,00	787,00
1082,00	0	1053,00	934,00	787,00	1081,00
1053,00	0	934,00	787,00	1081,00	908,00
934,00	0	787,00	1081,00	908,00	995,00
787,00	0	1081,00	908,00	995,00	825,00
1081,00	0	908,00	995,00	825,00	822,00
908,00	0	995,00	825,00	822,00	856,00
995,00	0	825,00	822,00	856,00	887,00
825,00	0	822,00	856,00	887,00	1094,00
822,00	0	856,00	887,00	1094,00	990,00
856,00	0	887,00	1094,00	990,00	936,00
887,00	0	1094,00	990,00	936,00	1097,00
1094,00	0	990,00	936,00	1097,00	918,00
990,00	0	936,00	1097,00	918,00	926,00
936,00	0	1097,00	918,00	926,00	907,00
1097,00	0	918,00	926,00	907,00	899,00
918,00	0	926,00	907,00	899,00	971,00
926,00	0	907,00	899,00	971,00	1087,00
907,00	0	899,00	971,00	1087,00	1000,00
899,00	0	971,00	1087,00	1000,00	1071,00
971,00	0	1087,00	1000,00	1071,00	1190,00
1087,00	0	1000,00	1071,00	1190,00	1116,00
1000,00	0	1071,00	1190,00	1116,00	1070,00
1071,00	0	1190,00	1116,00	1070,00	1314,00
1190,00	0	1116,00	1070,00	1314,00	1068,00
1116,00	0	1070,00	1314,00	1068,00	1185,00
1070,00	0	1314,00	1068,00	1185,00	1215,00
1314,00	0	1068,00	1185,00	1215,00	1145,00
1068,00	0	1185,00	1215,00	1145,00	1251,00
1185,00	0	1215,00	1145,00	1251,00	1363,00
1215,00	0	1145,00	1251,00	1363,00	1368,00
1145,00	0	1251,00	1363,00	1368,00	1535,00
1251,00	1	1363,00	1368,00	1535,00	1853,00
1363,00	1	1368,00	1535,00	1853,00	1866,00
1368,00	1	1535,00	1853,00	1866,00	2023,00
1535,00	1	1853,00	1866,00	2023,00	1373,00
1853,00	1	1866,00	2023,00	1373,00	1968,00
1866,00	1	2023,00	1373,00	1968,00	1424,00
2023,00	1	1373,00	1968,00	1424,00	1160,00
1373,00	1	1968,00	1424,00	1160,00	1243,00
1968,00	1	1424,00	1160,00	1243,00	1375,00
1424,00	1	1160,00	1243,00	1375,00	1539,00
1160,00	1	1243,00	1375,00	1539,00	1773,00
1243,00	1	1375,00	1539,00	1773,00	1906,00
1375,00	1	1539,00	1773,00	1906,00	2076,00
1539,00	1	1773,00	1906,00	2076,00	2004,00

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
Maandelijksewerkloosheid[t] = + 785.581646496084 + 316.837588957848x[t] + 0.113241666763825`y-1`[t] + 0.331362488209895`y-2`[t] + 0.0193980967903263`y-3`[t] -0.253615790411075`y-4`[t] -59.0113984962233M1[t] -35.8482054764646M2[t] -25.6599930393899M3[t] -136.285762455275M4[t] -141.100697932726M5[t] -153.268034800840M6[t] -123.621358861251M7[t] -197.682505736142M8[t] -180.794636617663M9[t] + 78.107982061271M10[t] + 15.0932390499574M11[t] + 4.08900526417693t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Maandelijksewerkloosheid[t] =  +  785.581646496084 +  316.837588957848x[t] +  0.113241666763825`y-1`[t] +  0.331362488209895`y-2`[t] +  0.0193980967903263`y-3`[t] -0.253615790411075`y-4`[t] -59.0113984962233M1[t] -35.8482054764646M2[t] -25.6599930393899M3[t] -136.285762455275M4[t] -141.100697932726M5[t] -153.268034800840M6[t] -123.621358861251M7[t] -197.682505736142M8[t] -180.794636617663M9[t] +  78.107982061271M10[t] +  15.0932390499574M11[t] +  4.08900526417693t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Maandelijksewerkloosheid[t] =  +  785.581646496084 +  316.837588957848x[t] +  0.113241666763825`y-1`[t] +  0.331362488209895`y-2`[t] +  0.0193980967903263`y-3`[t] -0.253615790411075`y-4`[t] -59.0113984962233M1[t] -35.8482054764646M2[t] -25.6599930393899M3[t] -136.285762455275M4[t] -141.100697932726M5[t] -153.268034800840M6[t] -123.621358861251M7[t] -197.682505736142M8[t] -180.794636617663M9[t] +  78.107982061271M10[t] +  15.0932390499574M11[t] +  4.08900526417693t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Maandelijksewerkloosheid[t] = + 785.581646496084 + 316.837588957848x[t] + 0.113241666763825`y-1`[t] + 0.331362488209895`y-2`[t] + 0.0193980967903263`y-3`[t] -0.253615790411075`y-4`[t] -59.0113984962233M1[t] -35.8482054764646M2[t] -25.6599930393899M3[t] -136.285762455275M4[t] -141.100697932726M5[t] -153.268034800840M6[t] -123.621358861251M7[t] -197.682505736142M8[t] -180.794636617663M9[t] + 78.107982061271M10[t] + 15.0932390499574M11[t] + 4.08900526417693t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	785.581646496084	187.243562	4.1955	0.000163	8.2e-05
x	316.837588957848	102.677091	3.0858	0.003832	0.001916
`y-1`	0.113241666763825	0.154518	0.7329	0.468255	0.234127
`y-2`	0.331362488209895	0.152241	2.1766	0.035969	0.017985
`y-3`	0.0193980967903263	0.151166	0.1283	0.898588	0.449294
`y-4`	-0.253615790411075	0.146221	-1.7345	0.091161	0.04558
M1	-59.0113984962233	100.972532	-0.5844	0.562478	0.281239
M2	-35.8482054764646	102.743999	-0.3489	0.729136	0.364568
M3	-25.6599930393899	105.464578	-0.2433	0.809114	0.404557
M4	-136.285762455275	106.342184	-1.2816	0.207964	0.103982
M5	-141.100697932726	106.655141	-1.323	0.193966	0.096983
M6	-153.268034800840	117.242164	-1.3073	0.199184	0.099592
M7	-123.621358861251	113.945213	-1.0849	0.284976	0.142488
M8	-197.682505736142	113.423447	-1.7429	0.089663	0.044831
M9	-180.794636617663	109.898744	-1.6451	0.108419	0.05421
M10	78.107982061271	107.728175	0.725	0.472984	0.236492
M11	15.0932390499574	107.050948	0.141	0.888642	0.444321
t	4.08900526417693	2.565665	1.5937	0.119502	0.059751

\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) & 785.581646496084 & 187.243562 & 4.1955 & 0.000163 & 8.2e-05 \tabularnewline
x & 316.837588957848 & 102.677091 & 3.0858 & 0.003832 & 0.001916 \tabularnewline
`y-1` & 0.113241666763825 & 0.154518 & 0.7329 & 0.468255 & 0.234127 \tabularnewline
`y-2` & 0.331362488209895 & 0.152241 & 2.1766 & 0.035969 & 0.017985 \tabularnewline
`y-3` & 0.0193980967903263 & 0.151166 & 0.1283 & 0.898588 & 0.449294 \tabularnewline
`y-4` & -0.253615790411075 & 0.146221 & -1.7345 & 0.091161 & 0.04558 \tabularnewline
M1 & -59.0113984962233 & 100.972532 & -0.5844 & 0.562478 & 0.281239 \tabularnewline
M2 & -35.8482054764646 & 102.743999 & -0.3489 & 0.729136 & 0.364568 \tabularnewline
M3 & -25.6599930393899 & 105.464578 & -0.2433 & 0.809114 & 0.404557 \tabularnewline
M4 & -136.285762455275 & 106.342184 & -1.2816 & 0.207964 & 0.103982 \tabularnewline
M5 & -141.100697932726 & 106.655141 & -1.323 & 0.193966 & 0.096983 \tabularnewline
M6 & -153.268034800840 & 117.242164 & -1.3073 & 0.199184 & 0.099592 \tabularnewline
M7 & -123.621358861251 & 113.945213 & -1.0849 & 0.284976 & 0.142488 \tabularnewline
M8 & -197.682505736142 & 113.423447 & -1.7429 & 0.089663 & 0.044831 \tabularnewline
M9 & -180.794636617663 & 109.898744 & -1.6451 & 0.108419 & 0.05421 \tabularnewline
M10 & 78.107982061271 & 107.728175 & 0.725 & 0.472984 & 0.236492 \tabularnewline
M11 & 15.0932390499574 & 107.050948 & 0.141 & 0.888642 & 0.444321 \tabularnewline
t & 4.08900526417693 & 2.565665 & 1.5937 & 0.119502 & 0.059751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&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]785.581646496084[/C][C]187.243562[/C][C]4.1955[/C][C]0.000163[/C][C]8.2e-05[/C][/ROW]
[ROW][C]x[/C][C]316.837588957848[/C][C]102.677091[/C][C]3.0858[/C][C]0.003832[/C][C]0.001916[/C][/ROW]
[ROW][C]`y-1`[/C][C]0.113241666763825[/C][C]0.154518[/C][C]0.7329[/C][C]0.468255[/C][C]0.234127[/C][/ROW]
[ROW][C]`y-2`[/C][C]0.331362488209895[/C][C]0.152241[/C][C]2.1766[/C][C]0.035969[/C][C]0.017985[/C][/ROW]
[ROW][C]`y-3`[/C][C]0.0193980967903263[/C][C]0.151166[/C][C]0.1283[/C][C]0.898588[/C][C]0.449294[/C][/ROW]
[ROW][C]`y-4`[/C][C]-0.253615790411075[/C][C]0.146221[/C][C]-1.7345[/C][C]0.091161[/C][C]0.04558[/C][/ROW]
[ROW][C]M1[/C][C]-59.0113984962233[/C][C]100.972532[/C][C]-0.5844[/C][C]0.562478[/C][C]0.281239[/C][/ROW]
[ROW][C]M2[/C][C]-35.8482054764646[/C][C]102.743999[/C][C]-0.3489[/C][C]0.729136[/C][C]0.364568[/C][/ROW]
[ROW][C]M3[/C][C]-25.6599930393899[/C][C]105.464578[/C][C]-0.2433[/C][C]0.809114[/C][C]0.404557[/C][/ROW]
[ROW][C]M4[/C][C]-136.285762455275[/C][C]106.342184[/C][C]-1.2816[/C][C]0.207964[/C][C]0.103982[/C][/ROW]
[ROW][C]M5[/C][C]-141.100697932726[/C][C]106.655141[/C][C]-1.323[/C][C]0.193966[/C][C]0.096983[/C][/ROW]
[ROW][C]M6[/C][C]-153.268034800840[/C][C]117.242164[/C][C]-1.3073[/C][C]0.199184[/C][C]0.099592[/C][/ROW]
[ROW][C]M7[/C][C]-123.621358861251[/C][C]113.945213[/C][C]-1.0849[/C][C]0.284976[/C][C]0.142488[/C][/ROW]
[ROW][C]M8[/C][C]-197.682505736142[/C][C]113.423447[/C][C]-1.7429[/C][C]0.089663[/C][C]0.044831[/C][/ROW]
[ROW][C]M9[/C][C]-180.794636617663[/C][C]109.898744[/C][C]-1.6451[/C][C]0.108419[/C][C]0.05421[/C][/ROW]
[ROW][C]M10[/C][C]78.107982061271[/C][C]107.728175[/C][C]0.725[/C][C]0.472984[/C][C]0.236492[/C][/ROW]
[ROW][C]M11[/C][C]15.0932390499574[/C][C]107.050948[/C][C]0.141[/C][C]0.888642[/C][C]0.444321[/C][/ROW]
[ROW][C]t[/C][C]4.08900526417693[/C][C]2.565665[/C][C]1.5937[/C][C]0.119502[/C][C]0.059751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	785.581646496084	187.243562	4.1955	0.000163	8.2e-05
x	316.837588957848	102.677091	3.0858	0.003832	0.001916
`y-1`	0.113241666763825	0.154518	0.7329	0.468255	0.234127
`y-2`	0.331362488209895	0.152241	2.1766	0.035969	0.017985
`y-3`	0.0193980967903263	0.151166	0.1283	0.898588	0.449294
`y-4`	-0.253615790411075	0.146221	-1.7345	0.091161	0.04558
M1	-59.0113984962233	100.972532	-0.5844	0.562478	0.281239
M2	-35.8482054764646	102.743999	-0.3489	0.729136	0.364568
M3	-25.6599930393899	105.464578	-0.2433	0.809114	0.404557
M4	-136.285762455275	106.342184	-1.2816	0.207964	0.103982
M5	-141.100697932726	106.655141	-1.323	0.193966	0.096983
M6	-153.268034800840	117.242164	-1.3073	0.199184	0.099592
M7	-123.621358861251	113.945213	-1.0849	0.284976	0.142488
M8	-197.682505736142	113.423447	-1.7429	0.089663	0.044831
M9	-180.794636617663	109.898744	-1.6451	0.108419	0.05421
M10	78.107982061271	107.728175	0.725	0.472984	0.236492
M11	15.0932390499574	107.050948	0.141	0.888642	0.444321
t	4.08900526417693	2.565665	1.5937	0.119502	0.059751

Multiple Linear Regression - Regression Statistics
Multiple R	0.907790108097507
R-squared	0.824082880359683
Adjusted R-squared	0.743256095660078
F-TEST (value)	10.195665748952
F-TEST (DF numerator)	17
F-TEST (DF denominator)	37
p-value	2.88513257729051e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	148.271370356329
Sum Squared Residuals	813422.77289172

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.907790108097507 \tabularnewline
R-squared & 0.824082880359683 \tabularnewline
Adjusted R-squared & 0.743256095660078 \tabularnewline
F-TEST (value) & 10.195665748952 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 37 \tabularnewline
p-value & 2.88513257729051e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 148.271370356329 \tabularnewline
Sum Squared Residuals & 813422.77289172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.907790108097507[/C][/ROW]
[ROW][C]R-squared[/C][C]0.824082880359683[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.743256095660078[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.195665748952[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]37[/C][/ROW]
[ROW][C]p-value[/C][C]2.88513257729051e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]148.271370356329[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]813422.77289172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.907790108097507
R-squared	0.824082880359683
Adjusted R-squared	0.743256095660078
F-TEST (value)	10.195665748952
F-TEST (DF numerator)	17
F-TEST (DF denominator)	37
p-value	2.88513257729051e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	148.271370356329
Sum Squared Residuals	813422.77289172

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1038	964.101567569352	73.8984324306477
2	934	963.129988509344	-29.1299885093441
3	988	948.717527749679	39.2824722503214
4	870	813.682280029876	56.3177199701244
5	854	846.177661364638	7.82233863536176
6	834	774.614186129275	59.3858138707251
7	872	836.503797921011	35.4962020789889
8	954	883.289506786007	70.7104932139932
9	870	923.864500629006	-53.8645006290055
10	1238	1194.55406007125	43.445939928748
11	1082	1015.49761528195	66.502384718047
12	1053	991.885909581895	61.1140904181054
13	934	992.317118358785	-58.3171183587849
14	787	1040.33897500161	-253.338975001614
15	1081	1061.31709174386	19.6829082561369
16	908	899.619598440578	8.38040155942176
17	995	871.445943200952	123.554056799048
18	825	822.397083581267	2.60291641873282
19	822	900.64666682786	-78.6466668278594
20	856	914.454902562276	-58.4549025622758
21	887	882.531463708354	4.46853629164575
22	1094	1164.37270001152	-70.372700011518
23	990	1147.18008721217	-157.180087212171
24	936	1100.06776117793	-164.067761177928
25	1097	1029.18637198511	67.8136280148916
26	918	1032.63309464325	-114.633094643247
27	926	1014.08505205153	-88.0850520515253
28	907	954.81520671026	-47.8152067102606
29	899	980.986369596385	-81.9863695963852
30	971	928.412520675986	42.587479324014
31	1087	996.89885554267	90.10114445733
32	1000	984.62987556559	15.3701244344101
33	1071	931.787118852952	139.212881147048
34	1190	1238.27880505585	-48.2788050558488
35	1116	1220.55141847227	-104.551418472275
36	1070	1150.32408288937	-80.3240828893692
37	1314	1124.64869898646	189.351301013535
38	1068	1146.84990636917	-78.8499063691678
39	1185	1114.98022963238	70.0197703676242
40	1215	1036.54548044591	178.454519554090
41	1145	1042.67891907441	102.321080925588
42	1251	1288.36771636018	-37.3677163601832
43	1363	1380.8787309328	-17.8787309328007
44	1368	1395.62571508613	-27.6257150861273
45	1535	1624.81691680969	-89.8169168096881
46	1853	1777.79443486138	75.2055651386188
47	1866	1670.7708790336	195.229120966398
48	2023	1839.72224635081	183.277753649192
49	1373	1645.74624310029	-272.74624310029
50	1968	1492.04803547663	475.951964523373
51	1424	1464.90009882256	-40.9000988225573
52	1160	1355.33743437338	-195.337434373375
53	1243	1394.71110676361	-151.711106763612
54	1375	1442.20849325329	-67.2084932532887
55	1539	1568.07194877566	-29.0719487756588

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1038 & 964.101567569352 & 73.8984324306477 \tabularnewline
2 & 934 & 963.129988509344 & -29.1299885093441 \tabularnewline
3 & 988 & 948.717527749679 & 39.2824722503214 \tabularnewline
4 & 870 & 813.682280029876 & 56.3177199701244 \tabularnewline
5 & 854 & 846.177661364638 & 7.82233863536176 \tabularnewline
6 & 834 & 774.614186129275 & 59.3858138707251 \tabularnewline
7 & 872 & 836.503797921011 & 35.4962020789889 \tabularnewline
8 & 954 & 883.289506786007 & 70.7104932139932 \tabularnewline
9 & 870 & 923.864500629006 & -53.8645006290055 \tabularnewline
10 & 1238 & 1194.55406007125 & 43.445939928748 \tabularnewline
11 & 1082 & 1015.49761528195 & 66.502384718047 \tabularnewline
12 & 1053 & 991.885909581895 & 61.1140904181054 \tabularnewline
13 & 934 & 992.317118358785 & -58.3171183587849 \tabularnewline
14 & 787 & 1040.33897500161 & -253.338975001614 \tabularnewline
15 & 1081 & 1061.31709174386 & 19.6829082561369 \tabularnewline
16 & 908 & 899.619598440578 & 8.38040155942176 \tabularnewline
17 & 995 & 871.445943200952 & 123.554056799048 \tabularnewline
18 & 825 & 822.397083581267 & 2.60291641873282 \tabularnewline
19 & 822 & 900.64666682786 & -78.6466668278594 \tabularnewline
20 & 856 & 914.454902562276 & -58.4549025622758 \tabularnewline
21 & 887 & 882.531463708354 & 4.46853629164575 \tabularnewline
22 & 1094 & 1164.37270001152 & -70.372700011518 \tabularnewline
23 & 990 & 1147.18008721217 & -157.180087212171 \tabularnewline
24 & 936 & 1100.06776117793 & -164.067761177928 \tabularnewline
25 & 1097 & 1029.18637198511 & 67.8136280148916 \tabularnewline
26 & 918 & 1032.63309464325 & -114.633094643247 \tabularnewline
27 & 926 & 1014.08505205153 & -88.0850520515253 \tabularnewline
28 & 907 & 954.81520671026 & -47.8152067102606 \tabularnewline
29 & 899 & 980.986369596385 & -81.9863695963852 \tabularnewline
30 & 971 & 928.412520675986 & 42.587479324014 \tabularnewline
31 & 1087 & 996.89885554267 & 90.10114445733 \tabularnewline
32 & 1000 & 984.62987556559 & 15.3701244344101 \tabularnewline
33 & 1071 & 931.787118852952 & 139.212881147048 \tabularnewline
34 & 1190 & 1238.27880505585 & -48.2788050558488 \tabularnewline
35 & 1116 & 1220.55141847227 & -104.551418472275 \tabularnewline
36 & 1070 & 1150.32408288937 & -80.3240828893692 \tabularnewline
37 & 1314 & 1124.64869898646 & 189.351301013535 \tabularnewline
38 & 1068 & 1146.84990636917 & -78.8499063691678 \tabularnewline
39 & 1185 & 1114.98022963238 & 70.0197703676242 \tabularnewline
40 & 1215 & 1036.54548044591 & 178.454519554090 \tabularnewline
41 & 1145 & 1042.67891907441 & 102.321080925588 \tabularnewline
42 & 1251 & 1288.36771636018 & -37.3677163601832 \tabularnewline
43 & 1363 & 1380.8787309328 & -17.8787309328007 \tabularnewline
44 & 1368 & 1395.62571508613 & -27.6257150861273 \tabularnewline
45 & 1535 & 1624.81691680969 & -89.8169168096881 \tabularnewline
46 & 1853 & 1777.79443486138 & 75.2055651386188 \tabularnewline
47 & 1866 & 1670.7708790336 & 195.229120966398 \tabularnewline
48 & 2023 & 1839.72224635081 & 183.277753649192 \tabularnewline
49 & 1373 & 1645.74624310029 & -272.74624310029 \tabularnewline
50 & 1968 & 1492.04803547663 & 475.951964523373 \tabularnewline
51 & 1424 & 1464.90009882256 & -40.9000988225573 \tabularnewline
52 & 1160 & 1355.33743437338 & -195.337434373375 \tabularnewline
53 & 1243 & 1394.71110676361 & -151.711106763612 \tabularnewline
54 & 1375 & 1442.20849325329 & -67.2084932532887 \tabularnewline
55 & 1539 & 1568.07194877566 & -29.0719487756588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&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]1038[/C][C]964.101567569352[/C][C]73.8984324306477[/C][/ROW]
[ROW][C]2[/C][C]934[/C][C]963.129988509344[/C][C]-29.1299885093441[/C][/ROW]
[ROW][C]3[/C][C]988[/C][C]948.717527749679[/C][C]39.2824722503214[/C][/ROW]
[ROW][C]4[/C][C]870[/C][C]813.682280029876[/C][C]56.3177199701244[/C][/ROW]
[ROW][C]5[/C][C]854[/C][C]846.177661364638[/C][C]7.82233863536176[/C][/ROW]
[ROW][C]6[/C][C]834[/C][C]774.614186129275[/C][C]59.3858138707251[/C][/ROW]
[ROW][C]7[/C][C]872[/C][C]836.503797921011[/C][C]35.4962020789889[/C][/ROW]
[ROW][C]8[/C][C]954[/C][C]883.289506786007[/C][C]70.7104932139932[/C][/ROW]
[ROW][C]9[/C][C]870[/C][C]923.864500629006[/C][C]-53.8645006290055[/C][/ROW]
[ROW][C]10[/C][C]1238[/C][C]1194.55406007125[/C][C]43.445939928748[/C][/ROW]
[ROW][C]11[/C][C]1082[/C][C]1015.49761528195[/C][C]66.502384718047[/C][/ROW]
[ROW][C]12[/C][C]1053[/C][C]991.885909581895[/C][C]61.1140904181054[/C][/ROW]
[ROW][C]13[/C][C]934[/C][C]992.317118358785[/C][C]-58.3171183587849[/C][/ROW]
[ROW][C]14[/C][C]787[/C][C]1040.33897500161[/C][C]-253.338975001614[/C][/ROW]
[ROW][C]15[/C][C]1081[/C][C]1061.31709174386[/C][C]19.6829082561369[/C][/ROW]
[ROW][C]16[/C][C]908[/C][C]899.619598440578[/C][C]8.38040155942176[/C][/ROW]
[ROW][C]17[/C][C]995[/C][C]871.445943200952[/C][C]123.554056799048[/C][/ROW]
[ROW][C]18[/C][C]825[/C][C]822.397083581267[/C][C]2.60291641873282[/C][/ROW]
[ROW][C]19[/C][C]822[/C][C]900.64666682786[/C][C]-78.6466668278594[/C][/ROW]
[ROW][C]20[/C][C]856[/C][C]914.454902562276[/C][C]-58.4549025622758[/C][/ROW]
[ROW][C]21[/C][C]887[/C][C]882.531463708354[/C][C]4.46853629164575[/C][/ROW]
[ROW][C]22[/C][C]1094[/C][C]1164.37270001152[/C][C]-70.372700011518[/C][/ROW]
[ROW][C]23[/C][C]990[/C][C]1147.18008721217[/C][C]-157.180087212171[/C][/ROW]
[ROW][C]24[/C][C]936[/C][C]1100.06776117793[/C][C]-164.067761177928[/C][/ROW]
[ROW][C]25[/C][C]1097[/C][C]1029.18637198511[/C][C]67.8136280148916[/C][/ROW]
[ROW][C]26[/C][C]918[/C][C]1032.63309464325[/C][C]-114.633094643247[/C][/ROW]
[ROW][C]27[/C][C]926[/C][C]1014.08505205153[/C][C]-88.0850520515253[/C][/ROW]
[ROW][C]28[/C][C]907[/C][C]954.81520671026[/C][C]-47.8152067102606[/C][/ROW]
[ROW][C]29[/C][C]899[/C][C]980.986369596385[/C][C]-81.9863695963852[/C][/ROW]
[ROW][C]30[/C][C]971[/C][C]928.412520675986[/C][C]42.587479324014[/C][/ROW]
[ROW][C]31[/C][C]1087[/C][C]996.89885554267[/C][C]90.10114445733[/C][/ROW]
[ROW][C]32[/C][C]1000[/C][C]984.62987556559[/C][C]15.3701244344101[/C][/ROW]
[ROW][C]33[/C][C]1071[/C][C]931.787118852952[/C][C]139.212881147048[/C][/ROW]
[ROW][C]34[/C][C]1190[/C][C]1238.27880505585[/C][C]-48.2788050558488[/C][/ROW]
[ROW][C]35[/C][C]1116[/C][C]1220.55141847227[/C][C]-104.551418472275[/C][/ROW]
[ROW][C]36[/C][C]1070[/C][C]1150.32408288937[/C][C]-80.3240828893692[/C][/ROW]
[ROW][C]37[/C][C]1314[/C][C]1124.64869898646[/C][C]189.351301013535[/C][/ROW]
[ROW][C]38[/C][C]1068[/C][C]1146.84990636917[/C][C]-78.8499063691678[/C][/ROW]
[ROW][C]39[/C][C]1185[/C][C]1114.98022963238[/C][C]70.0197703676242[/C][/ROW]
[ROW][C]40[/C][C]1215[/C][C]1036.54548044591[/C][C]178.454519554090[/C][/ROW]
[ROW][C]41[/C][C]1145[/C][C]1042.67891907441[/C][C]102.321080925588[/C][/ROW]
[ROW][C]42[/C][C]1251[/C][C]1288.36771636018[/C][C]-37.3677163601832[/C][/ROW]
[ROW][C]43[/C][C]1363[/C][C]1380.8787309328[/C][C]-17.8787309328007[/C][/ROW]
[ROW][C]44[/C][C]1368[/C][C]1395.62571508613[/C][C]-27.6257150861273[/C][/ROW]
[ROW][C]45[/C][C]1535[/C][C]1624.81691680969[/C][C]-89.8169168096881[/C][/ROW]
[ROW][C]46[/C][C]1853[/C][C]1777.79443486138[/C][C]75.2055651386188[/C][/ROW]
[ROW][C]47[/C][C]1866[/C][C]1670.7708790336[/C][C]195.229120966398[/C][/ROW]
[ROW][C]48[/C][C]2023[/C][C]1839.72224635081[/C][C]183.277753649192[/C][/ROW]
[ROW][C]49[/C][C]1373[/C][C]1645.74624310029[/C][C]-272.74624310029[/C][/ROW]
[ROW][C]50[/C][C]1968[/C][C]1492.04803547663[/C][C]475.951964523373[/C][/ROW]
[ROW][C]51[/C][C]1424[/C][C]1464.90009882256[/C][C]-40.9000988225573[/C][/ROW]
[ROW][C]52[/C][C]1160[/C][C]1355.33743437338[/C][C]-195.337434373375[/C][/ROW]
[ROW][C]53[/C][C]1243[/C][C]1394.71110676361[/C][C]-151.711106763612[/C][/ROW]
[ROW][C]54[/C][C]1375[/C][C]1442.20849325329[/C][C]-67.2084932532887[/C][/ROW]
[ROW][C]55[/C][C]1539[/C][C]1568.07194877566[/C][C]-29.0719487756588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1038	964.101567569352	73.8984324306477
2	934	963.129988509344	-29.1299885093441
3	988	948.717527749679	39.2824722503214
4	870	813.682280029876	56.3177199701244
5	854	846.177661364638	7.82233863536176
6	834	774.614186129275	59.3858138707251
7	872	836.503797921011	35.4962020789889
8	954	883.289506786007	70.7104932139932
9	870	923.864500629006	-53.8645006290055
10	1238	1194.55406007125	43.445939928748
11	1082	1015.49761528195	66.502384718047
12	1053	991.885909581895	61.1140904181054
13	934	992.317118358785	-58.3171183587849
14	787	1040.33897500161	-253.338975001614
15	1081	1061.31709174386	19.6829082561369
16	908	899.619598440578	8.38040155942176
17	995	871.445943200952	123.554056799048
18	825	822.397083581267	2.60291641873282
19	822	900.64666682786	-78.6466668278594
20	856	914.454902562276	-58.4549025622758
21	887	882.531463708354	4.46853629164575
22	1094	1164.37270001152	-70.372700011518
23	990	1147.18008721217	-157.180087212171
24	936	1100.06776117793	-164.067761177928
25	1097	1029.18637198511	67.8136280148916
26	918	1032.63309464325	-114.633094643247
27	926	1014.08505205153	-88.0850520515253
28	907	954.81520671026	-47.8152067102606
29	899	980.986369596385	-81.9863695963852
30	971	928.412520675986	42.587479324014
31	1087	996.89885554267	90.10114445733
32	1000	984.62987556559	15.3701244344101
33	1071	931.787118852952	139.212881147048
34	1190	1238.27880505585	-48.2788050558488
35	1116	1220.55141847227	-104.551418472275
36	1070	1150.32408288937	-80.3240828893692
37	1314	1124.64869898646	189.351301013535
38	1068	1146.84990636917	-78.8499063691678
39	1185	1114.98022963238	70.0197703676242
40	1215	1036.54548044591	178.454519554090
41	1145	1042.67891907441	102.321080925588
42	1251	1288.36771636018	-37.3677163601832
43	1363	1380.8787309328	-17.8787309328007
44	1368	1395.62571508613	-27.6257150861273
45	1535	1624.81691680969	-89.8169168096881
46	1853	1777.79443486138	75.2055651386188
47	1866	1670.7708790336	195.229120966398
48	2023	1839.72224635081	183.277753649192
49	1373	1645.74624310029	-272.74624310029
50	1968	1492.04803547663	475.951964523373
51	1424	1464.90009882256	-40.9000988225573
52	1160	1355.33743437338	-195.337434373375
53	1243	1394.71110676361	-151.711106763612
54	1375	1442.20849325329	-67.2084932532887
55	1539	1568.07194877566	-29.0719487756588

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.113092285054002	0.226184570108004	0.886907714945998
22	0.0406324150817447	0.0812648301634895	0.959367584918255
23	0.0138374800061041	0.0276749600122081	0.986162519993896
24	0.0153647089178795	0.0307294178357590	0.98463529108212
25	0.0139018442199219	0.0278036884398438	0.986098155780078
26	0.00843910902341185	0.0168782180468237	0.991560890976588
27	0.00325489615046637	0.00650979230093274	0.996745103849534
28	0.00176641421060536	0.00353282842121073	0.998233585789395
29	0.000575107586278198	0.00115021517255640	0.999424892413722
30	0.000366114533177452	0.000732229066354905	0.999633885466823
31	0.000449908718232617	0.000899817436465234	0.999550091281767
32	0.000124382381039456	0.000248764762078912	0.99987561761896
33	0.000193358145939456	0.000386716291878912	0.99980664185406
34	0.0284704132159483	0.0569408264318965	0.971529586784052

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.113092285054002 & 0.226184570108004 & 0.886907714945998 \tabularnewline
22 & 0.0406324150817447 & 0.0812648301634895 & 0.959367584918255 \tabularnewline
23 & 0.0138374800061041 & 0.0276749600122081 & 0.986162519993896 \tabularnewline
24 & 0.0153647089178795 & 0.0307294178357590 & 0.98463529108212 \tabularnewline
25 & 0.0139018442199219 & 0.0278036884398438 & 0.986098155780078 \tabularnewline
26 & 0.00843910902341185 & 0.0168782180468237 & 0.991560890976588 \tabularnewline
27 & 0.00325489615046637 & 0.00650979230093274 & 0.996745103849534 \tabularnewline
28 & 0.00176641421060536 & 0.00353282842121073 & 0.998233585789395 \tabularnewline
29 & 0.000575107586278198 & 0.00115021517255640 & 0.999424892413722 \tabularnewline
30 & 0.000366114533177452 & 0.000732229066354905 & 0.999633885466823 \tabularnewline
31 & 0.000449908718232617 & 0.000899817436465234 & 0.999550091281767 \tabularnewline
32 & 0.000124382381039456 & 0.000248764762078912 & 0.99987561761896 \tabularnewline
33 & 0.000193358145939456 & 0.000386716291878912 & 0.99980664185406 \tabularnewline
34 & 0.0284704132159483 & 0.0569408264318965 & 0.971529586784052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&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]0.113092285054002[/C][C]0.226184570108004[/C][C]0.886907714945998[/C][/ROW]
[ROW][C]22[/C][C]0.0406324150817447[/C][C]0.0812648301634895[/C][C]0.959367584918255[/C][/ROW]
[ROW][C]23[/C][C]0.0138374800061041[/C][C]0.0276749600122081[/C][C]0.986162519993896[/C][/ROW]
[ROW][C]24[/C][C]0.0153647089178795[/C][C]0.0307294178357590[/C][C]0.98463529108212[/C][/ROW]
[ROW][C]25[/C][C]0.0139018442199219[/C][C]0.0278036884398438[/C][C]0.986098155780078[/C][/ROW]
[ROW][C]26[/C][C]0.00843910902341185[/C][C]0.0168782180468237[/C][C]0.991560890976588[/C][/ROW]
[ROW][C]27[/C][C]0.00325489615046637[/C][C]0.00650979230093274[/C][C]0.996745103849534[/C][/ROW]
[ROW][C]28[/C][C]0.00176641421060536[/C][C]0.00353282842121073[/C][C]0.998233585789395[/C][/ROW]
[ROW][C]29[/C][C]0.000575107586278198[/C][C]0.00115021517255640[/C][C]0.999424892413722[/C][/ROW]
[ROW][C]30[/C][C]0.000366114533177452[/C][C]0.000732229066354905[/C][C]0.999633885466823[/C][/ROW]
[ROW][C]31[/C][C]0.000449908718232617[/C][C]0.000899817436465234[/C][C]0.999550091281767[/C][/ROW]
[ROW][C]32[/C][C]0.000124382381039456[/C][C]0.000248764762078912[/C][C]0.99987561761896[/C][/ROW]
[ROW][C]33[/C][C]0.000193358145939456[/C][C]0.000386716291878912[/C][C]0.99980664185406[/C][/ROW]
[ROW][C]34[/C][C]0.0284704132159483[/C][C]0.0569408264318965[/C][C]0.971529586784052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.113092285054002	0.226184570108004	0.886907714945998
22	0.0406324150817447	0.0812648301634895	0.959367584918255
23	0.0138374800061041	0.0276749600122081	0.986162519993896
24	0.0153647089178795	0.0307294178357590	0.98463529108212
25	0.0139018442199219	0.0278036884398438	0.986098155780078
26	0.00843910902341185	0.0168782180468237	0.991560890976588
27	0.00325489615046637	0.00650979230093274	0.996745103849534
28	0.00176641421060536	0.00353282842121073	0.998233585789395
29	0.000575107586278198	0.00115021517255640	0.999424892413722
30	0.000366114533177452	0.000732229066354905	0.999633885466823
31	0.000449908718232617	0.000899817436465234	0.999550091281767
32	0.000124382381039456	0.000248764762078912	0.99987561761896
33	0.000193358145939456	0.000386716291878912	0.99980664185406
34	0.0284704132159483	0.0569408264318965	0.971529586784052

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.5	NOK
5% type I error level	11	0.785714285714286	NOK
10% type I error level	13	0.928571428571429	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 7 & 0.5 & NOK \tabularnewline
5% type I error level & 11 & 0.785714285714286 & NOK \tabularnewline
10% type I error level & 13 & 0.928571428571429 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113766&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]7[/C][C]0.5[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]11[/C][C]0.785714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.928571428571429[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113766&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113766&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.5	NOK
5% type I error level	11	0.785714285714286	NOK
10% type I error level	13	0.928571428571429	NOK

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

Figure 10

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code