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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 computationFri, 17 Dec 2010 11:54:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/17/t1292586755k81cd0luv4lko98.htm/, Retrieved Wed, 19 Nov 2025 23:01:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111399, Retrieved Wed, 19 Nov 2025 23:01:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact470

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
-  M D  [Classical Decomposition] [] [2010-11-26 09:51:05] [7789b9488494790f41ddb7f073cada1b]
- RMPD      [Multiple Regression] [] [2010-12-17 11:54:43] [c05c5ae4ce2db58f67fd725429d7f25c] [Current]
-   PD        [Multiple Regression] [] [2010-12-19 13:30:08] [7789b9488494790f41ddb7f073cada1b]
-               [Multiple Regression] [] [2010-12-20 20:46:17] [504b6ff240ec7a3fcbc007044ae7a0bb]
-   PD        [Multiple Regression] [] [2010-12-19 13:42:28] [7789b9488494790f41ddb7f073cada1b]
-               [Multiple Regression] [] [2010-12-20 22:10:46] [504b6ff240ec7a3fcbc007044ae7a0bb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.82	107.34	93.63	99.85	101.76
101.68	107.34	93.63	99.91	102.37
101.68	107.34	93.63	99.87	102.38
102.45	107.34	96.13	99.86	102.86
102.45	107.34	96.13	100.10	102.87
102.45	107.34	96.13	100.10	102.92
102.45	107.34	96.13	100.12	102.95
102.45	107.34	96.13	99.95	103.02
102.45	112.60	96.13	99.94	104.08
102.52	112.60	96.13	100.18	104.16
102.52	112.60	96.13	100.31	104.24
102.85	112.60	96.13	100.65	104.33
102.85	112.61	96.13	100.65	104.73
102.85	112.61	96.13	100.69	104.86
103.25	112.61	96.13	101.26	105.03
103.25	112.61	98.73	101.26	105.62
103.25	112.61	98.73	101.38	105.63
103.25	112.61	98.73	101.38	105.63
104.45	112.61	98.73	101.38	105.94
104.45	112.61	98.73	101.44	106.61
104.45	118.65	98.73	101.40	107.69
104.80	118.65	98.73	101.40	107.78
104.80	118.65	98.73	100.58	107.93
105.29	118.65	98.73	100.58	108.48
105.29	114.29	98.73	100.58	108.14
105.29	114.29	98.73	100.59	108.48
105.29	114.29	98.73	100.81	108.48
106.04	114.29	101.67	100.75	108.89
105.94	114.29	101.67	100.75	108.93
105.94	114.29	101.67	100.96	109.21
105.94	114.29	101.67	101.31	109.47
106.28	114.29	101.67	101.64	109.80
106.48	123.33	101.67	101.46	111.73
107.19	123.33	101.67	101.73	111.85
108.14	123.33	101.67	101.73	112.12
108.22	123.33	101.67	101.64	112.15
108.22	123.33	101.67	101.77	112.17
108.61	123.33	101.67	101.74	112.67
108.61	123.33	101.67	101.89	112.80
108.61	123.33	107.94	101.89	113.44
108.61	123.33	107.94	101.93	113.53
109.06	123.33	107.94	101.93	114.53
109.06	123.33	107.94	102.32	114.51
112.93	123.33	107.94	102.41	115.05
115.84	129.03	107.94	103.58	116.67
118.57	128.76	107.94	104.12	117.07
118.57	128.76	107.94	104.10	116.92
118.86	128.76	107.94	104.15	117.00
118.98	128.76	107.94	104.15	117.02
119.27	128.76	107.94	104.16	117.35
119.39	128.76	107.94	102.94	117.36
119.49	128.76	110.30	103.07	117.82
119.59	128.76	110.30	103.04	117.88
120.12	128.76	110.30	103.06	118.24
120.14	128.76	110.30	103.05	118.50
120.14	128.76	110.30	102.95	118.80
120.14	132.63	110.30	102.95	119.76
120.14	132.63	110.30	103.05	120.09

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&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]9 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=111399&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
vrijetijdsbesteding[t] = + 35.2689359098687 + 0.0686290527084394bios[t] + 0.349632828334539schouwburg[t] + 0.533715451658278eedagsacttractie[t] -0.279710824870231huurDVD[t] + 0.316008799723908M1[t] + 0.695631656879148M2[t] + 0.734592742605774M3[t] -0.547693856402015M4[t] -0.484995255361616M5[t] -0.147579851748444M6[t] + 0.045631283121235M7[t] + 0.381593475385275M8[t] -0.370011739420981M9[t] -0.13577970566168M10[t] -0.188061168684507M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
vrijetijdsbesteding[t] =  +  35.2689359098687 +  0.0686290527084394bios[t] +  0.349632828334539schouwburg[t] +  0.533715451658278eedagsacttractie[t] -0.279710824870231huurDVD[t] +  0.316008799723908M1[t] +  0.695631656879148M2[t] +  0.734592742605774M3[t] -0.547693856402015M4[t] -0.484995255361616M5[t] -0.147579851748444M6[t] +  0.045631283121235M7[t] +  0.381593475385275M8[t] -0.370011739420981M9[t] -0.13577970566168M10[t] -0.188061168684507M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]vrijetijdsbesteding[t] =  +  35.2689359098687 +  0.0686290527084394bios[t] +  0.349632828334539schouwburg[t] +  0.533715451658278eedagsacttractie[t] -0.279710824870231huurDVD[t] +  0.316008799723908M1[t] +  0.695631656879148M2[t] +  0.734592742605774M3[t] -0.547693856402015M4[t] -0.484995255361616M5[t] -0.147579851748444M6[t] +  0.045631283121235M7[t] +  0.381593475385275M8[t] -0.370011739420981M9[t] -0.13577970566168M10[t] -0.188061168684507M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&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
vrijetijdsbesteding[t] = + 35.2689359098687 + 0.0686290527084394bios[t] + 0.349632828334539schouwburg[t] + 0.533715451658278eedagsacttractie[t] -0.279710824870231huurDVD[t] + 0.316008799723908M1[t] + 0.695631656879148M2[t] + 0.734592742605774M3[t] -0.547693856402015M4[t] -0.484995255361616M5[t] -0.147579851748444M6[t] + 0.045631283121235M7[t] + 0.381593475385275M8[t] -0.370011739420981M9[t] -0.13577970566168M10[t] -0.188061168684507M11[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)35.268935909868714.4066882.44810.0186210.00931
bios0.06862905270843940.0409391.67640.1010980.050549
schouwburg0.3496328283345390.0565536.182400
eedagsacttractie0.5337154516582780.0915555.82951e-060
huurDVD-0.2797108248702310.174489-1.6030.1164230.058211
M10.3160087997239080.3979690.79410.4316280.215814
M20.6956316568791480.398161.74710.0879260.043963
M30.7345927426057740.3983711.8440.0722470.036123
M4-0.5476938564020150.531577-1.03030.3087570.154379
M5-0.4849952553616160.531154-0.91310.3664040.183202
M6-0.1475798517484440.52955-0.27870.7818510.390925
M70.0456312831212350.5279950.08640.931540.46577
M80.3815934753852750.5229410.72970.469620.23481
M9-0.3700117394209810.393307-0.94080.3522020.176101
M10-0.135779705661680.390147-0.3480.7295620.364781
M11-0.1880611686845070.410028-0.45870.6488470.324423

\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) & 35.2689359098687 & 14.406688 & 2.4481 & 0.018621 & 0.00931 \tabularnewline
bios & 0.0686290527084394 & 0.040939 & 1.6764 & 0.101098 & 0.050549 \tabularnewline
schouwburg & 0.349632828334539 & 0.056553 & 6.1824 & 0 & 0 \tabularnewline
eedagsacttractie & 0.533715451658278 & 0.091555 & 5.8295 & 1e-06 & 0 \tabularnewline
huurDVD & -0.279710824870231 & 0.174489 & -1.603 & 0.116423 & 0.058211 \tabularnewline
M1 & 0.316008799723908 & 0.397969 & 0.7941 & 0.431628 & 0.215814 \tabularnewline
M2 & 0.695631656879148 & 0.39816 & 1.7471 & 0.087926 & 0.043963 \tabularnewline
M3 & 0.734592742605774 & 0.398371 & 1.844 & 0.072247 & 0.036123 \tabularnewline
M4 & -0.547693856402015 & 0.531577 & -1.0303 & 0.308757 & 0.154379 \tabularnewline
M5 & -0.484995255361616 & 0.531154 & -0.9131 & 0.366404 & 0.183202 \tabularnewline
M6 & -0.147579851748444 & 0.52955 & -0.2787 & 0.781851 & 0.390925 \tabularnewline
M7 & 0.045631283121235 & 0.527995 & 0.0864 & 0.93154 & 0.46577 \tabularnewline
M8 & 0.381593475385275 & 0.522941 & 0.7297 & 0.46962 & 0.23481 \tabularnewline
M9 & -0.370011739420981 & 0.393307 & -0.9408 & 0.352202 & 0.176101 \tabularnewline
M10 & -0.13577970566168 & 0.390147 & -0.348 & 0.729562 & 0.364781 \tabularnewline
M11 & -0.188061168684507 & 0.410028 & -0.4587 & 0.648847 & 0.324423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&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]35.2689359098687[/C][C]14.406688[/C][C]2.4481[/C][C]0.018621[/C][C]0.00931[/C][/ROW]
[ROW][C]bios[/C][C]0.0686290527084394[/C][C]0.040939[/C][C]1.6764[/C][C]0.101098[/C][C]0.050549[/C][/ROW]
[ROW][C]schouwburg[/C][C]0.349632828334539[/C][C]0.056553[/C][C]6.1824[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]eedagsacttractie[/C][C]0.533715451658278[/C][C]0.091555[/C][C]5.8295[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]huurDVD[/C][C]-0.279710824870231[/C][C]0.174489[/C][C]-1.603[/C][C]0.116423[/C][C]0.058211[/C][/ROW]
[ROW][C]M1[/C][C]0.316008799723908[/C][C]0.397969[/C][C]0.7941[/C][C]0.431628[/C][C]0.215814[/C][/ROW]
[ROW][C]M2[/C][C]0.695631656879148[/C][C]0.39816[/C][C]1.7471[/C][C]0.087926[/C][C]0.043963[/C][/ROW]
[ROW][C]M3[/C][C]0.734592742605774[/C][C]0.398371[/C][C]1.844[/C][C]0.072247[/C][C]0.036123[/C][/ROW]
[ROW][C]M4[/C][C]-0.547693856402015[/C][C]0.531577[/C][C]-1.0303[/C][C]0.308757[/C][C]0.154379[/C][/ROW]
[ROW][C]M5[/C][C]-0.484995255361616[/C][C]0.531154[/C][C]-0.9131[/C][C]0.366404[/C][C]0.183202[/C][/ROW]
[ROW][C]M6[/C][C]-0.147579851748444[/C][C]0.52955[/C][C]-0.2787[/C][C]0.781851[/C][C]0.390925[/C][/ROW]
[ROW][C]M7[/C][C]0.045631283121235[/C][C]0.527995[/C][C]0.0864[/C][C]0.93154[/C][C]0.46577[/C][/ROW]
[ROW][C]M8[/C][C]0.381593475385275[/C][C]0.522941[/C][C]0.7297[/C][C]0.46962[/C][C]0.23481[/C][/ROW]
[ROW][C]M9[/C][C]-0.370011739420981[/C][C]0.393307[/C][C]-0.9408[/C][C]0.352202[/C][C]0.176101[/C][/ROW]
[ROW][C]M10[/C][C]-0.13577970566168[/C][C]0.390147[/C][C]-0.348[/C][C]0.729562[/C][C]0.364781[/C][/ROW]
[ROW][C]M11[/C][C]-0.188061168684507[/C][C]0.410028[/C][C]-0.4587[/C][C]0.648847[/C][C]0.324423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&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)35.268935909868714.4066882.44810.0186210.00931
bios0.06862905270843940.0409391.67640.1010980.050549
schouwburg0.3496328283345390.0565536.182400
eedagsacttractie0.5337154516582780.0915555.82951e-060
huurDVD-0.2797108248702310.174489-1.6030.1164230.058211
M10.3160087997239080.3979690.79410.4316280.215814
M20.6956316568791480.398161.74710.0879260.043963
M30.7345927426057740.3983711.8440.0722470.036123
M4-0.5476938564020150.531577-1.03030.3087570.154379
M5-0.4849952553616160.531154-0.91310.3664040.183202
M6-0.1475798517484440.52955-0.27870.7818510.390925
M70.0456312831212350.5279950.08640.931540.46577
M80.3815934753852750.5229410.72970.469620.23481
M9-0.3700117394209810.393307-0.94080.3522020.176101
M10-0.135779705661680.390147-0.3480.7295620.364781
M11-0.1880611686845070.410028-0.45870.6488470.324423






Multiple Linear Regression - Regression Statistics
Multiple R0.99601068857855
R-squared0.99203729176272
Adjusted R-squared0.989193467392262
F-TEST (value)348.839155493686
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.579534663866987
Sum Squared Residuals14.1061379181837

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99601068857855 \tabularnewline
R-squared & 0.99203729176272 \tabularnewline
Adjusted R-squared & 0.989193467392262 \tabularnewline
F-TEST (value) & 348.839155493686 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.579534663866987 \tabularnewline
Sum Squared Residuals & 14.1061379181837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99601068857855[/C][/ROW]
[ROW][C]R-squared[/C][C]0.99203729176272[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.989193467392262[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]348.839155493686[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.579534663866987[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]14.1061379181837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.99601068857855
R-squared0.99203729176272
Adjusted R-squared0.989193467392262
F-TEST (value)348.839155493686
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.579534663866987
Sum Squared Residuals14.1061379181837






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1101.76102.144994525268-0.384994525267722
2102.37102.498226665551-0.128226665551124
3102.38102.548376184273-0.168376184272574
4102.86102.6560196932450.203980306755325
5102.87102.6515876963160.218412303683786
6102.92102.989003099929-0.0690030999293898
7102.95103.176620018302-0.22662001830166
8103.02103.560133050794-0.540133050793647
9104.08104.650393621276-0.570393621275765
10104.16104.822299090756-0.662299090755801
11104.24104.733655220500-0.493655220499847
12104.33104.849262296122-0.519262296122256
13104.73105.168767424130-0.438767424129506
14104.86105.53720184829-0.677201848289943
15105.03105.444179384924-0.414179384923909
16105.62105.5495529602280.0704470397723576
17105.63105.5786862622840.0513137377163745
18105.63105.916101665897-0.286101665896798
19105.94106.191667664017-0.251667664016602
20106.61106.5108472067880.0991527932115737
21107.69107.882212708118-0.192212708117599
22107.78108.140464910325-0.36046491032485
23107.93108.317546323696-0.387546323695609
24108.48108.539235728207-0.0592357282072548
25108.14107.3308453963930.809154603607425
26108.48107.7076711452990.772328854700892
27108.48107.6850958495540.794904150445718
28108.89108.0401871174450.849812882554624
29108.93108.0960228132150.833977186785076
30109.21108.3746989436050.835301056394638
31109.47108.4700112897700.999988710229548
32109.8108.7370027877481.06299721225181
33111.73111.2101521001040.51984789989551
34111.85111.4175888385720.432411161428172
35112.12111.4305049756220.689495024377992
36112.15111.6492304427620.500769557238488
37112.17111.9288768352520.241123164747705
38112.67112.343656347710.326343652290066
39112.8112.3406608097060.459339190293973
40113.44114.404770092596-0.964770092595634
41113.53114.456280260641-0.92628026064122
42114.53114.824578737973-0.29457873797319
43114.51114.908702651143-0.398702651143479
44115.05115.485085303151-0.435085303150866
45116.67116.5988360881350.0711639118651307
46117.07116.7749807267080.295019273292036
47116.92116.7282934801830.191706519817464
48117116.9222715329090.0777284670910233
49117.02117.246515818958-0.226515818957902
50117.35117.64324399315-0.293243993149891
51117.36118.031687771543-0.671687771543208
52117.82117.979470136487-0.159470136486672
53117.88118.057422967544-0.177422967544017
54118.24118.425617552595-0.18561755259526
55118.5118.622998376768-0.122998376767807
56118.8118.986931651519-0.186931651518871
57119.76119.5884054823670.171594517632724
58120.09119.7946664336400.295333566360443

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.76 & 102.144994525268 & -0.384994525267722 \tabularnewline
2 & 102.37 & 102.498226665551 & -0.128226665551124 \tabularnewline
3 & 102.38 & 102.548376184273 & -0.168376184272574 \tabularnewline
4 & 102.86 & 102.656019693245 & 0.203980306755325 \tabularnewline
5 & 102.87 & 102.651587696316 & 0.218412303683786 \tabularnewline
6 & 102.92 & 102.989003099929 & -0.0690030999293898 \tabularnewline
7 & 102.95 & 103.176620018302 & -0.22662001830166 \tabularnewline
8 & 103.02 & 103.560133050794 & -0.540133050793647 \tabularnewline
9 & 104.08 & 104.650393621276 & -0.570393621275765 \tabularnewline
10 & 104.16 & 104.822299090756 & -0.662299090755801 \tabularnewline
11 & 104.24 & 104.733655220500 & -0.493655220499847 \tabularnewline
12 & 104.33 & 104.849262296122 & -0.519262296122256 \tabularnewline
13 & 104.73 & 105.168767424130 & -0.438767424129506 \tabularnewline
14 & 104.86 & 105.53720184829 & -0.677201848289943 \tabularnewline
15 & 105.03 & 105.444179384924 & -0.414179384923909 \tabularnewline
16 & 105.62 & 105.549552960228 & 0.0704470397723576 \tabularnewline
17 & 105.63 & 105.578686262284 & 0.0513137377163745 \tabularnewline
18 & 105.63 & 105.916101665897 & -0.286101665896798 \tabularnewline
19 & 105.94 & 106.191667664017 & -0.251667664016602 \tabularnewline
20 & 106.61 & 106.510847206788 & 0.0991527932115737 \tabularnewline
21 & 107.69 & 107.882212708118 & -0.192212708117599 \tabularnewline
22 & 107.78 & 108.140464910325 & -0.36046491032485 \tabularnewline
23 & 107.93 & 108.317546323696 & -0.387546323695609 \tabularnewline
24 & 108.48 & 108.539235728207 & -0.0592357282072548 \tabularnewline
25 & 108.14 & 107.330845396393 & 0.809154603607425 \tabularnewline
26 & 108.48 & 107.707671145299 & 0.772328854700892 \tabularnewline
27 & 108.48 & 107.685095849554 & 0.794904150445718 \tabularnewline
28 & 108.89 & 108.040187117445 & 0.849812882554624 \tabularnewline
29 & 108.93 & 108.096022813215 & 0.833977186785076 \tabularnewline
30 & 109.21 & 108.374698943605 & 0.835301056394638 \tabularnewline
31 & 109.47 & 108.470011289770 & 0.999988710229548 \tabularnewline
32 & 109.8 & 108.737002787748 & 1.06299721225181 \tabularnewline
33 & 111.73 & 111.210152100104 & 0.51984789989551 \tabularnewline
34 & 111.85 & 111.417588838572 & 0.432411161428172 \tabularnewline
35 & 112.12 & 111.430504975622 & 0.689495024377992 \tabularnewline
36 & 112.15 & 111.649230442762 & 0.500769557238488 \tabularnewline
37 & 112.17 & 111.928876835252 & 0.241123164747705 \tabularnewline
38 & 112.67 & 112.34365634771 & 0.326343652290066 \tabularnewline
39 & 112.8 & 112.340660809706 & 0.459339190293973 \tabularnewline
40 & 113.44 & 114.404770092596 & -0.964770092595634 \tabularnewline
41 & 113.53 & 114.456280260641 & -0.92628026064122 \tabularnewline
42 & 114.53 & 114.824578737973 & -0.29457873797319 \tabularnewline
43 & 114.51 & 114.908702651143 & -0.398702651143479 \tabularnewline
44 & 115.05 & 115.485085303151 & -0.435085303150866 \tabularnewline
45 & 116.67 & 116.598836088135 & 0.0711639118651307 \tabularnewline
46 & 117.07 & 116.774980726708 & 0.295019273292036 \tabularnewline
47 & 116.92 & 116.728293480183 & 0.191706519817464 \tabularnewline
48 & 117 & 116.922271532909 & 0.0777284670910233 \tabularnewline
49 & 117.02 & 117.246515818958 & -0.226515818957902 \tabularnewline
50 & 117.35 & 117.64324399315 & -0.293243993149891 \tabularnewline
51 & 117.36 & 118.031687771543 & -0.671687771543208 \tabularnewline
52 & 117.82 & 117.979470136487 & -0.159470136486672 \tabularnewline
53 & 117.88 & 118.057422967544 & -0.177422967544017 \tabularnewline
54 & 118.24 & 118.425617552595 & -0.18561755259526 \tabularnewline
55 & 118.5 & 118.622998376768 & -0.122998376767807 \tabularnewline
56 & 118.8 & 118.986931651519 & -0.186931651518871 \tabularnewline
57 & 119.76 & 119.588405482367 & 0.171594517632724 \tabularnewline
58 & 120.09 & 119.794666433640 & 0.295333566360443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&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]101.76[/C][C]102.144994525268[/C][C]-0.384994525267722[/C][/ROW]
[ROW][C]2[/C][C]102.37[/C][C]102.498226665551[/C][C]-0.128226665551124[/C][/ROW]
[ROW][C]3[/C][C]102.38[/C][C]102.548376184273[/C][C]-0.168376184272574[/C][/ROW]
[ROW][C]4[/C][C]102.86[/C][C]102.656019693245[/C][C]0.203980306755325[/C][/ROW]
[ROW][C]5[/C][C]102.87[/C][C]102.651587696316[/C][C]0.218412303683786[/C][/ROW]
[ROW][C]6[/C][C]102.92[/C][C]102.989003099929[/C][C]-0.0690030999293898[/C][/ROW]
[ROW][C]7[/C][C]102.95[/C][C]103.176620018302[/C][C]-0.22662001830166[/C][/ROW]
[ROW][C]8[/C][C]103.02[/C][C]103.560133050794[/C][C]-0.540133050793647[/C][/ROW]
[ROW][C]9[/C][C]104.08[/C][C]104.650393621276[/C][C]-0.570393621275765[/C][/ROW]
[ROW][C]10[/C][C]104.16[/C][C]104.822299090756[/C][C]-0.662299090755801[/C][/ROW]
[ROW][C]11[/C][C]104.24[/C][C]104.733655220500[/C][C]-0.493655220499847[/C][/ROW]
[ROW][C]12[/C][C]104.33[/C][C]104.849262296122[/C][C]-0.519262296122256[/C][/ROW]
[ROW][C]13[/C][C]104.73[/C][C]105.168767424130[/C][C]-0.438767424129506[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]105.53720184829[/C][C]-0.677201848289943[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]105.444179384924[/C][C]-0.414179384923909[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.549552960228[/C][C]0.0704470397723576[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.578686262284[/C][C]0.0513137377163745[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]105.916101665897[/C][C]-0.286101665896798[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.191667664017[/C][C]-0.251667664016602[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.510847206788[/C][C]0.0991527932115737[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]107.882212708118[/C][C]-0.192212708117599[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]108.140464910325[/C][C]-0.36046491032485[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]108.317546323696[/C][C]-0.387546323695609[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.539235728207[/C][C]-0.0592357282072548[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]107.330845396393[/C][C]0.809154603607425[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]107.707671145299[/C][C]0.772328854700892[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]107.685095849554[/C][C]0.794904150445718[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]108.040187117445[/C][C]0.849812882554624[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]108.096022813215[/C][C]0.833977186785076[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]108.374698943605[/C][C]0.835301056394638[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]108.470011289770[/C][C]0.999988710229548[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]108.737002787748[/C][C]1.06299721225181[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]111.210152100104[/C][C]0.51984789989551[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]111.417588838572[/C][C]0.432411161428172[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]111.430504975622[/C][C]0.689495024377992[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]111.649230442762[/C][C]0.500769557238488[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]111.928876835252[/C][C]0.241123164747705[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]112.34365634771[/C][C]0.326343652290066[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]112.340660809706[/C][C]0.459339190293973[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]114.404770092596[/C][C]-0.964770092595634[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]114.456280260641[/C][C]-0.92628026064122[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]114.824578737973[/C][C]-0.29457873797319[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.908702651143[/C][C]-0.398702651143479[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]115.485085303151[/C][C]-0.435085303150866[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]116.598836088135[/C][C]0.0711639118651307[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.774980726708[/C][C]0.295019273292036[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]116.728293480183[/C][C]0.191706519817464[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]116.922271532909[/C][C]0.0777284670910233[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.246515818958[/C][C]-0.226515818957902[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]117.64324399315[/C][C]-0.293243993149891[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]118.031687771543[/C][C]-0.671687771543208[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]117.979470136487[/C][C]-0.159470136486672[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]118.057422967544[/C][C]-0.177422967544017[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]118.425617552595[/C][C]-0.18561755259526[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.622998376768[/C][C]-0.122998376767807[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.986931651519[/C][C]-0.186931651518871[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.588405482367[/C][C]0.171594517632724[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]119.794666433640[/C][C]0.295333566360443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&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
1101.76102.144994525268-0.384994525267722
2102.37102.498226665551-0.128226665551124
3102.38102.548376184273-0.168376184272574
4102.86102.6560196932450.203980306755325
5102.87102.6515876963160.218412303683786
6102.92102.989003099929-0.0690030999293898
7102.95103.176620018302-0.22662001830166
8103.02103.560133050794-0.540133050793647
9104.08104.650393621276-0.570393621275765
10104.16104.822299090756-0.662299090755801
11104.24104.733655220500-0.493655220499847
12104.33104.849262296122-0.519262296122256
13104.73105.168767424130-0.438767424129506
14104.86105.53720184829-0.677201848289943
15105.03105.444179384924-0.414179384923909
16105.62105.5495529602280.0704470397723576
17105.63105.5786862622840.0513137377163745
18105.63105.916101665897-0.286101665896798
19105.94106.191667664017-0.251667664016602
20106.61106.5108472067880.0991527932115737
21107.69107.882212708118-0.192212708117599
22107.78108.140464910325-0.36046491032485
23107.93108.317546323696-0.387546323695609
24108.48108.539235728207-0.0592357282072548
25108.14107.3308453963930.809154603607425
26108.48107.7076711452990.772328854700892
27108.48107.6850958495540.794904150445718
28108.89108.0401871174450.849812882554624
29108.93108.0960228132150.833977186785076
30109.21108.3746989436050.835301056394638
31109.47108.4700112897700.999988710229548
32109.8108.7370027877481.06299721225181
33111.73111.2101521001040.51984789989551
34111.85111.4175888385720.432411161428172
35112.12111.4305049756220.689495024377992
36112.15111.6492304427620.500769557238488
37112.17111.9288768352520.241123164747705
38112.67112.343656347710.326343652290066
39112.8112.3406608097060.459339190293973
40113.44114.404770092596-0.964770092595634
41113.53114.456280260641-0.92628026064122
42114.53114.824578737973-0.29457873797319
43114.51114.908702651143-0.398702651143479
44115.05115.485085303151-0.435085303150866
45116.67116.5988360881350.0711639118651307
46117.07116.7749807267080.295019273292036
47116.92116.7282934801830.191706519817464
48117116.9222715329090.0777284670910233
49117.02117.246515818958-0.226515818957902
50117.35117.64324399315-0.293243993149891
51117.36118.031687771543-0.671687771543208
52117.82117.979470136487-0.159470136486672
53117.88118.057422967544-0.177422967544017
54118.24118.425617552595-0.18561755259526
55118.5118.622998376768-0.122998376767807
56118.8118.986931651519-0.186931651518871
57119.76119.5884054823670.171594517632724
58120.09119.7946664336400.295333566360443






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.03333043285230040.06666086570460090.9666695671477
200.05653666885188760.1130733377037750.943463331148112
210.04582660690109750.0916532138021950.954173393098902
220.05204649738966080.1040929947793220.94795350261034
230.1036224724712120.2072449449424240.896377527528788
240.3024592052998810.6049184105997620.697540794700119
250.2393742275853570.4787484551707140.760625772414643
260.1703782875745100.3407565751490190.82962171242549
270.1058090594157430.2116181188314870.894190940584257
280.2074392724723460.4148785449446930.792560727527654
290.1896997875749260.3793995751498510.810300212425074
300.1279676887222010.2559353774444020.8720323112778
310.1452945841214820.2905891682429640.854705415878518
320.6095010145503460.7809979708993090.390498985449654
330.5945994091793920.8108011816412160.405400590820608
340.6897104104122570.6205791791754850.310289589587743
350.5780614333070550.843877133385890.421938566692945
360.4871095842885050.974219168577010.512890415711495
370.4631164767223740.9262329534447480.536883523277626
380.4268082217798240.8536164435596480.573191778220176
390.4083668546327990.8167337092655970.591633145367201

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.0333304328523004 & 0.0666608657046009 & 0.9666695671477 \tabularnewline
20 & 0.0565366688518876 & 0.113073337703775 & 0.943463331148112 \tabularnewline
21 & 0.0458266069010975 & 0.091653213802195 & 0.954173393098902 \tabularnewline
22 & 0.0520464973896608 & 0.104092994779322 & 0.94795350261034 \tabularnewline
23 & 0.103622472471212 & 0.207244944942424 & 0.896377527528788 \tabularnewline
24 & 0.302459205299881 & 0.604918410599762 & 0.697540794700119 \tabularnewline
25 & 0.239374227585357 & 0.478748455170714 & 0.760625772414643 \tabularnewline
26 & 0.170378287574510 & 0.340756575149019 & 0.82962171242549 \tabularnewline
27 & 0.105809059415743 & 0.211618118831487 & 0.894190940584257 \tabularnewline
28 & 0.207439272472346 & 0.414878544944693 & 0.792560727527654 \tabularnewline
29 & 0.189699787574926 & 0.379399575149851 & 0.810300212425074 \tabularnewline
30 & 0.127967688722201 & 0.255935377444402 & 0.8720323112778 \tabularnewline
31 & 0.145294584121482 & 0.290589168242964 & 0.854705415878518 \tabularnewline
32 & 0.609501014550346 & 0.780997970899309 & 0.390498985449654 \tabularnewline
33 & 0.594599409179392 & 0.810801181641216 & 0.405400590820608 \tabularnewline
34 & 0.689710410412257 & 0.620579179175485 & 0.310289589587743 \tabularnewline
35 & 0.578061433307055 & 0.84387713338589 & 0.421938566692945 \tabularnewline
36 & 0.487109584288505 & 0.97421916857701 & 0.512890415711495 \tabularnewline
37 & 0.463116476722374 & 0.926232953444748 & 0.536883523277626 \tabularnewline
38 & 0.426808221779824 & 0.853616443559648 & 0.573191778220176 \tabularnewline
39 & 0.408366854632799 & 0.816733709265597 & 0.591633145367201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&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]19[/C][C]0.0333304328523004[/C][C]0.0666608657046009[/C][C]0.9666695671477[/C][/ROW]
[ROW][C]20[/C][C]0.0565366688518876[/C][C]0.113073337703775[/C][C]0.943463331148112[/C][/ROW]
[ROW][C]21[/C][C]0.0458266069010975[/C][C]0.091653213802195[/C][C]0.954173393098902[/C][/ROW]
[ROW][C]22[/C][C]0.0520464973896608[/C][C]0.104092994779322[/C][C]0.94795350261034[/C][/ROW]
[ROW][C]23[/C][C]0.103622472471212[/C][C]0.207244944942424[/C][C]0.896377527528788[/C][/ROW]
[ROW][C]24[/C][C]0.302459205299881[/C][C]0.604918410599762[/C][C]0.697540794700119[/C][/ROW]
[ROW][C]25[/C][C]0.239374227585357[/C][C]0.478748455170714[/C][C]0.760625772414643[/C][/ROW]
[ROW][C]26[/C][C]0.170378287574510[/C][C]0.340756575149019[/C][C]0.82962171242549[/C][/ROW]
[ROW][C]27[/C][C]0.105809059415743[/C][C]0.211618118831487[/C][C]0.894190940584257[/C][/ROW]
[ROW][C]28[/C][C]0.207439272472346[/C][C]0.414878544944693[/C][C]0.792560727527654[/C][/ROW]
[ROW][C]29[/C][C]0.189699787574926[/C][C]0.379399575149851[/C][C]0.810300212425074[/C][/ROW]
[ROW][C]30[/C][C]0.127967688722201[/C][C]0.255935377444402[/C][C]0.8720323112778[/C][/ROW]
[ROW][C]31[/C][C]0.145294584121482[/C][C]0.290589168242964[/C][C]0.854705415878518[/C][/ROW]
[ROW][C]32[/C][C]0.609501014550346[/C][C]0.780997970899309[/C][C]0.390498985449654[/C][/ROW]
[ROW][C]33[/C][C]0.594599409179392[/C][C]0.810801181641216[/C][C]0.405400590820608[/C][/ROW]
[ROW][C]34[/C][C]0.689710410412257[/C][C]0.620579179175485[/C][C]0.310289589587743[/C][/ROW]
[ROW][C]35[/C][C]0.578061433307055[/C][C]0.84387713338589[/C][C]0.421938566692945[/C][/ROW]
[ROW][C]36[/C][C]0.487109584288505[/C][C]0.97421916857701[/C][C]0.512890415711495[/C][/ROW]
[ROW][C]37[/C][C]0.463116476722374[/C][C]0.926232953444748[/C][C]0.536883523277626[/C][/ROW]
[ROW][C]38[/C][C]0.426808221779824[/C][C]0.853616443559648[/C][C]0.573191778220176[/C][/ROW]
[ROW][C]39[/C][C]0.408366854632799[/C][C]0.816733709265597[/C][C]0.591633145367201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&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
190.03333043285230040.06666086570460090.9666695671477
200.05653666885188760.1130733377037750.943463331148112
210.04582660690109750.0916532138021950.954173393098902
220.05204649738966080.1040929947793220.94795350261034
230.1036224724712120.2072449449424240.896377527528788
240.3024592052998810.6049184105997620.697540794700119
250.2393742275853570.4787484551707140.760625772414643
260.1703782875745100.3407565751490190.82962171242549
270.1058090594157430.2116181188314870.894190940584257
280.2074392724723460.4148785449446930.792560727527654
290.1896997875749260.3793995751498510.810300212425074
300.1279676887222010.2559353774444020.8720323112778
310.1452945841214820.2905891682429640.854705415878518
320.6095010145503460.7809979708993090.390498985449654
330.5945994091793920.8108011816412160.405400590820608
340.6897104104122570.6205791791754850.310289589587743
350.5780614333070550.843877133385890.421938566692945
360.4871095842885050.974219168577010.512890415711495
370.4631164767223740.9262329534447480.536883523277626
380.4268082217798240.8536164435596480.573191778220176
390.4083668546327990.8167337092655970.591633145367201






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0952380952380952OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 2 & 0.0952380952380952 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111399&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.0952380952380952[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111399&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111399&T=6

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


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0952380952380952OK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;
Parameters (R input):
par1 = 5 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}