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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 computationWed, 18 Nov 2009 10:51:43 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/18/t1258566820axb2jbv1tw1fzdg.htm/, Retrieved Fri, 05 Dec 2025 06:14:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57555, Retrieved Fri, 05 Dec 2025 06:14:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact547

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [] [2009-11-18 17:51:43] [7dd0431c761b876151627bfbf92230c8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.5	7.2	1.5	1.6	1.8	1.6
1.3	7.4	1.5	1.5	1.6	1.8
1.4	8.8	1.3	1.5	1.5	1.6
1.4	9.3	1.4	1.3	1.5	1.5
1.3	9.3	1.4	1.4	1.3	1.5
1.3	8.7	1.3	1.4	1.4	1.3
1.2	8.2	1.3	1.3	1.4	1.4
1.1	8.3	1.2	1.3	1.3	1.4
1.4	8.5	1.1	1.2	1.3	1.3
1.2	8.6	1.4	1.1	1.2	1.3
1.5	8.5	1.2	1.4	1.1	1.2
1.1	8.2	1.5	1.2	1.4	1.1
1.3	8.1	1.1	1.5	1.2	1.4
1.5	7.9	1.3	1.1	1.5	1.2
1.1	8.6	1.5	1.3	1.1	1.5
1.4	8.7	1.1	1.5	1.3	1.1
1.3	8.7	1.4	1.1	1.5	1.3
1.5	8.5	1.3	1.4	1.1	1.5
1.6	8.4	1.5	1.3	1.4	1.1
1.7	8.5	1.6	1.5	1.3	1.4
1.1	8.7	1.7	1.6	1.5	1.3
1.6	8.7	1.1	1.7	1.6	1.5
1.3	8.6	1.6	1.1	1.7	1.6
1.7	8.5	1.3	1.6	1.1	1.7
1.6	8.3	1.7	1.3	1.6	1.1
1.7	8	1.6	1.7	1.3	1.6
1.9	8.2	1.7	1.6	1.7	1.3
1.8	8.1	1.9	1.7	1.6	1.7
1.9	8.1	1.8	1.9	1.7	1.6
1.6	8	1.9	1.8	1.9	1.7
1.5	7.9	1.6	1.9	1.8	1.9
1.6	7.9	1.5	1.6	1.9	1.8
1.6	8	1.6	1.5	1.6	1.9
1.7	8	1.6	1.6	1.5	1.6
2	7.9	1.7	1.6	1.6	1.5
2	8	2	1.7	1.6	1.6
1.9	7.7	2	2	1.7	1.6
1.7	7.2	1.9	2	2	1.7
1.8	7.5	1.7	1.9	2	2
1.9	7.3	1.8	1.7	1.9	2
1.7	7	1.9	1.8	1.7	1.9
2	7	1.7	1.9	1.8	1.7
2.1	7	2	1.7	1.9	1.8
2.4	7.2	2.1	2	1.7	1.9
2.5	7.3	2.4	2.1	2	1.7
2.5	7.1	2.5	2.4	2.1	2
2.6	6.8	2.5	2.5	2.4	2.1
2.2	6.4	2.6	2.5	2.5	2.4
2.5	6.1	2.2	2.6	2.5	2.5
2.8	6.5	2.5	2.2	2.6	2.5
2.8	7.7	2.8	2.5	2.2	2.6
2.9	7.9	2.8	2.8	2.5	2.2
3	7.5	2.9	2.8	2.8	2.5
3.1	6.9	3	2.9	2.8	2.8
2.9	6.6	3.1	3	2.9	2.8
2.7	6.9	2.9	3.1	3	2.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.184356379334972 + 0.00818805553395265X[t] + 0.379584054171523Y1[t] + 0.37974171622158Y2[t] -0.00603062858926295Y3[t] -0.034905189738258Y4[t] + 0.00996622977915651t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.184356379334972 +  0.00818805553395265X[t] +  0.379584054171523Y1[t] +  0.37974171622158Y2[t] -0.00603062858926295Y3[t] -0.034905189738258Y4[t] +  0.00996622977915651t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.184356379334972 +  0.00818805553395265X[t] +  0.379584054171523Y1[t] +  0.37974171622158Y2[t] -0.00603062858926295Y3[t] -0.034905189738258Y4[t] +  0.00996622977915651t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.184356379334972 + 0.00818805553395265X[t] + 0.379584054171523Y1[t] + 0.37974171622158Y2[t] -0.00603062858926295Y3[t] -0.034905189738258Y4[t] + 0.00996622977915651t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.1843563793349720.5933530.31070.7573440.378672
X0.008188055533952650.0605020.13530.89290.44645
Y10.3795840541715230.1477192.56960.0132740.006637
Y20.379741716221580.1555742.44090.0183110.009155
Y3-0.006030628589262950.159721-0.03780.9700350.485017
Y4-0.0349051897382580.145599-0.23970.8115360.405768
t0.009966229779156510.0036562.7260.0088660.004433

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.184356379334972 & 0.593353 & 0.3107 & 0.757344 & 0.378672 \tabularnewline
X & 0.00818805553395265 & 0.060502 & 0.1353 & 0.8929 & 0.44645 \tabularnewline
Y1 & 0.379584054171523 & 0.147719 & 2.5696 & 0.013274 & 0.006637 \tabularnewline
Y2 & 0.37974171622158 & 0.155574 & 2.4409 & 0.018311 & 0.009155 \tabularnewline
Y3 & -0.00603062858926295 & 0.159721 & -0.0378 & 0.970035 & 0.485017 \tabularnewline
Y4 & -0.034905189738258 & 0.145599 & -0.2397 & 0.811536 & 0.405768 \tabularnewline
t & 0.00996622977915651 & 0.003656 & 2.726 & 0.008866 & 0.004433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.184356379334972[/C][C]0.593353[/C][C]0.3107[/C][C]0.757344[/C][C]0.378672[/C][/ROW]
[ROW][C]X[/C][C]0.00818805553395265[/C][C]0.060502[/C][C]0.1353[/C][C]0.8929[/C][C]0.44645[/C][/ROW]
[ROW][C]Y1[/C][C]0.379584054171523[/C][C]0.147719[/C][C]2.5696[/C][C]0.013274[/C][C]0.006637[/C][/ROW]
[ROW][C]Y2[/C][C]0.37974171622158[/C][C]0.155574[/C][C]2.4409[/C][C]0.018311[/C][C]0.009155[/C][/ROW]
[ROW][C]Y3[/C][C]-0.00603062858926295[/C][C]0.159721[/C][C]-0.0378[/C][C]0.970035[/C][C]0.485017[/C][/ROW]
[ROW][C]Y4[/C][C]-0.034905189738258[/C][C]0.145599[/C][C]-0.2397[/C][C]0.811536[/C][C]0.405768[/C][/ROW]
[ROW][C]t[/C][C]0.00996622977915651[/C][C]0.003656[/C][C]2.726[/C][C]0.008866[/C][C]0.004433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.1843563793349720.5933530.31070.7573440.378672
X0.008188055533952650.0605020.13530.89290.44645
Y10.3795840541715230.1477192.56960.0132740.006637
Y20.379741716221580.1555742.44090.0183110.009155
Y3-0.006030628589262950.159721-0.03780.9700350.485017
Y4-0.0349051897382580.145599-0.23970.8115360.405768
t0.009966229779156510.0036562.7260.0088660.004433






Multiple Linear Regression - Regression Statistics
Multiple R0.942808386330887
R-squared0.888887653335852
Adjusted R-squared0.875282059866773
F-TEST (value)65.3325160240878
F-TEST (DF numerator)6
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.195155165199376
Sum Squared Residuals1.86619138669579

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.942808386330887 \tabularnewline
R-squared & 0.888887653335852 \tabularnewline
Adjusted R-squared & 0.875282059866773 \tabularnewline
F-TEST (value) & 65.3325160240878 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 49 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.195155165199376 \tabularnewline
Sum Squared Residuals & 1.86619138669579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.942808386330887[/C][/ROW]
[ROW][C]R-squared[/C][C]0.888887653335852[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.875282059866773[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]65.3325160240878[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]49[/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]0.195155165199376[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.86619138669579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&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 R0.942808386330887
R-squared0.888887653335852
Adjusted R-squared0.875282059866773
F-TEST (value)65.3325160240878
F-TEST (DF numerator)6
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.195155165199376
Sum Squared Residuals1.86619138669579






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.51.363536001128510.136463998871487
21.31.33139075816250-0.031390758162503
31.41.284487555661470.115512444338533
41.41.264048394354260.135951605645738
51.31.31319492147343-0.0131949214734296
61.31.286667887603790.0133321123962128
71.21.25107539901998-0.0510753990199833
81.11.22450509179431-0.124505091794309
91.41.163666874614770.236333125385228
101.21.25095601743555-0.0509560174355492
111.51.302202727526230.197797272473768
121.11.34932074404939-0.24932074404939
131.31.31129163026939-0.0112916302693913
141.51.248812222658300.251187777341697
151.11.40831593990407-0.308315939904075
161.41.355971646989780.0440283530102162
171.31.31972924286626-0.0197292428662611
181.51.399453184476000.100546815523998
191.61.458696135232430.141303864767566
201.71.573519425163900.126480574836096
211.11.66334023634513-0.563340236345134
221.61.475946104436960.124053895563043
231.31.44294694418278-0.142946944182780
241.71.528217868447610.171782131552394
251.61.592385393470430.00761460652956964
261.71.698190081368530.00180991863146940
271.91.717837461535240.182162538464756
281.81.82751685518109-0.0275168551810911
291.91.878360478902310.0216395210976891
301.61.88279549223139-0.282795492231388
311.51.80966389673912-0.309663896739125
321.61.67063666234955-0.0706366623495547
331.61.67972460108005-0.079724601080054
341.71.73873962226177-0.0387396222617723
3521.788732908019590.211267091980415
3621.947876812251930.0521231877480738
371.92.06870607737844-0.168706077378445
381.72.03132016642287-0.331320166422868
391.81.91938027348427-0.119380273484270
401.91.89032201718840.00967798281160137
411.71.97846105203836-0.278461052038358
4221.956862617694090.0431373823059071
432.12.000662138647640.0993378613523616
442.42.161862506561240.238137493438761
452.52.329668779138280.170331220861722
462.52.478803698313870.0211963016861333
472.62.518987975504390.0810120244956094
482.22.55256276870671-0.352562768706714
492.52.442722612805410.0572773871945918
502.82.417339531702040.382660468297955
512.82.663850891701750.136149108298245
522.92.80153013477270.0984698652272998
5332.833898802257170.166101197742828
543.12.904413218833790.195586781166211
552.92.98725254613314-0.0872525461331443
562.72.95763897152759-0.257638971527587

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.5 & 1.36353600112851 & 0.136463998871487 \tabularnewline
2 & 1.3 & 1.33139075816250 & -0.031390758162503 \tabularnewline
3 & 1.4 & 1.28448755566147 & 0.115512444338533 \tabularnewline
4 & 1.4 & 1.26404839435426 & 0.135951605645738 \tabularnewline
5 & 1.3 & 1.31319492147343 & -0.0131949214734296 \tabularnewline
6 & 1.3 & 1.28666788760379 & 0.0133321123962128 \tabularnewline
7 & 1.2 & 1.25107539901998 & -0.0510753990199833 \tabularnewline
8 & 1.1 & 1.22450509179431 & -0.124505091794309 \tabularnewline
9 & 1.4 & 1.16366687461477 & 0.236333125385228 \tabularnewline
10 & 1.2 & 1.25095601743555 & -0.0509560174355492 \tabularnewline
11 & 1.5 & 1.30220272752623 & 0.197797272473768 \tabularnewline
12 & 1.1 & 1.34932074404939 & -0.24932074404939 \tabularnewline
13 & 1.3 & 1.31129163026939 & -0.0112916302693913 \tabularnewline
14 & 1.5 & 1.24881222265830 & 0.251187777341697 \tabularnewline
15 & 1.1 & 1.40831593990407 & -0.308315939904075 \tabularnewline
16 & 1.4 & 1.35597164698978 & 0.0440283530102162 \tabularnewline
17 & 1.3 & 1.31972924286626 & -0.0197292428662611 \tabularnewline
18 & 1.5 & 1.39945318447600 & 0.100546815523998 \tabularnewline
19 & 1.6 & 1.45869613523243 & 0.141303864767566 \tabularnewline
20 & 1.7 & 1.57351942516390 & 0.126480574836096 \tabularnewline
21 & 1.1 & 1.66334023634513 & -0.563340236345134 \tabularnewline
22 & 1.6 & 1.47594610443696 & 0.124053895563043 \tabularnewline
23 & 1.3 & 1.44294694418278 & -0.142946944182780 \tabularnewline
24 & 1.7 & 1.52821786844761 & 0.171782131552394 \tabularnewline
25 & 1.6 & 1.59238539347043 & 0.00761460652956964 \tabularnewline
26 & 1.7 & 1.69819008136853 & 0.00180991863146940 \tabularnewline
27 & 1.9 & 1.71783746153524 & 0.182162538464756 \tabularnewline
28 & 1.8 & 1.82751685518109 & -0.0275168551810911 \tabularnewline
29 & 1.9 & 1.87836047890231 & 0.0216395210976891 \tabularnewline
30 & 1.6 & 1.88279549223139 & -0.282795492231388 \tabularnewline
31 & 1.5 & 1.80966389673912 & -0.309663896739125 \tabularnewline
32 & 1.6 & 1.67063666234955 & -0.0706366623495547 \tabularnewline
33 & 1.6 & 1.67972460108005 & -0.079724601080054 \tabularnewline
34 & 1.7 & 1.73873962226177 & -0.0387396222617723 \tabularnewline
35 & 2 & 1.78873290801959 & 0.211267091980415 \tabularnewline
36 & 2 & 1.94787681225193 & 0.0521231877480738 \tabularnewline
37 & 1.9 & 2.06870607737844 & -0.168706077378445 \tabularnewline
38 & 1.7 & 2.03132016642287 & -0.331320166422868 \tabularnewline
39 & 1.8 & 1.91938027348427 & -0.119380273484270 \tabularnewline
40 & 1.9 & 1.8903220171884 & 0.00967798281160137 \tabularnewline
41 & 1.7 & 1.97846105203836 & -0.278461052038358 \tabularnewline
42 & 2 & 1.95686261769409 & 0.0431373823059071 \tabularnewline
43 & 2.1 & 2.00066213864764 & 0.0993378613523616 \tabularnewline
44 & 2.4 & 2.16186250656124 & 0.238137493438761 \tabularnewline
45 & 2.5 & 2.32966877913828 & 0.170331220861722 \tabularnewline
46 & 2.5 & 2.47880369831387 & 0.0211963016861333 \tabularnewline
47 & 2.6 & 2.51898797550439 & 0.0810120244956094 \tabularnewline
48 & 2.2 & 2.55256276870671 & -0.352562768706714 \tabularnewline
49 & 2.5 & 2.44272261280541 & 0.0572773871945918 \tabularnewline
50 & 2.8 & 2.41733953170204 & 0.382660468297955 \tabularnewline
51 & 2.8 & 2.66385089170175 & 0.136149108298245 \tabularnewline
52 & 2.9 & 2.8015301347727 & 0.0984698652272998 \tabularnewline
53 & 3 & 2.83389880225717 & 0.166101197742828 \tabularnewline
54 & 3.1 & 2.90441321883379 & 0.195586781166211 \tabularnewline
55 & 2.9 & 2.98725254613314 & -0.0872525461331443 \tabularnewline
56 & 2.7 & 2.95763897152759 & -0.257638971527587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]1.5[/C][C]1.36353600112851[/C][C]0.136463998871487[/C][/ROW]
[ROW][C]2[/C][C]1.3[/C][C]1.33139075816250[/C][C]-0.031390758162503[/C][/ROW]
[ROW][C]3[/C][C]1.4[/C][C]1.28448755566147[/C][C]0.115512444338533[/C][/ROW]
[ROW][C]4[/C][C]1.4[/C][C]1.26404839435426[/C][C]0.135951605645738[/C][/ROW]
[ROW][C]5[/C][C]1.3[/C][C]1.31319492147343[/C][C]-0.0131949214734296[/C][/ROW]
[ROW][C]6[/C][C]1.3[/C][C]1.28666788760379[/C][C]0.0133321123962128[/C][/ROW]
[ROW][C]7[/C][C]1.2[/C][C]1.25107539901998[/C][C]-0.0510753990199833[/C][/ROW]
[ROW][C]8[/C][C]1.1[/C][C]1.22450509179431[/C][C]-0.124505091794309[/C][/ROW]
[ROW][C]9[/C][C]1.4[/C][C]1.16366687461477[/C][C]0.236333125385228[/C][/ROW]
[ROW][C]10[/C][C]1.2[/C][C]1.25095601743555[/C][C]-0.0509560174355492[/C][/ROW]
[ROW][C]11[/C][C]1.5[/C][C]1.30220272752623[/C][C]0.197797272473768[/C][/ROW]
[ROW][C]12[/C][C]1.1[/C][C]1.34932074404939[/C][C]-0.24932074404939[/C][/ROW]
[ROW][C]13[/C][C]1.3[/C][C]1.31129163026939[/C][C]-0.0112916302693913[/C][/ROW]
[ROW][C]14[/C][C]1.5[/C][C]1.24881222265830[/C][C]0.251187777341697[/C][/ROW]
[ROW][C]15[/C][C]1.1[/C][C]1.40831593990407[/C][C]-0.308315939904075[/C][/ROW]
[ROW][C]16[/C][C]1.4[/C][C]1.35597164698978[/C][C]0.0440283530102162[/C][/ROW]
[ROW][C]17[/C][C]1.3[/C][C]1.31972924286626[/C][C]-0.0197292428662611[/C][/ROW]
[ROW][C]18[/C][C]1.5[/C][C]1.39945318447600[/C][C]0.100546815523998[/C][/ROW]
[ROW][C]19[/C][C]1.6[/C][C]1.45869613523243[/C][C]0.141303864767566[/C][/ROW]
[ROW][C]20[/C][C]1.7[/C][C]1.57351942516390[/C][C]0.126480574836096[/C][/ROW]
[ROW][C]21[/C][C]1.1[/C][C]1.66334023634513[/C][C]-0.563340236345134[/C][/ROW]
[ROW][C]22[/C][C]1.6[/C][C]1.47594610443696[/C][C]0.124053895563043[/C][/ROW]
[ROW][C]23[/C][C]1.3[/C][C]1.44294694418278[/C][C]-0.142946944182780[/C][/ROW]
[ROW][C]24[/C][C]1.7[/C][C]1.52821786844761[/C][C]0.171782131552394[/C][/ROW]
[ROW][C]25[/C][C]1.6[/C][C]1.59238539347043[/C][C]0.00761460652956964[/C][/ROW]
[ROW][C]26[/C][C]1.7[/C][C]1.69819008136853[/C][C]0.00180991863146940[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.71783746153524[/C][C]0.182162538464756[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]1.82751685518109[/C][C]-0.0275168551810911[/C][/ROW]
[ROW][C]29[/C][C]1.9[/C][C]1.87836047890231[/C][C]0.0216395210976891[/C][/ROW]
[ROW][C]30[/C][C]1.6[/C][C]1.88279549223139[/C][C]-0.282795492231388[/C][/ROW]
[ROW][C]31[/C][C]1.5[/C][C]1.80966389673912[/C][C]-0.309663896739125[/C][/ROW]
[ROW][C]32[/C][C]1.6[/C][C]1.67063666234955[/C][C]-0.0706366623495547[/C][/ROW]
[ROW][C]33[/C][C]1.6[/C][C]1.67972460108005[/C][C]-0.079724601080054[/C][/ROW]
[ROW][C]34[/C][C]1.7[/C][C]1.73873962226177[/C][C]-0.0387396222617723[/C][/ROW]
[ROW][C]35[/C][C]2[/C][C]1.78873290801959[/C][C]0.211267091980415[/C][/ROW]
[ROW][C]36[/C][C]2[/C][C]1.94787681225193[/C][C]0.0521231877480738[/C][/ROW]
[ROW][C]37[/C][C]1.9[/C][C]2.06870607737844[/C][C]-0.168706077378445[/C][/ROW]
[ROW][C]38[/C][C]1.7[/C][C]2.03132016642287[/C][C]-0.331320166422868[/C][/ROW]
[ROW][C]39[/C][C]1.8[/C][C]1.91938027348427[/C][C]-0.119380273484270[/C][/ROW]
[ROW][C]40[/C][C]1.9[/C][C]1.8903220171884[/C][C]0.00967798281160137[/C][/ROW]
[ROW][C]41[/C][C]1.7[/C][C]1.97846105203836[/C][C]-0.278461052038358[/C][/ROW]
[ROW][C]42[/C][C]2[/C][C]1.95686261769409[/C][C]0.0431373823059071[/C][/ROW]
[ROW][C]43[/C][C]2.1[/C][C]2.00066213864764[/C][C]0.0993378613523616[/C][/ROW]
[ROW][C]44[/C][C]2.4[/C][C]2.16186250656124[/C][C]0.238137493438761[/C][/ROW]
[ROW][C]45[/C][C]2.5[/C][C]2.32966877913828[/C][C]0.170331220861722[/C][/ROW]
[ROW][C]46[/C][C]2.5[/C][C]2.47880369831387[/C][C]0.0211963016861333[/C][/ROW]
[ROW][C]47[/C][C]2.6[/C][C]2.51898797550439[/C][C]0.0810120244956094[/C][/ROW]
[ROW][C]48[/C][C]2.2[/C][C]2.55256276870671[/C][C]-0.352562768706714[/C][/ROW]
[ROW][C]49[/C][C]2.5[/C][C]2.44272261280541[/C][C]0.0572773871945918[/C][/ROW]
[ROW][C]50[/C][C]2.8[/C][C]2.41733953170204[/C][C]0.382660468297955[/C][/ROW]
[ROW][C]51[/C][C]2.8[/C][C]2.66385089170175[/C][C]0.136149108298245[/C][/ROW]
[ROW][C]52[/C][C]2.9[/C][C]2.8015301347727[/C][C]0.0984698652272998[/C][/ROW]
[ROW][C]53[/C][C]3[/C][C]2.83389880225717[/C][C]0.166101197742828[/C][/ROW]
[ROW][C]54[/C][C]3.1[/C][C]2.90441321883379[/C][C]0.195586781166211[/C][/ROW]
[ROW][C]55[/C][C]2.9[/C][C]2.98725254613314[/C][C]-0.0872525461331443[/C][/ROW]
[ROW][C]56[/C][C]2.7[/C][C]2.95763897152759[/C][C]-0.257638971527587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&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
11.51.363536001128510.136463998871487
21.31.33139075816250-0.031390758162503
31.41.284487555661470.115512444338533
41.41.264048394354260.135951605645738
51.31.31319492147343-0.0131949214734296
61.31.286667887603790.0133321123962128
71.21.25107539901998-0.0510753990199833
81.11.22450509179431-0.124505091794309
91.41.163666874614770.236333125385228
101.21.25095601743555-0.0509560174355492
111.51.302202727526230.197797272473768
121.11.34932074404939-0.24932074404939
131.31.31129163026939-0.0112916302693913
141.51.248812222658300.251187777341697
151.11.40831593990407-0.308315939904075
161.41.355971646989780.0440283530102162
171.31.31972924286626-0.0197292428662611
181.51.399453184476000.100546815523998
191.61.458696135232430.141303864767566
201.71.573519425163900.126480574836096
211.11.66334023634513-0.563340236345134
221.61.475946104436960.124053895563043
231.31.44294694418278-0.142946944182780
241.71.528217868447610.171782131552394
251.61.592385393470430.00761460652956964
261.71.698190081368530.00180991863146940
271.91.717837461535240.182162538464756
281.81.82751685518109-0.0275168551810911
291.91.878360478902310.0216395210976891
301.61.88279549223139-0.282795492231388
311.51.80966389673912-0.309663896739125
321.61.67063666234955-0.0706366623495547
331.61.67972460108005-0.079724601080054
341.71.73873962226177-0.0387396222617723
3521.788732908019590.211267091980415
3621.947876812251930.0521231877480738
371.92.06870607737844-0.168706077378445
381.72.03132016642287-0.331320166422868
391.81.91938027348427-0.119380273484270
401.91.89032201718840.00967798281160137
411.71.97846105203836-0.278461052038358
4221.956862617694090.0431373823059071
432.12.000662138647640.0993378613523616
442.42.161862506561240.238137493438761
452.52.329668779138280.170331220861722
462.52.478803698313870.0211963016861333
472.62.518987975504390.0810120244956094
482.22.55256276870671-0.352562768706714
492.52.442722612805410.0572773871945918
502.82.417339531702040.382660468297955
512.82.663850891701750.136149108298245
522.92.80153013477270.0984698652272998
5332.833898802257170.166101197742828
543.12.904413218833790.195586781166211
552.92.98725254613314-0.0872525461331443
562.72.95763897152759-0.257638971527587






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.1700745672602470.3401491345204930.829925432739753
110.1990930940326550.3981861880653110.800906905967345
120.2545734869231000.5091469738462000.7454265130769
130.1533440996910170.3066881993820340.846655900308983
140.2700359244384520.5400718488769040.729964075561548
150.1910659121089660.3821318242179320.808934087891034
160.1343255100443710.2686510200887420.865674489955629
170.08243494994337860.1648698998867570.917565050056621
180.1132765417170240.2265530834340480.886723458282976
190.1438875763732200.2877751527464400.85611242362678
200.1575552049934410.3151104099868810.84244479500656
210.5843199199463290.8313601601073420.415680080053671
220.5633678587130440.8732642825739110.436632141286956
230.4982884799128980.9965769598257970.501711520087102
240.5694021408573220.8611957182853560.430597859142678
250.5375412461339930.9249175077320140.462458753866007
260.525343692271340.949312615457320.47465630772866
270.606055663339360.787888673321280.39394433666064
280.56195109987650.8760978002470.4380489001235
290.6592667587976450.681466482404710.340733241202355
300.6399489007268640.7201021985462730.360051099273136
310.6667770819625250.666445836074950.333222918037475
320.597487598122090.805024803755820.40251240187791
330.5091169267654460.9817661464691080.490883073234554
340.4210822916833220.8421645833666430.578917708316678
350.5149667179284410.9700665641431170.485033282071559
360.5024187607427610.9951624785144770.497581239257239
370.4448518718016730.8897037436033460.555148128198327
380.3990074510588080.7980149021176170.600992548941192
390.3246143209548780.6492286419097560.675385679045122
400.3125245920146040.6250491840292080.687475407985396
410.3275812055467850.6551624110935710.672418794453215
420.2481080867665930.4962161735331860.751891913233407
430.3203060689654220.6406121379308450.679693931034578
440.2701071171549250.540214234309850.729892882845075
450.2263809592159620.4527619184319250.773619040784038
460.1294411020143830.2588822040287660.870558897985617

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.170074567260247 & 0.340149134520493 & 0.829925432739753 \tabularnewline
11 & 0.199093094032655 & 0.398186188065311 & 0.800906905967345 \tabularnewline
12 & 0.254573486923100 & 0.509146973846200 & 0.7454265130769 \tabularnewline
13 & 0.153344099691017 & 0.306688199382034 & 0.846655900308983 \tabularnewline
14 & 0.270035924438452 & 0.540071848876904 & 0.729964075561548 \tabularnewline
15 & 0.191065912108966 & 0.382131824217932 & 0.808934087891034 \tabularnewline
16 & 0.134325510044371 & 0.268651020088742 & 0.865674489955629 \tabularnewline
17 & 0.0824349499433786 & 0.164869899886757 & 0.917565050056621 \tabularnewline
18 & 0.113276541717024 & 0.226553083434048 & 0.886723458282976 \tabularnewline
19 & 0.143887576373220 & 0.287775152746440 & 0.85611242362678 \tabularnewline
20 & 0.157555204993441 & 0.315110409986881 & 0.84244479500656 \tabularnewline
21 & 0.584319919946329 & 0.831360160107342 & 0.415680080053671 \tabularnewline
22 & 0.563367858713044 & 0.873264282573911 & 0.436632141286956 \tabularnewline
23 & 0.498288479912898 & 0.996576959825797 & 0.501711520087102 \tabularnewline
24 & 0.569402140857322 & 0.861195718285356 & 0.430597859142678 \tabularnewline
25 & 0.537541246133993 & 0.924917507732014 & 0.462458753866007 \tabularnewline
26 & 0.52534369227134 & 0.94931261545732 & 0.47465630772866 \tabularnewline
27 & 0.60605566333936 & 0.78788867332128 & 0.39394433666064 \tabularnewline
28 & 0.5619510998765 & 0.876097800247 & 0.4380489001235 \tabularnewline
29 & 0.659266758797645 & 0.68146648240471 & 0.340733241202355 \tabularnewline
30 & 0.639948900726864 & 0.720102198546273 & 0.360051099273136 \tabularnewline
31 & 0.666777081962525 & 0.66644583607495 & 0.333222918037475 \tabularnewline
32 & 0.59748759812209 & 0.80502480375582 & 0.40251240187791 \tabularnewline
33 & 0.509116926765446 & 0.981766146469108 & 0.490883073234554 \tabularnewline
34 & 0.421082291683322 & 0.842164583366643 & 0.578917708316678 \tabularnewline
35 & 0.514966717928441 & 0.970066564143117 & 0.485033282071559 \tabularnewline
36 & 0.502418760742761 & 0.995162478514477 & 0.497581239257239 \tabularnewline
37 & 0.444851871801673 & 0.889703743603346 & 0.555148128198327 \tabularnewline
38 & 0.399007451058808 & 0.798014902117617 & 0.600992548941192 \tabularnewline
39 & 0.324614320954878 & 0.649228641909756 & 0.675385679045122 \tabularnewline
40 & 0.312524592014604 & 0.625049184029208 & 0.687475407985396 \tabularnewline
41 & 0.327581205546785 & 0.655162411093571 & 0.672418794453215 \tabularnewline
42 & 0.248108086766593 & 0.496216173533186 & 0.751891913233407 \tabularnewline
43 & 0.320306068965422 & 0.640612137930845 & 0.679693931034578 \tabularnewline
44 & 0.270107117154925 & 0.54021423430985 & 0.729892882845075 \tabularnewline
45 & 0.226380959215962 & 0.452761918431925 & 0.773619040784038 \tabularnewline
46 & 0.129441102014383 & 0.258882204028766 & 0.870558897985617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&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]10[/C][C]0.170074567260247[/C][C]0.340149134520493[/C][C]0.829925432739753[/C][/ROW]
[ROW][C]11[/C][C]0.199093094032655[/C][C]0.398186188065311[/C][C]0.800906905967345[/C][/ROW]
[ROW][C]12[/C][C]0.254573486923100[/C][C]0.509146973846200[/C][C]0.7454265130769[/C][/ROW]
[ROW][C]13[/C][C]0.153344099691017[/C][C]0.306688199382034[/C][C]0.846655900308983[/C][/ROW]
[ROW][C]14[/C][C]0.270035924438452[/C][C]0.540071848876904[/C][C]0.729964075561548[/C][/ROW]
[ROW][C]15[/C][C]0.191065912108966[/C][C]0.382131824217932[/C][C]0.808934087891034[/C][/ROW]
[ROW][C]16[/C][C]0.134325510044371[/C][C]0.268651020088742[/C][C]0.865674489955629[/C][/ROW]
[ROW][C]17[/C][C]0.0824349499433786[/C][C]0.164869899886757[/C][C]0.917565050056621[/C][/ROW]
[ROW][C]18[/C][C]0.113276541717024[/C][C]0.226553083434048[/C][C]0.886723458282976[/C][/ROW]
[ROW][C]19[/C][C]0.143887576373220[/C][C]0.287775152746440[/C][C]0.85611242362678[/C][/ROW]
[ROW][C]20[/C][C]0.157555204993441[/C][C]0.315110409986881[/C][C]0.84244479500656[/C][/ROW]
[ROW][C]21[/C][C]0.584319919946329[/C][C]0.831360160107342[/C][C]0.415680080053671[/C][/ROW]
[ROW][C]22[/C][C]0.563367858713044[/C][C]0.873264282573911[/C][C]0.436632141286956[/C][/ROW]
[ROW][C]23[/C][C]0.498288479912898[/C][C]0.996576959825797[/C][C]0.501711520087102[/C][/ROW]
[ROW][C]24[/C][C]0.569402140857322[/C][C]0.861195718285356[/C][C]0.430597859142678[/C][/ROW]
[ROW][C]25[/C][C]0.537541246133993[/C][C]0.924917507732014[/C][C]0.462458753866007[/C][/ROW]
[ROW][C]26[/C][C]0.52534369227134[/C][C]0.94931261545732[/C][C]0.47465630772866[/C][/ROW]
[ROW][C]27[/C][C]0.60605566333936[/C][C]0.78788867332128[/C][C]0.39394433666064[/C][/ROW]
[ROW][C]28[/C][C]0.5619510998765[/C][C]0.876097800247[/C][C]0.4380489001235[/C][/ROW]
[ROW][C]29[/C][C]0.659266758797645[/C][C]0.68146648240471[/C][C]0.340733241202355[/C][/ROW]
[ROW][C]30[/C][C]0.639948900726864[/C][C]0.720102198546273[/C][C]0.360051099273136[/C][/ROW]
[ROW][C]31[/C][C]0.666777081962525[/C][C]0.66644583607495[/C][C]0.333222918037475[/C][/ROW]
[ROW][C]32[/C][C]0.59748759812209[/C][C]0.80502480375582[/C][C]0.40251240187791[/C][/ROW]
[ROW][C]33[/C][C]0.509116926765446[/C][C]0.981766146469108[/C][C]0.490883073234554[/C][/ROW]
[ROW][C]34[/C][C]0.421082291683322[/C][C]0.842164583366643[/C][C]0.578917708316678[/C][/ROW]
[ROW][C]35[/C][C]0.514966717928441[/C][C]0.970066564143117[/C][C]0.485033282071559[/C][/ROW]
[ROW][C]36[/C][C]0.502418760742761[/C][C]0.995162478514477[/C][C]0.497581239257239[/C][/ROW]
[ROW][C]37[/C][C]0.444851871801673[/C][C]0.889703743603346[/C][C]0.555148128198327[/C][/ROW]
[ROW][C]38[/C][C]0.399007451058808[/C][C]0.798014902117617[/C][C]0.600992548941192[/C][/ROW]
[ROW][C]39[/C][C]0.324614320954878[/C][C]0.649228641909756[/C][C]0.675385679045122[/C][/ROW]
[ROW][C]40[/C][C]0.312524592014604[/C][C]0.625049184029208[/C][C]0.687475407985396[/C][/ROW]
[ROW][C]41[/C][C]0.327581205546785[/C][C]0.655162411093571[/C][C]0.672418794453215[/C][/ROW]
[ROW][C]42[/C][C]0.248108086766593[/C][C]0.496216173533186[/C][C]0.751891913233407[/C][/ROW]
[ROW][C]43[/C][C]0.320306068965422[/C][C]0.640612137930845[/C][C]0.679693931034578[/C][/ROW]
[ROW][C]44[/C][C]0.270107117154925[/C][C]0.54021423430985[/C][C]0.729892882845075[/C][/ROW]
[ROW][C]45[/C][C]0.226380959215962[/C][C]0.452761918431925[/C][C]0.773619040784038[/C][/ROW]
[ROW][C]46[/C][C]0.129441102014383[/C][C]0.258882204028766[/C][C]0.870558897985617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&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
100.1700745672602470.3401491345204930.829925432739753
110.1990930940326550.3981861880653110.800906905967345
120.2545734869231000.5091469738462000.7454265130769
130.1533440996910170.3066881993820340.846655900308983
140.2700359244384520.5400718488769040.729964075561548
150.1910659121089660.3821318242179320.808934087891034
160.1343255100443710.2686510200887420.865674489955629
170.08243494994337860.1648698998867570.917565050056621
180.1132765417170240.2265530834340480.886723458282976
190.1438875763732200.2877751527464400.85611242362678
200.1575552049934410.3151104099868810.84244479500656
210.5843199199463290.8313601601073420.415680080053671
220.5633678587130440.8732642825739110.436632141286956
230.4982884799128980.9965769598257970.501711520087102
240.5694021408573220.8611957182853560.430597859142678
250.5375412461339930.9249175077320140.462458753866007
260.525343692271340.949312615457320.47465630772866
270.606055663339360.787888673321280.39394433666064
280.56195109987650.8760978002470.4380489001235
290.6592667587976450.681466482404710.340733241202355
300.6399489007268640.7201021985462730.360051099273136
310.6667770819625250.666445836074950.333222918037475
320.597487598122090.805024803755820.40251240187791
330.5091169267654460.9817661464691080.490883073234554
340.4210822916833220.8421645833666430.578917708316678
350.5149667179284410.9700665641431170.485033282071559
360.5024187607427610.9951624785144770.497581239257239
370.4448518718016730.8897037436033460.555148128198327
380.3990074510588080.7980149021176170.600992548941192
390.3246143209548780.6492286419097560.675385679045122
400.3125245920146040.6250491840292080.687475407985396
410.3275812055467850.6551624110935710.672418794453215
420.2481080867665930.4962161735331860.751891913233407
430.3203060689654220.6406121379308450.679693931034578
440.2701071171549250.540214234309850.729892882845075
450.2263809592159620.4527619184319250.773619040784038
460.1294411020143830.2588822040287660.870558897985617






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 level00OK

\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 & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57555&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57555&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57555&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 level00OK


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 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}