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Description of Statistical Computation

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Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 09:06:40 -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/20/t1258734866sp3i3mfxwo20ntw.htm/, Retrieved Wed, 24 Apr 2024 06:53:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58311, Retrieved Wed, 24 Apr 2024 06:53:17 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [WS 7.4] [2009-11-20 16:06:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8	6,5	8,3	9,3	9,8	9,9
8,5	6,6	8	8,3	9,3	9,8
10,4	7,6	8,5	8	8,3	9,3
11,1	8	10,4	8,5	8	8,3
10,9	8,1	11,1	10,4	8,5	8
10	7,7	10,9	11,1	10,4	8,5
9,2	7,5	10	10,9	11,1	10,4
9,2	7,6	9,2	10	10,9	11,1
9,5	7,8	9,2	9,2	10	10,9
9,6	7,8	9,5	9,2	9,2	10
9,5	7,8	9,6	9,5	9,2	9,2
9,1	7,5	9,5	9,6	9,5	9,2
8,9	7,5	9,1	9,5	9,6	9,5
9	7,1	8,9	9,1	9,5	9,6
10,1	7,5	9	8,9	9,1	9,5
10,3	7,5	10,1	9	8,9	9,1
10,2	7,6	10,3	10,1	9	8,9
9,6	7,7	10,2	10,3	10,1	9
9,2	7,7	9,6	10,2	10,3	10,1
9,3	7,9	9,2	9,6	10,2	10,3
9,4	8,1	9,3	9,2	9,6	10,2
9,4	8,2	9,4	9,3	9,2	9,6
9,2	8,2	9,4	9,4	9,3	9,2
9	8,2	9,2	9,4	9,4	9,3
9	7,9	9	9,2	9,4	9,4
9	7,3	9	9	9,2	9,4
9,8	6,9	9	9	9	9,2
10	6,6	9,8	9	9	9
9,8	6,7	10	9,8	9	9
9,3	6,9	9,8	10	9,8	9
9	7	9,3	9,8	10	9,8
9	7,1	9	9,3	9,8	10
9,1	7,2	9	9	9,3	9,8
9,1	7,1	9,1	9	9	9,3
9,1	6,9	9,1	9,1	9	9
9,2	7	9,1	9,1	9,1	9
8,8	6,8	9,2	9,1	9,1	9,1
8,3	6,4	8,8	9,2	9,1	9,1
8,4	6,7	8,3	8,8	9,2	9,1
8,1	6,6	8,4	8,3	8,8	9,2
7,7	6,4	8,1	8,4	8,3	8,8
7,9	6,3	7,7	8,1	8,4	8,3
7,9	6,2	7,9	7,7	8,1	8,4
8	6,5	7,9	7,9	7,7	8,1
7,9	6,8	8	7,9	7,9	7,7
7,6	6,8	7,9	8	7,9	7,9
7,1	6,4	7,6	7,9	8	7,9
6,8	6,1	7,1	7,6	7,9	8
6,5	5,8	6,8	7,1	7,6	7,9
6,9	6,1	6,5	6,8	7,1	7,6
8,2	7,2	6,9	6,5	6,8	7,1
8,7	7,3	8,2	6,9	6,5	6,8
8,3	6,9	8,7	8,2	6,9	6,5
7,9	6,1	8,3	8,7	8,2	6,9
7,5	5,8	7,9	8,3	8,7	8,2
7,8	6,2	7,5	7,9	8,3	8,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&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]3 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=58311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
WLMan[t] = + 4.74589368190231 + 0.252977925543289WLVrouw[t] + 0.286731211867211`Yt-1`[t] -0.140281941699051`Yt-2`[t] + 0.0307676256758232`Yt-3`[t] -0.0942370090570313`Yt-4`[t] -0.211902844334609M1[t] -0.403473617050317M2[t] -0.249269058051509M3[t] -0.592689012093239M4[t] -0.528197626041862M5[t] -0.515370882802887M6[t] -0.326476270103165M7[t] -0.038971385595141M8[t] + 0.131030026188113M9[t] + 0.104218769786131M10[t] + 0.00936951584773028M11[t] -0.0130676658698532t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WLMan[t] =  +  4.74589368190231 +  0.252977925543289WLVrouw[t] +  0.286731211867211`Yt-1`[t] -0.140281941699051`Yt-2`[t] +  0.0307676256758232`Yt-3`[t] -0.0942370090570313`Yt-4`[t] -0.211902844334609M1[t] -0.403473617050317M2[t] -0.249269058051509M3[t] -0.592689012093239M4[t] -0.528197626041862M5[t] -0.515370882802887M6[t] -0.326476270103165M7[t] -0.038971385595141M8[t] +  0.131030026188113M9[t] +  0.104218769786131M10[t] +  0.00936951584773028M11[t] -0.0130676658698532t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WLMan[t] =  +  4.74589368190231 +  0.252977925543289WLVrouw[t] +  0.286731211867211`Yt-1`[t] -0.140281941699051`Yt-2`[t] +  0.0307676256758232`Yt-3`[t] -0.0942370090570313`Yt-4`[t] -0.211902844334609M1[t] -0.403473617050317M2[t] -0.249269058051509M3[t] -0.592689012093239M4[t] -0.528197626041862M5[t] -0.515370882802887M6[t] -0.326476270103165M7[t] -0.038971385595141M8[t] +  0.131030026188113M9[t] +  0.104218769786131M10[t] +  0.00936951584773028M11[t] -0.0130676658698532t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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
WLMan[t] = + 4.74589368190231 + 0.252977925543289WLVrouw[t] + 0.286731211867211`Yt-1`[t] -0.140281941699051`Yt-2`[t] + 0.0307676256758232`Yt-3`[t] -0.0942370090570313`Yt-4`[t] -0.211902844334609M1[t] -0.403473617050317M2[t] -0.249269058051509M3[t] -0.592689012093239M4[t] -0.528197626041862M5[t] -0.515370882802887M6[t] -0.326476270103165M7[t] -0.038971385595141M8[t] + 0.131030026188113M9[t] + 0.104218769786131M10[t] + 0.00936951584773028M11[t] -0.0130676658698532t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)4.745893681902311.4849753.19590.0028040.001402
WLVrouw0.2529779255432890.3588250.7050.4850990.242549
`Yt-1`0.2867312118672110.5761070.49770.621560.31078
`Yt-2`-0.1402819416990510.572234-0.24510.8076610.403831
`Yt-3`0.03076762567582320.5559720.05530.9561570.478079
`Yt-4`-0.09423700905703130.316676-0.29760.7676430.383821
M1-0.2119028443346090.286808-0.73880.4645490.232275
M2-0.4034736170503170.291209-1.38550.1739750.086988
M3-0.2492690580515090.414358-0.60160.5510270.275513
M4-0.5926890120932390.40213-1.47390.1487520.074376
M5-0.5281976260418620.394484-1.3390.1885390.09427
M6-0.5153708828028870.35084-1.4690.1500740.075037
M7-0.3264762701031650.292308-1.11690.2710540.135527
M8-0.0389713855951410.308159-0.12650.9000310.450015
M90.1310300261881130.3258350.40210.6898370.344918
M100.1042187697861310.3287110.31710.7529390.376469
M110.009369515847730280.2986610.03140.9751370.487569
t-0.01306766586985320.007412-1.7630.0859460.042973

\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) & 4.74589368190231 & 1.484975 & 3.1959 & 0.002804 & 0.001402 \tabularnewline
WLVrouw & 0.252977925543289 & 0.358825 & 0.705 & 0.485099 & 0.242549 \tabularnewline
`Yt-1` & 0.286731211867211 & 0.576107 & 0.4977 & 0.62156 & 0.31078 \tabularnewline
`Yt-2` & -0.140281941699051 & 0.572234 & -0.2451 & 0.807661 & 0.403831 \tabularnewline
`Yt-3` & 0.0307676256758232 & 0.555972 & 0.0553 & 0.956157 & 0.478079 \tabularnewline
`Yt-4` & -0.0942370090570313 & 0.316676 & -0.2976 & 0.767643 & 0.383821 \tabularnewline
M1 & -0.211902844334609 & 0.286808 & -0.7388 & 0.464549 & 0.232275 \tabularnewline
M2 & -0.403473617050317 & 0.291209 & -1.3855 & 0.173975 & 0.086988 \tabularnewline
M3 & -0.249269058051509 & 0.414358 & -0.6016 & 0.551027 & 0.275513 \tabularnewline
M4 & -0.592689012093239 & 0.40213 & -1.4739 & 0.148752 & 0.074376 \tabularnewline
M5 & -0.528197626041862 & 0.394484 & -1.339 & 0.188539 & 0.09427 \tabularnewline
M6 & -0.515370882802887 & 0.35084 & -1.469 & 0.150074 & 0.075037 \tabularnewline
M7 & -0.326476270103165 & 0.292308 & -1.1169 & 0.271054 & 0.135527 \tabularnewline
M8 & -0.038971385595141 & 0.308159 & -0.1265 & 0.900031 & 0.450015 \tabularnewline
M9 & 0.131030026188113 & 0.325835 & 0.4021 & 0.689837 & 0.344918 \tabularnewline
M10 & 0.104218769786131 & 0.328711 & 0.3171 & 0.752939 & 0.376469 \tabularnewline
M11 & 0.00936951584773028 & 0.298661 & 0.0314 & 0.975137 & 0.487569 \tabularnewline
t & -0.0130676658698532 & 0.007412 & -1.763 & 0.085946 & 0.042973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&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]4.74589368190231[/C][C]1.484975[/C][C]3.1959[/C][C]0.002804[/C][C]0.001402[/C][/ROW]
[ROW][C]WLVrouw[/C][C]0.252977925543289[/C][C]0.358825[/C][C]0.705[/C][C]0.485099[/C][C]0.242549[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]0.286731211867211[/C][C]0.576107[/C][C]0.4977[/C][C]0.62156[/C][C]0.31078[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]-0.140281941699051[/C][C]0.572234[/C][C]-0.2451[/C][C]0.807661[/C][C]0.403831[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]0.0307676256758232[/C][C]0.555972[/C][C]0.0553[/C][C]0.956157[/C][C]0.478079[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]-0.0942370090570313[/C][C]0.316676[/C][C]-0.2976[/C][C]0.767643[/C][C]0.383821[/C][/ROW]
[ROW][C]M1[/C][C]-0.211902844334609[/C][C]0.286808[/C][C]-0.7388[/C][C]0.464549[/C][C]0.232275[/C][/ROW]
[ROW][C]M2[/C][C]-0.403473617050317[/C][C]0.291209[/C][C]-1.3855[/C][C]0.173975[/C][C]0.086988[/C][/ROW]
[ROW][C]M3[/C][C]-0.249269058051509[/C][C]0.414358[/C][C]-0.6016[/C][C]0.551027[/C][C]0.275513[/C][/ROW]
[ROW][C]M4[/C][C]-0.592689012093239[/C][C]0.40213[/C][C]-1.4739[/C][C]0.148752[/C][C]0.074376[/C][/ROW]
[ROW][C]M5[/C][C]-0.528197626041862[/C][C]0.394484[/C][C]-1.339[/C][C]0.188539[/C][C]0.09427[/C][/ROW]
[ROW][C]M6[/C][C]-0.515370882802887[/C][C]0.35084[/C][C]-1.469[/C][C]0.150074[/C][C]0.075037[/C][/ROW]
[ROW][C]M7[/C][C]-0.326476270103165[/C][C]0.292308[/C][C]-1.1169[/C][C]0.271054[/C][C]0.135527[/C][/ROW]
[ROW][C]M8[/C][C]-0.038971385595141[/C][C]0.308159[/C][C]-0.1265[/C][C]0.900031[/C][C]0.450015[/C][/ROW]
[ROW][C]M9[/C][C]0.131030026188113[/C][C]0.325835[/C][C]0.4021[/C][C]0.689837[/C][C]0.344918[/C][/ROW]
[ROW][C]M10[/C][C]0.104218769786131[/C][C]0.328711[/C][C]0.3171[/C][C]0.752939[/C][C]0.376469[/C][/ROW]
[ROW][C]M11[/C][C]0.00936951584773028[/C][C]0.298661[/C][C]0.0314[/C][C]0.975137[/C][C]0.487569[/C][/ROW]
[ROW][C]t[/C][C]-0.0130676658698532[/C][C]0.007412[/C][C]-1.763[/C][C]0.085946[/C][C]0.042973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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)4.745893681902311.4849753.19590.0028040.001402
WLVrouw0.2529779255432890.3588250.7050.4850990.242549
`Yt-1`0.2867312118672110.5761070.49770.621560.31078
`Yt-2`-0.1402819416990510.572234-0.24510.8076610.403831
`Yt-3`0.03076762567582320.5559720.05530.9561570.478079
`Yt-4`-0.09423700905703130.316676-0.29760.7676430.383821
M1-0.2119028443346090.286808-0.73880.4645490.232275
M2-0.4034736170503170.291209-1.38550.1739750.086988
M3-0.2492690580515090.414358-0.60160.5510270.275513
M4-0.5926890120932390.40213-1.47390.1487520.074376
M5-0.5281976260418620.394484-1.3390.1885390.09427
M6-0.5153708828028870.35084-1.4690.1500740.075037
M7-0.3264762701031650.292308-1.11690.2710540.135527
M8-0.0389713855951410.308159-0.12650.9000310.450015
M90.1310300261881130.3258350.40210.6898370.344918
M100.1042187697861310.3287110.31710.7529390.376469
M110.009369515847730280.2986610.03140.9751370.487569
t-0.01306766586985320.007412-1.7630.0859460.042973






Multiple Linear Regression - Regression Statistics
Multiple R0.85370008363738
R-squared0.728803832802469
Adjusted R-squared0.607479231687784
F-TEST (value)6.00705731654168
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value2.25105635887068e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.416181974052504
Sum Squared Residuals6.58188254999708

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.85370008363738 \tabularnewline
R-squared & 0.728803832802469 \tabularnewline
Adjusted R-squared & 0.607479231687784 \tabularnewline
F-TEST (value) & 6.00705731654168 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 2.25105635887068e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.416181974052504 \tabularnewline
Sum Squared Residuals & 6.58188254999708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.85370008363738[/C][/ROW]
[ROW][C]R-squared[/C][C]0.728803832802469[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.607479231687784[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6.00705731654168[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]2.25105635887068e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.416181974052504[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.58188254999708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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 R0.85370008363738
R-squared0.728803832802469
Adjusted R-squared0.607479231687784
F-TEST (value)6.00705731654168
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value2.25105635887068e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.416181974052504
Sum Squared Residuals6.58188254999708






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.56.98856991869931-0.488569918699314
26.66.95872290909206-0.358722909092058
37.67.78231892804928-0.182318928049276
488.16257090907046-0.162570909070454
58.18.14123011877719-0.0412301187771918
67.77.76910544585012-0.0691054458501248
77.57.35503537066940.144964629330602
87.67.454221935867860.145778064132140
97.87.790431151506650.00956884849334667
107.87.92206859295998-0.122068592959981
117.87.85083202652003-0.0508320265200283
127.57.69373264693125-0.19373264693125
137.57.292307920891620.207692079108376
147.17.099233345693280.000766654306715076
157.57.57249211708176-0.0724921170817615
167.57.59951749965051-0.0995174996505113
177.67.550603698161180.049396301838819
187.77.36626719801550.3337328019845
197.77.185385256850060.514614743149939
207.97.432672783936120.467327216063881
218.17.69065334577040.4093466542296
228.27.709654505679270.490345494320729
238.27.577885372782850.622114627217151
248.27.441159425245040.758840574754956
257.97.177475360101250.722524639898754
267.36.994739784720330.305260215279669
276.97.35095289496016-0.450952894960158
286.67.29329323146241-0.693293231462409
296.77.23924205554948-0.539242055549475
306.97.05172363997436-0.151723639974359
3176.967111909436980.0328880905630153
327.17.20066980841795-0.100669808417948
337.27.42844951836889-0.228449518368886
347.17.45513193410954-0.355131934109542
356.97.36145792284849-0.461457922848491
3677.36739529625282-0.367395296252819
376.87.06048303611206-0.260483036112060
386.46.60063495583807-0.200634955838065
396.76.682893574834950.0171064251650543
406.66.327595918120590.27240408187941
416.46.200091901139630.199908098860370
426.36.228033928476340.0719660715236602
436.26.49866590575082-0.298665905750820
446.56.78630858105029-0.28630858105029
456.86.99046598435406-0.19046598435406
466.86.8131449672512-0.0131449672512064
476.46.50982467784863-0.109824677848631
486.16.29771263157089-0.197712631570886
495.85.98116376419576-0.181163764195756
506.15.846669004656260.253330995343740
517.26.511342485073860.688657514926141
527.36.617022441696040.682977558303964
536.96.568832226372520.331167773627478
546.16.28486978768368-0.184869787683677
555.86.19380155729274-0.393801557292736
566.26.42612689072778-0.226126890727784

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.5 & 6.98856991869931 & -0.488569918699314 \tabularnewline
2 & 6.6 & 6.95872290909206 & -0.358722909092058 \tabularnewline
3 & 7.6 & 7.78231892804928 & -0.182318928049276 \tabularnewline
4 & 8 & 8.16257090907046 & -0.162570909070454 \tabularnewline
5 & 8.1 & 8.14123011877719 & -0.0412301187771918 \tabularnewline
6 & 7.7 & 7.76910544585012 & -0.0691054458501248 \tabularnewline
7 & 7.5 & 7.3550353706694 & 0.144964629330602 \tabularnewline
8 & 7.6 & 7.45422193586786 & 0.145778064132140 \tabularnewline
9 & 7.8 & 7.79043115150665 & 0.00956884849334667 \tabularnewline
10 & 7.8 & 7.92206859295998 & -0.122068592959981 \tabularnewline
11 & 7.8 & 7.85083202652003 & -0.0508320265200283 \tabularnewline
12 & 7.5 & 7.69373264693125 & -0.19373264693125 \tabularnewline
13 & 7.5 & 7.29230792089162 & 0.207692079108376 \tabularnewline
14 & 7.1 & 7.09923334569328 & 0.000766654306715076 \tabularnewline
15 & 7.5 & 7.57249211708176 & -0.0724921170817615 \tabularnewline
16 & 7.5 & 7.59951749965051 & -0.0995174996505113 \tabularnewline
17 & 7.6 & 7.55060369816118 & 0.049396301838819 \tabularnewline
18 & 7.7 & 7.3662671980155 & 0.3337328019845 \tabularnewline
19 & 7.7 & 7.18538525685006 & 0.514614743149939 \tabularnewline
20 & 7.9 & 7.43267278393612 & 0.467327216063881 \tabularnewline
21 & 8.1 & 7.6906533457704 & 0.4093466542296 \tabularnewline
22 & 8.2 & 7.70965450567927 & 0.490345494320729 \tabularnewline
23 & 8.2 & 7.57788537278285 & 0.622114627217151 \tabularnewline
24 & 8.2 & 7.44115942524504 & 0.758840574754956 \tabularnewline
25 & 7.9 & 7.17747536010125 & 0.722524639898754 \tabularnewline
26 & 7.3 & 6.99473978472033 & 0.305260215279669 \tabularnewline
27 & 6.9 & 7.35095289496016 & -0.450952894960158 \tabularnewline
28 & 6.6 & 7.29329323146241 & -0.693293231462409 \tabularnewline
29 & 6.7 & 7.23924205554948 & -0.539242055549475 \tabularnewline
30 & 6.9 & 7.05172363997436 & -0.151723639974359 \tabularnewline
31 & 7 & 6.96711190943698 & 0.0328880905630153 \tabularnewline
32 & 7.1 & 7.20066980841795 & -0.100669808417948 \tabularnewline
33 & 7.2 & 7.42844951836889 & -0.228449518368886 \tabularnewline
34 & 7.1 & 7.45513193410954 & -0.355131934109542 \tabularnewline
35 & 6.9 & 7.36145792284849 & -0.461457922848491 \tabularnewline
36 & 7 & 7.36739529625282 & -0.367395296252819 \tabularnewline
37 & 6.8 & 7.06048303611206 & -0.260483036112060 \tabularnewline
38 & 6.4 & 6.60063495583807 & -0.200634955838065 \tabularnewline
39 & 6.7 & 6.68289357483495 & 0.0171064251650543 \tabularnewline
40 & 6.6 & 6.32759591812059 & 0.27240408187941 \tabularnewline
41 & 6.4 & 6.20009190113963 & 0.199908098860370 \tabularnewline
42 & 6.3 & 6.22803392847634 & 0.0719660715236602 \tabularnewline
43 & 6.2 & 6.49866590575082 & -0.298665905750820 \tabularnewline
44 & 6.5 & 6.78630858105029 & -0.28630858105029 \tabularnewline
45 & 6.8 & 6.99046598435406 & -0.19046598435406 \tabularnewline
46 & 6.8 & 6.8131449672512 & -0.0131449672512064 \tabularnewline
47 & 6.4 & 6.50982467784863 & -0.109824677848631 \tabularnewline
48 & 6.1 & 6.29771263157089 & -0.197712631570886 \tabularnewline
49 & 5.8 & 5.98116376419576 & -0.181163764195756 \tabularnewline
50 & 6.1 & 5.84666900465626 & 0.253330995343740 \tabularnewline
51 & 7.2 & 6.51134248507386 & 0.688657514926141 \tabularnewline
52 & 7.3 & 6.61702244169604 & 0.682977558303964 \tabularnewline
53 & 6.9 & 6.56883222637252 & 0.331167773627478 \tabularnewline
54 & 6.1 & 6.28486978768368 & -0.184869787683677 \tabularnewline
55 & 5.8 & 6.19380155729274 & -0.393801557292736 \tabularnewline
56 & 6.2 & 6.42612689072778 & -0.226126890727784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&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]6.5[/C][C]6.98856991869931[/C][C]-0.488569918699314[/C][/ROW]
[ROW][C]2[/C][C]6.6[/C][C]6.95872290909206[/C][C]-0.358722909092058[/C][/ROW]
[ROW][C]3[/C][C]7.6[/C][C]7.78231892804928[/C][C]-0.182318928049276[/C][/ROW]
[ROW][C]4[/C][C]8[/C][C]8.16257090907046[/C][C]-0.162570909070454[/C][/ROW]
[ROW][C]5[/C][C]8.1[/C][C]8.14123011877719[/C][C]-0.0412301187771918[/C][/ROW]
[ROW][C]6[/C][C]7.7[/C][C]7.76910544585012[/C][C]-0.0691054458501248[/C][/ROW]
[ROW][C]7[/C][C]7.5[/C][C]7.3550353706694[/C][C]0.144964629330602[/C][/ROW]
[ROW][C]8[/C][C]7.6[/C][C]7.45422193586786[/C][C]0.145778064132140[/C][/ROW]
[ROW][C]9[/C][C]7.8[/C][C]7.79043115150665[/C][C]0.00956884849334667[/C][/ROW]
[ROW][C]10[/C][C]7.8[/C][C]7.92206859295998[/C][C]-0.122068592959981[/C][/ROW]
[ROW][C]11[/C][C]7.8[/C][C]7.85083202652003[/C][C]-0.0508320265200283[/C][/ROW]
[ROW][C]12[/C][C]7.5[/C][C]7.69373264693125[/C][C]-0.19373264693125[/C][/ROW]
[ROW][C]13[/C][C]7.5[/C][C]7.29230792089162[/C][C]0.207692079108376[/C][/ROW]
[ROW][C]14[/C][C]7.1[/C][C]7.09923334569328[/C][C]0.000766654306715076[/C][/ROW]
[ROW][C]15[/C][C]7.5[/C][C]7.57249211708176[/C][C]-0.0724921170817615[/C][/ROW]
[ROW][C]16[/C][C]7.5[/C][C]7.59951749965051[/C][C]-0.0995174996505113[/C][/ROW]
[ROW][C]17[/C][C]7.6[/C][C]7.55060369816118[/C][C]0.049396301838819[/C][/ROW]
[ROW][C]18[/C][C]7.7[/C][C]7.3662671980155[/C][C]0.3337328019845[/C][/ROW]
[ROW][C]19[/C][C]7.7[/C][C]7.18538525685006[/C][C]0.514614743149939[/C][/ROW]
[ROW][C]20[/C][C]7.9[/C][C]7.43267278393612[/C][C]0.467327216063881[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.6906533457704[/C][C]0.4093466542296[/C][/ROW]
[ROW][C]22[/C][C]8.2[/C][C]7.70965450567927[/C][C]0.490345494320729[/C][/ROW]
[ROW][C]23[/C][C]8.2[/C][C]7.57788537278285[/C][C]0.622114627217151[/C][/ROW]
[ROW][C]24[/C][C]8.2[/C][C]7.44115942524504[/C][C]0.758840574754956[/C][/ROW]
[ROW][C]25[/C][C]7.9[/C][C]7.17747536010125[/C][C]0.722524639898754[/C][/ROW]
[ROW][C]26[/C][C]7.3[/C][C]6.99473978472033[/C][C]0.305260215279669[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]7.35095289496016[/C][C]-0.450952894960158[/C][/ROW]
[ROW][C]28[/C][C]6.6[/C][C]7.29329323146241[/C][C]-0.693293231462409[/C][/ROW]
[ROW][C]29[/C][C]6.7[/C][C]7.23924205554948[/C][C]-0.539242055549475[/C][/ROW]
[ROW][C]30[/C][C]6.9[/C][C]7.05172363997436[/C][C]-0.151723639974359[/C][/ROW]
[ROW][C]31[/C][C]7[/C][C]6.96711190943698[/C][C]0.0328880905630153[/C][/ROW]
[ROW][C]32[/C][C]7.1[/C][C]7.20066980841795[/C][C]-0.100669808417948[/C][/ROW]
[ROW][C]33[/C][C]7.2[/C][C]7.42844951836889[/C][C]-0.228449518368886[/C][/ROW]
[ROW][C]34[/C][C]7.1[/C][C]7.45513193410954[/C][C]-0.355131934109542[/C][/ROW]
[ROW][C]35[/C][C]6.9[/C][C]7.36145792284849[/C][C]-0.461457922848491[/C][/ROW]
[ROW][C]36[/C][C]7[/C][C]7.36739529625282[/C][C]-0.367395296252819[/C][/ROW]
[ROW][C]37[/C][C]6.8[/C][C]7.06048303611206[/C][C]-0.260483036112060[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.60063495583807[/C][C]-0.200634955838065[/C][/ROW]
[ROW][C]39[/C][C]6.7[/C][C]6.68289357483495[/C][C]0.0171064251650543[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]6.32759591812059[/C][C]0.27240408187941[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]6.20009190113963[/C][C]0.199908098860370[/C][/ROW]
[ROW][C]42[/C][C]6.3[/C][C]6.22803392847634[/C][C]0.0719660715236602[/C][/ROW]
[ROW][C]43[/C][C]6.2[/C][C]6.49866590575082[/C][C]-0.298665905750820[/C][/ROW]
[ROW][C]44[/C][C]6.5[/C][C]6.78630858105029[/C][C]-0.28630858105029[/C][/ROW]
[ROW][C]45[/C][C]6.8[/C][C]6.99046598435406[/C][C]-0.19046598435406[/C][/ROW]
[ROW][C]46[/C][C]6.8[/C][C]6.8131449672512[/C][C]-0.0131449672512064[/C][/ROW]
[ROW][C]47[/C][C]6.4[/C][C]6.50982467784863[/C][C]-0.109824677848631[/C][/ROW]
[ROW][C]48[/C][C]6.1[/C][C]6.29771263157089[/C][C]-0.197712631570886[/C][/ROW]
[ROW][C]49[/C][C]5.8[/C][C]5.98116376419576[/C][C]-0.181163764195756[/C][/ROW]
[ROW][C]50[/C][C]6.1[/C][C]5.84666900465626[/C][C]0.253330995343740[/C][/ROW]
[ROW][C]51[/C][C]7.2[/C][C]6.51134248507386[/C][C]0.688657514926141[/C][/ROW]
[ROW][C]52[/C][C]7.3[/C][C]6.61702244169604[/C][C]0.682977558303964[/C][/ROW]
[ROW][C]53[/C][C]6.9[/C][C]6.56883222637252[/C][C]0.331167773627478[/C][/ROW]
[ROW][C]54[/C][C]6.1[/C][C]6.28486978768368[/C][C]-0.184869787683677[/C][/ROW]
[ROW][C]55[/C][C]5.8[/C][C]6.19380155729274[/C][C]-0.393801557292736[/C][/ROW]
[ROW][C]56[/C][C]6.2[/C][C]6.42612689072778[/C][C]-0.226126890727784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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
16.56.98856991869931-0.488569918699314
26.66.95872290909206-0.358722909092058
37.67.78231892804928-0.182318928049276
488.16257090907046-0.162570909070454
58.18.14123011877719-0.0412301187771918
67.77.76910544585012-0.0691054458501248
77.57.35503537066940.144964629330602
87.67.454221935867860.145778064132140
97.87.790431151506650.00956884849334667
107.87.92206859295998-0.122068592959981
117.87.85083202652003-0.0508320265200283
127.57.69373264693125-0.19373264693125
137.57.292307920891620.207692079108376
147.17.099233345693280.000766654306715076
157.57.57249211708176-0.0724921170817615
167.57.59951749965051-0.0995174996505113
177.67.550603698161180.049396301838819
187.77.36626719801550.3337328019845
197.77.185385256850060.514614743149939
207.97.432672783936120.467327216063881
218.17.69065334577040.4093466542296
228.27.709654505679270.490345494320729
238.27.577885372782850.622114627217151
248.27.441159425245040.758840574754956
257.97.177475360101250.722524639898754
267.36.994739784720330.305260215279669
276.97.35095289496016-0.450952894960158
286.67.29329323146241-0.693293231462409
296.77.23924205554948-0.539242055549475
306.97.05172363997436-0.151723639974359
3176.967111909436980.0328880905630153
327.17.20066980841795-0.100669808417948
337.27.42844951836889-0.228449518368886
347.17.45513193410954-0.355131934109542
356.97.36145792284849-0.461457922848491
3677.36739529625282-0.367395296252819
376.87.06048303611206-0.260483036112060
386.46.60063495583807-0.200634955838065
396.76.682893574834950.0171064251650543
406.66.327595918120590.27240408187941
416.46.200091901139630.199908098860370
426.36.228033928476340.0719660715236602
436.26.49866590575082-0.298665905750820
446.56.78630858105029-0.28630858105029
456.86.99046598435406-0.19046598435406
466.86.8131449672512-0.0131449672512064
476.46.50982467784863-0.109824677848631
486.16.29771263157089-0.197712631570886
495.85.98116376419576-0.181163764195756
506.15.846669004656260.253330995343740
517.26.511342485073860.688657514926141
527.36.617022441696040.682977558303964
536.96.568832226372520.331167773627478
546.16.28486978768368-0.184869787683677
555.86.19380155729274-0.393801557292736
566.26.42612689072778-0.226126890727784






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.007501102739497970.01500220547899590.992498897260502
220.007983054140283740.01596610828056750.992016945859716
230.007403454693459230.01480690938691850.99259654530654
240.02225756132317550.04451512264635090.977742438676825
250.02940474268956190.05880948537912370.970595257310438
260.01668544919523080.03337089839046160.98331455080477
270.06077297686069420.1215459537213880.939227023139306
280.565485635792690.8690287284146190.434514364207309
290.9217404917456730.1565190165086540.078259508254327
300.902006687259240.1959866254815210.0979933127407606
310.9928982097807810.01420358043843740.00710179021921872
320.9927913683094980.01441726338100420.00720863169050208
330.9861185593043740.02776288139125130.0138814406956256
340.9834463797768740.03310724044625220.0165536202231261
350.9787079889447460.04258402211050790.0212920110552540

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.00750110273949797 & 0.0150022054789959 & 0.992498897260502 \tabularnewline
22 & 0.00798305414028374 & 0.0159661082805675 & 0.992016945859716 \tabularnewline
23 & 0.00740345469345923 & 0.0148069093869185 & 0.99259654530654 \tabularnewline
24 & 0.0222575613231755 & 0.0445151226463509 & 0.977742438676825 \tabularnewline
25 & 0.0294047426895619 & 0.0588094853791237 & 0.970595257310438 \tabularnewline
26 & 0.0166854491952308 & 0.0333708983904616 & 0.98331455080477 \tabularnewline
27 & 0.0607729768606942 & 0.121545953721388 & 0.939227023139306 \tabularnewline
28 & 0.56548563579269 & 0.869028728414619 & 0.434514364207309 \tabularnewline
29 & 0.921740491745673 & 0.156519016508654 & 0.078259508254327 \tabularnewline
30 & 0.90200668725924 & 0.195986625481521 & 0.0979933127407606 \tabularnewline
31 & 0.992898209780781 & 0.0142035804384374 & 0.00710179021921872 \tabularnewline
32 & 0.992791368309498 & 0.0144172633810042 & 0.00720863169050208 \tabularnewline
33 & 0.986118559304374 & 0.0277628813912513 & 0.0138814406956256 \tabularnewline
34 & 0.983446379776874 & 0.0331072404462522 & 0.0165536202231261 \tabularnewline
35 & 0.978707988944746 & 0.0425840221105079 & 0.0212920110552540 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.00750110273949797[/C][C]0.0150022054789959[/C][C]0.992498897260502[/C][/ROW]
[ROW][C]22[/C][C]0.00798305414028374[/C][C]0.0159661082805675[/C][C]0.992016945859716[/C][/ROW]
[ROW][C]23[/C][C]0.00740345469345923[/C][C]0.0148069093869185[/C][C]0.99259654530654[/C][/ROW]
[ROW][C]24[/C][C]0.0222575613231755[/C][C]0.0445151226463509[/C][C]0.977742438676825[/C][/ROW]
[ROW][C]25[/C][C]0.0294047426895619[/C][C]0.0588094853791237[/C][C]0.970595257310438[/C][/ROW]
[ROW][C]26[/C][C]0.0166854491952308[/C][C]0.0333708983904616[/C][C]0.98331455080477[/C][/ROW]
[ROW][C]27[/C][C]0.0607729768606942[/C][C]0.121545953721388[/C][C]0.939227023139306[/C][/ROW]
[ROW][C]28[/C][C]0.56548563579269[/C][C]0.869028728414619[/C][C]0.434514364207309[/C][/ROW]
[ROW][C]29[/C][C]0.921740491745673[/C][C]0.156519016508654[/C][C]0.078259508254327[/C][/ROW]
[ROW][C]30[/C][C]0.90200668725924[/C][C]0.195986625481521[/C][C]0.0979933127407606[/C][/ROW]
[ROW][C]31[/C][C]0.992898209780781[/C][C]0.0142035804384374[/C][C]0.00710179021921872[/C][/ROW]
[ROW][C]32[/C][C]0.992791368309498[/C][C]0.0144172633810042[/C][C]0.00720863169050208[/C][/ROW]
[ROW][C]33[/C][C]0.986118559304374[/C][C]0.0277628813912513[/C][C]0.0138814406956256[/C][/ROW]
[ROW][C]34[/C][C]0.983446379776874[/C][C]0.0331072404462522[/C][C]0.0165536202231261[/C][/ROW]
[ROW][C]35[/C][C]0.978707988944746[/C][C]0.0425840221105079[/C][C]0.0212920110552540[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.007501102739497970.01500220547899590.992498897260502
220.007983054140283740.01596610828056750.992016945859716
230.007403454693459230.01480690938691850.99259654530654
240.02225756132317550.04451512264635090.977742438676825
250.02940474268956190.05880948537912370.970595257310438
260.01668544919523080.03337089839046160.98331455080477
270.06077297686069420.1215459537213880.939227023139306
280.565485635792690.8690287284146190.434514364207309
290.9217404917456730.1565190165086540.078259508254327
300.902006687259240.1959866254815210.0979933127407606
310.9928982097807810.01420358043843740.00710179021921872
320.9927913683094980.01441726338100420.00720863169050208
330.9861185593043740.02776288139125130.0138814406956256
340.9834463797768740.03310724044625220.0165536202231261
350.9787079889447460.04258402211050790.0212920110552540






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level100.666666666666667NOK
10% type I error level110.733333333333333NOK

\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 & 10 & 0.666666666666667 & NOK \tabularnewline
10% type I error level & 11 & 0.733333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58311&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]10[/C][C]0.666666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.733333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58311&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58311&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 level100.666666666666667NOK
10% type I error level110.733333333333333NOK


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