FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationTue, 24 Nov 2009 14:03:26 -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/24/t125909664709bwct50kpk84xb.htm/, Retrieved Thu, 19 Jun 2025 20:24:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59284, Retrieved Thu, 19 Jun 2025 20:24:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact323

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] [4 lag ] [2009-11-19 20:53:48] [ba905ddf7cdf9ecb063c35348c4dab2e]
-   PD        [Multiple Regression] [multiple ] [2009-11-24 21:03:26] [244731fa3e7e6c85774b8c0902c58f85] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,4	0	1,7	1	1,2	1,4
2	0	2,4	1,7	1	1,2
2,1	0	2	2,4	1,7	1
2	0	2,1	2	2,4	1,7
1,8	0	2	2,1	2	2,4
2,7	0	1,8	2	2,1	2
2,3	0	2,7	1,8	2	2,1
1,9	0	2,3	2,7	1,8	2
2	0	1,9	2,3	2,7	1,8
2,3	0	2	1,9	2,3	2,7
2,8	0	2,3	2	1,9	2,3
2,4	0	2,8	2,3	2	1,9
2,3	0	2,4	2,8	2,3	2
2,7	0	2,3	2,4	2,8	2,3
2,7	0	2,7	2,3	2,4	2,8
2,9	0	2,7	2,7	2,3	2,4
3	0	2,9	2,7	2,7	2,3
2,2	0	3	2,9	2,7	2,7
2,3	0	2,2	3	2,9	2,7
2,8	0	2,3	2,2	3	2,9
2,8	0	2,8	2,3	2,2	3
2,8	0	2,8	2,8	2,3	2,2
2,2	0	2,8	2,8	2,8	2,3
2,6	0	2,2	2,8	2,8	2,8
2,8	0	2,6	2,2	2,8	2,8
2,5	0	2,8	2,6	2,2	2,8
2,4	0	2,5	2,8	2,6	2,2
2,3	0	2,4	2,5	2,8	2,6
1,9	0	2,3	2,4	2,5	2,8
1,7	0	1,9	2,3	2,4	2,5
2	0	1,7	1,9	2,3	2,4
2,1	0	2	1,7	1,9	2,3
1,7	0	2,1	2	1,7	1,9
1,8	0	1,7	2,1	2	1,7
1,8	0	1,8	1,7	2,1	2
1,8	0	1,8	1,8	1,7	2,1
1,3	1	1,8	1,8	1,8	1,7
1,3	1	1,3	1,8	1,8	1,8
1,3	1	1,3	1,3	1,8	1,8
1,2	1	1,3	1,3	1,3	1,8
1,4	1	1,2	1,3	1,3	1,3
2,2	1	1,4	1,2	1,3	1,3
2,9	1	2,2	1,4	1,2	1,3
3,1	1	2,9	2,2	1,4	1,2
3,5	1	3,1	2,9	2,2	1,4
3,6	1	3,5	3,1	2,9	2,2
4,4	1	3,6	3,5	3,1	2,9
4,1	1	4,4	3,6	3,5	3,1
5,1	1	4,1	4,4	3,6	3,5
5,8	1	5,1	4,1	4,4	3,6
5,9	1	5,8	5,1	4,1	4,4
5,4	1	5,9	5,8	5,1	4,1
5,5	1	5,4	5,9	5,8	5,1
4,8	1	5,5	5,4	5,9	5,8
3,2	1	4,8	5,5	5,4	5,9
2,7	1	3,2	4,8	5,5	5,4

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=59284&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=59284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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
y[t] = + 0.264585623036714 + 0.136019702329563x[t] + 1.1180927364462y1[t] -0.26871069986116y2[t] + 0.274416880874272y3[t] -0.284488421665747y4[t] + 0.289579993080271M1[t] + 0.0893609542088653M2[t] + 0.0956344083568998M3[t] -0.074459306273987M4[t] + 0.0764602746631292M5[t] + 0.105570035656608M6[t] -0.0471979987964152M7[t] + 0.110257357802178M8[t] + 0.027425940682833M9[t] + 0.152467811299498M10[t] + 0.216128371847527M11[t] + 0.00063940059680417t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  0.264585623036714 +  0.136019702329563x[t] +  1.1180927364462y1[t] -0.26871069986116y2[t] +  0.274416880874272y3[t] -0.284488421665747y4[t] +  0.289579993080271M1[t] +  0.0893609542088653M2[t] +  0.0956344083568998M3[t] -0.074459306273987M4[t] +  0.0764602746631292M5[t] +  0.105570035656608M6[t] -0.0471979987964152M7[t] +  0.110257357802178M8[t] +  0.027425940682833M9[t] +  0.152467811299498M10[t] +  0.216128371847527M11[t] +  0.00063940059680417t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59284&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  0.264585623036714 +  0.136019702329563x[t] +  1.1180927364462y1[t] -0.26871069986116y2[t] +  0.274416880874272y3[t] -0.284488421665747y4[t] +  0.289579993080271M1[t] +  0.0893609542088653M2[t] +  0.0956344083568998M3[t] -0.074459306273987M4[t] +  0.0764602746631292M5[t] +  0.105570035656608M6[t] -0.0471979987964152M7[t] +  0.110257357802178M8[t] +  0.027425940682833M9[t] +  0.152467811299498M10[t] +  0.216128371847527M11[t] +  0.00063940059680417t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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] = + 0.264585623036714 + 0.136019702329563x[t] + 1.1180927364462y1[t] -0.26871069986116y2[t] + 0.274416880874272y3[t] -0.284488421665747y4[t] + 0.289579993080271M1[t] + 0.0893609542088653M2[t] + 0.0956344083568998M3[t] -0.074459306273987M4[t] + 0.0764602746631292M5[t] + 0.105570035656608M6[t] -0.0471979987964152M7[t] + 0.110257357802178M8[t] + 0.027425940682833M9[t] + 0.152467811299498M10[t] + 0.216128371847527M11[t] + 0.00063940059680417t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.2645856230367140.3277440.80730.4245210.212261
x0.1360197023295630.2803440.48520.6303290.315164
y11.11809273644620.1553897.195400
y2-0.268710699861160.234661-1.14510.2593290.129665
y30.2744168808742720.2388751.14880.2578220.128911
y4-0.2844884216657470.187206-1.51970.1368760.068438
M10.2895799930802710.3403490.85080.4001920.200096
M20.08936095420886530.3377540.26460.7927680.396384
M30.09563440835689980.337340.28350.7783360.389168
M4-0.0744593062739870.337874-0.22040.8267580.413379
M50.07646027466312920.3392820.22540.8229080.411454
M60.1055700356566080.3393430.31110.7574240.378712
M7-0.04719799879641520.338018-0.13960.8896880.444844
M80.1102573578021780.3383320.32590.74630.37315
M90.0274259406828330.3506860.07820.9380740.469037
M100.1524678112994980.3503880.43510.6659220.332961
M110.2161283718475270.3488720.61950.539280.26964
t0.000639400596804170.0087950.07270.9424250.471213

\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) & 0.264585623036714 & 0.327744 & 0.8073 & 0.424521 & 0.212261 \tabularnewline
x & 0.136019702329563 & 0.280344 & 0.4852 & 0.630329 & 0.315164 \tabularnewline
y1 & 1.1180927364462 & 0.155389 & 7.1954 & 0 & 0 \tabularnewline
y2 & -0.26871069986116 & 0.234661 & -1.1451 & 0.259329 & 0.129665 \tabularnewline
y3 & 0.274416880874272 & 0.238875 & 1.1488 & 0.257822 & 0.128911 \tabularnewline
y4 & -0.284488421665747 & 0.187206 & -1.5197 & 0.136876 & 0.068438 \tabularnewline
M1 & 0.289579993080271 & 0.340349 & 0.8508 & 0.400192 & 0.200096 \tabularnewline
M2 & 0.0893609542088653 & 0.337754 & 0.2646 & 0.792768 & 0.396384 \tabularnewline
M3 & 0.0956344083568998 & 0.33734 & 0.2835 & 0.778336 & 0.389168 \tabularnewline
M4 & -0.074459306273987 & 0.337874 & -0.2204 & 0.826758 & 0.413379 \tabularnewline
M5 & 0.0764602746631292 & 0.339282 & 0.2254 & 0.822908 & 0.411454 \tabularnewline
M6 & 0.105570035656608 & 0.339343 & 0.3111 & 0.757424 & 0.378712 \tabularnewline
M7 & -0.0471979987964152 & 0.338018 & -0.1396 & 0.889688 & 0.444844 \tabularnewline
M8 & 0.110257357802178 & 0.338332 & 0.3259 & 0.7463 & 0.37315 \tabularnewline
M9 & 0.027425940682833 & 0.350686 & 0.0782 & 0.938074 & 0.469037 \tabularnewline
M10 & 0.152467811299498 & 0.350388 & 0.4351 & 0.665922 & 0.332961 \tabularnewline
M11 & 0.216128371847527 & 0.348872 & 0.6195 & 0.53928 & 0.26964 \tabularnewline
t & 0.00063940059680417 & 0.008795 & 0.0727 & 0.942425 & 0.471213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59284&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]0.264585623036714[/C][C]0.327744[/C][C]0.8073[/C][C]0.424521[/C][C]0.212261[/C][/ROW]
[ROW][C]x[/C][C]0.136019702329563[/C][C]0.280344[/C][C]0.4852[/C][C]0.630329[/C][C]0.315164[/C][/ROW]
[ROW][C]y1[/C][C]1.1180927364462[/C][C]0.155389[/C][C]7.1954[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]y2[/C][C]-0.26871069986116[/C][C]0.234661[/C][C]-1.1451[/C][C]0.259329[/C][C]0.129665[/C][/ROW]
[ROW][C]y3[/C][C]0.274416880874272[/C][C]0.238875[/C][C]1.1488[/C][C]0.257822[/C][C]0.128911[/C][/ROW]
[ROW][C]y4[/C][C]-0.284488421665747[/C][C]0.187206[/C][C]-1.5197[/C][C]0.136876[/C][C]0.068438[/C][/ROW]
[ROW][C]M1[/C][C]0.289579993080271[/C][C]0.340349[/C][C]0.8508[/C][C]0.400192[/C][C]0.200096[/C][/ROW]
[ROW][C]M2[/C][C]0.0893609542088653[/C][C]0.337754[/C][C]0.2646[/C][C]0.792768[/C][C]0.396384[/C][/ROW]
[ROW][C]M3[/C][C]0.0956344083568998[/C][C]0.33734[/C][C]0.2835[/C][C]0.778336[/C][C]0.389168[/C][/ROW]
[ROW][C]M4[/C][C]-0.074459306273987[/C][C]0.337874[/C][C]-0.2204[/C][C]0.826758[/C][C]0.413379[/C][/ROW]
[ROW][C]M5[/C][C]0.0764602746631292[/C][C]0.339282[/C][C]0.2254[/C][C]0.822908[/C][C]0.411454[/C][/ROW]
[ROW][C]M6[/C][C]0.105570035656608[/C][C]0.339343[/C][C]0.3111[/C][C]0.757424[/C][C]0.378712[/C][/ROW]
[ROW][C]M7[/C][C]-0.0471979987964152[/C][C]0.338018[/C][C]-0.1396[/C][C]0.889688[/C][C]0.444844[/C][/ROW]
[ROW][C]M8[/C][C]0.110257357802178[/C][C]0.338332[/C][C]0.3259[/C][C]0.7463[/C][C]0.37315[/C][/ROW]
[ROW][C]M9[/C][C]0.027425940682833[/C][C]0.350686[/C][C]0.0782[/C][C]0.938074[/C][C]0.469037[/C][/ROW]
[ROW][C]M10[/C][C]0.152467811299498[/C][C]0.350388[/C][C]0.4351[/C][C]0.665922[/C][C]0.332961[/C][/ROW]
[ROW][C]M11[/C][C]0.216128371847527[/C][C]0.348872[/C][C]0.6195[/C][C]0.53928[/C][C]0.26964[/C][/ROW]
[ROW][C]t[/C][C]0.00063940059680417[/C][C]0.008795[/C][C]0.0727[/C][C]0.942425[/C][C]0.471213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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)0.2645856230367140.3277440.80730.4245210.212261
x0.1360197023295630.2803440.48520.6303290.315164
y11.11809273644620.1553897.195400
y2-0.268710699861160.234661-1.14510.2593290.129665
y30.2744168808742720.2388751.14880.2578220.128911
y4-0.2844884216657470.187206-1.51970.1368760.068438
M10.2895799930802710.3403490.85080.4001920.200096
M20.08936095420886530.3377540.26460.7927680.396384
M30.09563440835689980.337340.28350.7783360.389168
M4-0.0744593062739870.337874-0.22040.8267580.413379
M50.07646027466312920.3392820.22540.8229080.411454
M60.1055700356566080.3393430.31110.7574240.378712
M7-0.04719799879641520.338018-0.13960.8896880.444844
M80.1102573578021780.3383320.32590.74630.37315
M90.0274259406828330.3506860.07820.9380740.469037
M100.1524678112994980.3503880.43510.6659220.332961
M110.2161283718475270.3488720.61950.539280.26964
t0.000639400596804170.0087950.07270.9424250.471213






Multiple Linear Regression - Regression Statistics
Multiple R0.934795605561394
R-squared0.873842824176893
Adjusted R-squared0.81740408762445
F-TEST (value)15.4830330647980
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.88156173869447e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.492188623641708
Sum Squared Residuals9.2054863672081

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.934795605561394 \tabularnewline
R-squared & 0.873842824176893 \tabularnewline
Adjusted R-squared & 0.81740408762445 \tabularnewline
F-TEST (value) & 15.4830330647980 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 3.88156173869447e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.492188623641708 \tabularnewline
Sum Squared Residuals & 9.2054863672081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59284&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.934795605561394[/C][/ROW]
[ROW][C]R-squared[/C][C]0.873842824176893[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.81740408762445[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.4830330647980[/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]3.88156173869447e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.492188623641708[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]9.2054863672081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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 R0.934795605561394
R-squared0.873842824176893
Adjusted R-squared0.81740408762445
F-TEST (value)15.4830330647980
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.88156173869447e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.492188623641708
Sum Squared Residuals9.2054863672081






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.42.117868435528250.282131564471752
222.51487053102147-0.51487053102147
32.12.13543830223016-0.0354383022301558
422.17822746323113-0.178227463231126
51.81.88219745361858-0.0821974536185777
62.71.856436194659460.843563805340538
72.32.70844263332305-0.408442633323055
81.92.15102613205665-0.251026132056648
922.03295417802008-0.0329541780200847
102.32.012122670973760.287877329026242
112.82.389007999382920.410992000617075
122.42.79318924315068-0.393189243150680
132.32.5556924144144-0.255692414414402
142.72.403649696377060.296350303622945
152.72.632659752503910.0673402474960914
162.92.442074839104230.457925160895766
1732.955467962443680.0445320375563233
182.22.92948888904005-0.72948888904005
192.31.910898372215610.389101627784392
202.82.366314966698830.433685033301168
212.82.568315901547280.231684098452717
222.82.8146742482502-0.0146742482501972
232.22.98773380766559-0.78773380766559
242.61.959144983714280.640855016285725
252.82.85782789188653-0.0578278918865263
262.52.60973239243214-0.109732392432137
272.42.50793509162004-0.107935091620041
282.32.248372721408240.0516272785917584
291.92.17577075068823-0.275770750688227
301.71.84305872609844-0.143058726098443
3121.575802978976600.424197021023405
322.12.041749786894950.058250213105049
331.72.04966582655013-0.349665826550127
341.81.84046168179443-0.0404616817944307
351.82.06615035811605-0.26615035811605
361.81.685574722362930.114425277637072
371.32.25305087512329-0.953050875123293
381.31.46597602645902-0.165976026459016
391.31.60724423113443-0.307244231134435
401.21.30058147666322-0.100581476663216
411.41.48257539538539-0.0825753953853896
422.21.762814174251030.437185825748971
432.92.423975901492110.476024098507889
443.13.23309923265235-0.133099232652350
453.53.349064093882510.150935906117495
463.63.83274139898162-0.232741398981615
474.43.757107834835430.642892165164565
484.14.46209105077212-0.362091050772117
495.14.115560383047530.984439616952469
505.85.305771353710320.494228646289679
515.95.516722622511460.38327737748854
525.45.63074349959318-0.230743499593182
535.55.103988437864130.396011562135871
544.85.20820201595102-0.408202015951016
553.24.08088011399263-0.88088011399263
562.72.80780988169722-0.107809881697220

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.4 & 2.11786843552825 & 0.282131564471752 \tabularnewline
2 & 2 & 2.51487053102147 & -0.51487053102147 \tabularnewline
3 & 2.1 & 2.13543830223016 & -0.0354383022301558 \tabularnewline
4 & 2 & 2.17822746323113 & -0.178227463231126 \tabularnewline
5 & 1.8 & 1.88219745361858 & -0.0821974536185777 \tabularnewline
6 & 2.7 & 1.85643619465946 & 0.843563805340538 \tabularnewline
7 & 2.3 & 2.70844263332305 & -0.408442633323055 \tabularnewline
8 & 1.9 & 2.15102613205665 & -0.251026132056648 \tabularnewline
9 & 2 & 2.03295417802008 & -0.0329541780200847 \tabularnewline
10 & 2.3 & 2.01212267097376 & 0.287877329026242 \tabularnewline
11 & 2.8 & 2.38900799938292 & 0.410992000617075 \tabularnewline
12 & 2.4 & 2.79318924315068 & -0.393189243150680 \tabularnewline
13 & 2.3 & 2.5556924144144 & -0.255692414414402 \tabularnewline
14 & 2.7 & 2.40364969637706 & 0.296350303622945 \tabularnewline
15 & 2.7 & 2.63265975250391 & 0.0673402474960914 \tabularnewline
16 & 2.9 & 2.44207483910423 & 0.457925160895766 \tabularnewline
17 & 3 & 2.95546796244368 & 0.0445320375563233 \tabularnewline
18 & 2.2 & 2.92948888904005 & -0.72948888904005 \tabularnewline
19 & 2.3 & 1.91089837221561 & 0.389101627784392 \tabularnewline
20 & 2.8 & 2.36631496669883 & 0.433685033301168 \tabularnewline
21 & 2.8 & 2.56831590154728 & 0.231684098452717 \tabularnewline
22 & 2.8 & 2.8146742482502 & -0.0146742482501972 \tabularnewline
23 & 2.2 & 2.98773380766559 & -0.78773380766559 \tabularnewline
24 & 2.6 & 1.95914498371428 & 0.640855016285725 \tabularnewline
25 & 2.8 & 2.85782789188653 & -0.0578278918865263 \tabularnewline
26 & 2.5 & 2.60973239243214 & -0.109732392432137 \tabularnewline
27 & 2.4 & 2.50793509162004 & -0.107935091620041 \tabularnewline
28 & 2.3 & 2.24837272140824 & 0.0516272785917584 \tabularnewline
29 & 1.9 & 2.17577075068823 & -0.275770750688227 \tabularnewline
30 & 1.7 & 1.84305872609844 & -0.143058726098443 \tabularnewline
31 & 2 & 1.57580297897660 & 0.424197021023405 \tabularnewline
32 & 2.1 & 2.04174978689495 & 0.058250213105049 \tabularnewline
33 & 1.7 & 2.04966582655013 & -0.349665826550127 \tabularnewline
34 & 1.8 & 1.84046168179443 & -0.0404616817944307 \tabularnewline
35 & 1.8 & 2.06615035811605 & -0.26615035811605 \tabularnewline
36 & 1.8 & 1.68557472236293 & 0.114425277637072 \tabularnewline
37 & 1.3 & 2.25305087512329 & -0.953050875123293 \tabularnewline
38 & 1.3 & 1.46597602645902 & -0.165976026459016 \tabularnewline
39 & 1.3 & 1.60724423113443 & -0.307244231134435 \tabularnewline
40 & 1.2 & 1.30058147666322 & -0.100581476663216 \tabularnewline
41 & 1.4 & 1.48257539538539 & -0.0825753953853896 \tabularnewline
42 & 2.2 & 1.76281417425103 & 0.437185825748971 \tabularnewline
43 & 2.9 & 2.42397590149211 & 0.476024098507889 \tabularnewline
44 & 3.1 & 3.23309923265235 & -0.133099232652350 \tabularnewline
45 & 3.5 & 3.34906409388251 & 0.150935906117495 \tabularnewline
46 & 3.6 & 3.83274139898162 & -0.232741398981615 \tabularnewline
47 & 4.4 & 3.75710783483543 & 0.642892165164565 \tabularnewline
48 & 4.1 & 4.46209105077212 & -0.362091050772117 \tabularnewline
49 & 5.1 & 4.11556038304753 & 0.984439616952469 \tabularnewline
50 & 5.8 & 5.30577135371032 & 0.494228646289679 \tabularnewline
51 & 5.9 & 5.51672262251146 & 0.38327737748854 \tabularnewline
52 & 5.4 & 5.63074349959318 & -0.230743499593182 \tabularnewline
53 & 5.5 & 5.10398843786413 & 0.396011562135871 \tabularnewline
54 & 4.8 & 5.20820201595102 & -0.408202015951016 \tabularnewline
55 & 3.2 & 4.08088011399263 & -0.88088011399263 \tabularnewline
56 & 2.7 & 2.80780988169722 & -0.107809881697220 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59284&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]2.4[/C][C]2.11786843552825[/C][C]0.282131564471752[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]2.51487053102147[/C][C]-0.51487053102147[/C][/ROW]
[ROW][C]3[/C][C]2.1[/C][C]2.13543830223016[/C][C]-0.0354383022301558[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.17822746323113[/C][C]-0.178227463231126[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]1.88219745361858[/C][C]-0.0821974536185777[/C][/ROW]
[ROW][C]6[/C][C]2.7[/C][C]1.85643619465946[/C][C]0.843563805340538[/C][/ROW]
[ROW][C]7[/C][C]2.3[/C][C]2.70844263332305[/C][C]-0.408442633323055[/C][/ROW]
[ROW][C]8[/C][C]1.9[/C][C]2.15102613205665[/C][C]-0.251026132056648[/C][/ROW]
[ROW][C]9[/C][C]2[/C][C]2.03295417802008[/C][C]-0.0329541780200847[/C][/ROW]
[ROW][C]10[/C][C]2.3[/C][C]2.01212267097376[/C][C]0.287877329026242[/C][/ROW]
[ROW][C]11[/C][C]2.8[/C][C]2.38900799938292[/C][C]0.410992000617075[/C][/ROW]
[ROW][C]12[/C][C]2.4[/C][C]2.79318924315068[/C][C]-0.393189243150680[/C][/ROW]
[ROW][C]13[/C][C]2.3[/C][C]2.5556924144144[/C][C]-0.255692414414402[/C][/ROW]
[ROW][C]14[/C][C]2.7[/C][C]2.40364969637706[/C][C]0.296350303622945[/C][/ROW]
[ROW][C]15[/C][C]2.7[/C][C]2.63265975250391[/C][C]0.0673402474960914[/C][/ROW]
[ROW][C]16[/C][C]2.9[/C][C]2.44207483910423[/C][C]0.457925160895766[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]2.95546796244368[/C][C]0.0445320375563233[/C][/ROW]
[ROW][C]18[/C][C]2.2[/C][C]2.92948888904005[/C][C]-0.72948888904005[/C][/ROW]
[ROW][C]19[/C][C]2.3[/C][C]1.91089837221561[/C][C]0.389101627784392[/C][/ROW]
[ROW][C]20[/C][C]2.8[/C][C]2.36631496669883[/C][C]0.433685033301168[/C][/ROW]
[ROW][C]21[/C][C]2.8[/C][C]2.56831590154728[/C][C]0.231684098452717[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]2.8146742482502[/C][C]-0.0146742482501972[/C][/ROW]
[ROW][C]23[/C][C]2.2[/C][C]2.98773380766559[/C][C]-0.78773380766559[/C][/ROW]
[ROW][C]24[/C][C]2.6[/C][C]1.95914498371428[/C][C]0.640855016285725[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.85782789188653[/C][C]-0.0578278918865263[/C][/ROW]
[ROW][C]26[/C][C]2.5[/C][C]2.60973239243214[/C][C]-0.109732392432137[/C][/ROW]
[ROW][C]27[/C][C]2.4[/C][C]2.50793509162004[/C][C]-0.107935091620041[/C][/ROW]
[ROW][C]28[/C][C]2.3[/C][C]2.24837272140824[/C][C]0.0516272785917584[/C][/ROW]
[ROW][C]29[/C][C]1.9[/C][C]2.17577075068823[/C][C]-0.275770750688227[/C][/ROW]
[ROW][C]30[/C][C]1.7[/C][C]1.84305872609844[/C][C]-0.143058726098443[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]1.57580297897660[/C][C]0.424197021023405[/C][/ROW]
[ROW][C]32[/C][C]2.1[/C][C]2.04174978689495[/C][C]0.058250213105049[/C][/ROW]
[ROW][C]33[/C][C]1.7[/C][C]2.04966582655013[/C][C]-0.349665826550127[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.84046168179443[/C][C]-0.0404616817944307[/C][/ROW]
[ROW][C]35[/C][C]1.8[/C][C]2.06615035811605[/C][C]-0.26615035811605[/C][/ROW]
[ROW][C]36[/C][C]1.8[/C][C]1.68557472236293[/C][C]0.114425277637072[/C][/ROW]
[ROW][C]37[/C][C]1.3[/C][C]2.25305087512329[/C][C]-0.953050875123293[/C][/ROW]
[ROW][C]38[/C][C]1.3[/C][C]1.46597602645902[/C][C]-0.165976026459016[/C][/ROW]
[ROW][C]39[/C][C]1.3[/C][C]1.60724423113443[/C][C]-0.307244231134435[/C][/ROW]
[ROW][C]40[/C][C]1.2[/C][C]1.30058147666322[/C][C]-0.100581476663216[/C][/ROW]
[ROW][C]41[/C][C]1.4[/C][C]1.48257539538539[/C][C]-0.0825753953853896[/C][/ROW]
[ROW][C]42[/C][C]2.2[/C][C]1.76281417425103[/C][C]0.437185825748971[/C][/ROW]
[ROW][C]43[/C][C]2.9[/C][C]2.42397590149211[/C][C]0.476024098507889[/C][/ROW]
[ROW][C]44[/C][C]3.1[/C][C]3.23309923265235[/C][C]-0.133099232652350[/C][/ROW]
[ROW][C]45[/C][C]3.5[/C][C]3.34906409388251[/C][C]0.150935906117495[/C][/ROW]
[ROW][C]46[/C][C]3.6[/C][C]3.83274139898162[/C][C]-0.232741398981615[/C][/ROW]
[ROW][C]47[/C][C]4.4[/C][C]3.75710783483543[/C][C]0.642892165164565[/C][/ROW]
[ROW][C]48[/C][C]4.1[/C][C]4.46209105077212[/C][C]-0.362091050772117[/C][/ROW]
[ROW][C]49[/C][C]5.1[/C][C]4.11556038304753[/C][C]0.984439616952469[/C][/ROW]
[ROW][C]50[/C][C]5.8[/C][C]5.30577135371032[/C][C]0.494228646289679[/C][/ROW]
[ROW][C]51[/C][C]5.9[/C][C]5.51672262251146[/C][C]0.38327737748854[/C][/ROW]
[ROW][C]52[/C][C]5.4[/C][C]5.63074349959318[/C][C]-0.230743499593182[/C][/ROW]
[ROW][C]53[/C][C]5.5[/C][C]5.10398843786413[/C][C]0.396011562135871[/C][/ROW]
[ROW][C]54[/C][C]4.8[/C][C]5.20820201595102[/C][C]-0.408202015951016[/C][/ROW]
[ROW][C]55[/C][C]3.2[/C][C]4.08088011399263[/C][C]-0.88088011399263[/C][/ROW]
[ROW][C]56[/C][C]2.7[/C][C]2.80780988169722[/C][C]-0.107809881697220[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59284&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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
12.42.117868435528250.282131564471752
222.51487053102147-0.51487053102147
32.12.13543830223016-0.0354383022301558
422.17822746323113-0.178227463231126
51.81.88219745361858-0.0821974536185777
62.71.856436194659460.843563805340538
72.32.70844263332305-0.408442633323055
81.92.15102613205665-0.251026132056648
922.03295417802008-0.0329541780200847
102.32.012122670973760.287877329026242
112.82.389007999382920.410992000617075
122.42.79318924315068-0.393189243150680
132.32.5556924144144-0.255692414414402
142.72.403649696377060.296350303622945
152.72.632659752503910.0673402474960914
162.92.442074839104230.457925160895766
1732.955467962443680.0445320375563233
182.22.92948888904005-0.72948888904005
192.31.910898372215610.389101627784392
202.82.366314966698830.433685033301168
212.82.568315901547280.231684098452717
222.82.8146742482502-0.0146742482501972
232.22.98773380766559-0.78773380766559
242.61.959144983714280.640855016285725
252.82.85782789188653-0.0578278918865263
262.52.60973239243214-0.109732392432137
272.42.50793509162004-0.107935091620041
282.32.248372721408240.0516272785917584
291.92.17577075068823-0.275770750688227
301.71.84305872609844-0.143058726098443
3121.575802978976600.424197021023405
322.12.041749786894950.058250213105049
331.72.04966582655013-0.349665826550127
341.81.84046168179443-0.0404616817944307
351.82.06615035811605-0.26615035811605
361.81.685574722362930.114425277637072
371.32.25305087512329-0.953050875123293
381.31.46597602645902-0.165976026459016
391.31.60724423113443-0.307244231134435
401.21.30058147666322-0.100581476663216
411.41.48257539538539-0.0825753953853896
422.21.762814174251030.437185825748971
432.92.423975901492110.476024098507889
443.13.23309923265235-0.133099232652350
453.53.349064093882510.150935906117495
463.63.83274139898162-0.232741398981615
474.43.757107834835430.642892165164565
484.14.46209105077212-0.362091050772117
495.14.115560383047530.984439616952469
505.85.305771353710320.494228646289679
515.95.516722622511460.38327737748854
525.45.63074349959318-0.230743499593182
535.55.103988437864130.396011562135871
544.85.20820201595102-0.408202015951016
553.24.08088011399263-0.88088011399263
562.72.80780988169722-0.107809881697220






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.4261129160160040.8522258320320080.573887083983996
220.2831482302976100.5662964605952210.71685176970239
230.4338258991977540.8676517983955080.566174100802246
240.4364714388532960.8729428777065920.563528561146704
250.3616351881008640.7232703762017280.638364811899136
260.2983718803722550.5967437607445090.701628119627745
270.239437169997240.478874339994480.76056283000276
280.2274436472918650.454887294583730.772556352708135
290.1854530820705980.3709061641411950.814546917929402
300.1285338670411270.2570677340822530.871466132958873
310.1498785147119730.2997570294239460.850121485288027
320.2326656914846370.4653313829692740.767334308515363
330.1680294195465170.3360588390930340.831970580453483
340.1226244661328810.2452489322657610.87737553386712
350.08432487869439320.1686497573887860.915675121305607

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.426112916016004 & 0.852225832032008 & 0.573887083983996 \tabularnewline
22 & 0.283148230297610 & 0.566296460595221 & 0.71685176970239 \tabularnewline
23 & 0.433825899197754 & 0.867651798395508 & 0.566174100802246 \tabularnewline
24 & 0.436471438853296 & 0.872942877706592 & 0.563528561146704 \tabularnewline
25 & 0.361635188100864 & 0.723270376201728 & 0.638364811899136 \tabularnewline
26 & 0.298371880372255 & 0.596743760744509 & 0.701628119627745 \tabularnewline
27 & 0.23943716999724 & 0.47887433999448 & 0.76056283000276 \tabularnewline
28 & 0.227443647291865 & 0.45488729458373 & 0.772556352708135 \tabularnewline
29 & 0.185453082070598 & 0.370906164141195 & 0.814546917929402 \tabularnewline
30 & 0.128533867041127 & 0.257067734082253 & 0.871466132958873 \tabularnewline
31 & 0.149878514711973 & 0.299757029423946 & 0.850121485288027 \tabularnewline
32 & 0.232665691484637 & 0.465331382969274 & 0.767334308515363 \tabularnewline
33 & 0.168029419546517 & 0.336058839093034 & 0.831970580453483 \tabularnewline
34 & 0.122624466132881 & 0.245248932265761 & 0.87737553386712 \tabularnewline
35 & 0.0843248786943932 & 0.168649757388786 & 0.915675121305607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59284&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]0.426112916016004[/C][C]0.852225832032008[/C][C]0.573887083983996[/C][/ROW]
[ROW][C]22[/C][C]0.283148230297610[/C][C]0.566296460595221[/C][C]0.71685176970239[/C][/ROW]
[ROW][C]23[/C][C]0.433825899197754[/C][C]0.867651798395508[/C][C]0.566174100802246[/C][/ROW]
[ROW][C]24[/C][C]0.436471438853296[/C][C]0.872942877706592[/C][C]0.563528561146704[/C][/ROW]
[ROW][C]25[/C][C]0.361635188100864[/C][C]0.723270376201728[/C][C]0.638364811899136[/C][/ROW]
[ROW][C]26[/C][C]0.298371880372255[/C][C]0.596743760744509[/C][C]0.701628119627745[/C][/ROW]
[ROW][C]27[/C][C]0.23943716999724[/C][C]0.47887433999448[/C][C]0.76056283000276[/C][/ROW]
[ROW][C]28[/C][C]0.227443647291865[/C][C]0.45488729458373[/C][C]0.772556352708135[/C][/ROW]
[ROW][C]29[/C][C]0.185453082070598[/C][C]0.370906164141195[/C][C]0.814546917929402[/C][/ROW]
[ROW][C]30[/C][C]0.128533867041127[/C][C]0.257067734082253[/C][C]0.871466132958873[/C][/ROW]
[ROW][C]31[/C][C]0.149878514711973[/C][C]0.299757029423946[/C][C]0.850121485288027[/C][/ROW]
[ROW][C]32[/C][C]0.232665691484637[/C][C]0.465331382969274[/C][C]0.767334308515363[/C][/ROW]
[ROW][C]33[/C][C]0.168029419546517[/C][C]0.336058839093034[/C][C]0.831970580453483[/C][/ROW]
[ROW][C]34[/C][C]0.122624466132881[/C][C]0.245248932265761[/C][C]0.87737553386712[/C][/ROW]
[ROW][C]35[/C][C]0.0843248786943932[/C][C]0.168649757388786[/C][C]0.915675121305607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59284&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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
210.4261129160160040.8522258320320080.573887083983996
220.2831482302976100.5662964605952210.71685176970239
230.4338258991977540.8676517983955080.566174100802246
240.4364714388532960.8729428777065920.563528561146704
250.3616351881008640.7232703762017280.638364811899136
260.2983718803722550.5967437607445090.701628119627745
270.239437169997240.478874339994480.76056283000276
280.2274436472918650.454887294583730.772556352708135
290.1854530820705980.3709061641411950.814546917929402
300.1285338670411270.2570677340822530.871466132958873
310.1498785147119730.2997570294239460.850121485288027
320.2326656914846370.4653313829692740.767334308515363
330.1680294195465170.3360588390930340.831970580453483
340.1226244661328810.2452489322657610.87737553386712
350.08432487869439320.1686497573887860.915675121305607






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=59284&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=59284&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59284&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
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 2
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 3
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 4
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 5
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 6
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 7
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 8
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 9
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 10
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Input Parameters & R Code

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