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 computationWed, 18 Nov 2009 09:26:23 -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/t1258561638rg49k5jue0r6599.htm/, Retrieved Wed, 13 Aug 2025 22:28:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57514, Retrieved Wed, 13 Aug 2025 22:28:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact409

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]
-    D      [Multiple Regression] [WS7 Y(t-4)] [2009-11-18 16:26:23] [82f421ff86a0429b20e3ed68bd89f1bd] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,59	43,14	7,59	7,59	7,55	7,55
7,57	43,39	7,59	7,59	7,59	7,55
7,57	43,46	7,57	7,59	7,59	7,59
7,59	43,54	7,57	7,57	7,59	7,59
7,6	43,62	7,59	7,57	7,57	7,59
7,64	44,01	7,6	7,59	7,57	7,57
7,64	44,5	7,64	7,6	7,59	7,57
7,76	44,73	7,64	7,64	7,6	7,59
7,76	44,89	7,76	7,64	7,64	7,6
7,76	45,09	7,76	7,76	7,64	7,64
7,77	45,17	7,76	7,76	7,76	7,64
7,83	45,24	7,77	7,76	7,76	7,76
7,94	45,42	7,83	7,77	7,76	7,76
7,94	45,67	7,94	7,83	7,77	7,76
7,94	45,68	7,94	7,94	7,83	7,77
8,09	46,56	7,94	7,94	7,94	7,83
8,18	46,72	8,09	7,94	7,94	7,94
8,26	47,01	8,18	8,09	7,94	7,94
8,28	47,26	8,26	8,18	8,09	7,94
8,28	47,49	8,28	8,26	8,18	8,09
8,28	47,51	8,28	8,28	8,26	8,18
8,29	47,52	8,28	8,28	8,28	8,26
8,3	47,66	8,29	8,28	8,28	8,28
8,3	47,71	8,3	8,29	8,28	8,28
8,31	47,87	8,3	8,3	8,29	8,28
8,33	48	8,31	8,3	8,3	8,29
8,33	48	8,33	8,31	8,3	8,3
8,34	48,05	8,33	8,33	8,31	8,3
8,48	48,25	8,34	8,33	8,33	8,31
8,59	48,72	8,48	8,34	8,33	8,33
8,67	48,94	8,59	8,48	8,34	8,33
8,67	49,16	8,67	8,59	8,48	8,34
8,67	49,18	8,67	8,67	8,59	8,48
8,71	49,25	8,67	8,67	8,67	8,59
8,72	49,34	8,71	8,67	8,67	8,67
8,72	49,49	8,72	8,71	8,67	8,67
8,72	49,57	8,72	8,72	8,71	8,67
8,74	49,63	8,72	8,72	8,72	8,71
8,74	49,67	8,74	8,72	8,72	8,72
8,74	49,7	8,74	8,74	8,72	8,72
8,74	49,8	8,74	8,74	8,74	8,72
8,79	50,09	8,74	8,74	8,74	8,74
8,85	50,49	8,79	8,74	8,74	8,74
8,86	50,73	8,85	8,79	8,74	8,74
8,87	51,12	8,86	8,85	8,79	8,74
8,92	51,15	8,87	8,86	8,85	8,79
8,96	51,41	8,92	8,87	8,86	8,85
8,97	51,61	8,96	8,92	8,87	8,86
8,99	52,06	8,97	8,96	8,92	8,87
8,98	52,17	8,99	8,97	8,96	8,92
8,98	52,18	8,98	8,99	8,97	8,96
9,01	52,19	8,98	8,98	8,99	8,97
9,01	52,74	9,01	8,98	8,98	8,99
9,03	53,05	9,01	9,01	8,98	8,98
9,05	53,38	9,03	9,01	9,01	8,98
9,05	53,78	9,05	9,03	9,01	9,01

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=57514&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=57514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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] = + 0.0140552377191030 + 0.0139606102770509X[t] + 1.23654257042361Y1[t] -0.419623941627338Y2[t] + 0.222584543954599Y3[t] -0.118384183953442Y4[t] + 0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] + 0.0209832902930584M4[t] + 0.0172570665543621M5[t] + 0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] + 0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.0140552377191030 +  0.0139606102770509X[t] +  1.23654257042361Y1[t] -0.419623941627338Y2[t] +  0.222584543954599Y3[t] -0.118384183953442Y4[t] +  0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] +  0.0209832902930584M4[t] +  0.0172570665543621M5[t] +  0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] +  0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.0140552377191030 +  0.0139606102770509X[t] +  1.23654257042361Y1[t] -0.419623941627338Y2[t] +  0.222584543954599Y3[t] -0.118384183953442Y4[t] +  0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] +  0.0209832902930584M4[t] +  0.0172570665543621M5[t] +  0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] +  0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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] = + 0.0140552377191030 + 0.0139606102770509X[t] + 1.23654257042361Y1[t] -0.419623941627338Y2[t] + 0.222584543954599Y3[t] -0.118384183953442Y4[t] + 0.00761324456546221M1[t] -0.0235156969591707M2[t] -0.0147316299733394M3[t] + 0.0209832902930584M4[t] + 0.0172570665543621M5[t] + 0.0312601726900203M6[t] -0.000475280260314817M7[t] -0.00282851059813795M8[t] -0.0261443878669578M9[t] + 0.00808598682866219M10[t] -0.00838414566602145M11[t] -0.000382389196704658t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.01405523771910300.9845150.01430.9886840.494342
X0.01396061027705090.0190850.73150.4689750.234487
Y11.236542570423610.1637127.553200
Y2-0.4196239416273380.254319-1.650.1071880.053594
Y30.2225845439545990.2551160.87250.3884250.194212
Y4-0.1183841839534420.172133-0.68770.4957880.247894
M10.007613244565462210.0261930.29070.7728930.386447
M2-0.02351569695917070.02647-0.88840.3799260.189963
M3-0.01473162997333940.026501-0.55590.5815450.290773
M40.02098329029305840.0271710.77230.4447260.222363
M50.01725706655436210.0270820.63720.5278020.263901
M60.03126017269002030.0268221.16550.2510960.125548
M7-0.0004752802603148170.028046-0.01690.9865680.493284
M8-0.002828510598137950.027802-0.10170.9194990.459749
M9-0.02614438786695780.029397-0.88940.3794060.189703
M100.008085986828662190.0280240.28850.7745030.387252
M11-0.008384145666021450.028244-0.29680.7682030.384102
t-0.0003823891967046580.004024-0.0950.9247980.462399

\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) & 0.0140552377191030 & 0.984515 & 0.0143 & 0.988684 & 0.494342 \tabularnewline
X & 0.0139606102770509 & 0.019085 & 0.7315 & 0.468975 & 0.234487 \tabularnewline
Y1 & 1.23654257042361 & 0.163712 & 7.5532 & 0 & 0 \tabularnewline
Y2 & -0.419623941627338 & 0.254319 & -1.65 & 0.107188 & 0.053594 \tabularnewline
Y3 & 0.222584543954599 & 0.255116 & 0.8725 & 0.388425 & 0.194212 \tabularnewline
Y4 & -0.118384183953442 & 0.172133 & -0.6877 & 0.495788 & 0.247894 \tabularnewline
M1 & 0.00761324456546221 & 0.026193 & 0.2907 & 0.772893 & 0.386447 \tabularnewline
M2 & -0.0235156969591707 & 0.02647 & -0.8884 & 0.379926 & 0.189963 \tabularnewline
M3 & -0.0147316299733394 & 0.026501 & -0.5559 & 0.581545 & 0.290773 \tabularnewline
M4 & 0.0209832902930584 & 0.027171 & 0.7723 & 0.444726 & 0.222363 \tabularnewline
M5 & 0.0172570665543621 & 0.027082 & 0.6372 & 0.527802 & 0.263901 \tabularnewline
M6 & 0.0312601726900203 & 0.026822 & 1.1655 & 0.251096 & 0.125548 \tabularnewline
M7 & -0.000475280260314817 & 0.028046 & -0.0169 & 0.986568 & 0.493284 \tabularnewline
M8 & -0.00282851059813795 & 0.027802 & -0.1017 & 0.919499 & 0.459749 \tabularnewline
M9 & -0.0261443878669578 & 0.029397 & -0.8894 & 0.379406 & 0.189703 \tabularnewline
M10 & 0.00808598682866219 & 0.028024 & 0.2885 & 0.774503 & 0.387252 \tabularnewline
M11 & -0.00838414566602145 & 0.028244 & -0.2968 & 0.768203 & 0.384102 \tabularnewline
t & -0.000382389196704658 & 0.004024 & -0.095 & 0.924798 & 0.462399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]0.0140552377191030[/C][C]0.984515[/C][C]0.0143[/C][C]0.988684[/C][C]0.494342[/C][/ROW]
[ROW][C]X[/C][C]0.0139606102770509[/C][C]0.019085[/C][C]0.7315[/C][C]0.468975[/C][C]0.234487[/C][/ROW]
[ROW][C]Y1[/C][C]1.23654257042361[/C][C]0.163712[/C][C]7.5532[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.419623941627338[/C][C]0.254319[/C][C]-1.65[/C][C]0.107188[/C][C]0.053594[/C][/ROW]
[ROW][C]Y3[/C][C]0.222584543954599[/C][C]0.255116[/C][C]0.8725[/C][C]0.388425[/C][C]0.194212[/C][/ROW]
[ROW][C]Y4[/C][C]-0.118384183953442[/C][C]0.172133[/C][C]-0.6877[/C][C]0.495788[/C][C]0.247894[/C][/ROW]
[ROW][C]M1[/C][C]0.00761324456546221[/C][C]0.026193[/C][C]0.2907[/C][C]0.772893[/C][C]0.386447[/C][/ROW]
[ROW][C]M2[/C][C]-0.0235156969591707[/C][C]0.02647[/C][C]-0.8884[/C][C]0.379926[/C][C]0.189963[/C][/ROW]
[ROW][C]M3[/C][C]-0.0147316299733394[/C][C]0.026501[/C][C]-0.5559[/C][C]0.581545[/C][C]0.290773[/C][/ROW]
[ROW][C]M4[/C][C]0.0209832902930584[/C][C]0.027171[/C][C]0.7723[/C][C]0.444726[/C][C]0.222363[/C][/ROW]
[ROW][C]M5[/C][C]0.0172570665543621[/C][C]0.027082[/C][C]0.6372[/C][C]0.527802[/C][C]0.263901[/C][/ROW]
[ROW][C]M6[/C][C]0.0312601726900203[/C][C]0.026822[/C][C]1.1655[/C][C]0.251096[/C][C]0.125548[/C][/ROW]
[ROW][C]M7[/C][C]-0.000475280260314817[/C][C]0.028046[/C][C]-0.0169[/C][C]0.986568[/C][C]0.493284[/C][/ROW]
[ROW][C]M8[/C][C]-0.00282851059813795[/C][C]0.027802[/C][C]-0.1017[/C][C]0.919499[/C][C]0.459749[/C][/ROW]
[ROW][C]M9[/C][C]-0.0261443878669578[/C][C]0.029397[/C][C]-0.8894[/C][C]0.379406[/C][C]0.189703[/C][/ROW]
[ROW][C]M10[/C][C]0.00808598682866219[/C][C]0.028024[/C][C]0.2885[/C][C]0.774503[/C][C]0.387252[/C][/ROW]
[ROW][C]M11[/C][C]-0.00838414566602145[/C][C]0.028244[/C][C]-0.2968[/C][C]0.768203[/C][C]0.384102[/C][/ROW]
[ROW][C]t[/C][C]-0.000382389196704658[/C][C]0.004024[/C][C]-0.095[/C][C]0.924798[/C][C]0.462399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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)0.01405523771910300.9845150.01430.9886840.494342
X0.01396061027705090.0190850.73150.4689750.234487
Y11.236542570423610.1637127.553200
Y2-0.4196239416273380.254319-1.650.1071880.053594
Y30.2225845439545990.2551160.87250.3884250.194212
Y4-0.1183841839534420.172133-0.68770.4957880.247894
M10.007613244565462210.0261930.29070.7728930.386447
M2-0.02351569695917070.02647-0.88840.3799260.189963
M3-0.01473162997333940.026501-0.55590.5815450.290773
M40.02098329029305840.0271710.77230.4447260.222363
M50.01725706655436210.0270820.63720.5278020.263901
M60.03126017269002030.0268221.16550.2510960.125548
M7-0.0004752802603148170.028046-0.01690.9865680.493284
M8-0.002828510598137950.027802-0.10170.9194990.459749
M9-0.02614438786695780.029397-0.88940.3794060.189703
M100.008085986828662190.0280240.28850.7745030.387252
M11-0.008384145666021450.028244-0.29680.7682030.384102
t-0.0003823891967046580.004024-0.0950.9247980.462399






Multiple Linear Regression - Regression Statistics
Multiple R0.997836985175587
R-squared0.995678648984306
Adjusted R-squared0.9937454130036
F-TEST (value)515.032132094405
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0386849910476448
Sum Squared Residuals0.0568680842295417

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.997836985175587 \tabularnewline
R-squared & 0.995678648984306 \tabularnewline
Adjusted R-squared & 0.9937454130036 \tabularnewline
F-TEST (value) & 515.032132094405 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0386849910476448 \tabularnewline
Sum Squared Residuals & 0.0568680842295417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.997836985175587[/C][/ROW]
[ROW][C]R-squared[/C][C]0.995678648984306[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.9937454130036[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]515.032132094405[/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]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0386849910476448[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0568680842295417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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 R0.997836985175587
R-squared0.995678648984306
Adjusted R-squared0.9937454130036
F-TEST (value)515.032132094405
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0386849910476448
Sum Squared Residuals0.0568680842295417






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.597.61067193101227-0.0206719310122711
27.577.59155413461837-0.0215541346183736
37.577.57146683636028-0.00146683636028320
47.597.61630869508469-0.0263086950846871
57.67.63359609150083-0.0335960915008302
67.647.65900207699859-0.0190020769985917
77.647.68344208816707-0.0434420881670698
87.767.666990613091650.0930093869083528
97.767.80163069263993-0.0416306926399335
107.767.78318055984084-0.0231805598408407
117.777.79415503224617-0.0241550322461685
127.837.80129335506470.0287066449352988
137.947.881033435092470.0589665649075286
147.947.9660803486289-0.0260803486288992
157.947.94063422973953-0.000634229739530575
168.098.005633346650830.0843666533491716
178.188.176217556688420.00378244331158241
188.268.242232090701740.0177679092982602
198.288.30814933360458-0.0281493336045811
208.288.30206057187496-0.0220605718749573
218.288.277401225742980.00259877425701461
228.298.30636977350749-0.016369773507488
238.38.30146947928005-0.00146947928005223
248.38.31833845255119-0.0183384525511864
258.318.32583261158755-0.0158326115875441
268.338.309543589506470.0204564104935287
278.338.33729603744826-0.00729603744826175
288.348.3671599656388-0.0271599656388069
298.488.381476749502610.098523250497391
308.598.568210990035740.0217890099642594
318.678.618662658507970.0513373414920335
328.678.70174113960338-0.0317411396033811
338.678.652662684094730.0173373159052656
348.718.692272415594530.0177275844054682
358.728.716667316928750.00333268307125159
368.728.72234363297876-0.00234363297876473
378.728.7353984795116-0.0153984795115971
388.748.70221526348830.0377847365117088
398.748.734722375257440.00527762474256289
408.748.7620812458029-0.0220812458028952
418.748.7638203847743-0.0238203847742912
428.798.779121995014520.0108780049854782
438.858.814415525499480.035584474500519
448.868.8682418095755-0.00824180957549614
458.878.848305397522350.0216946024776533
468.928.898177251057140.0218227489428605
478.968.937708171545030.0222918284549692
488.978.97802455940535-0.00802455940534777
498.998.99706354279612-0.00706354279611632
508.988.99060666375797-0.0106066637579645
518.988.975880521194490.00411947880551261
529.019.01881674682278-0.0088167468227824
539.019.05488921753385-0.0448892175338521
549.039.0614328472494-0.0314328472494062
559.059.0653303942209-0.0153303942209016
569.059.08096586585452-0.0309658658545183

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.59 & 7.61067193101227 & -0.0206719310122711 \tabularnewline
2 & 7.57 & 7.59155413461837 & -0.0215541346183736 \tabularnewline
3 & 7.57 & 7.57146683636028 & -0.00146683636028320 \tabularnewline
4 & 7.59 & 7.61630869508469 & -0.0263086950846871 \tabularnewline
5 & 7.6 & 7.63359609150083 & -0.0335960915008302 \tabularnewline
6 & 7.64 & 7.65900207699859 & -0.0190020769985917 \tabularnewline
7 & 7.64 & 7.68344208816707 & -0.0434420881670698 \tabularnewline
8 & 7.76 & 7.66699061309165 & 0.0930093869083528 \tabularnewline
9 & 7.76 & 7.80163069263993 & -0.0416306926399335 \tabularnewline
10 & 7.76 & 7.78318055984084 & -0.0231805598408407 \tabularnewline
11 & 7.77 & 7.79415503224617 & -0.0241550322461685 \tabularnewline
12 & 7.83 & 7.8012933550647 & 0.0287066449352988 \tabularnewline
13 & 7.94 & 7.88103343509247 & 0.0589665649075286 \tabularnewline
14 & 7.94 & 7.9660803486289 & -0.0260803486288992 \tabularnewline
15 & 7.94 & 7.94063422973953 & -0.000634229739530575 \tabularnewline
16 & 8.09 & 8.00563334665083 & 0.0843666533491716 \tabularnewline
17 & 8.18 & 8.17621755668842 & 0.00378244331158241 \tabularnewline
18 & 8.26 & 8.24223209070174 & 0.0177679092982602 \tabularnewline
19 & 8.28 & 8.30814933360458 & -0.0281493336045811 \tabularnewline
20 & 8.28 & 8.30206057187496 & -0.0220605718749573 \tabularnewline
21 & 8.28 & 8.27740122574298 & 0.00259877425701461 \tabularnewline
22 & 8.29 & 8.30636977350749 & -0.016369773507488 \tabularnewline
23 & 8.3 & 8.30146947928005 & -0.00146947928005223 \tabularnewline
24 & 8.3 & 8.31833845255119 & -0.0183384525511864 \tabularnewline
25 & 8.31 & 8.32583261158755 & -0.0158326115875441 \tabularnewline
26 & 8.33 & 8.30954358950647 & 0.0204564104935287 \tabularnewline
27 & 8.33 & 8.33729603744826 & -0.00729603744826175 \tabularnewline
28 & 8.34 & 8.3671599656388 & -0.0271599656388069 \tabularnewline
29 & 8.48 & 8.38147674950261 & 0.098523250497391 \tabularnewline
30 & 8.59 & 8.56821099003574 & 0.0217890099642594 \tabularnewline
31 & 8.67 & 8.61866265850797 & 0.0513373414920335 \tabularnewline
32 & 8.67 & 8.70174113960338 & -0.0317411396033811 \tabularnewline
33 & 8.67 & 8.65266268409473 & 0.0173373159052656 \tabularnewline
34 & 8.71 & 8.69227241559453 & 0.0177275844054682 \tabularnewline
35 & 8.72 & 8.71666731692875 & 0.00333268307125159 \tabularnewline
36 & 8.72 & 8.72234363297876 & -0.00234363297876473 \tabularnewline
37 & 8.72 & 8.7353984795116 & -0.0153984795115971 \tabularnewline
38 & 8.74 & 8.7022152634883 & 0.0377847365117088 \tabularnewline
39 & 8.74 & 8.73472237525744 & 0.00527762474256289 \tabularnewline
40 & 8.74 & 8.7620812458029 & -0.0220812458028952 \tabularnewline
41 & 8.74 & 8.7638203847743 & -0.0238203847742912 \tabularnewline
42 & 8.79 & 8.77912199501452 & 0.0108780049854782 \tabularnewline
43 & 8.85 & 8.81441552549948 & 0.035584474500519 \tabularnewline
44 & 8.86 & 8.8682418095755 & -0.00824180957549614 \tabularnewline
45 & 8.87 & 8.84830539752235 & 0.0216946024776533 \tabularnewline
46 & 8.92 & 8.89817725105714 & 0.0218227489428605 \tabularnewline
47 & 8.96 & 8.93770817154503 & 0.0222918284549692 \tabularnewline
48 & 8.97 & 8.97802455940535 & -0.00802455940534777 \tabularnewline
49 & 8.99 & 8.99706354279612 & -0.00706354279611632 \tabularnewline
50 & 8.98 & 8.99060666375797 & -0.0106066637579645 \tabularnewline
51 & 8.98 & 8.97588052119449 & 0.00411947880551261 \tabularnewline
52 & 9.01 & 9.01881674682278 & -0.0088167468227824 \tabularnewline
53 & 9.01 & 9.05488921753385 & -0.0448892175338521 \tabularnewline
54 & 9.03 & 9.0614328472494 & -0.0314328472494062 \tabularnewline
55 & 9.05 & 9.0653303942209 & -0.0153303942209016 \tabularnewline
56 & 9.05 & 9.08096586585452 & -0.0309658658545183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]7.59[/C][C]7.61067193101227[/C][C]-0.0206719310122711[/C][/ROW]
[ROW][C]2[/C][C]7.57[/C][C]7.59155413461837[/C][C]-0.0215541346183736[/C][/ROW]
[ROW][C]3[/C][C]7.57[/C][C]7.57146683636028[/C][C]-0.00146683636028320[/C][/ROW]
[ROW][C]4[/C][C]7.59[/C][C]7.61630869508469[/C][C]-0.0263086950846871[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.63359609150083[/C][C]-0.0335960915008302[/C][/ROW]
[ROW][C]6[/C][C]7.64[/C][C]7.65900207699859[/C][C]-0.0190020769985917[/C][/ROW]
[ROW][C]7[/C][C]7.64[/C][C]7.68344208816707[/C][C]-0.0434420881670698[/C][/ROW]
[ROW][C]8[/C][C]7.76[/C][C]7.66699061309165[/C][C]0.0930093869083528[/C][/ROW]
[ROW][C]9[/C][C]7.76[/C][C]7.80163069263993[/C][C]-0.0416306926399335[/C][/ROW]
[ROW][C]10[/C][C]7.76[/C][C]7.78318055984084[/C][C]-0.0231805598408407[/C][/ROW]
[ROW][C]11[/C][C]7.77[/C][C]7.79415503224617[/C][C]-0.0241550322461685[/C][/ROW]
[ROW][C]12[/C][C]7.83[/C][C]7.8012933550647[/C][C]0.0287066449352988[/C][/ROW]
[ROW][C]13[/C][C]7.94[/C][C]7.88103343509247[/C][C]0.0589665649075286[/C][/ROW]
[ROW][C]14[/C][C]7.94[/C][C]7.9660803486289[/C][C]-0.0260803486288992[/C][/ROW]
[ROW][C]15[/C][C]7.94[/C][C]7.94063422973953[/C][C]-0.000634229739530575[/C][/ROW]
[ROW][C]16[/C][C]8.09[/C][C]8.00563334665083[/C][C]0.0843666533491716[/C][/ROW]
[ROW][C]17[/C][C]8.18[/C][C]8.17621755668842[/C][C]0.00378244331158241[/C][/ROW]
[ROW][C]18[/C][C]8.26[/C][C]8.24223209070174[/C][C]0.0177679092982602[/C][/ROW]
[ROW][C]19[/C][C]8.28[/C][C]8.30814933360458[/C][C]-0.0281493336045811[/C][/ROW]
[ROW][C]20[/C][C]8.28[/C][C]8.30206057187496[/C][C]-0.0220605718749573[/C][/ROW]
[ROW][C]21[/C][C]8.28[/C][C]8.27740122574298[/C][C]0.00259877425701461[/C][/ROW]
[ROW][C]22[/C][C]8.29[/C][C]8.30636977350749[/C][C]-0.016369773507488[/C][/ROW]
[ROW][C]23[/C][C]8.3[/C][C]8.30146947928005[/C][C]-0.00146947928005223[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.31833845255119[/C][C]-0.0183384525511864[/C][/ROW]
[ROW][C]25[/C][C]8.31[/C][C]8.32583261158755[/C][C]-0.0158326115875441[/C][/ROW]
[ROW][C]26[/C][C]8.33[/C][C]8.30954358950647[/C][C]0.0204564104935287[/C][/ROW]
[ROW][C]27[/C][C]8.33[/C][C]8.33729603744826[/C][C]-0.00729603744826175[/C][/ROW]
[ROW][C]28[/C][C]8.34[/C][C]8.3671599656388[/C][C]-0.0271599656388069[/C][/ROW]
[ROW][C]29[/C][C]8.48[/C][C]8.38147674950261[/C][C]0.098523250497391[/C][/ROW]
[ROW][C]30[/C][C]8.59[/C][C]8.56821099003574[/C][C]0.0217890099642594[/C][/ROW]
[ROW][C]31[/C][C]8.67[/C][C]8.61866265850797[/C][C]0.0513373414920335[/C][/ROW]
[ROW][C]32[/C][C]8.67[/C][C]8.70174113960338[/C][C]-0.0317411396033811[/C][/ROW]
[ROW][C]33[/C][C]8.67[/C][C]8.65266268409473[/C][C]0.0173373159052656[/C][/ROW]
[ROW][C]34[/C][C]8.71[/C][C]8.69227241559453[/C][C]0.0177275844054682[/C][/ROW]
[ROW][C]35[/C][C]8.72[/C][C]8.71666731692875[/C][C]0.00333268307125159[/C][/ROW]
[ROW][C]36[/C][C]8.72[/C][C]8.72234363297876[/C][C]-0.00234363297876473[/C][/ROW]
[ROW][C]37[/C][C]8.72[/C][C]8.7353984795116[/C][C]-0.0153984795115971[/C][/ROW]
[ROW][C]38[/C][C]8.74[/C][C]8.7022152634883[/C][C]0.0377847365117088[/C][/ROW]
[ROW][C]39[/C][C]8.74[/C][C]8.73472237525744[/C][C]0.00527762474256289[/C][/ROW]
[ROW][C]40[/C][C]8.74[/C][C]8.7620812458029[/C][C]-0.0220812458028952[/C][/ROW]
[ROW][C]41[/C][C]8.74[/C][C]8.7638203847743[/C][C]-0.0238203847742912[/C][/ROW]
[ROW][C]42[/C][C]8.79[/C][C]8.77912199501452[/C][C]0.0108780049854782[/C][/ROW]
[ROW][C]43[/C][C]8.85[/C][C]8.81441552549948[/C][C]0.035584474500519[/C][/ROW]
[ROW][C]44[/C][C]8.86[/C][C]8.8682418095755[/C][C]-0.00824180957549614[/C][/ROW]
[ROW][C]45[/C][C]8.87[/C][C]8.84830539752235[/C][C]0.0216946024776533[/C][/ROW]
[ROW][C]46[/C][C]8.92[/C][C]8.89817725105714[/C][C]0.0218227489428605[/C][/ROW]
[ROW][C]47[/C][C]8.96[/C][C]8.93770817154503[/C][C]0.0222918284549692[/C][/ROW]
[ROW][C]48[/C][C]8.97[/C][C]8.97802455940535[/C][C]-0.00802455940534777[/C][/ROW]
[ROW][C]49[/C][C]8.99[/C][C]8.99706354279612[/C][C]-0.00706354279611632[/C][/ROW]
[ROW][C]50[/C][C]8.98[/C][C]8.99060666375797[/C][C]-0.0106066637579645[/C][/ROW]
[ROW][C]51[/C][C]8.98[/C][C]8.97588052119449[/C][C]0.00411947880551261[/C][/ROW]
[ROW][C]52[/C][C]9.01[/C][C]9.01881674682278[/C][C]-0.0088167468227824[/C][/ROW]
[ROW][C]53[/C][C]9.01[/C][C]9.05488921753385[/C][C]-0.0448892175338521[/C][/ROW]
[ROW][C]54[/C][C]9.03[/C][C]9.0614328472494[/C][C]-0.0314328472494062[/C][/ROW]
[ROW][C]55[/C][C]9.05[/C][C]9.0653303942209[/C][C]-0.0153303942209016[/C][/ROW]
[ROW][C]56[/C][C]9.05[/C][C]9.08096586585452[/C][C]-0.0309658658545183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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
17.597.61067193101227-0.0206719310122711
27.577.59155413461837-0.0215541346183736
37.577.57146683636028-0.00146683636028320
47.597.61630869508469-0.0263086950846871
57.67.63359609150083-0.0335960915008302
67.647.65900207699859-0.0190020769985917
77.647.68344208816707-0.0434420881670698
87.767.666990613091650.0930093869083528
97.767.80163069263993-0.0416306926399335
107.767.78318055984084-0.0231805598408407
117.777.79415503224617-0.0241550322461685
127.837.80129335506470.0287066449352988
137.947.881033435092470.0589665649075286
147.947.9660803486289-0.0260803486288992
157.947.94063422973953-0.000634229739530575
168.098.005633346650830.0843666533491716
178.188.176217556688420.00378244331158241
188.268.242232090701740.0177679092982602
198.288.30814933360458-0.0281493336045811
208.288.30206057187496-0.0220605718749573
218.288.277401225742980.00259877425701461
228.298.30636977350749-0.016369773507488
238.38.30146947928005-0.00146947928005223
248.38.31833845255119-0.0183384525511864
258.318.32583261158755-0.0158326115875441
268.338.309543589506470.0204564104935287
278.338.33729603744826-0.00729603744826175
288.348.3671599656388-0.0271599656388069
298.488.381476749502610.098523250497391
308.598.568210990035740.0217890099642594
318.678.618662658507970.0513373414920335
328.678.70174113960338-0.0317411396033811
338.678.652662684094730.0173373159052656
348.718.692272415594530.0177275844054682
358.728.716667316928750.00333268307125159
368.728.72234363297876-0.00234363297876473
378.728.7353984795116-0.0153984795115971
388.748.70221526348830.0377847365117088
398.748.734722375257440.00527762474256289
408.748.7620812458029-0.0220812458028952
418.748.7638203847743-0.0238203847742912
428.798.779121995014520.0108780049854782
438.858.814415525499480.035584474500519
448.868.8682418095755-0.00824180957549614
458.878.848305397522350.0216946024776533
468.928.898177251057140.0218227489428605
478.968.937708171545030.0222918284549692
488.978.97802455940535-0.00802455940534777
498.998.99706354279612-0.00706354279611632
508.988.99060666375797-0.0106066637579645
518.988.975880521194490.00411947880551261
529.019.01881674682278-0.0088167468227824
539.019.05488921753385-0.0448892175338521
549.039.0614328472494-0.0314328472494062
559.059.0653303942209-0.0153303942209016
569.059.08096586585452-0.0309658658545183






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.8300458221099940.3399083557800120.169954177890006
220.7912649679490030.4174700641019930.208735032050997
230.6808162512343960.6383674975312080.319183748765604
240.6146777636145830.7706444727708340.385322236385417
250.7595045300685820.4809909398628360.240495469931418
260.6748964893284570.6502070213430860.325103510671543
270.6968271120091390.6063457759817210.303172887990861
280.987131531764880.02573693647023860.0128684682351193
290.9968989732579420.006202053484115920.00310102674205796
300.9934244946420570.0131510107158860.006575505357943
310.9950395971572840.009920805685432840.00496040284271642
320.9855181822663350.02896363546732940.0144818177336647
330.9751526981736640.04969460365267220.0248473018263361
340.981517968297190.03696406340561890.0184820317028095
350.9374075811049050.1251848377901890.0625924188950947

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.830045822109994 & 0.339908355780012 & 0.169954177890006 \tabularnewline
22 & 0.791264967949003 & 0.417470064101993 & 0.208735032050997 \tabularnewline
23 & 0.680816251234396 & 0.638367497531208 & 0.319183748765604 \tabularnewline
24 & 0.614677763614583 & 0.770644472770834 & 0.385322236385417 \tabularnewline
25 & 0.759504530068582 & 0.480990939862836 & 0.240495469931418 \tabularnewline
26 & 0.674896489328457 & 0.650207021343086 & 0.325103510671543 \tabularnewline
27 & 0.696827112009139 & 0.606345775981721 & 0.303172887990861 \tabularnewline
28 & 0.98713153176488 & 0.0257369364702386 & 0.0128684682351193 \tabularnewline
29 & 0.996898973257942 & 0.00620205348411592 & 0.00310102674205796 \tabularnewline
30 & 0.993424494642057 & 0.013151010715886 & 0.006575505357943 \tabularnewline
31 & 0.995039597157284 & 0.00992080568543284 & 0.00496040284271642 \tabularnewline
32 & 0.985518182266335 & 0.0289636354673294 & 0.0144818177336647 \tabularnewline
33 & 0.975152698173664 & 0.0496946036526722 & 0.0248473018263361 \tabularnewline
34 & 0.98151796829719 & 0.0369640634056189 & 0.0184820317028095 \tabularnewline
35 & 0.937407581104905 & 0.125184837790189 & 0.0625924188950947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]0.830045822109994[/C][C]0.339908355780012[/C][C]0.169954177890006[/C][/ROW]
[ROW][C]22[/C][C]0.791264967949003[/C][C]0.417470064101993[/C][C]0.208735032050997[/C][/ROW]
[ROW][C]23[/C][C]0.680816251234396[/C][C]0.638367497531208[/C][C]0.319183748765604[/C][/ROW]
[ROW][C]24[/C][C]0.614677763614583[/C][C]0.770644472770834[/C][C]0.385322236385417[/C][/ROW]
[ROW][C]25[/C][C]0.759504530068582[/C][C]0.480990939862836[/C][C]0.240495469931418[/C][/ROW]
[ROW][C]26[/C][C]0.674896489328457[/C][C]0.650207021343086[/C][C]0.325103510671543[/C][/ROW]
[ROW][C]27[/C][C]0.696827112009139[/C][C]0.606345775981721[/C][C]0.303172887990861[/C][/ROW]
[ROW][C]28[/C][C]0.98713153176488[/C][C]0.0257369364702386[/C][C]0.0128684682351193[/C][/ROW]
[ROW][C]29[/C][C]0.996898973257942[/C][C]0.00620205348411592[/C][C]0.00310102674205796[/C][/ROW]
[ROW][C]30[/C][C]0.993424494642057[/C][C]0.013151010715886[/C][C]0.006575505357943[/C][/ROW]
[ROW][C]31[/C][C]0.995039597157284[/C][C]0.00992080568543284[/C][C]0.00496040284271642[/C][/ROW]
[ROW][C]32[/C][C]0.985518182266335[/C][C]0.0289636354673294[/C][C]0.0144818177336647[/C][/ROW]
[ROW][C]33[/C][C]0.975152698173664[/C][C]0.0496946036526722[/C][C]0.0248473018263361[/C][/ROW]
[ROW][C]34[/C][C]0.98151796829719[/C][C]0.0369640634056189[/C][C]0.0184820317028095[/C][/ROW]
[ROW][C]35[/C][C]0.937407581104905[/C][C]0.125184837790189[/C][C]0.0625924188950947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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
210.8300458221099940.3399083557800120.169954177890006
220.7912649679490030.4174700641019930.208735032050997
230.6808162512343960.6383674975312080.319183748765604
240.6146777636145830.7706444727708340.385322236385417
250.7595045300685820.4809909398628360.240495469931418
260.6748964893284570.6502070213430860.325103510671543
270.6968271120091390.6063457759817210.303172887990861
280.987131531764880.02573693647023860.0128684682351193
290.9968989732579420.006202053484115920.00310102674205796
300.9934244946420570.0131510107158860.006575505357943
310.9950395971572840.009920805685432840.00496040284271642
320.9855181822663350.02896363546732940.0144818177336647
330.9751526981736640.04969460365267220.0248473018263361
340.981517968297190.03696406340561890.0184820317028095
350.9374075811049050.1251848377901890.0625924188950947






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.133333333333333NOK
5% type I error level70.466666666666667NOK
10% type I error level70.466666666666667NOK

\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 & 2 & 0.133333333333333 & NOK \tabularnewline
5% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
10% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57514&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]2[/C][C]0.133333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57514&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57514&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 level20.133333333333333NOK
5% type I error level70.466666666666667NOK
10% type I error level70.466666666666667NOK


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')
}