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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 15:38:53 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258756776jdhh1urot8f9jge.htm/, Retrieved Fri, 29 Mar 2024 00:59:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58479, Retrieved Fri, 29 Mar 2024 00:59:00 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [Seatbelt Law part 2] [2009-11-20 22:38:53] [befe6dd6a614b6d3a2a74a47a0a4f514] [Current]
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Dataseries X:
8.9	1,6
8.8	1,3
8.3	1,1
7.5	1,6
7.2	1,9
7.4	1,6
8.8	1,7
9.3	1,6
9.3	1,4
8.7	2,1
8.2	1,9
8.3	1,7
8.5	1,8
8.6	2
8.5	2,5
8.2	2,1
8.1	2,1
7.9	2,3
8.6	2,4
8.7	2,4
8.7	2,3
8.5	1,7
8.4	2
8.5	2,3
8.7	2
8.7	2
8.6	1,3
8.5	1,7
8.3	1,9
8	1,7
8.2	1,6
8.1	1,7
8.1	1,8
8	1,9
7.9	1,9
7.9	1,9
8	2
8	2,1
7.9	1,9
8	1,9
7.7	1,3
7.2	1,3
7.5	1,4
7.3	1,2
7	1,3
7	1,8
7	2,2
7.2	2,6
7.3	2,8
7.1	3,1
6.8	3,9
6.4	3,7
6.1	4,6
6.5	5,1
7.7	5,2
7.9	4,9
7.5	5,1
6.9	4,8
6.6	3,9
6.9	3,5




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=58479&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=58479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=0

As an alternative you can also use a 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
TWIB[t] = + 8.60763772508468 -0.353182385451952GI[t] + 0.392854341237291M1[t] + 0.374045284364414M2[t] + 0.168172579782492M3[t] -0.110636477090391M4[t] -0.294127295418079M5[t] -0.360000000000001M6[t] + 0.421190943127117M7[t] + 0.485872704581921M8[t] + 0.35293635229096M9[t] + 0.0811909431271165M10[t] -0.147063647709040M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TWIB[t] =  +  8.60763772508468 -0.353182385451952GI[t] +  0.392854341237291M1[t] +  0.374045284364414M2[t] +  0.168172579782492M3[t] -0.110636477090391M4[t] -0.294127295418079M5[t] -0.360000000000001M6[t] +  0.421190943127117M7[t] +  0.485872704581921M8[t] +  0.35293635229096M9[t] +  0.0811909431271165M10[t] -0.147063647709040M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TWIB[t] =  +  8.60763772508468 -0.353182385451952GI[t] +  0.392854341237291M1[t] +  0.374045284364414M2[t] +  0.168172579782492M3[t] -0.110636477090391M4[t] -0.294127295418079M5[t] -0.360000000000001M6[t] +  0.421190943127117M7[t] +  0.485872704581921M8[t] +  0.35293635229096M9[t] +  0.0811909431271165M10[t] -0.147063647709040M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
TWIB[t] = + 8.60763772508468 -0.353182385451952GI[t] + 0.392854341237291M1[t] + 0.374045284364414M2[t] + 0.168172579782492M3[t] -0.110636477090391M4[t] -0.294127295418079M5[t] -0.360000000000001M6[t] + 0.421190943127117M7[t] + 0.485872704581921M8[t] + 0.35293635229096M9[t] + 0.0811909431271165M10[t] -0.147063647709040M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.607637725084680.33787425.475900
GI-0.3531823854519520.077065-4.58293.4e-051.7e-05
M10.3928543412372910.4008350.98010.332060.16603
M20.3740452843644140.4005420.93380.3551550.177578
M30.1681725797824920.4003760.420.6763720.338186
M4-0.1106364770903910.400171-0.27650.7833970.391698
M5-0.2941272954180790.399886-0.73550.4656730.232836
M6-0.3600000000000010.399874-0.90030.3725590.18628
M70.4211909431271170.3999011.05320.2976160.148808
M80.4858727045819210.3998861.2150.2304240.115212
M90.352936352290960.3998770.88260.3819380.190969
M100.08119094312711650.3999010.2030.839990.419995
M11-0.1470636477090400.399877-0.36780.7146940.357347

\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) & 8.60763772508468 & 0.337874 & 25.4759 & 0 & 0 \tabularnewline
GI & -0.353182385451952 & 0.077065 & -4.5829 & 3.4e-05 & 1.7e-05 \tabularnewline
M1 & 0.392854341237291 & 0.400835 & 0.9801 & 0.33206 & 0.16603 \tabularnewline
M2 & 0.374045284364414 & 0.400542 & 0.9338 & 0.355155 & 0.177578 \tabularnewline
M3 & 0.168172579782492 & 0.400376 & 0.42 & 0.676372 & 0.338186 \tabularnewline
M4 & -0.110636477090391 & 0.400171 & -0.2765 & 0.783397 & 0.391698 \tabularnewline
M5 & -0.294127295418079 & 0.399886 & -0.7355 & 0.465673 & 0.232836 \tabularnewline
M6 & -0.360000000000001 & 0.399874 & -0.9003 & 0.372559 & 0.18628 \tabularnewline
M7 & 0.421190943127117 & 0.399901 & 1.0532 & 0.297616 & 0.148808 \tabularnewline
M8 & 0.485872704581921 & 0.399886 & 1.215 & 0.230424 & 0.115212 \tabularnewline
M9 & 0.35293635229096 & 0.399877 & 0.8826 & 0.381938 & 0.190969 \tabularnewline
M10 & 0.0811909431271165 & 0.399901 & 0.203 & 0.83999 & 0.419995 \tabularnewline
M11 & -0.147063647709040 & 0.399877 & -0.3678 & 0.714694 & 0.357347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&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]8.60763772508468[/C][C]0.337874[/C][C]25.4759[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]GI[/C][C]-0.353182385451952[/C][C]0.077065[/C][C]-4.5829[/C][C]3.4e-05[/C][C]1.7e-05[/C][/ROW]
[ROW][C]M1[/C][C]0.392854341237291[/C][C]0.400835[/C][C]0.9801[/C][C]0.33206[/C][C]0.16603[/C][/ROW]
[ROW][C]M2[/C][C]0.374045284364414[/C][C]0.400542[/C][C]0.9338[/C][C]0.355155[/C][C]0.177578[/C][/ROW]
[ROW][C]M3[/C][C]0.168172579782492[/C][C]0.400376[/C][C]0.42[/C][C]0.676372[/C][C]0.338186[/C][/ROW]
[ROW][C]M4[/C][C]-0.110636477090391[/C][C]0.400171[/C][C]-0.2765[/C][C]0.783397[/C][C]0.391698[/C][/ROW]
[ROW][C]M5[/C][C]-0.294127295418079[/C][C]0.399886[/C][C]-0.7355[/C][C]0.465673[/C][C]0.232836[/C][/ROW]
[ROW][C]M6[/C][C]-0.360000000000001[/C][C]0.399874[/C][C]-0.9003[/C][C]0.372559[/C][C]0.18628[/C][/ROW]
[ROW][C]M7[/C][C]0.421190943127117[/C][C]0.399901[/C][C]1.0532[/C][C]0.297616[/C][C]0.148808[/C][/ROW]
[ROW][C]M8[/C][C]0.485872704581921[/C][C]0.399886[/C][C]1.215[/C][C]0.230424[/C][C]0.115212[/C][/ROW]
[ROW][C]M9[/C][C]0.35293635229096[/C][C]0.399877[/C][C]0.8826[/C][C]0.381938[/C][C]0.190969[/C][/ROW]
[ROW][C]M10[/C][C]0.0811909431271165[/C][C]0.399901[/C][C]0.203[/C][C]0.83999[/C][C]0.419995[/C][/ROW]
[ROW][C]M11[/C][C]-0.147063647709040[/C][C]0.399877[/C][C]-0.3678[/C][C]0.714694[/C][C]0.357347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=2

As an alternative you can also use a 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)8.607637725084680.33787425.475900
GI-0.3531823854519520.077065-4.58293.4e-051.7e-05
M10.3928543412372910.4008350.98010.332060.16603
M20.3740452843644140.4005420.93380.3551550.177578
M30.1681725797824920.4003760.420.6763720.338186
M4-0.1106364770903910.400171-0.27650.7833970.391698
M5-0.2941272954180790.399886-0.73550.4656730.232836
M6-0.3600000000000010.399874-0.90030.3725590.18628
M70.4211909431271170.3999011.05320.2976160.148808
M80.4858727045819210.3998861.2150.2304240.115212
M90.352936352290960.3998770.88260.3819380.190969
M100.08119094312711650.3999010.2030.839990.419995
M11-0.1470636477090400.399877-0.36780.7146940.357347







Multiple Linear Regression - Regression Statistics
Multiple R0.65086810078016
R-squared0.423629284613173
Adjusted R-squared0.276470804088877
F-TEST (value)2.87872831456174
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.00472867820596834
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.632256148149712
Sum Squared Residuals18.7881483330362

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.65086810078016 \tabularnewline
R-squared & 0.423629284613173 \tabularnewline
Adjusted R-squared & 0.276470804088877 \tabularnewline
F-TEST (value) & 2.87872831456174 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.00472867820596834 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.632256148149712 \tabularnewline
Sum Squared Residuals & 18.7881483330362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.65086810078016[/C][/ROW]
[ROW][C]R-squared[/C][C]0.423629284613173[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.276470804088877[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.87872831456174[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.00472867820596834[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.632256148149712[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]18.7881483330362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.65086810078016
R-squared0.423629284613173
Adjusted R-squared0.276470804088877
F-TEST (value)2.87872831456174
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.00472867820596834
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.632256148149712
Sum Squared Residuals18.7881483330362







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.98.435400249598880.464599750401121
28.88.522545908361560.277454091638439
38.38.38730968087003-0.0873096808700303
47.57.93190943127117-0.431909431271172
57.27.6424638973079-0.442463897307898
67.47.68254590836156-0.282545908361562
78.88.428418612943480.371581387056518
89.38.528418612943480.771581387056518
99.38.466118737742910.833881262257088
108.77.94714565876270.752854341237297
118.27.789527545016940.410472454983062
128.38.007227669816370.292772330183634
138.58.364763772508460.135236227491537
148.68.27531823854520.324681761454805
158.57.89285434123730.607145658762702
168.27.75531823854520.444681761454804
178.17.571827420217510.528172579782492
187.97.43531823854520.464681761454805
198.68.181190943127120.418809056872882
208.78.245872704581920.454127295418077
218.78.148254590836160.551745409163843
228.58.088418612943480.411581387056516
238.47.754209306471740.645790693528259
248.57.79531823854520.704681761454804
258.78.294127295418070.405872704581927
268.78.27531823854520.424681761454804
278.68.316673203779640.28332679622036
288.57.896591192725980.603408807274024
298.37.64246389730790.657536102692103
3087.647227669816370.352772330183633
318.28.46373685148868-0.263736851488680
328.18.49310037439829-0.393100374398289
338.18.32484578356213-0.224845783562133
3488.0177821358531-0.0177821358530932
357.97.789527545016940.110472454983063
367.97.93659119272598-0.0365911927259764
3788.29412729541807-0.294127295418073
3888.24-0.24
397.98.10476377250847-0.204763772508468
4087.825954715635590.174045284364415
417.77.85437332857907-0.154373328579069
427.27.78850062399715-0.588500623997148
437.58.53437332857907-1.03437332857907
447.38.66969156712426-1.36969156712426
4578.50143697628811-1.50143697628811
4678.05310037439829-1.05310037439829
4777.68357282938135-0.683572829381351
487.27.68936352290961-0.48936352290961
497.38.01158138705651-0.711581387056511
507.17.88681761454805-0.786817614548048
516.87.39839900160456-0.598399001604565
526.47.19022642182207-0.790226421822071
536.16.68887145658763-0.588871456587628
546.56.446407559279730.0535924407202706
557.77.192280263861650.507719736138349
567.97.362916740952040.537083259047959
577.57.159343911570690.34065608842931
586.96.99355321804243-0.0935532180424317
596.67.08316277411303-0.483162774113033
606.97.37149937600285-0.471499376002853

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 8.43540024959888 & 0.464599750401121 \tabularnewline
2 & 8.8 & 8.52254590836156 & 0.277454091638439 \tabularnewline
3 & 8.3 & 8.38730968087003 & -0.0873096808700303 \tabularnewline
4 & 7.5 & 7.93190943127117 & -0.431909431271172 \tabularnewline
5 & 7.2 & 7.6424638973079 & -0.442463897307898 \tabularnewline
6 & 7.4 & 7.68254590836156 & -0.282545908361562 \tabularnewline
7 & 8.8 & 8.42841861294348 & 0.371581387056518 \tabularnewline
8 & 9.3 & 8.52841861294348 & 0.771581387056518 \tabularnewline
9 & 9.3 & 8.46611873774291 & 0.833881262257088 \tabularnewline
10 & 8.7 & 7.9471456587627 & 0.752854341237297 \tabularnewline
11 & 8.2 & 7.78952754501694 & 0.410472454983062 \tabularnewline
12 & 8.3 & 8.00722766981637 & 0.292772330183634 \tabularnewline
13 & 8.5 & 8.36476377250846 & 0.135236227491537 \tabularnewline
14 & 8.6 & 8.2753182385452 & 0.324681761454805 \tabularnewline
15 & 8.5 & 7.8928543412373 & 0.607145658762702 \tabularnewline
16 & 8.2 & 7.7553182385452 & 0.444681761454804 \tabularnewline
17 & 8.1 & 7.57182742021751 & 0.528172579782492 \tabularnewline
18 & 7.9 & 7.4353182385452 & 0.464681761454805 \tabularnewline
19 & 8.6 & 8.18119094312712 & 0.418809056872882 \tabularnewline
20 & 8.7 & 8.24587270458192 & 0.454127295418077 \tabularnewline
21 & 8.7 & 8.14825459083616 & 0.551745409163843 \tabularnewline
22 & 8.5 & 8.08841861294348 & 0.411581387056516 \tabularnewline
23 & 8.4 & 7.75420930647174 & 0.645790693528259 \tabularnewline
24 & 8.5 & 7.7953182385452 & 0.704681761454804 \tabularnewline
25 & 8.7 & 8.29412729541807 & 0.405872704581927 \tabularnewline
26 & 8.7 & 8.2753182385452 & 0.424681761454804 \tabularnewline
27 & 8.6 & 8.31667320377964 & 0.28332679622036 \tabularnewline
28 & 8.5 & 7.89659119272598 & 0.603408807274024 \tabularnewline
29 & 8.3 & 7.6424638973079 & 0.657536102692103 \tabularnewline
30 & 8 & 7.64722766981637 & 0.352772330183633 \tabularnewline
31 & 8.2 & 8.46373685148868 & -0.263736851488680 \tabularnewline
32 & 8.1 & 8.49310037439829 & -0.393100374398289 \tabularnewline
33 & 8.1 & 8.32484578356213 & -0.224845783562133 \tabularnewline
34 & 8 & 8.0177821358531 & -0.0177821358530932 \tabularnewline
35 & 7.9 & 7.78952754501694 & 0.110472454983063 \tabularnewline
36 & 7.9 & 7.93659119272598 & -0.0365911927259764 \tabularnewline
37 & 8 & 8.29412729541807 & -0.294127295418073 \tabularnewline
38 & 8 & 8.24 & -0.24 \tabularnewline
39 & 7.9 & 8.10476377250847 & -0.204763772508468 \tabularnewline
40 & 8 & 7.82595471563559 & 0.174045284364415 \tabularnewline
41 & 7.7 & 7.85437332857907 & -0.154373328579069 \tabularnewline
42 & 7.2 & 7.78850062399715 & -0.588500623997148 \tabularnewline
43 & 7.5 & 8.53437332857907 & -1.03437332857907 \tabularnewline
44 & 7.3 & 8.66969156712426 & -1.36969156712426 \tabularnewline
45 & 7 & 8.50143697628811 & -1.50143697628811 \tabularnewline
46 & 7 & 8.05310037439829 & -1.05310037439829 \tabularnewline
47 & 7 & 7.68357282938135 & -0.683572829381351 \tabularnewline
48 & 7.2 & 7.68936352290961 & -0.48936352290961 \tabularnewline
49 & 7.3 & 8.01158138705651 & -0.711581387056511 \tabularnewline
50 & 7.1 & 7.88681761454805 & -0.786817614548048 \tabularnewline
51 & 6.8 & 7.39839900160456 & -0.598399001604565 \tabularnewline
52 & 6.4 & 7.19022642182207 & -0.790226421822071 \tabularnewline
53 & 6.1 & 6.68887145658763 & -0.588871456587628 \tabularnewline
54 & 6.5 & 6.44640755927973 & 0.0535924407202706 \tabularnewline
55 & 7.7 & 7.19228026386165 & 0.507719736138349 \tabularnewline
56 & 7.9 & 7.36291674095204 & 0.537083259047959 \tabularnewline
57 & 7.5 & 7.15934391157069 & 0.34065608842931 \tabularnewline
58 & 6.9 & 6.99355321804243 & -0.0935532180424317 \tabularnewline
59 & 6.6 & 7.08316277411303 & -0.483162774113033 \tabularnewline
60 & 6.9 & 7.37149937600285 & -0.471499376002853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&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]8.9[/C][C]8.43540024959888[/C][C]0.464599750401121[/C][/ROW]
[ROW][C]2[/C][C]8.8[/C][C]8.52254590836156[/C][C]0.277454091638439[/C][/ROW]
[ROW][C]3[/C][C]8.3[/C][C]8.38730968087003[/C][C]-0.0873096808700303[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]7.93190943127117[/C][C]-0.431909431271172[/C][/ROW]
[ROW][C]5[/C][C]7.2[/C][C]7.6424638973079[/C][C]-0.442463897307898[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]7.68254590836156[/C][C]-0.282545908361562[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.42841861294348[/C][C]0.371581387056518[/C][/ROW]
[ROW][C]8[/C][C]9.3[/C][C]8.52841861294348[/C][C]0.771581387056518[/C][/ROW]
[ROW][C]9[/C][C]9.3[/C][C]8.46611873774291[/C][C]0.833881262257088[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]7.9471456587627[/C][C]0.752854341237297[/C][/ROW]
[ROW][C]11[/C][C]8.2[/C][C]7.78952754501694[/C][C]0.410472454983062[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.00722766981637[/C][C]0.292772330183634[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.36476377250846[/C][C]0.135236227491537[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]8.2753182385452[/C][C]0.324681761454805[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]7.8928543412373[/C][C]0.607145658762702[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]7.7553182385452[/C][C]0.444681761454804[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]7.57182742021751[/C][C]0.528172579782492[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.4353182385452[/C][C]0.464681761454805[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.18119094312712[/C][C]0.418809056872882[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]8.24587270458192[/C][C]0.454127295418077[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.14825459083616[/C][C]0.551745409163843[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.08841861294348[/C][C]0.411581387056516[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]7.75420930647174[/C][C]0.645790693528259[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]7.7953182385452[/C][C]0.704681761454804[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.29412729541807[/C][C]0.405872704581927[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.2753182385452[/C][C]0.424681761454804[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.31667320377964[/C][C]0.28332679622036[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]7.89659119272598[/C][C]0.603408807274024[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]7.6424638973079[/C][C]0.657536102692103[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.64722766981637[/C][C]0.352772330183633[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.46373685148868[/C][C]-0.263736851488680[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.49310037439829[/C][C]-0.393100374398289[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.32484578356213[/C][C]-0.224845783562133[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.0177821358531[/C][C]-0.0177821358530932[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.78952754501694[/C][C]0.110472454983063[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.93659119272598[/C][C]-0.0365911927259764[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.29412729541807[/C][C]-0.294127295418073[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.24[/C][C]-0.24[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]8.10476377250847[/C][C]-0.204763772508468[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.82595471563559[/C][C]0.174045284364415[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]7.85437332857907[/C][C]-0.154373328579069[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.78850062399715[/C][C]-0.588500623997148[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]8.53437332857907[/C][C]-1.03437332857907[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]8.66969156712426[/C][C]-1.36969156712426[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]8.50143697628811[/C][C]-1.50143697628811[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]8.05310037439829[/C][C]-1.05310037439829[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]7.68357282938135[/C][C]-0.683572829381351[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.68936352290961[/C][C]-0.48936352290961[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]8.01158138705651[/C][C]-0.711581387056511[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.88681761454805[/C][C]-0.786817614548048[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.39839900160456[/C][C]-0.598399001604565[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]7.19022642182207[/C][C]-0.790226421822071[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]6.68887145658763[/C][C]-0.588871456587628[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.44640755927973[/C][C]0.0535924407202706[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.19228026386165[/C][C]0.507719736138349[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.36291674095204[/C][C]0.537083259047959[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.15934391157069[/C][C]0.34065608842931[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]6.99355321804243[/C][C]-0.0935532180424317[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]7.08316277411303[/C][C]-0.483162774113033[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]7.37149937600285[/C][C]-0.471499376002853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.98.435400249598880.464599750401121
28.88.522545908361560.277454091638439
38.38.38730968087003-0.0873096808700303
47.57.93190943127117-0.431909431271172
57.27.6424638973079-0.442463897307898
67.47.68254590836156-0.282545908361562
78.88.428418612943480.371581387056518
89.38.528418612943480.771581387056518
99.38.466118737742910.833881262257088
108.77.94714565876270.752854341237297
118.27.789527545016940.410472454983062
128.38.007227669816370.292772330183634
138.58.364763772508460.135236227491537
148.68.27531823854520.324681761454805
158.57.89285434123730.607145658762702
168.27.75531823854520.444681761454804
178.17.571827420217510.528172579782492
187.97.43531823854520.464681761454805
198.68.181190943127120.418809056872882
208.78.245872704581920.454127295418077
218.78.148254590836160.551745409163843
228.58.088418612943480.411581387056516
238.47.754209306471740.645790693528259
248.57.79531823854520.704681761454804
258.78.294127295418070.405872704581927
268.78.27531823854520.424681761454804
278.68.316673203779640.28332679622036
288.57.896591192725980.603408807274024
298.37.64246389730790.657536102692103
3087.647227669816370.352772330183633
318.28.46373685148868-0.263736851488680
328.18.49310037439829-0.393100374398289
338.18.32484578356213-0.224845783562133
3488.0177821358531-0.0177821358530932
357.97.789527545016940.110472454983063
367.97.93659119272598-0.0365911927259764
3788.29412729541807-0.294127295418073
3888.24-0.24
397.98.10476377250847-0.204763772508468
4087.825954715635590.174045284364415
417.77.85437332857907-0.154373328579069
427.27.78850062399715-0.588500623997148
437.58.53437332857907-1.03437332857907
447.38.66969156712426-1.36969156712426
4578.50143697628811-1.50143697628811
4678.05310037439829-1.05310037439829
4777.68357282938135-0.683572829381351
487.27.68936352290961-0.48936352290961
497.38.01158138705651-0.711581387056511
507.17.88681761454805-0.786817614548048
516.87.39839900160456-0.598399001604565
526.47.19022642182207-0.790226421822071
536.16.68887145658763-0.588871456587628
546.56.446407559279730.0535924407202706
557.77.192280263861650.507719736138349
567.97.362916740952040.537083259047959
577.57.159343911570690.34065608842931
586.96.99355321804243-0.0935532180424317
596.67.08316277411303-0.483162774113033
606.97.37149937600285-0.471499376002853







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1371318642305220.2742637284610430.862868135769478
170.1832659141577540.3665318283155080.816734085842246
180.1069443096586970.2138886193173940.893055690341303
190.06563631839125840.1312726367825170.934363681608742
200.06787279280257370.1357455856051470.932127207197426
210.06337672148061150.1267534429612230.936623278519388
220.0399840512667950.079968102533590.960015948733205
230.02729204329125730.05458408658251460.972707956708743
240.01959434893840820.03918869787681630.980405651061592
250.01229712809386790.02459425618773580.987702871906132
260.008140740044712780.01628148008942560.991859259955287
270.005512912879948430.01102582575989690.994487087120052
280.01036285502596670.02072571005193330.989637144974033
290.02131989159707550.04263978319415110.978680108402924
300.02010544721010920.04021089442021840.97989455278989
310.01710654997924610.03421309995849220.982893450020754
320.02759805886935430.05519611773870850.972401941130646
330.04338819745107440.08677639490214880.956611802548926
340.0511205783654030.1022411567308060.948879421634597
350.05921181046464210.1184236209292840.940788189535358
360.05914381992984460.1182876398596890.940856180070155
370.06240437558293810.1248087511658760.937595624417062
380.07214416725577460.1442883345115490.927855832744225
390.08270582083018240.1654116416603650.917294179169818
400.202769507899190.405539015798380.79723049210081
410.6674029999385110.6651940001229770.332597000061489
420.8521625656086270.2956748687827470.147837434391373
430.7818781298061750.4362437403876490.218121870193825
440.7774284037245460.4451431925509070.222571596275454

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.137131864230522 & 0.274263728461043 & 0.862868135769478 \tabularnewline
17 & 0.183265914157754 & 0.366531828315508 & 0.816734085842246 \tabularnewline
18 & 0.106944309658697 & 0.213888619317394 & 0.893055690341303 \tabularnewline
19 & 0.0656363183912584 & 0.131272636782517 & 0.934363681608742 \tabularnewline
20 & 0.0678727928025737 & 0.135745585605147 & 0.932127207197426 \tabularnewline
21 & 0.0633767214806115 & 0.126753442961223 & 0.936623278519388 \tabularnewline
22 & 0.039984051266795 & 0.07996810253359 & 0.960015948733205 \tabularnewline
23 & 0.0272920432912573 & 0.0545840865825146 & 0.972707956708743 \tabularnewline
24 & 0.0195943489384082 & 0.0391886978768163 & 0.980405651061592 \tabularnewline
25 & 0.0122971280938679 & 0.0245942561877358 & 0.987702871906132 \tabularnewline
26 & 0.00814074004471278 & 0.0162814800894256 & 0.991859259955287 \tabularnewline
27 & 0.00551291287994843 & 0.0110258257598969 & 0.994487087120052 \tabularnewline
28 & 0.0103628550259667 & 0.0207257100519333 & 0.989637144974033 \tabularnewline
29 & 0.0213198915970755 & 0.0426397831941511 & 0.978680108402924 \tabularnewline
30 & 0.0201054472101092 & 0.0402108944202184 & 0.97989455278989 \tabularnewline
31 & 0.0171065499792461 & 0.0342130999584922 & 0.982893450020754 \tabularnewline
32 & 0.0275980588693543 & 0.0551961177387085 & 0.972401941130646 \tabularnewline
33 & 0.0433881974510744 & 0.0867763949021488 & 0.956611802548926 \tabularnewline
34 & 0.051120578365403 & 0.102241156730806 & 0.948879421634597 \tabularnewline
35 & 0.0592118104646421 & 0.118423620929284 & 0.940788189535358 \tabularnewline
36 & 0.0591438199298446 & 0.118287639859689 & 0.940856180070155 \tabularnewline
37 & 0.0624043755829381 & 0.124808751165876 & 0.937595624417062 \tabularnewline
38 & 0.0721441672557746 & 0.144288334511549 & 0.927855832744225 \tabularnewline
39 & 0.0827058208301824 & 0.165411641660365 & 0.917294179169818 \tabularnewline
40 & 0.20276950789919 & 0.40553901579838 & 0.79723049210081 \tabularnewline
41 & 0.667402999938511 & 0.665194000122977 & 0.332597000061489 \tabularnewline
42 & 0.852162565608627 & 0.295674868782747 & 0.147837434391373 \tabularnewline
43 & 0.781878129806175 & 0.436243740387649 & 0.218121870193825 \tabularnewline
44 & 0.777428403724546 & 0.445143192550907 & 0.222571596275454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&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]16[/C][C]0.137131864230522[/C][C]0.274263728461043[/C][C]0.862868135769478[/C][/ROW]
[ROW][C]17[/C][C]0.183265914157754[/C][C]0.366531828315508[/C][C]0.816734085842246[/C][/ROW]
[ROW][C]18[/C][C]0.106944309658697[/C][C]0.213888619317394[/C][C]0.893055690341303[/C][/ROW]
[ROW][C]19[/C][C]0.0656363183912584[/C][C]0.131272636782517[/C][C]0.934363681608742[/C][/ROW]
[ROW][C]20[/C][C]0.0678727928025737[/C][C]0.135745585605147[/C][C]0.932127207197426[/C][/ROW]
[ROW][C]21[/C][C]0.0633767214806115[/C][C]0.126753442961223[/C][C]0.936623278519388[/C][/ROW]
[ROW][C]22[/C][C]0.039984051266795[/C][C]0.07996810253359[/C][C]0.960015948733205[/C][/ROW]
[ROW][C]23[/C][C]0.0272920432912573[/C][C]0.0545840865825146[/C][C]0.972707956708743[/C][/ROW]
[ROW][C]24[/C][C]0.0195943489384082[/C][C]0.0391886978768163[/C][C]0.980405651061592[/C][/ROW]
[ROW][C]25[/C][C]0.0122971280938679[/C][C]0.0245942561877358[/C][C]0.987702871906132[/C][/ROW]
[ROW][C]26[/C][C]0.00814074004471278[/C][C]0.0162814800894256[/C][C]0.991859259955287[/C][/ROW]
[ROW][C]27[/C][C]0.00551291287994843[/C][C]0.0110258257598969[/C][C]0.994487087120052[/C][/ROW]
[ROW][C]28[/C][C]0.0103628550259667[/C][C]0.0207257100519333[/C][C]0.989637144974033[/C][/ROW]
[ROW][C]29[/C][C]0.0213198915970755[/C][C]0.0426397831941511[/C][C]0.978680108402924[/C][/ROW]
[ROW][C]30[/C][C]0.0201054472101092[/C][C]0.0402108944202184[/C][C]0.97989455278989[/C][/ROW]
[ROW][C]31[/C][C]0.0171065499792461[/C][C]0.0342130999584922[/C][C]0.982893450020754[/C][/ROW]
[ROW][C]32[/C][C]0.0275980588693543[/C][C]0.0551961177387085[/C][C]0.972401941130646[/C][/ROW]
[ROW][C]33[/C][C]0.0433881974510744[/C][C]0.0867763949021488[/C][C]0.956611802548926[/C][/ROW]
[ROW][C]34[/C][C]0.051120578365403[/C][C]0.102241156730806[/C][C]0.948879421634597[/C][/ROW]
[ROW][C]35[/C][C]0.0592118104646421[/C][C]0.118423620929284[/C][C]0.940788189535358[/C][/ROW]
[ROW][C]36[/C][C]0.0591438199298446[/C][C]0.118287639859689[/C][C]0.940856180070155[/C][/ROW]
[ROW][C]37[/C][C]0.0624043755829381[/C][C]0.124808751165876[/C][C]0.937595624417062[/C][/ROW]
[ROW][C]38[/C][C]0.0721441672557746[/C][C]0.144288334511549[/C][C]0.927855832744225[/C][/ROW]
[ROW][C]39[/C][C]0.0827058208301824[/C][C]0.165411641660365[/C][C]0.917294179169818[/C][/ROW]
[ROW][C]40[/C][C]0.20276950789919[/C][C]0.40553901579838[/C][C]0.79723049210081[/C][/ROW]
[ROW][C]41[/C][C]0.667402999938511[/C][C]0.665194000122977[/C][C]0.332597000061489[/C][/ROW]
[ROW][C]42[/C][C]0.852162565608627[/C][C]0.295674868782747[/C][C]0.147837434391373[/C][/ROW]
[ROW][C]43[/C][C]0.781878129806175[/C][C]0.436243740387649[/C][C]0.218121870193825[/C][/ROW]
[ROW][C]44[/C][C]0.777428403724546[/C][C]0.445143192550907[/C][C]0.222571596275454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1371318642305220.2742637284610430.862868135769478
170.1832659141577540.3665318283155080.816734085842246
180.1069443096586970.2138886193173940.893055690341303
190.06563631839125840.1312726367825170.934363681608742
200.06787279280257370.1357455856051470.932127207197426
210.06337672148061150.1267534429612230.936623278519388
220.0399840512667950.079968102533590.960015948733205
230.02729204329125730.05458408658251460.972707956708743
240.01959434893840820.03918869787681630.980405651061592
250.01229712809386790.02459425618773580.987702871906132
260.008140740044712780.01628148008942560.991859259955287
270.005512912879948430.01102582575989690.994487087120052
280.01036285502596670.02072571005193330.989637144974033
290.02131989159707550.04263978319415110.978680108402924
300.02010544721010920.04021089442021840.97989455278989
310.01710654997924610.03421309995849220.982893450020754
320.02759805886935430.05519611773870850.972401941130646
330.04338819745107440.08677639490214880.956611802548926
340.0511205783654030.1022411567308060.948879421634597
350.05921181046464210.1184236209292840.940788189535358
360.05914381992984460.1182876398596890.940856180070155
370.06240437558293810.1248087511658760.937595624417062
380.07214416725577460.1442883345115490.927855832744225
390.08270582083018240.1654116416603650.917294179169818
400.202769507899190.405539015798380.79723049210081
410.6674029999385110.6651940001229770.332597000061489
420.8521625656086270.2956748687827470.147837434391373
430.7818781298061750.4362437403876490.218121870193825
440.7774284037245460.4451431925509070.222571596275454







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level80.275862068965517NOK
10% type I error level120.413793103448276NOK

\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 & 8 & 0.275862068965517 & NOK \tabularnewline
10% type I error level & 12 & 0.413793103448276 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58479&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]8[/C][C]0.275862068965517[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.413793103448276[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58479&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58479&T=6

As an alternative you can also use a 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 level80.275862068965517NOK
10% type I error level120.413793103448276NOK



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