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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 02 Dec 2009 11:37:08 -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/Dec/02/t1259779126midcyhsa5gecrn5.htm/, Retrieved Sat, 27 Apr 2024 14:15:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62522, Retrieved Sat, 27 Apr 2024 14:15:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

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]
- R  D    [Multiple Regression] [Model 4] [2009-11-19 15:08:36] [1f74ef2f756548f1f3a7b6136ea56d7f]
-    D        [Multiple Regression] [4e Link] [2009-12-02 18:37:08] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
656	677	825	696	627	0
785	656	677	825	696	0
412	785	656	677	825	0
352	412	785	656	677	0
839	352	412	785	656	0
729	839	352	412	785	0
696	729	839	352	412	0
641	696	729	839	352	0
695	641	696	729	839	0
638	695	641	696	729	0
762	638	695	641	696	0
635	762	638	695	641	0
721	635	762	638	695	0
854	721	635	762	638	0
418	854	721	635	762	0
367	418	854	721	635	0
824	367	418	854	721	0
687	824	367	418	854	0
601	687	824	367	418	0
676	601	687	824	367	0
740	676	601	687	824	0
691	740	676	601	687	0
683	691	740	676	601	0
594	683	691	740	676	0
729	594	683	691	740	0
731	729	594	683	691	0
386	731	729	594	683	0
331	386	731	729	594	0
707	331	386	731	729	0
715	707	331	386	731	0
657	715	707	331	386	0
653	657	715	707	331	0
642	653	657	715	707	0
643	642	653	657	715	0
718	643	642	653	657	0
654	718	643	642	653	0
632	654	718	643	642	0
731	632	654	718	643	0
392	731	632	654	718	0
344	392	731	632	654	0
792	344	392	731	632	0
852	792	344	392	731	0
649	852	792	344	392	0
629	649	852	792	344	0
685	629	649	852	792	1
617	685	629	649	852	1
715	617	685	629	649	1
715	715	617	685	629	1
629	715	715	617	685	1
916	629	715	715	617	1
531	916	629	715	715	1
357	531	916	629	715	1
917	357	531	916	629	1
828	917	357	531	916	1
708	828	917	357	531	1
858	708	828	917	357	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&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]4 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=62522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 498.427859024053 + 0.130784812235800`Y(t-1)`[t] + 0.0162915608389134`Y(t-2)`[t] + 0.263994243417347`Y(t-3)`[t] -0.219932791022093`Y(t-4)`[t] + 59.7224027781905X[t] + 47.4989221017373M1[t] + 150.105502994404M2[t] -201.549014116771M3[t] -255.564897907489M4[t] + 196.293610116600M5[t] + 211.074911954083M6[t] + 48.6418087775556M7[t] -47.9260020233859M8[t] + 65.6461246792301M9[t] + 32.5833805008135M10[t] + 89.4593062550886M11[t] -0.262984632943971t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y(t)[t] =  +  498.427859024053 +  0.130784812235800`Y(t-1)`[t] +  0.0162915608389134`Y(t-2)`[t] +  0.263994243417347`Y(t-3)`[t] -0.219932791022093`Y(t-4)`[t] +  59.7224027781905X[t] +  47.4989221017373M1[t] +  150.105502994404M2[t] -201.549014116771M3[t] -255.564897907489M4[t] +  196.293610116600M5[t] +  211.074911954083M6[t] +  48.6418087775556M7[t] -47.9260020233859M8[t] +  65.6461246792301M9[t] +  32.5833805008135M10[t] +  89.4593062550886M11[t] -0.262984632943971t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y(t)[t] =  +  498.427859024053 +  0.130784812235800`Y(t-1)`[t] +  0.0162915608389134`Y(t-2)`[t] +  0.263994243417347`Y(t-3)`[t] -0.219932791022093`Y(t-4)`[t] +  59.7224027781905X[t] +  47.4989221017373M1[t] +  150.105502994404M2[t] -201.549014116771M3[t] -255.564897907489M4[t] +  196.293610116600M5[t] +  211.074911954083M6[t] +  48.6418087775556M7[t] -47.9260020233859M8[t] +  65.6461246792301M9[t] +  32.5833805008135M10[t] +  89.4593062550886M11[t] -0.262984632943971t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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)[t] = + 498.427859024053 + 0.130784812235800`Y(t-1)`[t] + 0.0162915608389134`Y(t-2)`[t] + 0.263994243417347`Y(t-3)`[t] -0.219932791022093`Y(t-4)`[t] + 59.7224027781905X[t] + 47.4989221017373M1[t] + 150.105502994404M2[t] -201.549014116771M3[t] -255.564897907489M4[t] + 196.293610116600M5[t] + 211.074911954083M6[t] + 48.6418087775556M7[t] -47.9260020233859M8[t] + 65.6461246792301M9[t] + 32.5833805008135M10[t] + 89.4593062550886M11[t] -0.262984632943971t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)498.427859024053216.5241192.3020.0269110.013456
`Y(t-1)`0.1307848122358000.1666030.7850.4373150.218657
`Y(t-2)`0.01629156083891340.1591490.10240.9190040.459502
`Y(t-3)`0.2639942434173470.1678971.57240.1241580.062079
`Y(t-4)`-0.2199327910220930.171296-1.28390.2069390.103469
X59.722402778190531.4756111.89740.0653910.032695
M147.498922101737341.6545041.14030.2612950.130647
M2150.10550299440437.2128494.03370.0002550.000128
M3-201.54901411677140.935964-4.92351.7e-058e-06
M4-255.56489790748967.716821-3.7740.0005490.000274
M5196.29361011660078.4886212.50090.0168160.008408
M6211.07491195408375.4530022.79740.0080410.004021
M748.641808777555682.4468480.590.5586980.279349
M8-47.926002023385965.654753-0.730.4698850.234942
M965.646124679230147.5338811.3810.1753350.087668
M1032.583380500813541.8744090.77810.4413160.220658
M1189.459306255088640.8802542.18830.0348640.017432
t-0.2629846329439710.709166-0.37080.7128190.356409

\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) & 498.427859024053 & 216.524119 & 2.302 & 0.026911 & 0.013456 \tabularnewline
`Y(t-1)` & 0.130784812235800 & 0.166603 & 0.785 & 0.437315 & 0.218657 \tabularnewline
`Y(t-2)` & 0.0162915608389134 & 0.159149 & 0.1024 & 0.919004 & 0.459502 \tabularnewline
`Y(t-3)` & 0.263994243417347 & 0.167897 & 1.5724 & 0.124158 & 0.062079 \tabularnewline
`Y(t-4)` & -0.219932791022093 & 0.171296 & -1.2839 & 0.206939 & 0.103469 \tabularnewline
X & 59.7224027781905 & 31.475611 & 1.8974 & 0.065391 & 0.032695 \tabularnewline
M1 & 47.4989221017373 & 41.654504 & 1.1403 & 0.261295 & 0.130647 \tabularnewline
M2 & 150.105502994404 & 37.212849 & 4.0337 & 0.000255 & 0.000128 \tabularnewline
M3 & -201.549014116771 & 40.935964 & -4.9235 & 1.7e-05 & 8e-06 \tabularnewline
M4 & -255.564897907489 & 67.716821 & -3.774 & 0.000549 & 0.000274 \tabularnewline
M5 & 196.293610116600 & 78.488621 & 2.5009 & 0.016816 & 0.008408 \tabularnewline
M6 & 211.074911954083 & 75.453002 & 2.7974 & 0.008041 & 0.004021 \tabularnewline
M7 & 48.6418087775556 & 82.446848 & 0.59 & 0.558698 & 0.279349 \tabularnewline
M8 & -47.9260020233859 & 65.654753 & -0.73 & 0.469885 & 0.234942 \tabularnewline
M9 & 65.6461246792301 & 47.533881 & 1.381 & 0.175335 & 0.087668 \tabularnewline
M10 & 32.5833805008135 & 41.874409 & 0.7781 & 0.441316 & 0.220658 \tabularnewline
M11 & 89.4593062550886 & 40.880254 & 2.1883 & 0.034864 & 0.017432 \tabularnewline
t & -0.262984632943971 & 0.709166 & -0.3708 & 0.712819 & 0.356409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&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]498.427859024053[/C][C]216.524119[/C][C]2.302[/C][C]0.026911[/C][C]0.013456[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.130784812235800[/C][C]0.166603[/C][C]0.785[/C][C]0.437315[/C][C]0.218657[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.0162915608389134[/C][C]0.159149[/C][C]0.1024[/C][C]0.919004[/C][C]0.459502[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]0.263994243417347[/C][C]0.167897[/C][C]1.5724[/C][C]0.124158[/C][C]0.062079[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.219932791022093[/C][C]0.171296[/C][C]-1.2839[/C][C]0.206939[/C][C]0.103469[/C][/ROW]
[ROW][C]X[/C][C]59.7224027781905[/C][C]31.475611[/C][C]1.8974[/C][C]0.065391[/C][C]0.032695[/C][/ROW]
[ROW][C]M1[/C][C]47.4989221017373[/C][C]41.654504[/C][C]1.1403[/C][C]0.261295[/C][C]0.130647[/C][/ROW]
[ROW][C]M2[/C][C]150.105502994404[/C][C]37.212849[/C][C]4.0337[/C][C]0.000255[/C][C]0.000128[/C][/ROW]
[ROW][C]M3[/C][C]-201.549014116771[/C][C]40.935964[/C][C]-4.9235[/C][C]1.7e-05[/C][C]8e-06[/C][/ROW]
[ROW][C]M4[/C][C]-255.564897907489[/C][C]67.716821[/C][C]-3.774[/C][C]0.000549[/C][C]0.000274[/C][/ROW]
[ROW][C]M5[/C][C]196.293610116600[/C][C]78.488621[/C][C]2.5009[/C][C]0.016816[/C][C]0.008408[/C][/ROW]
[ROW][C]M6[/C][C]211.074911954083[/C][C]75.453002[/C][C]2.7974[/C][C]0.008041[/C][C]0.004021[/C][/ROW]
[ROW][C]M7[/C][C]48.6418087775556[/C][C]82.446848[/C][C]0.59[/C][C]0.558698[/C][C]0.279349[/C][/ROW]
[ROW][C]M8[/C][C]-47.9260020233859[/C][C]65.654753[/C][C]-0.73[/C][C]0.469885[/C][C]0.234942[/C][/ROW]
[ROW][C]M9[/C][C]65.6461246792301[/C][C]47.533881[/C][C]1.381[/C][C]0.175335[/C][C]0.087668[/C][/ROW]
[ROW][C]M10[/C][C]32.5833805008135[/C][C]41.874409[/C][C]0.7781[/C][C]0.441316[/C][C]0.220658[/C][/ROW]
[ROW][C]M11[/C][C]89.4593062550886[/C][C]40.880254[/C][C]2.1883[/C][C]0.034864[/C][C]0.017432[/C][/ROW]
[ROW][C]t[/C][C]-0.262984632943971[/C][C]0.709166[/C][C]-0.3708[/C][C]0.712819[/C][C]0.356409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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)498.427859024053216.5241192.3020.0269110.013456
`Y(t-1)`0.1307848122358000.1666030.7850.4373150.218657
`Y(t-2)`0.01629156083891340.1591490.10240.9190040.459502
`Y(t-3)`0.2639942434173470.1678971.57240.1241580.062079
`Y(t-4)`-0.2199327910220930.171296-1.28390.2069390.103469
X59.722402778190531.4756111.89740.0653910.032695
M147.498922101737341.6545041.14030.2612950.130647
M2150.10550299440437.2128494.03370.0002550.000128
M3-201.54901411677140.935964-4.92351.7e-058e-06
M4-255.56489790748967.716821-3.7740.0005490.000274
M5196.29361011660078.4886212.50090.0168160.008408
M6211.07491195408375.4530022.79740.0080410.004021
M748.641808777555682.4468480.590.5586980.279349
M8-47.926002023385965.654753-0.730.4698850.234942
M965.646124679230147.5338811.3810.1753350.087668
M1032.583380500813541.8744090.77810.4413160.220658
M1189.459306255088640.8802542.18830.0348640.017432
t-0.2629846329439710.709166-0.37080.7128190.356409






Multiple Linear Regression - Regression Statistics
Multiple R0.955072487884467
R-squared0.912163457113825
Adjusted R-squared0.872868161612115
F-TEST (value)23.2130448560728
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value5.32907051820075e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation52.8072951092583
Sum Squared Residuals105967.195836739

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.955072487884467 \tabularnewline
R-squared & 0.912163457113825 \tabularnewline
Adjusted R-squared & 0.872868161612115 \tabularnewline
F-TEST (value) & 23.2130448560728 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 5.32907051820075e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 52.8072951092583 \tabularnewline
Sum Squared Residuals & 105967.195836739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.955072487884467[/C][/ROW]
[ROW][C]R-squared[/C][C]0.912163457113825[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.872868161612115[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]23.2130448560728[/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]5.32907051820075e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]52.8072951092583[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]105967.195836739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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 R0.955072487884467
R-squared0.912163457113825
Adjusted R-squared0.872868161612115
F-TEST (value)23.2130448560728
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value5.32907051820075e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation52.8072951092583
Sum Squared Residuals105967.195836739






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1656693.487785516207-37.4877855162073
2785809.553644535133-24.5536445351328
3412406.7227827241995.27721727580146
4352332.76896464430819.2310353556923
5839809.11449312069229.885506879308
6729759.50633739721-30.5063373972103
7696656.55318681655239.4468131834482
8641695.375584892178-54.3755848921782
9695664.8073047775330.1926952224705
10638653.12871696042-15.1287169604194
11762695.90476678538666.0952332146137
12635647.823166297527-12.8231662975268
13721653.54554356641767.454456433583
14854810.33906072388643.6609392761136
15418416.4180782385341.58192176146643
16367357.9187786653359.08122133466464
17824811.93817045329612.0618295467042
18687741.041725910909-54.0417259109090
19601650.300352599864-49.3003525998645
20676671.8520610626234.14793893737662
21740656.89249297256183.1075070274392
22691640.58614664334550.4138533566552
23683730.547080143013-47.5470801430132
24594639.380896528041-45.3808965280408
25729647.83523666827381.1647633317275
26731775.049586477908-44.0495864779083
27386403.856989735548-17.8569897355479
28331359.70318547452-28.7031854745202
29707769.322017402124-62.3220174021237
30715740.601508600154-25.6015086001542
31657646.43445567866910.5655443213312
32653653.506612652956-0.506612652955813
33642684.76492946806-42.7649294680594
34643632.86427303236710.1357269676335
35718701.12891670231716.8710832976826
36654619.20757277930634.7924272206937
37632661.978404272587-29.9784042725873
38731779.98171023471-48.9817102347105
39392407.262899658113-15.2628996581132
40344318.52866967979925.4713303202008
41792789.2976344600382.70236553996208
42852750.35815779628101.641842203721
43649664.693270449246-15.6932704492463
44629671.11684680186-42.1168468018602
45685755.53527278185-70.5352727818503
46617662.42086336387-45.4208633638693
47715750.419236369283-35.4192363692831
48715691.58836439512623.4116356048739
49629710.153029976516-81.1530299765161
50916842.07599802836273.924001971638
51531504.73924964360726.2607503563933
52357382.080401536038-25.0804015360375
53917899.3276845638517.6723154361493
54828819.4922702954478.50772970455288
55708693.01873445566914.9812655443313
56858765.14889459038292.8511054096175

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 656 & 693.487785516207 & -37.4877855162073 \tabularnewline
2 & 785 & 809.553644535133 & -24.5536445351328 \tabularnewline
3 & 412 & 406.722782724199 & 5.27721727580146 \tabularnewline
4 & 352 & 332.768964644308 & 19.2310353556923 \tabularnewline
5 & 839 & 809.114493120692 & 29.885506879308 \tabularnewline
6 & 729 & 759.50633739721 & -30.5063373972103 \tabularnewline
7 & 696 & 656.553186816552 & 39.4468131834482 \tabularnewline
8 & 641 & 695.375584892178 & -54.3755848921782 \tabularnewline
9 & 695 & 664.80730477753 & 30.1926952224705 \tabularnewline
10 & 638 & 653.12871696042 & -15.1287169604194 \tabularnewline
11 & 762 & 695.904766785386 & 66.0952332146137 \tabularnewline
12 & 635 & 647.823166297527 & -12.8231662975268 \tabularnewline
13 & 721 & 653.545543566417 & 67.454456433583 \tabularnewline
14 & 854 & 810.339060723886 & 43.6609392761136 \tabularnewline
15 & 418 & 416.418078238534 & 1.58192176146643 \tabularnewline
16 & 367 & 357.918778665335 & 9.08122133466464 \tabularnewline
17 & 824 & 811.938170453296 & 12.0618295467042 \tabularnewline
18 & 687 & 741.041725910909 & -54.0417259109090 \tabularnewline
19 & 601 & 650.300352599864 & -49.3003525998645 \tabularnewline
20 & 676 & 671.852061062623 & 4.14793893737662 \tabularnewline
21 & 740 & 656.892492972561 & 83.1075070274392 \tabularnewline
22 & 691 & 640.586146643345 & 50.4138533566552 \tabularnewline
23 & 683 & 730.547080143013 & -47.5470801430132 \tabularnewline
24 & 594 & 639.380896528041 & -45.3808965280408 \tabularnewline
25 & 729 & 647.835236668273 & 81.1647633317275 \tabularnewline
26 & 731 & 775.049586477908 & -44.0495864779083 \tabularnewline
27 & 386 & 403.856989735548 & -17.8569897355479 \tabularnewline
28 & 331 & 359.70318547452 & -28.7031854745202 \tabularnewline
29 & 707 & 769.322017402124 & -62.3220174021237 \tabularnewline
30 & 715 & 740.601508600154 & -25.6015086001542 \tabularnewline
31 & 657 & 646.434455678669 & 10.5655443213312 \tabularnewline
32 & 653 & 653.506612652956 & -0.506612652955813 \tabularnewline
33 & 642 & 684.76492946806 & -42.7649294680594 \tabularnewline
34 & 643 & 632.864273032367 & 10.1357269676335 \tabularnewline
35 & 718 & 701.128916702317 & 16.8710832976826 \tabularnewline
36 & 654 & 619.207572779306 & 34.7924272206937 \tabularnewline
37 & 632 & 661.978404272587 & -29.9784042725873 \tabularnewline
38 & 731 & 779.98171023471 & -48.9817102347105 \tabularnewline
39 & 392 & 407.262899658113 & -15.2628996581132 \tabularnewline
40 & 344 & 318.528669679799 & 25.4713303202008 \tabularnewline
41 & 792 & 789.297634460038 & 2.70236553996208 \tabularnewline
42 & 852 & 750.35815779628 & 101.641842203721 \tabularnewline
43 & 649 & 664.693270449246 & -15.6932704492463 \tabularnewline
44 & 629 & 671.11684680186 & -42.1168468018602 \tabularnewline
45 & 685 & 755.53527278185 & -70.5352727818503 \tabularnewline
46 & 617 & 662.42086336387 & -45.4208633638693 \tabularnewline
47 & 715 & 750.419236369283 & -35.4192363692831 \tabularnewline
48 & 715 & 691.588364395126 & 23.4116356048739 \tabularnewline
49 & 629 & 710.153029976516 & -81.1530299765161 \tabularnewline
50 & 916 & 842.075998028362 & 73.924001971638 \tabularnewline
51 & 531 & 504.739249643607 & 26.2607503563933 \tabularnewline
52 & 357 & 382.080401536038 & -25.0804015360375 \tabularnewline
53 & 917 & 899.32768456385 & 17.6723154361493 \tabularnewline
54 & 828 & 819.492270295447 & 8.50772970455288 \tabularnewline
55 & 708 & 693.018734455669 & 14.9812655443313 \tabularnewline
56 & 858 & 765.148894590382 & 92.8511054096175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&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]656[/C][C]693.487785516207[/C][C]-37.4877855162073[/C][/ROW]
[ROW][C]2[/C][C]785[/C][C]809.553644535133[/C][C]-24.5536445351328[/C][/ROW]
[ROW][C]3[/C][C]412[/C][C]406.722782724199[/C][C]5.27721727580146[/C][/ROW]
[ROW][C]4[/C][C]352[/C][C]332.768964644308[/C][C]19.2310353556923[/C][/ROW]
[ROW][C]5[/C][C]839[/C][C]809.114493120692[/C][C]29.885506879308[/C][/ROW]
[ROW][C]6[/C][C]729[/C][C]759.50633739721[/C][C]-30.5063373972103[/C][/ROW]
[ROW][C]7[/C][C]696[/C][C]656.553186816552[/C][C]39.4468131834482[/C][/ROW]
[ROW][C]8[/C][C]641[/C][C]695.375584892178[/C][C]-54.3755848921782[/C][/ROW]
[ROW][C]9[/C][C]695[/C][C]664.80730477753[/C][C]30.1926952224705[/C][/ROW]
[ROW][C]10[/C][C]638[/C][C]653.12871696042[/C][C]-15.1287169604194[/C][/ROW]
[ROW][C]11[/C][C]762[/C][C]695.904766785386[/C][C]66.0952332146137[/C][/ROW]
[ROW][C]12[/C][C]635[/C][C]647.823166297527[/C][C]-12.8231662975268[/C][/ROW]
[ROW][C]13[/C][C]721[/C][C]653.545543566417[/C][C]67.454456433583[/C][/ROW]
[ROW][C]14[/C][C]854[/C][C]810.339060723886[/C][C]43.6609392761136[/C][/ROW]
[ROW][C]15[/C][C]418[/C][C]416.418078238534[/C][C]1.58192176146643[/C][/ROW]
[ROW][C]16[/C][C]367[/C][C]357.918778665335[/C][C]9.08122133466464[/C][/ROW]
[ROW][C]17[/C][C]824[/C][C]811.938170453296[/C][C]12.0618295467042[/C][/ROW]
[ROW][C]18[/C][C]687[/C][C]741.041725910909[/C][C]-54.0417259109090[/C][/ROW]
[ROW][C]19[/C][C]601[/C][C]650.300352599864[/C][C]-49.3003525998645[/C][/ROW]
[ROW][C]20[/C][C]676[/C][C]671.852061062623[/C][C]4.14793893737662[/C][/ROW]
[ROW][C]21[/C][C]740[/C][C]656.892492972561[/C][C]83.1075070274392[/C][/ROW]
[ROW][C]22[/C][C]691[/C][C]640.586146643345[/C][C]50.4138533566552[/C][/ROW]
[ROW][C]23[/C][C]683[/C][C]730.547080143013[/C][C]-47.5470801430132[/C][/ROW]
[ROW][C]24[/C][C]594[/C][C]639.380896528041[/C][C]-45.3808965280408[/C][/ROW]
[ROW][C]25[/C][C]729[/C][C]647.835236668273[/C][C]81.1647633317275[/C][/ROW]
[ROW][C]26[/C][C]731[/C][C]775.049586477908[/C][C]-44.0495864779083[/C][/ROW]
[ROW][C]27[/C][C]386[/C][C]403.856989735548[/C][C]-17.8569897355479[/C][/ROW]
[ROW][C]28[/C][C]331[/C][C]359.70318547452[/C][C]-28.7031854745202[/C][/ROW]
[ROW][C]29[/C][C]707[/C][C]769.322017402124[/C][C]-62.3220174021237[/C][/ROW]
[ROW][C]30[/C][C]715[/C][C]740.601508600154[/C][C]-25.6015086001542[/C][/ROW]
[ROW][C]31[/C][C]657[/C][C]646.434455678669[/C][C]10.5655443213312[/C][/ROW]
[ROW][C]32[/C][C]653[/C][C]653.506612652956[/C][C]-0.506612652955813[/C][/ROW]
[ROW][C]33[/C][C]642[/C][C]684.76492946806[/C][C]-42.7649294680594[/C][/ROW]
[ROW][C]34[/C][C]643[/C][C]632.864273032367[/C][C]10.1357269676335[/C][/ROW]
[ROW][C]35[/C][C]718[/C][C]701.128916702317[/C][C]16.8710832976826[/C][/ROW]
[ROW][C]36[/C][C]654[/C][C]619.207572779306[/C][C]34.7924272206937[/C][/ROW]
[ROW][C]37[/C][C]632[/C][C]661.978404272587[/C][C]-29.9784042725873[/C][/ROW]
[ROW][C]38[/C][C]731[/C][C]779.98171023471[/C][C]-48.9817102347105[/C][/ROW]
[ROW][C]39[/C][C]392[/C][C]407.262899658113[/C][C]-15.2628996581132[/C][/ROW]
[ROW][C]40[/C][C]344[/C][C]318.528669679799[/C][C]25.4713303202008[/C][/ROW]
[ROW][C]41[/C][C]792[/C][C]789.297634460038[/C][C]2.70236553996208[/C][/ROW]
[ROW][C]42[/C][C]852[/C][C]750.35815779628[/C][C]101.641842203721[/C][/ROW]
[ROW][C]43[/C][C]649[/C][C]664.693270449246[/C][C]-15.6932704492463[/C][/ROW]
[ROW][C]44[/C][C]629[/C][C]671.11684680186[/C][C]-42.1168468018602[/C][/ROW]
[ROW][C]45[/C][C]685[/C][C]755.53527278185[/C][C]-70.5352727818503[/C][/ROW]
[ROW][C]46[/C][C]617[/C][C]662.42086336387[/C][C]-45.4208633638693[/C][/ROW]
[ROW][C]47[/C][C]715[/C][C]750.419236369283[/C][C]-35.4192363692831[/C][/ROW]
[ROW][C]48[/C][C]715[/C][C]691.588364395126[/C][C]23.4116356048739[/C][/ROW]
[ROW][C]49[/C][C]629[/C][C]710.153029976516[/C][C]-81.1530299765161[/C][/ROW]
[ROW][C]50[/C][C]916[/C][C]842.075998028362[/C][C]73.924001971638[/C][/ROW]
[ROW][C]51[/C][C]531[/C][C]504.739249643607[/C][C]26.2607503563933[/C][/ROW]
[ROW][C]52[/C][C]357[/C][C]382.080401536038[/C][C]-25.0804015360375[/C][/ROW]
[ROW][C]53[/C][C]917[/C][C]899.32768456385[/C][C]17.6723154361493[/C][/ROW]
[ROW][C]54[/C][C]828[/C][C]819.492270295447[/C][C]8.50772970455288[/C][/ROW]
[ROW][C]55[/C][C]708[/C][C]693.018734455669[/C][C]14.9812655443313[/C][/ROW]
[ROW][C]56[/C][C]858[/C][C]765.148894590382[/C][C]92.8511054096175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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
1656693.487785516207-37.4877855162073
2785809.553644535133-24.5536445351328
3412406.7227827241995.27721727580146
4352332.76896464430819.2310353556923
5839809.11449312069229.885506879308
6729759.50633739721-30.5063373972103
7696656.55318681655239.4468131834482
8641695.375584892178-54.3755848921782
9695664.8073047775330.1926952224705
10638653.12871696042-15.1287169604194
11762695.90476678538666.0952332146137
12635647.823166297527-12.8231662975268
13721653.54554356641767.454456433583
14854810.33906072388643.6609392761136
15418416.4180782385341.58192176146643
16367357.9187786653359.08122133466464
17824811.93817045329612.0618295467042
18687741.041725910909-54.0417259109090
19601650.300352599864-49.3003525998645
20676671.8520610626234.14793893737662
21740656.89249297256183.1075070274392
22691640.58614664334550.4138533566552
23683730.547080143013-47.5470801430132
24594639.380896528041-45.3808965280408
25729647.83523666827381.1647633317275
26731775.049586477908-44.0495864779083
27386403.856989735548-17.8569897355479
28331359.70318547452-28.7031854745202
29707769.322017402124-62.3220174021237
30715740.601508600154-25.6015086001542
31657646.43445567866910.5655443213312
32653653.506612652956-0.506612652955813
33642684.76492946806-42.7649294680594
34643632.86427303236710.1357269676335
35718701.12891670231716.8710832976826
36654619.20757277930634.7924272206937
37632661.978404272587-29.9784042725873
38731779.98171023471-48.9817102347105
39392407.262899658113-15.2628996581132
40344318.52866967979925.4713303202008
41792789.2976344600382.70236553996208
42852750.35815779628101.641842203721
43649664.693270449246-15.6932704492463
44629671.11684680186-42.1168468018602
45685755.53527278185-70.5352727818503
46617662.42086336387-45.4208633638693
47715750.419236369283-35.4192363692831
48715691.58836439512623.4116356048739
49629710.153029976516-81.1530299765161
50916842.07599802836273.924001971638
51531504.73924964360726.2607503563933
52357382.080401536038-25.0804015360375
53917899.3276845638517.6723154361493
54828819.4922702954478.50772970455288
55708693.01873445566914.9812655443313
56858765.14889459038292.8511054096175






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.4719058599986090.9438117199972180.528094140001391
220.3402170329308810.6804340658617620.659782967069119
230.2803928882463220.5607857764926430.719607111753678
240.1859214479742510.3718428959485010.81407855202575
250.3177790277957480.6355580555914970.682220972204252
260.6291533899508790.7416932200982430.370846610049121
270.5284671466902360.9430657066195290.471532853309764
280.4306219002109850.861243800421970.569378099789015
290.4950487034518730.9900974069037460.504951296548127
300.4659444157819260.9318888315638510.534055584218074
310.3388590734909850.6777181469819710.661140926509015
320.2287662185263250.457532437052650.771233781473675
330.1698898574895070.3397797149790130.830110142510493
340.09161010583312980.1832202116662600.90838989416687
350.08158878700195640.1631775740039130.918411212998044

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.471905859998609 & 0.943811719997218 & 0.528094140001391 \tabularnewline
22 & 0.340217032930881 & 0.680434065861762 & 0.659782967069119 \tabularnewline
23 & 0.280392888246322 & 0.560785776492643 & 0.719607111753678 \tabularnewline
24 & 0.185921447974251 & 0.371842895948501 & 0.81407855202575 \tabularnewline
25 & 0.317779027795748 & 0.635558055591497 & 0.682220972204252 \tabularnewline
26 & 0.629153389950879 & 0.741693220098243 & 0.370846610049121 \tabularnewline
27 & 0.528467146690236 & 0.943065706619529 & 0.471532853309764 \tabularnewline
28 & 0.430621900210985 & 0.86124380042197 & 0.569378099789015 \tabularnewline
29 & 0.495048703451873 & 0.990097406903746 & 0.504951296548127 \tabularnewline
30 & 0.465944415781926 & 0.931888831563851 & 0.534055584218074 \tabularnewline
31 & 0.338859073490985 & 0.677718146981971 & 0.661140926509015 \tabularnewline
32 & 0.228766218526325 & 0.45753243705265 & 0.771233781473675 \tabularnewline
33 & 0.169889857489507 & 0.339779714979013 & 0.830110142510493 \tabularnewline
34 & 0.0916101058331298 & 0.183220211666260 & 0.90838989416687 \tabularnewline
35 & 0.0815887870019564 & 0.163177574003913 & 0.918411212998044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&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]0.471905859998609[/C][C]0.943811719997218[/C][C]0.528094140001391[/C][/ROW]
[ROW][C]22[/C][C]0.340217032930881[/C][C]0.680434065861762[/C][C]0.659782967069119[/C][/ROW]
[ROW][C]23[/C][C]0.280392888246322[/C][C]0.560785776492643[/C][C]0.719607111753678[/C][/ROW]
[ROW][C]24[/C][C]0.185921447974251[/C][C]0.371842895948501[/C][C]0.81407855202575[/C][/ROW]
[ROW][C]25[/C][C]0.317779027795748[/C][C]0.635558055591497[/C][C]0.682220972204252[/C][/ROW]
[ROW][C]26[/C][C]0.629153389950879[/C][C]0.741693220098243[/C][C]0.370846610049121[/C][/ROW]
[ROW][C]27[/C][C]0.528467146690236[/C][C]0.943065706619529[/C][C]0.471532853309764[/C][/ROW]
[ROW][C]28[/C][C]0.430621900210985[/C][C]0.86124380042197[/C][C]0.569378099789015[/C][/ROW]
[ROW][C]29[/C][C]0.495048703451873[/C][C]0.990097406903746[/C][C]0.504951296548127[/C][/ROW]
[ROW][C]30[/C][C]0.465944415781926[/C][C]0.931888831563851[/C][C]0.534055584218074[/C][/ROW]
[ROW][C]31[/C][C]0.338859073490985[/C][C]0.677718146981971[/C][C]0.661140926509015[/C][/ROW]
[ROW][C]32[/C][C]0.228766218526325[/C][C]0.45753243705265[/C][C]0.771233781473675[/C][/ROW]
[ROW][C]33[/C][C]0.169889857489507[/C][C]0.339779714979013[/C][C]0.830110142510493[/C][/ROW]
[ROW][C]34[/C][C]0.0916101058331298[/C][C]0.183220211666260[/C][C]0.90838989416687[/C][/ROW]
[ROW][C]35[/C][C]0.0815887870019564[/C][C]0.163177574003913[/C][C]0.918411212998044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&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
210.4719058599986090.9438117199972180.528094140001391
220.3402170329308810.6804340658617620.659782967069119
230.2803928882463220.5607857764926430.719607111753678
240.1859214479742510.3718428959485010.81407855202575
250.3177790277957480.6355580555914970.682220972204252
260.6291533899508790.7416932200982430.370846610049121
270.5284671466902360.9430657066195290.471532853309764
280.4306219002109850.861243800421970.569378099789015
290.4950487034518730.9900974069037460.504951296548127
300.4659444157819260.9318888315638510.534055584218074
310.3388590734909850.6777181469819710.661140926509015
320.2287662185263250.457532437052650.771233781473675
330.1698898574895070.3397797149790130.830110142510493
340.09161010583312980.1832202116662600.90838989416687
350.08158878700195640.1631775740039130.918411212998044






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62522&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62522&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62522&T=6

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

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


Figures (Output of Computation)

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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')
}