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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 computationThu, 19 Nov 2009 09:48:04 -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/19/t12586496679vxf4o9jxkhjgfe.htm/, Retrieved Sat, 20 Apr 2024 01:20:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57821, Retrieved Sat, 20 Apr 2024 01:20:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [] [2009-11-19 16:48:04] [5858ea01c9bd81debbf921a11363ad90] [Current]
-   P         [Multiple Regression] [] [2009-11-19 16:55:45] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 13:51:57] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 13:56:39] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 14:41:53] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 14:44:36] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 14:48:29] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD        [Multiple Regression] [] [2009-12-15 14:51:18] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   P         [Multiple Regression] [] [2009-12-15 14:56:44] [2f674a53c3d7aaa1bcf80e66074d3c9b]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
50.9	0	52.7	54.8	56	56.6
50.6	0	50.9	52.7	54.8	56
52.1	0	50.6	50.9	52.7	54.8
53.3	0	52.1	50.6	50.9	52.7
53.9	0	53.3	52.1	50.6	50.9
54.3	0	53.9	53.3	52.1	50.6
54.2	0	54.3	53.9	53.3	52.1
54.2	0	54.2	54.3	53.9	53.3
53.5	0	54.2	54.2	54.3	53.9
51.4	0	53.5	54.2	54.2	54.3
50.5	0	51.4	53.5	54.2	54.2
50.3	0	50.5	51.4	53.5	54.2
49.8	0	50.3	50.5	51.4	53.5
50.7	0	49.8	50.3	50.5	51.4
52.8	0	50.7	49.8	50.3	50.5
55.3	0	52.8	50.7	49.8	50.3
57.3	0	55.3	52.8	50.7	49.8
57.5	0	57.3	55.3	52.8	50.7
56.8	0	57.5	57.3	55.3	52.8
56.4	0	56.8	57.5	57.3	55.3
56.3	0	56.4	56.8	57.5	57.3
56.4	0	56.3	56.4	56.8	57.5
57	0	56.4	56.3	56.4	56.8
57.9	0	57	56.4	56.3	56.4
58.9	0	57.9	57	56.4	56.3
58.8	0	58.9	57.9	57	56.4
56.5	1	58.8	58.9	57.9	57
51.9	1	56.5	58.8	58.9	57.9
47.4	1	51.9	56.5	58.8	58.9
44.9	1	47.4	51.9	56.5	58.8
43.9	1	44.9	47.4	51.9	56.5
43.4	1	43.9	44.9	47.4	51.9
42.9	1	43.4	43.9	44.9	47.4
42.6	1	42.9	43.4	43.9	44.9
42.2	1	42.6	42.9	43.4	43.9
41.2	1	42.2	42.6	42.9	43.4
40.2	1	41.2	42.2	42.6	42.9
39.3	1	40.2	41.2	42.2	42.6
38.5	1	39.3	40.2	41.2	42.2
38.3	1	38.5	39.3	40.2	41.2
37.9	1	38.3	38.5	39.3	40.2
37.6	1	37.9	38.3	38.5	39.3
37.3	1	37.6	37.9	38.3	38.5
36	1	37.3	37.6	37.9	38.3
34.5	1	36	37.3	37.6	37.9
33.5	1	34.5	36	37.3	37.6
32.9	1	33.5	34.5	36	37.3
32.9	1	32.9	33.5	34.5	36
32.8	1	32.9	32.9	33.5	34.5
31.9	1	32.8	32.9	32.9	33.5
30.5	1	31.9	32.8	32.9	32.9
29.2	1	30.5	31.9	32.8	32.9
28.7	1	29.2	30.5	31.9	32.8
28.4	1	28.7	29.2	30.5	31.9
28	1	28.4	28.7	29.2	30.5
27.4	1	28	28.4	28.7	29.2
26.9	1	27.4	28	28.4	28.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&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=57821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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] = + 2.05759809137512 -1.34349590744337X[t] + 2.04020190088604Y1[t] -1.68946994756172Y2[t] + 0.618936790208306Y3[t] -0.00770865748085621Y4[t] -0.100396827439893M1[t] + 0.107169039936851M2[t] + 0.204369358897789M3[t] -0.0585080940876201M4[t] + 0.209666525151896M5[t] + 0.146397273622895M6[t] + 0.0118560418967594M7[t] -0.0341146470032650M8[t] -0.0954261218610972M9[t] -0.126692471979731M10[t] + 0.380972209907139M11[t] + 0.00424111248802652t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.05759809137512 -1.34349590744337X[t] +  2.04020190088604Y1[t] -1.68946994756172Y2[t] +  0.618936790208306Y3[t] -0.00770865748085621Y4[t] -0.100396827439893M1[t] +  0.107169039936851M2[t] +  0.204369358897789M3[t] -0.0585080940876201M4[t] +  0.209666525151896M5[t] +  0.146397273622895M6[t] +  0.0118560418967594M7[t] -0.0341146470032650M8[t] -0.0954261218610972M9[t] -0.126692471979731M10[t] +  0.380972209907139M11[t] +  0.00424111248802652t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.05759809137512 -1.34349590744337X[t] +  2.04020190088604Y1[t] -1.68946994756172Y2[t] +  0.618936790208306Y3[t] -0.00770865748085621Y4[t] -0.100396827439893M1[t] +  0.107169039936851M2[t] +  0.204369358897789M3[t] -0.0585080940876201M4[t] +  0.209666525151896M5[t] +  0.146397273622895M6[t] +  0.0118560418967594M7[t] -0.0341146470032650M8[t] -0.0954261218610972M9[t] -0.126692471979731M10[t] +  0.380972209907139M11[t] +  0.00424111248802652t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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] = + 2.05759809137512 -1.34349590744337X[t] + 2.04020190088604Y1[t] -1.68946994756172Y2[t] + 0.618936790208306Y3[t] -0.00770865748085621Y4[t] -0.100396827439893M1[t] + 0.107169039936851M2[t] + 0.204369358897789M3[t] -0.0585080940876201M4[t] + 0.209666525151896M5[t] + 0.146397273622895M6[t] + 0.0118560418967594M7[t] -0.0341146470032650M8[t] -0.0954261218610972M9[t] -0.126692471979731M10[t] + 0.380972209907139M11[t] + 0.00424111248802652t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.057598091375121.0986341.87290.0685960.034298
X-1.343495907443370.422544-3.17950.0028880.001444
Y12.040201900886040.15931712.805900
Y2-1.689469947561720.353097-4.78472.5e-051.2e-05
Y30.6189367902083060.3417791.81090.077860.03893
Y4-0.007708657480856210.146222-0.05270.9582250.479112
M1-0.1003968274398930.399058-0.25160.8026830.401342
M20.1071690399368510.3930120.27270.7865330.393266
M30.2043693588977890.3928210.52030.6058230.302911
M4-0.05850809408762010.394326-0.14840.8828120.441406
M50.2096665251518960.3986370.5260.6018950.300948
M60.1463972736228950.390330.37510.7096480.354824
M70.01185604189675940.3884590.03050.9758070.487904
M8-0.03411464700326500.391009-0.08720.9309210.465461
M9-0.09542612186109720.391833-0.24350.8088660.404433
M10-0.1266924719797310.414571-0.30560.7615350.380768
M110.3809722099071390.4136360.9210.3626960.181348
t0.004241112488026520.0135610.31270.7561430.378071

\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) & 2.05759809137512 & 1.098634 & 1.8729 & 0.068596 & 0.034298 \tabularnewline
X & -1.34349590744337 & 0.422544 & -3.1795 & 0.002888 & 0.001444 \tabularnewline
Y1 & 2.04020190088604 & 0.159317 & 12.8059 & 0 & 0 \tabularnewline
Y2 & -1.68946994756172 & 0.353097 & -4.7847 & 2.5e-05 & 1.2e-05 \tabularnewline
Y3 & 0.618936790208306 & 0.341779 & 1.8109 & 0.07786 & 0.03893 \tabularnewline
Y4 & -0.00770865748085621 & 0.146222 & -0.0527 & 0.958225 & 0.479112 \tabularnewline
M1 & -0.100396827439893 & 0.399058 & -0.2516 & 0.802683 & 0.401342 \tabularnewline
M2 & 0.107169039936851 & 0.393012 & 0.2727 & 0.786533 & 0.393266 \tabularnewline
M3 & 0.204369358897789 & 0.392821 & 0.5203 & 0.605823 & 0.302911 \tabularnewline
M4 & -0.0585080940876201 & 0.394326 & -0.1484 & 0.882812 & 0.441406 \tabularnewline
M5 & 0.209666525151896 & 0.398637 & 0.526 & 0.601895 & 0.300948 \tabularnewline
M6 & 0.146397273622895 & 0.39033 & 0.3751 & 0.709648 & 0.354824 \tabularnewline
M7 & 0.0118560418967594 & 0.388459 & 0.0305 & 0.975807 & 0.487904 \tabularnewline
M8 & -0.0341146470032650 & 0.391009 & -0.0872 & 0.930921 & 0.465461 \tabularnewline
M9 & -0.0954261218610972 & 0.391833 & -0.2435 & 0.808866 & 0.404433 \tabularnewline
M10 & -0.126692471979731 & 0.414571 & -0.3056 & 0.761535 & 0.380768 \tabularnewline
M11 & 0.380972209907139 & 0.413636 & 0.921 & 0.362696 & 0.181348 \tabularnewline
t & 0.00424111248802652 & 0.013561 & 0.3127 & 0.756143 & 0.378071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&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]2.05759809137512[/C][C]1.098634[/C][C]1.8729[/C][C]0.068596[/C][C]0.034298[/C][/ROW]
[ROW][C]X[/C][C]-1.34349590744337[/C][C]0.422544[/C][C]-3.1795[/C][C]0.002888[/C][C]0.001444[/C][/ROW]
[ROW][C]Y1[/C][C]2.04020190088604[/C][C]0.159317[/C][C]12.8059[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-1.68946994756172[/C][C]0.353097[/C][C]-4.7847[/C][C]2.5e-05[/C][C]1.2e-05[/C][/ROW]
[ROW][C]Y3[/C][C]0.618936790208306[/C][C]0.341779[/C][C]1.8109[/C][C]0.07786[/C][C]0.03893[/C][/ROW]
[ROW][C]Y4[/C][C]-0.00770865748085621[/C][C]0.146222[/C][C]-0.0527[/C][C]0.958225[/C][C]0.479112[/C][/ROW]
[ROW][C]M1[/C][C]-0.100396827439893[/C][C]0.399058[/C][C]-0.2516[/C][C]0.802683[/C][C]0.401342[/C][/ROW]
[ROW][C]M2[/C][C]0.107169039936851[/C][C]0.393012[/C][C]0.2727[/C][C]0.786533[/C][C]0.393266[/C][/ROW]
[ROW][C]M3[/C][C]0.204369358897789[/C][C]0.392821[/C][C]0.5203[/C][C]0.605823[/C][C]0.302911[/C][/ROW]
[ROW][C]M4[/C][C]-0.0585080940876201[/C][C]0.394326[/C][C]-0.1484[/C][C]0.882812[/C][C]0.441406[/C][/ROW]
[ROW][C]M5[/C][C]0.209666525151896[/C][C]0.398637[/C][C]0.526[/C][C]0.601895[/C][C]0.300948[/C][/ROW]
[ROW][C]M6[/C][C]0.146397273622895[/C][C]0.39033[/C][C]0.3751[/C][C]0.709648[/C][C]0.354824[/C][/ROW]
[ROW][C]M7[/C][C]0.0118560418967594[/C][C]0.388459[/C][C]0.0305[/C][C]0.975807[/C][C]0.487904[/C][/ROW]
[ROW][C]M8[/C][C]-0.0341146470032650[/C][C]0.391009[/C][C]-0.0872[/C][C]0.930921[/C][C]0.465461[/C][/ROW]
[ROW][C]M9[/C][C]-0.0954261218610972[/C][C]0.391833[/C][C]-0.2435[/C][C]0.808866[/C][C]0.404433[/C][/ROW]
[ROW][C]M10[/C][C]-0.126692471979731[/C][C]0.414571[/C][C]-0.3056[/C][C]0.761535[/C][C]0.380768[/C][/ROW]
[ROW][C]M11[/C][C]0.380972209907139[/C][C]0.413636[/C][C]0.921[/C][C]0.362696[/C][C]0.181348[/C][/ROW]
[ROW][C]t[/C][C]0.00424111248802652[/C][C]0.013561[/C][C]0.3127[/C][C]0.756143[/C][C]0.378071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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)2.057598091375121.0986341.87290.0685960.034298
X-1.343495907443370.422544-3.17950.0028880.001444
Y12.040201900886040.15931712.805900
Y2-1.689469947561720.353097-4.78472.5e-051.2e-05
Y30.6189367902083060.3417791.81090.077860.03893
Y4-0.007708657480856210.146222-0.05270.9582250.479112
M1-0.1003968274398930.399058-0.25160.8026830.401342
M20.1071690399368510.3930120.27270.7865330.393266
M30.2043693588977890.3928210.52030.6058230.302911
M4-0.05850809408762010.394326-0.14840.8828120.441406
M50.2096665251518960.3986370.5260.6018950.300948
M60.1463972736228950.390330.37510.7096480.354824
M70.01185604189675940.3884590.03050.9758070.487904
M8-0.03411464700326500.391009-0.08720.9309210.465461
M9-0.09542612186109720.391833-0.24350.8088660.404433
M10-0.1266924719797310.414571-0.30560.7615350.380768
M110.3809722099071390.4136360.9210.3626960.181348
t0.004241112488026520.0135610.31270.7561430.378071






Multiple Linear Regression - Regression Statistics
Multiple R0.998902011700706
R-squared0.997805228979716
Adjusted R-squared0.996848533919593
F-TEST (value)1042.97102657850
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.573066554643035
Sum Squared Residuals12.8078057659671

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.998902011700706 \tabularnewline
R-squared & 0.997805228979716 \tabularnewline
Adjusted R-squared & 0.996848533919593 \tabularnewline
F-TEST (value) & 1042.97102657850 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.573066554643035 \tabularnewline
Sum Squared Residuals & 12.8078057659671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.998902011700706[/C][/ROW]
[ROW][C]R-squared[/C][C]0.997805228979716[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.996848533919593[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1042.97102657850[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/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]0.573066554643035[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]12.8078057659671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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 R0.998902011700706
R-squared0.997805228979716
Adjusted R-squared0.996848533919593
F-TEST (value)1042.97102657850
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.573066554643035
Sum Squared Residuals12.8078057659671






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
150.951.1212796649841-0.221279664984063
250.650.47051115937210.129488840627942
352.151.7104210557060.389578944294044
453.353.921030509141-0.62103050914098
553.953.9356781469922-0.0356781469922387
654.354.00412499396550.295875006034448
754.254.4073848285735-0.207384828573497
854.253.84795876819620.352041231803821
953.554.2027849221773-0.702784922177347
1051.452.6826412119133-1.28264121191334
1150.550.09352284346880.406477156531164
1250.350.9952411719861-0.69524117198609
1349.850.7171968304617-0.91719683046171
1450.749.70594191891810.994058081081873
1552.852.37145046863650.428549531363487
1655.354.56878850358630.731211496413733
1757.356.95471953757720.345280462422786
1857.558.0452497991087-0.545249799108692
1956.856.47520395973530.324796040264674
2056.455.88604099990520.513959000094783
2156.356.3038888835542-0.00388888355415752
2256.456.31383395021760.0861660497823591
235756.95652827359060.0434717264094057
2457.957.57616110591840.323838894081553
2558.958.36516967799590.534830322004101
2658.859.4672468143181-0.667246814318064
2756.556.8841201173723-0.384120117372298
2851.952.7139653980687-0.813965398068738
2947.447.4176309286107-0.0176309286107529
3044.944.52647224263550.373527757364507
3143.944.0689028124578-0.16890281245778
3243.443.4608904725386-0.0608904725386027
3342.942.56053609043060.339463909569416
3442.641.75847972963160.841520270368353
3542.242.2013001898983-0.00130018989829765
3641.241.2097152500296-0.00971525002955794
3740.239.56731890489430.632681095105726
3839.339.18313181259570.116868187404336
3938.538.5220081535929-0.0220081535929321
4038.337.54050511246480.759494887535167
4137.938.2071219683579-0.307121968357908
4237.637.1816954180410.418304581959006
4337.336.99750227550480.302497724495209
443636.6045201285083-0.604520128508329
4534.534.21943070518510.280569294814949
4633.533.14504510823740.354954891762624
4732.933.3486486930423-0.448648693042271
4832.932.51888247206590.381117527934092
4932.832.8290349216641-0.0290349216640542
5031.932.4731682947961-0.573168294796087
5130.530.9120002046923-0.412000204692302
5229.229.2557104767392-0.0557104767391808
5328.728.68484941846190.0151505815381141
5428.428.9424575462493-0.54245754624927
552828.2510061237286-0.251006123728606
5627.427.6005896308517-0.200589630851673
5726.926.81335939865290.0866406013471385

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 50.9 & 51.1212796649841 & -0.221279664984063 \tabularnewline
2 & 50.6 & 50.4705111593721 & 0.129488840627942 \tabularnewline
3 & 52.1 & 51.710421055706 & 0.389578944294044 \tabularnewline
4 & 53.3 & 53.921030509141 & -0.62103050914098 \tabularnewline
5 & 53.9 & 53.9356781469922 & -0.0356781469922387 \tabularnewline
6 & 54.3 & 54.0041249939655 & 0.295875006034448 \tabularnewline
7 & 54.2 & 54.4073848285735 & -0.207384828573497 \tabularnewline
8 & 54.2 & 53.8479587681962 & 0.352041231803821 \tabularnewline
9 & 53.5 & 54.2027849221773 & -0.702784922177347 \tabularnewline
10 & 51.4 & 52.6826412119133 & -1.28264121191334 \tabularnewline
11 & 50.5 & 50.0935228434688 & 0.406477156531164 \tabularnewline
12 & 50.3 & 50.9952411719861 & -0.69524117198609 \tabularnewline
13 & 49.8 & 50.7171968304617 & -0.91719683046171 \tabularnewline
14 & 50.7 & 49.7059419189181 & 0.994058081081873 \tabularnewline
15 & 52.8 & 52.3714504686365 & 0.428549531363487 \tabularnewline
16 & 55.3 & 54.5687885035863 & 0.731211496413733 \tabularnewline
17 & 57.3 & 56.9547195375772 & 0.345280462422786 \tabularnewline
18 & 57.5 & 58.0452497991087 & -0.545249799108692 \tabularnewline
19 & 56.8 & 56.4752039597353 & 0.324796040264674 \tabularnewline
20 & 56.4 & 55.8860409999052 & 0.513959000094783 \tabularnewline
21 & 56.3 & 56.3038888835542 & -0.00388888355415752 \tabularnewline
22 & 56.4 & 56.3138339502176 & 0.0861660497823591 \tabularnewline
23 & 57 & 56.9565282735906 & 0.0434717264094057 \tabularnewline
24 & 57.9 & 57.5761611059184 & 0.323838894081553 \tabularnewline
25 & 58.9 & 58.3651696779959 & 0.534830322004101 \tabularnewline
26 & 58.8 & 59.4672468143181 & -0.667246814318064 \tabularnewline
27 & 56.5 & 56.8841201173723 & -0.384120117372298 \tabularnewline
28 & 51.9 & 52.7139653980687 & -0.813965398068738 \tabularnewline
29 & 47.4 & 47.4176309286107 & -0.0176309286107529 \tabularnewline
30 & 44.9 & 44.5264722426355 & 0.373527757364507 \tabularnewline
31 & 43.9 & 44.0689028124578 & -0.16890281245778 \tabularnewline
32 & 43.4 & 43.4608904725386 & -0.0608904725386027 \tabularnewline
33 & 42.9 & 42.5605360904306 & 0.339463909569416 \tabularnewline
34 & 42.6 & 41.7584797296316 & 0.841520270368353 \tabularnewline
35 & 42.2 & 42.2013001898983 & -0.00130018989829765 \tabularnewline
36 & 41.2 & 41.2097152500296 & -0.00971525002955794 \tabularnewline
37 & 40.2 & 39.5673189048943 & 0.632681095105726 \tabularnewline
38 & 39.3 & 39.1831318125957 & 0.116868187404336 \tabularnewline
39 & 38.5 & 38.5220081535929 & -0.0220081535929321 \tabularnewline
40 & 38.3 & 37.5405051124648 & 0.759494887535167 \tabularnewline
41 & 37.9 & 38.2071219683579 & -0.307121968357908 \tabularnewline
42 & 37.6 & 37.181695418041 & 0.418304581959006 \tabularnewline
43 & 37.3 & 36.9975022755048 & 0.302497724495209 \tabularnewline
44 & 36 & 36.6045201285083 & -0.604520128508329 \tabularnewline
45 & 34.5 & 34.2194307051851 & 0.280569294814949 \tabularnewline
46 & 33.5 & 33.1450451082374 & 0.354954891762624 \tabularnewline
47 & 32.9 & 33.3486486930423 & -0.448648693042271 \tabularnewline
48 & 32.9 & 32.5188824720659 & 0.381117527934092 \tabularnewline
49 & 32.8 & 32.8290349216641 & -0.0290349216640542 \tabularnewline
50 & 31.9 & 32.4731682947961 & -0.573168294796087 \tabularnewline
51 & 30.5 & 30.9120002046923 & -0.412000204692302 \tabularnewline
52 & 29.2 & 29.2557104767392 & -0.0557104767391808 \tabularnewline
53 & 28.7 & 28.6848494184619 & 0.0151505815381141 \tabularnewline
54 & 28.4 & 28.9424575462493 & -0.54245754624927 \tabularnewline
55 & 28 & 28.2510061237286 & -0.251006123728606 \tabularnewline
56 & 27.4 & 27.6005896308517 & -0.200589630851673 \tabularnewline
57 & 26.9 & 26.8133593986529 & 0.0866406013471385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&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]50.9[/C][C]51.1212796649841[/C][C]-0.221279664984063[/C][/ROW]
[ROW][C]2[/C][C]50.6[/C][C]50.4705111593721[/C][C]0.129488840627942[/C][/ROW]
[ROW][C]3[/C][C]52.1[/C][C]51.710421055706[/C][C]0.389578944294044[/C][/ROW]
[ROW][C]4[/C][C]53.3[/C][C]53.921030509141[/C][C]-0.62103050914098[/C][/ROW]
[ROW][C]5[/C][C]53.9[/C][C]53.9356781469922[/C][C]-0.0356781469922387[/C][/ROW]
[ROW][C]6[/C][C]54.3[/C][C]54.0041249939655[/C][C]0.295875006034448[/C][/ROW]
[ROW][C]7[/C][C]54.2[/C][C]54.4073848285735[/C][C]-0.207384828573497[/C][/ROW]
[ROW][C]8[/C][C]54.2[/C][C]53.8479587681962[/C][C]0.352041231803821[/C][/ROW]
[ROW][C]9[/C][C]53.5[/C][C]54.2027849221773[/C][C]-0.702784922177347[/C][/ROW]
[ROW][C]10[/C][C]51.4[/C][C]52.6826412119133[/C][C]-1.28264121191334[/C][/ROW]
[ROW][C]11[/C][C]50.5[/C][C]50.0935228434688[/C][C]0.406477156531164[/C][/ROW]
[ROW][C]12[/C][C]50.3[/C][C]50.9952411719861[/C][C]-0.69524117198609[/C][/ROW]
[ROW][C]13[/C][C]49.8[/C][C]50.7171968304617[/C][C]-0.91719683046171[/C][/ROW]
[ROW][C]14[/C][C]50.7[/C][C]49.7059419189181[/C][C]0.994058081081873[/C][/ROW]
[ROW][C]15[/C][C]52.8[/C][C]52.3714504686365[/C][C]0.428549531363487[/C][/ROW]
[ROW][C]16[/C][C]55.3[/C][C]54.5687885035863[/C][C]0.731211496413733[/C][/ROW]
[ROW][C]17[/C][C]57.3[/C][C]56.9547195375772[/C][C]0.345280462422786[/C][/ROW]
[ROW][C]18[/C][C]57.5[/C][C]58.0452497991087[/C][C]-0.545249799108692[/C][/ROW]
[ROW][C]19[/C][C]56.8[/C][C]56.4752039597353[/C][C]0.324796040264674[/C][/ROW]
[ROW][C]20[/C][C]56.4[/C][C]55.8860409999052[/C][C]0.513959000094783[/C][/ROW]
[ROW][C]21[/C][C]56.3[/C][C]56.3038888835542[/C][C]-0.00388888355415752[/C][/ROW]
[ROW][C]22[/C][C]56.4[/C][C]56.3138339502176[/C][C]0.0861660497823591[/C][/ROW]
[ROW][C]23[/C][C]57[/C][C]56.9565282735906[/C][C]0.0434717264094057[/C][/ROW]
[ROW][C]24[/C][C]57.9[/C][C]57.5761611059184[/C][C]0.323838894081553[/C][/ROW]
[ROW][C]25[/C][C]58.9[/C][C]58.3651696779959[/C][C]0.534830322004101[/C][/ROW]
[ROW][C]26[/C][C]58.8[/C][C]59.4672468143181[/C][C]-0.667246814318064[/C][/ROW]
[ROW][C]27[/C][C]56.5[/C][C]56.8841201173723[/C][C]-0.384120117372298[/C][/ROW]
[ROW][C]28[/C][C]51.9[/C][C]52.7139653980687[/C][C]-0.813965398068738[/C][/ROW]
[ROW][C]29[/C][C]47.4[/C][C]47.4176309286107[/C][C]-0.0176309286107529[/C][/ROW]
[ROW][C]30[/C][C]44.9[/C][C]44.5264722426355[/C][C]0.373527757364507[/C][/ROW]
[ROW][C]31[/C][C]43.9[/C][C]44.0689028124578[/C][C]-0.16890281245778[/C][/ROW]
[ROW][C]32[/C][C]43.4[/C][C]43.4608904725386[/C][C]-0.0608904725386027[/C][/ROW]
[ROW][C]33[/C][C]42.9[/C][C]42.5605360904306[/C][C]0.339463909569416[/C][/ROW]
[ROW][C]34[/C][C]42.6[/C][C]41.7584797296316[/C][C]0.841520270368353[/C][/ROW]
[ROW][C]35[/C][C]42.2[/C][C]42.2013001898983[/C][C]-0.00130018989829765[/C][/ROW]
[ROW][C]36[/C][C]41.2[/C][C]41.2097152500296[/C][C]-0.00971525002955794[/C][/ROW]
[ROW][C]37[/C][C]40.2[/C][C]39.5673189048943[/C][C]0.632681095105726[/C][/ROW]
[ROW][C]38[/C][C]39.3[/C][C]39.1831318125957[/C][C]0.116868187404336[/C][/ROW]
[ROW][C]39[/C][C]38.5[/C][C]38.5220081535929[/C][C]-0.0220081535929321[/C][/ROW]
[ROW][C]40[/C][C]38.3[/C][C]37.5405051124648[/C][C]0.759494887535167[/C][/ROW]
[ROW][C]41[/C][C]37.9[/C][C]38.2071219683579[/C][C]-0.307121968357908[/C][/ROW]
[ROW][C]42[/C][C]37.6[/C][C]37.181695418041[/C][C]0.418304581959006[/C][/ROW]
[ROW][C]43[/C][C]37.3[/C][C]36.9975022755048[/C][C]0.302497724495209[/C][/ROW]
[ROW][C]44[/C][C]36[/C][C]36.6045201285083[/C][C]-0.604520128508329[/C][/ROW]
[ROW][C]45[/C][C]34.5[/C][C]34.2194307051851[/C][C]0.280569294814949[/C][/ROW]
[ROW][C]46[/C][C]33.5[/C][C]33.1450451082374[/C][C]0.354954891762624[/C][/ROW]
[ROW][C]47[/C][C]32.9[/C][C]33.3486486930423[/C][C]-0.448648693042271[/C][/ROW]
[ROW][C]48[/C][C]32.9[/C][C]32.5188824720659[/C][C]0.381117527934092[/C][/ROW]
[ROW][C]49[/C][C]32.8[/C][C]32.8290349216641[/C][C]-0.0290349216640542[/C][/ROW]
[ROW][C]50[/C][C]31.9[/C][C]32.4731682947961[/C][C]-0.573168294796087[/C][/ROW]
[ROW][C]51[/C][C]30.5[/C][C]30.9120002046923[/C][C]-0.412000204692302[/C][/ROW]
[ROW][C]52[/C][C]29.2[/C][C]29.2557104767392[/C][C]-0.0557104767391808[/C][/ROW]
[ROW][C]53[/C][C]28.7[/C][C]28.6848494184619[/C][C]0.0151505815381141[/C][/ROW]
[ROW][C]54[/C][C]28.4[/C][C]28.9424575462493[/C][C]-0.54245754624927[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]28.2510061237286[/C][C]-0.251006123728606[/C][/ROW]
[ROW][C]56[/C][C]27.4[/C][C]27.6005896308517[/C][C]-0.200589630851673[/C][/ROW]
[ROW][C]57[/C][C]26.9[/C][C]26.8133593986529[/C][C]0.0866406013471385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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
150.951.1212796649841-0.221279664984063
250.650.47051115937210.129488840627942
352.151.7104210557060.389578944294044
453.353.921030509141-0.62103050914098
553.953.9356781469922-0.0356781469922387
654.354.00412499396550.295875006034448
754.254.4073848285735-0.207384828573497
854.253.84795876819620.352041231803821
953.554.2027849221773-0.702784922177347
1051.452.6826412119133-1.28264121191334
1150.550.09352284346880.406477156531164
1250.350.9952411719861-0.69524117198609
1349.850.7171968304617-0.91719683046171
1450.749.70594191891810.994058081081873
1552.852.37145046863650.428549531363487
1655.354.56878850358630.731211496413733
1757.356.95471953757720.345280462422786
1857.558.0452497991087-0.545249799108692
1956.856.47520395973530.324796040264674
2056.455.88604099990520.513959000094783
2156.356.3038888835542-0.00388888355415752
2256.456.31383395021760.0861660497823591
235756.95652827359060.0434717264094057
2457.957.57616110591840.323838894081553
2558.958.36516967799590.534830322004101
2658.859.4672468143181-0.667246814318064
2756.556.8841201173723-0.384120117372298
2851.952.7139653980687-0.813965398068738
2947.447.4176309286107-0.0176309286107529
3044.944.52647224263550.373527757364507
3143.944.0689028124578-0.16890281245778
3243.443.4608904725386-0.0608904725386027
3342.942.56053609043060.339463909569416
3442.641.75847972963160.841520270368353
3542.242.2013001898983-0.00130018989829765
3641.241.2097152500296-0.00971525002955794
3740.239.56731890489430.632681095105726
3839.339.18313181259570.116868187404336
3938.538.5220081535929-0.0220081535929321
4038.337.54050511246480.759494887535167
4137.938.2071219683579-0.307121968357908
4237.637.1816954180410.418304581959006
4337.336.99750227550480.302497724495209
443636.6045201285083-0.604520128508329
4534.534.21943070518510.280569294814949
4633.533.14504510823740.354954891762624
4732.933.3486486930423-0.448648693042271
4832.932.51888247206590.381117527934092
4932.832.8290349216641-0.0290349216640542
5031.932.4731682947961-0.573168294796087
5130.530.9120002046923-0.412000204692302
5229.229.2557104767392-0.0557104767391808
5328.728.68484941846190.0151505815381141
5428.428.9424575462493-0.54245754624927
552828.2510061237286-0.251006123728606
5627.427.6005896308517-0.200589630851673
5726.926.81335939865290.0866406013471385






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.9253993698641440.1492012602717120.0746006301358558
220.9909680453393670.01806390932126690.00903195466063344
230.9779139010320720.04417219793585520.0220860989679276
240.9659679708323850.06806405833523060.0340320291676153
250.9581165381069410.08376692378611710.0418834618930585
260.9855313180128460.02893736397430770.0144686819871538
270.996553396713010.006893206573980140.00344660328699007
280.993852900582950.01229419883409990.00614709941704995
290.9852569501357240.02948609972855260.0147430498642763
300.9835942429514880.03281151409702320.0164057570485116
310.9672587837462730.06548243250745420.0327412162537271
320.9553494580560770.08930108388784640.0446505419439232
330.9256200792940630.1487598414118740.0743799207059372
340.8771608035034360.2456783929931270.122839196496564
350.7815402745303950.4369194509392110.218459725469605
360.7958856132905180.4082287734189640.204114386709482

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.925399369864144 & 0.149201260271712 & 0.0746006301358558 \tabularnewline
22 & 0.990968045339367 & 0.0180639093212669 & 0.00903195466063344 \tabularnewline
23 & 0.977913901032072 & 0.0441721979358552 & 0.0220860989679276 \tabularnewline
24 & 0.965967970832385 & 0.0680640583352306 & 0.0340320291676153 \tabularnewline
25 & 0.958116538106941 & 0.0837669237861171 & 0.0418834618930585 \tabularnewline
26 & 0.985531318012846 & 0.0289373639743077 & 0.0144686819871538 \tabularnewline
27 & 0.99655339671301 & 0.00689320657398014 & 0.00344660328699007 \tabularnewline
28 & 0.99385290058295 & 0.0122941988340999 & 0.00614709941704995 \tabularnewline
29 & 0.985256950135724 & 0.0294860997285526 & 0.0147430498642763 \tabularnewline
30 & 0.983594242951488 & 0.0328115140970232 & 0.0164057570485116 \tabularnewline
31 & 0.967258783746273 & 0.0654824325074542 & 0.0327412162537271 \tabularnewline
32 & 0.955349458056077 & 0.0893010838878464 & 0.0446505419439232 \tabularnewline
33 & 0.925620079294063 & 0.148759841411874 & 0.0743799207059372 \tabularnewline
34 & 0.877160803503436 & 0.245678392993127 & 0.122839196496564 \tabularnewline
35 & 0.781540274530395 & 0.436919450939211 & 0.218459725469605 \tabularnewline
36 & 0.795885613290518 & 0.408228773418964 & 0.204114386709482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&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]0.925399369864144[/C][C]0.149201260271712[/C][C]0.0746006301358558[/C][/ROW]
[ROW][C]22[/C][C]0.990968045339367[/C][C]0.0180639093212669[/C][C]0.00903195466063344[/C][/ROW]
[ROW][C]23[/C][C]0.977913901032072[/C][C]0.0441721979358552[/C][C]0.0220860989679276[/C][/ROW]
[ROW][C]24[/C][C]0.965967970832385[/C][C]0.0680640583352306[/C][C]0.0340320291676153[/C][/ROW]
[ROW][C]25[/C][C]0.958116538106941[/C][C]0.0837669237861171[/C][C]0.0418834618930585[/C][/ROW]
[ROW][C]26[/C][C]0.985531318012846[/C][C]0.0289373639743077[/C][C]0.0144686819871538[/C][/ROW]
[ROW][C]27[/C][C]0.99655339671301[/C][C]0.00689320657398014[/C][C]0.00344660328699007[/C][/ROW]
[ROW][C]28[/C][C]0.99385290058295[/C][C]0.0122941988340999[/C][C]0.00614709941704995[/C][/ROW]
[ROW][C]29[/C][C]0.985256950135724[/C][C]0.0294860997285526[/C][C]0.0147430498642763[/C][/ROW]
[ROW][C]30[/C][C]0.983594242951488[/C][C]0.0328115140970232[/C][C]0.0164057570485116[/C][/ROW]
[ROW][C]31[/C][C]0.967258783746273[/C][C]0.0654824325074542[/C][C]0.0327412162537271[/C][/ROW]
[ROW][C]32[/C][C]0.955349458056077[/C][C]0.0893010838878464[/C][C]0.0446505419439232[/C][/ROW]
[ROW][C]33[/C][C]0.925620079294063[/C][C]0.148759841411874[/C][C]0.0743799207059372[/C][/ROW]
[ROW][C]34[/C][C]0.877160803503436[/C][C]0.245678392993127[/C][C]0.122839196496564[/C][/ROW]
[ROW][C]35[/C][C]0.781540274530395[/C][C]0.436919450939211[/C][C]0.218459725469605[/C][/ROW]
[ROW][C]36[/C][C]0.795885613290518[/C][C]0.408228773418964[/C][C]0.204114386709482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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
210.9253993698641440.1492012602717120.0746006301358558
220.9909680453393670.01806390932126690.00903195466063344
230.9779139010320720.04417219793585520.0220860989679276
240.9659679708323850.06806405833523060.0340320291676153
250.9581165381069410.08376692378611710.0418834618930585
260.9855313180128460.02893736397430770.0144686819871538
270.996553396713010.006893206573980140.00344660328699007
280.993852900582950.01229419883409990.00614709941704995
290.9852569501357240.02948609972855260.0147430498642763
300.9835942429514880.03281151409702320.0164057570485116
310.9672587837462730.06548243250745420.0327412162537271
320.9553494580560770.08930108388784640.0446505419439232
330.9256200792940630.1487598414118740.0743799207059372
340.8771608035034360.2456783929931270.122839196496564
350.7815402745303950.4369194509392110.218459725469605
360.7958856132905180.4082287734189640.204114386709482






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0625NOK
5% type I error level70.4375NOK
10% type I error level110.6875NOK

\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 & 1 & 0.0625 & NOK \tabularnewline
5% type I error level & 7 & 0.4375 & NOK \tabularnewline
10% type I error level & 11 & 0.6875 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57821&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]1[/C][C]0.0625[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.4375[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.6875[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57821&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57821&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 level10.0625NOK
5% type I error level70.4375NOK
10% type I error level110.6875NOK


Figures (Output of Computation)

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Figure 10
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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')
}