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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 26 Nov 2011 13:32:22 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/26/t1322332393g1q2pwkgtfllmgr.htm/, Retrieved Mon, 30 Jan 2023 01:48:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147440, Retrieved Mon, 30 Jan 2023 01:48:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
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] [Multivariate regr...] [2009-11-19 09:46:44] [21324e9cdf3569788a3d630236984d87]
-    D      [Multiple Regression] [] [2010-12-07 13:11:12] [f47feae0308dca73181bb669fbad1c56]
- R             [Multiple Regression] [] [2011-11-26 18:32:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R P             [Multiple Regression] [] [2011-11-27 16:58:04] [3931071255a6f7f4a767409781cc5f7d]
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Dataseries X:
112.3	0	117.2	96.8	
117.3	0	112.3	117.2	
111.1	1	117.3	112.3	
102.2	1	111.1	117.3	
104.3	1	102.2	111.1	
122.9	1	104.3	102.2	
107.6	1	122.9	104.3	
121.3	1	107.6	122.9	
131.5	1	121.3	107.6	
89	1	131.5	121.3	
104.4	1	89	131.5	
128.9	1	104.4	89	
135.9	1	128.9	104.4	
133.3	1	135.9	128.9	
121.3	1	133.3	135.9	
120.5	0	121.3	133.3	
120.4	0	120.5	121.3	
137.9	0	120.4	120.5	
126.1	0	137.9	120.4	
133.2	0	126.1	137.9	
151.1	0	133.2	126.1	
105	0	151.1	133.2	
119	0	105	151.1
140.4	0	119	105	
156.6	0	140.4	119	
137.1	0	156.6	140.4	
122.7	0	137.1	156.6	
125.8	0	122.7	137.1	
139.3	0	125.8	122.7	
134.9	0	139.3	125.8	
149.2	0	134.9	139.3	
132.3	0	149.2	134.9	
149	0	132.3	149.2	
117.2	0	149	132.3	
119.6	0	117.2	149	
152	0	119.6	117.2	
149.4	0	152	119.6	
127.3	0	149.4	152	
114.1	0	127.3	149.4	
102.1	0	114.1	127.3	
107.7	0	102.1	114.1	
104.4	0	107.7	102.1	
102.1	0	104.4	107.7	
96	1	102.1	104.4	
109.3	0	96	102.1	
90	1	109.3	96	
83.9	1	90	109.3	
112	1	83.9	90	
114.3	1	112	83.9	
103.6	1	114.3	112	
91.7	1	103.6	114.3	
80.8	1	91.7	103.6	
87.2	1	80.8	91.7	
109.2	1	87.2	80.8	
102.7	1	109.2	87.2	
95.1	1	102.7	109.2	
117.5	1	95.1	102.7	
85.1	1	117.5	95.1	
92.1	1	85.1	117.5	
113.5	1	92.1	85.1	




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
X[t] = + 39.5718545572898 + 1.4428225092746Y[t] + 0.462651817415592`y(t)`[t] + 0.456836619187371`y(t-1)`[t] -12.0357634082612M1[t] -35.1685550498614M2[t] -43.9263346792956M3[t] -39.5414071812871M4[t] -25.9417353094251M5[t] -15.6128526883177M6[t] -27.0108528497098M7[t] -31.7675430580503M8[t] -12.4005152354837M9[t] -53.5642426604347M10[t] -38.356705110219M11[t] -0.0981315636876872t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  39.5718545572898 +  1.4428225092746Y[t] +  0.462651817415592`y(t)`[t] +  0.456836619187371`y(t-1)`[t] -12.0357634082612M1[t] -35.1685550498614M2[t] -43.9263346792956M3[t] -39.5414071812871M4[t] -25.9417353094251M5[t] -15.6128526883177M6[t] -27.0108528497098M7[t] -31.7675430580503M8[t] -12.4005152354837M9[t] -53.5642426604347M10[t] -38.356705110219M11[t] -0.0981315636876872t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  39.5718545572898 +  1.4428225092746Y[t] +  0.462651817415592`y(t)`[t] +  0.456836619187371`y(t-1)`[t] -12.0357634082612M1[t] -35.1685550498614M2[t] -43.9263346792956M3[t] -39.5414071812871M4[t] -25.9417353094251M5[t] -15.6128526883177M6[t] -27.0108528497098M7[t] -31.7675430580503M8[t] -12.4005152354837M9[t] -53.5642426604347M10[t] -38.356705110219M11[t] -0.0981315636876872t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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
X[t] = + 39.5718545572898 + 1.4428225092746Y[t] + 0.462651817415592`y(t)`[t] + 0.456836619187371`y(t-1)`[t] -12.0357634082612M1[t] -35.1685550498614M2[t] -43.9263346792956M3[t] -39.5414071812871M4[t] -25.9417353094251M5[t] -15.6128526883177M6[t] -27.0108528497098M7[t] -31.7675430580503M8[t] -12.4005152354837M9[t] -53.5642426604347M10[t] -38.356705110219M11[t] -0.0981315636876872t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)39.571854557289814.9169872.65280.0110620.005531
Y1.44282250927463.3520620.43040.6689850.334493
`y(t)`0.4626518174155920.1345183.43930.0012870.000644
`y(t-1)`0.4568366191873710.1554032.93970.0052180.002609
M1-12.03576340826125.673619-2.12140.0395620.019781
M2-35.16855504986145.876229-5.984900
M3-43.92633467929566.513124-6.744300
M4-39.54140718128715.828352-6.784300
M5-25.94173530942515.317747-4.87831.4e-057e-06
M6-15.61285268831775.046647-3.09370.0034290.001715
M7-27.01085284970985.191112-5.20335e-062e-06
M8-31.76754305805035.75193-5.52292e-061e-06
M9-12.40051523548375.350115-2.31780.0251720.012586
M10-53.56424266043475.698954-9.39900
M11-38.3567051102197.794011-4.92131.2e-056e-06
t-0.09813156368768720.067336-1.45730.1521240.076062

\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) & 39.5718545572898 & 14.916987 & 2.6528 & 0.011062 & 0.005531 \tabularnewline
Y & 1.4428225092746 & 3.352062 & 0.4304 & 0.668985 & 0.334493 \tabularnewline
`y(t)` & 0.462651817415592 & 0.134518 & 3.4393 & 0.001287 & 0.000644 \tabularnewline
`y(t-1)` & 0.456836619187371 & 0.155403 & 2.9397 & 0.005218 & 0.002609 \tabularnewline
M1 & -12.0357634082612 & 5.673619 & -2.1214 & 0.039562 & 0.019781 \tabularnewline
M2 & -35.1685550498614 & 5.876229 & -5.9849 & 0 & 0 \tabularnewline
M3 & -43.9263346792956 & 6.513124 & -6.7443 & 0 & 0 \tabularnewline
M4 & -39.5414071812871 & 5.828352 & -6.7843 & 0 & 0 \tabularnewline
M5 & -25.9417353094251 & 5.317747 & -4.8783 & 1.4e-05 & 7e-06 \tabularnewline
M6 & -15.6128526883177 & 5.046647 & -3.0937 & 0.003429 & 0.001715 \tabularnewline
M7 & -27.0108528497098 & 5.191112 & -5.2033 & 5e-06 & 2e-06 \tabularnewline
M8 & -31.7675430580503 & 5.75193 & -5.5229 & 2e-06 & 1e-06 \tabularnewline
M9 & -12.4005152354837 & 5.350115 & -2.3178 & 0.025172 & 0.012586 \tabularnewline
M10 & -53.5642426604347 & 5.698954 & -9.399 & 0 & 0 \tabularnewline
M11 & -38.356705110219 & 7.794011 & -4.9213 & 1.2e-05 & 6e-06 \tabularnewline
t & -0.0981315636876872 & 0.067336 & -1.4573 & 0.152124 & 0.076062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&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]39.5718545572898[/C][C]14.916987[/C][C]2.6528[/C][C]0.011062[/C][C]0.005531[/C][/ROW]
[ROW][C]Y[/C][C]1.4428225092746[/C][C]3.352062[/C][C]0.4304[/C][C]0.668985[/C][C]0.334493[/C][/ROW]
[ROW][C]`y(t)`[/C][C]0.462651817415592[/C][C]0.134518[/C][C]3.4393[/C][C]0.001287[/C][C]0.000644[/C][/ROW]
[ROW][C]`y(t-1)`[/C][C]0.456836619187371[/C][C]0.155403[/C][C]2.9397[/C][C]0.005218[/C][C]0.002609[/C][/ROW]
[ROW][C]M1[/C][C]-12.0357634082612[/C][C]5.673619[/C][C]-2.1214[/C][C]0.039562[/C][C]0.019781[/C][/ROW]
[ROW][C]M2[/C][C]-35.1685550498614[/C][C]5.876229[/C][C]-5.9849[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]-43.9263346792956[/C][C]6.513124[/C][C]-6.7443[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-39.5414071812871[/C][C]5.828352[/C][C]-6.7843[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-25.9417353094251[/C][C]5.317747[/C][C]-4.8783[/C][C]1.4e-05[/C][C]7e-06[/C][/ROW]
[ROW][C]M6[/C][C]-15.6128526883177[/C][C]5.046647[/C][C]-3.0937[/C][C]0.003429[/C][C]0.001715[/C][/ROW]
[ROW][C]M7[/C][C]-27.0108528497098[/C][C]5.191112[/C][C]-5.2033[/C][C]5e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M8[/C][C]-31.7675430580503[/C][C]5.75193[/C][C]-5.5229[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M9[/C][C]-12.4005152354837[/C][C]5.350115[/C][C]-2.3178[/C][C]0.025172[/C][C]0.012586[/C][/ROW]
[ROW][C]M10[/C][C]-53.5642426604347[/C][C]5.698954[/C][C]-9.399[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-38.356705110219[/C][C]7.794011[/C][C]-4.9213[/C][C]1.2e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]t[/C][C]-0.0981315636876872[/C][C]0.067336[/C][C]-1.4573[/C][C]0.152124[/C][C]0.076062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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)39.571854557289814.9169872.65280.0110620.005531
Y1.44282250927463.3520620.43040.6689850.334493
`y(t)`0.4626518174155920.1345183.43930.0012870.000644
`y(t-1)`0.4568366191873710.1554032.93970.0052180.002609
M1-12.03576340826125.673619-2.12140.0395620.019781
M2-35.16855504986145.876229-5.984900
M3-43.92633467929566.513124-6.744300
M4-39.54140718128715.828352-6.784300
M5-25.94173530942515.317747-4.87831.4e-057e-06
M6-15.61285268831775.046647-3.09370.0034290.001715
M7-27.01085284970985.191112-5.20335e-062e-06
M8-31.76754305805035.75193-5.52292e-061e-06
M9-12.40051523548375.350115-2.31780.0251720.012586
M10-53.56424266043475.698954-9.39900
M11-38.3567051102197.794011-4.92131.2e-056e-06
t-0.09813156368768720.067336-1.45730.1521240.076062







Multiple Linear Regression - Regression Statistics
Multiple R0.932787352234213
R-squared0.870092244488114
Adjusted R-squared0.825805509654517
F-TEST (value)19.6467914773439
F-TEST (DF numerator)15
F-TEST (DF denominator)44
p-value1.04360964314765e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.91699716280575
Sum Squared Residuals2757.86913933847

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.932787352234213 \tabularnewline
R-squared & 0.870092244488114 \tabularnewline
Adjusted R-squared & 0.825805509654517 \tabularnewline
F-TEST (value) & 19.6467914773439 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 44 \tabularnewline
p-value & 1.04360964314765e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 7.91699716280575 \tabularnewline
Sum Squared Residuals & 2757.86913933847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.932787352234213[/C][/ROW]
[ROW][C]R-squared[/C][C]0.870092244488114[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.825805509654517[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]19.6467914773439[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]44[/C][/ROW]
[ROW][C]p-value[/C][C]1.04360964314765e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]7.91699716280575[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2757.86913933847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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 R0.932787352234213
R-squared0.870092244488114
Adjusted R-squared0.825805509654517
F-TEST (value)19.6467914773439
F-TEST (DF numerator)15
F-TEST (DF denominator)44
p-value1.04360964314765e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.91699716280575
Sum Squared Residuals2757.86913933847







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1112.3125.882537323786-13.5825373237857
2117.3109.7040872445847.5959127554161
3111.1102.3657582137968.73424178620351
4102.2106.068295976077-3.86829597607748
5104.3112.619848070291-8.31984807029128
6122.9119.7563220335163.14367796648385
7107.6117.82487101266-10.2248710126599
8121.3114.3886375510586.91136244894178
9131.5133.006263434964-1.50626343496396
1089102.722114666831-13.7221146668313
11104.4102.8285519289081.57144807109218
12128.9128.7964071481760.103592851824
13135.9135.0327656383950.867234361605378
14133.3126.2329023251067.06709767489355
15121.3119.3719527410161.92804725898431
16120.5115.4763291471885.02367085281238
17120.4123.125708571181-2.72570857118096
18137.9132.9447251515094.95527484849077
19126.1129.499316569284-3.39931656928365
20133.2127.179844187536.0201558124696
21151.1144.3428962436496.75710375635096
22105114.60604478298-9.60604478297976
23119116.5645774701032.43542252989708
24140.4140.2401083159150.159891684085257
25156.6144.40267490528312.1973250947173
26137.1138.443014792737-1.34301479273715
27122.7127.966146390847-5.26614639084666
28125.8116.6824420802299.11755791977077
29139.3125.03975570609414.2602442939063
30134.9142.932499818105-8.03249981810474
31149.2135.56799445542613.6320055445741
32132.3135.319012548016-3.01901254801619
33149153.301856746951-4.30185674695104
34117.2112.0457442448865.15425575511385
35119.6120.071993978027-0.471993978027431
36152144.9135273961987.08647260380221
37149.4148.8659591945640.534040805436261
38127.3139.233647725666-11.9336477256661
39114.1118.965356157773-4.86535615777254
40102.1107.049058818167-4.94905881816664
41107.7108.96853394408-1.26853394408049
42104.4116.308095748779-11.9080957487791
43102.1105.843498093677-3.7434980936772
449699.8598388075494-3.85983880754935
45109.3113.813012246788-4.51301224678761
469077.360541562007912.6394584379921
4783.989.616694507607-5.71669450760702
48112116.236145217587-4.23614521758701
49114.3114.316062937973-0.0160629379732617
50103.6104.986347911906-1.38634791190635
5191.792.2307864965686-0.530786496568621
5280.886.123873978339-5.32387397833903
5387.289.1461537083536-1.94615370835361
54109.297.358357248090811.8416427519092
55102.798.96431986895333.73568013104673
5695.1101.152666905846-6.05266690584585
57117.5113.9359713276483.56402867235165
5885.179.56555474329495.53444525670511
5992.189.91818211535482.18181788464518
60113.5116.613811922124-3.11381192212449

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 112.3 & 125.882537323786 & -13.5825373237857 \tabularnewline
2 & 117.3 & 109.704087244584 & 7.5959127554161 \tabularnewline
3 & 111.1 & 102.365758213796 & 8.73424178620351 \tabularnewline
4 & 102.2 & 106.068295976077 & -3.86829597607748 \tabularnewline
5 & 104.3 & 112.619848070291 & -8.31984807029128 \tabularnewline
6 & 122.9 & 119.756322033516 & 3.14367796648385 \tabularnewline
7 & 107.6 & 117.82487101266 & -10.2248710126599 \tabularnewline
8 & 121.3 & 114.388637551058 & 6.91136244894178 \tabularnewline
9 & 131.5 & 133.006263434964 & -1.50626343496396 \tabularnewline
10 & 89 & 102.722114666831 & -13.7221146668313 \tabularnewline
11 & 104.4 & 102.828551928908 & 1.57144807109218 \tabularnewline
12 & 128.9 & 128.796407148176 & 0.103592851824 \tabularnewline
13 & 135.9 & 135.032765638395 & 0.867234361605378 \tabularnewline
14 & 133.3 & 126.232902325106 & 7.06709767489355 \tabularnewline
15 & 121.3 & 119.371952741016 & 1.92804725898431 \tabularnewline
16 & 120.5 & 115.476329147188 & 5.02367085281238 \tabularnewline
17 & 120.4 & 123.125708571181 & -2.72570857118096 \tabularnewline
18 & 137.9 & 132.944725151509 & 4.95527484849077 \tabularnewline
19 & 126.1 & 129.499316569284 & -3.39931656928365 \tabularnewline
20 & 133.2 & 127.17984418753 & 6.0201558124696 \tabularnewline
21 & 151.1 & 144.342896243649 & 6.75710375635096 \tabularnewline
22 & 105 & 114.60604478298 & -9.60604478297976 \tabularnewline
23 & 119 & 116.564577470103 & 2.43542252989708 \tabularnewline
24 & 140.4 & 140.240108315915 & 0.159891684085257 \tabularnewline
25 & 156.6 & 144.402674905283 & 12.1973250947173 \tabularnewline
26 & 137.1 & 138.443014792737 & -1.34301479273715 \tabularnewline
27 & 122.7 & 127.966146390847 & -5.26614639084666 \tabularnewline
28 & 125.8 & 116.682442080229 & 9.11755791977077 \tabularnewline
29 & 139.3 & 125.039755706094 & 14.2602442939063 \tabularnewline
30 & 134.9 & 142.932499818105 & -8.03249981810474 \tabularnewline
31 & 149.2 & 135.567994455426 & 13.6320055445741 \tabularnewline
32 & 132.3 & 135.319012548016 & -3.01901254801619 \tabularnewline
33 & 149 & 153.301856746951 & -4.30185674695104 \tabularnewline
34 & 117.2 & 112.045744244886 & 5.15425575511385 \tabularnewline
35 & 119.6 & 120.071993978027 & -0.471993978027431 \tabularnewline
36 & 152 & 144.913527396198 & 7.08647260380221 \tabularnewline
37 & 149.4 & 148.865959194564 & 0.534040805436261 \tabularnewline
38 & 127.3 & 139.233647725666 & -11.9336477256661 \tabularnewline
39 & 114.1 & 118.965356157773 & -4.86535615777254 \tabularnewline
40 & 102.1 & 107.049058818167 & -4.94905881816664 \tabularnewline
41 & 107.7 & 108.96853394408 & -1.26853394408049 \tabularnewline
42 & 104.4 & 116.308095748779 & -11.9080957487791 \tabularnewline
43 & 102.1 & 105.843498093677 & -3.7434980936772 \tabularnewline
44 & 96 & 99.8598388075494 & -3.85983880754935 \tabularnewline
45 & 109.3 & 113.813012246788 & -4.51301224678761 \tabularnewline
46 & 90 & 77.3605415620079 & 12.6394584379921 \tabularnewline
47 & 83.9 & 89.616694507607 & -5.71669450760702 \tabularnewline
48 & 112 & 116.236145217587 & -4.23614521758701 \tabularnewline
49 & 114.3 & 114.316062937973 & -0.0160629379732617 \tabularnewline
50 & 103.6 & 104.986347911906 & -1.38634791190635 \tabularnewline
51 & 91.7 & 92.2307864965686 & -0.530786496568621 \tabularnewline
52 & 80.8 & 86.123873978339 & -5.32387397833903 \tabularnewline
53 & 87.2 & 89.1461537083536 & -1.94615370835361 \tabularnewline
54 & 109.2 & 97.3583572480908 & 11.8416427519092 \tabularnewline
55 & 102.7 & 98.9643198689533 & 3.73568013104673 \tabularnewline
56 & 95.1 & 101.152666905846 & -6.05266690584585 \tabularnewline
57 & 117.5 & 113.935971327648 & 3.56402867235165 \tabularnewline
58 & 85.1 & 79.5655547432949 & 5.53444525670511 \tabularnewline
59 & 92.1 & 89.9181821153548 & 2.18181788464518 \tabularnewline
60 & 113.5 & 116.613811922124 & -3.11381192212449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&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]112.3[/C][C]125.882537323786[/C][C]-13.5825373237857[/C][/ROW]
[ROW][C]2[/C][C]117.3[/C][C]109.704087244584[/C][C]7.5959127554161[/C][/ROW]
[ROW][C]3[/C][C]111.1[/C][C]102.365758213796[/C][C]8.73424178620351[/C][/ROW]
[ROW][C]4[/C][C]102.2[/C][C]106.068295976077[/C][C]-3.86829597607748[/C][/ROW]
[ROW][C]5[/C][C]104.3[/C][C]112.619848070291[/C][C]-8.31984807029128[/C][/ROW]
[ROW][C]6[/C][C]122.9[/C][C]119.756322033516[/C][C]3.14367796648385[/C][/ROW]
[ROW][C]7[/C][C]107.6[/C][C]117.82487101266[/C][C]-10.2248710126599[/C][/ROW]
[ROW][C]8[/C][C]121.3[/C][C]114.388637551058[/C][C]6.91136244894178[/C][/ROW]
[ROW][C]9[/C][C]131.5[/C][C]133.006263434964[/C][C]-1.50626343496396[/C][/ROW]
[ROW][C]10[/C][C]89[/C][C]102.722114666831[/C][C]-13.7221146668313[/C][/ROW]
[ROW][C]11[/C][C]104.4[/C][C]102.828551928908[/C][C]1.57144807109218[/C][/ROW]
[ROW][C]12[/C][C]128.9[/C][C]128.796407148176[/C][C]0.103592851824[/C][/ROW]
[ROW][C]13[/C][C]135.9[/C][C]135.032765638395[/C][C]0.867234361605378[/C][/ROW]
[ROW][C]14[/C][C]133.3[/C][C]126.232902325106[/C][C]7.06709767489355[/C][/ROW]
[ROW][C]15[/C][C]121.3[/C][C]119.371952741016[/C][C]1.92804725898431[/C][/ROW]
[ROW][C]16[/C][C]120.5[/C][C]115.476329147188[/C][C]5.02367085281238[/C][/ROW]
[ROW][C]17[/C][C]120.4[/C][C]123.125708571181[/C][C]-2.72570857118096[/C][/ROW]
[ROW][C]18[/C][C]137.9[/C][C]132.944725151509[/C][C]4.95527484849077[/C][/ROW]
[ROW][C]19[/C][C]126.1[/C][C]129.499316569284[/C][C]-3.39931656928365[/C][/ROW]
[ROW][C]20[/C][C]133.2[/C][C]127.17984418753[/C][C]6.0201558124696[/C][/ROW]
[ROW][C]21[/C][C]151.1[/C][C]144.342896243649[/C][C]6.75710375635096[/C][/ROW]
[ROW][C]22[/C][C]105[/C][C]114.60604478298[/C][C]-9.60604478297976[/C][/ROW]
[ROW][C]23[/C][C]119[/C][C]116.564577470103[/C][C]2.43542252989708[/C][/ROW]
[ROW][C]24[/C][C]140.4[/C][C]140.240108315915[/C][C]0.159891684085257[/C][/ROW]
[ROW][C]25[/C][C]156.6[/C][C]144.402674905283[/C][C]12.1973250947173[/C][/ROW]
[ROW][C]26[/C][C]137.1[/C][C]138.443014792737[/C][C]-1.34301479273715[/C][/ROW]
[ROW][C]27[/C][C]122.7[/C][C]127.966146390847[/C][C]-5.26614639084666[/C][/ROW]
[ROW][C]28[/C][C]125.8[/C][C]116.682442080229[/C][C]9.11755791977077[/C][/ROW]
[ROW][C]29[/C][C]139.3[/C][C]125.039755706094[/C][C]14.2602442939063[/C][/ROW]
[ROW][C]30[/C][C]134.9[/C][C]142.932499818105[/C][C]-8.03249981810474[/C][/ROW]
[ROW][C]31[/C][C]149.2[/C][C]135.567994455426[/C][C]13.6320055445741[/C][/ROW]
[ROW][C]32[/C][C]132.3[/C][C]135.319012548016[/C][C]-3.01901254801619[/C][/ROW]
[ROW][C]33[/C][C]149[/C][C]153.301856746951[/C][C]-4.30185674695104[/C][/ROW]
[ROW][C]34[/C][C]117.2[/C][C]112.045744244886[/C][C]5.15425575511385[/C][/ROW]
[ROW][C]35[/C][C]119.6[/C][C]120.071993978027[/C][C]-0.471993978027431[/C][/ROW]
[ROW][C]36[/C][C]152[/C][C]144.913527396198[/C][C]7.08647260380221[/C][/ROW]
[ROW][C]37[/C][C]149.4[/C][C]148.865959194564[/C][C]0.534040805436261[/C][/ROW]
[ROW][C]38[/C][C]127.3[/C][C]139.233647725666[/C][C]-11.9336477256661[/C][/ROW]
[ROW][C]39[/C][C]114.1[/C][C]118.965356157773[/C][C]-4.86535615777254[/C][/ROW]
[ROW][C]40[/C][C]102.1[/C][C]107.049058818167[/C][C]-4.94905881816664[/C][/ROW]
[ROW][C]41[/C][C]107.7[/C][C]108.96853394408[/C][C]-1.26853394408049[/C][/ROW]
[ROW][C]42[/C][C]104.4[/C][C]116.308095748779[/C][C]-11.9080957487791[/C][/ROW]
[ROW][C]43[/C][C]102.1[/C][C]105.843498093677[/C][C]-3.7434980936772[/C][/ROW]
[ROW][C]44[/C][C]96[/C][C]99.8598388075494[/C][C]-3.85983880754935[/C][/ROW]
[ROW][C]45[/C][C]109.3[/C][C]113.813012246788[/C][C]-4.51301224678761[/C][/ROW]
[ROW][C]46[/C][C]90[/C][C]77.3605415620079[/C][C]12.6394584379921[/C][/ROW]
[ROW][C]47[/C][C]83.9[/C][C]89.616694507607[/C][C]-5.71669450760702[/C][/ROW]
[ROW][C]48[/C][C]112[/C][C]116.236145217587[/C][C]-4.23614521758701[/C][/ROW]
[ROW][C]49[/C][C]114.3[/C][C]114.316062937973[/C][C]-0.0160629379732617[/C][/ROW]
[ROW][C]50[/C][C]103.6[/C][C]104.986347911906[/C][C]-1.38634791190635[/C][/ROW]
[ROW][C]51[/C][C]91.7[/C][C]92.2307864965686[/C][C]-0.530786496568621[/C][/ROW]
[ROW][C]52[/C][C]80.8[/C][C]86.123873978339[/C][C]-5.32387397833903[/C][/ROW]
[ROW][C]53[/C][C]87.2[/C][C]89.1461537083536[/C][C]-1.94615370835361[/C][/ROW]
[ROW][C]54[/C][C]109.2[/C][C]97.3583572480908[/C][C]11.8416427519092[/C][/ROW]
[ROW][C]55[/C][C]102.7[/C][C]98.9643198689533[/C][C]3.73568013104673[/C][/ROW]
[ROW][C]56[/C][C]95.1[/C][C]101.152666905846[/C][C]-6.05266690584585[/C][/ROW]
[ROW][C]57[/C][C]117.5[/C][C]113.935971327648[/C][C]3.56402867235165[/C][/ROW]
[ROW][C]58[/C][C]85.1[/C][C]79.5655547432949[/C][C]5.53444525670511[/C][/ROW]
[ROW][C]59[/C][C]92.1[/C][C]89.9181821153548[/C][C]2.18181788464518[/C][/ROW]
[ROW][C]60[/C][C]113.5[/C][C]116.613811922124[/C][C]-3.11381192212449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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
1112.3125.882537323786-13.5825373237857
2117.3109.7040872445847.5959127554161
3111.1102.3657582137968.73424178620351
4102.2106.068295976077-3.86829597607748
5104.3112.619848070291-8.31984807029128
6122.9119.7563220335163.14367796648385
7107.6117.82487101266-10.2248710126599
8121.3114.3886375510586.91136244894178
9131.5133.006263434964-1.50626343496396
1089102.722114666831-13.7221146668313
11104.4102.8285519289081.57144807109218
12128.9128.7964071481760.103592851824
13135.9135.0327656383950.867234361605378
14133.3126.2329023251067.06709767489355
15121.3119.3719527410161.92804725898431
16120.5115.4763291471885.02367085281238
17120.4123.125708571181-2.72570857118096
18137.9132.9447251515094.95527484849077
19126.1129.499316569284-3.39931656928365
20133.2127.179844187536.0201558124696
21151.1144.3428962436496.75710375635096
22105114.60604478298-9.60604478297976
23119116.5645774701032.43542252989708
24140.4140.2401083159150.159891684085257
25156.6144.40267490528312.1973250947173
26137.1138.443014792737-1.34301479273715
27122.7127.966146390847-5.26614639084666
28125.8116.6824420802299.11755791977077
29139.3125.03975570609414.2602442939063
30134.9142.932499818105-8.03249981810474
31149.2135.56799445542613.6320055445741
32132.3135.319012548016-3.01901254801619
33149153.301856746951-4.30185674695104
34117.2112.0457442448865.15425575511385
35119.6120.071993978027-0.471993978027431
36152144.9135273961987.08647260380221
37149.4148.8659591945640.534040805436261
38127.3139.233647725666-11.9336477256661
39114.1118.965356157773-4.86535615777254
40102.1107.049058818167-4.94905881816664
41107.7108.96853394408-1.26853394408049
42104.4116.308095748779-11.9080957487791
43102.1105.843498093677-3.7434980936772
449699.8598388075494-3.85983880754935
45109.3113.813012246788-4.51301224678761
469077.360541562007912.6394584379921
4783.989.616694507607-5.71669450760702
48112116.236145217587-4.23614521758701
49114.3114.316062937973-0.0160629379732617
50103.6104.986347911906-1.38634791190635
5191.792.2307864965686-0.530786496568621
5280.886.123873978339-5.32387397833903
5387.289.1461537083536-1.94615370835361
54109.297.358357248090811.8416427519092
55102.798.96431986895333.73568013104673
5695.1101.152666905846-6.05266690584585
57117.5113.9359713276483.56402867235165
5885.179.56555474329495.53444525670511
5992.189.91818211535482.18181788464518
60113.5116.613811922124-3.11381192212449







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.01031662458044970.02063324916089950.98968337541955
200.00435753517348270.008715070346965390.995642464826517
210.002028567615971130.004057135231942270.997971432384029
220.0009449644670377820.001889928934075560.999055035532962
230.0002091860422947850.0004183720845895690.999790813957705
240.0003681084555474810.0007362169110949610.999631891544453
250.0001345388085416020.0002690776170832030.999865461191458
260.00111688794899440.002233775897988810.998883112051006
270.07812915699641930.1562583139928390.921870843003581
280.2216972725128770.4433945450257540.778302727487123
290.2372747285860440.4745494571720870.762725271413956
300.5147635553585840.9704728892828330.485236444641416
310.6017481221442780.7965037557114440.398251877855722
320.5741346902843240.8517306194313520.425865309715676
330.6680146331164840.6639707337670330.331985366883516
340.5762489458841070.8475021082317860.423751054115893
350.5133391396109880.9733217207780240.486660860389012
360.6556826875591720.6886346248816560.344317312440828
370.6341537401038370.7316925197923270.365846259896163
380.7139558512441510.5720882975116980.286044148755849
390.6656465653519170.6687068692961670.334353434648083
400.6565966518369220.6868066963261550.343403348163078
410.9487824657622910.1024350684754180.0512175342377092

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.0103166245804497 & 0.0206332491608995 & 0.98968337541955 \tabularnewline
20 & 0.0043575351734827 & 0.00871507034696539 & 0.995642464826517 \tabularnewline
21 & 0.00202856761597113 & 0.00405713523194227 & 0.997971432384029 \tabularnewline
22 & 0.000944964467037782 & 0.00188992893407556 & 0.999055035532962 \tabularnewline
23 & 0.000209186042294785 & 0.000418372084589569 & 0.999790813957705 \tabularnewline
24 & 0.000368108455547481 & 0.000736216911094961 & 0.999631891544453 \tabularnewline
25 & 0.000134538808541602 & 0.000269077617083203 & 0.999865461191458 \tabularnewline
26 & 0.0011168879489944 & 0.00223377589798881 & 0.998883112051006 \tabularnewline
27 & 0.0781291569964193 & 0.156258313992839 & 0.921870843003581 \tabularnewline
28 & 0.221697272512877 & 0.443394545025754 & 0.778302727487123 \tabularnewline
29 & 0.237274728586044 & 0.474549457172087 & 0.762725271413956 \tabularnewline
30 & 0.514763555358584 & 0.970472889282833 & 0.485236444641416 \tabularnewline
31 & 0.601748122144278 & 0.796503755711444 & 0.398251877855722 \tabularnewline
32 & 0.574134690284324 & 0.851730619431352 & 0.425865309715676 \tabularnewline
33 & 0.668014633116484 & 0.663970733767033 & 0.331985366883516 \tabularnewline
34 & 0.576248945884107 & 0.847502108231786 & 0.423751054115893 \tabularnewline
35 & 0.513339139610988 & 0.973321720778024 & 0.486660860389012 \tabularnewline
36 & 0.655682687559172 & 0.688634624881656 & 0.344317312440828 \tabularnewline
37 & 0.634153740103837 & 0.731692519792327 & 0.365846259896163 \tabularnewline
38 & 0.713955851244151 & 0.572088297511698 & 0.286044148755849 \tabularnewline
39 & 0.665646565351917 & 0.668706869296167 & 0.334353434648083 \tabularnewline
40 & 0.656596651836922 & 0.686806696326155 & 0.343403348163078 \tabularnewline
41 & 0.948782465762291 & 0.102435068475418 & 0.0512175342377092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&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]19[/C][C]0.0103166245804497[/C][C]0.0206332491608995[/C][C]0.98968337541955[/C][/ROW]
[ROW][C]20[/C][C]0.0043575351734827[/C][C]0.00871507034696539[/C][C]0.995642464826517[/C][/ROW]
[ROW][C]21[/C][C]0.00202856761597113[/C][C]0.00405713523194227[/C][C]0.997971432384029[/C][/ROW]
[ROW][C]22[/C][C]0.000944964467037782[/C][C]0.00188992893407556[/C][C]0.999055035532962[/C][/ROW]
[ROW][C]23[/C][C]0.000209186042294785[/C][C]0.000418372084589569[/C][C]0.999790813957705[/C][/ROW]
[ROW][C]24[/C][C]0.000368108455547481[/C][C]0.000736216911094961[/C][C]0.999631891544453[/C][/ROW]
[ROW][C]25[/C][C]0.000134538808541602[/C][C]0.000269077617083203[/C][C]0.999865461191458[/C][/ROW]
[ROW][C]26[/C][C]0.0011168879489944[/C][C]0.00223377589798881[/C][C]0.998883112051006[/C][/ROW]
[ROW][C]27[/C][C]0.0781291569964193[/C][C]0.156258313992839[/C][C]0.921870843003581[/C][/ROW]
[ROW][C]28[/C][C]0.221697272512877[/C][C]0.443394545025754[/C][C]0.778302727487123[/C][/ROW]
[ROW][C]29[/C][C]0.237274728586044[/C][C]0.474549457172087[/C][C]0.762725271413956[/C][/ROW]
[ROW][C]30[/C][C]0.514763555358584[/C][C]0.970472889282833[/C][C]0.485236444641416[/C][/ROW]
[ROW][C]31[/C][C]0.601748122144278[/C][C]0.796503755711444[/C][C]0.398251877855722[/C][/ROW]
[ROW][C]32[/C][C]0.574134690284324[/C][C]0.851730619431352[/C][C]0.425865309715676[/C][/ROW]
[ROW][C]33[/C][C]0.668014633116484[/C][C]0.663970733767033[/C][C]0.331985366883516[/C][/ROW]
[ROW][C]34[/C][C]0.576248945884107[/C][C]0.847502108231786[/C][C]0.423751054115893[/C][/ROW]
[ROW][C]35[/C][C]0.513339139610988[/C][C]0.973321720778024[/C][C]0.486660860389012[/C][/ROW]
[ROW][C]36[/C][C]0.655682687559172[/C][C]0.688634624881656[/C][C]0.344317312440828[/C][/ROW]
[ROW][C]37[/C][C]0.634153740103837[/C][C]0.731692519792327[/C][C]0.365846259896163[/C][/ROW]
[ROW][C]38[/C][C]0.713955851244151[/C][C]0.572088297511698[/C][C]0.286044148755849[/C][/ROW]
[ROW][C]39[/C][C]0.665646565351917[/C][C]0.668706869296167[/C][C]0.334353434648083[/C][/ROW]
[ROW][C]40[/C][C]0.656596651836922[/C][C]0.686806696326155[/C][C]0.343403348163078[/C][/ROW]
[ROW][C]41[/C][C]0.948782465762291[/C][C]0.102435068475418[/C][C]0.0512175342377092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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
190.01031662458044970.02063324916089950.98968337541955
200.00435753517348270.008715070346965390.995642464826517
210.002028567615971130.004057135231942270.997971432384029
220.0009449644670377820.001889928934075560.999055035532962
230.0002091860422947850.0004183720845895690.999790813957705
240.0003681084555474810.0007362169110949610.999631891544453
250.0001345388085416020.0002690776170832030.999865461191458
260.00111688794899440.002233775897988810.998883112051006
270.07812915699641930.1562583139928390.921870843003581
280.2216972725128770.4433945450257540.778302727487123
290.2372747285860440.4745494571720870.762725271413956
300.5147635553585840.9704728892828330.485236444641416
310.6017481221442780.7965037557114440.398251877855722
320.5741346902843240.8517306194313520.425865309715676
330.6680146331164840.6639707337670330.331985366883516
340.5762489458841070.8475021082317860.423751054115893
350.5133391396109880.9733217207780240.486660860389012
360.6556826875591720.6886346248816560.344317312440828
370.6341537401038370.7316925197923270.365846259896163
380.7139558512441510.5720882975116980.286044148755849
390.6656465653519170.6687068692961670.334353434648083
400.6565966518369220.6868066963261550.343403348163078
410.9487824657622910.1024350684754180.0512175342377092







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level70.304347826086957NOK
5% type I error level80.347826086956522NOK
10% type I error level80.347826086956522NOK

\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 & 7 & 0.304347826086957 & NOK \tabularnewline
5% type I error level & 8 & 0.347826086956522 & NOK \tabularnewline
10% type I error level & 8 & 0.347826086956522 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147440&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]7[/C][C]0.304347826086957[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.347826086956522[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.347826086956522[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147440&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147440&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 level70.304347826086957NOK
5% type I error level80.347826086956522NOK
10% type I error level80.347826086956522NOK



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')
}