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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 13:10:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t12587480390r6ewzr9sabtnt0.htm/, Retrieved Thu, 28 Mar 2024 12:40:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58451, Retrieved Thu, 28 Mar 2024 12:40:18 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
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] [JJ Workshop 7, op...] [2009-11-20 20:10:08] [e31f2fa83f4a5291b9a51009566cf69b] [Current]
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Dataseries X:
95,1	93,8	111,7
97	93,8	98,6
112,7	107,6	96,9
102,9	101	95,1
97,4	95,4	97
111,4	96,5	112,7
87,4	89,2	102,9
96,8	87,1	97,4
114,1	110,5	111,4
110,3	110,8	87,4
103,9	104,2	96,8
101,6	88,9	114,1
94,6	89,8	110,3
95,9	90	103,9
104,7	93,9	101,6
102,8	91,3	94,6
98,1	87,8	95,9
113,9	99,7	104,7
80,9	73,5	102,8
95,7	79,2	98,1
113,2	96,9	113,9
105,9	95,2	80,9
108,8	95,6	95,7
102,3	89,7	113,2
99	92,8	105,9
100,7	88	108,8
115,5	101,1	102,3
100,7	92,7	99
109,9	95,8	100,7
114,6	103,8	115,5
85,4	81,8	100,7
100,5	87,1	109,9
114,8	105,9	114,6
116,5	108,1	85,4
112,9	102,6	100,5
102	93,7	114,8
106	103,5	116,5
105,3	100,6	112,9
118,8	113,3	102
106,1	102,4	106
109,3	102,1	105,3
117,2	106,9	118,8
92,5	87,3	106,1
104,2	93,1	109,3
112,5	109,1	117,2
122,4	120,3	92,5
113,3	104,9	104,2
100	92,6	112,5
110,7	109,8	122,4
112,8	111,4	113,3
109,8	117,9	100
117,3	121,6	110,7
109,1	117,8	112,8
115,9	124,2	109,8
96	106,8	117,3
99,8	102,7	109,1
116,8	116,8	115,9
115,7	113,6	96
99,4	96,1	99,8
94,3	85	116,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&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]5 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=58451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
TIA[t] = + 32.5049364211236 + 0.303638779125189IAidM[t] + 0.354779288294477`TIA(t-3)`[t] -1.15156326894194M1[t] + 2.55491853186197M2[t] + 11.9498804134043M3[t] + 6.94062493998272M4[t] + 5.91613478259514M5[t] + 10.2762807456465M6[t] -8.00791974071992M7[t] + 2.74328260551863M8[t] + 8.67593779647815M9[t] + 17.3117411390319M10[t] + 9.64099946115172M11[t] -0.0091814120305812t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TIA[t] =  +  32.5049364211236 +  0.303638779125189IAidM[t] +  0.354779288294477`TIA(t-3)`[t] -1.15156326894194M1[t] +  2.55491853186197M2[t] +  11.9498804134043M3[t] +  6.94062493998272M4[t] +  5.91613478259514M5[t] +  10.2762807456465M6[t] -8.00791974071992M7[t] +  2.74328260551863M8[t] +  8.67593779647815M9[t] +  17.3117411390319M10[t] +  9.64099946115172M11[t] -0.0091814120305812t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TIA[t] =  +  32.5049364211236 +  0.303638779125189IAidM[t] +  0.354779288294477`TIA(t-3)`[t] -1.15156326894194M1[t] +  2.55491853186197M2[t] +  11.9498804134043M3[t] +  6.94062493998272M4[t] +  5.91613478259514M5[t] +  10.2762807456465M6[t] -8.00791974071992M7[t] +  2.74328260551863M8[t] +  8.67593779647815M9[t] +  17.3117411390319M10[t] +  9.64099946115172M11[t] -0.0091814120305812t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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
TIA[t] = + 32.5049364211236 + 0.303638779125189IAidM[t] + 0.354779288294477`TIA(t-3)`[t] -1.15156326894194M1[t] + 2.55491853186197M2[t] + 11.9498804134043M3[t] + 6.94062493998272M4[t] + 5.91613478259514M5[t] + 10.2762807456465M6[t] -8.00791974071992M7[t] + 2.74328260551863M8[t] + 8.67593779647815M9[t] + 17.3117411390319M10[t] + 9.64099946115172M11[t] -0.0091814120305812t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)32.504936421123614.5658392.23160.0306680.015334
IAidM0.3036387791251890.0757234.00990.0002260.000113
`TIA(t-3)`0.3547792882944770.1446992.45180.0181580.009079
M1-1.151563268941942.402733-0.47930.6340660.317033
M22.554918531861972.5499271.0020.3217220.160861
M311.94988041340433.4756513.43820.0012720.000636
M46.940624939982723.2185192.15650.0364280.018214
M55.916134782595143.0324121.9510.0573040.028652
M610.27628074564652.6555373.86980.0003490.000174
M7-8.007919740719922.475079-3.23540.002280.00114
M82.743282605518632.5904361.0590.2952490.147625
M98.675937796478152.6340673.29370.0019310.000966
M1017.31174113903194.9989953.4630.0011830.000592
M119.640999461151723.392722.84170.0067210.00336
t-0.00918141203058120.040456-0.22690.8214920.410746

\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) & 32.5049364211236 & 14.565839 & 2.2316 & 0.030668 & 0.015334 \tabularnewline
IAidM & 0.303638779125189 & 0.075723 & 4.0099 & 0.000226 & 0.000113 \tabularnewline
`TIA(t-3)` & 0.354779288294477 & 0.144699 & 2.4518 & 0.018158 & 0.009079 \tabularnewline
M1 & -1.15156326894194 & 2.402733 & -0.4793 & 0.634066 & 0.317033 \tabularnewline
M2 & 2.55491853186197 & 2.549927 & 1.002 & 0.321722 & 0.160861 \tabularnewline
M3 & 11.9498804134043 & 3.475651 & 3.4382 & 0.001272 & 0.000636 \tabularnewline
M4 & 6.94062493998272 & 3.218519 & 2.1565 & 0.036428 & 0.018214 \tabularnewline
M5 & 5.91613478259514 & 3.032412 & 1.951 & 0.057304 & 0.028652 \tabularnewline
M6 & 10.2762807456465 & 2.655537 & 3.8698 & 0.000349 & 0.000174 \tabularnewline
M7 & -8.00791974071992 & 2.475079 & -3.2354 & 0.00228 & 0.00114 \tabularnewline
M8 & 2.74328260551863 & 2.590436 & 1.059 & 0.295249 & 0.147625 \tabularnewline
M9 & 8.67593779647815 & 2.634067 & 3.2937 & 0.001931 & 0.000966 \tabularnewline
M10 & 17.3117411390319 & 4.998995 & 3.463 & 0.001183 & 0.000592 \tabularnewline
M11 & 9.64099946115172 & 3.39272 & 2.8417 & 0.006721 & 0.00336 \tabularnewline
t & -0.0091814120305812 & 0.040456 & -0.2269 & 0.821492 & 0.410746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&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]32.5049364211236[/C][C]14.565839[/C][C]2.2316[/C][C]0.030668[/C][C]0.015334[/C][/ROW]
[ROW][C]IAidM[/C][C]0.303638779125189[/C][C]0.075723[/C][C]4.0099[/C][C]0.000226[/C][C]0.000113[/C][/ROW]
[ROW][C]`TIA(t-3)`[/C][C]0.354779288294477[/C][C]0.144699[/C][C]2.4518[/C][C]0.018158[/C][C]0.009079[/C][/ROW]
[ROW][C]M1[/C][C]-1.15156326894194[/C][C]2.402733[/C][C]-0.4793[/C][C]0.634066[/C][C]0.317033[/C][/ROW]
[ROW][C]M2[/C][C]2.55491853186197[/C][C]2.549927[/C][C]1.002[/C][C]0.321722[/C][C]0.160861[/C][/ROW]
[ROW][C]M3[/C][C]11.9498804134043[/C][C]3.475651[/C][C]3.4382[/C][C]0.001272[/C][C]0.000636[/C][/ROW]
[ROW][C]M4[/C][C]6.94062493998272[/C][C]3.218519[/C][C]2.1565[/C][C]0.036428[/C][C]0.018214[/C][/ROW]
[ROW][C]M5[/C][C]5.91613478259514[/C][C]3.032412[/C][C]1.951[/C][C]0.057304[/C][C]0.028652[/C][/ROW]
[ROW][C]M6[/C][C]10.2762807456465[/C][C]2.655537[/C][C]3.8698[/C][C]0.000349[/C][C]0.000174[/C][/ROW]
[ROW][C]M7[/C][C]-8.00791974071992[/C][C]2.475079[/C][C]-3.2354[/C][C]0.00228[/C][C]0.00114[/C][/ROW]
[ROW][C]M8[/C][C]2.74328260551863[/C][C]2.590436[/C][C]1.059[/C][C]0.295249[/C][C]0.147625[/C][/ROW]
[ROW][C]M9[/C][C]8.67593779647815[/C][C]2.634067[/C][C]3.2937[/C][C]0.001931[/C][C]0.000966[/C][/ROW]
[ROW][C]M10[/C][C]17.3117411390319[/C][C]4.998995[/C][C]3.463[/C][C]0.001183[/C][C]0.000592[/C][/ROW]
[ROW][C]M11[/C][C]9.64099946115172[/C][C]3.39272[/C][C]2.8417[/C][C]0.006721[/C][C]0.00336[/C][/ROW]
[ROW][C]t[/C][C]-0.0091814120305812[/C][C]0.040456[/C][C]-0.2269[/C][C]0.821492[/C][C]0.410746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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)32.504936421123614.5658392.23160.0306680.015334
IAidM0.3036387791251890.0757234.00990.0002260.000113
`TIA(t-3)`0.3547792882944770.1446992.45180.0181580.009079
M1-1.151563268941942.402733-0.47930.6340660.317033
M22.554918531861972.5499271.0020.3217220.160861
M311.94988041340433.4756513.43820.0012720.000636
M46.940624939982723.2185192.15650.0364280.018214
M55.916134782595143.0324121.9510.0573040.028652
M610.27628074564652.6555373.86980.0003490.000174
M7-8.007919740719922.475079-3.23540.002280.00114
M82.743282605518632.5904361.0590.2952490.147625
M98.675937796478152.6340673.29370.0019310.000966
M1017.31174113903194.9989953.4630.0011830.000592
M119.640999461151723.392722.84170.0067210.00336
t-0.00918141203058120.040456-0.22690.8214920.410746







Multiple Linear Regression - Regression Statistics
Multiple R0.93894829808783
R-squared0.881623906482032
Adjusted R-squared0.844795788498664
F-TEST (value)23.9388802566611
F-TEST (DF numerator)14
F-TEST (DF denominator)45
p-value2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.54551443401741
Sum Squared Residuals565.68026708216

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.93894829808783 \tabularnewline
R-squared & 0.881623906482032 \tabularnewline
Adjusted R-squared & 0.844795788498664 \tabularnewline
F-TEST (value) & 23.9388802566611 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 45 \tabularnewline
p-value & 2.22044604925031e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.54551443401741 \tabularnewline
Sum Squared Residuals & 565.68026708216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.93894829808783[/C][/ROW]
[ROW][C]R-squared[/C][C]0.881623906482032[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.844795788498664[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]23.9388802566611[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]45[/C][/ROW]
[ROW][C]p-value[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.54551443401741[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]565.68026708216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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 R0.93894829808783
R-squared0.881623906482032
Adjusted R-squared0.844795788498664
F-TEST (value)23.9388802566611
F-TEST (DF numerator)14
F-TEST (DF denominator)45
p-value2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.54551443401741
Sum Squared Residuals565.68026708216







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
195.199.4543557245867-4.35435572458669
29798.5040474367025-1.50404743670252
3112.7111.4769182680411.22308173195868
4102.9103.815862721433-0.915862721432816
597.4101.755894636673-4.35589463667311
6111.4112.010896670955-0.610896670954898
787.488.0241146596581-0.624114659658122
896.896.17720807208360.622791927916421
9114.1114.172739318665-0.0727393186646354
10110.3114.375749963858-4.07574996385792
11103.9108.026736241689-4.12673624168897
12101.699.86856373538571.73143626461426
1394.697.6329326601069-3.03293266010687
1495.999.1203733596206-3.22037335962058
15104.7108.874352704643-4.1743527046433
16102.8100.5829999754042.21700002459573
1798.198.9478057538308-0.84780575383078
18113.9110.0341295134333.86587048656729
1980.983.1113309541962-2.21133095419624
2095.793.91663027443371.78336972556626
21113.2110.8200231989312.37997680106873
22105.9107.222742691224-1.32274269122390
23108.8104.9150085797213.88499142027855
24102.399.68199645485392.61800354514611
259996.87264318461982.12735681538024
26100.7100.1413373696460.558662630353834
27115.5111.1987204717844.30127952821619
28100.7102.458946190308-1.75894619030826
29109.9102.9696796262796.9303203737212
30114.6115.000487877059-0.400487877059376
3185.484.776319371150.623680628850072
32100.5100.3915952870310.108404712969405
33114.8113.6909407684971.10905923150287
34116.5112.6260127948973.87398720510299
35112.9108.6332436730444.26675632695571
36102101.3540214882590.645978511741171
37106103.7720616328142.22793836718623
38105.3105.311604124264-0.0116041242639373
39118.8114.6865028462564.11349715374419
40106.1107.777520421517-1.67752042151698
41109.3106.4044117165552.89558828344488
42117.2117.0023627993520.197637200647743
4392.588.25196386876174.24803613123832
44104.2101.8903834444382.30961655556194
45112.5115.474834066896-2.9748340668964
46122.4118.7391619027483.66083809725188
47113.3110.5341192873552.76588071264518
48100100.093849523777-0.0938495237768465
49110.7107.6680067978733.03199320212709
50112.8108.6226377097674.1773622902332
51109.8115.263505709276-5.46350570927576
52117.3115.1646706913382.13532930866233
53109.1113.722208266662-4.62220826666220
54115.9118.952123139201-3.05212313920076
559698.036271146234-2.03627114623404
5699.8104.624182922014-4.82418292201402
57116.8117.241462647011-0.441462647010568
58115.7117.836332647273-2.13633264727305
5999.4106.190892218190-6.79089221819047
6094.399.2015687977247-4.90156879772469

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 95.1 & 99.4543557245867 & -4.35435572458669 \tabularnewline
2 & 97 & 98.5040474367025 & -1.50404743670252 \tabularnewline
3 & 112.7 & 111.476918268041 & 1.22308173195868 \tabularnewline
4 & 102.9 & 103.815862721433 & -0.915862721432816 \tabularnewline
5 & 97.4 & 101.755894636673 & -4.35589463667311 \tabularnewline
6 & 111.4 & 112.010896670955 & -0.610896670954898 \tabularnewline
7 & 87.4 & 88.0241146596581 & -0.624114659658122 \tabularnewline
8 & 96.8 & 96.1772080720836 & 0.622791927916421 \tabularnewline
9 & 114.1 & 114.172739318665 & -0.0727393186646354 \tabularnewline
10 & 110.3 & 114.375749963858 & -4.07574996385792 \tabularnewline
11 & 103.9 & 108.026736241689 & -4.12673624168897 \tabularnewline
12 & 101.6 & 99.8685637353857 & 1.73143626461426 \tabularnewline
13 & 94.6 & 97.6329326601069 & -3.03293266010687 \tabularnewline
14 & 95.9 & 99.1203733596206 & -3.22037335962058 \tabularnewline
15 & 104.7 & 108.874352704643 & -4.1743527046433 \tabularnewline
16 & 102.8 & 100.582999975404 & 2.21700002459573 \tabularnewline
17 & 98.1 & 98.9478057538308 & -0.84780575383078 \tabularnewline
18 & 113.9 & 110.034129513433 & 3.86587048656729 \tabularnewline
19 & 80.9 & 83.1113309541962 & -2.21133095419624 \tabularnewline
20 & 95.7 & 93.9166302744337 & 1.78336972556626 \tabularnewline
21 & 113.2 & 110.820023198931 & 2.37997680106873 \tabularnewline
22 & 105.9 & 107.222742691224 & -1.32274269122390 \tabularnewline
23 & 108.8 & 104.915008579721 & 3.88499142027855 \tabularnewline
24 & 102.3 & 99.6819964548539 & 2.61800354514611 \tabularnewline
25 & 99 & 96.8726431846198 & 2.12735681538024 \tabularnewline
26 & 100.7 & 100.141337369646 & 0.558662630353834 \tabularnewline
27 & 115.5 & 111.198720471784 & 4.30127952821619 \tabularnewline
28 & 100.7 & 102.458946190308 & -1.75894619030826 \tabularnewline
29 & 109.9 & 102.969679626279 & 6.9303203737212 \tabularnewline
30 & 114.6 & 115.000487877059 & -0.400487877059376 \tabularnewline
31 & 85.4 & 84.77631937115 & 0.623680628850072 \tabularnewline
32 & 100.5 & 100.391595287031 & 0.108404712969405 \tabularnewline
33 & 114.8 & 113.690940768497 & 1.10905923150287 \tabularnewline
34 & 116.5 & 112.626012794897 & 3.87398720510299 \tabularnewline
35 & 112.9 & 108.633243673044 & 4.26675632695571 \tabularnewline
36 & 102 & 101.354021488259 & 0.645978511741171 \tabularnewline
37 & 106 & 103.772061632814 & 2.22793836718623 \tabularnewline
38 & 105.3 & 105.311604124264 & -0.0116041242639373 \tabularnewline
39 & 118.8 & 114.686502846256 & 4.11349715374419 \tabularnewline
40 & 106.1 & 107.777520421517 & -1.67752042151698 \tabularnewline
41 & 109.3 & 106.404411716555 & 2.89558828344488 \tabularnewline
42 & 117.2 & 117.002362799352 & 0.197637200647743 \tabularnewline
43 & 92.5 & 88.2519638687617 & 4.24803613123832 \tabularnewline
44 & 104.2 & 101.890383444438 & 2.30961655556194 \tabularnewline
45 & 112.5 & 115.474834066896 & -2.9748340668964 \tabularnewline
46 & 122.4 & 118.739161902748 & 3.66083809725188 \tabularnewline
47 & 113.3 & 110.534119287355 & 2.76588071264518 \tabularnewline
48 & 100 & 100.093849523777 & -0.0938495237768465 \tabularnewline
49 & 110.7 & 107.668006797873 & 3.03199320212709 \tabularnewline
50 & 112.8 & 108.622637709767 & 4.1773622902332 \tabularnewline
51 & 109.8 & 115.263505709276 & -5.46350570927576 \tabularnewline
52 & 117.3 & 115.164670691338 & 2.13532930866233 \tabularnewline
53 & 109.1 & 113.722208266662 & -4.62220826666220 \tabularnewline
54 & 115.9 & 118.952123139201 & -3.05212313920076 \tabularnewline
55 & 96 & 98.036271146234 & -2.03627114623404 \tabularnewline
56 & 99.8 & 104.624182922014 & -4.82418292201402 \tabularnewline
57 & 116.8 & 117.241462647011 & -0.441462647010568 \tabularnewline
58 & 115.7 & 117.836332647273 & -2.13633264727305 \tabularnewline
59 & 99.4 & 106.190892218190 & -6.79089221819047 \tabularnewline
60 & 94.3 & 99.2015687977247 & -4.90156879772469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&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]95.1[/C][C]99.4543557245867[/C][C]-4.35435572458669[/C][/ROW]
[ROW][C]2[/C][C]97[/C][C]98.5040474367025[/C][C]-1.50404743670252[/C][/ROW]
[ROW][C]3[/C][C]112.7[/C][C]111.476918268041[/C][C]1.22308173195868[/C][/ROW]
[ROW][C]4[/C][C]102.9[/C][C]103.815862721433[/C][C]-0.915862721432816[/C][/ROW]
[ROW][C]5[/C][C]97.4[/C][C]101.755894636673[/C][C]-4.35589463667311[/C][/ROW]
[ROW][C]6[/C][C]111.4[/C][C]112.010896670955[/C][C]-0.610896670954898[/C][/ROW]
[ROW][C]7[/C][C]87.4[/C][C]88.0241146596581[/C][C]-0.624114659658122[/C][/ROW]
[ROW][C]8[/C][C]96.8[/C][C]96.1772080720836[/C][C]0.622791927916421[/C][/ROW]
[ROW][C]9[/C][C]114.1[/C][C]114.172739318665[/C][C]-0.0727393186646354[/C][/ROW]
[ROW][C]10[/C][C]110.3[/C][C]114.375749963858[/C][C]-4.07574996385792[/C][/ROW]
[ROW][C]11[/C][C]103.9[/C][C]108.026736241689[/C][C]-4.12673624168897[/C][/ROW]
[ROW][C]12[/C][C]101.6[/C][C]99.8685637353857[/C][C]1.73143626461426[/C][/ROW]
[ROW][C]13[/C][C]94.6[/C][C]97.6329326601069[/C][C]-3.03293266010687[/C][/ROW]
[ROW][C]14[/C][C]95.9[/C][C]99.1203733596206[/C][C]-3.22037335962058[/C][/ROW]
[ROW][C]15[/C][C]104.7[/C][C]108.874352704643[/C][C]-4.1743527046433[/C][/ROW]
[ROW][C]16[/C][C]102.8[/C][C]100.582999975404[/C][C]2.21700002459573[/C][/ROW]
[ROW][C]17[/C][C]98.1[/C][C]98.9478057538308[/C][C]-0.84780575383078[/C][/ROW]
[ROW][C]18[/C][C]113.9[/C][C]110.034129513433[/C][C]3.86587048656729[/C][/ROW]
[ROW][C]19[/C][C]80.9[/C][C]83.1113309541962[/C][C]-2.21133095419624[/C][/ROW]
[ROW][C]20[/C][C]95.7[/C][C]93.9166302744337[/C][C]1.78336972556626[/C][/ROW]
[ROW][C]21[/C][C]113.2[/C][C]110.820023198931[/C][C]2.37997680106873[/C][/ROW]
[ROW][C]22[/C][C]105.9[/C][C]107.222742691224[/C][C]-1.32274269122390[/C][/ROW]
[ROW][C]23[/C][C]108.8[/C][C]104.915008579721[/C][C]3.88499142027855[/C][/ROW]
[ROW][C]24[/C][C]102.3[/C][C]99.6819964548539[/C][C]2.61800354514611[/C][/ROW]
[ROW][C]25[/C][C]99[/C][C]96.8726431846198[/C][C]2.12735681538024[/C][/ROW]
[ROW][C]26[/C][C]100.7[/C][C]100.141337369646[/C][C]0.558662630353834[/C][/ROW]
[ROW][C]27[/C][C]115.5[/C][C]111.198720471784[/C][C]4.30127952821619[/C][/ROW]
[ROW][C]28[/C][C]100.7[/C][C]102.458946190308[/C][C]-1.75894619030826[/C][/ROW]
[ROW][C]29[/C][C]109.9[/C][C]102.969679626279[/C][C]6.9303203737212[/C][/ROW]
[ROW][C]30[/C][C]114.6[/C][C]115.000487877059[/C][C]-0.400487877059376[/C][/ROW]
[ROW][C]31[/C][C]85.4[/C][C]84.77631937115[/C][C]0.623680628850072[/C][/ROW]
[ROW][C]32[/C][C]100.5[/C][C]100.391595287031[/C][C]0.108404712969405[/C][/ROW]
[ROW][C]33[/C][C]114.8[/C][C]113.690940768497[/C][C]1.10905923150287[/C][/ROW]
[ROW][C]34[/C][C]116.5[/C][C]112.626012794897[/C][C]3.87398720510299[/C][/ROW]
[ROW][C]35[/C][C]112.9[/C][C]108.633243673044[/C][C]4.26675632695571[/C][/ROW]
[ROW][C]36[/C][C]102[/C][C]101.354021488259[/C][C]0.645978511741171[/C][/ROW]
[ROW][C]37[/C][C]106[/C][C]103.772061632814[/C][C]2.22793836718623[/C][/ROW]
[ROW][C]38[/C][C]105.3[/C][C]105.311604124264[/C][C]-0.0116041242639373[/C][/ROW]
[ROW][C]39[/C][C]118.8[/C][C]114.686502846256[/C][C]4.11349715374419[/C][/ROW]
[ROW][C]40[/C][C]106.1[/C][C]107.777520421517[/C][C]-1.67752042151698[/C][/ROW]
[ROW][C]41[/C][C]109.3[/C][C]106.404411716555[/C][C]2.89558828344488[/C][/ROW]
[ROW][C]42[/C][C]117.2[/C][C]117.002362799352[/C][C]0.197637200647743[/C][/ROW]
[ROW][C]43[/C][C]92.5[/C][C]88.2519638687617[/C][C]4.24803613123832[/C][/ROW]
[ROW][C]44[/C][C]104.2[/C][C]101.890383444438[/C][C]2.30961655556194[/C][/ROW]
[ROW][C]45[/C][C]112.5[/C][C]115.474834066896[/C][C]-2.9748340668964[/C][/ROW]
[ROW][C]46[/C][C]122.4[/C][C]118.739161902748[/C][C]3.66083809725188[/C][/ROW]
[ROW][C]47[/C][C]113.3[/C][C]110.534119287355[/C][C]2.76588071264518[/C][/ROW]
[ROW][C]48[/C][C]100[/C][C]100.093849523777[/C][C]-0.0938495237768465[/C][/ROW]
[ROW][C]49[/C][C]110.7[/C][C]107.668006797873[/C][C]3.03199320212709[/C][/ROW]
[ROW][C]50[/C][C]112.8[/C][C]108.622637709767[/C][C]4.1773622902332[/C][/ROW]
[ROW][C]51[/C][C]109.8[/C][C]115.263505709276[/C][C]-5.46350570927576[/C][/ROW]
[ROW][C]52[/C][C]117.3[/C][C]115.164670691338[/C][C]2.13532930866233[/C][/ROW]
[ROW][C]53[/C][C]109.1[/C][C]113.722208266662[/C][C]-4.62220826666220[/C][/ROW]
[ROW][C]54[/C][C]115.9[/C][C]118.952123139201[/C][C]-3.05212313920076[/C][/ROW]
[ROW][C]55[/C][C]96[/C][C]98.036271146234[/C][C]-2.03627114623404[/C][/ROW]
[ROW][C]56[/C][C]99.8[/C][C]104.624182922014[/C][C]-4.82418292201402[/C][/ROW]
[ROW][C]57[/C][C]116.8[/C][C]117.241462647011[/C][C]-0.441462647010568[/C][/ROW]
[ROW][C]58[/C][C]115.7[/C][C]117.836332647273[/C][C]-2.13633264727305[/C][/ROW]
[ROW][C]59[/C][C]99.4[/C][C]106.190892218190[/C][C]-6.79089221819047[/C][/ROW]
[ROW][C]60[/C][C]94.3[/C][C]99.2015687977247[/C][C]-4.90156879772469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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
195.199.4543557245867-4.35435572458669
29798.5040474367025-1.50404743670252
3112.7111.4769182680411.22308173195868
4102.9103.815862721433-0.915862721432816
597.4101.755894636673-4.35589463667311
6111.4112.010896670955-0.610896670954898
787.488.0241146596581-0.624114659658122
896.896.17720807208360.622791927916421
9114.1114.172739318665-0.0727393186646354
10110.3114.375749963858-4.07574996385792
11103.9108.026736241689-4.12673624168897
12101.699.86856373538571.73143626461426
1394.697.6329326601069-3.03293266010687
1495.999.1203733596206-3.22037335962058
15104.7108.874352704643-4.1743527046433
16102.8100.5829999754042.21700002459573
1798.198.9478057538308-0.84780575383078
18113.9110.0341295134333.86587048656729
1980.983.1113309541962-2.21133095419624
2095.793.91663027443371.78336972556626
21113.2110.8200231989312.37997680106873
22105.9107.222742691224-1.32274269122390
23108.8104.9150085797213.88499142027855
24102.399.68199645485392.61800354514611
259996.87264318461982.12735681538024
26100.7100.1413373696460.558662630353834
27115.5111.1987204717844.30127952821619
28100.7102.458946190308-1.75894619030826
29109.9102.9696796262796.9303203737212
30114.6115.000487877059-0.400487877059376
3185.484.776319371150.623680628850072
32100.5100.3915952870310.108404712969405
33114.8113.6909407684971.10905923150287
34116.5112.6260127948973.87398720510299
35112.9108.6332436730444.26675632695571
36102101.3540214882590.645978511741171
37106103.7720616328142.22793836718623
38105.3105.311604124264-0.0116041242639373
39118.8114.6865028462564.11349715374419
40106.1107.777520421517-1.67752042151698
41109.3106.4044117165552.89558828344488
42117.2117.0023627993520.197637200647743
4392.588.25196386876174.24803613123832
44104.2101.8903834444382.30961655556194
45112.5115.474834066896-2.9748340668964
46122.4118.7391619027483.66083809725188
47113.3110.5341192873552.76588071264518
48100100.093849523777-0.0938495237768465
49110.7107.6680067978733.03199320212709
50112.8108.6226377097674.1773622902332
51109.8115.263505709276-5.46350570927576
52117.3115.1646706913382.13532930866233
53109.1113.722208266662-4.62220826666220
54115.9118.952123139201-3.05212313920076
559698.036271146234-2.03627114623404
5699.8104.624182922014-4.82418292201402
57116.8117.241462647011-0.441462647010568
58115.7117.836332647273-2.13633264727305
5999.4106.190892218190-6.79089221819047
6094.399.2015687977247-4.90156879772469







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.2404027677185950.480805535437190.759597232281405
190.1560693233080350.3121386466160710.843930676691965
200.08037440968588770.1607488193717750.919625590314112
210.08921720021470460.1784344004294090.910782799785295
220.05828383671209070.1165676734241810.94171616328791
230.1843660692860900.3687321385721790.81563393071391
240.1271937528958960.2543875057917930.872806247104104
250.07997637135177870.1599527427035570.920023628648221
260.07802155974703130.1560431194940630.921978440252969
270.06032998499903490.120659969998070.939670015000965
280.1041407200313130.2082814400626260.895859279968687
290.2047756869339310.4095513738678630.795224313066069
300.2469610598707210.4939221197414430.753038940129279
310.2240269363893580.4480538727787170.775973063610642
320.1685039053578240.3370078107156480.831496094642176
330.1392216768472520.2784433536945040.860778323152748
340.1063271159712490.2126542319424970.893672884028751
350.06886467294321350.1377293458864270.931135327056786
360.08892015042703390.1778403008540680.911079849572966
370.07531024812241370.1506204962448270.924689751877586
380.1257543591326000.2515087182651990.8742456408674
390.1227668710737350.2455337421474700.877233128926265
400.2704927021291140.5409854042582280.729507297870886
410.1947402755557430.3894805511114870.805259724444257
420.1137018580181650.2274037160363310.886298141981835

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
18 & 0.240402767718595 & 0.48080553543719 & 0.759597232281405 \tabularnewline
19 & 0.156069323308035 & 0.312138646616071 & 0.843930676691965 \tabularnewline
20 & 0.0803744096858877 & 0.160748819371775 & 0.919625590314112 \tabularnewline
21 & 0.0892172002147046 & 0.178434400429409 & 0.910782799785295 \tabularnewline
22 & 0.0582838367120907 & 0.116567673424181 & 0.94171616328791 \tabularnewline
23 & 0.184366069286090 & 0.368732138572179 & 0.81563393071391 \tabularnewline
24 & 0.127193752895896 & 0.254387505791793 & 0.872806247104104 \tabularnewline
25 & 0.0799763713517787 & 0.159952742703557 & 0.920023628648221 \tabularnewline
26 & 0.0780215597470313 & 0.156043119494063 & 0.921978440252969 \tabularnewline
27 & 0.0603299849990349 & 0.12065996999807 & 0.939670015000965 \tabularnewline
28 & 0.104140720031313 & 0.208281440062626 & 0.895859279968687 \tabularnewline
29 & 0.204775686933931 & 0.409551373867863 & 0.795224313066069 \tabularnewline
30 & 0.246961059870721 & 0.493922119741443 & 0.753038940129279 \tabularnewline
31 & 0.224026936389358 & 0.448053872778717 & 0.775973063610642 \tabularnewline
32 & 0.168503905357824 & 0.337007810715648 & 0.831496094642176 \tabularnewline
33 & 0.139221676847252 & 0.278443353694504 & 0.860778323152748 \tabularnewline
34 & 0.106327115971249 & 0.212654231942497 & 0.893672884028751 \tabularnewline
35 & 0.0688646729432135 & 0.137729345886427 & 0.931135327056786 \tabularnewline
36 & 0.0889201504270339 & 0.177840300854068 & 0.911079849572966 \tabularnewline
37 & 0.0753102481224137 & 0.150620496244827 & 0.924689751877586 \tabularnewline
38 & 0.125754359132600 & 0.251508718265199 & 0.8742456408674 \tabularnewline
39 & 0.122766871073735 & 0.245533742147470 & 0.877233128926265 \tabularnewline
40 & 0.270492702129114 & 0.540985404258228 & 0.729507297870886 \tabularnewline
41 & 0.194740275555743 & 0.389480551111487 & 0.805259724444257 \tabularnewline
42 & 0.113701858018165 & 0.227403716036331 & 0.886298141981835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&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]18[/C][C]0.240402767718595[/C][C]0.48080553543719[/C][C]0.759597232281405[/C][/ROW]
[ROW][C]19[/C][C]0.156069323308035[/C][C]0.312138646616071[/C][C]0.843930676691965[/C][/ROW]
[ROW][C]20[/C][C]0.0803744096858877[/C][C]0.160748819371775[/C][C]0.919625590314112[/C][/ROW]
[ROW][C]21[/C][C]0.0892172002147046[/C][C]0.178434400429409[/C][C]0.910782799785295[/C][/ROW]
[ROW][C]22[/C][C]0.0582838367120907[/C][C]0.116567673424181[/C][C]0.94171616328791[/C][/ROW]
[ROW][C]23[/C][C]0.184366069286090[/C][C]0.368732138572179[/C][C]0.81563393071391[/C][/ROW]
[ROW][C]24[/C][C]0.127193752895896[/C][C]0.254387505791793[/C][C]0.872806247104104[/C][/ROW]
[ROW][C]25[/C][C]0.0799763713517787[/C][C]0.159952742703557[/C][C]0.920023628648221[/C][/ROW]
[ROW][C]26[/C][C]0.0780215597470313[/C][C]0.156043119494063[/C][C]0.921978440252969[/C][/ROW]
[ROW][C]27[/C][C]0.0603299849990349[/C][C]0.12065996999807[/C][C]0.939670015000965[/C][/ROW]
[ROW][C]28[/C][C]0.104140720031313[/C][C]0.208281440062626[/C][C]0.895859279968687[/C][/ROW]
[ROW][C]29[/C][C]0.204775686933931[/C][C]0.409551373867863[/C][C]0.795224313066069[/C][/ROW]
[ROW][C]30[/C][C]0.246961059870721[/C][C]0.493922119741443[/C][C]0.753038940129279[/C][/ROW]
[ROW][C]31[/C][C]0.224026936389358[/C][C]0.448053872778717[/C][C]0.775973063610642[/C][/ROW]
[ROW][C]32[/C][C]0.168503905357824[/C][C]0.337007810715648[/C][C]0.831496094642176[/C][/ROW]
[ROW][C]33[/C][C]0.139221676847252[/C][C]0.278443353694504[/C][C]0.860778323152748[/C][/ROW]
[ROW][C]34[/C][C]0.106327115971249[/C][C]0.212654231942497[/C][C]0.893672884028751[/C][/ROW]
[ROW][C]35[/C][C]0.0688646729432135[/C][C]0.137729345886427[/C][C]0.931135327056786[/C][/ROW]
[ROW][C]36[/C][C]0.0889201504270339[/C][C]0.177840300854068[/C][C]0.911079849572966[/C][/ROW]
[ROW][C]37[/C][C]0.0753102481224137[/C][C]0.150620496244827[/C][C]0.924689751877586[/C][/ROW]
[ROW][C]38[/C][C]0.125754359132600[/C][C]0.251508718265199[/C][C]0.8742456408674[/C][/ROW]
[ROW][C]39[/C][C]0.122766871073735[/C][C]0.245533742147470[/C][C]0.877233128926265[/C][/ROW]
[ROW][C]40[/C][C]0.270492702129114[/C][C]0.540985404258228[/C][C]0.729507297870886[/C][/ROW]
[ROW][C]41[/C][C]0.194740275555743[/C][C]0.389480551111487[/C][C]0.805259724444257[/C][/ROW]
[ROW][C]42[/C][C]0.113701858018165[/C][C]0.227403716036331[/C][C]0.886298141981835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&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
180.2404027677185950.480805535437190.759597232281405
190.1560693233080350.3121386466160710.843930676691965
200.08037440968588770.1607488193717750.919625590314112
210.08921720021470460.1784344004294090.910782799785295
220.05828383671209070.1165676734241810.94171616328791
230.1843660692860900.3687321385721790.81563393071391
240.1271937528958960.2543875057917930.872806247104104
250.07997637135177870.1599527427035570.920023628648221
260.07802155974703130.1560431194940630.921978440252969
270.06032998499903490.120659969998070.939670015000965
280.1041407200313130.2082814400626260.895859279968687
290.2047756869339310.4095513738678630.795224313066069
300.2469610598707210.4939221197414430.753038940129279
310.2240269363893580.4480538727787170.775973063610642
320.1685039053578240.3370078107156480.831496094642176
330.1392216768472520.2784433536945040.860778323152748
340.1063271159712490.2126542319424970.893672884028751
350.06886467294321350.1377293458864270.931135327056786
360.08892015042703390.1778403008540680.911079849572966
370.07531024812241370.1506204962448270.924689751877586
380.1257543591326000.2515087182651990.8742456408674
390.1227668710737350.2455337421474700.877233128926265
400.2704927021291140.5409854042582280.729507297870886
410.1947402755557430.3894805511114870.805259724444257
420.1137018580181650.2274037160363310.886298141981835







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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58451&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58451&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58451&T=6

As an alternative you can also use a QR Code:  

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

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



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')
}