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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 21 Nov 2009 08:04:45 -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/21/t1258816090qtids9tojnr5fox.htm/, Retrieved Wed, 19 Nov 2025 22:12:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58563, Retrieved Wed, 19 Nov 2025 22:12:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact483

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D            [Multiple Regression] [WS7] [2009-11-21 15:04:45] [48076ccf082563ab8a2c81e57fdb5364] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10414.9	10723.8
12476.8	13938.9
12384.6	13979.8
12266.7	13807.4
12919.9	12973.9
11497.3	12509.8
12142	12934.1
13919.4	14908.3
12656.8	13772.1
12034.1	13012.6
13199.7	14049.9
10881.3	11816.5
11301.2	11593.2
13643.9	14466.2
12517	13615.9
13981.1	14733.9
14275.7	13880.7
13435	13527.5
13565.7	13584
16216.3	16170.2
12970	13260.6
14079.9	14741.9
14235	15486.5
12213.4	13154.5
12581	12621.2
14130.4	15031.6
14210.8	15452.4
14378.5	15428
13142.8	13105.9
13714.7	14716.8
13621.9	14180
15379.8	16202.2
13306.3	14392.4
14391.2	15140.6
14909.9	15960.1
14025.4	14351.3
12951.2	13230.2
14344.3	15202.1
16093.4	17056
15413.6	16077.7
14705.7	13348.2
15972.8	16402.4
16241.4	16559.1
16626.4	16579
17136.2	17561.2
15622.9	16129.6
18003.9	18484.3
16136.1	16402.6
14423.7	14032.3
16789.4	17109.1
16782.2	17157.2
14133.8	13879.8
12607	12362.4
12004.5	12683.5
12175.4	12608.8
13268	13583.7
12299.3	12846.3
11800.6	12347.1
13873.3	13967
12269.6	13114.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
InIEU[t] = -1948.67388499954 + 1.09340563842981UitIEU[t] + 680.954666143251M1[t] -339.002306844012M2[t] -549.314325483949M3[t] -182.982105215105M4[t] + 1117.86368062190M5[t] + 0.843927411887669M6[t] + 219.578218092053M7[t] + 95.2438411644369M8[t] -86.0400876151622M9[t] -73.2518239774703M10[t] -252.678919640362M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
InIEU[t] =  -1948.67388499954 +  1.09340563842981UitIEU[t] +  680.954666143251M1[t] -339.002306844012M2[t] -549.314325483949M3[t] -182.982105215105M4[t] +  1117.86368062190M5[t] +  0.843927411887669M6[t] +  219.578218092053M7[t] +  95.2438411644369M8[t] -86.0400876151622M9[t] -73.2518239774703M10[t] -252.678919640362M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]InIEU[t] =  -1948.67388499954 +  1.09340563842981UitIEU[t] +  680.954666143251M1[t] -339.002306844012M2[t] -549.314325483949M3[t] -182.982105215105M4[t] +  1117.86368062190M5[t] +  0.843927411887669M6[t] +  219.578218092053M7[t] +  95.2438411644369M8[t] -86.0400876151622M9[t] -73.2518239774703M10[t] -252.678919640362M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
InIEU[t] = -1948.67388499954 + 1.09340563842981UitIEU[t] + 680.954666143251M1[t] -339.002306844012M2[t] -549.314325483949M3[t] -182.982105215105M4[t] + 1117.86368062190M5[t] + 0.843927411887669M6[t] + 219.578218092053M7[t] + 95.2438411644369M8[t] -86.0400876151622M9[t] -73.2518239774703M10[t] -252.678919640362M11[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-1948.67388499954579.424605-3.36310.001540.00077
UitIEU1.093405638429810.03994327.374100
M1680.954666143251263.5042632.58420.0129270.006463
M2-339.002306844012263.947151-1.28440.2053120.102656
M3-549.314325483949266.737276-2.05940.0450210.022511
M4-182.982105215105261.29276-0.70030.4871950.243598
M51117.86368062190259.3503394.31028.3e-054.1e-05
M60.843927411887669258.2363030.00330.9974060.498703
M7219.578218092053258.2428170.85030.3994810.199741
M895.2438411644369267.107920.35660.7230060.361503
M9-86.0400876151622259.217869-0.33190.7414240.370712
M10-73.2518239774703258.904229-0.28290.7784730.389236
M11-252.678919640362268.173097-0.94220.3508960.175448

\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) & -1948.67388499954 & 579.424605 & -3.3631 & 0.00154 & 0.00077 \tabularnewline
UitIEU & 1.09340563842981 & 0.039943 & 27.3741 & 0 & 0 \tabularnewline
M1 & 680.954666143251 & 263.504263 & 2.5842 & 0.012927 & 0.006463 \tabularnewline
M2 & -339.002306844012 & 263.947151 & -1.2844 & 0.205312 & 0.102656 \tabularnewline
M3 & -549.314325483949 & 266.737276 & -2.0594 & 0.045021 & 0.022511 \tabularnewline
M4 & -182.982105215105 & 261.29276 & -0.7003 & 0.487195 & 0.243598 \tabularnewline
M5 & 1117.86368062190 & 259.350339 & 4.3102 & 8.3e-05 & 4.1e-05 \tabularnewline
M6 & 0.843927411887669 & 258.236303 & 0.0033 & 0.997406 & 0.498703 \tabularnewline
M7 & 219.578218092053 & 258.242817 & 0.8503 & 0.399481 & 0.199741 \tabularnewline
M8 & 95.2438411644369 & 267.10792 & 0.3566 & 0.723006 & 0.361503 \tabularnewline
M9 & -86.0400876151622 & 259.217869 & -0.3319 & 0.741424 & 0.370712 \tabularnewline
M10 & -73.2518239774703 & 258.904229 & -0.2829 & 0.778473 & 0.389236 \tabularnewline
M11 & -252.678919640362 & 268.173097 & -0.9422 & 0.350896 & 0.175448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&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]-1948.67388499954[/C][C]579.424605[/C][C]-3.3631[/C][C]0.00154[/C][C]0.00077[/C][/ROW]
[ROW][C]UitIEU[/C][C]1.09340563842981[/C][C]0.039943[/C][C]27.3741[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]680.954666143251[/C][C]263.504263[/C][C]2.5842[/C][C]0.012927[/C][C]0.006463[/C][/ROW]
[ROW][C]M2[/C][C]-339.002306844012[/C][C]263.947151[/C][C]-1.2844[/C][C]0.205312[/C][C]0.102656[/C][/ROW]
[ROW][C]M3[/C][C]-549.314325483949[/C][C]266.737276[/C][C]-2.0594[/C][C]0.045021[/C][C]0.022511[/C][/ROW]
[ROW][C]M4[/C][C]-182.982105215105[/C][C]261.29276[/C][C]-0.7003[/C][C]0.487195[/C][C]0.243598[/C][/ROW]
[ROW][C]M5[/C][C]1117.86368062190[/C][C]259.350339[/C][C]4.3102[/C][C]8.3e-05[/C][C]4.1e-05[/C][/ROW]
[ROW][C]M6[/C][C]0.843927411887669[/C][C]258.236303[/C][C]0.0033[/C][C]0.997406[/C][C]0.498703[/C][/ROW]
[ROW][C]M7[/C][C]219.578218092053[/C][C]258.242817[/C][C]0.8503[/C][C]0.399481[/C][C]0.199741[/C][/ROW]
[ROW][C]M8[/C][C]95.2438411644369[/C][C]267.10792[/C][C]0.3566[/C][C]0.723006[/C][C]0.361503[/C][/ROW]
[ROW][C]M9[/C][C]-86.0400876151622[/C][C]259.217869[/C][C]-0.3319[/C][C]0.741424[/C][C]0.370712[/C][/ROW]
[ROW][C]M10[/C][C]-73.2518239774703[/C][C]258.904229[/C][C]-0.2829[/C][C]0.778473[/C][C]0.389236[/C][/ROW]
[ROW][C]M11[/C][C]-252.678919640362[/C][C]268.173097[/C][C]-0.9422[/C][C]0.350896[/C][C]0.175448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-1948.67388499954579.424605-3.36310.001540.00077
UitIEU1.093405638429810.03994327.374100
M1680.954666143251263.5042632.58420.0129270.006463
M2-339.002306844012263.947151-1.28440.2053120.102656
M3-549.314325483949266.737276-2.05940.0450210.022511
M4-182.982105215105261.29276-0.70030.4871950.243598
M51117.86368062190259.3503394.31028.3e-054.1e-05
M60.843927411887669258.2363030.00330.9974060.498703
M7219.578218092053258.2428170.85030.3994810.199741
M895.2438411644369267.107920.35660.7230060.361503
M9-86.0400876151622259.217869-0.33190.7414240.370712
M10-73.2518239774703258.904229-0.28290.7784730.389236
M11-252.678919640362268.173097-0.94220.3508960.175448






Multiple Linear Regression - Regression Statistics
Multiple R0.975955859594136
R-squared0.952489839876129
Adjusted R-squared0.94035958622748
F-TEST (value)78.5218403064713
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation408.111714102607
Sum Squared Residuals7828093.0458251

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.975955859594136 \tabularnewline
R-squared & 0.952489839876129 \tabularnewline
Adjusted R-squared & 0.94035958622748 \tabularnewline
F-TEST (value) & 78.5218403064713 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 408.111714102607 \tabularnewline
Sum Squared Residuals & 7828093.0458251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.975955859594136[/C][/ROW]
[ROW][C]R-squared[/C][C]0.952489839876129[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.94035958622748[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]78.5218403064713[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]408.111714102607[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7828093.0458251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.975955859594136
R-squared0.952489839876129
Adjusted R-squared0.94035958622748
F-TEST (value)78.5218403064713
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation408.111714102607
Sum Squared Residuals7828093.0458251






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110414.910457.7441665374-42.8441665374268
212476.812953.1956616658-476.39566166579
312384.612787.6039336376-403.003933637635
412266.712965.4330218412-698.733021841177
512919.913354.9252080469-435.025208046931
611497.311730.4558980416-233.155898041644
71214212413.1222011076-271.122201107582
813919.414447.3892355681-527.989235568103
912656.813023.7778204045-366.97782040455
1012034.112206.1245016548-172.024501654797
1113199.713160.887074735238.8129252648492
1210881.310971.5538415064-90.2538415063668
1311301.211408.3510285882-107.151028588239
1413643.913529.7484548098114.151545190165
151251712389.7136218130127.286378186975
1613981.113978.47334584642.62665415359883
1714275.714346.4254409751-70.7254409750882
181343512843.2148162717591.785183728333
1913565.713123.7265255231441.973474476884
2016216.315827.1578107027389.142189297312
211297012464.5008363477505.4991636523
2214079.914096.9508721915-17.0508721914754
231423514731.6736149034-496.673614903423
2412213.412434.5305857255-221.130585725459
251258112532.372024894148.6279751059106
2614130.414147.9600027781-17.5600027780517
2714210.814397.7530767894-186.953076789381
2814378.514737.4061994805-358.906199480536
2913142.813499.2547523197-356.454752319668
3013714.714143.6021420562-428.902142056244
3113621.913775.3962860273-153.496286027286
3215379.815862.1467911324-482.346791132442
3313306.313702.0173379226-395.717337922564
3414391.214532.8917002334-141.691700233442
3514909.915249.5105252638-339.610525263785
3614025.413743.1184537983282.28154620174
3712951.213198.2560586978-247.056058697846
3814344.314334.38566413039.91433586966418
3916093.416151.1383585754-57.7383585754312
4015413.615447.7918427684-34.1918427683873
4114705.713764.1869385112941.513061488788
4215972.815986.6466861935-13.8466861935425
4316241.416376.7176404157-135.317640415656
4416626.416274.1420356928352.257964307206
4517136.217166.8011249790-30.6011249789598
4615622.915614.26987664058.63012335947014
4718003.918009.4850377883-5.58503778832015
4816136.115986.0214399093150.078560090663
4914423.714075.2767212824348.423278717601
5016789.416419.510216616369.889783384012
5116782.216261.7910091845520.408990815472
5214133.813044.59559006351089.20440993650
531260712686.3076601471-79.3076601471001
5412004.511920.380457436984.119542563097
5512175.412057.4373469264117.962653073639
561326812999.0641269040268.935873096028
5712299.312011.5028803462287.797119653773
5811800.611478.4630492798322.136950720244
5913873.313070.2437473093803.05625269068
6012269.612390.5756790606-120.975679060578

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10414.9 & 10457.7441665374 & -42.8441665374268 \tabularnewline
2 & 12476.8 & 12953.1956616658 & -476.39566166579 \tabularnewline
3 & 12384.6 & 12787.6039336376 & -403.003933637635 \tabularnewline
4 & 12266.7 & 12965.4330218412 & -698.733021841177 \tabularnewline
5 & 12919.9 & 13354.9252080469 & -435.025208046931 \tabularnewline
6 & 11497.3 & 11730.4558980416 & -233.155898041644 \tabularnewline
7 & 12142 & 12413.1222011076 & -271.122201107582 \tabularnewline
8 & 13919.4 & 14447.3892355681 & -527.989235568103 \tabularnewline
9 & 12656.8 & 13023.7778204045 & -366.97782040455 \tabularnewline
10 & 12034.1 & 12206.1245016548 & -172.024501654797 \tabularnewline
11 & 13199.7 & 13160.8870747352 & 38.8129252648492 \tabularnewline
12 & 10881.3 & 10971.5538415064 & -90.2538415063668 \tabularnewline
13 & 11301.2 & 11408.3510285882 & -107.151028588239 \tabularnewline
14 & 13643.9 & 13529.7484548098 & 114.151545190165 \tabularnewline
15 & 12517 & 12389.7136218130 & 127.286378186975 \tabularnewline
16 & 13981.1 & 13978.4733458464 & 2.62665415359883 \tabularnewline
17 & 14275.7 & 14346.4254409751 & -70.7254409750882 \tabularnewline
18 & 13435 & 12843.2148162717 & 591.785183728333 \tabularnewline
19 & 13565.7 & 13123.7265255231 & 441.973474476884 \tabularnewline
20 & 16216.3 & 15827.1578107027 & 389.142189297312 \tabularnewline
21 & 12970 & 12464.5008363477 & 505.4991636523 \tabularnewline
22 & 14079.9 & 14096.9508721915 & -17.0508721914754 \tabularnewline
23 & 14235 & 14731.6736149034 & -496.673614903423 \tabularnewline
24 & 12213.4 & 12434.5305857255 & -221.130585725459 \tabularnewline
25 & 12581 & 12532.3720248941 & 48.6279751059106 \tabularnewline
26 & 14130.4 & 14147.9600027781 & -17.5600027780517 \tabularnewline
27 & 14210.8 & 14397.7530767894 & -186.953076789381 \tabularnewline
28 & 14378.5 & 14737.4061994805 & -358.906199480536 \tabularnewline
29 & 13142.8 & 13499.2547523197 & -356.454752319668 \tabularnewline
30 & 13714.7 & 14143.6021420562 & -428.902142056244 \tabularnewline
31 & 13621.9 & 13775.3962860273 & -153.496286027286 \tabularnewline
32 & 15379.8 & 15862.1467911324 & -482.346791132442 \tabularnewline
33 & 13306.3 & 13702.0173379226 & -395.717337922564 \tabularnewline
34 & 14391.2 & 14532.8917002334 & -141.691700233442 \tabularnewline
35 & 14909.9 & 15249.5105252638 & -339.610525263785 \tabularnewline
36 & 14025.4 & 13743.1184537983 & 282.28154620174 \tabularnewline
37 & 12951.2 & 13198.2560586978 & -247.056058697846 \tabularnewline
38 & 14344.3 & 14334.3856641303 & 9.91433586966418 \tabularnewline
39 & 16093.4 & 16151.1383585754 & -57.7383585754312 \tabularnewline
40 & 15413.6 & 15447.7918427684 & -34.1918427683873 \tabularnewline
41 & 14705.7 & 13764.1869385112 & 941.513061488788 \tabularnewline
42 & 15972.8 & 15986.6466861935 & -13.8466861935425 \tabularnewline
43 & 16241.4 & 16376.7176404157 & -135.317640415656 \tabularnewline
44 & 16626.4 & 16274.1420356928 & 352.257964307206 \tabularnewline
45 & 17136.2 & 17166.8011249790 & -30.6011249789598 \tabularnewline
46 & 15622.9 & 15614.2698766405 & 8.63012335947014 \tabularnewline
47 & 18003.9 & 18009.4850377883 & -5.58503778832015 \tabularnewline
48 & 16136.1 & 15986.0214399093 & 150.078560090663 \tabularnewline
49 & 14423.7 & 14075.2767212824 & 348.423278717601 \tabularnewline
50 & 16789.4 & 16419.510216616 & 369.889783384012 \tabularnewline
51 & 16782.2 & 16261.7910091845 & 520.408990815472 \tabularnewline
52 & 14133.8 & 13044.5955900635 & 1089.20440993650 \tabularnewline
53 & 12607 & 12686.3076601471 & -79.3076601471001 \tabularnewline
54 & 12004.5 & 11920.3804574369 & 84.119542563097 \tabularnewline
55 & 12175.4 & 12057.4373469264 & 117.962653073639 \tabularnewline
56 & 13268 & 12999.0641269040 & 268.935873096028 \tabularnewline
57 & 12299.3 & 12011.5028803462 & 287.797119653773 \tabularnewline
58 & 11800.6 & 11478.4630492798 & 322.136950720244 \tabularnewline
59 & 13873.3 & 13070.2437473093 & 803.05625269068 \tabularnewline
60 & 12269.6 & 12390.5756790606 & -120.975679060578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&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]10414.9[/C][C]10457.7441665374[/C][C]-42.8441665374268[/C][/ROW]
[ROW][C]2[/C][C]12476.8[/C][C]12953.1956616658[/C][C]-476.39566166579[/C][/ROW]
[ROW][C]3[/C][C]12384.6[/C][C]12787.6039336376[/C][C]-403.003933637635[/C][/ROW]
[ROW][C]4[/C][C]12266.7[/C][C]12965.4330218412[/C][C]-698.733021841177[/C][/ROW]
[ROW][C]5[/C][C]12919.9[/C][C]13354.9252080469[/C][C]-435.025208046931[/C][/ROW]
[ROW][C]6[/C][C]11497.3[/C][C]11730.4558980416[/C][C]-233.155898041644[/C][/ROW]
[ROW][C]7[/C][C]12142[/C][C]12413.1222011076[/C][C]-271.122201107582[/C][/ROW]
[ROW][C]8[/C][C]13919.4[/C][C]14447.3892355681[/C][C]-527.989235568103[/C][/ROW]
[ROW][C]9[/C][C]12656.8[/C][C]13023.7778204045[/C][C]-366.97782040455[/C][/ROW]
[ROW][C]10[/C][C]12034.1[/C][C]12206.1245016548[/C][C]-172.024501654797[/C][/ROW]
[ROW][C]11[/C][C]13199.7[/C][C]13160.8870747352[/C][C]38.8129252648492[/C][/ROW]
[ROW][C]12[/C][C]10881.3[/C][C]10971.5538415064[/C][C]-90.2538415063668[/C][/ROW]
[ROW][C]13[/C][C]11301.2[/C][C]11408.3510285882[/C][C]-107.151028588239[/C][/ROW]
[ROW][C]14[/C][C]13643.9[/C][C]13529.7484548098[/C][C]114.151545190165[/C][/ROW]
[ROW][C]15[/C][C]12517[/C][C]12389.7136218130[/C][C]127.286378186975[/C][/ROW]
[ROW][C]16[/C][C]13981.1[/C][C]13978.4733458464[/C][C]2.62665415359883[/C][/ROW]
[ROW][C]17[/C][C]14275.7[/C][C]14346.4254409751[/C][C]-70.7254409750882[/C][/ROW]
[ROW][C]18[/C][C]13435[/C][C]12843.2148162717[/C][C]591.785183728333[/C][/ROW]
[ROW][C]19[/C][C]13565.7[/C][C]13123.7265255231[/C][C]441.973474476884[/C][/ROW]
[ROW][C]20[/C][C]16216.3[/C][C]15827.1578107027[/C][C]389.142189297312[/C][/ROW]
[ROW][C]21[/C][C]12970[/C][C]12464.5008363477[/C][C]505.4991636523[/C][/ROW]
[ROW][C]22[/C][C]14079.9[/C][C]14096.9508721915[/C][C]-17.0508721914754[/C][/ROW]
[ROW][C]23[/C][C]14235[/C][C]14731.6736149034[/C][C]-496.673614903423[/C][/ROW]
[ROW][C]24[/C][C]12213.4[/C][C]12434.5305857255[/C][C]-221.130585725459[/C][/ROW]
[ROW][C]25[/C][C]12581[/C][C]12532.3720248941[/C][C]48.6279751059106[/C][/ROW]
[ROW][C]26[/C][C]14130.4[/C][C]14147.9600027781[/C][C]-17.5600027780517[/C][/ROW]
[ROW][C]27[/C][C]14210.8[/C][C]14397.7530767894[/C][C]-186.953076789381[/C][/ROW]
[ROW][C]28[/C][C]14378.5[/C][C]14737.4061994805[/C][C]-358.906199480536[/C][/ROW]
[ROW][C]29[/C][C]13142.8[/C][C]13499.2547523197[/C][C]-356.454752319668[/C][/ROW]
[ROW][C]30[/C][C]13714.7[/C][C]14143.6021420562[/C][C]-428.902142056244[/C][/ROW]
[ROW][C]31[/C][C]13621.9[/C][C]13775.3962860273[/C][C]-153.496286027286[/C][/ROW]
[ROW][C]32[/C][C]15379.8[/C][C]15862.1467911324[/C][C]-482.346791132442[/C][/ROW]
[ROW][C]33[/C][C]13306.3[/C][C]13702.0173379226[/C][C]-395.717337922564[/C][/ROW]
[ROW][C]34[/C][C]14391.2[/C][C]14532.8917002334[/C][C]-141.691700233442[/C][/ROW]
[ROW][C]35[/C][C]14909.9[/C][C]15249.5105252638[/C][C]-339.610525263785[/C][/ROW]
[ROW][C]36[/C][C]14025.4[/C][C]13743.1184537983[/C][C]282.28154620174[/C][/ROW]
[ROW][C]37[/C][C]12951.2[/C][C]13198.2560586978[/C][C]-247.056058697846[/C][/ROW]
[ROW][C]38[/C][C]14344.3[/C][C]14334.3856641303[/C][C]9.91433586966418[/C][/ROW]
[ROW][C]39[/C][C]16093.4[/C][C]16151.1383585754[/C][C]-57.7383585754312[/C][/ROW]
[ROW][C]40[/C][C]15413.6[/C][C]15447.7918427684[/C][C]-34.1918427683873[/C][/ROW]
[ROW][C]41[/C][C]14705.7[/C][C]13764.1869385112[/C][C]941.513061488788[/C][/ROW]
[ROW][C]42[/C][C]15972.8[/C][C]15986.6466861935[/C][C]-13.8466861935425[/C][/ROW]
[ROW][C]43[/C][C]16241.4[/C][C]16376.7176404157[/C][C]-135.317640415656[/C][/ROW]
[ROW][C]44[/C][C]16626.4[/C][C]16274.1420356928[/C][C]352.257964307206[/C][/ROW]
[ROW][C]45[/C][C]17136.2[/C][C]17166.8011249790[/C][C]-30.6011249789598[/C][/ROW]
[ROW][C]46[/C][C]15622.9[/C][C]15614.2698766405[/C][C]8.63012335947014[/C][/ROW]
[ROW][C]47[/C][C]18003.9[/C][C]18009.4850377883[/C][C]-5.58503778832015[/C][/ROW]
[ROW][C]48[/C][C]16136.1[/C][C]15986.0214399093[/C][C]150.078560090663[/C][/ROW]
[ROW][C]49[/C][C]14423.7[/C][C]14075.2767212824[/C][C]348.423278717601[/C][/ROW]
[ROW][C]50[/C][C]16789.4[/C][C]16419.510216616[/C][C]369.889783384012[/C][/ROW]
[ROW][C]51[/C][C]16782.2[/C][C]16261.7910091845[/C][C]520.408990815472[/C][/ROW]
[ROW][C]52[/C][C]14133.8[/C][C]13044.5955900635[/C][C]1089.20440993650[/C][/ROW]
[ROW][C]53[/C][C]12607[/C][C]12686.3076601471[/C][C]-79.3076601471001[/C][/ROW]
[ROW][C]54[/C][C]12004.5[/C][C]11920.3804574369[/C][C]84.119542563097[/C][/ROW]
[ROW][C]55[/C][C]12175.4[/C][C]12057.4373469264[/C][C]117.962653073639[/C][/ROW]
[ROW][C]56[/C][C]13268[/C][C]12999.0641269040[/C][C]268.935873096028[/C][/ROW]
[ROW][C]57[/C][C]12299.3[/C][C]12011.5028803462[/C][C]287.797119653773[/C][/ROW]
[ROW][C]58[/C][C]11800.6[/C][C]11478.4630492798[/C][C]322.136950720244[/C][/ROW]
[ROW][C]59[/C][C]13873.3[/C][C]13070.2437473093[/C][C]803.05625269068[/C][/ROW]
[ROW][C]60[/C][C]12269.6[/C][C]12390.5756790606[/C][C]-120.975679060578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110414.910457.7441665374-42.8441665374268
212476.812953.1956616658-476.39566166579
312384.612787.6039336376-403.003933637635
412266.712965.4330218412-698.733021841177
512919.913354.9252080469-435.025208046931
611497.311730.4558980416-233.155898041644
71214212413.1222011076-271.122201107582
813919.414447.3892355681-527.989235568103
912656.813023.7778204045-366.97782040455
1012034.112206.1245016548-172.024501654797
1113199.713160.887074735238.8129252648492
1210881.310971.5538415064-90.2538415063668
1311301.211408.3510285882-107.151028588239
1413643.913529.7484548098114.151545190165
151251712389.7136218130127.286378186975
1613981.113978.47334584642.62665415359883
1714275.714346.4254409751-70.7254409750882
181343512843.2148162717591.785183728333
1913565.713123.7265255231441.973474476884
2016216.315827.1578107027389.142189297312
211297012464.5008363477505.4991636523
2214079.914096.9508721915-17.0508721914754
231423514731.6736149034-496.673614903423
2412213.412434.5305857255-221.130585725459
251258112532.372024894148.6279751059106
2614130.414147.9600027781-17.5600027780517
2714210.814397.7530767894-186.953076789381
2814378.514737.4061994805-358.906199480536
2913142.813499.2547523197-356.454752319668
3013714.714143.6021420562-428.902142056244
3113621.913775.3962860273-153.496286027286
3215379.815862.1467911324-482.346791132442
3313306.313702.0173379226-395.717337922564
3414391.214532.8917002334-141.691700233442
3514909.915249.5105252638-339.610525263785
3614025.413743.1184537983282.28154620174
3712951.213198.2560586978-247.056058697846
3814344.314334.38566413039.91433586966418
3916093.416151.1383585754-57.7383585754312
4015413.615447.7918427684-34.1918427683873
4114705.713764.1869385112941.513061488788
4215972.815986.6466861935-13.8466861935425
4316241.416376.7176404157-135.317640415656
4416626.416274.1420356928352.257964307206
4517136.217166.8011249790-30.6011249789598
4615622.915614.26987664058.63012335947014
4718003.918009.4850377883-5.58503778832015
4816136.115986.0214399093150.078560090663
4914423.714075.2767212824348.423278717601
5016789.416419.510216616369.889783384012
5116782.216261.7910091845520.408990815472
5214133.813044.59559006351089.20440993650
531260712686.3076601471-79.3076601471001
5412004.511920.380457436984.119542563097
5512175.412057.4373469264117.962653073639
561326812999.0641269040268.935873096028
5712299.312011.5028803462287.797119653773
5811800.611478.4630492798322.136950720244
5913873.313070.2437473093803.05625269068
6012269.612390.5756790606-120.975679060578






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.5152610064594630.9694779870810740.484738993540537
170.3414343286549860.6828686573099720.658565671345014
180.290028420992540.580056841985080.70997157900746
190.2377381496495790.4754762992991590.762261850350421
200.1624282557920960.3248565115841920.837571744207904
210.4582959370022990.9165918740045980.541704062997701
220.426429315397650.85285863079530.57357068460235
230.5688206272379880.8623587455240240.431179372762012
240.5147668107299630.9704663785400740.485233189270037
250.4145588234340490.8291176468680970.585441176565952
260.3252336994543980.6504673989087960.674766300545602
270.2859616012213510.5719232024427010.71403839877865
280.2937941558877720.5875883117755430.706205844112228
290.2922729502161420.5845459004322840.707727049783858
300.3581175337591150.716235067518230.641882466240885
310.2892487885412970.5784975770825930.710751211458703
320.3292376124186030.6584752248372060.670762387581397
330.3454798428374390.6909596856748780.654520157162561
340.2704947572365430.5409895144730860.729505242763457
350.3086586658940370.6173173317880740.691341334105963
360.2615489148551780.5230978297103550.738451085144822
370.2589659087632300.5179318175264600.74103409123677
380.2206510407614850.4413020815229690.779348959238515
390.203023728280060.406047456560120.79697627171994
400.3750048938364610.7500097876729220.624995106163539
410.9102679588660240.1794640822679510.0897320411339757
420.8399449319467260.3201101361065480.160055068053274
430.7200070276393950.5599859447212110.279992972360605
440.6362231418530160.7275537162939680.363776858146984

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.515261006459463 & 0.969477987081074 & 0.484738993540537 \tabularnewline
17 & 0.341434328654986 & 0.682868657309972 & 0.658565671345014 \tabularnewline
18 & 0.29002842099254 & 0.58005684198508 & 0.70997157900746 \tabularnewline
19 & 0.237738149649579 & 0.475476299299159 & 0.762261850350421 \tabularnewline
20 & 0.162428255792096 & 0.324856511584192 & 0.837571744207904 \tabularnewline
21 & 0.458295937002299 & 0.916591874004598 & 0.541704062997701 \tabularnewline
22 & 0.42642931539765 & 0.8528586307953 & 0.57357068460235 \tabularnewline
23 & 0.568820627237988 & 0.862358745524024 & 0.431179372762012 \tabularnewline
24 & 0.514766810729963 & 0.970466378540074 & 0.485233189270037 \tabularnewline
25 & 0.414558823434049 & 0.829117646868097 & 0.585441176565952 \tabularnewline
26 & 0.325233699454398 & 0.650467398908796 & 0.674766300545602 \tabularnewline
27 & 0.285961601221351 & 0.571923202442701 & 0.71403839877865 \tabularnewline
28 & 0.293794155887772 & 0.587588311775543 & 0.706205844112228 \tabularnewline
29 & 0.292272950216142 & 0.584545900432284 & 0.707727049783858 \tabularnewline
30 & 0.358117533759115 & 0.71623506751823 & 0.641882466240885 \tabularnewline
31 & 0.289248788541297 & 0.578497577082593 & 0.710751211458703 \tabularnewline
32 & 0.329237612418603 & 0.658475224837206 & 0.670762387581397 \tabularnewline
33 & 0.345479842837439 & 0.690959685674878 & 0.654520157162561 \tabularnewline
34 & 0.270494757236543 & 0.540989514473086 & 0.729505242763457 \tabularnewline
35 & 0.308658665894037 & 0.617317331788074 & 0.691341334105963 \tabularnewline
36 & 0.261548914855178 & 0.523097829710355 & 0.738451085144822 \tabularnewline
37 & 0.258965908763230 & 0.517931817526460 & 0.74103409123677 \tabularnewline
38 & 0.220651040761485 & 0.441302081522969 & 0.779348959238515 \tabularnewline
39 & 0.20302372828006 & 0.40604745656012 & 0.79697627171994 \tabularnewline
40 & 0.375004893836461 & 0.750009787672922 & 0.624995106163539 \tabularnewline
41 & 0.910267958866024 & 0.179464082267951 & 0.0897320411339757 \tabularnewline
42 & 0.839944931946726 & 0.320110136106548 & 0.160055068053274 \tabularnewline
43 & 0.720007027639395 & 0.559985944721211 & 0.279992972360605 \tabularnewline
44 & 0.636223141853016 & 0.727553716293968 & 0.363776858146984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58563&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]16[/C][C]0.515261006459463[/C][C]0.969477987081074[/C][C]0.484738993540537[/C][/ROW]
[ROW][C]17[/C][C]0.341434328654986[/C][C]0.682868657309972[/C][C]0.658565671345014[/C][/ROW]
[ROW][C]18[/C][C]0.29002842099254[/C][C]0.58005684198508[/C][C]0.70997157900746[/C][/ROW]
[ROW][C]19[/C][C]0.237738149649579[/C][C]0.475476299299159[/C][C]0.762261850350421[/C][/ROW]
[ROW][C]20[/C][C]0.162428255792096[/C][C]0.324856511584192[/C][C]0.837571744207904[/C][/ROW]
[ROW][C]21[/C][C]0.458295937002299[/C][C]0.916591874004598[/C][C]0.541704062997701[/C][/ROW]
[ROW][C]22[/C][C]0.42642931539765[/C][C]0.8528586307953[/C][C]0.57357068460235[/C][/ROW]
[ROW][C]23[/C][C]0.568820627237988[/C][C]0.862358745524024[/C][C]0.431179372762012[/C][/ROW]
[ROW][C]24[/C][C]0.514766810729963[/C][C]0.970466378540074[/C][C]0.485233189270037[/C][/ROW]
[ROW][C]25[/C][C]0.414558823434049[/C][C]0.829117646868097[/C][C]0.585441176565952[/C][/ROW]
[ROW][C]26[/C][C]0.325233699454398[/C][C]0.650467398908796[/C][C]0.674766300545602[/C][/ROW]
[ROW][C]27[/C][C]0.285961601221351[/C][C]0.571923202442701[/C][C]0.71403839877865[/C][/ROW]
[ROW][C]28[/C][C]0.293794155887772[/C][C]0.587588311775543[/C][C]0.706205844112228[/C][/ROW]
[ROW][C]29[/C][C]0.292272950216142[/C][C]0.584545900432284[/C][C]0.707727049783858[/C][/ROW]
[ROW][C]30[/C][C]0.358117533759115[/C][C]0.71623506751823[/C][C]0.641882466240885[/C][/ROW]
[ROW][C]31[/C][C]0.289248788541297[/C][C]0.578497577082593[/C][C]0.710751211458703[/C][/ROW]
[ROW][C]32[/C][C]0.329237612418603[/C][C]0.658475224837206[/C][C]0.670762387581397[/C][/ROW]
[ROW][C]33[/C][C]0.345479842837439[/C][C]0.690959685674878[/C][C]0.654520157162561[/C][/ROW]
[ROW][C]34[/C][C]0.270494757236543[/C][C]0.540989514473086[/C][C]0.729505242763457[/C][/ROW]
[ROW][C]35[/C][C]0.308658665894037[/C][C]0.617317331788074[/C][C]0.691341334105963[/C][/ROW]
[ROW][C]36[/C][C]0.261548914855178[/C][C]0.523097829710355[/C][C]0.738451085144822[/C][/ROW]
[ROW][C]37[/C][C]0.258965908763230[/C][C]0.517931817526460[/C][C]0.74103409123677[/C][/ROW]
[ROW][C]38[/C][C]0.220651040761485[/C][C]0.441302081522969[/C][C]0.779348959238515[/C][/ROW]
[ROW][C]39[/C][C]0.20302372828006[/C][C]0.40604745656012[/C][C]0.79697627171994[/C][/ROW]
[ROW][C]40[/C][C]0.375004893836461[/C][C]0.750009787672922[/C][C]0.624995106163539[/C][/ROW]
[ROW][C]41[/C][C]0.910267958866024[/C][C]0.179464082267951[/C][C]0.0897320411339757[/C][/ROW]
[ROW][C]42[/C][C]0.839944931946726[/C][C]0.320110136106548[/C][C]0.160055068053274[/C][/ROW]
[ROW][C]43[/C][C]0.720007027639395[/C][C]0.559985944721211[/C][C]0.279992972360605[/C][/ROW]
[ROW][C]44[/C][C]0.636223141853016[/C][C]0.727553716293968[/C][C]0.363776858146984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58563&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.5152610064594630.9694779870810740.484738993540537
170.3414343286549860.6828686573099720.658565671345014
180.290028420992540.580056841985080.70997157900746
190.2377381496495790.4754762992991590.762261850350421
200.1624282557920960.3248565115841920.837571744207904
210.4582959370022990.9165918740045980.541704062997701
220.426429315397650.85285863079530.57357068460235
230.5688206272379880.8623587455240240.431179372762012
240.5147668107299630.9704663785400740.485233189270037
250.4145588234340490.8291176468680970.585441176565952
260.3252336994543980.6504673989087960.674766300545602
270.2859616012213510.5719232024427010.71403839877865
280.2937941558877720.5875883117755430.706205844112228
290.2922729502161420.5845459004322840.707727049783858
300.3581175337591150.716235067518230.641882466240885
310.2892487885412970.5784975770825930.710751211458703
320.3292376124186030.6584752248372060.670762387581397
330.3454798428374390.6909596856748780.654520157162561
340.2704947572365430.5409895144730860.729505242763457
350.3086586658940370.6173173317880740.691341334105963
360.2615489148551780.5230978297103550.738451085144822
370.2589659087632300.5179318175264600.74103409123677
380.2206510407614850.4413020815229690.779348959238515
390.203023728280060.406047456560120.79697627171994
400.3750048938364610.7500097876729220.624995106163539
410.9102679588660240.1794640822679510.0897320411339757
420.8399449319467260.3201101361065480.160055068053274
430.7200070276393950.5599859447212110.279992972360605
440.6362231418530160.7275537162939680.363776858146984






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=58563&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=58563&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58563&T=6

As an alternative you can also use a QR Code:  
QR Code


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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