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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 computationSun, 22 Nov 2009 07:13:11 -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/22/t12589003933lwvnkfiy7actt9.htm/, Retrieved Tue, 10 Jun 2025 05:41:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58633, Retrieved Tue, 10 Jun 2025 05:41:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact358

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]
-   P           [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D              [Multiple Regression] [] [2009-11-22 14:13:11] [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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
In_IEU[t] = -1635.22504557635 + 1.03943856780702Uit_IEU[t] + 740.557383587982M1[t] -145.111303853829M2[t] -351.020823840440M3[t] -32.611497252725M4[t] + 1167.19484531337M5[t] + 83.2395019644493M6[t] + 290.322167129069M7[t] + 235.841552106109M8[t] -17.9343189263537M9[t] -22.0519148000427M10[t] -142.433773462613M11[t] + 11.9322542827837t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
In_IEU[t] =  -1635.22504557635 +  1.03943856780702Uit_IEU[t] +  740.557383587982M1[t] -145.111303853829M2[t] -351.020823840440M3[t] -32.611497252725M4[t] +  1167.19484531337M5[t] +  83.2395019644493M6[t] +  290.322167129069M7[t] +  235.841552106109M8[t] -17.9343189263537M9[t] -22.0519148000427M10[t] -142.433773462613M11[t] +  11.9322542827837t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]In_IEU[t] =  -1635.22504557635 +  1.03943856780702Uit_IEU[t] +  740.557383587982M1[t] -145.111303853829M2[t] -351.020823840440M3[t] -32.611497252725M4[t] +  1167.19484531337M5[t] +  83.2395019644493M6[t] +  290.322167129069M7[t] +  235.841552106109M8[t] -17.9343189263537M9[t] -22.0519148000427M10[t] -142.433773462613M11[t] +  11.9322542827837t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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
In_IEU[t] = -1635.22504557635 + 1.03943856780702Uit_IEU[t] + 740.557383587982M1[t] -145.111303853829M2[t] -351.020823840440M3[t] -32.611497252725M4[t] + 1167.19484531337M5[t] + 83.2395019644493M6[t] + 290.322167129069M7[t] + 235.841552106109M8[t] -17.9343189263537M9[t] -22.0519148000427M10[t] -142.433773462613M11[t] + 11.9322542827837t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-1635.22504557635504.143869-3.24360.0022010.001101
Uit_IEU1.039438567807020.0367128.314600
M1740.557383587982227.1683413.25990.0021010.00105
M2-145.111303853829231.786449-0.62610.5343730.267186
M3-351.020823840440234.349808-1.49780.1410040.070502
M4-32.611497252725227.675438-0.14320.8867290.443364
M51167.19484531337223.4583125.22334e-062e-06
M683.2395019644493223.0601050.37320.7107360.355368
M7290.322167129069222.8368661.30280.1991120.099556
M8235.841552106109232.2676131.01540.3152320.157616
M9-17.9343189263537223.626566-0.08020.9364280.468214
M10-22.0519148000427223.09909-0.09880.9216920.460846
M11-142.433773462613232.23903-0.61330.5426940.271347
t11.93225428278372.8533474.18180.0001286.4e-05

\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) & -1635.22504557635 & 504.143869 & -3.2436 & 0.002201 & 0.001101 \tabularnewline
Uit_IEU & 1.03943856780702 & 0.03671 & 28.3146 & 0 & 0 \tabularnewline
M1 & 740.557383587982 & 227.168341 & 3.2599 & 0.002101 & 0.00105 \tabularnewline
M2 & -145.111303853829 & 231.786449 & -0.6261 & 0.534373 & 0.267186 \tabularnewline
M3 & -351.020823840440 & 234.349808 & -1.4978 & 0.141004 & 0.070502 \tabularnewline
M4 & -32.611497252725 & 227.675438 & -0.1432 & 0.886729 & 0.443364 \tabularnewline
M5 & 1167.19484531337 & 223.458312 & 5.2233 & 4e-06 & 2e-06 \tabularnewline
M6 & 83.2395019644493 & 223.060105 & 0.3732 & 0.710736 & 0.355368 \tabularnewline
M7 & 290.322167129069 & 222.836866 & 1.3028 & 0.199112 & 0.099556 \tabularnewline
M8 & 235.841552106109 & 232.267613 & 1.0154 & 0.315232 & 0.157616 \tabularnewline
M9 & -17.9343189263537 & 223.626566 & -0.0802 & 0.936428 & 0.468214 \tabularnewline
M10 & -22.0519148000427 & 223.09909 & -0.0988 & 0.921692 & 0.460846 \tabularnewline
M11 & -142.433773462613 & 232.23903 & -0.6133 & 0.542694 & 0.271347 \tabularnewline
t & 11.9322542827837 & 2.853347 & 4.1818 & 0.000128 & 6.4e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&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]-1635.22504557635[/C][C]504.143869[/C][C]-3.2436[/C][C]0.002201[/C][C]0.001101[/C][/ROW]
[ROW][C]Uit_IEU[/C][C]1.03943856780702[/C][C]0.03671[/C][C]28.3146[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]740.557383587982[/C][C]227.168341[/C][C]3.2599[/C][C]0.002101[/C][C]0.00105[/C][/ROW]
[ROW][C]M2[/C][C]-145.111303853829[/C][C]231.786449[/C][C]-0.6261[/C][C]0.534373[/C][C]0.267186[/C][/ROW]
[ROW][C]M3[/C][C]-351.020823840440[/C][C]234.349808[/C][C]-1.4978[/C][C]0.141004[/C][C]0.070502[/C][/ROW]
[ROW][C]M4[/C][C]-32.611497252725[/C][C]227.675438[/C][C]-0.1432[/C][C]0.886729[/C][C]0.443364[/C][/ROW]
[ROW][C]M5[/C][C]1167.19484531337[/C][C]223.458312[/C][C]5.2233[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M6[/C][C]83.2395019644493[/C][C]223.060105[/C][C]0.3732[/C][C]0.710736[/C][C]0.355368[/C][/ROW]
[ROW][C]M7[/C][C]290.322167129069[/C][C]222.836866[/C][C]1.3028[/C][C]0.199112[/C][C]0.099556[/C][/ROW]
[ROW][C]M8[/C][C]235.841552106109[/C][C]232.267613[/C][C]1.0154[/C][C]0.315232[/C][C]0.157616[/C][/ROW]
[ROW][C]M9[/C][C]-17.9343189263537[/C][C]223.626566[/C][C]-0.0802[/C][C]0.936428[/C][C]0.468214[/C][/ROW]
[ROW][C]M10[/C][C]-22.0519148000427[/C][C]223.09909[/C][C]-0.0988[/C][C]0.921692[/C][C]0.460846[/C][/ROW]
[ROW][C]M11[/C][C]-142.433773462613[/C][C]232.23903[/C][C]-0.6133[/C][C]0.542694[/C][C]0.271347[/C][/ROW]
[ROW][C]t[/C][C]11.9322542827837[/C][C]2.853347[/C][C]4.1818[/C][C]0.000128[/C][C]6.4e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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)-1635.22504557635504.143869-3.24360.0022010.001101
Uit_IEU1.039438567807020.0367128.314600
M1740.557383587982227.1683413.25990.0021010.00105
M2-145.111303853829231.786449-0.62610.5343730.267186
M3-351.020823840440234.349808-1.49780.1410040.070502
M4-32.611497252725227.675438-0.14320.8867290.443364
M51167.19484531337223.4583125.22334e-062e-06
M683.2395019644493223.0601050.37320.7107360.355368
M7290.322167129069222.8368661.30280.1991120.099556
M8235.841552106109232.2676131.01540.3152320.157616
M9-17.9343189263537223.626566-0.08020.9364280.468214
M10-22.0519148000427223.09909-0.09880.9216920.460846
M11-142.433773462613232.23903-0.61330.5426940.271347
t11.93225428278372.8533474.18180.0001286.4e-05






Multiple Linear Regression - Regression Statistics
Multiple R0.982637569441814
R-squared0.965576592878516
Adjusted R-squared0.95584823869201
F-TEST (value)99.253848530496
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation351.141979660972
Sum Squared Residuals5671831.73449042

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.982637569441814 \tabularnewline
R-squared & 0.965576592878516 \tabularnewline
Adjusted R-squared & 0.95584823869201 \tabularnewline
F-TEST (value) & 99.253848530496 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 351.141979660972 \tabularnewline
Sum Squared Residuals & 5671831.73449042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.982637569441814[/C][/ROW]
[ROW][C]R-squared[/C][C]0.965576592878516[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.95584823869201[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]99.253848530496[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/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]351.141979660972[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5671831.73449042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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 R0.982637569441814
R-squared0.965576592878516
Adjusted R-squared0.95584823869201
F-TEST (value)99.253848530496
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation351.141979660972
Sum Squared Residuals5671831.73449042






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
110414.910263.9959057434150.904094256648
212476.812732.1584119406-255.358411940591
312384.612580.6941836601-196.094183660072
412266.712731.8365554406-465.136555440641
512919.913077.2031060224-157.303106022370
611497.311522.776577637-25.4765776370010
71214212182.8252814049-40.8252814049234
813919.414192.3365412294-272.936541229355
912656.812769.4828237373-112.682823737346
1012034.111987.84388989746.2561101029888
1113199.712957.6039119034242.096088096559
1210881.310790.487842308790.8121576913492
1311301.211310.8708479881-9.67084798810856
1413643.913423.4414201386220.458579861361
151251712345.6295402285171.370459771496
1613981.113838.0634399072143.036560092754
1714275.714162.9530507032112.746949296823
181343512723.8002594876711.199740512395
1913565.713001.5434580161564.156541983896
2016216.315647.1911213384569.108878661566
211297012380.9970476975589.002952302539
2214079.913928.5320565991151.367943400912
231423514594.0484098084-359.048409808405
2412213.412324.4436974278-111.043697427842
251258112522.600747087158.3992529128742
2614130.414154.3270377701-23.9270377701293
2714210.814397.7455213995-186.945521399493
2814378.514702.7248012155-324.224801215501
2913142.813500.7830997597-357.983099759706
3013714.714103.1915995739-388.491599573892
3113621.913764.2358958225-142.335895822491
3215379.815823.6402069017-443.840206901663
3313306.313700.6206701348-394.320670134846
3414391.214486.1432649771-94.9432649771486
3514909.915229.5135669152-319.613566915213
3614025.413711.6308267727313.769173227319
3712951.213298.805886275-347.605886275002
3814344.314474.7383649746-130.438364974631
3916093.416207.7762601282-114.376260128228
4015413.615521.2350901131-107.635090113123
4114705.713895.8261161328809.87388386725
4215972.815998.4563008628-25.6563008628048
4316241.416380.3512438856-138.951243885565
4416626.416358.4877106447267.912289355252
4517136.217137.5806551951-1.38065519512051
4615622.915657.3350599317-34.4350599316925
4718003.917996.45145116717.44854883291681
4816136.115987.0182123086149.081787691385
4914423.714275.7266129064147.973387093588
5016789.416600.134765176189.265234823990
5116782.216456.1544945837326.045505416298
5214133.813379.8401133235753.959886676512
531260713014.334627382-407.334627381998
5412004.512276.0752624387-271.575262438697
5512175.412417.4441208709-242.044120870916
561326813388.2444198858-120.244419885800
5712299.312379.9188032352-80.6188032352273
5811800.611868.8457285951-68.2457285950599
5913873.313444.1826602059429.117339794142
6012269.612712.2194211822-442.619421182211

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10414.9 & 10263.9959057434 & 150.904094256648 \tabularnewline
2 & 12476.8 & 12732.1584119406 & -255.358411940591 \tabularnewline
3 & 12384.6 & 12580.6941836601 & -196.094183660072 \tabularnewline
4 & 12266.7 & 12731.8365554406 & -465.136555440641 \tabularnewline
5 & 12919.9 & 13077.2031060224 & -157.303106022370 \tabularnewline
6 & 11497.3 & 11522.776577637 & -25.4765776370010 \tabularnewline
7 & 12142 & 12182.8252814049 & -40.8252814049234 \tabularnewline
8 & 13919.4 & 14192.3365412294 & -272.936541229355 \tabularnewline
9 & 12656.8 & 12769.4828237373 & -112.682823737346 \tabularnewline
10 & 12034.1 & 11987.843889897 & 46.2561101029888 \tabularnewline
11 & 13199.7 & 12957.6039119034 & 242.096088096559 \tabularnewline
12 & 10881.3 & 10790.4878423087 & 90.8121576913492 \tabularnewline
13 & 11301.2 & 11310.8708479881 & -9.67084798810856 \tabularnewline
14 & 13643.9 & 13423.4414201386 & 220.458579861361 \tabularnewline
15 & 12517 & 12345.6295402285 & 171.370459771496 \tabularnewline
16 & 13981.1 & 13838.0634399072 & 143.036560092754 \tabularnewline
17 & 14275.7 & 14162.9530507032 & 112.746949296823 \tabularnewline
18 & 13435 & 12723.8002594876 & 711.199740512395 \tabularnewline
19 & 13565.7 & 13001.5434580161 & 564.156541983896 \tabularnewline
20 & 16216.3 & 15647.1911213384 & 569.108878661566 \tabularnewline
21 & 12970 & 12380.9970476975 & 589.002952302539 \tabularnewline
22 & 14079.9 & 13928.5320565991 & 151.367943400912 \tabularnewline
23 & 14235 & 14594.0484098084 & -359.048409808405 \tabularnewline
24 & 12213.4 & 12324.4436974278 & -111.043697427842 \tabularnewline
25 & 12581 & 12522.6007470871 & 58.3992529128742 \tabularnewline
26 & 14130.4 & 14154.3270377701 & -23.9270377701293 \tabularnewline
27 & 14210.8 & 14397.7455213995 & -186.945521399493 \tabularnewline
28 & 14378.5 & 14702.7248012155 & -324.224801215501 \tabularnewline
29 & 13142.8 & 13500.7830997597 & -357.983099759706 \tabularnewline
30 & 13714.7 & 14103.1915995739 & -388.491599573892 \tabularnewline
31 & 13621.9 & 13764.2358958225 & -142.335895822491 \tabularnewline
32 & 15379.8 & 15823.6402069017 & -443.840206901663 \tabularnewline
33 & 13306.3 & 13700.6206701348 & -394.320670134846 \tabularnewline
34 & 14391.2 & 14486.1432649771 & -94.9432649771486 \tabularnewline
35 & 14909.9 & 15229.5135669152 & -319.613566915213 \tabularnewline
36 & 14025.4 & 13711.6308267727 & 313.769173227319 \tabularnewline
37 & 12951.2 & 13298.805886275 & -347.605886275002 \tabularnewline
38 & 14344.3 & 14474.7383649746 & -130.438364974631 \tabularnewline
39 & 16093.4 & 16207.7762601282 & -114.376260128228 \tabularnewline
40 & 15413.6 & 15521.2350901131 & -107.635090113123 \tabularnewline
41 & 14705.7 & 13895.8261161328 & 809.87388386725 \tabularnewline
42 & 15972.8 & 15998.4563008628 & -25.6563008628048 \tabularnewline
43 & 16241.4 & 16380.3512438856 & -138.951243885565 \tabularnewline
44 & 16626.4 & 16358.4877106447 & 267.912289355252 \tabularnewline
45 & 17136.2 & 17137.5806551951 & -1.38065519512051 \tabularnewline
46 & 15622.9 & 15657.3350599317 & -34.4350599316925 \tabularnewline
47 & 18003.9 & 17996.4514511671 & 7.44854883291681 \tabularnewline
48 & 16136.1 & 15987.0182123086 & 149.081787691385 \tabularnewline
49 & 14423.7 & 14275.7266129064 & 147.973387093588 \tabularnewline
50 & 16789.4 & 16600.134765176 & 189.265234823990 \tabularnewline
51 & 16782.2 & 16456.1544945837 & 326.045505416298 \tabularnewline
52 & 14133.8 & 13379.8401133235 & 753.959886676512 \tabularnewline
53 & 12607 & 13014.334627382 & -407.334627381998 \tabularnewline
54 & 12004.5 & 12276.0752624387 & -271.575262438697 \tabularnewline
55 & 12175.4 & 12417.4441208709 & -242.044120870916 \tabularnewline
56 & 13268 & 13388.2444198858 & -120.244419885800 \tabularnewline
57 & 12299.3 & 12379.9188032352 & -80.6188032352273 \tabularnewline
58 & 11800.6 & 11868.8457285951 & -68.2457285950599 \tabularnewline
59 & 13873.3 & 13444.1826602059 & 429.117339794142 \tabularnewline
60 & 12269.6 & 12712.2194211822 & -442.619421182211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&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]10263.9959057434[/C][C]150.904094256648[/C][/ROW]
[ROW][C]2[/C][C]12476.8[/C][C]12732.1584119406[/C][C]-255.358411940591[/C][/ROW]
[ROW][C]3[/C][C]12384.6[/C][C]12580.6941836601[/C][C]-196.094183660072[/C][/ROW]
[ROW][C]4[/C][C]12266.7[/C][C]12731.8365554406[/C][C]-465.136555440641[/C][/ROW]
[ROW][C]5[/C][C]12919.9[/C][C]13077.2031060224[/C][C]-157.303106022370[/C][/ROW]
[ROW][C]6[/C][C]11497.3[/C][C]11522.776577637[/C][C]-25.4765776370010[/C][/ROW]
[ROW][C]7[/C][C]12142[/C][C]12182.8252814049[/C][C]-40.8252814049234[/C][/ROW]
[ROW][C]8[/C][C]13919.4[/C][C]14192.3365412294[/C][C]-272.936541229355[/C][/ROW]
[ROW][C]9[/C][C]12656.8[/C][C]12769.4828237373[/C][C]-112.682823737346[/C][/ROW]
[ROW][C]10[/C][C]12034.1[/C][C]11987.843889897[/C][C]46.2561101029888[/C][/ROW]
[ROW][C]11[/C][C]13199.7[/C][C]12957.6039119034[/C][C]242.096088096559[/C][/ROW]
[ROW][C]12[/C][C]10881.3[/C][C]10790.4878423087[/C][C]90.8121576913492[/C][/ROW]
[ROW][C]13[/C][C]11301.2[/C][C]11310.8708479881[/C][C]-9.67084798810856[/C][/ROW]
[ROW][C]14[/C][C]13643.9[/C][C]13423.4414201386[/C][C]220.458579861361[/C][/ROW]
[ROW][C]15[/C][C]12517[/C][C]12345.6295402285[/C][C]171.370459771496[/C][/ROW]
[ROW][C]16[/C][C]13981.1[/C][C]13838.0634399072[/C][C]143.036560092754[/C][/ROW]
[ROW][C]17[/C][C]14275.7[/C][C]14162.9530507032[/C][C]112.746949296823[/C][/ROW]
[ROW][C]18[/C][C]13435[/C][C]12723.8002594876[/C][C]711.199740512395[/C][/ROW]
[ROW][C]19[/C][C]13565.7[/C][C]13001.5434580161[/C][C]564.156541983896[/C][/ROW]
[ROW][C]20[/C][C]16216.3[/C][C]15647.1911213384[/C][C]569.108878661566[/C][/ROW]
[ROW][C]21[/C][C]12970[/C][C]12380.9970476975[/C][C]589.002952302539[/C][/ROW]
[ROW][C]22[/C][C]14079.9[/C][C]13928.5320565991[/C][C]151.367943400912[/C][/ROW]
[ROW][C]23[/C][C]14235[/C][C]14594.0484098084[/C][C]-359.048409808405[/C][/ROW]
[ROW][C]24[/C][C]12213.4[/C][C]12324.4436974278[/C][C]-111.043697427842[/C][/ROW]
[ROW][C]25[/C][C]12581[/C][C]12522.6007470871[/C][C]58.3992529128742[/C][/ROW]
[ROW][C]26[/C][C]14130.4[/C][C]14154.3270377701[/C][C]-23.9270377701293[/C][/ROW]
[ROW][C]27[/C][C]14210.8[/C][C]14397.7455213995[/C][C]-186.945521399493[/C][/ROW]
[ROW][C]28[/C][C]14378.5[/C][C]14702.7248012155[/C][C]-324.224801215501[/C][/ROW]
[ROW][C]29[/C][C]13142.8[/C][C]13500.7830997597[/C][C]-357.983099759706[/C][/ROW]
[ROW][C]30[/C][C]13714.7[/C][C]14103.1915995739[/C][C]-388.491599573892[/C][/ROW]
[ROW][C]31[/C][C]13621.9[/C][C]13764.2358958225[/C][C]-142.335895822491[/C][/ROW]
[ROW][C]32[/C][C]15379.8[/C][C]15823.6402069017[/C][C]-443.840206901663[/C][/ROW]
[ROW][C]33[/C][C]13306.3[/C][C]13700.6206701348[/C][C]-394.320670134846[/C][/ROW]
[ROW][C]34[/C][C]14391.2[/C][C]14486.1432649771[/C][C]-94.9432649771486[/C][/ROW]
[ROW][C]35[/C][C]14909.9[/C][C]15229.5135669152[/C][C]-319.613566915213[/C][/ROW]
[ROW][C]36[/C][C]14025.4[/C][C]13711.6308267727[/C][C]313.769173227319[/C][/ROW]
[ROW][C]37[/C][C]12951.2[/C][C]13298.805886275[/C][C]-347.605886275002[/C][/ROW]
[ROW][C]38[/C][C]14344.3[/C][C]14474.7383649746[/C][C]-130.438364974631[/C][/ROW]
[ROW][C]39[/C][C]16093.4[/C][C]16207.7762601282[/C][C]-114.376260128228[/C][/ROW]
[ROW][C]40[/C][C]15413.6[/C][C]15521.2350901131[/C][C]-107.635090113123[/C][/ROW]
[ROW][C]41[/C][C]14705.7[/C][C]13895.8261161328[/C][C]809.87388386725[/C][/ROW]
[ROW][C]42[/C][C]15972.8[/C][C]15998.4563008628[/C][C]-25.6563008628048[/C][/ROW]
[ROW][C]43[/C][C]16241.4[/C][C]16380.3512438856[/C][C]-138.951243885565[/C][/ROW]
[ROW][C]44[/C][C]16626.4[/C][C]16358.4877106447[/C][C]267.912289355252[/C][/ROW]
[ROW][C]45[/C][C]17136.2[/C][C]17137.5806551951[/C][C]-1.38065519512051[/C][/ROW]
[ROW][C]46[/C][C]15622.9[/C][C]15657.3350599317[/C][C]-34.4350599316925[/C][/ROW]
[ROW][C]47[/C][C]18003.9[/C][C]17996.4514511671[/C][C]7.44854883291681[/C][/ROW]
[ROW][C]48[/C][C]16136.1[/C][C]15987.0182123086[/C][C]149.081787691385[/C][/ROW]
[ROW][C]49[/C][C]14423.7[/C][C]14275.7266129064[/C][C]147.973387093588[/C][/ROW]
[ROW][C]50[/C][C]16789.4[/C][C]16600.134765176[/C][C]189.265234823990[/C][/ROW]
[ROW][C]51[/C][C]16782.2[/C][C]16456.1544945837[/C][C]326.045505416298[/C][/ROW]
[ROW][C]52[/C][C]14133.8[/C][C]13379.8401133235[/C][C]753.959886676512[/C][/ROW]
[ROW][C]53[/C][C]12607[/C][C]13014.334627382[/C][C]-407.334627381998[/C][/ROW]
[ROW][C]54[/C][C]12004.5[/C][C]12276.0752624387[/C][C]-271.575262438697[/C][/ROW]
[ROW][C]55[/C][C]12175.4[/C][C]12417.4441208709[/C][C]-242.044120870916[/C][/ROW]
[ROW][C]56[/C][C]13268[/C][C]13388.2444198858[/C][C]-120.244419885800[/C][/ROW]
[ROW][C]57[/C][C]12299.3[/C][C]12379.9188032352[/C][C]-80.6188032352273[/C][/ROW]
[ROW][C]58[/C][C]11800.6[/C][C]11868.8457285951[/C][C]-68.2457285950599[/C][/ROW]
[ROW][C]59[/C][C]13873.3[/C][C]13444.1826602059[/C][C]429.117339794142[/C][/ROW]
[ROW][C]60[/C][C]12269.6[/C][C]12712.2194211822[/C][C]-442.619421182211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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
110414.910263.9959057434150.904094256648
212476.812732.1584119406-255.358411940591
312384.612580.6941836601-196.094183660072
412266.712731.8365554406-465.136555440641
512919.913077.2031060224-157.303106022370
611497.311522.776577637-25.4765776370010
71214212182.8252814049-40.8252814049234
813919.414192.3365412294-272.936541229355
912656.812769.4828237373-112.682823737346
1012034.111987.84388989746.2561101029888
1113199.712957.6039119034242.096088096559
1210881.310790.487842308790.8121576913492
1311301.211310.8708479881-9.67084798810856
1413643.913423.4414201386220.458579861361
151251712345.6295402285171.370459771496
1613981.113838.0634399072143.036560092754
1714275.714162.9530507032112.746949296823
181343512723.8002594876711.199740512395
1913565.713001.5434580161564.156541983896
2016216.315647.1911213384569.108878661566
211297012380.9970476975589.002952302539
2214079.913928.5320565991151.367943400912
231423514594.0484098084-359.048409808405
2412213.412324.4436974278-111.043697427842
251258112522.600747087158.3992529128742
2614130.414154.3270377701-23.9270377701293
2714210.814397.7455213995-186.945521399493
2814378.514702.7248012155-324.224801215501
2913142.813500.7830997597-357.983099759706
3013714.714103.1915995739-388.491599573892
3113621.913764.2358958225-142.335895822491
3215379.815823.6402069017-443.840206901663
3313306.313700.6206701348-394.320670134846
3414391.214486.1432649771-94.9432649771486
3514909.915229.5135669152-319.613566915213
3614025.413711.6308267727313.769173227319
3712951.213298.805886275-347.605886275002
3814344.314474.7383649746-130.438364974631
3916093.416207.7762601282-114.376260128228
4015413.615521.2350901131-107.635090113123
4114705.713895.8261161328809.87388386725
4215972.815998.4563008628-25.6563008628048
4316241.416380.3512438856-138.951243885565
4416626.416358.4877106447267.912289355252
4517136.217137.5806551951-1.38065519512051
4615622.915657.3350599317-34.4350599316925
4718003.917996.45145116717.44854883291681
4816136.115987.0182123086149.081787691385
4914423.714275.7266129064147.973387093588
5016789.416600.134765176189.265234823990
5116782.216456.1544945837326.045505416298
5214133.813379.8401133235753.959886676512
531260713014.334627382-407.334627381998
5412004.512276.0752624387-271.575262438697
5512175.412417.4441208709-242.044120870916
561326813388.2444198858-120.244419885800
5712299.312379.9188032352-80.6188032352273
5811800.611868.8457285951-68.2457285950599
5913873.313444.1826602059429.117339794142
6012269.612712.2194211822-442.619421182211






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1956573847819050.391314769563810.804342615218095
180.1940636529004670.3881273058009340.805936347099533
190.1388209032473690.2776418064947390.86117909675263
200.1341193726133470.2682387452266950.865880627386653
210.1599714937697240.3199429875394470.840028506230276
220.1435903846386280.2871807692772560.856409615361372
230.383084694378130.766169388756260.61691530562187
240.3412486700572700.6824973401145410.65875132994273
250.3303000729131530.6606001458263060.669699927086847
260.3284623861836320.6569247723672650.671537613816368
270.2777005626328040.5554011252656080.722299437367196
280.2806984985165660.5613969970331330.719301501483434
290.3850201678312370.7700403356624740.614979832168763
300.4455916695618470.8911833391236940.554408330438153
310.4083334098935420.8166668197870840.591666590106458
320.4325668866413470.8651337732826940.567433113358653
330.4077031479539620.8154062959079230.592296852046039
340.3114666024067750.622933204813550.688533397593225
350.2815292089256040.5630584178512080.718470791074396
360.2886039947793720.5772079895587450.711396005220628
370.2382245072499450.4764490144998890.761775492750055
380.1767883644933320.3535767289866640.823211635506668
390.2420913499414850.484182699882970.757908650058515
400.978536145761330.04292770847733880.0214638542386694
410.963739591506140.07252081698771830.0362604084938592
420.9111594940117740.1776810119764530.0888405059882265
430.7992613005260340.4014773989479320.200738699473966

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.195657384781905 & 0.39131476956381 & 0.804342615218095 \tabularnewline
18 & 0.194063652900467 & 0.388127305800934 & 0.805936347099533 \tabularnewline
19 & 0.138820903247369 & 0.277641806494739 & 0.86117909675263 \tabularnewline
20 & 0.134119372613347 & 0.268238745226695 & 0.865880627386653 \tabularnewline
21 & 0.159971493769724 & 0.319942987539447 & 0.840028506230276 \tabularnewline
22 & 0.143590384638628 & 0.287180769277256 & 0.856409615361372 \tabularnewline
23 & 0.38308469437813 & 0.76616938875626 & 0.61691530562187 \tabularnewline
24 & 0.341248670057270 & 0.682497340114541 & 0.65875132994273 \tabularnewline
25 & 0.330300072913153 & 0.660600145826306 & 0.669699927086847 \tabularnewline
26 & 0.328462386183632 & 0.656924772367265 & 0.671537613816368 \tabularnewline
27 & 0.277700562632804 & 0.555401125265608 & 0.722299437367196 \tabularnewline
28 & 0.280698498516566 & 0.561396997033133 & 0.719301501483434 \tabularnewline
29 & 0.385020167831237 & 0.770040335662474 & 0.614979832168763 \tabularnewline
30 & 0.445591669561847 & 0.891183339123694 & 0.554408330438153 \tabularnewline
31 & 0.408333409893542 & 0.816666819787084 & 0.591666590106458 \tabularnewline
32 & 0.432566886641347 & 0.865133773282694 & 0.567433113358653 \tabularnewline
33 & 0.407703147953962 & 0.815406295907923 & 0.592296852046039 \tabularnewline
34 & 0.311466602406775 & 0.62293320481355 & 0.688533397593225 \tabularnewline
35 & 0.281529208925604 & 0.563058417851208 & 0.718470791074396 \tabularnewline
36 & 0.288603994779372 & 0.577207989558745 & 0.711396005220628 \tabularnewline
37 & 0.238224507249945 & 0.476449014499889 & 0.761775492750055 \tabularnewline
38 & 0.176788364493332 & 0.353576728986664 & 0.823211635506668 \tabularnewline
39 & 0.242091349941485 & 0.48418269988297 & 0.757908650058515 \tabularnewline
40 & 0.97853614576133 & 0.0429277084773388 & 0.0214638542386694 \tabularnewline
41 & 0.96373959150614 & 0.0725208169877183 & 0.0362604084938592 \tabularnewline
42 & 0.911159494011774 & 0.177681011976453 & 0.0888405059882265 \tabularnewline
43 & 0.799261300526034 & 0.401477398947932 & 0.200738699473966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&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]17[/C][C]0.195657384781905[/C][C]0.39131476956381[/C][C]0.804342615218095[/C][/ROW]
[ROW][C]18[/C][C]0.194063652900467[/C][C]0.388127305800934[/C][C]0.805936347099533[/C][/ROW]
[ROW][C]19[/C][C]0.138820903247369[/C][C]0.277641806494739[/C][C]0.86117909675263[/C][/ROW]
[ROW][C]20[/C][C]0.134119372613347[/C][C]0.268238745226695[/C][C]0.865880627386653[/C][/ROW]
[ROW][C]21[/C][C]0.159971493769724[/C][C]0.319942987539447[/C][C]0.840028506230276[/C][/ROW]
[ROW][C]22[/C][C]0.143590384638628[/C][C]0.287180769277256[/C][C]0.856409615361372[/C][/ROW]
[ROW][C]23[/C][C]0.38308469437813[/C][C]0.76616938875626[/C][C]0.61691530562187[/C][/ROW]
[ROW][C]24[/C][C]0.341248670057270[/C][C]0.682497340114541[/C][C]0.65875132994273[/C][/ROW]
[ROW][C]25[/C][C]0.330300072913153[/C][C]0.660600145826306[/C][C]0.669699927086847[/C][/ROW]
[ROW][C]26[/C][C]0.328462386183632[/C][C]0.656924772367265[/C][C]0.671537613816368[/C][/ROW]
[ROW][C]27[/C][C]0.277700562632804[/C][C]0.555401125265608[/C][C]0.722299437367196[/C][/ROW]
[ROW][C]28[/C][C]0.280698498516566[/C][C]0.561396997033133[/C][C]0.719301501483434[/C][/ROW]
[ROW][C]29[/C][C]0.385020167831237[/C][C]0.770040335662474[/C][C]0.614979832168763[/C][/ROW]
[ROW][C]30[/C][C]0.445591669561847[/C][C]0.891183339123694[/C][C]0.554408330438153[/C][/ROW]
[ROW][C]31[/C][C]0.408333409893542[/C][C]0.816666819787084[/C][C]0.591666590106458[/C][/ROW]
[ROW][C]32[/C][C]0.432566886641347[/C][C]0.865133773282694[/C][C]0.567433113358653[/C][/ROW]
[ROW][C]33[/C][C]0.407703147953962[/C][C]0.815406295907923[/C][C]0.592296852046039[/C][/ROW]
[ROW][C]34[/C][C]0.311466602406775[/C][C]0.62293320481355[/C][C]0.688533397593225[/C][/ROW]
[ROW][C]35[/C][C]0.281529208925604[/C][C]0.563058417851208[/C][C]0.718470791074396[/C][/ROW]
[ROW][C]36[/C][C]0.288603994779372[/C][C]0.577207989558745[/C][C]0.711396005220628[/C][/ROW]
[ROW][C]37[/C][C]0.238224507249945[/C][C]0.476449014499889[/C][C]0.761775492750055[/C][/ROW]
[ROW][C]38[/C][C]0.176788364493332[/C][C]0.353576728986664[/C][C]0.823211635506668[/C][/ROW]
[ROW][C]39[/C][C]0.242091349941485[/C][C]0.48418269988297[/C][C]0.757908650058515[/C][/ROW]
[ROW][C]40[/C][C]0.97853614576133[/C][C]0.0429277084773388[/C][C]0.0214638542386694[/C][/ROW]
[ROW][C]41[/C][C]0.96373959150614[/C][C]0.0725208169877183[/C][C]0.0362604084938592[/C][/ROW]
[ROW][C]42[/C][C]0.911159494011774[/C][C]0.177681011976453[/C][C]0.0888405059882265[/C][/ROW]
[ROW][C]43[/C][C]0.799261300526034[/C][C]0.401477398947932[/C][C]0.200738699473966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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
170.1956573847819050.391314769563810.804342615218095
180.1940636529004670.3881273058009340.805936347099533
190.1388209032473690.2776418064947390.86117909675263
200.1341193726133470.2682387452266950.865880627386653
210.1599714937697240.3199429875394470.840028506230276
220.1435903846386280.2871807692772560.856409615361372
230.383084694378130.766169388756260.61691530562187
240.3412486700572700.6824973401145410.65875132994273
250.3303000729131530.6606001458263060.669699927086847
260.3284623861836320.6569247723672650.671537613816368
270.2777005626328040.5554011252656080.722299437367196
280.2806984985165660.5613969970331330.719301501483434
290.3850201678312370.7700403356624740.614979832168763
300.4455916695618470.8911833391236940.554408330438153
310.4083334098935420.8166668197870840.591666590106458
320.4325668866413470.8651337732826940.567433113358653
330.4077031479539620.8154062959079230.592296852046039
340.3114666024067750.622933204813550.688533397593225
350.2815292089256040.5630584178512080.718470791074396
360.2886039947793720.5772079895587450.711396005220628
370.2382245072499450.4764490144998890.761775492750055
380.1767883644933320.3535767289866640.823211635506668
390.2420913499414850.484182699882970.757908650058515
400.978536145761330.04292770847733880.0214638542386694
410.963739591506140.07252081698771830.0362604084938592
420.9111594940117740.1776810119764530.0888405059882265
430.7992613005260340.4014773989479320.200738699473966






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0370370370370370OK
10% type I error level20.0740740740740741OK

\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 & 1 & 0.0370370370370370 & OK \tabularnewline
10% type I error level & 2 & 0.0740740740740741 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58633&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]1[/C][C]0.0370370370370370[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.0740740740740741[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58633&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58633&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 level10.0370370370370370OK
10% type I error level20.0740740740740741OK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}