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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 computationTue, 17 Nov 2009 09:47:07 -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/17/t12584764532ydpyv80hluodqs.htm/, Retrieved Wed, 19 Nov 2025 20:22:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57375, Retrieved Wed, 19 Nov 2025 20:22:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact515

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]
-   PD      [Multiple Regression] [] [2009-11-17 16:47:07] [0f1f1142419956a95ff6f880845f2408] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20604.6	2.05
18714.9	2.03
18492.6	2.04
18183.6	2.03
19435.1	2.01
22686.8	2.01
20396.7	2.01
19233.6	2.01
22751	2.01
19864	2.01
17165.4	2.02
22309.7	2.02
21786.3	2.03
21927.6	2.05
20957.9	2.08
19726	2.07
21315.7	2.06
24771.5	2.05
22592.4	2.05
21942.1	2.05
23973.7	2.05
20815.7	2.05
19931.4	2.06
24436.8	2.06
22838.7	2.07
24465.3	2.07
23007.3	2.3
22720.8	2.31
23045.7	2.31
27198.5	2.53
22401.9	2.58
25122.7	2.59
26100.5	2.73
22904.9	2.82
22040.4	3
25981.5	3.04
26157.1	3.23
25975.4	3.32
22589.8	3.49
25370.4	3.57
25091.1	3.56
28760.9	3.72
24325.9	3.82
25821.7	3.82
27645.7	3.98
26296.9	4.06
24141.5	4.08
27268.1	4.19
29060.3	4.16
28226.4	4.17
23268.5	4.21
26938.2	4.21
27217.5	4.17
27540.5	4.19
29167.6	4.25
26671.5	4.25
30184	4.2
28422.3	4.33
23774.3	4.41
29601	4.56
28523.6	5.18
23622	3.42
21320.3	2.71
20423.6	2.29
21174.9	2
23050.2	1.64
21202.9	1.3
20476.4	1.08
23173.3	1
22468	1
19842.7	1

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=57375&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=57375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 18289.7802466385 + 2000.13295416083X[t] -805.032576467682M1[t] -1293.75184128471M2[t] -3468.53612684340M3[t] -2766.41775331888M4[t] -2025.76560328049M5[t] + 716.711016480509M6[t] -1595.7088183142M7[t] -1697.8602137201M8[t] + 636.579970443811M9[t] -1675.08272606575M10[t] -4123.36208924199M11[t] + 35.5893821348614t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  18289.7802466385 +  2000.13295416083X[t] -805.032576467682M1[t] -1293.75184128471M2[t] -3468.53612684340M3[t] -2766.41775331888M4[t] -2025.76560328049M5[t] +  716.711016480509M6[t] -1595.7088183142M7[t] -1697.8602137201M8[t] +  636.579970443811M9[t] -1675.08272606575M10[t] -4123.36208924199M11[t] +  35.5893821348614t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  18289.7802466385 +  2000.13295416083X[t] -805.032576467682M1[t] -1293.75184128471M2[t] -3468.53612684340M3[t] -2766.41775331888M4[t] -2025.76560328049M5[t] +  716.711016480509M6[t] -1595.7088183142M7[t] -1697.8602137201M8[t] +  636.579970443811M9[t] -1675.08272606575M10[t] -4123.36208924199M11[t] +  35.5893821348614t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 18289.7802466385 + 2000.13295416083X[t] -805.032576467682M1[t] -1293.75184128471M2[t] -3468.53612684340M3[t] -2766.41775331888M4[t] -2025.76560328049M5[t] + 716.711016480509M6[t] -1595.7088183142M7[t] -1697.8602137201M8[t] + 636.579970443811M9[t] -1675.08272606575M10[t] -4123.36208924199M11[t] + 35.5893821348614t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)18289.7802466385781.62134423.399800
X2000.13295416083170.61844611.722800
M1-805.032576467682813.59104-0.98950.326610.163305
M2-1293.75184128471814.295708-1.58880.1176380.058819
M3-3468.53612684340814.616086-4.25797.8e-053.9e-05
M4-2766.41775331888815.4056-3.39270.0012640.000632
M5-2025.76560328049816.549286-2.48090.0160810.00804
M6716.711016480509816.7812360.87750.3839080.191954
M7-1595.7088183142817.58516-1.95170.0558890.027945
M8-1697.8602137201818.801181-2.07360.0426470.021323
M9636.579970443811818.8367350.77740.4401260.220063
M10-1675.08272606575818.520758-2.04650.0453320.022666
M11-4123.36208924199818.310266-5.03895e-063e-06
t35.58938213486148.6295954.12410.0001226.1e-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) & 18289.7802466385 & 781.621344 & 23.3998 & 0 & 0 \tabularnewline
X & 2000.13295416083 & 170.618446 & 11.7228 & 0 & 0 \tabularnewline
M1 & -805.032576467682 & 813.59104 & -0.9895 & 0.32661 & 0.163305 \tabularnewline
M2 & -1293.75184128471 & 814.295708 & -1.5888 & 0.117638 & 0.058819 \tabularnewline
M3 & -3468.53612684340 & 814.616086 & -4.2579 & 7.8e-05 & 3.9e-05 \tabularnewline
M4 & -2766.41775331888 & 815.4056 & -3.3927 & 0.001264 & 0.000632 \tabularnewline
M5 & -2025.76560328049 & 816.549286 & -2.4809 & 0.016081 & 0.00804 \tabularnewline
M6 & 716.711016480509 & 816.781236 & 0.8775 & 0.383908 & 0.191954 \tabularnewline
M7 & -1595.7088183142 & 817.58516 & -1.9517 & 0.055889 & 0.027945 \tabularnewline
M8 & -1697.8602137201 & 818.801181 & -2.0736 & 0.042647 & 0.021323 \tabularnewline
M9 & 636.579970443811 & 818.836735 & 0.7774 & 0.440126 & 0.220063 \tabularnewline
M10 & -1675.08272606575 & 818.520758 & -2.0465 & 0.045332 & 0.022666 \tabularnewline
M11 & -4123.36208924199 & 818.310266 & -5.0389 & 5e-06 & 3e-06 \tabularnewline
t & 35.5893821348614 & 8.629595 & 4.1241 & 0.000122 & 6.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&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]18289.7802466385[/C][C]781.621344[/C][C]23.3998[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]2000.13295416083[/C][C]170.618446[/C][C]11.7228[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-805.032576467682[/C][C]813.59104[/C][C]-0.9895[/C][C]0.32661[/C][C]0.163305[/C][/ROW]
[ROW][C]M2[/C][C]-1293.75184128471[/C][C]814.295708[/C][C]-1.5888[/C][C]0.117638[/C][C]0.058819[/C][/ROW]
[ROW][C]M3[/C][C]-3468.53612684340[/C][C]814.616086[/C][C]-4.2579[/C][C]7.8e-05[/C][C]3.9e-05[/C][/ROW]
[ROW][C]M4[/C][C]-2766.41775331888[/C][C]815.4056[/C][C]-3.3927[/C][C]0.001264[/C][C]0.000632[/C][/ROW]
[ROW][C]M5[/C][C]-2025.76560328049[/C][C]816.549286[/C][C]-2.4809[/C][C]0.016081[/C][C]0.00804[/C][/ROW]
[ROW][C]M6[/C][C]716.711016480509[/C][C]816.781236[/C][C]0.8775[/C][C]0.383908[/C][C]0.191954[/C][/ROW]
[ROW][C]M7[/C][C]-1595.7088183142[/C][C]817.58516[/C][C]-1.9517[/C][C]0.055889[/C][C]0.027945[/C][/ROW]
[ROW][C]M8[/C][C]-1697.8602137201[/C][C]818.801181[/C][C]-2.0736[/C][C]0.042647[/C][C]0.021323[/C][/ROW]
[ROW][C]M9[/C][C]636.579970443811[/C][C]818.836735[/C][C]0.7774[/C][C]0.440126[/C][C]0.220063[/C][/ROW]
[ROW][C]M10[/C][C]-1675.08272606575[/C][C]818.520758[/C][C]-2.0465[/C][C]0.045332[/C][C]0.022666[/C][/ROW]
[ROW][C]M11[/C][C]-4123.36208924199[/C][C]818.310266[/C][C]-5.0389[/C][C]5e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]t[/C][C]35.5893821348614[/C][C]8.629595[/C][C]4.1241[/C][C]0.000122[/C][C]6.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&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)18289.7802466385781.62134423.399800
X2000.13295416083170.61844611.722800
M1-805.032576467682813.59104-0.98950.326610.163305
M2-1293.75184128471814.295708-1.58880.1176380.058819
M3-3468.53612684340814.616086-4.25797.8e-053.9e-05
M4-2766.41775331888815.4056-3.39270.0012640.000632
M5-2025.76560328049816.549286-2.48090.0160810.00804
M6716.711016480509816.7812360.87750.3839080.191954
M7-1595.7088183142817.58516-1.95170.0558890.027945
M8-1697.8602137201818.801181-2.07360.0426470.021323
M9636.579970443811818.8367350.77740.4401260.220063
M10-1675.08272606575818.520758-2.04650.0453320.022666
M11-4123.36208924199818.310266-5.03895e-063e-06
t35.58938213486148.6295954.12410.0001226.1e-05






Multiple Linear Regression - Regression Statistics
Multiple R0.922305259300235
R-squared0.850646991332874
Adjusted R-squared0.81658402444388
F-TEST (value)24.9727803836058
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1341.95811085843
Sum Squared Residuals102648539.564028

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.922305259300235 \tabularnewline
R-squared & 0.850646991332874 \tabularnewline
Adjusted R-squared & 0.81658402444388 \tabularnewline
F-TEST (value) & 24.9727803836058 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1341.95811085843 \tabularnewline
Sum Squared Residuals & 102648539.564028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.922305259300235[/C][/ROW]
[ROW][C]R-squared[/C][C]0.850646991332874[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.81658402444388[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]24.9727803836058[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/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]1341.95811085843[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]102648539.564028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&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 R0.922305259300235
R-squared0.850646991332874
Adjusted R-squared0.81658402444388
F-TEST (value)24.9727803836058
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1341.95811085843
Sum Squared Residuals102648539.564028






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
120604.621620.6096083354-1016.00960833543
218714.921127.4770665700-2412.57706657003
318492.619008.2834926878-515.683492687790
418183.619725.9899188056-1542.38991880557
519435.120462.2287918956-1027.12879189560
622686.823240.2947937915-553.494793791462
720396.720963.4643411316-566.764341131614
819233.620896.9023278606-1663.30232786058
92275123266.9318941594-515.931894159351
101986420990.8585797846-1126.85857978465
1117165.418598.1699282849-1432.76992828487
1222309.722757.1213996617-447.421399661726
1321786.322007.6795348705-221.379534870516
1421927.621594.5523112716333.047688728432
1520957.919515.36139647261442.53860352744
161972620233.0678225903-507.067822590333
1721315.720989.3080252220326.391974778024
1824771.523747.37269757621024.12730242377
1922592.421470.54224491641121.85775508362
2021942.121403.9802316453538.119768354654
2123973.723774.0097979441199.69020205588
2220815.721497.9364835694-682.236483569412
2319931.419105.2478320697826.152167930353
2424436.823264.19930344651172.6006965535
2522838.722514.7574386553323.942561344714
2624465.322061.62755597312403.67244402688
2723007.320382.46323200632624.83676799372
2822720.821140.17231720731580.62768279273
2923045.721916.41384938051129.28615061948
3027198.525134.50910119182063.99089880823
3122401.922957.6852962400-555.785296239958
3225122.722911.12461251052211.57538748947
3326100.525561.1727923918539.327207608178
3422904.923465.1114438916-560.211443891587
3522040.421412.4453945992627.954605400836
3625981.525651.4021841424330.097815857552
3726157.125261.9842511002895.115748899812
3825975.424988.8663342925986.533665707505
3922589.823189.694033076-599.894033076004
4025370.424087.41242506831282.98757493175
4125091.124843.6526276999247.447372300104
4228760.927941.7399022615819.16009773851
4324325.925864.9227450177-1539.02274501772
4425821.725798.360731746723.3392682533148
4527645.728488.4115707112-842.711570711195
4626296.926372.3488926694-75.448892669352
4724141.523999.6615707112141.838429288803
4827268.128378.6276670457-1110.52766704574
4929060.327549.18048408811511.11951591190
5028226.427116.05193094751110.34806905246
5123268.525056.8623456901-1788.36234569014
5226938.225794.57010134951143.62989865048
5327217.526490.8063153563726.693684643663
5427540.529308.8749763354-1768.37497633542
5529167.627152.05250092522015.54749907478
5626671.527085.4904876542-413.99048765418
573018429355.5134062449828.486593755084
5828422.327339.45737591111082.84262408888
5923774.325086.7780312026-1312.47803120261
602960129545.749445703655.2505542964189
6128523.630016.3886829505-1492.78868295048
622362226043.0248009453-2421.02480094525
6321320.322483.7355000672-1163.43550006723
6420423.622381.3874149791-1957.78741497906
6521174.922577.5903904457-1402.69039044567
6623050.224635.6085288436-1585.40852884364
6721202.921678.7328717691-475.832871769106
6820476.421172.1416085827-695.741608582684
6923173.323382.1605385486-208.860538548597
702246821106.08722417391361.91277582611
7119842.718693.39724313251149.30275686749

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 20604.6 & 21620.6096083354 & -1016.00960833543 \tabularnewline
2 & 18714.9 & 21127.4770665700 & -2412.57706657003 \tabularnewline
3 & 18492.6 & 19008.2834926878 & -515.683492687790 \tabularnewline
4 & 18183.6 & 19725.9899188056 & -1542.38991880557 \tabularnewline
5 & 19435.1 & 20462.2287918956 & -1027.12879189560 \tabularnewline
6 & 22686.8 & 23240.2947937915 & -553.494793791462 \tabularnewline
7 & 20396.7 & 20963.4643411316 & -566.764341131614 \tabularnewline
8 & 19233.6 & 20896.9023278606 & -1663.30232786058 \tabularnewline
9 & 22751 & 23266.9318941594 & -515.931894159351 \tabularnewline
10 & 19864 & 20990.8585797846 & -1126.85857978465 \tabularnewline
11 & 17165.4 & 18598.1699282849 & -1432.76992828487 \tabularnewline
12 & 22309.7 & 22757.1213996617 & -447.421399661726 \tabularnewline
13 & 21786.3 & 22007.6795348705 & -221.379534870516 \tabularnewline
14 & 21927.6 & 21594.5523112716 & 333.047688728432 \tabularnewline
15 & 20957.9 & 19515.3613964726 & 1442.53860352744 \tabularnewline
16 & 19726 & 20233.0678225903 & -507.067822590333 \tabularnewline
17 & 21315.7 & 20989.3080252220 & 326.391974778024 \tabularnewline
18 & 24771.5 & 23747.3726975762 & 1024.12730242377 \tabularnewline
19 & 22592.4 & 21470.5422449164 & 1121.85775508362 \tabularnewline
20 & 21942.1 & 21403.9802316453 & 538.119768354654 \tabularnewline
21 & 23973.7 & 23774.0097979441 & 199.69020205588 \tabularnewline
22 & 20815.7 & 21497.9364835694 & -682.236483569412 \tabularnewline
23 & 19931.4 & 19105.2478320697 & 826.152167930353 \tabularnewline
24 & 24436.8 & 23264.1993034465 & 1172.6006965535 \tabularnewline
25 & 22838.7 & 22514.7574386553 & 323.942561344714 \tabularnewline
26 & 24465.3 & 22061.6275559731 & 2403.67244402688 \tabularnewline
27 & 23007.3 & 20382.4632320063 & 2624.83676799372 \tabularnewline
28 & 22720.8 & 21140.1723172073 & 1580.62768279273 \tabularnewline
29 & 23045.7 & 21916.4138493805 & 1129.28615061948 \tabularnewline
30 & 27198.5 & 25134.5091011918 & 2063.99089880823 \tabularnewline
31 & 22401.9 & 22957.6852962400 & -555.785296239958 \tabularnewline
32 & 25122.7 & 22911.1246125105 & 2211.57538748947 \tabularnewline
33 & 26100.5 & 25561.1727923918 & 539.327207608178 \tabularnewline
34 & 22904.9 & 23465.1114438916 & -560.211443891587 \tabularnewline
35 & 22040.4 & 21412.4453945992 & 627.954605400836 \tabularnewline
36 & 25981.5 & 25651.4021841424 & 330.097815857552 \tabularnewline
37 & 26157.1 & 25261.9842511002 & 895.115748899812 \tabularnewline
38 & 25975.4 & 24988.8663342925 & 986.533665707505 \tabularnewline
39 & 22589.8 & 23189.694033076 & -599.894033076004 \tabularnewline
40 & 25370.4 & 24087.4124250683 & 1282.98757493175 \tabularnewline
41 & 25091.1 & 24843.6526276999 & 247.447372300104 \tabularnewline
42 & 28760.9 & 27941.7399022615 & 819.16009773851 \tabularnewline
43 & 24325.9 & 25864.9227450177 & -1539.02274501772 \tabularnewline
44 & 25821.7 & 25798.3607317467 & 23.3392682533148 \tabularnewline
45 & 27645.7 & 28488.4115707112 & -842.711570711195 \tabularnewline
46 & 26296.9 & 26372.3488926694 & -75.448892669352 \tabularnewline
47 & 24141.5 & 23999.6615707112 & 141.838429288803 \tabularnewline
48 & 27268.1 & 28378.6276670457 & -1110.52766704574 \tabularnewline
49 & 29060.3 & 27549.1804840881 & 1511.11951591190 \tabularnewline
50 & 28226.4 & 27116.0519309475 & 1110.34806905246 \tabularnewline
51 & 23268.5 & 25056.8623456901 & -1788.36234569014 \tabularnewline
52 & 26938.2 & 25794.5701013495 & 1143.62989865048 \tabularnewline
53 & 27217.5 & 26490.8063153563 & 726.693684643663 \tabularnewline
54 & 27540.5 & 29308.8749763354 & -1768.37497633542 \tabularnewline
55 & 29167.6 & 27152.0525009252 & 2015.54749907478 \tabularnewline
56 & 26671.5 & 27085.4904876542 & -413.99048765418 \tabularnewline
57 & 30184 & 29355.5134062449 & 828.486593755084 \tabularnewline
58 & 28422.3 & 27339.4573759111 & 1082.84262408888 \tabularnewline
59 & 23774.3 & 25086.7780312026 & -1312.47803120261 \tabularnewline
60 & 29601 & 29545.7494457036 & 55.2505542964189 \tabularnewline
61 & 28523.6 & 30016.3886829505 & -1492.78868295048 \tabularnewline
62 & 23622 & 26043.0248009453 & -2421.02480094525 \tabularnewline
63 & 21320.3 & 22483.7355000672 & -1163.43550006723 \tabularnewline
64 & 20423.6 & 22381.3874149791 & -1957.78741497906 \tabularnewline
65 & 21174.9 & 22577.5903904457 & -1402.69039044567 \tabularnewline
66 & 23050.2 & 24635.6085288436 & -1585.40852884364 \tabularnewline
67 & 21202.9 & 21678.7328717691 & -475.832871769106 \tabularnewline
68 & 20476.4 & 21172.1416085827 & -695.741608582684 \tabularnewline
69 & 23173.3 & 23382.1605385486 & -208.860538548597 \tabularnewline
70 & 22468 & 21106.0872241739 & 1361.91277582611 \tabularnewline
71 & 19842.7 & 18693.3972431325 & 1149.30275686749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&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]20604.6[/C][C]21620.6096083354[/C][C]-1016.00960833543[/C][/ROW]
[ROW][C]2[/C][C]18714.9[/C][C]21127.4770665700[/C][C]-2412.57706657003[/C][/ROW]
[ROW][C]3[/C][C]18492.6[/C][C]19008.2834926878[/C][C]-515.683492687790[/C][/ROW]
[ROW][C]4[/C][C]18183.6[/C][C]19725.9899188056[/C][C]-1542.38991880557[/C][/ROW]
[ROW][C]5[/C][C]19435.1[/C][C]20462.2287918956[/C][C]-1027.12879189560[/C][/ROW]
[ROW][C]6[/C][C]22686.8[/C][C]23240.2947937915[/C][C]-553.494793791462[/C][/ROW]
[ROW][C]7[/C][C]20396.7[/C][C]20963.4643411316[/C][C]-566.764341131614[/C][/ROW]
[ROW][C]8[/C][C]19233.6[/C][C]20896.9023278606[/C][C]-1663.30232786058[/C][/ROW]
[ROW][C]9[/C][C]22751[/C][C]23266.9318941594[/C][C]-515.931894159351[/C][/ROW]
[ROW][C]10[/C][C]19864[/C][C]20990.8585797846[/C][C]-1126.85857978465[/C][/ROW]
[ROW][C]11[/C][C]17165.4[/C][C]18598.1699282849[/C][C]-1432.76992828487[/C][/ROW]
[ROW][C]12[/C][C]22309.7[/C][C]22757.1213996617[/C][C]-447.421399661726[/C][/ROW]
[ROW][C]13[/C][C]21786.3[/C][C]22007.6795348705[/C][C]-221.379534870516[/C][/ROW]
[ROW][C]14[/C][C]21927.6[/C][C]21594.5523112716[/C][C]333.047688728432[/C][/ROW]
[ROW][C]15[/C][C]20957.9[/C][C]19515.3613964726[/C][C]1442.53860352744[/C][/ROW]
[ROW][C]16[/C][C]19726[/C][C]20233.0678225903[/C][C]-507.067822590333[/C][/ROW]
[ROW][C]17[/C][C]21315.7[/C][C]20989.3080252220[/C][C]326.391974778024[/C][/ROW]
[ROW][C]18[/C][C]24771.5[/C][C]23747.3726975762[/C][C]1024.12730242377[/C][/ROW]
[ROW][C]19[/C][C]22592.4[/C][C]21470.5422449164[/C][C]1121.85775508362[/C][/ROW]
[ROW][C]20[/C][C]21942.1[/C][C]21403.9802316453[/C][C]538.119768354654[/C][/ROW]
[ROW][C]21[/C][C]23973.7[/C][C]23774.0097979441[/C][C]199.69020205588[/C][/ROW]
[ROW][C]22[/C][C]20815.7[/C][C]21497.9364835694[/C][C]-682.236483569412[/C][/ROW]
[ROW][C]23[/C][C]19931.4[/C][C]19105.2478320697[/C][C]826.152167930353[/C][/ROW]
[ROW][C]24[/C][C]24436.8[/C][C]23264.1993034465[/C][C]1172.6006965535[/C][/ROW]
[ROW][C]25[/C][C]22838.7[/C][C]22514.7574386553[/C][C]323.942561344714[/C][/ROW]
[ROW][C]26[/C][C]24465.3[/C][C]22061.6275559731[/C][C]2403.67244402688[/C][/ROW]
[ROW][C]27[/C][C]23007.3[/C][C]20382.4632320063[/C][C]2624.83676799372[/C][/ROW]
[ROW][C]28[/C][C]22720.8[/C][C]21140.1723172073[/C][C]1580.62768279273[/C][/ROW]
[ROW][C]29[/C][C]23045.7[/C][C]21916.4138493805[/C][C]1129.28615061948[/C][/ROW]
[ROW][C]30[/C][C]27198.5[/C][C]25134.5091011918[/C][C]2063.99089880823[/C][/ROW]
[ROW][C]31[/C][C]22401.9[/C][C]22957.6852962400[/C][C]-555.785296239958[/C][/ROW]
[ROW][C]32[/C][C]25122.7[/C][C]22911.1246125105[/C][C]2211.57538748947[/C][/ROW]
[ROW][C]33[/C][C]26100.5[/C][C]25561.1727923918[/C][C]539.327207608178[/C][/ROW]
[ROW][C]34[/C][C]22904.9[/C][C]23465.1114438916[/C][C]-560.211443891587[/C][/ROW]
[ROW][C]35[/C][C]22040.4[/C][C]21412.4453945992[/C][C]627.954605400836[/C][/ROW]
[ROW][C]36[/C][C]25981.5[/C][C]25651.4021841424[/C][C]330.097815857552[/C][/ROW]
[ROW][C]37[/C][C]26157.1[/C][C]25261.9842511002[/C][C]895.115748899812[/C][/ROW]
[ROW][C]38[/C][C]25975.4[/C][C]24988.8663342925[/C][C]986.533665707505[/C][/ROW]
[ROW][C]39[/C][C]22589.8[/C][C]23189.694033076[/C][C]-599.894033076004[/C][/ROW]
[ROW][C]40[/C][C]25370.4[/C][C]24087.4124250683[/C][C]1282.98757493175[/C][/ROW]
[ROW][C]41[/C][C]25091.1[/C][C]24843.6526276999[/C][C]247.447372300104[/C][/ROW]
[ROW][C]42[/C][C]28760.9[/C][C]27941.7399022615[/C][C]819.16009773851[/C][/ROW]
[ROW][C]43[/C][C]24325.9[/C][C]25864.9227450177[/C][C]-1539.02274501772[/C][/ROW]
[ROW][C]44[/C][C]25821.7[/C][C]25798.3607317467[/C][C]23.3392682533148[/C][/ROW]
[ROW][C]45[/C][C]27645.7[/C][C]28488.4115707112[/C][C]-842.711570711195[/C][/ROW]
[ROW][C]46[/C][C]26296.9[/C][C]26372.3488926694[/C][C]-75.448892669352[/C][/ROW]
[ROW][C]47[/C][C]24141.5[/C][C]23999.6615707112[/C][C]141.838429288803[/C][/ROW]
[ROW][C]48[/C][C]27268.1[/C][C]28378.6276670457[/C][C]-1110.52766704574[/C][/ROW]
[ROW][C]49[/C][C]29060.3[/C][C]27549.1804840881[/C][C]1511.11951591190[/C][/ROW]
[ROW][C]50[/C][C]28226.4[/C][C]27116.0519309475[/C][C]1110.34806905246[/C][/ROW]
[ROW][C]51[/C][C]23268.5[/C][C]25056.8623456901[/C][C]-1788.36234569014[/C][/ROW]
[ROW][C]52[/C][C]26938.2[/C][C]25794.5701013495[/C][C]1143.62989865048[/C][/ROW]
[ROW][C]53[/C][C]27217.5[/C][C]26490.8063153563[/C][C]726.693684643663[/C][/ROW]
[ROW][C]54[/C][C]27540.5[/C][C]29308.8749763354[/C][C]-1768.37497633542[/C][/ROW]
[ROW][C]55[/C][C]29167.6[/C][C]27152.0525009252[/C][C]2015.54749907478[/C][/ROW]
[ROW][C]56[/C][C]26671.5[/C][C]27085.4904876542[/C][C]-413.99048765418[/C][/ROW]
[ROW][C]57[/C][C]30184[/C][C]29355.5134062449[/C][C]828.486593755084[/C][/ROW]
[ROW][C]58[/C][C]28422.3[/C][C]27339.4573759111[/C][C]1082.84262408888[/C][/ROW]
[ROW][C]59[/C][C]23774.3[/C][C]25086.7780312026[/C][C]-1312.47803120261[/C][/ROW]
[ROW][C]60[/C][C]29601[/C][C]29545.7494457036[/C][C]55.2505542964189[/C][/ROW]
[ROW][C]61[/C][C]28523.6[/C][C]30016.3886829505[/C][C]-1492.78868295048[/C][/ROW]
[ROW][C]62[/C][C]23622[/C][C]26043.0248009453[/C][C]-2421.02480094525[/C][/ROW]
[ROW][C]63[/C][C]21320.3[/C][C]22483.7355000672[/C][C]-1163.43550006723[/C][/ROW]
[ROW][C]64[/C][C]20423.6[/C][C]22381.3874149791[/C][C]-1957.78741497906[/C][/ROW]
[ROW][C]65[/C][C]21174.9[/C][C]22577.5903904457[/C][C]-1402.69039044567[/C][/ROW]
[ROW][C]66[/C][C]23050.2[/C][C]24635.6085288436[/C][C]-1585.40852884364[/C][/ROW]
[ROW][C]67[/C][C]21202.9[/C][C]21678.7328717691[/C][C]-475.832871769106[/C][/ROW]
[ROW][C]68[/C][C]20476.4[/C][C]21172.1416085827[/C][C]-695.741608582684[/C][/ROW]
[ROW][C]69[/C][C]23173.3[/C][C]23382.1605385486[/C][C]-208.860538548597[/C][/ROW]
[ROW][C]70[/C][C]22468[/C][C]21106.0872241739[/C][C]1361.91277582611[/C][/ROW]
[ROW][C]71[/C][C]19842.7[/C][C]18693.3972431325[/C][C]1149.30275686749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&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
120604.621620.6096083354-1016.00960833543
218714.921127.4770665700-2412.57706657003
318492.619008.2834926878-515.683492687790
418183.619725.9899188056-1542.38991880557
519435.120462.2287918956-1027.12879189560
622686.823240.2947937915-553.494793791462
720396.720963.4643411316-566.764341131614
819233.620896.9023278606-1663.30232786058
92275123266.9318941594-515.931894159351
101986420990.8585797846-1126.85857978465
1117165.418598.1699282849-1432.76992828487
1222309.722757.1213996617-447.421399661726
1321786.322007.6795348705-221.379534870516
1421927.621594.5523112716333.047688728432
1520957.919515.36139647261442.53860352744
161972620233.0678225903-507.067822590333
1721315.720989.3080252220326.391974778024
1824771.523747.37269757621024.12730242377
1922592.421470.54224491641121.85775508362
2021942.121403.9802316453538.119768354654
2123973.723774.0097979441199.69020205588
2220815.721497.9364835694-682.236483569412
2319931.419105.2478320697826.152167930353
2424436.823264.19930344651172.6006965535
2522838.722514.7574386553323.942561344714
2624465.322061.62755597312403.67244402688
2723007.320382.46323200632624.83676799372
2822720.821140.17231720731580.62768279273
2923045.721916.41384938051129.28615061948
3027198.525134.50910119182063.99089880823
3122401.922957.6852962400-555.785296239958
3225122.722911.12461251052211.57538748947
3326100.525561.1727923918539.327207608178
3422904.923465.1114438916-560.211443891587
3522040.421412.4453945992627.954605400836
3625981.525651.4021841424330.097815857552
3726157.125261.9842511002895.115748899812
3825975.424988.8663342925986.533665707505
3922589.823189.694033076-599.894033076004
4025370.424087.41242506831282.98757493175
4125091.124843.6526276999247.447372300104
4228760.927941.7399022615819.16009773851
4324325.925864.9227450177-1539.02274501772
4425821.725798.360731746723.3392682533148
4527645.728488.4115707112-842.711570711195
4626296.926372.3488926694-75.448892669352
4724141.523999.6615707112141.838429288803
4827268.128378.6276670457-1110.52766704574
4929060.327549.18048408811511.11951591190
5028226.427116.05193094751110.34806905246
5123268.525056.8623456901-1788.36234569014
5226938.225794.57010134951143.62989865048
5327217.526490.8063153563726.693684643663
5427540.529308.8749763354-1768.37497633542
5529167.627152.05250092522015.54749907478
5626671.527085.4904876542-413.99048765418
573018429355.5134062449828.486593755084
5828422.327339.45737591111082.84262408888
5923774.325086.7780312026-1312.47803120261
602960129545.749445703655.2505542964189
6128523.630016.3886829505-1492.78868295048
622362226043.0248009453-2421.02480094525
6321320.322483.7355000672-1163.43550006723
6420423.622381.3874149791-1957.78741497906
6521174.922577.5903904457-1402.69039044567
6623050.224635.6085288436-1585.40852884364
6721202.921678.7328717691-475.832871769106
6820476.421172.1416085827-695.741608582684
6923173.323382.1605385486-208.860538548597
702246821106.08722417391361.91277582611
7119842.718693.39724313251149.30275686749






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1413416954784320.2826833909568650.858658304521568
180.05552555935572620.1110511187114520.944474440644274
190.01959938721741840.03919877443483680.980400612782582
200.008532801785463070.01706560357092610.991467198214537
210.007187123617614920.01437424723522980.992812876382385
220.009081016475988730.01816203295197750.990918983524011
230.005488134674617140.01097626934923430.994511865325383
240.002099960815335890.004199921630671780.997900039184664
250.002744186718686710.005488373437373420.997255813281313
260.005586100642457770.01117220128491550.994413899357542
270.004254069433896250.00850813886779250.995745930566104
280.001977160053708520.003954320107417050.998022839946291
290.001304579437383230.002609158874766460.998695420562617
300.0008217034979631710.001643406995926340.999178296502037
310.00490310933941250.0098062186788250.995096890660587
320.01265290238518070.02530580477036140.98734709761482
330.006946530177493550.01389306035498710.993053469822506
340.006704393277672340.01340878655534470.993295606722328
350.004109645174714630.008219290349429260.995890354825285
360.002167197601686860.004334395203373730.997832802398313
370.001157915387707980.002315830775415960.998842084612292
380.0005939170361552620.001187834072310520.999406082963845
390.001861984989708450.00372396997941690.998138015010292
400.002319903572390660.004639807144781320.99768009642761
410.001132467031386670.002264934062773340.998867532968613
420.001116586784968110.002233173569936220.998883413215032
430.002889874729661190.005779749459322380.99711012527034
440.001415095037582320.002830190075164640.998584904962418
450.001332937146217840.002665874292435680.998667062853782
460.00448472369954520.00896944739909040.995515276300455
470.004142056196117260.008284112392234520.995857943803883
480.03030729469038310.06061458938076620.969692705309617
490.03321973310614970.06643946621229940.96678026689385
500.02180333414535270.04360666829070550.978196665854647
510.2693961954110290.5387923908220590.73060380458897
520.1840410402090570.3680820804181150.815958959790942
530.1065589651081420.2131179302162830.893441034891858
540.808621909690660.3827561806186810.191378090309341

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.141341695478432 & 0.282683390956865 & 0.858658304521568 \tabularnewline
18 & 0.0555255593557262 & 0.111051118711452 & 0.944474440644274 \tabularnewline
19 & 0.0195993872174184 & 0.0391987744348368 & 0.980400612782582 \tabularnewline
20 & 0.00853280178546307 & 0.0170656035709261 & 0.991467198214537 \tabularnewline
21 & 0.00718712361761492 & 0.0143742472352298 & 0.992812876382385 \tabularnewline
22 & 0.00908101647598873 & 0.0181620329519775 & 0.990918983524011 \tabularnewline
23 & 0.00548813467461714 & 0.0109762693492343 & 0.994511865325383 \tabularnewline
24 & 0.00209996081533589 & 0.00419992163067178 & 0.997900039184664 \tabularnewline
25 & 0.00274418671868671 & 0.00548837343737342 & 0.997255813281313 \tabularnewline
26 & 0.00558610064245777 & 0.0111722012849155 & 0.994413899357542 \tabularnewline
27 & 0.00425406943389625 & 0.0085081388677925 & 0.995745930566104 \tabularnewline
28 & 0.00197716005370852 & 0.00395432010741705 & 0.998022839946291 \tabularnewline
29 & 0.00130457943738323 & 0.00260915887476646 & 0.998695420562617 \tabularnewline
30 & 0.000821703497963171 & 0.00164340699592634 & 0.999178296502037 \tabularnewline
31 & 0.0049031093394125 & 0.009806218678825 & 0.995096890660587 \tabularnewline
32 & 0.0126529023851807 & 0.0253058047703614 & 0.98734709761482 \tabularnewline
33 & 0.00694653017749355 & 0.0138930603549871 & 0.993053469822506 \tabularnewline
34 & 0.00670439327767234 & 0.0134087865553447 & 0.993295606722328 \tabularnewline
35 & 0.00410964517471463 & 0.00821929034942926 & 0.995890354825285 \tabularnewline
36 & 0.00216719760168686 & 0.00433439520337373 & 0.997832802398313 \tabularnewline
37 & 0.00115791538770798 & 0.00231583077541596 & 0.998842084612292 \tabularnewline
38 & 0.000593917036155262 & 0.00118783407231052 & 0.999406082963845 \tabularnewline
39 & 0.00186198498970845 & 0.0037239699794169 & 0.998138015010292 \tabularnewline
40 & 0.00231990357239066 & 0.00463980714478132 & 0.99768009642761 \tabularnewline
41 & 0.00113246703138667 & 0.00226493406277334 & 0.998867532968613 \tabularnewline
42 & 0.00111658678496811 & 0.00223317356993622 & 0.998883413215032 \tabularnewline
43 & 0.00288987472966119 & 0.00577974945932238 & 0.99711012527034 \tabularnewline
44 & 0.00141509503758232 & 0.00283019007516464 & 0.998584904962418 \tabularnewline
45 & 0.00133293714621784 & 0.00266587429243568 & 0.998667062853782 \tabularnewline
46 & 0.0044847236995452 & 0.0089694473990904 & 0.995515276300455 \tabularnewline
47 & 0.00414205619611726 & 0.00828411239223452 & 0.995857943803883 \tabularnewline
48 & 0.0303072946903831 & 0.0606145893807662 & 0.969692705309617 \tabularnewline
49 & 0.0332197331061497 & 0.0664394662122994 & 0.96678026689385 \tabularnewline
50 & 0.0218033341453527 & 0.0436066682907055 & 0.978196665854647 \tabularnewline
51 & 0.269396195411029 & 0.538792390822059 & 0.73060380458897 \tabularnewline
52 & 0.184041040209057 & 0.368082080418115 & 0.815958959790942 \tabularnewline
53 & 0.106558965108142 & 0.213117930216283 & 0.893441034891858 \tabularnewline
54 & 0.80862190969066 & 0.382756180618681 & 0.191378090309341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&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]0.141341695478432[/C][C]0.282683390956865[/C][C]0.858658304521568[/C][/ROW]
[ROW][C]18[/C][C]0.0555255593557262[/C][C]0.111051118711452[/C][C]0.944474440644274[/C][/ROW]
[ROW][C]19[/C][C]0.0195993872174184[/C][C]0.0391987744348368[/C][C]0.980400612782582[/C][/ROW]
[ROW][C]20[/C][C]0.00853280178546307[/C][C]0.0170656035709261[/C][C]0.991467198214537[/C][/ROW]
[ROW][C]21[/C][C]0.00718712361761492[/C][C]0.0143742472352298[/C][C]0.992812876382385[/C][/ROW]
[ROW][C]22[/C][C]0.00908101647598873[/C][C]0.0181620329519775[/C][C]0.990918983524011[/C][/ROW]
[ROW][C]23[/C][C]0.00548813467461714[/C][C]0.0109762693492343[/C][C]0.994511865325383[/C][/ROW]
[ROW][C]24[/C][C]0.00209996081533589[/C][C]0.00419992163067178[/C][C]0.997900039184664[/C][/ROW]
[ROW][C]25[/C][C]0.00274418671868671[/C][C]0.00548837343737342[/C][C]0.997255813281313[/C][/ROW]
[ROW][C]26[/C][C]0.00558610064245777[/C][C]0.0111722012849155[/C][C]0.994413899357542[/C][/ROW]
[ROW][C]27[/C][C]0.00425406943389625[/C][C]0.0085081388677925[/C][C]0.995745930566104[/C][/ROW]
[ROW][C]28[/C][C]0.00197716005370852[/C][C]0.00395432010741705[/C][C]0.998022839946291[/C][/ROW]
[ROW][C]29[/C][C]0.00130457943738323[/C][C]0.00260915887476646[/C][C]0.998695420562617[/C][/ROW]
[ROW][C]30[/C][C]0.000821703497963171[/C][C]0.00164340699592634[/C][C]0.999178296502037[/C][/ROW]
[ROW][C]31[/C][C]0.0049031093394125[/C][C]0.009806218678825[/C][C]0.995096890660587[/C][/ROW]
[ROW][C]32[/C][C]0.0126529023851807[/C][C]0.0253058047703614[/C][C]0.98734709761482[/C][/ROW]
[ROW][C]33[/C][C]0.00694653017749355[/C][C]0.0138930603549871[/C][C]0.993053469822506[/C][/ROW]
[ROW][C]34[/C][C]0.00670439327767234[/C][C]0.0134087865553447[/C][C]0.993295606722328[/C][/ROW]
[ROW][C]35[/C][C]0.00410964517471463[/C][C]0.00821929034942926[/C][C]0.995890354825285[/C][/ROW]
[ROW][C]36[/C][C]0.00216719760168686[/C][C]0.00433439520337373[/C][C]0.997832802398313[/C][/ROW]
[ROW][C]37[/C][C]0.00115791538770798[/C][C]0.00231583077541596[/C][C]0.998842084612292[/C][/ROW]
[ROW][C]38[/C][C]0.000593917036155262[/C][C]0.00118783407231052[/C][C]0.999406082963845[/C][/ROW]
[ROW][C]39[/C][C]0.00186198498970845[/C][C]0.0037239699794169[/C][C]0.998138015010292[/C][/ROW]
[ROW][C]40[/C][C]0.00231990357239066[/C][C]0.00463980714478132[/C][C]0.99768009642761[/C][/ROW]
[ROW][C]41[/C][C]0.00113246703138667[/C][C]0.00226493406277334[/C][C]0.998867532968613[/C][/ROW]
[ROW][C]42[/C][C]0.00111658678496811[/C][C]0.00223317356993622[/C][C]0.998883413215032[/C][/ROW]
[ROW][C]43[/C][C]0.00288987472966119[/C][C]0.00577974945932238[/C][C]0.99711012527034[/C][/ROW]
[ROW][C]44[/C][C]0.00141509503758232[/C][C]0.00283019007516464[/C][C]0.998584904962418[/C][/ROW]
[ROW][C]45[/C][C]0.00133293714621784[/C][C]0.00266587429243568[/C][C]0.998667062853782[/C][/ROW]
[ROW][C]46[/C][C]0.0044847236995452[/C][C]0.0089694473990904[/C][C]0.995515276300455[/C][/ROW]
[ROW][C]47[/C][C]0.00414205619611726[/C][C]0.00828411239223452[/C][C]0.995857943803883[/C][/ROW]
[ROW][C]48[/C][C]0.0303072946903831[/C][C]0.0606145893807662[/C][C]0.969692705309617[/C][/ROW]
[ROW][C]49[/C][C]0.0332197331061497[/C][C]0.0664394662122994[/C][C]0.96678026689385[/C][/ROW]
[ROW][C]50[/C][C]0.0218033341453527[/C][C]0.0436066682907055[/C][C]0.978196665854647[/C][/ROW]
[ROW][C]51[/C][C]0.269396195411029[/C][C]0.538792390822059[/C][C]0.73060380458897[/C][/ROW]
[ROW][C]52[/C][C]0.184041040209057[/C][C]0.368082080418115[/C][C]0.815958959790942[/C][/ROW]
[ROW][C]53[/C][C]0.106558965108142[/C][C]0.213117930216283[/C][C]0.893441034891858[/C][/ROW]
[ROW][C]54[/C][C]0.80862190969066[/C][C]0.382756180618681[/C][C]0.191378090309341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&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
170.1413416954784320.2826833909568650.858658304521568
180.05552555935572620.1110511187114520.944474440644274
190.01959938721741840.03919877443483680.980400612782582
200.008532801785463070.01706560357092610.991467198214537
210.007187123617614920.01437424723522980.992812876382385
220.009081016475988730.01816203295197750.990918983524011
230.005488134674617140.01097626934923430.994511865325383
240.002099960815335890.004199921630671780.997900039184664
250.002744186718686710.005488373437373420.997255813281313
260.005586100642457770.01117220128491550.994413899357542
270.004254069433896250.00850813886779250.995745930566104
280.001977160053708520.003954320107417050.998022839946291
290.001304579437383230.002609158874766460.998695420562617
300.0008217034979631710.001643406995926340.999178296502037
310.00490310933941250.0098062186788250.995096890660587
320.01265290238518070.02530580477036140.98734709761482
330.006946530177493550.01389306035498710.993053469822506
340.006704393277672340.01340878655534470.993295606722328
350.004109645174714630.008219290349429260.995890354825285
360.002167197601686860.004334395203373730.997832802398313
370.001157915387707980.002315830775415960.998842084612292
380.0005939170361552620.001187834072310520.999406082963845
390.001861984989708450.00372396997941690.998138015010292
400.002319903572390660.004639807144781320.99768009642761
410.001132467031386670.002264934062773340.998867532968613
420.001116586784968110.002233173569936220.998883413215032
430.002889874729661190.005779749459322380.99711012527034
440.001415095037582320.002830190075164640.998584904962418
450.001332937146217840.002665874292435680.998667062853782
460.00448472369954520.00896944739909040.995515276300455
470.004142056196117260.008284112392234520.995857943803883
480.03030729469038310.06061458938076620.969692705309617
490.03321973310614970.06643946621229940.96678026689385
500.02180333414535270.04360666829070550.978196665854647
510.2693961954110290.5387923908220590.73060380458897
520.1840410402090570.3680820804181150.815958959790942
530.1065589651081420.2131179302162830.893441034891858
540.808621909690660.3827561806186810.191378090309341






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level200.526315789473684NOK
5% type I error level300.789473684210526NOK
10% type I error level320.842105263157895NOK

\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 & 20 & 0.526315789473684 & NOK \tabularnewline
5% type I error level & 30 & 0.789473684210526 & NOK \tabularnewline
10% type I error level & 32 & 0.842105263157895 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57375&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]20[/C][C]0.526315789473684[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]30[/C][C]0.789473684210526[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]32[/C][C]0.842105263157895[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57375&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57375&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 level200.526315789473684NOK
5% type I error level300.789473684210526NOK
10% type I error level320.842105263157895NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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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')
}