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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 10:00:20 -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/t1258477257i4iseb14jpb6n4z.htm/, Retrieved Tue, 04 Nov 2025 01:21:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57378, Retrieved Tue, 04 Nov 2025 01:21:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact512

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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-17 17:00:20] [0f1f1142419956a95ff6f880845f2408] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19435,1	2,01	20604,6	20604,6	20604,6
22686,8	2,01	19435,1	18714,9	18714,9
20396,7	2,01	22686,8	19435,1	18492,6
19233,6	2,01	20396,7	22686,8	19435,1
22751	2,01	19233,6	20396,7	22686,8
19864	2,01	22751	19233,6	20396,7
17165,4	2,02	19864	22751	19233,6
22309,7	2,02	17165,4	19864	22751
21786,3	2,03	22309,7	17165,4	19864
21927,6	2,05	21786,3	22309,7	17165,4
20957,9	2,08	21927,6	21786,3	22309,7
19726	2,07	20957,9	21927,6	21786,3
21315,7	2,06	19726	20957,9	21927,6
24771,5	2,05	21315,7	19726	20957,9
22592,4	2,05	24771,5	21315,7	19726
21942,1	2,05	22592,4	24771,5	21315,7
23973,7	2,05	21942,1	22592,4	24771,5
20815,7	2,05	23973,7	21942,1	22592,4
19931,4	2,06	20815,7	23973,7	21942,1
24436,8	2,06	19931,4	20815,7	23973,7
22838,7	2,07	24436,8	19931,4	20815,7
24465,3	2,07	22838,7	24436,8	19931,4
23007,3	2,3	24465,3	22838,7	24436,8
22720,8	2,31	23007,3	24465,3	22838,7
23045,7	2,31	22720,8	23007,3	24465,3
27198,5	2,53	23045,7	22720,8	23007,3
22401,9	2,58	27198,5	23045,7	22720,8
25122,7	2,59	22401,9	27198,5	23045,7
26100,5	2,73	25122,7	22401,9	27198,5
22904,9	2,82	26100,5	25122,7	22401,9
22040,4	3	22904,9	26100,5	25122,7
25981,5	3,04	22040,4	22904,9	26100,5
26157,1	3,23	25981,5	22040,4	22904,9
25975,4	3,32	26157,1	25981,5	22040,4
22589,8	3,49	25975,4	26157,1	25981,5
25370,4	3,57	22589,8	25975,4	26157,1
25091,1	3,56	25370,4	22589,8	25975,4
28760,9	3,72	25091,1	25370,4	22589,8
24325,9	3,82	28760,9	25091,1	25370,4
25821,7	3,82	24325,9	28760,9	25091,1
27645,7	3,98	25821,7	24325,9	28760,9
26296,9	4,06	27645,7	25821,7	24325,9
24141,5	4,08	26296,9	27645,7	25821,7
27268,1	4,19	24141,5	26296,9	27645,7
29060,3	4,16	27268,1	24141,5	26296,9
28226,4	4,17	29060,3	27268,1	24141,5
23268,5	4,21	28226,4	29060,3	27268,1
26938,2	4,21	23268,5	28226,4	29060,3
27217,5	4,17	26938,2	23268,5	28226,4
27540,5	4,19	27217,5	26938,2	23268,5
29167,6	4,25	27540,5	27217,5	26938,2
26671,5	4,25	29167,6	27540,5	27217,5
30184	4,2	26671,5	29167,6	27540,5
28422,3	4,33	30184	26671,5	29167,6
23774,3	4,41	28422,3	30184	26671,5
29601	4,56	23774,3	28422,3	30184
28523,6	5,18	29601	23774,3	28422,3
23622	3,42	28523,6	29601	23774,3
21320,3	2,71	23622	28523,6	29601
20423,6	2,29	21320,3	23622	28523,6
21174,9	2	20423,6	21320,3	23622
23050,2	1,64	21174,9	20423,6	21320,3
21202,9	1,3	23050,2	21174,9	20423,6
20476,4	1,08	21202,9	23050,2	21174,9
23173,3	1	20476,4	21202,9	23050,2
22468	1	23173,3	20476,4	21202,9
19842,7	1	22468	23173,3	20476,4

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9374.57467049922 + 1224.00784219445X[t] + 0.0977062231002342Y1[t] + 0.115952759659355Y2[t] + 0.182520307490899Y3[t] + 724.35433075174M1[t] + 3884.92719146509M2[t] + 1126.73655843838M3[t] + 815.94703196878M4[t] + 2970.75504633567M5[t] + 924.990992066053M6[t] -1503.43996923854M7[t] + 2712.33484127727M8[t] + 2530.80527012911M9[t] + 2003.66072271356M10[t] -1276.19185810045M11[t] + 10.7061192035070t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  9374.57467049922 +  1224.00784219445X[t] +  0.0977062231002342Y1[t] +  0.115952759659355Y2[t] +  0.182520307490899Y3[t] +  724.35433075174M1[t] +  3884.92719146509M2[t] +  1126.73655843838M3[t] +  815.94703196878M4[t] +  2970.75504633567M5[t] +  924.990992066053M6[t] -1503.43996923854M7[t] +  2712.33484127727M8[t] +  2530.80527012911M9[t] +  2003.66072271356M10[t] -1276.19185810045M11[t] +  10.7061192035070t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  9374.57467049922 +  1224.00784219445X[t] +  0.0977062231002342Y1[t] +  0.115952759659355Y2[t] +  0.182520307490899Y3[t] +  724.35433075174M1[t] +  3884.92719146509M2[t] +  1126.73655843838M3[t] +  815.94703196878M4[t] +  2970.75504633567M5[t] +  924.990992066053M6[t] -1503.43996923854M7[t] +  2712.33484127727M8[t] +  2530.80527012911M9[t] +  2003.66072271356M10[t] -1276.19185810045M11[t] +  10.7061192035070t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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] = + 9374.57467049922 + 1224.00784219445X[t] + 0.0977062231002342Y1[t] + 0.115952759659355Y2[t] + 0.182520307490899Y3[t] + 724.35433075174M1[t] + 3884.92719146509M2[t] + 1126.73655843838M3[t] + 815.94703196878M4[t] + 2970.75504633567M5[t] + 924.990992066053M6[t] -1503.43996923854M7[t] + 2712.33484127727M8[t] + 2530.80527012911M9[t] + 2003.66072271356M10[t] -1276.19185810045M11[t] + 10.7061192035070t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9374.574670499224382.6376922.1390.0373410.01867
X1224.00784219445508.1315032.40880.0197290.009865
Y10.09770622310023420.1551020.62990.5315980.265799
Y20.1159527596593550.148310.78180.4380030.219001
Y30.1825203074908990.1524851.1970.2369610.118481
M1724.35433075174885.5241560.8180.4172410.208621
M23884.927191465091009.6605853.84780.0003390.000169
M31126.736558438381123.544221.00280.3207660.160383
M4815.94703196878929.4637140.87790.3842140.192107
M52970.75504633567841.0758873.53210.0008970.000449
M6924.9909920660531055.7927170.87610.385160.19258
M7-1503.43996923854910.49508-1.65120.1049590.052479
M82712.33484127727880.5964493.08010.0033590.001679
M92530.805270129111204.3316152.10140.0406650.020333
M102003.660722713561199.4338411.67050.1010690.050534
M11-1276.19185810045916.869508-1.39190.1701130.085057
t10.706119203507013.8910990.77070.4445010.22225

\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) & 9374.57467049922 & 4382.637692 & 2.139 & 0.037341 & 0.01867 \tabularnewline
X & 1224.00784219445 & 508.131503 & 2.4088 & 0.019729 & 0.009865 \tabularnewline
Y1 & 0.0977062231002342 & 0.155102 & 0.6299 & 0.531598 & 0.265799 \tabularnewline
Y2 & 0.115952759659355 & 0.14831 & 0.7818 & 0.438003 & 0.219001 \tabularnewline
Y3 & 0.182520307490899 & 0.152485 & 1.197 & 0.236961 & 0.118481 \tabularnewline
M1 & 724.35433075174 & 885.524156 & 0.818 & 0.417241 & 0.208621 \tabularnewline
M2 & 3884.92719146509 & 1009.660585 & 3.8478 & 0.000339 & 0.000169 \tabularnewline
M3 & 1126.73655843838 & 1123.54422 & 1.0028 & 0.320766 & 0.160383 \tabularnewline
M4 & 815.94703196878 & 929.463714 & 0.8779 & 0.384214 & 0.192107 \tabularnewline
M5 & 2970.75504633567 & 841.075887 & 3.5321 & 0.000897 & 0.000449 \tabularnewline
M6 & 924.990992066053 & 1055.792717 & 0.8761 & 0.38516 & 0.19258 \tabularnewline
M7 & -1503.43996923854 & 910.49508 & -1.6512 & 0.104959 & 0.052479 \tabularnewline
M8 & 2712.33484127727 & 880.596449 & 3.0801 & 0.003359 & 0.001679 \tabularnewline
M9 & 2530.80527012911 & 1204.331615 & 2.1014 & 0.040665 & 0.020333 \tabularnewline
M10 & 2003.66072271356 & 1199.433841 & 1.6705 & 0.101069 & 0.050534 \tabularnewline
M11 & -1276.19185810045 & 916.869508 & -1.3919 & 0.170113 & 0.085057 \tabularnewline
t & 10.7061192035070 & 13.891099 & 0.7707 & 0.444501 & 0.22225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&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]9374.57467049922[/C][C]4382.637692[/C][C]2.139[/C][C]0.037341[/C][C]0.01867[/C][/ROW]
[ROW][C]X[/C][C]1224.00784219445[/C][C]508.131503[/C][C]2.4088[/C][C]0.019729[/C][C]0.009865[/C][/ROW]
[ROW][C]Y1[/C][C]0.0977062231002342[/C][C]0.155102[/C][C]0.6299[/C][C]0.531598[/C][C]0.265799[/C][/ROW]
[ROW][C]Y2[/C][C]0.115952759659355[/C][C]0.14831[/C][C]0.7818[/C][C]0.438003[/C][C]0.219001[/C][/ROW]
[ROW][C]Y3[/C][C]0.182520307490899[/C][C]0.152485[/C][C]1.197[/C][C]0.236961[/C][C]0.118481[/C][/ROW]
[ROW][C]M1[/C][C]724.35433075174[/C][C]885.524156[/C][C]0.818[/C][C]0.417241[/C][C]0.208621[/C][/ROW]
[ROW][C]M2[/C][C]3884.92719146509[/C][C]1009.660585[/C][C]3.8478[/C][C]0.000339[/C][C]0.000169[/C][/ROW]
[ROW][C]M3[/C][C]1126.73655843838[/C][C]1123.54422[/C][C]1.0028[/C][C]0.320766[/C][C]0.160383[/C][/ROW]
[ROW][C]M4[/C][C]815.94703196878[/C][C]929.463714[/C][C]0.8779[/C][C]0.384214[/C][C]0.192107[/C][/ROW]
[ROW][C]M5[/C][C]2970.75504633567[/C][C]841.075887[/C][C]3.5321[/C][C]0.000897[/C][C]0.000449[/C][/ROW]
[ROW][C]M6[/C][C]924.990992066053[/C][C]1055.792717[/C][C]0.8761[/C][C]0.38516[/C][C]0.19258[/C][/ROW]
[ROW][C]M7[/C][C]-1503.43996923854[/C][C]910.49508[/C][C]-1.6512[/C][C]0.104959[/C][C]0.052479[/C][/ROW]
[ROW][C]M8[/C][C]2712.33484127727[/C][C]880.596449[/C][C]3.0801[/C][C]0.003359[/C][C]0.001679[/C][/ROW]
[ROW][C]M9[/C][C]2530.80527012911[/C][C]1204.331615[/C][C]2.1014[/C][C]0.040665[/C][C]0.020333[/C][/ROW]
[ROW][C]M10[/C][C]2003.66072271356[/C][C]1199.433841[/C][C]1.6705[/C][C]0.101069[/C][C]0.050534[/C][/ROW]
[ROW][C]M11[/C][C]-1276.19185810045[/C][C]916.869508[/C][C]-1.3919[/C][C]0.170113[/C][C]0.085057[/C][/ROW]
[ROW][C]t[/C][C]10.7061192035070[/C][C]13.891099[/C][C]0.7707[/C][C]0.444501[/C][C]0.22225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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)9374.574670499224382.6376922.1390.0373410.01867
X1224.00784219445508.1315032.40880.0197290.009865
Y10.09770622310023420.1551020.62990.5315980.265799
Y20.1159527596593550.148310.78180.4380030.219001
Y30.1825203074908990.1524851.1970.2369610.118481
M1724.35433075174885.5241560.8180.4172410.208621
M23884.927191465091009.6605853.84780.0003390.000169
M31126.736558438381123.544221.00280.3207660.160383
M4815.94703196878929.4637140.87790.3842140.192107
M52970.75504633567841.0758873.53210.0008970.000449
M6924.9909920660531055.7927170.87610.385160.19258
M7-1503.43996923854910.49508-1.65120.1049590.052479
M82712.33484127727880.5964493.08010.0033590.001679
M92530.805270129111204.3316152.10140.0406650.020333
M102003.660722713561199.4338411.67050.1010690.050534
M11-1276.19185810045916.869508-1.39190.1701130.085057
t10.706119203507013.8910990.77070.4445010.22225






Multiple Linear Regression - Regression Statistics
Multiple R0.925534667128993
R-squared0.856614420057577
Adjusted R-squared0.810731034476001
F-TEST (value)18.6693812847488
F-TEST (DF numerator)16
F-TEST (DF denominator)50
p-value9.9920072216264e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1304.49441924886
Sum Squared Residuals85085284.4925715

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.925534667128993 \tabularnewline
R-squared & 0.856614420057577 \tabularnewline
Adjusted R-squared & 0.810731034476001 \tabularnewline
F-TEST (value) & 18.6693812847488 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 9.9920072216264e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1304.49441924886 \tabularnewline
Sum Squared Residuals & 85085284.4925715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.925534667128993[/C][/ROW]
[ROW][C]R-squared[/C][C]0.856614420057577[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.810731034476001[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]18.6693812847488[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/C][/ROW]
[ROW][C]p-value[/C][C]9.9920072216264e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1304.49441924886[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]85085284.4925715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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 R0.925534667128993
R-squared0.856614420057577
Adjusted R-squared0.810731034476001
F-TEST (value)18.6693812847488
F-TEST (DF numerator)16
F-TEST (DF denominator)50
p-value9.9920072216264e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1304.49441924886
Sum Squared Residuals85085284.4925715






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
119435.120733.0066871605-1297.90668716053
222686.823225.9936841678-539.193684167838
320396.720839.1554091511-442.455409151094
419233.620864.3839587577-1630.78395875766
52275123244.2138532124-493.213853212446
61986420999.9733763344-1135.97337633439
717165.418507.9736137480-1342.57361374802
822309.722778.0258422410-468.325842240976
921786.322282.2263472698-495.926347269849
1021927.621843.075118451784.5248815482946
1120957.919502.70432485081455.19567514917
121972620603.4694951917-877.469495191672
1321315.721119.2762988946196.423701105413
1424771.524113.8066364537657.693363546343
1522592.421663.4586236527928.941376347327
1621942.121841.3256652779100.774334722052
1723973.724321.3824620196-347.682462019612
1820815.722011.6904081440-1195.99040814404
1919931.419414.5260624770516.873937523033
2024436.823559.234820803877.565179196982
2122838.723161.9209084131-323.220908413080
2224465.322850.34902051961614.95097948040
2323007.320658.67619326662348.62380673344
2422720.821712.2816311731008.51836882699
2523045.722547.1776567914498.522343208602
2627198.525720.14803991221478.35196008783
2722401.923424.9993050065-1023.09930500651
2825122.723209.32777465701913.37222534305
2926100.526013.833423911886.6665760881643
3022904.923624.4807011610-719.580701160957
3122040.421724.8271251319315.572874868083
3225981.525723.731056566257.768943433971
3326157.125487.0360351552670.063964844769
3425975.425397.1081407847578.29185921532
3522589.823057.9818800585-468.181880058498
3625370.424122.98824537521247.41175462485
3725091.124691.7569378872399.343062112842
3828760.927736.06531491081024.83468508915
3924325.925944.6742440767-1618.77424407666
4025821.725585.8092528767235.890747123276
4127645.728248.8761450524-603.176145052429
4226296.925853.9195624730442.980437526976
4324141.523813.4004330618328.09956693822
4427268.128140.4461907871-872.346190787106
4529060.327742.28281180831318.01718819168
4628226.427382.3271826435844.072817356496
4723268.524859.1423445400-1590.64234454005
4826938.225892.04252714061046.1574728594
4927217.526209.60931878721007.89068121278
5027540.528953.2522132727-1412.75221327267
5129167.627012.94765821472154.65234178528
5226671.526960.2727098072-288.772709807198
533018429068.32274234871115.67725765132
5428422.327543.1280443401879.171955659858
5523774.325002.8899051544-1228.58990515438
562960129395.6620896029205.337910397129
5728523.629692.5338973535-1168.93389735352
582362226743.8405376005-3121.84053760050
5921320.323065.2952572841-1744.99525728407
6020423.622848.2181011196-2424.61810111956
6121174.921979.1731004791-804.273100479103
6223050.224259.1341112828-1208.93411128282
6321202.921202.16475989830.735240101653204
6420476.420806.8806386235-330.480638623518
6523173.322931.571373455241.728626545
662246820738.60790754741729.39209245255
6719842.718432.08286042691410.61713957306

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 19435.1 & 20733.0066871605 & -1297.90668716053 \tabularnewline
2 & 22686.8 & 23225.9936841678 & -539.193684167838 \tabularnewline
3 & 20396.7 & 20839.1554091511 & -442.455409151094 \tabularnewline
4 & 19233.6 & 20864.3839587577 & -1630.78395875766 \tabularnewline
5 & 22751 & 23244.2138532124 & -493.213853212446 \tabularnewline
6 & 19864 & 20999.9733763344 & -1135.97337633439 \tabularnewline
7 & 17165.4 & 18507.9736137480 & -1342.57361374802 \tabularnewline
8 & 22309.7 & 22778.0258422410 & -468.325842240976 \tabularnewline
9 & 21786.3 & 22282.2263472698 & -495.926347269849 \tabularnewline
10 & 21927.6 & 21843.0751184517 & 84.5248815482946 \tabularnewline
11 & 20957.9 & 19502.7043248508 & 1455.19567514917 \tabularnewline
12 & 19726 & 20603.4694951917 & -877.469495191672 \tabularnewline
13 & 21315.7 & 21119.2762988946 & 196.423701105413 \tabularnewline
14 & 24771.5 & 24113.8066364537 & 657.693363546343 \tabularnewline
15 & 22592.4 & 21663.4586236527 & 928.941376347327 \tabularnewline
16 & 21942.1 & 21841.3256652779 & 100.774334722052 \tabularnewline
17 & 23973.7 & 24321.3824620196 & -347.682462019612 \tabularnewline
18 & 20815.7 & 22011.6904081440 & -1195.99040814404 \tabularnewline
19 & 19931.4 & 19414.5260624770 & 516.873937523033 \tabularnewline
20 & 24436.8 & 23559.234820803 & 877.565179196982 \tabularnewline
21 & 22838.7 & 23161.9209084131 & -323.220908413080 \tabularnewline
22 & 24465.3 & 22850.3490205196 & 1614.95097948040 \tabularnewline
23 & 23007.3 & 20658.6761932666 & 2348.62380673344 \tabularnewline
24 & 22720.8 & 21712.281631173 & 1008.51836882699 \tabularnewline
25 & 23045.7 & 22547.1776567914 & 498.522343208602 \tabularnewline
26 & 27198.5 & 25720.1480399122 & 1478.35196008783 \tabularnewline
27 & 22401.9 & 23424.9993050065 & -1023.09930500651 \tabularnewline
28 & 25122.7 & 23209.3277746570 & 1913.37222534305 \tabularnewline
29 & 26100.5 & 26013.8334239118 & 86.6665760881643 \tabularnewline
30 & 22904.9 & 23624.4807011610 & -719.580701160957 \tabularnewline
31 & 22040.4 & 21724.8271251319 & 315.572874868083 \tabularnewline
32 & 25981.5 & 25723.731056566 & 257.768943433971 \tabularnewline
33 & 26157.1 & 25487.0360351552 & 670.063964844769 \tabularnewline
34 & 25975.4 & 25397.1081407847 & 578.29185921532 \tabularnewline
35 & 22589.8 & 23057.9818800585 & -468.181880058498 \tabularnewline
36 & 25370.4 & 24122.9882453752 & 1247.41175462485 \tabularnewline
37 & 25091.1 & 24691.7569378872 & 399.343062112842 \tabularnewline
38 & 28760.9 & 27736.0653149108 & 1024.83468508915 \tabularnewline
39 & 24325.9 & 25944.6742440767 & -1618.77424407666 \tabularnewline
40 & 25821.7 & 25585.8092528767 & 235.890747123276 \tabularnewline
41 & 27645.7 & 28248.8761450524 & -603.176145052429 \tabularnewline
42 & 26296.9 & 25853.9195624730 & 442.980437526976 \tabularnewline
43 & 24141.5 & 23813.4004330618 & 328.09956693822 \tabularnewline
44 & 27268.1 & 28140.4461907871 & -872.346190787106 \tabularnewline
45 & 29060.3 & 27742.2828118083 & 1318.01718819168 \tabularnewline
46 & 28226.4 & 27382.3271826435 & 844.072817356496 \tabularnewline
47 & 23268.5 & 24859.1423445400 & -1590.64234454005 \tabularnewline
48 & 26938.2 & 25892.0425271406 & 1046.1574728594 \tabularnewline
49 & 27217.5 & 26209.6093187872 & 1007.89068121278 \tabularnewline
50 & 27540.5 & 28953.2522132727 & -1412.75221327267 \tabularnewline
51 & 29167.6 & 27012.9476582147 & 2154.65234178528 \tabularnewline
52 & 26671.5 & 26960.2727098072 & -288.772709807198 \tabularnewline
53 & 30184 & 29068.3227423487 & 1115.67725765132 \tabularnewline
54 & 28422.3 & 27543.1280443401 & 879.171955659858 \tabularnewline
55 & 23774.3 & 25002.8899051544 & -1228.58990515438 \tabularnewline
56 & 29601 & 29395.6620896029 & 205.337910397129 \tabularnewline
57 & 28523.6 & 29692.5338973535 & -1168.93389735352 \tabularnewline
58 & 23622 & 26743.8405376005 & -3121.84053760050 \tabularnewline
59 & 21320.3 & 23065.2952572841 & -1744.99525728407 \tabularnewline
60 & 20423.6 & 22848.2181011196 & -2424.61810111956 \tabularnewline
61 & 21174.9 & 21979.1731004791 & -804.273100479103 \tabularnewline
62 & 23050.2 & 24259.1341112828 & -1208.93411128282 \tabularnewline
63 & 21202.9 & 21202.1647598983 & 0.735240101653204 \tabularnewline
64 & 20476.4 & 20806.8806386235 & -330.480638623518 \tabularnewline
65 & 23173.3 & 22931.571373455 & 241.728626545 \tabularnewline
66 & 22468 & 20738.6079075474 & 1729.39209245255 \tabularnewline
67 & 19842.7 & 18432.0828604269 & 1410.61713957306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&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]19435.1[/C][C]20733.0066871605[/C][C]-1297.90668716053[/C][/ROW]
[ROW][C]2[/C][C]22686.8[/C][C]23225.9936841678[/C][C]-539.193684167838[/C][/ROW]
[ROW][C]3[/C][C]20396.7[/C][C]20839.1554091511[/C][C]-442.455409151094[/C][/ROW]
[ROW][C]4[/C][C]19233.6[/C][C]20864.3839587577[/C][C]-1630.78395875766[/C][/ROW]
[ROW][C]5[/C][C]22751[/C][C]23244.2138532124[/C][C]-493.213853212446[/C][/ROW]
[ROW][C]6[/C][C]19864[/C][C]20999.9733763344[/C][C]-1135.97337633439[/C][/ROW]
[ROW][C]7[/C][C]17165.4[/C][C]18507.9736137480[/C][C]-1342.57361374802[/C][/ROW]
[ROW][C]8[/C][C]22309.7[/C][C]22778.0258422410[/C][C]-468.325842240976[/C][/ROW]
[ROW][C]9[/C][C]21786.3[/C][C]22282.2263472698[/C][C]-495.926347269849[/C][/ROW]
[ROW][C]10[/C][C]21927.6[/C][C]21843.0751184517[/C][C]84.5248815482946[/C][/ROW]
[ROW][C]11[/C][C]20957.9[/C][C]19502.7043248508[/C][C]1455.19567514917[/C][/ROW]
[ROW][C]12[/C][C]19726[/C][C]20603.4694951917[/C][C]-877.469495191672[/C][/ROW]
[ROW][C]13[/C][C]21315.7[/C][C]21119.2762988946[/C][C]196.423701105413[/C][/ROW]
[ROW][C]14[/C][C]24771.5[/C][C]24113.8066364537[/C][C]657.693363546343[/C][/ROW]
[ROW][C]15[/C][C]22592.4[/C][C]21663.4586236527[/C][C]928.941376347327[/C][/ROW]
[ROW][C]16[/C][C]21942.1[/C][C]21841.3256652779[/C][C]100.774334722052[/C][/ROW]
[ROW][C]17[/C][C]23973.7[/C][C]24321.3824620196[/C][C]-347.682462019612[/C][/ROW]
[ROW][C]18[/C][C]20815.7[/C][C]22011.6904081440[/C][C]-1195.99040814404[/C][/ROW]
[ROW][C]19[/C][C]19931.4[/C][C]19414.5260624770[/C][C]516.873937523033[/C][/ROW]
[ROW][C]20[/C][C]24436.8[/C][C]23559.234820803[/C][C]877.565179196982[/C][/ROW]
[ROW][C]21[/C][C]22838.7[/C][C]23161.9209084131[/C][C]-323.220908413080[/C][/ROW]
[ROW][C]22[/C][C]24465.3[/C][C]22850.3490205196[/C][C]1614.95097948040[/C][/ROW]
[ROW][C]23[/C][C]23007.3[/C][C]20658.6761932666[/C][C]2348.62380673344[/C][/ROW]
[ROW][C]24[/C][C]22720.8[/C][C]21712.281631173[/C][C]1008.51836882699[/C][/ROW]
[ROW][C]25[/C][C]23045.7[/C][C]22547.1776567914[/C][C]498.522343208602[/C][/ROW]
[ROW][C]26[/C][C]27198.5[/C][C]25720.1480399122[/C][C]1478.35196008783[/C][/ROW]
[ROW][C]27[/C][C]22401.9[/C][C]23424.9993050065[/C][C]-1023.09930500651[/C][/ROW]
[ROW][C]28[/C][C]25122.7[/C][C]23209.3277746570[/C][C]1913.37222534305[/C][/ROW]
[ROW][C]29[/C][C]26100.5[/C][C]26013.8334239118[/C][C]86.6665760881643[/C][/ROW]
[ROW][C]30[/C][C]22904.9[/C][C]23624.4807011610[/C][C]-719.580701160957[/C][/ROW]
[ROW][C]31[/C][C]22040.4[/C][C]21724.8271251319[/C][C]315.572874868083[/C][/ROW]
[ROW][C]32[/C][C]25981.5[/C][C]25723.731056566[/C][C]257.768943433971[/C][/ROW]
[ROW][C]33[/C][C]26157.1[/C][C]25487.0360351552[/C][C]670.063964844769[/C][/ROW]
[ROW][C]34[/C][C]25975.4[/C][C]25397.1081407847[/C][C]578.29185921532[/C][/ROW]
[ROW][C]35[/C][C]22589.8[/C][C]23057.9818800585[/C][C]-468.181880058498[/C][/ROW]
[ROW][C]36[/C][C]25370.4[/C][C]24122.9882453752[/C][C]1247.41175462485[/C][/ROW]
[ROW][C]37[/C][C]25091.1[/C][C]24691.7569378872[/C][C]399.343062112842[/C][/ROW]
[ROW][C]38[/C][C]28760.9[/C][C]27736.0653149108[/C][C]1024.83468508915[/C][/ROW]
[ROW][C]39[/C][C]24325.9[/C][C]25944.6742440767[/C][C]-1618.77424407666[/C][/ROW]
[ROW][C]40[/C][C]25821.7[/C][C]25585.8092528767[/C][C]235.890747123276[/C][/ROW]
[ROW][C]41[/C][C]27645.7[/C][C]28248.8761450524[/C][C]-603.176145052429[/C][/ROW]
[ROW][C]42[/C][C]26296.9[/C][C]25853.9195624730[/C][C]442.980437526976[/C][/ROW]
[ROW][C]43[/C][C]24141.5[/C][C]23813.4004330618[/C][C]328.09956693822[/C][/ROW]
[ROW][C]44[/C][C]27268.1[/C][C]28140.4461907871[/C][C]-872.346190787106[/C][/ROW]
[ROW][C]45[/C][C]29060.3[/C][C]27742.2828118083[/C][C]1318.01718819168[/C][/ROW]
[ROW][C]46[/C][C]28226.4[/C][C]27382.3271826435[/C][C]844.072817356496[/C][/ROW]
[ROW][C]47[/C][C]23268.5[/C][C]24859.1423445400[/C][C]-1590.64234454005[/C][/ROW]
[ROW][C]48[/C][C]26938.2[/C][C]25892.0425271406[/C][C]1046.1574728594[/C][/ROW]
[ROW][C]49[/C][C]27217.5[/C][C]26209.6093187872[/C][C]1007.89068121278[/C][/ROW]
[ROW][C]50[/C][C]27540.5[/C][C]28953.2522132727[/C][C]-1412.75221327267[/C][/ROW]
[ROW][C]51[/C][C]29167.6[/C][C]27012.9476582147[/C][C]2154.65234178528[/C][/ROW]
[ROW][C]52[/C][C]26671.5[/C][C]26960.2727098072[/C][C]-288.772709807198[/C][/ROW]
[ROW][C]53[/C][C]30184[/C][C]29068.3227423487[/C][C]1115.67725765132[/C][/ROW]
[ROW][C]54[/C][C]28422.3[/C][C]27543.1280443401[/C][C]879.171955659858[/C][/ROW]
[ROW][C]55[/C][C]23774.3[/C][C]25002.8899051544[/C][C]-1228.58990515438[/C][/ROW]
[ROW][C]56[/C][C]29601[/C][C]29395.6620896029[/C][C]205.337910397129[/C][/ROW]
[ROW][C]57[/C][C]28523.6[/C][C]29692.5338973535[/C][C]-1168.93389735352[/C][/ROW]
[ROW][C]58[/C][C]23622[/C][C]26743.8405376005[/C][C]-3121.84053760050[/C][/ROW]
[ROW][C]59[/C][C]21320.3[/C][C]23065.2952572841[/C][C]-1744.99525728407[/C][/ROW]
[ROW][C]60[/C][C]20423.6[/C][C]22848.2181011196[/C][C]-2424.61810111956[/C][/ROW]
[ROW][C]61[/C][C]21174.9[/C][C]21979.1731004791[/C][C]-804.273100479103[/C][/ROW]
[ROW][C]62[/C][C]23050.2[/C][C]24259.1341112828[/C][C]-1208.93411128282[/C][/ROW]
[ROW][C]63[/C][C]21202.9[/C][C]21202.1647598983[/C][C]0.735240101653204[/C][/ROW]
[ROW][C]64[/C][C]20476.4[/C][C]20806.8806386235[/C][C]-330.480638623518[/C][/ROW]
[ROW][C]65[/C][C]23173.3[/C][C]22931.571373455[/C][C]241.728626545[/C][/ROW]
[ROW][C]66[/C][C]22468[/C][C]20738.6079075474[/C][C]1729.39209245255[/C][/ROW]
[ROW][C]67[/C][C]19842.7[/C][C]18432.0828604269[/C][C]1410.61713957306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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
119435.120733.0066871605-1297.90668716053
222686.823225.9936841678-539.193684167838
320396.720839.1554091511-442.455409151094
419233.620864.3839587577-1630.78395875766
52275123244.2138532124-493.213853212446
61986420999.9733763344-1135.97337633439
717165.418507.9736137480-1342.57361374802
822309.722778.0258422410-468.325842240976
921786.322282.2263472698-495.926347269849
1021927.621843.075118451784.5248815482946
1120957.919502.70432485081455.19567514917
121972620603.4694951917-877.469495191672
1321315.721119.2762988946196.423701105413
1424771.524113.8066364537657.693363546343
1522592.421663.4586236527928.941376347327
1621942.121841.3256652779100.774334722052
1723973.724321.3824620196-347.682462019612
1820815.722011.6904081440-1195.99040814404
1919931.419414.5260624770516.873937523033
2024436.823559.234820803877.565179196982
2122838.723161.9209084131-323.220908413080
2224465.322850.34902051961614.95097948040
2323007.320658.67619326662348.62380673344
2422720.821712.2816311731008.51836882699
2523045.722547.1776567914498.522343208602
2627198.525720.14803991221478.35196008783
2722401.923424.9993050065-1023.09930500651
2825122.723209.32777465701913.37222534305
2926100.526013.833423911886.6665760881643
3022904.923624.4807011610-719.580701160957
3122040.421724.8271251319315.572874868083
3225981.525723.731056566257.768943433971
3326157.125487.0360351552670.063964844769
3425975.425397.1081407847578.29185921532
3522589.823057.9818800585-468.181880058498
3625370.424122.98824537521247.41175462485
3725091.124691.7569378872399.343062112842
3828760.927736.06531491081024.83468508915
3924325.925944.6742440767-1618.77424407666
4025821.725585.8092528767235.890747123276
4127645.728248.8761450524-603.176145052429
4226296.925853.9195624730442.980437526976
4324141.523813.4004330618328.09956693822
4427268.128140.4461907871-872.346190787106
4529060.327742.28281180831318.01718819168
4628226.427382.3271826435844.072817356496
4723268.524859.1423445400-1590.64234454005
4826938.225892.04252714061046.1574728594
4927217.526209.60931878721007.89068121278
5027540.528953.2522132727-1412.75221327267
5129167.627012.94765821472154.65234178528
5226671.526960.2727098072-288.772709807198
533018429068.32274234871115.67725765132
5428422.327543.1280443401879.171955659858
5523774.325002.8899051544-1228.58990515438
562960129395.6620896029205.337910397129
5728523.629692.5338973535-1168.93389735352
582362226743.8405376005-3121.84053760050
5921320.323065.2952572841-1744.99525728407
6020423.622848.2181011196-2424.61810111956
6121174.921979.1731004791-804.273100479103
6223050.224259.1341112828-1208.93411128282
6321202.921202.16475989830.735240101653204
6420476.420806.8806386235-330.480638623518
6523173.322931.571373455241.728626545
662246820738.60790754741729.39209245255
6719842.718432.08286042691410.61713957306






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.08160564986103190.1632112997220640.918394350138968
210.02996176134267730.05992352268535460.970038238657323
220.01134985811411850.02269971622823700.988650141885882
230.007229063103817570.01445812620763510.992770936896182
240.01122821670040810.02245643340081610.988771783299592
250.007652746274358960.01530549254871790.99234725372564
260.003691580596699010.007383161193398020.9963084194033
270.02020677710173780.04041355420347560.979793222898262
280.02133751901517600.04267503803035190.978662480984824
290.01191097418620050.02382194837240110.9880890258138
300.01128848770947650.02257697541895290.988711512290524
310.006217302371210230.01243460474242050.99378269762879
320.002893062043017920.005786124086035840.997106937956982
330.001511501932229670.003023003864459340.99848849806777
340.0006533759295736660.001306751859147330.999346624070426
350.003592707496510430.007185414993020850.99640729250349
360.002092699072921520.004185398145843040.997907300927078
370.0009180905257131330.001836181051426270.999081909474287
380.0007463948495886020.001492789699177200.999253605150411
390.001289292588635160.002578585177270310.998710707411365
400.0005826278730341160.001165255746068230.999417372126966
410.0005595974355520290.001119194871104060.999440402564448
420.001499526422867080.002999052845734160.998500473577133
430.005434353977198580.01086870795439720.994565646022801
440.02415377366516230.04830754733032450.975846226334838
450.1363072004075080.2726144008150160.863692799592492
460.1023433993084950.2046867986169900.897656600691505
470.1183131662947880.2366263325895770.881686833705212

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.0816056498610319 & 0.163211299722064 & 0.918394350138968 \tabularnewline
21 & 0.0299617613426773 & 0.0599235226853546 & 0.970038238657323 \tabularnewline
22 & 0.0113498581141185 & 0.0226997162282370 & 0.988650141885882 \tabularnewline
23 & 0.00722906310381757 & 0.0144581262076351 & 0.992770936896182 \tabularnewline
24 & 0.0112282167004081 & 0.0224564334008161 & 0.988771783299592 \tabularnewline
25 & 0.00765274627435896 & 0.0153054925487179 & 0.99234725372564 \tabularnewline
26 & 0.00369158059669901 & 0.00738316119339802 & 0.9963084194033 \tabularnewline
27 & 0.0202067771017378 & 0.0404135542034756 & 0.979793222898262 \tabularnewline
28 & 0.0213375190151760 & 0.0426750380303519 & 0.978662480984824 \tabularnewline
29 & 0.0119109741862005 & 0.0238219483724011 & 0.9880890258138 \tabularnewline
30 & 0.0112884877094765 & 0.0225769754189529 & 0.988711512290524 \tabularnewline
31 & 0.00621730237121023 & 0.0124346047424205 & 0.99378269762879 \tabularnewline
32 & 0.00289306204301792 & 0.00578612408603584 & 0.997106937956982 \tabularnewline
33 & 0.00151150193222967 & 0.00302300386445934 & 0.99848849806777 \tabularnewline
34 & 0.000653375929573666 & 0.00130675185914733 & 0.999346624070426 \tabularnewline
35 & 0.00359270749651043 & 0.00718541499302085 & 0.99640729250349 \tabularnewline
36 & 0.00209269907292152 & 0.00418539814584304 & 0.997907300927078 \tabularnewline
37 & 0.000918090525713133 & 0.00183618105142627 & 0.999081909474287 \tabularnewline
38 & 0.000746394849588602 & 0.00149278969917720 & 0.999253605150411 \tabularnewline
39 & 0.00128929258863516 & 0.00257858517727031 & 0.998710707411365 \tabularnewline
40 & 0.000582627873034116 & 0.00116525574606823 & 0.999417372126966 \tabularnewline
41 & 0.000559597435552029 & 0.00111919487110406 & 0.999440402564448 \tabularnewline
42 & 0.00149952642286708 & 0.00299905284573416 & 0.998500473577133 \tabularnewline
43 & 0.00543435397719858 & 0.0108687079543972 & 0.994565646022801 \tabularnewline
44 & 0.0241537736651623 & 0.0483075473303245 & 0.975846226334838 \tabularnewline
45 & 0.136307200407508 & 0.272614400815016 & 0.863692799592492 \tabularnewline
46 & 0.102343399308495 & 0.204686798616990 & 0.897656600691505 \tabularnewline
47 & 0.118313166294788 & 0.236626332589577 & 0.881686833705212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&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]20[/C][C]0.0816056498610319[/C][C]0.163211299722064[/C][C]0.918394350138968[/C][/ROW]
[ROW][C]21[/C][C]0.0299617613426773[/C][C]0.0599235226853546[/C][C]0.970038238657323[/C][/ROW]
[ROW][C]22[/C][C]0.0113498581141185[/C][C]0.0226997162282370[/C][C]0.988650141885882[/C][/ROW]
[ROW][C]23[/C][C]0.00722906310381757[/C][C]0.0144581262076351[/C][C]0.992770936896182[/C][/ROW]
[ROW][C]24[/C][C]0.0112282167004081[/C][C]0.0224564334008161[/C][C]0.988771783299592[/C][/ROW]
[ROW][C]25[/C][C]0.00765274627435896[/C][C]0.0153054925487179[/C][C]0.99234725372564[/C][/ROW]
[ROW][C]26[/C][C]0.00369158059669901[/C][C]0.00738316119339802[/C][C]0.9963084194033[/C][/ROW]
[ROW][C]27[/C][C]0.0202067771017378[/C][C]0.0404135542034756[/C][C]0.979793222898262[/C][/ROW]
[ROW][C]28[/C][C]0.0213375190151760[/C][C]0.0426750380303519[/C][C]0.978662480984824[/C][/ROW]
[ROW][C]29[/C][C]0.0119109741862005[/C][C]0.0238219483724011[/C][C]0.9880890258138[/C][/ROW]
[ROW][C]30[/C][C]0.0112884877094765[/C][C]0.0225769754189529[/C][C]0.988711512290524[/C][/ROW]
[ROW][C]31[/C][C]0.00621730237121023[/C][C]0.0124346047424205[/C][C]0.99378269762879[/C][/ROW]
[ROW][C]32[/C][C]0.00289306204301792[/C][C]0.00578612408603584[/C][C]0.997106937956982[/C][/ROW]
[ROW][C]33[/C][C]0.00151150193222967[/C][C]0.00302300386445934[/C][C]0.99848849806777[/C][/ROW]
[ROW][C]34[/C][C]0.000653375929573666[/C][C]0.00130675185914733[/C][C]0.999346624070426[/C][/ROW]
[ROW][C]35[/C][C]0.00359270749651043[/C][C]0.00718541499302085[/C][C]0.99640729250349[/C][/ROW]
[ROW][C]36[/C][C]0.00209269907292152[/C][C]0.00418539814584304[/C][C]0.997907300927078[/C][/ROW]
[ROW][C]37[/C][C]0.000918090525713133[/C][C]0.00183618105142627[/C][C]0.999081909474287[/C][/ROW]
[ROW][C]38[/C][C]0.000746394849588602[/C][C]0.00149278969917720[/C][C]0.999253605150411[/C][/ROW]
[ROW][C]39[/C][C]0.00128929258863516[/C][C]0.00257858517727031[/C][C]0.998710707411365[/C][/ROW]
[ROW][C]40[/C][C]0.000582627873034116[/C][C]0.00116525574606823[/C][C]0.999417372126966[/C][/ROW]
[ROW][C]41[/C][C]0.000559597435552029[/C][C]0.00111919487110406[/C][C]0.999440402564448[/C][/ROW]
[ROW][C]42[/C][C]0.00149952642286708[/C][C]0.00299905284573416[/C][C]0.998500473577133[/C][/ROW]
[ROW][C]43[/C][C]0.00543435397719858[/C][C]0.0108687079543972[/C][C]0.994565646022801[/C][/ROW]
[ROW][C]44[/C][C]0.0241537736651623[/C][C]0.0483075473303245[/C][C]0.975846226334838[/C][/ROW]
[ROW][C]45[/C][C]0.136307200407508[/C][C]0.272614400815016[/C][C]0.863692799592492[/C][/ROW]
[ROW][C]46[/C][C]0.102343399308495[/C][C]0.204686798616990[/C][C]0.897656600691505[/C][/ROW]
[ROW][C]47[/C][C]0.118313166294788[/C][C]0.236626332589577[/C][C]0.881686833705212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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
200.08160564986103190.1632112997220640.918394350138968
210.02996176134267730.05992352268535460.970038238657323
220.01134985811411850.02269971622823700.988650141885882
230.007229063103817570.01445812620763510.992770936896182
240.01122821670040810.02245643340081610.988771783299592
250.007652746274358960.01530549254871790.99234725372564
260.003691580596699010.007383161193398020.9963084194033
270.02020677710173780.04041355420347560.979793222898262
280.02133751901517600.04267503803035190.978662480984824
290.01191097418620050.02382194837240110.9880890258138
300.01128848770947650.02257697541895290.988711512290524
310.006217302371210230.01243460474242050.99378269762879
320.002893062043017920.005786124086035840.997106937956982
330.001511501932229670.003023003864459340.99848849806777
340.0006533759295736660.001306751859147330.999346624070426
350.003592707496510430.007185414993020850.99640729250349
360.002092699072921520.004185398145843040.997907300927078
370.0009180905257131330.001836181051426270.999081909474287
380.0007463948495886020.001492789699177200.999253605150411
390.001289292588635160.002578585177270310.998710707411365
400.0005826278730341160.001165255746068230.999417372126966
410.0005595974355520290.001119194871104060.999440402564448
420.001499526422867080.002999052845734160.998500473577133
430.005434353977198580.01086870795439720.994565646022801
440.02415377366516230.04830754733032450.975846226334838
450.1363072004075080.2726144008150160.863692799592492
460.1023433993084950.2046867986169900.897656600691505
470.1183131662947880.2366263325895770.881686833705212






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.428571428571429NOK
5% type I error level230.821428571428571NOK
10% type I error level240.857142857142857NOK

\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 & 12 & 0.428571428571429 & NOK \tabularnewline
5% type I error level & 23 & 0.821428571428571 & NOK \tabularnewline
10% type I error level & 24 & 0.857142857142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57378&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]12[/C][C]0.428571428571429[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]23[/C][C]0.821428571428571[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]24[/C][C]0.857142857142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57378&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57378&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 level120.428571428571429NOK
5% type I error level230.821428571428571NOK
10% type I error level240.857142857142857NOK


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')
}