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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 20 Dec 2009 07:49:21 -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/Dec/20/t1261320803qwssciaryzxotcv.htm/, Retrieved Tue, 04 Nov 2025 01:22:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69903, Retrieved Tue, 04 Nov 2025 01:22:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact386

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] [Multiple regressi...] [2009-11-17 17:36:08] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-    D      [Multiple Regression] [Multiple Regressi...] [2009-12-20 13:25:49] [73863f7f907331e734eff34b7de6fc83]
-    D          [Multiple Regression] [Multiple Regressi...] [2009-12-20 14:49:21] [8cd69d0f4298074aa572ca2f9b39b6ae] [Current]
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Dataset

Dataseries X:
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Histogram
Boxplots 
-1,2	23,6	0,2	-1,9	-1,6	-4,2	-2,2
-2,4	25,7	-1,2	0,2	-1,9	-1,6	-4,2
0,8	32,5	-2,4	-1,2	0,2	-1,9	-1,6
-0,1	33,5	0,8	-2,4	-1,2	0,2	-1,9
-1,5	34,5	-0,1	0,8	-2,4	-1,2	0,2
-4,4	27,9	-1,5	-0,1	0,8	-2,4	-1,2
-4,2	45,3	-4,4	-1,5	-0,1	0,8	-2,4
3,5	40,8	-4,2	-4,4	-1,5	-0,1	0,8
10	58,5	3,5	-4,2	-4,4	-1,5	-0,1
8,6	32,5	10	3,5	-4,2	-4,4	-1,5
9,5	35,5	8,6	10	3,5	-4,2	-4,4
9,9	46,7	9,5	8,6	10	3,5	-4,2
10,4	53,2	9,9	9,5	8,6	10	3,5
16	36,1	10,4	9,9	9,5	8,6	10
12,7	54	16	10,4	9,9	9,5	8,6
10,2	58,1	12,7	16	10,4	9,9	9,5
8,9	41,8	10,2	12,7	16	10,4	9,9
12,6	43,1	8,9	10,2	12,7	16	10,4
13,6	76	12,6	8,9	10,2	12,7	16
14,8	42,8	13,6	12,6	8,9	10,2	12,7
9,5	41	14,8	13,6	12,6	8,9	10,2
13,7	61,4	9,5	14,8	13,6	12,6	8,9
17	34,2	13,7	9,5	14,8	13,6	12,6
14,7	53,8	17	13,7	9,5	14,8	13,6
17,4	80,7	14,7	17	13,7	9,5	14,8
9	79,5	17,4	14,7	17	13,7	9,5
9,1	96,5	9	17,4	14,7	17	13,7
12,2	108,3	9,1	9	17,4	14,7	17
15,9	100,1	12,2	9,1	9	17,4	14,7
12,9	108,5	15,9	12,2	9,1	9	17,4
10,9	127,4	12,9	15,9	12,2	9,1	9
10,6	86,5	10,9	12,9	15,9	12,2	9,1
13,2	71,4	10,6	10,9	12,9	15,9	12,2
9,6	88,2	13,2	10,6	10,9	12,9	15,9
6,4	135,6	9,6	13,2	10,6	10,9	12,9
5,8	70,5	6,4	9,6	13,2	10,6	10,9
-1	87,5	5,8	6,4	9,6	13,2	10,6
-0,2	73,3	-1	5,8	6,4	9,6	13,2
2,7	92,2	-0,2	-1	5,8	6,4	9,6
3,6	61,1	2,7	-0,2	-1	5,8	6,4
-0,9	45,7	3,6	2,7	-0,2	-1	5,8
0,3	30,5	-0,9	3,6	2,7	-0,2	-1
-1,1	34,8	0,3	-0,9	3,6	2,7	-0,2
-2,5	29,2	-1,1	0,3	-0,9	3,6	2,7
-3,4	56,7	-2,5	-1,1	0,3	-0,9	3,6
-3,5	67,1	-3,4	-2,5	-1,1	0,3	-0,9
-3,9	41,8	-3,5	-3,4	-2,5	-1,1	0,3
-4,6	46,8	-3,9	-3,5	-3,4	-2,5	-1,1
-0,1	50,1	-4,6	-3,9	-3,5	-3,4	-2,5
4,3	81,9	-0,1	-4,6	-3,9	-3,5	-3,4
10,2	115,8	4,3	-0,1	-4,6	-3,9	-3,5
8,7	102,5	10,2	4,3	-0,1	-4,6	-3,9
13,3	106,6	8,7	10,2	4,3	-0,1	-4,6
15	101,4	13,3	8,7	10,2	4,3	-0,1
20,7	136,1	15	13,3	8,7	10,2	4,3
20,7	143,4	20,7	15	13,3	8,7	10,2
26,4	127,5	20,7	20,7	15	13,3	8,7
31,2	113,8	26,4	20,7	20,7	15	13,3
31,4	75,3	31,2	26,4	20,7	20,7	15
26,6	98,5	31,4	31,2	26,4	20,7	20,7
26,6	113,7	26,6	31,4	31,2	26,4	20,7
19,2	103,7	26,6	26,6	31,4	31,2	26,4
6,5	73,9	19,2	26,6	26,6	31,4	31,2
3,1	52,5	6,5	19,2	26,6	26,6	31,4
-0,2	63,9	3,1	6,5	19,2	26,6	26,6
-4	44,9	-0,2	3,1	6,5	19,2	26,6
-12,6	31,3	-4	-0,2	3,1	6,5	19,2
-13	24,9	-12,6	-4	-0,2	3,1	6,5
-17,6	22,8	-13	-12,6	-4	-0,2	3,1
-21,7	24,8	-17,6	-13	-12,6	-4	-0,2
-23,2	22,8	-21,7	-17,6	-13	-12,6	-4
-16,8	20,9	-23,2	-21,7	-17,6	-13	-12,6
-19,8	21,5	-16,8	-23,2	-21,7	-17,6	-13

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=69903&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=69903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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] = -0.322809223089442 + 0.0518061441391626X[t] + 0.975170502562991Y1[t] -0.116024070052944Y2[t] + 0.00885828143121708Y3[t] + 0.247106653868723Y4[t] -0.332969323286305Y5[t] -0.688673468306776M1[t] -1.09191559338719M2[t] -0.90814048713177M3[t] -0.371568623488736M4[t] -0.164833511373571M5[t] + 0.185268234324544M6[t] -1.15177125372001M7[t] + 1.4792396079914M8[t] + 0.75528855950583M9[t] + 0.176543249138199M10[t] + 0.611097713715677M11[t] -0.0455753246002475t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.322809223089442 +  0.0518061441391626X[t] +  0.975170502562991Y1[t] -0.116024070052944Y2[t] +  0.00885828143121708Y3[t] +  0.247106653868723Y4[t] -0.332969323286305Y5[t] -0.688673468306776M1[t] -1.09191559338719M2[t] -0.90814048713177M3[t] -0.371568623488736M4[t] -0.164833511373571M5[t] +  0.185268234324544M6[t] -1.15177125372001M7[t] +  1.4792396079914M8[t] +  0.75528855950583M9[t] +  0.176543249138199M10[t] +  0.611097713715677M11[t] -0.0455753246002475t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.322809223089442 +  0.0518061441391626X[t] +  0.975170502562991Y1[t] -0.116024070052944Y2[t] +  0.00885828143121708Y3[t] +  0.247106653868723Y4[t] -0.332969323286305Y5[t] -0.688673468306776M1[t] -1.09191559338719M2[t] -0.90814048713177M3[t] -0.371568623488736M4[t] -0.164833511373571M5[t] +  0.185268234324544M6[t] -1.15177125372001M7[t] +  1.4792396079914M8[t] +  0.75528855950583M9[t] +  0.176543249138199M10[t] +  0.611097713715677M11[t] -0.0455753246002475t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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] = -0.322809223089442 + 0.0518061441391626X[t] + 0.975170502562991Y1[t] -0.116024070052944Y2[t] + 0.00885828143121708Y3[t] + 0.247106653868723Y4[t] -0.332969323286305Y5[t] -0.688673468306776M1[t] -1.09191559338719M2[t] -0.90814048713177M3[t] -0.371568623488736M4[t] -0.164833511373571M5[t] + 0.185268234324544M6[t] -1.15177125372001M7[t] + 1.4792396079914M8[t] + 0.75528855950583M9[t] + 0.176543249138199M10[t] + 0.611097713715677M11[t] -0.0455753246002475t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.3228092230894421.850837-0.17440.8621930.431097
X0.05180614413916260.0197552.62250.011320.00566
Y10.9751705025629910.129627.523300
Y2-0.1160240700529440.188871-0.61430.5415940.270797
Y30.008858281431217080.191860.04620.9633450.481672
Y40.2471066538687230.1903091.29840.1996510.099825
Y5-0.3329693232863050.132367-2.51550.0148930.007447
M1-0.6886734683067762.086495-0.33010.742630.371315
M2-1.091915593387192.193078-0.49790.6205820.310291
M3-0.908140487131772.253233-0.4030.6885110.344255
M4-0.3715686234887362.226363-0.16690.8680760.434038
M5-0.1648335113735712.203134-0.07480.9406360.470318
M60.1852682343245442.192780.08450.9329790.46649
M7-1.151771253720012.232651-0.51590.6080470.304023
M81.47923960799142.1826470.67770.5008380.250419
M90.755288559505832.1818340.34620.7305590.36528
M100.1765432491381992.1832370.08090.935850.467925
M110.6110977137156772.165320.28220.7788530.389427
t-0.04557532460024750.025781-1.76780.0827510.041376

\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) & -0.322809223089442 & 1.850837 & -0.1744 & 0.862193 & 0.431097 \tabularnewline
X & 0.0518061441391626 & 0.019755 & 2.6225 & 0.01132 & 0.00566 \tabularnewline
Y1 & 0.975170502562991 & 0.12962 & 7.5233 & 0 & 0 \tabularnewline
Y2 & -0.116024070052944 & 0.188871 & -0.6143 & 0.541594 & 0.270797 \tabularnewline
Y3 & 0.00885828143121708 & 0.19186 & 0.0462 & 0.963345 & 0.481672 \tabularnewline
Y4 & 0.247106653868723 & 0.190309 & 1.2984 & 0.199651 & 0.099825 \tabularnewline
Y5 & -0.332969323286305 & 0.132367 & -2.5155 & 0.014893 & 0.007447 \tabularnewline
M1 & -0.688673468306776 & 2.086495 & -0.3301 & 0.74263 & 0.371315 \tabularnewline
M2 & -1.09191559338719 & 2.193078 & -0.4979 & 0.620582 & 0.310291 \tabularnewline
M3 & -0.90814048713177 & 2.253233 & -0.403 & 0.688511 & 0.344255 \tabularnewline
M4 & -0.371568623488736 & 2.226363 & -0.1669 & 0.868076 & 0.434038 \tabularnewline
M5 & -0.164833511373571 & 2.203134 & -0.0748 & 0.940636 & 0.470318 \tabularnewline
M6 & 0.185268234324544 & 2.19278 & 0.0845 & 0.932979 & 0.46649 \tabularnewline
M7 & -1.15177125372001 & 2.232651 & -0.5159 & 0.608047 & 0.304023 \tabularnewline
M8 & 1.4792396079914 & 2.182647 & 0.6777 & 0.500838 & 0.250419 \tabularnewline
M9 & 0.75528855950583 & 2.181834 & 0.3462 & 0.730559 & 0.36528 \tabularnewline
M10 & 0.176543249138199 & 2.183237 & 0.0809 & 0.93585 & 0.467925 \tabularnewline
M11 & 0.611097713715677 & 2.16532 & 0.2822 & 0.778853 & 0.389427 \tabularnewline
t & -0.0455753246002475 & 0.025781 & -1.7678 & 0.082751 & 0.041376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&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]-0.322809223089442[/C][C]1.850837[/C][C]-0.1744[/C][C]0.862193[/C][C]0.431097[/C][/ROW]
[ROW][C]X[/C][C]0.0518061441391626[/C][C]0.019755[/C][C]2.6225[/C][C]0.01132[/C][C]0.00566[/C][/ROW]
[ROW][C]Y1[/C][C]0.975170502562991[/C][C]0.12962[/C][C]7.5233[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.116024070052944[/C][C]0.188871[/C][C]-0.6143[/C][C]0.541594[/C][C]0.270797[/C][/ROW]
[ROW][C]Y3[/C][C]0.00885828143121708[/C][C]0.19186[/C][C]0.0462[/C][C]0.963345[/C][C]0.481672[/C][/ROW]
[ROW][C]Y4[/C][C]0.247106653868723[/C][C]0.190309[/C][C]1.2984[/C][C]0.199651[/C][C]0.099825[/C][/ROW]
[ROW][C]Y5[/C][C]-0.332969323286305[/C][C]0.132367[/C][C]-2.5155[/C][C]0.014893[/C][C]0.007447[/C][/ROW]
[ROW][C]M1[/C][C]-0.688673468306776[/C][C]2.086495[/C][C]-0.3301[/C][C]0.74263[/C][C]0.371315[/C][/ROW]
[ROW][C]M2[/C][C]-1.09191559338719[/C][C]2.193078[/C][C]-0.4979[/C][C]0.620582[/C][C]0.310291[/C][/ROW]
[ROW][C]M3[/C][C]-0.90814048713177[/C][C]2.253233[/C][C]-0.403[/C][C]0.688511[/C][C]0.344255[/C][/ROW]
[ROW][C]M4[/C][C]-0.371568623488736[/C][C]2.226363[/C][C]-0.1669[/C][C]0.868076[/C][C]0.434038[/C][/ROW]
[ROW][C]M5[/C][C]-0.164833511373571[/C][C]2.203134[/C][C]-0.0748[/C][C]0.940636[/C][C]0.470318[/C][/ROW]
[ROW][C]M6[/C][C]0.185268234324544[/C][C]2.19278[/C][C]0.0845[/C][C]0.932979[/C][C]0.46649[/C][/ROW]
[ROW][C]M7[/C][C]-1.15177125372001[/C][C]2.232651[/C][C]-0.5159[/C][C]0.608047[/C][C]0.304023[/C][/ROW]
[ROW][C]M8[/C][C]1.4792396079914[/C][C]2.182647[/C][C]0.6777[/C][C]0.500838[/C][C]0.250419[/C][/ROW]
[ROW][C]M9[/C][C]0.75528855950583[/C][C]2.181834[/C][C]0.3462[/C][C]0.730559[/C][C]0.36528[/C][/ROW]
[ROW][C]M10[/C][C]0.176543249138199[/C][C]2.183237[/C][C]0.0809[/C][C]0.93585[/C][C]0.467925[/C][/ROW]
[ROW][C]M11[/C][C]0.611097713715677[/C][C]2.16532[/C][C]0.2822[/C][C]0.778853[/C][C]0.389427[/C][/ROW]
[ROW][C]t[/C][C]-0.0455753246002475[/C][C]0.025781[/C][C]-1.7678[/C][C]0.082751[/C][C]0.041376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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)-0.3228092230894421.850837-0.17440.8621930.431097
X0.05180614413916260.0197552.62250.011320.00566
Y10.9751705025629910.129627.523300
Y2-0.1160240700529440.188871-0.61430.5415940.270797
Y30.008858281431217080.191860.04620.9633450.481672
Y40.2471066538687230.1903091.29840.1996510.099825
Y5-0.3329693232863050.132367-2.51550.0148930.007447
M1-0.6886734683067762.086495-0.33010.742630.371315
M2-1.091915593387192.193078-0.49790.6205820.310291
M3-0.908140487131772.253233-0.4030.6885110.344255
M4-0.3715686234887362.226363-0.16690.8680760.434038
M5-0.1648335113735712.203134-0.07480.9406360.470318
M60.1852682343245442.192780.08450.9329790.46649
M7-1.151771253720012.232651-0.51590.6080470.304023
M81.47923960799142.1826470.67770.5008380.250419
M90.755288559505832.1818340.34620.7305590.36528
M100.1765432491381992.1832370.08090.935850.467925
M110.6110977137156772.165320.28220.7788530.389427
t-0.04557532460024750.025781-1.76780.0827510.041376






Multiple Linear Regression - Regression Statistics
Multiple R0.961390629342346
R-squared0.924271942187273
Adjusted R-squared0.899029256249697
F-TEST (value)36.6154356344236
F-TEST (DF numerator)18
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.71751652208532
Sum Squared Residuals746.276170966775

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.961390629342346 \tabularnewline
R-squared & 0.924271942187273 \tabularnewline
Adjusted R-squared & 0.899029256249697 \tabularnewline
F-TEST (value) & 36.6154356344236 \tabularnewline
F-TEST (DF numerator) & 18 \tabularnewline
F-TEST (DF denominator) & 54 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.71751652208532 \tabularnewline
Sum Squared Residuals & 746.276170966775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.961390629342346[/C][/ROW]
[ROW][C]R-squared[/C][C]0.924271942187273[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.899029256249697[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]36.6154356344236[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]18[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]54[/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]3.71751652208532[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]746.276170966775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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 R0.961390629342346
R-squared0.924271942187273
Adjusted R-squared0.899029256249697
F-TEST (value)36.6154356344236
F-TEST (DF numerator)18
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.71751652208532
Sum Squared Residuals746.276170966775






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1-1.20.261558133992251-1.46155813399225
2-2.4-0.381597201493626-2.01840279850637
30.8-1.820136390393042.62013639039304
4-0.12.5888539611605-2.6888539611605
5-1.50.497074584303551-1.99707458430355
6-4.4-0.603161017919336-3.79683898208066
7-4.2-2.56757765486589-1.63242234513411
83.5-0.9840652797165564.48406527971656
9106.57701921357623.4229807864238
108.69.80228117090963-1.20228117090963
119.59.310524719696420.189475280303575
129.912.1678738455548-2.26787384555476
1310.411.0859393943683-0.685939394368294
14167.690135039679168.30986496032084
1512.714.8507039344068-2.15070393440679
1610.211.4899076249712-1.28990762497121
178.98.791552411419670.108447588580332
1812.69.37384561299763.2261543870024
1913.610.7523892213352.84761077866499
2014.812.63325858270552.16674141729452
219.513.3686219826737-3.86862198267375
2213.79.84952716151513.85047283848491
231712.56577295837914.43422704162089
2414.715.571871679197-0.871871679197
2517.411.93341290512725.46658709487283
26917.1540614889104-8.15406148891044
279.19.06487526293180.0351247370681950
2812.29.596076830639162.60392316936084
2915.913.70246023213472.19753976786525
3012.914.7167872690934-1.81678726909335
3110.913.8076216672225-2.90762166722246
3210.613.4374264500346-2.83742645003463
3313.211.68063916261751.51936083738247
349.612.5058892562393-2.90588925623931
356.412.0402404147405-5.64024041474054
365.85.9229666190873-0.122966619087303
37-16.56607528306986-7.56607528306986
38-0.2-2.963585083835172.76358508383517
392.70.1254842030526422.57451579694736
403.62.597486389220451.00251361077955
41-0.91.02855817895485-1.92855817895485
420.3-1.459491977851291.75949197785129
43-1.1-0.468821161505506-0.631178838494494
44-2.5-0.461044934714281-2.03895506528572
45-3.4-2.40972974513665-0.990270254863347
46-3.5-1.42799788986268-2.07200211013732
47-3.9-3.10072368117839-0.799276318821605
48-4.6-3.76459650892189-0.835403491078113
49-0.1-4.721219513966734.62121951396673
504.31.218300943546823.08169905645318
5110.26.809624381337813.39037561866219
528.711.8546745982653-3.15467459826532
5313.311.46497671660101.83502328339904
541515.8011027877226-0.801102787722553
5520.717.31981712203913.38018287796087
5620.723.3502375632766-2.65023756327655
5726.422.74685997023493.65314002976508
5831.225.91018165378735.28981834621268
5931.429.16656553487242.23343446512764
6026.627.5024806662695-0.902480666269482
6126.624.30268971588642.29731028411364
6219.223.1826848131924-3.98268481319238
636.512.969448608664-6.469448608664
643.1-0.4269994042566313.52699940425663
65-0.20.0153778765862193-0.215377876586219
66-4-5.429082674042881.42908267404288
67-12.6-11.5434291942252-1.05657080577479
68-13-13.87581238158580.875812381585828
69-17.6-13.8634105839657-3.73658941603426
70-21.7-18.7398813525887-2.96011864741131
71-23.2-22.7823799465100-0.417620053489954
72-16.8-21.80059630118675.00059630118666
73-19.8-17.1284559184772-2.67154408152278

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -1.2 & 0.261558133992251 & -1.46155813399225 \tabularnewline
2 & -2.4 & -0.381597201493626 & -2.01840279850637 \tabularnewline
3 & 0.8 & -1.82013639039304 & 2.62013639039304 \tabularnewline
4 & -0.1 & 2.5888539611605 & -2.6888539611605 \tabularnewline
5 & -1.5 & 0.497074584303551 & -1.99707458430355 \tabularnewline
6 & -4.4 & -0.603161017919336 & -3.79683898208066 \tabularnewline
7 & -4.2 & -2.56757765486589 & -1.63242234513411 \tabularnewline
8 & 3.5 & -0.984065279716556 & 4.48406527971656 \tabularnewline
9 & 10 & 6.5770192135762 & 3.4229807864238 \tabularnewline
10 & 8.6 & 9.80228117090963 & -1.20228117090963 \tabularnewline
11 & 9.5 & 9.31052471969642 & 0.189475280303575 \tabularnewline
12 & 9.9 & 12.1678738455548 & -2.26787384555476 \tabularnewline
13 & 10.4 & 11.0859393943683 & -0.685939394368294 \tabularnewline
14 & 16 & 7.69013503967916 & 8.30986496032084 \tabularnewline
15 & 12.7 & 14.8507039344068 & -2.15070393440679 \tabularnewline
16 & 10.2 & 11.4899076249712 & -1.28990762497121 \tabularnewline
17 & 8.9 & 8.79155241141967 & 0.108447588580332 \tabularnewline
18 & 12.6 & 9.3738456129976 & 3.2261543870024 \tabularnewline
19 & 13.6 & 10.752389221335 & 2.84761077866499 \tabularnewline
20 & 14.8 & 12.6332585827055 & 2.16674141729452 \tabularnewline
21 & 9.5 & 13.3686219826737 & -3.86862198267375 \tabularnewline
22 & 13.7 & 9.8495271615151 & 3.85047283848491 \tabularnewline
23 & 17 & 12.5657729583791 & 4.43422704162089 \tabularnewline
24 & 14.7 & 15.571871679197 & -0.871871679197 \tabularnewline
25 & 17.4 & 11.9334129051272 & 5.46658709487283 \tabularnewline
26 & 9 & 17.1540614889104 & -8.15406148891044 \tabularnewline
27 & 9.1 & 9.0648752629318 & 0.0351247370681950 \tabularnewline
28 & 12.2 & 9.59607683063916 & 2.60392316936084 \tabularnewline
29 & 15.9 & 13.7024602321347 & 2.19753976786525 \tabularnewline
30 & 12.9 & 14.7167872690934 & -1.81678726909335 \tabularnewline
31 & 10.9 & 13.8076216672225 & -2.90762166722246 \tabularnewline
32 & 10.6 & 13.4374264500346 & -2.83742645003463 \tabularnewline
33 & 13.2 & 11.6806391626175 & 1.51936083738247 \tabularnewline
34 & 9.6 & 12.5058892562393 & -2.90588925623931 \tabularnewline
35 & 6.4 & 12.0402404147405 & -5.64024041474054 \tabularnewline
36 & 5.8 & 5.9229666190873 & -0.122966619087303 \tabularnewline
37 & -1 & 6.56607528306986 & -7.56607528306986 \tabularnewline
38 & -0.2 & -2.96358508383517 & 2.76358508383517 \tabularnewline
39 & 2.7 & 0.125484203052642 & 2.57451579694736 \tabularnewline
40 & 3.6 & 2.59748638922045 & 1.00251361077955 \tabularnewline
41 & -0.9 & 1.02855817895485 & -1.92855817895485 \tabularnewline
42 & 0.3 & -1.45949197785129 & 1.75949197785129 \tabularnewline
43 & -1.1 & -0.468821161505506 & -0.631178838494494 \tabularnewline
44 & -2.5 & -0.461044934714281 & -2.03895506528572 \tabularnewline
45 & -3.4 & -2.40972974513665 & -0.990270254863347 \tabularnewline
46 & -3.5 & -1.42799788986268 & -2.07200211013732 \tabularnewline
47 & -3.9 & -3.10072368117839 & -0.799276318821605 \tabularnewline
48 & -4.6 & -3.76459650892189 & -0.835403491078113 \tabularnewline
49 & -0.1 & -4.72121951396673 & 4.62121951396673 \tabularnewline
50 & 4.3 & 1.21830094354682 & 3.08169905645318 \tabularnewline
51 & 10.2 & 6.80962438133781 & 3.39037561866219 \tabularnewline
52 & 8.7 & 11.8546745982653 & -3.15467459826532 \tabularnewline
53 & 13.3 & 11.4649767166010 & 1.83502328339904 \tabularnewline
54 & 15 & 15.8011027877226 & -0.801102787722553 \tabularnewline
55 & 20.7 & 17.3198171220391 & 3.38018287796087 \tabularnewline
56 & 20.7 & 23.3502375632766 & -2.65023756327655 \tabularnewline
57 & 26.4 & 22.7468599702349 & 3.65314002976508 \tabularnewline
58 & 31.2 & 25.9101816537873 & 5.28981834621268 \tabularnewline
59 & 31.4 & 29.1665655348724 & 2.23343446512764 \tabularnewline
60 & 26.6 & 27.5024806662695 & -0.902480666269482 \tabularnewline
61 & 26.6 & 24.3026897158864 & 2.29731028411364 \tabularnewline
62 & 19.2 & 23.1826848131924 & -3.98268481319238 \tabularnewline
63 & 6.5 & 12.969448608664 & -6.469448608664 \tabularnewline
64 & 3.1 & -0.426999404256631 & 3.52699940425663 \tabularnewline
65 & -0.2 & 0.0153778765862193 & -0.215377876586219 \tabularnewline
66 & -4 & -5.42908267404288 & 1.42908267404288 \tabularnewline
67 & -12.6 & -11.5434291942252 & -1.05657080577479 \tabularnewline
68 & -13 & -13.8758123815858 & 0.875812381585828 \tabularnewline
69 & -17.6 & -13.8634105839657 & -3.73658941603426 \tabularnewline
70 & -21.7 & -18.7398813525887 & -2.96011864741131 \tabularnewline
71 & -23.2 & -22.7823799465100 & -0.417620053489954 \tabularnewline
72 & -16.8 & -21.8005963011867 & 5.00059630118666 \tabularnewline
73 & -19.8 & -17.1284559184772 & -2.67154408152278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&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]-1.2[/C][C]0.261558133992251[/C][C]-1.46155813399225[/C][/ROW]
[ROW][C]2[/C][C]-2.4[/C][C]-0.381597201493626[/C][C]-2.01840279850637[/C][/ROW]
[ROW][C]3[/C][C]0.8[/C][C]-1.82013639039304[/C][C]2.62013639039304[/C][/ROW]
[ROW][C]4[/C][C]-0.1[/C][C]2.5888539611605[/C][C]-2.6888539611605[/C][/ROW]
[ROW][C]5[/C][C]-1.5[/C][C]0.497074584303551[/C][C]-1.99707458430355[/C][/ROW]
[ROW][C]6[/C][C]-4.4[/C][C]-0.603161017919336[/C][C]-3.79683898208066[/C][/ROW]
[ROW][C]7[/C][C]-4.2[/C][C]-2.56757765486589[/C][C]-1.63242234513411[/C][/ROW]
[ROW][C]8[/C][C]3.5[/C][C]-0.984065279716556[/C][C]4.48406527971656[/C][/ROW]
[ROW][C]9[/C][C]10[/C][C]6.5770192135762[/C][C]3.4229807864238[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]9.80228117090963[/C][C]-1.20228117090963[/C][/ROW]
[ROW][C]11[/C][C]9.5[/C][C]9.31052471969642[/C][C]0.189475280303575[/C][/ROW]
[ROW][C]12[/C][C]9.9[/C][C]12.1678738455548[/C][C]-2.26787384555476[/C][/ROW]
[ROW][C]13[/C][C]10.4[/C][C]11.0859393943683[/C][C]-0.685939394368294[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]7.69013503967916[/C][C]8.30986496032084[/C][/ROW]
[ROW][C]15[/C][C]12.7[/C][C]14.8507039344068[/C][C]-2.15070393440679[/C][/ROW]
[ROW][C]16[/C][C]10.2[/C][C]11.4899076249712[/C][C]-1.28990762497121[/C][/ROW]
[ROW][C]17[/C][C]8.9[/C][C]8.79155241141967[/C][C]0.108447588580332[/C][/ROW]
[ROW][C]18[/C][C]12.6[/C][C]9.3738456129976[/C][C]3.2261543870024[/C][/ROW]
[ROW][C]19[/C][C]13.6[/C][C]10.752389221335[/C][C]2.84761077866499[/C][/ROW]
[ROW][C]20[/C][C]14.8[/C][C]12.6332585827055[/C][C]2.16674141729452[/C][/ROW]
[ROW][C]21[/C][C]9.5[/C][C]13.3686219826737[/C][C]-3.86862198267375[/C][/ROW]
[ROW][C]22[/C][C]13.7[/C][C]9.8495271615151[/C][C]3.85047283848491[/C][/ROW]
[ROW][C]23[/C][C]17[/C][C]12.5657729583791[/C][C]4.43422704162089[/C][/ROW]
[ROW][C]24[/C][C]14.7[/C][C]15.571871679197[/C][C]-0.871871679197[/C][/ROW]
[ROW][C]25[/C][C]17.4[/C][C]11.9334129051272[/C][C]5.46658709487283[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]17.1540614889104[/C][C]-8.15406148891044[/C][/ROW]
[ROW][C]27[/C][C]9.1[/C][C]9.0648752629318[/C][C]0.0351247370681950[/C][/ROW]
[ROW][C]28[/C][C]12.2[/C][C]9.59607683063916[/C][C]2.60392316936084[/C][/ROW]
[ROW][C]29[/C][C]15.9[/C][C]13.7024602321347[/C][C]2.19753976786525[/C][/ROW]
[ROW][C]30[/C][C]12.9[/C][C]14.7167872690934[/C][C]-1.81678726909335[/C][/ROW]
[ROW][C]31[/C][C]10.9[/C][C]13.8076216672225[/C][C]-2.90762166722246[/C][/ROW]
[ROW][C]32[/C][C]10.6[/C][C]13.4374264500346[/C][C]-2.83742645003463[/C][/ROW]
[ROW][C]33[/C][C]13.2[/C][C]11.6806391626175[/C][C]1.51936083738247[/C][/ROW]
[ROW][C]34[/C][C]9.6[/C][C]12.5058892562393[/C][C]-2.90588925623931[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]12.0402404147405[/C][C]-5.64024041474054[/C][/ROW]
[ROW][C]36[/C][C]5.8[/C][C]5.9229666190873[/C][C]-0.122966619087303[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]6.56607528306986[/C][C]-7.56607528306986[/C][/ROW]
[ROW][C]38[/C][C]-0.2[/C][C]-2.96358508383517[/C][C]2.76358508383517[/C][/ROW]
[ROW][C]39[/C][C]2.7[/C][C]0.125484203052642[/C][C]2.57451579694736[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]2.59748638922045[/C][C]1.00251361077955[/C][/ROW]
[ROW][C]41[/C][C]-0.9[/C][C]1.02855817895485[/C][C]-1.92855817895485[/C][/ROW]
[ROW][C]42[/C][C]0.3[/C][C]-1.45949197785129[/C][C]1.75949197785129[/C][/ROW]
[ROW][C]43[/C][C]-1.1[/C][C]-0.468821161505506[/C][C]-0.631178838494494[/C][/ROW]
[ROW][C]44[/C][C]-2.5[/C][C]-0.461044934714281[/C][C]-2.03895506528572[/C][/ROW]
[ROW][C]45[/C][C]-3.4[/C][C]-2.40972974513665[/C][C]-0.990270254863347[/C][/ROW]
[ROW][C]46[/C][C]-3.5[/C][C]-1.42799788986268[/C][C]-2.07200211013732[/C][/ROW]
[ROW][C]47[/C][C]-3.9[/C][C]-3.10072368117839[/C][C]-0.799276318821605[/C][/ROW]
[ROW][C]48[/C][C]-4.6[/C][C]-3.76459650892189[/C][C]-0.835403491078113[/C][/ROW]
[ROW][C]49[/C][C]-0.1[/C][C]-4.72121951396673[/C][C]4.62121951396673[/C][/ROW]
[ROW][C]50[/C][C]4.3[/C][C]1.21830094354682[/C][C]3.08169905645318[/C][/ROW]
[ROW][C]51[/C][C]10.2[/C][C]6.80962438133781[/C][C]3.39037561866219[/C][/ROW]
[ROW][C]52[/C][C]8.7[/C][C]11.8546745982653[/C][C]-3.15467459826532[/C][/ROW]
[ROW][C]53[/C][C]13.3[/C][C]11.4649767166010[/C][C]1.83502328339904[/C][/ROW]
[ROW][C]54[/C][C]15[/C][C]15.8011027877226[/C][C]-0.801102787722553[/C][/ROW]
[ROW][C]55[/C][C]20.7[/C][C]17.3198171220391[/C][C]3.38018287796087[/C][/ROW]
[ROW][C]56[/C][C]20.7[/C][C]23.3502375632766[/C][C]-2.65023756327655[/C][/ROW]
[ROW][C]57[/C][C]26.4[/C][C]22.7468599702349[/C][C]3.65314002976508[/C][/ROW]
[ROW][C]58[/C][C]31.2[/C][C]25.9101816537873[/C][C]5.28981834621268[/C][/ROW]
[ROW][C]59[/C][C]31.4[/C][C]29.1665655348724[/C][C]2.23343446512764[/C][/ROW]
[ROW][C]60[/C][C]26.6[/C][C]27.5024806662695[/C][C]-0.902480666269482[/C][/ROW]
[ROW][C]61[/C][C]26.6[/C][C]24.3026897158864[/C][C]2.29731028411364[/C][/ROW]
[ROW][C]62[/C][C]19.2[/C][C]23.1826848131924[/C][C]-3.98268481319238[/C][/ROW]
[ROW][C]63[/C][C]6.5[/C][C]12.969448608664[/C][C]-6.469448608664[/C][/ROW]
[ROW][C]64[/C][C]3.1[/C][C]-0.426999404256631[/C][C]3.52699940425663[/C][/ROW]
[ROW][C]65[/C][C]-0.2[/C][C]0.0153778765862193[/C][C]-0.215377876586219[/C][/ROW]
[ROW][C]66[/C][C]-4[/C][C]-5.42908267404288[/C][C]1.42908267404288[/C][/ROW]
[ROW][C]67[/C][C]-12.6[/C][C]-11.5434291942252[/C][C]-1.05657080577479[/C][/ROW]
[ROW][C]68[/C][C]-13[/C][C]-13.8758123815858[/C][C]0.875812381585828[/C][/ROW]
[ROW][C]69[/C][C]-17.6[/C][C]-13.8634105839657[/C][C]-3.73658941603426[/C][/ROW]
[ROW][C]70[/C][C]-21.7[/C][C]-18.7398813525887[/C][C]-2.96011864741131[/C][/ROW]
[ROW][C]71[/C][C]-23.2[/C][C]-22.7823799465100[/C][C]-0.417620053489954[/C][/ROW]
[ROW][C]72[/C][C]-16.8[/C][C]-21.8005963011867[/C][C]5.00059630118666[/C][/ROW]
[ROW][C]73[/C][C]-19.8[/C][C]-17.1284559184772[/C][C]-2.67154408152278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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
1-1.20.261558133992251-1.46155813399225
2-2.4-0.381597201493626-2.01840279850637
30.8-1.820136390393042.62013639039304
4-0.12.5888539611605-2.6888539611605
5-1.50.497074584303551-1.99707458430355
6-4.4-0.603161017919336-3.79683898208066
7-4.2-2.56757765486589-1.63242234513411
83.5-0.9840652797165564.48406527971656
9106.57701921357623.4229807864238
108.69.80228117090963-1.20228117090963
119.59.310524719696420.189475280303575
129.912.1678738455548-2.26787384555476
1310.411.0859393943683-0.685939394368294
14167.690135039679168.30986496032084
1512.714.8507039344068-2.15070393440679
1610.211.4899076249712-1.28990762497121
178.98.791552411419670.108447588580332
1812.69.37384561299763.2261543870024
1913.610.7523892213352.84761077866499
2014.812.63325858270552.16674141729452
219.513.3686219826737-3.86862198267375
2213.79.84952716151513.85047283848491
231712.56577295837914.43422704162089
2414.715.571871679197-0.871871679197
2517.411.93341290512725.46658709487283
26917.1540614889104-8.15406148891044
279.19.06487526293180.0351247370681950
2812.29.596076830639162.60392316936084
2915.913.70246023213472.19753976786525
3012.914.7167872690934-1.81678726909335
3110.913.8076216672225-2.90762166722246
3210.613.4374264500346-2.83742645003463
3313.211.68063916261751.51936083738247
349.612.5058892562393-2.90588925623931
356.412.0402404147405-5.64024041474054
365.85.9229666190873-0.122966619087303
37-16.56607528306986-7.56607528306986
38-0.2-2.963585083835172.76358508383517
392.70.1254842030526422.57451579694736
403.62.597486389220451.00251361077955
41-0.91.02855817895485-1.92855817895485
420.3-1.459491977851291.75949197785129
43-1.1-0.468821161505506-0.631178838494494
44-2.5-0.461044934714281-2.03895506528572
45-3.4-2.40972974513665-0.990270254863347
46-3.5-1.42799788986268-2.07200211013732
47-3.9-3.10072368117839-0.799276318821605
48-4.6-3.76459650892189-0.835403491078113
49-0.1-4.721219513966734.62121951396673
504.31.218300943546823.08169905645318
5110.26.809624381337813.39037561866219
528.711.8546745982653-3.15467459826532
5313.311.46497671660101.83502328339904
541515.8011027877226-0.801102787722553
5520.717.31981712203913.38018287796087
5620.723.3502375632766-2.65023756327655
5726.422.74685997023493.65314002976508
5831.225.91018165378735.28981834621268
5931.429.16656553487242.23343446512764
6026.627.5024806662695-0.902480666269482
6126.624.30268971588642.29731028411364
6219.223.1826848131924-3.98268481319238
636.512.969448608664-6.469448608664
643.1-0.4269994042566313.52699940425663
65-0.20.0153778765862193-0.215377876586219
66-4-5.429082674042881.42908267404288
67-12.6-11.5434291942252-1.05657080577479
68-13-13.87581238158580.875812381585828
69-17.6-13.8634105839657-3.73658941603426
70-21.7-18.7398813525887-2.96011864741131
71-23.2-22.7823799465100-0.417620053489954
72-16.8-21.80059630118675.00059630118666
73-19.8-17.1284559184772-2.67154408152278






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
220.412818722334430.825637444668860.58718127766557
230.5890035117309780.8219929765380440.410996488269022
240.4727717996399690.9455435992799390.527228200360031
250.4056864321155690.8113728642311370.594313567884431
260.6826568761755960.6346862476488080.317343123824404
270.5846655244061920.8306689511876170.415334475593808
280.4886193601904970.9772387203809940.511380639809503
290.4916988986544550.9833977973089090.508301101345545
300.4109000977677850.821800195535570.589099902232215
310.3744092760039880.7488185520079760.625590723996012
320.2854089330278250.5708178660556510.714591066972175
330.2651553448133380.5303106896266750.734844655186662
340.2631747276174090.5263494552348180.736825272382591
350.4857647546352260.9715295092704510.514235245364774
360.4057919215640420.8115838431280840.594208078435958
370.5926170408452910.8147659183094190.407382959154709
380.547872520062870.904254959874260.45212747993713
390.555625877118790.8887482457624210.444374122881211
400.5071972665684090.9856054668631820.492802733431591
410.4077720465168990.8155440930337970.592227953483101
420.3665903460519770.7331806921039540.633409653948023
430.2745261503710300.5490523007420610.72547384962897
440.2080077944809720.4160155889619440.791992205519028
450.1410024759303630.2820049518607260.858997524069637
460.1191227545661240.2382455091322490.880877245433876
470.09225789468828010.1845157893765600.90774210531172
480.1246827504162080.2493655008324160.875317249583792
490.1447454582124010.2894909164248020.855254541787599
500.1073832628523900.2147665257047800.89261673714761
510.237872977948450.47574595589690.76212702205155

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
22 & 0.41281872233443 & 0.82563744466886 & 0.58718127766557 \tabularnewline
23 & 0.589003511730978 & 0.821992976538044 & 0.410996488269022 \tabularnewline
24 & 0.472771799639969 & 0.945543599279939 & 0.527228200360031 \tabularnewline
25 & 0.405686432115569 & 0.811372864231137 & 0.594313567884431 \tabularnewline
26 & 0.682656876175596 & 0.634686247648808 & 0.317343123824404 \tabularnewline
27 & 0.584665524406192 & 0.830668951187617 & 0.415334475593808 \tabularnewline
28 & 0.488619360190497 & 0.977238720380994 & 0.511380639809503 \tabularnewline
29 & 0.491698898654455 & 0.983397797308909 & 0.508301101345545 \tabularnewline
30 & 0.410900097767785 & 0.82180019553557 & 0.589099902232215 \tabularnewline
31 & 0.374409276003988 & 0.748818552007976 & 0.625590723996012 \tabularnewline
32 & 0.285408933027825 & 0.570817866055651 & 0.714591066972175 \tabularnewline
33 & 0.265155344813338 & 0.530310689626675 & 0.734844655186662 \tabularnewline
34 & 0.263174727617409 & 0.526349455234818 & 0.736825272382591 \tabularnewline
35 & 0.485764754635226 & 0.971529509270451 & 0.514235245364774 \tabularnewline
36 & 0.405791921564042 & 0.811583843128084 & 0.594208078435958 \tabularnewline
37 & 0.592617040845291 & 0.814765918309419 & 0.407382959154709 \tabularnewline
38 & 0.54787252006287 & 0.90425495987426 & 0.45212747993713 \tabularnewline
39 & 0.55562587711879 & 0.888748245762421 & 0.444374122881211 \tabularnewline
40 & 0.507197266568409 & 0.985605466863182 & 0.492802733431591 \tabularnewline
41 & 0.407772046516899 & 0.815544093033797 & 0.592227953483101 \tabularnewline
42 & 0.366590346051977 & 0.733180692103954 & 0.633409653948023 \tabularnewline
43 & 0.274526150371030 & 0.549052300742061 & 0.72547384962897 \tabularnewline
44 & 0.208007794480972 & 0.416015588961944 & 0.791992205519028 \tabularnewline
45 & 0.141002475930363 & 0.282004951860726 & 0.858997524069637 \tabularnewline
46 & 0.119122754566124 & 0.238245509132249 & 0.880877245433876 \tabularnewline
47 & 0.0922578946882801 & 0.184515789376560 & 0.90774210531172 \tabularnewline
48 & 0.124682750416208 & 0.249365500832416 & 0.875317249583792 \tabularnewline
49 & 0.144745458212401 & 0.289490916424802 & 0.855254541787599 \tabularnewline
50 & 0.107383262852390 & 0.214766525704780 & 0.89261673714761 \tabularnewline
51 & 0.23787297794845 & 0.4757459558969 & 0.76212702205155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&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]22[/C][C]0.41281872233443[/C][C]0.82563744466886[/C][C]0.58718127766557[/C][/ROW]
[ROW][C]23[/C][C]0.589003511730978[/C][C]0.821992976538044[/C][C]0.410996488269022[/C][/ROW]
[ROW][C]24[/C][C]0.472771799639969[/C][C]0.945543599279939[/C][C]0.527228200360031[/C][/ROW]
[ROW][C]25[/C][C]0.405686432115569[/C][C]0.811372864231137[/C][C]0.594313567884431[/C][/ROW]
[ROW][C]26[/C][C]0.682656876175596[/C][C]0.634686247648808[/C][C]0.317343123824404[/C][/ROW]
[ROW][C]27[/C][C]0.584665524406192[/C][C]0.830668951187617[/C][C]0.415334475593808[/C][/ROW]
[ROW][C]28[/C][C]0.488619360190497[/C][C]0.977238720380994[/C][C]0.511380639809503[/C][/ROW]
[ROW][C]29[/C][C]0.491698898654455[/C][C]0.983397797308909[/C][C]0.508301101345545[/C][/ROW]
[ROW][C]30[/C][C]0.410900097767785[/C][C]0.82180019553557[/C][C]0.589099902232215[/C][/ROW]
[ROW][C]31[/C][C]0.374409276003988[/C][C]0.748818552007976[/C][C]0.625590723996012[/C][/ROW]
[ROW][C]32[/C][C]0.285408933027825[/C][C]0.570817866055651[/C][C]0.714591066972175[/C][/ROW]
[ROW][C]33[/C][C]0.265155344813338[/C][C]0.530310689626675[/C][C]0.734844655186662[/C][/ROW]
[ROW][C]34[/C][C]0.263174727617409[/C][C]0.526349455234818[/C][C]0.736825272382591[/C][/ROW]
[ROW][C]35[/C][C]0.485764754635226[/C][C]0.971529509270451[/C][C]0.514235245364774[/C][/ROW]
[ROW][C]36[/C][C]0.405791921564042[/C][C]0.811583843128084[/C][C]0.594208078435958[/C][/ROW]
[ROW][C]37[/C][C]0.592617040845291[/C][C]0.814765918309419[/C][C]0.407382959154709[/C][/ROW]
[ROW][C]38[/C][C]0.54787252006287[/C][C]0.90425495987426[/C][C]0.45212747993713[/C][/ROW]
[ROW][C]39[/C][C]0.55562587711879[/C][C]0.888748245762421[/C][C]0.444374122881211[/C][/ROW]
[ROW][C]40[/C][C]0.507197266568409[/C][C]0.985605466863182[/C][C]0.492802733431591[/C][/ROW]
[ROW][C]41[/C][C]0.407772046516899[/C][C]0.815544093033797[/C][C]0.592227953483101[/C][/ROW]
[ROW][C]42[/C][C]0.366590346051977[/C][C]0.733180692103954[/C][C]0.633409653948023[/C][/ROW]
[ROW][C]43[/C][C]0.274526150371030[/C][C]0.549052300742061[/C][C]0.72547384962897[/C][/ROW]
[ROW][C]44[/C][C]0.208007794480972[/C][C]0.416015588961944[/C][C]0.791992205519028[/C][/ROW]
[ROW][C]45[/C][C]0.141002475930363[/C][C]0.282004951860726[/C][C]0.858997524069637[/C][/ROW]
[ROW][C]46[/C][C]0.119122754566124[/C][C]0.238245509132249[/C][C]0.880877245433876[/C][/ROW]
[ROW][C]47[/C][C]0.0922578946882801[/C][C]0.184515789376560[/C][C]0.90774210531172[/C][/ROW]
[ROW][C]48[/C][C]0.124682750416208[/C][C]0.249365500832416[/C][C]0.875317249583792[/C][/ROW]
[ROW][C]49[/C][C]0.144745458212401[/C][C]0.289490916424802[/C][C]0.855254541787599[/C][/ROW]
[ROW][C]50[/C][C]0.107383262852390[/C][C]0.214766525704780[/C][C]0.89261673714761[/C][/ROW]
[ROW][C]51[/C][C]0.23787297794845[/C][C]0.4757459558969[/C][C]0.76212702205155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&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
220.412818722334430.825637444668860.58718127766557
230.5890035117309780.8219929765380440.410996488269022
240.4727717996399690.9455435992799390.527228200360031
250.4056864321155690.8113728642311370.594313567884431
260.6826568761755960.6346862476488080.317343123824404
270.5846655244061920.8306689511876170.415334475593808
280.4886193601904970.9772387203809940.511380639809503
290.4916988986544550.9833977973089090.508301101345545
300.4109000977677850.821800195535570.589099902232215
310.3744092760039880.7488185520079760.625590723996012
320.2854089330278250.5708178660556510.714591066972175
330.2651553448133380.5303106896266750.734844655186662
340.2631747276174090.5263494552348180.736825272382591
350.4857647546352260.9715295092704510.514235245364774
360.4057919215640420.8115838431280840.594208078435958
370.5926170408452910.8147659183094190.407382959154709
380.547872520062870.904254959874260.45212747993713
390.555625877118790.8887482457624210.444374122881211
400.5071972665684090.9856054668631820.492802733431591
410.4077720465168990.8155440930337970.592227953483101
420.3665903460519770.7331806921039540.633409653948023
430.2745261503710300.5490523007420610.72547384962897
440.2080077944809720.4160155889619440.791992205519028
450.1410024759303630.2820049518607260.858997524069637
460.1191227545661240.2382455091322490.880877245433876
470.09225789468828010.1845157893765600.90774210531172
480.1246827504162080.2493655008324160.875317249583792
490.1447454582124010.2894909164248020.855254541787599
500.1073832628523900.2147665257047800.89261673714761
510.237872977948450.47574595589690.76212702205155






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69903&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69903&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69903&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 4
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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')
}