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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 08:10:27 -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/t1261322907lhub228tel3oudq.htm/, Retrieved Sat, 27 Apr 2024 08:44:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69916, Retrieved Sat, 27 Apr 2024 08:44:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

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 15:10:27] [8cd69d0f4298074aa572ca2f9b39b6ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-1,2	23,6	0,2	-2,2
-2,4	25,7	-1,2	-4,2
0,8	32,5	-2,4	-1,6
-0,1	33,5	0,8	-1,9
-1,5	34,5	-0,1	0,2
-4,4	27,9	-1,5	-1,2
-4,2	45,3	-4,4	-2,4
3,5	40,8	-4,2	0,8
10	58,5	3,5	-0,1
8,6	32,5	10	-1,5
9,5	35,5	8,6	-4,4
9,9	46,7	9,5	-4,2
10,4	53,2	9,9	3,5
16	36,1	10,4	10
12,7	54	16	8,6
10,2	58,1	12,7	9,5
8,9	41,8	10,2	9,9
12,6	43,1	8,9	10,4
13,6	76	12,6	16
14,8	42,8	13,6	12,7
9,5	41	14,8	10,2
13,7	61,4	9,5	8,9
17	34,2	13,7	12,6
14,7	53,8	17	13,6
17,4	80,7	14,7	14,8
9	79,5	17,4	9,5
9,1	96,5	9	13,7
12,2	108,3	9,1	17
15,9	100,1	12,2	14,7
12,9	108,5	15,9	17,4
10,9	127,4	12,9	9
10,6	86,5	10,9	9,1
13,2	71,4	10,6	12,2
9,6	88,2	13,2	15,9
6,4	135,6	9,6	12,9
5,8	70,5	6,4	10,9
-1	87,5	5,8	10,6
-0,2	73,3	-1	13,2
2,7	92,2	-0,2	9,6
3,6	61,1	2,7	6,4
-0,9	45,7	3,6	5,8
0,3	30,5	-0,9	-1
-1,1	34,8	0,3	-0,2
-2,5	29,2	-1,1	2,7
-3,4	56,7	-2,5	3,6
-3,5	67,1	-3,4	-0,9
-3,9	41,8	-3,5	0,3
-4,6	46,8	-3,9	-1,1
-0,1	50,1	-4,6	-2,5
4,3	81,9	-0,1	-3,4
10,2	115,8	4,3	-3,5
8,7	102,5	10,2	-3,9
13,3	106,6	8,7	-4,6
15	101,4	13,3	-0,1
20,7	136,1	15	4,3
20,7	143,4	20,7	10,2
26,4	127,5	20,7	8,7
31,2	113,8	26,4	13,3
31,4	75,3	31,2	15
26,6	98,5	31,4	20,7
26,6	113,7	26,6	20,7
19,2	103,7	26,6	26,4
6,5	73,9	19,2	31,2
3,1	52,5	6,5	31,4
-0,2	63,9	3,1	26,6
-4	44,9	-0,2	26,6
-12,6	31,3	-4	19,2
-13	24,9	-12,6	6,5
-17,6	22,8	-13	3,1
-21,7	24,8	-17,6	-0,2
-23,2	22,8	-21,7	-4
-16,8	20,9	-23,2	-12,6
-19,8	21,5	-16,8	-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=69916&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=69916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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] = -0.228903714593018 + 0.0512220684067442X[t] + 0.953263571164633Y1[t] -0.166874438987276Y5[t] -0.775206618339435M1[t] -0.959994739976522M2[t] -0.952057839466697M3[t] -0.573275251722887M4[t] -0.176634951549861M5[t] -0.00332245912141396M6[t] -1.29637927379665M7[t] + 1.29435463178808M8[t] + 0.71759322481859M9[t] -0.0524909907347402M10[t] + 0.184537892904761M11[t] -0.0444618723895546t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.228903714593018 +  0.0512220684067442X[t] +  0.953263571164633Y1[t] -0.166874438987276Y5[t] -0.775206618339435M1[t] -0.959994739976522M2[t] -0.952057839466697M3[t] -0.573275251722887M4[t] -0.176634951549861M5[t] -0.00332245912141396M6[t] -1.29637927379665M7[t] +  1.29435463178808M8[t] +  0.71759322481859M9[t] -0.0524909907347402M10[t] +  0.184537892904761M11[t] -0.0444618723895546t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69916&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.228903714593018 +  0.0512220684067442X[t] +  0.953263571164633Y1[t] -0.166874438987276Y5[t] -0.775206618339435M1[t] -0.959994739976522M2[t] -0.952057839466697M3[t] -0.573275251722887M4[t] -0.176634951549861M5[t] -0.00332245912141396M6[t] -1.29637927379665M7[t] +  1.29435463178808M8[t] +  0.71759322481859M9[t] -0.0524909907347402M10[t] +  0.184537892904761M11[t] -0.0444618723895546t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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] = -0.228903714593018 + 0.0512220684067442X[t] + 0.953263571164633Y1[t] -0.166874438987276Y5[t] -0.775206618339435M1[t] -0.959994739976522M2[t] -0.952057839466697M3[t] -0.573275251722887M4[t] -0.176634951549861M5[t] -0.00332245912141396M6[t] -1.29637927379665M7[t] + 1.29435463178808M8[t] + 0.71759322481859M9[t] -0.0524909907347402M10[t] + 0.184537892904761M11[t] -0.0444618723895546t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.2289037145930181.840167-0.12440.9014420.450721
X0.05122206840674420.0196642.60490.01170.00585
Y10.9532635711646330.06862513.890900
Y5-0.1668744389872760.062741-2.65970.0101360.005068
M1-0.7752066183394352.075813-0.37340.7102010.355101
M2-0.9599947399765222.18014-0.44030.6613590.330679
M3-0.9520578394666972.237315-0.42550.6720490.336024
M4-0.5732752517228872.208944-0.25950.7961660.398083
M5-0.1766349515498612.189287-0.08070.9359780.467989
M6-0.003322459121413962.173918-0.00150.9987860.499393
M7-1.296379273796652.216391-0.58490.560920.28046
M81.294354631788082.1690920.59670.5530530.276526
M90.717593224818592.1548670.3330.7403480.370174
M10-0.05249099073474022.149686-0.02440.9806040.490302
M110.1845378929047612.1389320.08630.931550.465775
t-0.04446187238955460.025632-1.73460.0882130.044106

\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) & -0.228903714593018 & 1.840167 & -0.1244 & 0.901442 & 0.450721 \tabularnewline
X & 0.0512220684067442 & 0.019664 & 2.6049 & 0.0117 & 0.00585 \tabularnewline
Y1 & 0.953263571164633 & 0.068625 & 13.8909 & 0 & 0 \tabularnewline
Y5 & -0.166874438987276 & 0.062741 & -2.6597 & 0.010136 & 0.005068 \tabularnewline
M1 & -0.775206618339435 & 2.075813 & -0.3734 & 0.710201 & 0.355101 \tabularnewline
M2 & -0.959994739976522 & 2.18014 & -0.4403 & 0.661359 & 0.330679 \tabularnewline
M3 & -0.952057839466697 & 2.237315 & -0.4255 & 0.672049 & 0.336024 \tabularnewline
M4 & -0.573275251722887 & 2.208944 & -0.2595 & 0.796166 & 0.398083 \tabularnewline
M5 & -0.176634951549861 & 2.189287 & -0.0807 & 0.935978 & 0.467989 \tabularnewline
M6 & -0.00332245912141396 & 2.173918 & -0.0015 & 0.998786 & 0.499393 \tabularnewline
M7 & -1.29637927379665 & 2.216391 & -0.5849 & 0.56092 & 0.28046 \tabularnewline
M8 & 1.29435463178808 & 2.169092 & 0.5967 & 0.553053 & 0.276526 \tabularnewline
M9 & 0.71759322481859 & 2.154867 & 0.333 & 0.740348 & 0.370174 \tabularnewline
M10 & -0.0524909907347402 & 2.149686 & -0.0244 & 0.980604 & 0.490302 \tabularnewline
M11 & 0.184537892904761 & 2.138932 & 0.0863 & 0.93155 & 0.465775 \tabularnewline
t & -0.0444618723895546 & 0.025632 & -1.7346 & 0.088213 & 0.044106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69916&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]-0.228903714593018[/C][C]1.840167[/C][C]-0.1244[/C][C]0.901442[/C][C]0.450721[/C][/ROW]
[ROW][C]X[/C][C]0.0512220684067442[/C][C]0.019664[/C][C]2.6049[/C][C]0.0117[/C][C]0.00585[/C][/ROW]
[ROW][C]Y1[/C][C]0.953263571164633[/C][C]0.068625[/C][C]13.8909[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y5[/C][C]-0.166874438987276[/C][C]0.062741[/C][C]-2.6597[/C][C]0.010136[/C][C]0.005068[/C][/ROW]
[ROW][C]M1[/C][C]-0.775206618339435[/C][C]2.075813[/C][C]-0.3734[/C][C]0.710201[/C][C]0.355101[/C][/ROW]
[ROW][C]M2[/C][C]-0.959994739976522[/C][C]2.18014[/C][C]-0.4403[/C][C]0.661359[/C][C]0.330679[/C][/ROW]
[ROW][C]M3[/C][C]-0.952057839466697[/C][C]2.237315[/C][C]-0.4255[/C][C]0.672049[/C][C]0.336024[/C][/ROW]
[ROW][C]M4[/C][C]-0.573275251722887[/C][C]2.208944[/C][C]-0.2595[/C][C]0.796166[/C][C]0.398083[/C][/ROW]
[ROW][C]M5[/C][C]-0.176634951549861[/C][C]2.189287[/C][C]-0.0807[/C][C]0.935978[/C][C]0.467989[/C][/ROW]
[ROW][C]M6[/C][C]-0.00332245912141396[/C][C]2.173918[/C][C]-0.0015[/C][C]0.998786[/C][C]0.499393[/C][/ROW]
[ROW][C]M7[/C][C]-1.29637927379665[/C][C]2.216391[/C][C]-0.5849[/C][C]0.56092[/C][C]0.28046[/C][/ROW]
[ROW][C]M8[/C][C]1.29435463178808[/C][C]2.169092[/C][C]0.5967[/C][C]0.553053[/C][C]0.276526[/C][/ROW]
[ROW][C]M9[/C][C]0.71759322481859[/C][C]2.154867[/C][C]0.333[/C][C]0.740348[/C][C]0.370174[/C][/ROW]
[ROW][C]M10[/C][C]-0.0524909907347402[/C][C]2.149686[/C][C]-0.0244[/C][C]0.980604[/C][C]0.490302[/C][/ROW]
[ROW][C]M11[/C][C]0.184537892904761[/C][C]2.138932[/C][C]0.0863[/C][C]0.93155[/C][C]0.465775[/C][/ROW]
[ROW][C]t[/C][C]-0.0444618723895546[/C][C]0.025632[/C][C]-1.7346[/C][C]0.088213[/C][C]0.044106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69916&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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)-0.2289037145930181.840167-0.12440.9014420.450721
X0.05122206840674420.0196642.60490.01170.00585
Y10.9532635711646330.06862513.890900
Y5-0.1668744389872760.062741-2.65970.0101360.005068
M1-0.7752066183394352.075813-0.37340.7102010.355101
M2-0.9599947399765222.18014-0.44030.6613590.330679
M3-0.9520578394666972.237315-0.42550.6720490.336024
M4-0.5732752517228872.208944-0.25950.7961660.398083
M5-0.1766349515498612.189287-0.08070.9359780.467989
M6-0.003322459121413962.173918-0.00150.9987860.499393
M7-1.296379273796652.216391-0.58490.560920.28046
M81.294354631788082.1690920.59670.5530530.276526
M90.717593224818592.1548670.3330.7403480.370174
M10-0.05249099073474022.149686-0.02440.9806040.490302
M110.1845378929047612.1389320.08630.931550.465775
t-0.04446187238955460.025632-1.73460.0882130.044106






Multiple Linear Regression - Regression Statistics
Multiple R0.959537170376185
R-squared0.920711581333536
Adjusted R-squared0.899846208000257
F-TEST (value)44.1262931952921
F-TEST (DF numerator)15
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.70244681163037
Sum Squared Residuals781.36240639826

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.959537170376185 \tabularnewline
R-squared & 0.920711581333536 \tabularnewline
Adjusted R-squared & 0.899846208000257 \tabularnewline
F-TEST (value) & 44.1262931952921 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.70244681163037 \tabularnewline
Sum Squared Residuals & 781.36240639826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69916&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.959537170376185[/C][/ROW]
[ROW][C]R-squared[/C][C]0.920711581333536[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.899846208000257[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]44.1262931952921[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.70244681163037[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]781.36240639826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69916&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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 R0.959537170376185
R-squared0.920711581333536
Adjusted R-squared0.899846208000257
F-TEST (value)44.1262931952921
F-TEST (DF numerator)15
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.70244681163037
Sum Squared Residuals781.36240639826






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1-1.20.718045089082084-1.91804508908208
2-2.4-0.404458682946338-1.99554131705366
30.8-1.670463416424652.47046341642465
4-0.11.81558512675933-1.91558512675933
5-1.51.0106120870281-2.5106120870281
6-4.4-0.299547729465815-4.10045227053419
7-4.2-3.31001745584596-0.889982544154035
83.5-1.337590221007494.83759022100749
9106.438133603489073.56186639651093
108.610.7216511641231-2.12165116412312
119.510.2172512540259-0.717251254025916
129.911.3865009811379-1.48650098113786
1310.49.996148183316530.40385181668347
14168.282948751699597.71705124830041
1512.714.7351990174047-2.03519901740471
1610.211.9835734332948-1.78357343329478
178.99.05092344254182-0.150923442541823
1812.67.923682889501834.67631711049817
1913.610.86394860799932.73605139200068
2014.813.21359718991321.58640281008678
219.514.0612765702878-4.56127657028779
2213.79.45630052135344.2436994786466
231711.64189884657845.35810115342156
2414.715.3957469679123-0.695746967912321
2517.413.56119657686143.83880342313863
26916.7287262695237-7.7287262695237
279.18.854689819029150.245310180970845
2812.29.338071650041452.86192834995855
2915.912.60915739717073.29084260282929
3012.916.2447876198698-3.34478761986975
3110.914.4173205996916-3.51732059969164
3210.612.9453954488230-2.34539544882298
3313.210.74742910431222.45257089568784
349.612.6544636263777-3.0544636263777
356.412.3438311408765-5.94383114087648
365.86.06358017255083-0.263580172550834
37-15.5927910337339-6.5927910337339
38-0.2-2.279878156954932.07987815695493
392.70.01505280133870722.68494719866129
403.62.054829750379931.54517024962007
41-0.92.57625020214007-3.47625020214007
420.3-1.228414502730921.52841450273092
43-1.1-1.335261561438980.235261561438975
44-2.5-0.894337984015153-1.60566201598485
45-3.4-1.59171037690776-1.80828962309224
46-3.5-1.98054919202594-1.51945080797406
47-3.9-3.37947619536781-0.520523804632187
48-4.6-3.50004683251207-1.09995316748792
49-0.1-4.584342782731864.48434278273186
504.31.255142063905363.04485793609464
5110.27.166092368037383.03390763196262
528.712.5101644190482-3.81016441904818
5313.311.75927007784341.54072992215656
541515.2558433940818-0.255843394081838
5520.716.58203102016694.11796897983307
5620.723.9512673183448-3.25126731834483
5726.422.76592480979953.63407519020054
5831.225.91561632098115.28438367901888
5931.428.42811229388332.97188770611673
6026.628.6269329276309-2.02693292763088
6126.624.01017473509422.58982526490583
6219.222.3175197547726-3.11751975477262
636.512.8994294106147-6.3994294106147
643.1-0.002224379523669833.10222437952367
65-0.2-1.506213206724141.30621320672414
66-4-5.496351671256681.49635167125668
67-12.6-9.91802121057296-2.68197878942704
68-13-13.77833175205840.77833175205839
69-17.6-14.3210537109807-3.27894628901929
70-21.7-18.8674824408094-2.83251755919059
71-23.2-22.0516173399963-1.1483826600037
72-16.8-22.37271421671985.57271421671981
73-19.8-16.9940128353562-2.80598716464381

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -1.2 & 0.718045089082084 & -1.91804508908208 \tabularnewline
2 & -2.4 & -0.404458682946338 & -1.99554131705366 \tabularnewline
3 & 0.8 & -1.67046341642465 & 2.47046341642465 \tabularnewline
4 & -0.1 & 1.81558512675933 & -1.91558512675933 \tabularnewline
5 & -1.5 & 1.0106120870281 & -2.5106120870281 \tabularnewline
6 & -4.4 & -0.299547729465815 & -4.10045227053419 \tabularnewline
7 & -4.2 & -3.31001745584596 & -0.889982544154035 \tabularnewline
8 & 3.5 & -1.33759022100749 & 4.83759022100749 \tabularnewline
9 & 10 & 6.43813360348907 & 3.56186639651093 \tabularnewline
10 & 8.6 & 10.7216511641231 & -2.12165116412312 \tabularnewline
11 & 9.5 & 10.2172512540259 & -0.717251254025916 \tabularnewline
12 & 9.9 & 11.3865009811379 & -1.48650098113786 \tabularnewline
13 & 10.4 & 9.99614818331653 & 0.40385181668347 \tabularnewline
14 & 16 & 8.28294875169959 & 7.71705124830041 \tabularnewline
15 & 12.7 & 14.7351990174047 & -2.03519901740471 \tabularnewline
16 & 10.2 & 11.9835734332948 & -1.78357343329478 \tabularnewline
17 & 8.9 & 9.05092344254182 & -0.150923442541823 \tabularnewline
18 & 12.6 & 7.92368288950183 & 4.67631711049817 \tabularnewline
19 & 13.6 & 10.8639486079993 & 2.73605139200068 \tabularnewline
20 & 14.8 & 13.2135971899132 & 1.58640281008678 \tabularnewline
21 & 9.5 & 14.0612765702878 & -4.56127657028779 \tabularnewline
22 & 13.7 & 9.4563005213534 & 4.2436994786466 \tabularnewline
23 & 17 & 11.6418988465784 & 5.35810115342156 \tabularnewline
24 & 14.7 & 15.3957469679123 & -0.695746967912321 \tabularnewline
25 & 17.4 & 13.5611965768614 & 3.83880342313863 \tabularnewline
26 & 9 & 16.7287262695237 & -7.7287262695237 \tabularnewline
27 & 9.1 & 8.85468981902915 & 0.245310180970845 \tabularnewline
28 & 12.2 & 9.33807165004145 & 2.86192834995855 \tabularnewline
29 & 15.9 & 12.6091573971707 & 3.29084260282929 \tabularnewline
30 & 12.9 & 16.2447876198698 & -3.34478761986975 \tabularnewline
31 & 10.9 & 14.4173205996916 & -3.51732059969164 \tabularnewline
32 & 10.6 & 12.9453954488230 & -2.34539544882298 \tabularnewline
33 & 13.2 & 10.7474291043122 & 2.45257089568784 \tabularnewline
34 & 9.6 & 12.6544636263777 & -3.0544636263777 \tabularnewline
35 & 6.4 & 12.3438311408765 & -5.94383114087648 \tabularnewline
36 & 5.8 & 6.06358017255083 & -0.263580172550834 \tabularnewline
37 & -1 & 5.5927910337339 & -6.5927910337339 \tabularnewline
38 & -0.2 & -2.27987815695493 & 2.07987815695493 \tabularnewline
39 & 2.7 & 0.0150528013387072 & 2.68494719866129 \tabularnewline
40 & 3.6 & 2.05482975037993 & 1.54517024962007 \tabularnewline
41 & -0.9 & 2.57625020214007 & -3.47625020214007 \tabularnewline
42 & 0.3 & -1.22841450273092 & 1.52841450273092 \tabularnewline
43 & -1.1 & -1.33526156143898 & 0.235261561438975 \tabularnewline
44 & -2.5 & -0.894337984015153 & -1.60566201598485 \tabularnewline
45 & -3.4 & -1.59171037690776 & -1.80828962309224 \tabularnewline
46 & -3.5 & -1.98054919202594 & -1.51945080797406 \tabularnewline
47 & -3.9 & -3.37947619536781 & -0.520523804632187 \tabularnewline
48 & -4.6 & -3.50004683251207 & -1.09995316748792 \tabularnewline
49 & -0.1 & -4.58434278273186 & 4.48434278273186 \tabularnewline
50 & 4.3 & 1.25514206390536 & 3.04485793609464 \tabularnewline
51 & 10.2 & 7.16609236803738 & 3.03390763196262 \tabularnewline
52 & 8.7 & 12.5101644190482 & -3.81016441904818 \tabularnewline
53 & 13.3 & 11.7592700778434 & 1.54072992215656 \tabularnewline
54 & 15 & 15.2558433940818 & -0.255843394081838 \tabularnewline
55 & 20.7 & 16.5820310201669 & 4.11796897983307 \tabularnewline
56 & 20.7 & 23.9512673183448 & -3.25126731834483 \tabularnewline
57 & 26.4 & 22.7659248097995 & 3.63407519020054 \tabularnewline
58 & 31.2 & 25.9156163209811 & 5.28438367901888 \tabularnewline
59 & 31.4 & 28.4281122938833 & 2.97188770611673 \tabularnewline
60 & 26.6 & 28.6269329276309 & -2.02693292763088 \tabularnewline
61 & 26.6 & 24.0101747350942 & 2.58982526490583 \tabularnewline
62 & 19.2 & 22.3175197547726 & -3.11751975477262 \tabularnewline
63 & 6.5 & 12.8994294106147 & -6.3994294106147 \tabularnewline
64 & 3.1 & -0.00222437952366983 & 3.10222437952367 \tabularnewline
65 & -0.2 & -1.50621320672414 & 1.30621320672414 \tabularnewline
66 & -4 & -5.49635167125668 & 1.49635167125668 \tabularnewline
67 & -12.6 & -9.91802121057296 & -2.68197878942704 \tabularnewline
68 & -13 & -13.7783317520584 & 0.77833175205839 \tabularnewline
69 & -17.6 & -14.3210537109807 & -3.27894628901929 \tabularnewline
70 & -21.7 & -18.8674824408094 & -2.83251755919059 \tabularnewline
71 & -23.2 & -22.0516173399963 & -1.1483826600037 \tabularnewline
72 & -16.8 & -22.3727142167198 & 5.57271421671981 \tabularnewline
73 & -19.8 & -16.9940128353562 & -2.80598716464381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69916&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]0.718045089082084[/C][C]-1.91804508908208[/C][/ROW]
[ROW][C]2[/C][C]-2.4[/C][C]-0.404458682946338[/C][C]-1.99554131705366[/C][/ROW]
[ROW][C]3[/C][C]0.8[/C][C]-1.67046341642465[/C][C]2.47046341642465[/C][/ROW]
[ROW][C]4[/C][C]-0.1[/C][C]1.81558512675933[/C][C]-1.91558512675933[/C][/ROW]
[ROW][C]5[/C][C]-1.5[/C][C]1.0106120870281[/C][C]-2.5106120870281[/C][/ROW]
[ROW][C]6[/C][C]-4.4[/C][C]-0.299547729465815[/C][C]-4.10045227053419[/C][/ROW]
[ROW][C]7[/C][C]-4.2[/C][C]-3.31001745584596[/C][C]-0.889982544154035[/C][/ROW]
[ROW][C]8[/C][C]3.5[/C][C]-1.33759022100749[/C][C]4.83759022100749[/C][/ROW]
[ROW][C]9[/C][C]10[/C][C]6.43813360348907[/C][C]3.56186639651093[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]10.7216511641231[/C][C]-2.12165116412312[/C][/ROW]
[ROW][C]11[/C][C]9.5[/C][C]10.2172512540259[/C][C]-0.717251254025916[/C][/ROW]
[ROW][C]12[/C][C]9.9[/C][C]11.3865009811379[/C][C]-1.48650098113786[/C][/ROW]
[ROW][C]13[/C][C]10.4[/C][C]9.99614818331653[/C][C]0.40385181668347[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]8.28294875169959[/C][C]7.71705124830041[/C][/ROW]
[ROW][C]15[/C][C]12.7[/C][C]14.7351990174047[/C][C]-2.03519901740471[/C][/ROW]
[ROW][C]16[/C][C]10.2[/C][C]11.9835734332948[/C][C]-1.78357343329478[/C][/ROW]
[ROW][C]17[/C][C]8.9[/C][C]9.05092344254182[/C][C]-0.150923442541823[/C][/ROW]
[ROW][C]18[/C][C]12.6[/C][C]7.92368288950183[/C][C]4.67631711049817[/C][/ROW]
[ROW][C]19[/C][C]13.6[/C][C]10.8639486079993[/C][C]2.73605139200068[/C][/ROW]
[ROW][C]20[/C][C]14.8[/C][C]13.2135971899132[/C][C]1.58640281008678[/C][/ROW]
[ROW][C]21[/C][C]9.5[/C][C]14.0612765702878[/C][C]-4.56127657028779[/C][/ROW]
[ROW][C]22[/C][C]13.7[/C][C]9.4563005213534[/C][C]4.2436994786466[/C][/ROW]
[ROW][C]23[/C][C]17[/C][C]11.6418988465784[/C][C]5.35810115342156[/C][/ROW]
[ROW][C]24[/C][C]14.7[/C][C]15.3957469679123[/C][C]-0.695746967912321[/C][/ROW]
[ROW][C]25[/C][C]17.4[/C][C]13.5611965768614[/C][C]3.83880342313863[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]16.7287262695237[/C][C]-7.7287262695237[/C][/ROW]
[ROW][C]27[/C][C]9.1[/C][C]8.85468981902915[/C][C]0.245310180970845[/C][/ROW]
[ROW][C]28[/C][C]12.2[/C][C]9.33807165004145[/C][C]2.86192834995855[/C][/ROW]
[ROW][C]29[/C][C]15.9[/C][C]12.6091573971707[/C][C]3.29084260282929[/C][/ROW]
[ROW][C]30[/C][C]12.9[/C][C]16.2447876198698[/C][C]-3.34478761986975[/C][/ROW]
[ROW][C]31[/C][C]10.9[/C][C]14.4173205996916[/C][C]-3.51732059969164[/C][/ROW]
[ROW][C]32[/C][C]10.6[/C][C]12.9453954488230[/C][C]-2.34539544882298[/C][/ROW]
[ROW][C]33[/C][C]13.2[/C][C]10.7474291043122[/C][C]2.45257089568784[/C][/ROW]
[ROW][C]34[/C][C]9.6[/C][C]12.6544636263777[/C][C]-3.0544636263777[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]12.3438311408765[/C][C]-5.94383114087648[/C][/ROW]
[ROW][C]36[/C][C]5.8[/C][C]6.06358017255083[/C][C]-0.263580172550834[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]5.5927910337339[/C][C]-6.5927910337339[/C][/ROW]
[ROW][C]38[/C][C]-0.2[/C][C]-2.27987815695493[/C][C]2.07987815695493[/C][/ROW]
[ROW][C]39[/C][C]2.7[/C][C]0.0150528013387072[/C][C]2.68494719866129[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]2.05482975037993[/C][C]1.54517024962007[/C][/ROW]
[ROW][C]41[/C][C]-0.9[/C][C]2.57625020214007[/C][C]-3.47625020214007[/C][/ROW]
[ROW][C]42[/C][C]0.3[/C][C]-1.22841450273092[/C][C]1.52841450273092[/C][/ROW]
[ROW][C]43[/C][C]-1.1[/C][C]-1.33526156143898[/C][C]0.235261561438975[/C][/ROW]
[ROW][C]44[/C][C]-2.5[/C][C]-0.894337984015153[/C][C]-1.60566201598485[/C][/ROW]
[ROW][C]45[/C][C]-3.4[/C][C]-1.59171037690776[/C][C]-1.80828962309224[/C][/ROW]
[ROW][C]46[/C][C]-3.5[/C][C]-1.98054919202594[/C][C]-1.51945080797406[/C][/ROW]
[ROW][C]47[/C][C]-3.9[/C][C]-3.37947619536781[/C][C]-0.520523804632187[/C][/ROW]
[ROW][C]48[/C][C]-4.6[/C][C]-3.50004683251207[/C][C]-1.09995316748792[/C][/ROW]
[ROW][C]49[/C][C]-0.1[/C][C]-4.58434278273186[/C][C]4.48434278273186[/C][/ROW]
[ROW][C]50[/C][C]4.3[/C][C]1.25514206390536[/C][C]3.04485793609464[/C][/ROW]
[ROW][C]51[/C][C]10.2[/C][C]7.16609236803738[/C][C]3.03390763196262[/C][/ROW]
[ROW][C]52[/C][C]8.7[/C][C]12.5101644190482[/C][C]-3.81016441904818[/C][/ROW]
[ROW][C]53[/C][C]13.3[/C][C]11.7592700778434[/C][C]1.54072992215656[/C][/ROW]
[ROW][C]54[/C][C]15[/C][C]15.2558433940818[/C][C]-0.255843394081838[/C][/ROW]
[ROW][C]55[/C][C]20.7[/C][C]16.5820310201669[/C][C]4.11796897983307[/C][/ROW]
[ROW][C]56[/C][C]20.7[/C][C]23.9512673183448[/C][C]-3.25126731834483[/C][/ROW]
[ROW][C]57[/C][C]26.4[/C][C]22.7659248097995[/C][C]3.63407519020054[/C][/ROW]
[ROW][C]58[/C][C]31.2[/C][C]25.9156163209811[/C][C]5.28438367901888[/C][/ROW]
[ROW][C]59[/C][C]31.4[/C][C]28.4281122938833[/C][C]2.97188770611673[/C][/ROW]
[ROW][C]60[/C][C]26.6[/C][C]28.6269329276309[/C][C]-2.02693292763088[/C][/ROW]
[ROW][C]61[/C][C]26.6[/C][C]24.0101747350942[/C][C]2.58982526490583[/C][/ROW]
[ROW][C]62[/C][C]19.2[/C][C]22.3175197547726[/C][C]-3.11751975477262[/C][/ROW]
[ROW][C]63[/C][C]6.5[/C][C]12.8994294106147[/C][C]-6.3994294106147[/C][/ROW]
[ROW][C]64[/C][C]3.1[/C][C]-0.00222437952366983[/C][C]3.10222437952367[/C][/ROW]
[ROW][C]65[/C][C]-0.2[/C][C]-1.50621320672414[/C][C]1.30621320672414[/C][/ROW]
[ROW][C]66[/C][C]-4[/C][C]-5.49635167125668[/C][C]1.49635167125668[/C][/ROW]
[ROW][C]67[/C][C]-12.6[/C][C]-9.91802121057296[/C][C]-2.68197878942704[/C][/ROW]
[ROW][C]68[/C][C]-13[/C][C]-13.7783317520584[/C][C]0.77833175205839[/C][/ROW]
[ROW][C]69[/C][C]-17.6[/C][C]-14.3210537109807[/C][C]-3.27894628901929[/C][/ROW]
[ROW][C]70[/C][C]-21.7[/C][C]-18.8674824408094[/C][C]-2.83251755919059[/C][/ROW]
[ROW][C]71[/C][C]-23.2[/C][C]-22.0516173399963[/C][C]-1.1483826600037[/C][/ROW]
[ROW][C]72[/C][C]-16.8[/C][C]-22.3727142167198[/C][C]5.57271421671981[/C][/ROW]
[ROW][C]73[/C][C]-19.8[/C][C]-16.9940128353562[/C][C]-2.80598716464381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69916&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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
1-1.20.718045089082084-1.91804508908208
2-2.4-0.404458682946338-1.99554131705366
30.8-1.670463416424652.47046341642465
4-0.11.81558512675933-1.91558512675933
5-1.51.0106120870281-2.5106120870281
6-4.4-0.299547729465815-4.10045227053419
7-4.2-3.31001745584596-0.889982544154035
83.5-1.337590221007494.83759022100749
9106.438133603489073.56186639651093
108.610.7216511641231-2.12165116412312
119.510.2172512540259-0.717251254025916
129.911.3865009811379-1.48650098113786
1310.49.996148183316530.40385181668347
14168.282948751699597.71705124830041
1512.714.7351990174047-2.03519901740471
1610.211.9835734332948-1.78357343329478
178.99.05092344254182-0.150923442541823
1812.67.923682889501834.67631711049817
1913.610.86394860799932.73605139200068
2014.813.21359718991321.58640281008678
219.514.0612765702878-4.56127657028779
2213.79.45630052135344.2436994786466
231711.64189884657845.35810115342156
2414.715.3957469679123-0.695746967912321
2517.413.56119657686143.83880342313863
26916.7287262695237-7.7287262695237
279.18.854689819029150.245310180970845
2812.29.338071650041452.86192834995855
2915.912.60915739717073.29084260282929
3012.916.2447876198698-3.34478761986975
3110.914.4173205996916-3.51732059969164
3210.612.9453954488230-2.34539544882298
3313.210.74742910431222.45257089568784
349.612.6544636263777-3.0544636263777
356.412.3438311408765-5.94383114087648
365.86.06358017255083-0.263580172550834
37-15.5927910337339-6.5927910337339
38-0.2-2.279878156954932.07987815695493
392.70.01505280133870722.68494719866129
403.62.054829750379931.54517024962007
41-0.92.57625020214007-3.47625020214007
420.3-1.228414502730921.52841450273092
43-1.1-1.335261561438980.235261561438975
44-2.5-0.894337984015153-1.60566201598485
45-3.4-1.59171037690776-1.80828962309224
46-3.5-1.98054919202594-1.51945080797406
47-3.9-3.37947619536781-0.520523804632187
48-4.6-3.50004683251207-1.09995316748792
49-0.1-4.584342782731864.48434278273186
504.31.255142063905363.04485793609464
5110.27.166092368037383.03390763196262
528.712.5101644190482-3.81016441904818
5313.311.75927007784341.54072992215656
541515.2558433940818-0.255843394081838
5520.716.58203102016694.11796897983307
5620.723.9512673183448-3.25126731834483
5726.422.76592480979953.63407519020054
5831.225.91561632098115.28438367901888
5931.428.42811229388332.97188770611673
6026.628.6269329276309-2.02693292763088
6126.624.01017473509422.58982526490583
6219.222.3175197547726-3.11751975477262
636.512.8994294106147-6.3994294106147
643.1-0.002224379523669833.10222437952367
65-0.2-1.506213206724141.30621320672414
66-4-5.496351671256681.49635167125668
67-12.6-9.91802121057296-2.68197878942704
68-13-13.77833175205840.77833175205839
69-17.6-14.3210537109807-3.27894628901929
70-21.7-18.8674824408094-2.83251755919059
71-23.2-22.0516173399963-1.1483826600037
72-16.8-22.37271421671985.57271421671981
73-19.8-16.9940128353562-2.80598716464381






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2303218622849950.4606437245699910.769678137715005
200.1152132678827930.2304265357655850.884786732117207
210.3230686276215840.6461372552431670.676931372378416
220.4157363477554670.8314726955109330.584263652244533
230.3438585931291840.6877171862583690.656141406870816
240.3379177264329580.6758354528659160.662082273567042
250.293881121196880.587762242393760.70611887880312
260.5572964679997120.8854070640005770.442703532000288
270.4821026071078230.9642052142156460.517897392892177
280.4055457715848510.8110915431697030.594454228415149
290.3986154295868890.7972308591737780.601384570413111
300.4282883780516190.8565767561032380.571711621948381
310.3662248915622960.7324497831245920.633775108437704
320.28205555675170.56411111350340.7179444432483
330.2580437916844980.5160875833689960.741956208315502
340.3145028329590380.6290056659180760.685497167040962
350.5053154573001600.9893690853996810.494684542699840
360.4183634825666150.836726965133230.581636517433385
370.579123041504640.841753916990720.42087695849536
380.5026537982148380.9946924035703230.497346201785162
390.484068088024230.968136176048460.51593191197577
400.4436472511855580.8872945023711160.556352748814442
410.3918885498362440.7837770996724870.608111450163756
420.3639357290519490.7278714581038990.636064270948051
430.2849856284950730.5699712569901460.715014371504927
440.2342983883895580.4685967767791160.765701611610442
450.1760935366354640.3521870732709290.823906463364536
460.1438110529691170.2876221059382340.856188947030883
470.1108452448930080.2216904897860150.889154755106992
480.1316243597154160.2632487194308310.868375640284584
490.1371125751395180.2742251502790360.862887424860482
500.1212613239601970.2425226479203940.878738676039803
510.1536606451885810.3073212903771630.846339354811419
520.143124803954620.286249607909240.85687519604538
530.09263100575130.18526201150260.9073689942487
540.1682987682381230.3365975364762450.831701231761877

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.230321862284995 & 0.460643724569991 & 0.769678137715005 \tabularnewline
20 & 0.115213267882793 & 0.230426535765585 & 0.884786732117207 \tabularnewline
21 & 0.323068627621584 & 0.646137255243167 & 0.676931372378416 \tabularnewline
22 & 0.415736347755467 & 0.831472695510933 & 0.584263652244533 \tabularnewline
23 & 0.343858593129184 & 0.687717186258369 & 0.656141406870816 \tabularnewline
24 & 0.337917726432958 & 0.675835452865916 & 0.662082273567042 \tabularnewline
25 & 0.29388112119688 & 0.58776224239376 & 0.70611887880312 \tabularnewline
26 & 0.557296467999712 & 0.885407064000577 & 0.442703532000288 \tabularnewline
27 & 0.482102607107823 & 0.964205214215646 & 0.517897392892177 \tabularnewline
28 & 0.405545771584851 & 0.811091543169703 & 0.594454228415149 \tabularnewline
29 & 0.398615429586889 & 0.797230859173778 & 0.601384570413111 \tabularnewline
30 & 0.428288378051619 & 0.856576756103238 & 0.571711621948381 \tabularnewline
31 & 0.366224891562296 & 0.732449783124592 & 0.633775108437704 \tabularnewline
32 & 0.2820555567517 & 0.5641111135034 & 0.7179444432483 \tabularnewline
33 & 0.258043791684498 & 0.516087583368996 & 0.741956208315502 \tabularnewline
34 & 0.314502832959038 & 0.629005665918076 & 0.685497167040962 \tabularnewline
35 & 0.505315457300160 & 0.989369085399681 & 0.494684542699840 \tabularnewline
36 & 0.418363482566615 & 0.83672696513323 & 0.581636517433385 \tabularnewline
37 & 0.57912304150464 & 0.84175391699072 & 0.42087695849536 \tabularnewline
38 & 0.502653798214838 & 0.994692403570323 & 0.497346201785162 \tabularnewline
39 & 0.48406808802423 & 0.96813617604846 & 0.51593191197577 \tabularnewline
40 & 0.443647251185558 & 0.887294502371116 & 0.556352748814442 \tabularnewline
41 & 0.391888549836244 & 0.783777099672487 & 0.608111450163756 \tabularnewline
42 & 0.363935729051949 & 0.727871458103899 & 0.636064270948051 \tabularnewline
43 & 0.284985628495073 & 0.569971256990146 & 0.715014371504927 \tabularnewline
44 & 0.234298388389558 & 0.468596776779116 & 0.765701611610442 \tabularnewline
45 & 0.176093536635464 & 0.352187073270929 & 0.823906463364536 \tabularnewline
46 & 0.143811052969117 & 0.287622105938234 & 0.856188947030883 \tabularnewline
47 & 0.110845244893008 & 0.221690489786015 & 0.889154755106992 \tabularnewline
48 & 0.131624359715416 & 0.263248719430831 & 0.868375640284584 \tabularnewline
49 & 0.137112575139518 & 0.274225150279036 & 0.862887424860482 \tabularnewline
50 & 0.121261323960197 & 0.242522647920394 & 0.878738676039803 \tabularnewline
51 & 0.153660645188581 & 0.307321290377163 & 0.846339354811419 \tabularnewline
52 & 0.14312480395462 & 0.28624960790924 & 0.85687519604538 \tabularnewline
53 & 0.0926310057513 & 0.1852620115026 & 0.9073689942487 \tabularnewline
54 & 0.168298768238123 & 0.336597536476245 & 0.831701231761877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69916&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]19[/C][C]0.230321862284995[/C][C]0.460643724569991[/C][C]0.769678137715005[/C][/ROW]
[ROW][C]20[/C][C]0.115213267882793[/C][C]0.230426535765585[/C][C]0.884786732117207[/C][/ROW]
[ROW][C]21[/C][C]0.323068627621584[/C][C]0.646137255243167[/C][C]0.676931372378416[/C][/ROW]
[ROW][C]22[/C][C]0.415736347755467[/C][C]0.831472695510933[/C][C]0.584263652244533[/C][/ROW]
[ROW][C]23[/C][C]0.343858593129184[/C][C]0.687717186258369[/C][C]0.656141406870816[/C][/ROW]
[ROW][C]24[/C][C]0.337917726432958[/C][C]0.675835452865916[/C][C]0.662082273567042[/C][/ROW]
[ROW][C]25[/C][C]0.29388112119688[/C][C]0.58776224239376[/C][C]0.70611887880312[/C][/ROW]
[ROW][C]26[/C][C]0.557296467999712[/C][C]0.885407064000577[/C][C]0.442703532000288[/C][/ROW]
[ROW][C]27[/C][C]0.482102607107823[/C][C]0.964205214215646[/C][C]0.517897392892177[/C][/ROW]
[ROW][C]28[/C][C]0.405545771584851[/C][C]0.811091543169703[/C][C]0.594454228415149[/C][/ROW]
[ROW][C]29[/C][C]0.398615429586889[/C][C]0.797230859173778[/C][C]0.601384570413111[/C][/ROW]
[ROW][C]30[/C][C]0.428288378051619[/C][C]0.856576756103238[/C][C]0.571711621948381[/C][/ROW]
[ROW][C]31[/C][C]0.366224891562296[/C][C]0.732449783124592[/C][C]0.633775108437704[/C][/ROW]
[ROW][C]32[/C][C]0.2820555567517[/C][C]0.5641111135034[/C][C]0.7179444432483[/C][/ROW]
[ROW][C]33[/C][C]0.258043791684498[/C][C]0.516087583368996[/C][C]0.741956208315502[/C][/ROW]
[ROW][C]34[/C][C]0.314502832959038[/C][C]0.629005665918076[/C][C]0.685497167040962[/C][/ROW]
[ROW][C]35[/C][C]0.505315457300160[/C][C]0.989369085399681[/C][C]0.494684542699840[/C][/ROW]
[ROW][C]36[/C][C]0.418363482566615[/C][C]0.83672696513323[/C][C]0.581636517433385[/C][/ROW]
[ROW][C]37[/C][C]0.57912304150464[/C][C]0.84175391699072[/C][C]0.42087695849536[/C][/ROW]
[ROW][C]38[/C][C]0.502653798214838[/C][C]0.994692403570323[/C][C]0.497346201785162[/C][/ROW]
[ROW][C]39[/C][C]0.48406808802423[/C][C]0.96813617604846[/C][C]0.51593191197577[/C][/ROW]
[ROW][C]40[/C][C]0.443647251185558[/C][C]0.887294502371116[/C][C]0.556352748814442[/C][/ROW]
[ROW][C]41[/C][C]0.391888549836244[/C][C]0.783777099672487[/C][C]0.608111450163756[/C][/ROW]
[ROW][C]42[/C][C]0.363935729051949[/C][C]0.727871458103899[/C][C]0.636064270948051[/C][/ROW]
[ROW][C]43[/C][C]0.284985628495073[/C][C]0.569971256990146[/C][C]0.715014371504927[/C][/ROW]
[ROW][C]44[/C][C]0.234298388389558[/C][C]0.468596776779116[/C][C]0.765701611610442[/C][/ROW]
[ROW][C]45[/C][C]0.176093536635464[/C][C]0.352187073270929[/C][C]0.823906463364536[/C][/ROW]
[ROW][C]46[/C][C]0.143811052969117[/C][C]0.287622105938234[/C][C]0.856188947030883[/C][/ROW]
[ROW][C]47[/C][C]0.110845244893008[/C][C]0.221690489786015[/C][C]0.889154755106992[/C][/ROW]
[ROW][C]48[/C][C]0.131624359715416[/C][C]0.263248719430831[/C][C]0.868375640284584[/C][/ROW]
[ROW][C]49[/C][C]0.137112575139518[/C][C]0.274225150279036[/C][C]0.862887424860482[/C][/ROW]
[ROW][C]50[/C][C]0.121261323960197[/C][C]0.242522647920394[/C][C]0.878738676039803[/C][/ROW]
[ROW][C]51[/C][C]0.153660645188581[/C][C]0.307321290377163[/C][C]0.846339354811419[/C][/ROW]
[ROW][C]52[/C][C]0.14312480395462[/C][C]0.28624960790924[/C][C]0.85687519604538[/C][/ROW]
[ROW][C]53[/C][C]0.0926310057513[/C][C]0.1852620115026[/C][C]0.9073689942487[/C][/ROW]
[ROW][C]54[/C][C]0.168298768238123[/C][C]0.336597536476245[/C][C]0.831701231761877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69916&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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
190.2303218622849950.4606437245699910.769678137715005
200.1152132678827930.2304265357655850.884786732117207
210.3230686276215840.6461372552431670.676931372378416
220.4157363477554670.8314726955109330.584263652244533
230.3438585931291840.6877171862583690.656141406870816
240.3379177264329580.6758354528659160.662082273567042
250.293881121196880.587762242393760.70611887880312
260.5572964679997120.8854070640005770.442703532000288
270.4821026071078230.9642052142156460.517897392892177
280.4055457715848510.8110915431697030.594454228415149
290.3986154295868890.7972308591737780.601384570413111
300.4282883780516190.8565767561032380.571711621948381
310.3662248915622960.7324497831245920.633775108437704
320.28205555675170.56411111350340.7179444432483
330.2580437916844980.5160875833689960.741956208315502
340.3145028329590380.6290056659180760.685497167040962
350.5053154573001600.9893690853996810.494684542699840
360.4183634825666150.836726965133230.581636517433385
370.579123041504640.841753916990720.42087695849536
380.5026537982148380.9946924035703230.497346201785162
390.484068088024230.968136176048460.51593191197577
400.4436472511855580.8872945023711160.556352748814442
410.3918885498362440.7837770996724870.608111450163756
420.3639357290519490.7278714581038990.636064270948051
430.2849856284950730.5699712569901460.715014371504927
440.2342983883895580.4685967767791160.765701611610442
450.1760935366354640.3521870732709290.823906463364536
460.1438110529691170.2876221059382340.856188947030883
470.1108452448930080.2216904897860150.889154755106992
480.1316243597154160.2632487194308310.868375640284584
490.1371125751395180.2742251502790360.862887424860482
500.1212613239601970.2425226479203940.878738676039803
510.1536606451885810.3073212903771630.846339354811419
520.143124803954620.286249607909240.85687519604538
530.09263100575130.18526201150260.9073689942487
540.1682987682381230.3365975364762450.831701231761877






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=69916&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=69916&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69916&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 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')
}