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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 06:13:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258723192kkqvzswfcp2gfx1.htm/, Retrieved Thu, 28 Mar 2024 23:43:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58131, Retrieved Thu, 28 Mar 2024 23:43:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
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 14:06:21] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [Model 3] [2009-11-20 13:13:45] [cf272a759dc2b193d9a85354803ede7b] [Current]
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Dataseries X:
108.5	98.71
112.3	98.54
116.6	98.2
115.5	96.92
120.1	99.06
132.9	99.65
128.1	99.82
129.3	99.99
132.5	100.33
131	99.31
124.9	101.1
120.8	101.1
122	100.93
122.1	100.85
127.4	100.93
135.2	99.6
137.3	101.88
135	101.81
136	102.38
138.4	102.74
134.7	102.82
138.4	101.72
133.9	103.47
133.6	102.98
141.2	102.68
151.8	102.9
155.4	103.03
156.6	101.29
161.6	103.69
160.7	103.68
156	104.2
159.5	104.08
168.7	104.16
169.9	103.05
169.9	104.66
185.9	104.46
190.8	104.95
195.8	105.85
211.9	106.23
227.1	104.86
251.3	107.44
256.7	108.23
251.9	108.45
251.2	109.39
270.3	110.15
267.2	109.13
243	110.28
229.9	110.17
187.2	109.99
178.2	109.26
175.2	109.11
192.4	107.06
187	109.53
184	108.92
194.1	109.24
212.7	109.12
217.5	109
200.5	107.23
205.9	109.49
196.5	109.04
206.3	109.02




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=58131&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=58131&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=0

As an alternative you can also use a 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] = -1581.71366541556 + 17.1393927894853X[t] -1.45486092444313M1[t] -0.824024568713355M2[t] + 5.5934443397917M3[t] + 41.7883174989466M4[t] + 8.69965578100341M5[t] + 10.2346763403491M6[t] + 4.92475170042933M7[t] + 7.20871783851072M8[t] + 11.3211930468029M9[t] + 30.1172787296379M10[t] -3.60510496166605M11[t] -1.50025676429478t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -1581.71366541556 +  17.1393927894853X[t] -1.45486092444313M1[t] -0.824024568713355M2[t] +  5.5934443397917M3[t] +  41.7883174989466M4[t] +  8.69965578100341M5[t] +  10.2346763403491M6[t] +  4.92475170042933M7[t] +  7.20871783851072M8[t] +  11.3211930468029M9[t] +  30.1172787296379M10[t] -3.60510496166605M11[t] -1.50025676429478t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -1581.71366541556 +  17.1393927894853X[t] -1.45486092444313M1[t] -0.824024568713355M2[t] +  5.5934443397917M3[t] +  41.7883174989466M4[t] +  8.69965578100341M5[t] +  10.2346763403491M6[t] +  4.92475170042933M7[t] +  7.20871783851072M8[t] +  11.3211930468029M9[t] +  30.1172787296379M10[t] -3.60510496166605M11[t] -1.50025676429478t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -1581.71366541556 + 17.1393927894853X[t] -1.45486092444313M1[t] -0.824024568713355M2[t] + 5.5934443397917M3[t] + 41.7883174989466M4[t] + 8.69965578100341M5[t] + 10.2346763403491M6[t] + 4.92475170042933M7[t] + 7.20871783851072M8[t] + 11.3211930468029M9[t] + 30.1172787296379M10[t] -3.60510496166605M11[t] -1.50025676429478t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-1581.71366541556282.09094-5.60711e-061e-06
X17.13939278948532.8725225.966700
M1-1.4548609244431312.93169-0.11250.9109030.455452
M2-0.82402456871335513.566718-0.06070.9518250.475912
M35.593444339791713.560870.41250.6818710.340935
M441.788317498946614.6522082.8520.0064370.003218
M58.6996557810034113.5340180.64280.5234780.261739
M610.234676340349113.5146810.75730.452650.226325
M74.9247517004293313.5254630.36410.7174090.358705
M87.2087178385107213.5249810.5330.596550.298275
M911.321193046802913.5232370.83720.4067360.203368
M1030.117278729637913.8120412.18050.034260.01713
M11-3.6051049616660513.539742-0.26630.7912030.395601
t-1.500256764294780.612783-2.44830.0181420.009071

\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) & -1581.71366541556 & 282.09094 & -5.6071 & 1e-06 & 1e-06 \tabularnewline
X & 17.1393927894853 & 2.872522 & 5.9667 & 0 & 0 \tabularnewline
M1 & -1.45486092444313 & 12.93169 & -0.1125 & 0.910903 & 0.455452 \tabularnewline
M2 & -0.824024568713355 & 13.566718 & -0.0607 & 0.951825 & 0.475912 \tabularnewline
M3 & 5.5934443397917 & 13.56087 & 0.4125 & 0.681871 & 0.340935 \tabularnewline
M4 & 41.7883174989466 & 14.652208 & 2.852 & 0.006437 & 0.003218 \tabularnewline
M5 & 8.69965578100341 & 13.534018 & 0.6428 & 0.523478 & 0.261739 \tabularnewline
M6 & 10.2346763403491 & 13.514681 & 0.7573 & 0.45265 & 0.226325 \tabularnewline
M7 & 4.92475170042933 & 13.525463 & 0.3641 & 0.717409 & 0.358705 \tabularnewline
M8 & 7.20871783851072 & 13.524981 & 0.533 & 0.59655 & 0.298275 \tabularnewline
M9 & 11.3211930468029 & 13.523237 & 0.8372 & 0.406736 & 0.203368 \tabularnewline
M10 & 30.1172787296379 & 13.812041 & 2.1805 & 0.03426 & 0.01713 \tabularnewline
M11 & -3.60510496166605 & 13.539742 & -0.2663 & 0.791203 & 0.395601 \tabularnewline
t & -1.50025676429478 & 0.612783 & -2.4483 & 0.018142 & 0.009071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&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]-1581.71366541556[/C][C]282.09094[/C][C]-5.6071[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]X[/C][C]17.1393927894853[/C][C]2.872522[/C][C]5.9667[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-1.45486092444313[/C][C]12.93169[/C][C]-0.1125[/C][C]0.910903[/C][C]0.455452[/C][/ROW]
[ROW][C]M2[/C][C]-0.824024568713355[/C][C]13.566718[/C][C]-0.0607[/C][C]0.951825[/C][C]0.475912[/C][/ROW]
[ROW][C]M3[/C][C]5.5934443397917[/C][C]13.56087[/C][C]0.4125[/C][C]0.681871[/C][C]0.340935[/C][/ROW]
[ROW][C]M4[/C][C]41.7883174989466[/C][C]14.652208[/C][C]2.852[/C][C]0.006437[/C][C]0.003218[/C][/ROW]
[ROW][C]M5[/C][C]8.69965578100341[/C][C]13.534018[/C][C]0.6428[/C][C]0.523478[/C][C]0.261739[/C][/ROW]
[ROW][C]M6[/C][C]10.2346763403491[/C][C]13.514681[/C][C]0.7573[/C][C]0.45265[/C][C]0.226325[/C][/ROW]
[ROW][C]M7[/C][C]4.92475170042933[/C][C]13.525463[/C][C]0.3641[/C][C]0.717409[/C][C]0.358705[/C][/ROW]
[ROW][C]M8[/C][C]7.20871783851072[/C][C]13.524981[/C][C]0.533[/C][C]0.59655[/C][C]0.298275[/C][/ROW]
[ROW][C]M9[/C][C]11.3211930468029[/C][C]13.523237[/C][C]0.8372[/C][C]0.406736[/C][C]0.203368[/C][/ROW]
[ROW][C]M10[/C][C]30.1172787296379[/C][C]13.812041[/C][C]2.1805[/C][C]0.03426[/C][C]0.01713[/C][/ROW]
[ROW][C]M11[/C][C]-3.60510496166605[/C][C]13.539742[/C][C]-0.2663[/C][C]0.791203[/C][C]0.395601[/C][/ROW]
[ROW][C]t[/C][C]-1.50025676429478[/C][C]0.612783[/C][C]-2.4483[/C][C]0.018142[/C][C]0.009071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=2

As an alternative you can also use a 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)-1581.71366541556282.09094-5.60711e-061e-06
X17.13939278948532.8725225.966700
M1-1.4548609244431312.93169-0.11250.9109030.455452
M2-0.82402456871335513.566718-0.06070.9518250.475912
M35.593444339791713.560870.41250.6818710.340935
M441.788317498946614.6522082.8520.0064370.003218
M58.6996557810034113.5340180.64280.5234780.261739
M610.234676340349113.5146810.75730.452650.226325
M74.9247517004293313.5254630.36410.7174090.358705
M87.2087178385107213.5249810.5330.596550.298275
M911.321193046802913.5232370.83720.4067360.203368
M1030.117278729637913.8120412.18050.034260.01713
M11-3.6051049616660513.539742-0.26630.7912030.395601
t-1.500256764294780.612783-2.44830.0181420.009071







Multiple Linear Regression - Regression Statistics
Multiple R0.905968603940365
R-squared0.820779111325654
Adjusted R-squared0.771207376160409
F-TEST (value)16.5574012809846
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value2.46247466861860e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21.3062643774529
Sum Squared Residuals21335.9743809301

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.905968603940365 \tabularnewline
R-squared & 0.820779111325654 \tabularnewline
Adjusted R-squared & 0.771207376160409 \tabularnewline
F-TEST (value) & 16.5574012809846 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 2.46247466861860e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 21.3062643774529 \tabularnewline
Sum Squared Residuals & 21335.9743809301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.905968603940365[/C][/ROW]
[ROW][C]R-squared[/C][C]0.820779111325654[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.771207376160409[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]16.5574012809846[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]2.46247466861860e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]21.3062643774529[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]21335.9743809301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.905968603940365
R-squared0.820779111325654
Adjusted R-squared0.771207376160409
F-TEST (value)16.5574012809846
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value2.46247466861860e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21.3062643774529
Sum Squared Residuals21335.9743809301







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1108.5107.1606791457971.33932085420329
2112.3103.3775619630188.9224380369823
3116.6102.46738055880314.1326194411971
4115.5115.2235741831220.276425816878101
5120.1117.3129562703822.78704372961763
6132.9127.4599618112305.44003818877033
7128.1123.5634771812274.53652281877262
8129.3127.2608833292272.03911667077351
9132.5135.700495321649-3.20049532164891
10131135.514143594914-4.51414359491423
11124.9130.971016232494-6.071016232494
12120.8133.075864429865-12.2758644298653
13122127.207049966915-5.20704996691508
14122.1124.966478135191-2.86647813519102
15127.4131.254841702560-3.85484170256033
16135.2143.154065687405-7.95406568740485
17137.3147.642962765193-10.3429627651933
18135146.477969064980-11.4779690649804
19136149.437241550772-13.4372415507723
20138.4156.391132328774-17.9911323287736
21134.7160.374502195930-25.6745021959297
22138.4158.816999046036-20.4169990460363
23133.9153.588295972037-19.6882959720368
24133.6147.294841702560-13.6948417025603
25141.2139.1979061769772.00209382302308
26151.8142.0991521820999.7008478179014
27155.4149.2444853889426.1555146110581
28156.6154.1165583300982.48344166990224
29161.6160.6621825426240.937817457375732
30160.7160.5255524097810.174447590219479
31156162.627855256098-6.62785525609819
32159.5161.354837495146-1.85483749514650
33168.7165.3382073623033.36179263769735
34169.9163.6093102845146.29068971548574
35169.9155.98109221998713.9189077800132
36185.9154.65806185946131.2419381405390
37190.8160.10124663757130.698753362429
38195.8174.65727973954321.1427202604575
39211.9186.08746114375725.8125388562426
40227.1197.30110941702329.7988905829774
41251.3206.93182433165744.3681756683434
42256.7220.50670843040136.193291569599
43251.9217.46719343987334.4328065601268
44251.2234.36193203577616.8380679642241
45270.3250.00008899978220.2999110002179
46267.2249.81373727304717.3862627269528
47243234.3013985253578.69860147464335
48229.9234.520913515885-4.62091351588456
49187.2228.480705125039-41.2807051250392
50178.2215.09952798015-36.8995279801501
51175.2217.445831205937-42.2458312059375
52192.4217.004692382353-24.6046923823529
53187224.750074090143-37.7500740901435
54184214.329808283608-30.3298082836084
55194.1213.004232572029-18.904232572029
56212.7211.7312148110780.968785188922443
57217.5212.2867061203375.21329387966342
58200.5199.2458098014881.25419019851200
59205.9202.7581970501263.14180294987420
60196.5197.150318492229-0.65031849222889
61206.3193.85241294770112.4475870522989

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 108.5 & 107.160679145797 & 1.33932085420329 \tabularnewline
2 & 112.3 & 103.377561963018 & 8.9224380369823 \tabularnewline
3 & 116.6 & 102.467380558803 & 14.1326194411971 \tabularnewline
4 & 115.5 & 115.223574183122 & 0.276425816878101 \tabularnewline
5 & 120.1 & 117.312956270382 & 2.78704372961763 \tabularnewline
6 & 132.9 & 127.459961811230 & 5.44003818877033 \tabularnewline
7 & 128.1 & 123.563477181227 & 4.53652281877262 \tabularnewline
8 & 129.3 & 127.260883329227 & 2.03911667077351 \tabularnewline
9 & 132.5 & 135.700495321649 & -3.20049532164891 \tabularnewline
10 & 131 & 135.514143594914 & -4.51414359491423 \tabularnewline
11 & 124.9 & 130.971016232494 & -6.071016232494 \tabularnewline
12 & 120.8 & 133.075864429865 & -12.2758644298653 \tabularnewline
13 & 122 & 127.207049966915 & -5.20704996691508 \tabularnewline
14 & 122.1 & 124.966478135191 & -2.86647813519102 \tabularnewline
15 & 127.4 & 131.254841702560 & -3.85484170256033 \tabularnewline
16 & 135.2 & 143.154065687405 & -7.95406568740485 \tabularnewline
17 & 137.3 & 147.642962765193 & -10.3429627651933 \tabularnewline
18 & 135 & 146.477969064980 & -11.4779690649804 \tabularnewline
19 & 136 & 149.437241550772 & -13.4372415507723 \tabularnewline
20 & 138.4 & 156.391132328774 & -17.9911323287736 \tabularnewline
21 & 134.7 & 160.374502195930 & -25.6745021959297 \tabularnewline
22 & 138.4 & 158.816999046036 & -20.4169990460363 \tabularnewline
23 & 133.9 & 153.588295972037 & -19.6882959720368 \tabularnewline
24 & 133.6 & 147.294841702560 & -13.6948417025603 \tabularnewline
25 & 141.2 & 139.197906176977 & 2.00209382302308 \tabularnewline
26 & 151.8 & 142.099152182099 & 9.7008478179014 \tabularnewline
27 & 155.4 & 149.244485388942 & 6.1555146110581 \tabularnewline
28 & 156.6 & 154.116558330098 & 2.48344166990224 \tabularnewline
29 & 161.6 & 160.662182542624 & 0.937817457375732 \tabularnewline
30 & 160.7 & 160.525552409781 & 0.174447590219479 \tabularnewline
31 & 156 & 162.627855256098 & -6.62785525609819 \tabularnewline
32 & 159.5 & 161.354837495146 & -1.85483749514650 \tabularnewline
33 & 168.7 & 165.338207362303 & 3.36179263769735 \tabularnewline
34 & 169.9 & 163.609310284514 & 6.29068971548574 \tabularnewline
35 & 169.9 & 155.981092219987 & 13.9189077800132 \tabularnewline
36 & 185.9 & 154.658061859461 & 31.2419381405390 \tabularnewline
37 & 190.8 & 160.101246637571 & 30.698753362429 \tabularnewline
38 & 195.8 & 174.657279739543 & 21.1427202604575 \tabularnewline
39 & 211.9 & 186.087461143757 & 25.8125388562426 \tabularnewline
40 & 227.1 & 197.301109417023 & 29.7988905829774 \tabularnewline
41 & 251.3 & 206.931824331657 & 44.3681756683434 \tabularnewline
42 & 256.7 & 220.506708430401 & 36.193291569599 \tabularnewline
43 & 251.9 & 217.467193439873 & 34.4328065601268 \tabularnewline
44 & 251.2 & 234.361932035776 & 16.8380679642241 \tabularnewline
45 & 270.3 & 250.000088999782 & 20.2999110002179 \tabularnewline
46 & 267.2 & 249.813737273047 & 17.3862627269528 \tabularnewline
47 & 243 & 234.301398525357 & 8.69860147464335 \tabularnewline
48 & 229.9 & 234.520913515885 & -4.62091351588456 \tabularnewline
49 & 187.2 & 228.480705125039 & -41.2807051250392 \tabularnewline
50 & 178.2 & 215.09952798015 & -36.8995279801501 \tabularnewline
51 & 175.2 & 217.445831205937 & -42.2458312059375 \tabularnewline
52 & 192.4 & 217.004692382353 & -24.6046923823529 \tabularnewline
53 & 187 & 224.750074090143 & -37.7500740901435 \tabularnewline
54 & 184 & 214.329808283608 & -30.3298082836084 \tabularnewline
55 & 194.1 & 213.004232572029 & -18.904232572029 \tabularnewline
56 & 212.7 & 211.731214811078 & 0.968785188922443 \tabularnewline
57 & 217.5 & 212.286706120337 & 5.21329387966342 \tabularnewline
58 & 200.5 & 199.245809801488 & 1.25419019851200 \tabularnewline
59 & 205.9 & 202.758197050126 & 3.14180294987420 \tabularnewline
60 & 196.5 & 197.150318492229 & -0.65031849222889 \tabularnewline
61 & 206.3 & 193.852412947701 & 12.4475870522989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&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]108.5[/C][C]107.160679145797[/C][C]1.33932085420329[/C][/ROW]
[ROW][C]2[/C][C]112.3[/C][C]103.377561963018[/C][C]8.9224380369823[/C][/ROW]
[ROW][C]3[/C][C]116.6[/C][C]102.467380558803[/C][C]14.1326194411971[/C][/ROW]
[ROW][C]4[/C][C]115.5[/C][C]115.223574183122[/C][C]0.276425816878101[/C][/ROW]
[ROW][C]5[/C][C]120.1[/C][C]117.312956270382[/C][C]2.78704372961763[/C][/ROW]
[ROW][C]6[/C][C]132.9[/C][C]127.459961811230[/C][C]5.44003818877033[/C][/ROW]
[ROW][C]7[/C][C]128.1[/C][C]123.563477181227[/C][C]4.53652281877262[/C][/ROW]
[ROW][C]8[/C][C]129.3[/C][C]127.260883329227[/C][C]2.03911667077351[/C][/ROW]
[ROW][C]9[/C][C]132.5[/C][C]135.700495321649[/C][C]-3.20049532164891[/C][/ROW]
[ROW][C]10[/C][C]131[/C][C]135.514143594914[/C][C]-4.51414359491423[/C][/ROW]
[ROW][C]11[/C][C]124.9[/C][C]130.971016232494[/C][C]-6.071016232494[/C][/ROW]
[ROW][C]12[/C][C]120.8[/C][C]133.075864429865[/C][C]-12.2758644298653[/C][/ROW]
[ROW][C]13[/C][C]122[/C][C]127.207049966915[/C][C]-5.20704996691508[/C][/ROW]
[ROW][C]14[/C][C]122.1[/C][C]124.966478135191[/C][C]-2.86647813519102[/C][/ROW]
[ROW][C]15[/C][C]127.4[/C][C]131.254841702560[/C][C]-3.85484170256033[/C][/ROW]
[ROW][C]16[/C][C]135.2[/C][C]143.154065687405[/C][C]-7.95406568740485[/C][/ROW]
[ROW][C]17[/C][C]137.3[/C][C]147.642962765193[/C][C]-10.3429627651933[/C][/ROW]
[ROW][C]18[/C][C]135[/C][C]146.477969064980[/C][C]-11.4779690649804[/C][/ROW]
[ROW][C]19[/C][C]136[/C][C]149.437241550772[/C][C]-13.4372415507723[/C][/ROW]
[ROW][C]20[/C][C]138.4[/C][C]156.391132328774[/C][C]-17.9911323287736[/C][/ROW]
[ROW][C]21[/C][C]134.7[/C][C]160.374502195930[/C][C]-25.6745021959297[/C][/ROW]
[ROW][C]22[/C][C]138.4[/C][C]158.816999046036[/C][C]-20.4169990460363[/C][/ROW]
[ROW][C]23[/C][C]133.9[/C][C]153.588295972037[/C][C]-19.6882959720368[/C][/ROW]
[ROW][C]24[/C][C]133.6[/C][C]147.294841702560[/C][C]-13.6948417025603[/C][/ROW]
[ROW][C]25[/C][C]141.2[/C][C]139.197906176977[/C][C]2.00209382302308[/C][/ROW]
[ROW][C]26[/C][C]151.8[/C][C]142.099152182099[/C][C]9.7008478179014[/C][/ROW]
[ROW][C]27[/C][C]155.4[/C][C]149.244485388942[/C][C]6.1555146110581[/C][/ROW]
[ROW][C]28[/C][C]156.6[/C][C]154.116558330098[/C][C]2.48344166990224[/C][/ROW]
[ROW][C]29[/C][C]161.6[/C][C]160.662182542624[/C][C]0.937817457375732[/C][/ROW]
[ROW][C]30[/C][C]160.7[/C][C]160.525552409781[/C][C]0.174447590219479[/C][/ROW]
[ROW][C]31[/C][C]156[/C][C]162.627855256098[/C][C]-6.62785525609819[/C][/ROW]
[ROW][C]32[/C][C]159.5[/C][C]161.354837495146[/C][C]-1.85483749514650[/C][/ROW]
[ROW][C]33[/C][C]168.7[/C][C]165.338207362303[/C][C]3.36179263769735[/C][/ROW]
[ROW][C]34[/C][C]169.9[/C][C]163.609310284514[/C][C]6.29068971548574[/C][/ROW]
[ROW][C]35[/C][C]169.9[/C][C]155.981092219987[/C][C]13.9189077800132[/C][/ROW]
[ROW][C]36[/C][C]185.9[/C][C]154.658061859461[/C][C]31.2419381405390[/C][/ROW]
[ROW][C]37[/C][C]190.8[/C][C]160.101246637571[/C][C]30.698753362429[/C][/ROW]
[ROW][C]38[/C][C]195.8[/C][C]174.657279739543[/C][C]21.1427202604575[/C][/ROW]
[ROW][C]39[/C][C]211.9[/C][C]186.087461143757[/C][C]25.8125388562426[/C][/ROW]
[ROW][C]40[/C][C]227.1[/C][C]197.301109417023[/C][C]29.7988905829774[/C][/ROW]
[ROW][C]41[/C][C]251.3[/C][C]206.931824331657[/C][C]44.3681756683434[/C][/ROW]
[ROW][C]42[/C][C]256.7[/C][C]220.506708430401[/C][C]36.193291569599[/C][/ROW]
[ROW][C]43[/C][C]251.9[/C][C]217.467193439873[/C][C]34.4328065601268[/C][/ROW]
[ROW][C]44[/C][C]251.2[/C][C]234.361932035776[/C][C]16.8380679642241[/C][/ROW]
[ROW][C]45[/C][C]270.3[/C][C]250.000088999782[/C][C]20.2999110002179[/C][/ROW]
[ROW][C]46[/C][C]267.2[/C][C]249.813737273047[/C][C]17.3862627269528[/C][/ROW]
[ROW][C]47[/C][C]243[/C][C]234.301398525357[/C][C]8.69860147464335[/C][/ROW]
[ROW][C]48[/C][C]229.9[/C][C]234.520913515885[/C][C]-4.62091351588456[/C][/ROW]
[ROW][C]49[/C][C]187.2[/C][C]228.480705125039[/C][C]-41.2807051250392[/C][/ROW]
[ROW][C]50[/C][C]178.2[/C][C]215.09952798015[/C][C]-36.8995279801501[/C][/ROW]
[ROW][C]51[/C][C]175.2[/C][C]217.445831205937[/C][C]-42.2458312059375[/C][/ROW]
[ROW][C]52[/C][C]192.4[/C][C]217.004692382353[/C][C]-24.6046923823529[/C][/ROW]
[ROW][C]53[/C][C]187[/C][C]224.750074090143[/C][C]-37.7500740901435[/C][/ROW]
[ROW][C]54[/C][C]184[/C][C]214.329808283608[/C][C]-30.3298082836084[/C][/ROW]
[ROW][C]55[/C][C]194.1[/C][C]213.004232572029[/C][C]-18.904232572029[/C][/ROW]
[ROW][C]56[/C][C]212.7[/C][C]211.731214811078[/C][C]0.968785188922443[/C][/ROW]
[ROW][C]57[/C][C]217.5[/C][C]212.286706120337[/C][C]5.21329387966342[/C][/ROW]
[ROW][C]58[/C][C]200.5[/C][C]199.245809801488[/C][C]1.25419019851200[/C][/ROW]
[ROW][C]59[/C][C]205.9[/C][C]202.758197050126[/C][C]3.14180294987420[/C][/ROW]
[ROW][C]60[/C][C]196.5[/C][C]197.150318492229[/C][C]-0.65031849222889[/C][/ROW]
[ROW][C]61[/C][C]206.3[/C][C]193.852412947701[/C][C]12.4475870522989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1108.5107.1606791457971.33932085420329
2112.3103.3775619630188.9224380369823
3116.6102.46738055880314.1326194411971
4115.5115.2235741831220.276425816878101
5120.1117.3129562703822.78704372961763
6132.9127.4599618112305.44003818877033
7128.1123.5634771812274.53652281877262
8129.3127.2608833292272.03911667077351
9132.5135.700495321649-3.20049532164891
10131135.514143594914-4.51414359491423
11124.9130.971016232494-6.071016232494
12120.8133.075864429865-12.2758644298653
13122127.207049966915-5.20704996691508
14122.1124.966478135191-2.86647813519102
15127.4131.254841702560-3.85484170256033
16135.2143.154065687405-7.95406568740485
17137.3147.642962765193-10.3429627651933
18135146.477969064980-11.4779690649804
19136149.437241550772-13.4372415507723
20138.4156.391132328774-17.9911323287736
21134.7160.374502195930-25.6745021959297
22138.4158.816999046036-20.4169990460363
23133.9153.588295972037-19.6882959720368
24133.6147.294841702560-13.6948417025603
25141.2139.1979061769772.00209382302308
26151.8142.0991521820999.7008478179014
27155.4149.2444853889426.1555146110581
28156.6154.1165583300982.48344166990224
29161.6160.6621825426240.937817457375732
30160.7160.5255524097810.174447590219479
31156162.627855256098-6.62785525609819
32159.5161.354837495146-1.85483749514650
33168.7165.3382073623033.36179263769735
34169.9163.6093102845146.29068971548574
35169.9155.98109221998713.9189077800132
36185.9154.65806185946131.2419381405390
37190.8160.10124663757130.698753362429
38195.8174.65727973954321.1427202604575
39211.9186.08746114375725.8125388562426
40227.1197.30110941702329.7988905829774
41251.3206.93182433165744.3681756683434
42256.7220.50670843040136.193291569599
43251.9217.46719343987334.4328065601268
44251.2234.36193203577616.8380679642241
45270.3250.00008899978220.2999110002179
46267.2249.81373727304717.3862627269528
47243234.3013985253578.69860147464335
48229.9234.520913515885-4.62091351588456
49187.2228.480705125039-41.2807051250392
50178.2215.09952798015-36.8995279801501
51175.2217.445831205937-42.2458312059375
52192.4217.004692382353-24.6046923823529
53187224.750074090143-37.7500740901435
54184214.329808283608-30.3298082836084
55194.1213.004232572029-18.904232572029
56212.7211.7312148110780.968785188922443
57217.5212.2867061203375.21329387966342
58200.5199.2458098014881.25419019851200
59205.9202.7581970501263.14180294987420
60196.5197.150318492229-0.65031849222889
61206.3193.85241294770112.4475870522989







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.002124620278085440.004249240556170880.997875379721915
180.0006927598577876160.001385519715575230.999307240142212
190.0001358207927183600.0002716415854367190.999864179207282
203.01176146051441e-056.02352292102883e-050.999969882385395
211.5122937970789e-053.0245875941578e-050.99998487706203
222.66196150550665e-065.32392301101329e-060.999997338038495
234.89844127617984e-079.79688255235967e-070.999999510155872
242.75890669522639e-075.51781339045279e-070.99999972410933
253.17759141901912e-076.35518283803824e-070.999999682240858
269.41698248552693e-071.88339649710539e-060.999999058301752
278.36624539081892e-071.67324907816378e-060.99999916337546
282.4593381047624e-074.9186762095248e-070.99999975406619
299.530040488934e-081.9060080977868e-070.999999904699595
302.24664589048073e-084.49329178096146e-080.999999977533541
317.9373040972106e-091.58746081944212e-080.999999992062696
323.40417084429783e-096.80834168859566e-090.99999999659583
332.60978357669981e-095.21956715339962e-090.999999997390216
342.88085556322412e-095.76171112644824e-090.999999997119144
359.18010066600592e-091.83602013320118e-080.9999999908199
369.74112769617927e-071.94822553923585e-060.99999902588723
370.0003740971177990970.0007481942355981940.9996259028822
380.005835047783954670.01167009556790930.994164952216045
390.02015647960839760.04031295921679520.979843520391602
400.04903226687032380.09806453374064770.950967733129676
410.07008434536754520.1401686907350900.929915654632455
420.07249868564995440.1449973712999090.927501314350046
430.09275583487389170.1855116697477830.907244165126108
440.09919956674854830.1983991334970970.900800433251452

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00212462027808544 & 0.00424924055617088 & 0.997875379721915 \tabularnewline
18 & 0.000692759857787616 & 0.00138551971557523 & 0.999307240142212 \tabularnewline
19 & 0.000135820792718360 & 0.000271641585436719 & 0.999864179207282 \tabularnewline
20 & 3.01176146051441e-05 & 6.02352292102883e-05 & 0.999969882385395 \tabularnewline
21 & 1.5122937970789e-05 & 3.0245875941578e-05 & 0.99998487706203 \tabularnewline
22 & 2.66196150550665e-06 & 5.32392301101329e-06 & 0.999997338038495 \tabularnewline
23 & 4.89844127617984e-07 & 9.79688255235967e-07 & 0.999999510155872 \tabularnewline
24 & 2.75890669522639e-07 & 5.51781339045279e-07 & 0.99999972410933 \tabularnewline
25 & 3.17759141901912e-07 & 6.35518283803824e-07 & 0.999999682240858 \tabularnewline
26 & 9.41698248552693e-07 & 1.88339649710539e-06 & 0.999999058301752 \tabularnewline
27 & 8.36624539081892e-07 & 1.67324907816378e-06 & 0.99999916337546 \tabularnewline
28 & 2.4593381047624e-07 & 4.9186762095248e-07 & 0.99999975406619 \tabularnewline
29 & 9.530040488934e-08 & 1.9060080977868e-07 & 0.999999904699595 \tabularnewline
30 & 2.24664589048073e-08 & 4.49329178096146e-08 & 0.999999977533541 \tabularnewline
31 & 7.9373040972106e-09 & 1.58746081944212e-08 & 0.999999992062696 \tabularnewline
32 & 3.40417084429783e-09 & 6.80834168859566e-09 & 0.99999999659583 \tabularnewline
33 & 2.60978357669981e-09 & 5.21956715339962e-09 & 0.999999997390216 \tabularnewline
34 & 2.88085556322412e-09 & 5.76171112644824e-09 & 0.999999997119144 \tabularnewline
35 & 9.18010066600592e-09 & 1.83602013320118e-08 & 0.9999999908199 \tabularnewline
36 & 9.74112769617927e-07 & 1.94822553923585e-06 & 0.99999902588723 \tabularnewline
37 & 0.000374097117799097 & 0.000748194235598194 & 0.9996259028822 \tabularnewline
38 & 0.00583504778395467 & 0.0116700955679093 & 0.994164952216045 \tabularnewline
39 & 0.0201564796083976 & 0.0403129592167952 & 0.979843520391602 \tabularnewline
40 & 0.0490322668703238 & 0.0980645337406477 & 0.950967733129676 \tabularnewline
41 & 0.0700843453675452 & 0.140168690735090 & 0.929915654632455 \tabularnewline
42 & 0.0724986856499544 & 0.144997371299909 & 0.927501314350046 \tabularnewline
43 & 0.0927558348738917 & 0.185511669747783 & 0.907244165126108 \tabularnewline
44 & 0.0991995667485483 & 0.198399133497097 & 0.900800433251452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.00212462027808544[/C][C]0.00424924055617088[/C][C]0.997875379721915[/C][/ROW]
[ROW][C]18[/C][C]0.000692759857787616[/C][C]0.00138551971557523[/C][C]0.999307240142212[/C][/ROW]
[ROW][C]19[/C][C]0.000135820792718360[/C][C]0.000271641585436719[/C][C]0.999864179207282[/C][/ROW]
[ROW][C]20[/C][C]3.01176146051441e-05[/C][C]6.02352292102883e-05[/C][C]0.999969882385395[/C][/ROW]
[ROW][C]21[/C][C]1.5122937970789e-05[/C][C]3.0245875941578e-05[/C][C]0.99998487706203[/C][/ROW]
[ROW][C]22[/C][C]2.66196150550665e-06[/C][C]5.32392301101329e-06[/C][C]0.999997338038495[/C][/ROW]
[ROW][C]23[/C][C]4.89844127617984e-07[/C][C]9.79688255235967e-07[/C][C]0.999999510155872[/C][/ROW]
[ROW][C]24[/C][C]2.75890669522639e-07[/C][C]5.51781339045279e-07[/C][C]0.99999972410933[/C][/ROW]
[ROW][C]25[/C][C]3.17759141901912e-07[/C][C]6.35518283803824e-07[/C][C]0.999999682240858[/C][/ROW]
[ROW][C]26[/C][C]9.41698248552693e-07[/C][C]1.88339649710539e-06[/C][C]0.999999058301752[/C][/ROW]
[ROW][C]27[/C][C]8.36624539081892e-07[/C][C]1.67324907816378e-06[/C][C]0.99999916337546[/C][/ROW]
[ROW][C]28[/C][C]2.4593381047624e-07[/C][C]4.9186762095248e-07[/C][C]0.99999975406619[/C][/ROW]
[ROW][C]29[/C][C]9.530040488934e-08[/C][C]1.9060080977868e-07[/C][C]0.999999904699595[/C][/ROW]
[ROW][C]30[/C][C]2.24664589048073e-08[/C][C]4.49329178096146e-08[/C][C]0.999999977533541[/C][/ROW]
[ROW][C]31[/C][C]7.9373040972106e-09[/C][C]1.58746081944212e-08[/C][C]0.999999992062696[/C][/ROW]
[ROW][C]32[/C][C]3.40417084429783e-09[/C][C]6.80834168859566e-09[/C][C]0.99999999659583[/C][/ROW]
[ROW][C]33[/C][C]2.60978357669981e-09[/C][C]5.21956715339962e-09[/C][C]0.999999997390216[/C][/ROW]
[ROW][C]34[/C][C]2.88085556322412e-09[/C][C]5.76171112644824e-09[/C][C]0.999999997119144[/C][/ROW]
[ROW][C]35[/C][C]9.18010066600592e-09[/C][C]1.83602013320118e-08[/C][C]0.9999999908199[/C][/ROW]
[ROW][C]36[/C][C]9.74112769617927e-07[/C][C]1.94822553923585e-06[/C][C]0.99999902588723[/C][/ROW]
[ROW][C]37[/C][C]0.000374097117799097[/C][C]0.000748194235598194[/C][C]0.9996259028822[/C][/ROW]
[ROW][C]38[/C][C]0.00583504778395467[/C][C]0.0116700955679093[/C][C]0.994164952216045[/C][/ROW]
[ROW][C]39[/C][C]0.0201564796083976[/C][C]0.0403129592167952[/C][C]0.979843520391602[/C][/ROW]
[ROW][C]40[/C][C]0.0490322668703238[/C][C]0.0980645337406477[/C][C]0.950967733129676[/C][/ROW]
[ROW][C]41[/C][C]0.0700843453675452[/C][C]0.140168690735090[/C][C]0.929915654632455[/C][/ROW]
[ROW][C]42[/C][C]0.0724986856499544[/C][C]0.144997371299909[/C][C]0.927501314350046[/C][/ROW]
[ROW][C]43[/C][C]0.0927558348738917[/C][C]0.185511669747783[/C][C]0.907244165126108[/C][/ROW]
[ROW][C]44[/C][C]0.0991995667485483[/C][C]0.198399133497097[/C][C]0.900800433251452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.002124620278085440.004249240556170880.997875379721915
180.0006927598577876160.001385519715575230.999307240142212
190.0001358207927183600.0002716415854367190.999864179207282
203.01176146051441e-056.02352292102883e-050.999969882385395
211.5122937970789e-053.0245875941578e-050.99998487706203
222.66196150550665e-065.32392301101329e-060.999997338038495
234.89844127617984e-079.79688255235967e-070.999999510155872
242.75890669522639e-075.51781339045279e-070.99999972410933
253.17759141901912e-076.35518283803824e-070.999999682240858
269.41698248552693e-071.88339649710539e-060.999999058301752
278.36624539081892e-071.67324907816378e-060.99999916337546
282.4593381047624e-074.9186762095248e-070.99999975406619
299.530040488934e-081.9060080977868e-070.999999904699595
302.24664589048073e-084.49329178096146e-080.999999977533541
317.9373040972106e-091.58746081944212e-080.999999992062696
323.40417084429783e-096.80834168859566e-090.99999999659583
332.60978357669981e-095.21956715339962e-090.999999997390216
342.88085556322412e-095.76171112644824e-090.999999997119144
359.18010066600592e-091.83602013320118e-080.9999999908199
369.74112769617927e-071.94822553923585e-060.99999902588723
370.0003740971177990970.0007481942355981940.9996259028822
380.005835047783954670.01167009556790930.994164952216045
390.02015647960839760.04031295921679520.979843520391602
400.04903226687032380.09806453374064770.950967733129676
410.07008434536754520.1401686907350900.929915654632455
420.07249868564995440.1449973712999090.927501314350046
430.09275583487389170.1855116697477830.907244165126108
440.09919956674854830.1983991334970970.900800433251452







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level210.75NOK
5% type I error level230.821428571428571NOK
10% type I error level240.857142857142857NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 21 & 0.75 & NOK \tabularnewline
5% type I error level & 23 & 0.821428571428571 & NOK \tabularnewline
10% type I error level & 24 & 0.857142857142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58131&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]21[/C][C]0.75[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]23[/C][C]0.821428571428571[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]24[/C][C]0.857142857142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58131&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58131&T=6

As an alternative you can also use a 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 level210.75NOK
5% type I error level230.821428571428571NOK
10% type I error level240.857142857142857NOK



Parameters (Session):
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')
}