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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 07:18:00 -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/t12587267417hiww43homjaglr.htm/, Retrieved Fri, 29 Mar 2024 02:13:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58193, Retrieved Fri, 29 Mar 2024 02:13:54 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 14:18:00] [fc845972e0ebdb725d2fb9537c0c51aa] [Current]
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Dataseries X:
111.4	91,2
111.5	92,2
111.6	93,2
111.7	94,2
111.8	95,2
111.9	96,2
111.10	97,2
111.11	98,2
111.12	99,2
111.13	100,2
111.14	101,2
111.15	102,2
111.16	103,2
111.17	104,2
111.18	105,2
111.19	106,2
111.20	107,2
111.21	108,2
111.22	109,2
111.23	110,2
111.24	111,2
111.25	112,2
111.26	113,2
111.27	114,2
111.28	115,2
111.29	116,2
111.30	117,2
111.31	118,2
111.32	119,2
111.33	120,2
111.34	121,2
111.35	122,2
111.36	123,2
111.37	124,2
111.38	125,2
111.39	126,2
111.40	127,2
111.41	128,2
111.42	129,2
111.43	130,2
111.44	131,2
111.45	132,2
111.46	133,2
111.47	134,2
111.48	135,2
111.49	136,2
111.50	137,2
111.51	138,2
111.52	139,2
111.53	140,2
111.54	141,2
111.55	142,2
111.56	143,2
111.57	144,2
111.58	145,2
111.59	146,2
111.60	147,2
111.61	148,2
111.62	149,2
111.63	150,2
111.64	151,2




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=58193&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=58193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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
biti[t] = + 110.721882352941 + 0.00529411764705877bikl[t] + 0.0364705882352985M1[t] + 0.0429411764705881M2[t] + 0.0656470588235293M3[t] + 0.0883529411764707M4[t] + 0.111058823529409M5[t] + 0.133764705882351M6[t] -0.0235294117647092M7[t] -0.0188235294117657M8[t] -0.0141176470588251M9[t] -0.00941176470588437M10[t] -0.00470588235294089M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
biti[t] =  +  110.721882352941 +  0.00529411764705877bikl[t] +  0.0364705882352985M1[t] +  0.0429411764705881M2[t] +  0.0656470588235293M3[t] +  0.0883529411764707M4[t] +  0.111058823529409M5[t] +  0.133764705882351M6[t] -0.0235294117647092M7[t] -0.0188235294117657M8[t] -0.0141176470588251M9[t] -0.00941176470588437M10[t] -0.00470588235294089M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]biti[t] =  +  110.721882352941 +  0.00529411764705877bikl[t] +  0.0364705882352985M1[t] +  0.0429411764705881M2[t] +  0.0656470588235293M3[t] +  0.0883529411764707M4[t] +  0.111058823529409M5[t] +  0.133764705882351M6[t] -0.0235294117647092M7[t] -0.0188235294117657M8[t] -0.0141176470588251M9[t] -0.00941176470588437M10[t] -0.00470588235294089M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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
biti[t] = + 110.721882352941 + 0.00529411764705877bikl[t] + 0.0364705882352985M1[t] + 0.0429411764705881M2[t] + 0.0656470588235293M3[t] + 0.0883529411764707M4[t] + 0.111058823529409M5[t] + 0.133764705882351M6[t] -0.0235294117647092M7[t] -0.0188235294117657M8[t] -0.0141176470588251M9[t] -0.00941176470588437M10[t] -0.00470588235294089M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)110.7218823529410.173513638.117300
bikl0.005294117647058770.0012394.27149.1e-054.6e-05
M10.03647058823529850.1018820.3580.7219370.360969
M20.04294117647058810.1069360.40160.6897910.344896
M30.06564705882352930.10680.61470.5416730.270836
M40.08835294117647070.1066770.82820.4116420.205821
M50.1110588235294090.1065691.04210.3025730.151287
M60.1337647058823510.1064761.25630.215090.107545
M7-0.02352941176470920.106396-0.22110.8259150.412957
M8-0.01882352941176570.106331-0.1770.8602320.430116
M9-0.01411764705882510.106281-0.13280.894880.44744
M10-0.009411764705884370.106245-0.08860.929780.46489
M11-0.004705882352940890.106223-0.04430.9648470.482424

\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) & 110.721882352941 & 0.173513 & 638.1173 & 0 & 0 \tabularnewline
bikl & 0.00529411764705877 & 0.001239 & 4.2714 & 9.1e-05 & 4.6e-05 \tabularnewline
M1 & 0.0364705882352985 & 0.101882 & 0.358 & 0.721937 & 0.360969 \tabularnewline
M2 & 0.0429411764705881 & 0.106936 & 0.4016 & 0.689791 & 0.344896 \tabularnewline
M3 & 0.0656470588235293 & 0.1068 & 0.6147 & 0.541673 & 0.270836 \tabularnewline
M4 & 0.0883529411764707 & 0.106677 & 0.8282 & 0.411642 & 0.205821 \tabularnewline
M5 & 0.111058823529409 & 0.106569 & 1.0421 & 0.302573 & 0.151287 \tabularnewline
M6 & 0.133764705882351 & 0.106476 & 1.2563 & 0.21509 & 0.107545 \tabularnewline
M7 & -0.0235294117647092 & 0.106396 & -0.2211 & 0.825915 & 0.412957 \tabularnewline
M8 & -0.0188235294117657 & 0.106331 & -0.177 & 0.860232 & 0.430116 \tabularnewline
M9 & -0.0141176470588251 & 0.106281 & -0.1328 & 0.89488 & 0.44744 \tabularnewline
M10 & -0.00941176470588437 & 0.106245 & -0.0886 & 0.92978 & 0.46489 \tabularnewline
M11 & -0.00470588235294089 & 0.106223 & -0.0443 & 0.964847 & 0.482424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&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]110.721882352941[/C][C]0.173513[/C][C]638.1173[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]bikl[/C][C]0.00529411764705877[/C][C]0.001239[/C][C]4.2714[/C][C]9.1e-05[/C][C]4.6e-05[/C][/ROW]
[ROW][C]M1[/C][C]0.0364705882352985[/C][C]0.101882[/C][C]0.358[/C][C]0.721937[/C][C]0.360969[/C][/ROW]
[ROW][C]M2[/C][C]0.0429411764705881[/C][C]0.106936[/C][C]0.4016[/C][C]0.689791[/C][C]0.344896[/C][/ROW]
[ROW][C]M3[/C][C]0.0656470588235293[/C][C]0.1068[/C][C]0.6147[/C][C]0.541673[/C][C]0.270836[/C][/ROW]
[ROW][C]M4[/C][C]0.0883529411764707[/C][C]0.106677[/C][C]0.8282[/C][C]0.411642[/C][C]0.205821[/C][/ROW]
[ROW][C]M5[/C][C]0.111058823529409[/C][C]0.106569[/C][C]1.0421[/C][C]0.302573[/C][C]0.151287[/C][/ROW]
[ROW][C]M6[/C][C]0.133764705882351[/C][C]0.106476[/C][C]1.2563[/C][C]0.21509[/C][C]0.107545[/C][/ROW]
[ROW][C]M7[/C][C]-0.0235294117647092[/C][C]0.106396[/C][C]-0.2211[/C][C]0.825915[/C][C]0.412957[/C][/ROW]
[ROW][C]M8[/C][C]-0.0188235294117657[/C][C]0.106331[/C][C]-0.177[/C][C]0.860232[/C][C]0.430116[/C][/ROW]
[ROW][C]M9[/C][C]-0.0141176470588251[/C][C]0.106281[/C][C]-0.1328[/C][C]0.89488[/C][C]0.44744[/C][/ROW]
[ROW][C]M10[/C][C]-0.00941176470588437[/C][C]0.106245[/C][C]-0.0886[/C][C]0.92978[/C][C]0.46489[/C][/ROW]
[ROW][C]M11[/C][C]-0.00470588235294089[/C][C]0.106223[/C][C]-0.0443[/C][C]0.964847[/C][C]0.482424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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)110.7218823529410.173513638.117300
bikl0.005294117647058770.0012394.27149.1e-054.6e-05
M10.03647058823529850.1018820.3580.7219370.360969
M20.04294117647058810.1069360.40160.6897910.344896
M30.06564705882352930.10680.61470.5416730.270836
M40.08835294117647070.1066770.82820.4116420.205821
M50.1110588235294090.1065691.04210.3025730.151287
M60.1337647058823510.1064761.25630.215090.107545
M7-0.02352941176470920.106396-0.22110.8259150.412957
M8-0.01882352941176570.106331-0.1770.8602320.430116
M9-0.01411764705882510.106281-0.13280.894880.44744
M10-0.009411764705884370.106245-0.08860.929780.46489
M11-0.004705882352940890.106223-0.04430.9648470.482424







Multiple Linear Regression - Regression Statistics
Multiple R0.563936182129659
R-squared0.318024017514976
Adjusted R-squared0.14753002189372
F-TEST (value)1.86530919377038
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.0636996367660261
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.167941691562001
Sum Squared Residuals1.35381176470589

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.563936182129659 \tabularnewline
R-squared & 0.318024017514976 \tabularnewline
Adjusted R-squared & 0.14753002189372 \tabularnewline
F-TEST (value) & 1.86530919377038 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.0636996367660261 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.167941691562001 \tabularnewline
Sum Squared Residuals & 1.35381176470589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.563936182129659[/C][/ROW]
[ROW][C]R-squared[/C][C]0.318024017514976[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.14753002189372[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.86530919377038[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.0636996367660261[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.167941691562001[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.35381176470589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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 R0.563936182129659
R-squared0.318024017514976
Adjusted R-squared0.14753002189372
F-TEST (value)1.86530919377038
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.0636996367660261
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.167941691562001
Sum Squared Residuals1.35381176470589







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1111.4111.2411764705880.158823529411790
2111.5111.2529411764710.247058823529409
3111.6111.2809411764710.319058823529404
4111.7111.3089411764710.391058823529412
5111.8111.3369411764710.463058823529409
6111.9111.3649411764710.535058823529417
7111.1111.212941176471-0.112941176470593
8111.11111.222941176471-0.112941176470590
9111.12111.232941176471-0.112941176470584
10111.13111.242941176471-0.112941176470593
11111.14111.252941176471-0.112941176470590
12111.15111.262941176471-0.112941176470585
13111.16111.304705882353-0.144705882352951
14111.17111.316470588235-0.146470588235294
15111.18111.344470588235-0.164470588235289
16111.19111.372470588235-0.182470588235298
17111.2111.400470588235-0.200470588235290
18111.21111.428470588235-0.218470588235300
19111.22111.276470588235-0.0564705882352936
20111.23111.286470588235-0.0564705882352909
21111.24111.296470588235-0.0564705882352994
22111.25111.306470588235-0.0564705882352937
23111.26111.316470588235-0.0564705882352908
24111.27111.326470588235-0.0564705882352996
25111.28111.368235294118-0.0882352941176518
26111.29111.38-0.0899999999999949
27111.3111.408-0.108000000000004
28111.31111.436-0.125999999999999
29111.32111.464-0.144000000000005
30111.33111.492-0.162000000000000
31111.34111.345.66560687254025e-15
32111.35111.35-5.75234304633909e-15
33111.36111.360
34111.37111.375.64132074387658e-15
35111.38111.38-5.68989300120393e-15
36111.39111.39-2.56739074444567e-16
37111.4111.431764705882-0.0317647058823524
38111.41111.443529411765-0.0335294117647097
39111.42111.471529411765-0.0515294117647047
40111.43111.499529411765-0.0695294117646996
41111.44111.527529411765-0.087529411764706
42111.45111.555529411765-0.105529411764701
43111.46111.4035294117650.0564705882352908
44111.47111.4135294117650.0564705882352936
45111.48111.4235294117650.0564705882352994
46111.49111.4335294117650.0564705882352909
47111.5111.4435294117650.0564705882352937
48111.51111.4535294117650.0564705882352991
49111.52111.4952941176470.0247058823529328
50111.53111.5070588235290.0229411764705896
51111.54111.5350588235290.00494117647059468
52111.55111.563058823529-0.0130588235294145
53111.56111.591058823529-0.0310588235294067
54111.57111.619058823529-0.0490588235294159
55111.58111.4670588235290.112941176470590
56111.59111.4770588235290.112941176470593
57111.6111.4870588235290.112941176470585
58111.61111.4970588235290.112941176470590
59111.62111.5070588235290.112941176470593
60111.63111.5170588235290.112941176470584
61111.64111.5588235294120.0811764705882321

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 111.4 & 111.241176470588 & 0.158823529411790 \tabularnewline
2 & 111.5 & 111.252941176471 & 0.247058823529409 \tabularnewline
3 & 111.6 & 111.280941176471 & 0.319058823529404 \tabularnewline
4 & 111.7 & 111.308941176471 & 0.391058823529412 \tabularnewline
5 & 111.8 & 111.336941176471 & 0.463058823529409 \tabularnewline
6 & 111.9 & 111.364941176471 & 0.535058823529417 \tabularnewline
7 & 111.1 & 111.212941176471 & -0.112941176470593 \tabularnewline
8 & 111.11 & 111.222941176471 & -0.112941176470590 \tabularnewline
9 & 111.12 & 111.232941176471 & -0.112941176470584 \tabularnewline
10 & 111.13 & 111.242941176471 & -0.112941176470593 \tabularnewline
11 & 111.14 & 111.252941176471 & -0.112941176470590 \tabularnewline
12 & 111.15 & 111.262941176471 & -0.112941176470585 \tabularnewline
13 & 111.16 & 111.304705882353 & -0.144705882352951 \tabularnewline
14 & 111.17 & 111.316470588235 & -0.146470588235294 \tabularnewline
15 & 111.18 & 111.344470588235 & -0.164470588235289 \tabularnewline
16 & 111.19 & 111.372470588235 & -0.182470588235298 \tabularnewline
17 & 111.2 & 111.400470588235 & -0.200470588235290 \tabularnewline
18 & 111.21 & 111.428470588235 & -0.218470588235300 \tabularnewline
19 & 111.22 & 111.276470588235 & -0.0564705882352936 \tabularnewline
20 & 111.23 & 111.286470588235 & -0.0564705882352909 \tabularnewline
21 & 111.24 & 111.296470588235 & -0.0564705882352994 \tabularnewline
22 & 111.25 & 111.306470588235 & -0.0564705882352937 \tabularnewline
23 & 111.26 & 111.316470588235 & -0.0564705882352908 \tabularnewline
24 & 111.27 & 111.326470588235 & -0.0564705882352996 \tabularnewline
25 & 111.28 & 111.368235294118 & -0.0882352941176518 \tabularnewline
26 & 111.29 & 111.38 & -0.0899999999999949 \tabularnewline
27 & 111.3 & 111.408 & -0.108000000000004 \tabularnewline
28 & 111.31 & 111.436 & -0.125999999999999 \tabularnewline
29 & 111.32 & 111.464 & -0.144000000000005 \tabularnewline
30 & 111.33 & 111.492 & -0.162000000000000 \tabularnewline
31 & 111.34 & 111.34 & 5.66560687254025e-15 \tabularnewline
32 & 111.35 & 111.35 & -5.75234304633909e-15 \tabularnewline
33 & 111.36 & 111.36 & 0 \tabularnewline
34 & 111.37 & 111.37 & 5.64132074387658e-15 \tabularnewline
35 & 111.38 & 111.38 & -5.68989300120393e-15 \tabularnewline
36 & 111.39 & 111.39 & -2.56739074444567e-16 \tabularnewline
37 & 111.4 & 111.431764705882 & -0.0317647058823524 \tabularnewline
38 & 111.41 & 111.443529411765 & -0.0335294117647097 \tabularnewline
39 & 111.42 & 111.471529411765 & -0.0515294117647047 \tabularnewline
40 & 111.43 & 111.499529411765 & -0.0695294117646996 \tabularnewline
41 & 111.44 & 111.527529411765 & -0.087529411764706 \tabularnewline
42 & 111.45 & 111.555529411765 & -0.105529411764701 \tabularnewline
43 & 111.46 & 111.403529411765 & 0.0564705882352908 \tabularnewline
44 & 111.47 & 111.413529411765 & 0.0564705882352936 \tabularnewline
45 & 111.48 & 111.423529411765 & 0.0564705882352994 \tabularnewline
46 & 111.49 & 111.433529411765 & 0.0564705882352909 \tabularnewline
47 & 111.5 & 111.443529411765 & 0.0564705882352937 \tabularnewline
48 & 111.51 & 111.453529411765 & 0.0564705882352991 \tabularnewline
49 & 111.52 & 111.495294117647 & 0.0247058823529328 \tabularnewline
50 & 111.53 & 111.507058823529 & 0.0229411764705896 \tabularnewline
51 & 111.54 & 111.535058823529 & 0.00494117647059468 \tabularnewline
52 & 111.55 & 111.563058823529 & -0.0130588235294145 \tabularnewline
53 & 111.56 & 111.591058823529 & -0.0310588235294067 \tabularnewline
54 & 111.57 & 111.619058823529 & -0.0490588235294159 \tabularnewline
55 & 111.58 & 111.467058823529 & 0.112941176470590 \tabularnewline
56 & 111.59 & 111.477058823529 & 0.112941176470593 \tabularnewline
57 & 111.6 & 111.487058823529 & 0.112941176470585 \tabularnewline
58 & 111.61 & 111.497058823529 & 0.112941176470590 \tabularnewline
59 & 111.62 & 111.507058823529 & 0.112941176470593 \tabularnewline
60 & 111.63 & 111.517058823529 & 0.112941176470584 \tabularnewline
61 & 111.64 & 111.558823529412 & 0.0811764705882321 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&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]111.4[/C][C]111.241176470588[/C][C]0.158823529411790[/C][/ROW]
[ROW][C]2[/C][C]111.5[/C][C]111.252941176471[/C][C]0.247058823529409[/C][/ROW]
[ROW][C]3[/C][C]111.6[/C][C]111.280941176471[/C][C]0.319058823529404[/C][/ROW]
[ROW][C]4[/C][C]111.7[/C][C]111.308941176471[/C][C]0.391058823529412[/C][/ROW]
[ROW][C]5[/C][C]111.8[/C][C]111.336941176471[/C][C]0.463058823529409[/C][/ROW]
[ROW][C]6[/C][C]111.9[/C][C]111.364941176471[/C][C]0.535058823529417[/C][/ROW]
[ROW][C]7[/C][C]111.1[/C][C]111.212941176471[/C][C]-0.112941176470593[/C][/ROW]
[ROW][C]8[/C][C]111.11[/C][C]111.222941176471[/C][C]-0.112941176470590[/C][/ROW]
[ROW][C]9[/C][C]111.12[/C][C]111.232941176471[/C][C]-0.112941176470584[/C][/ROW]
[ROW][C]10[/C][C]111.13[/C][C]111.242941176471[/C][C]-0.112941176470593[/C][/ROW]
[ROW][C]11[/C][C]111.14[/C][C]111.252941176471[/C][C]-0.112941176470590[/C][/ROW]
[ROW][C]12[/C][C]111.15[/C][C]111.262941176471[/C][C]-0.112941176470585[/C][/ROW]
[ROW][C]13[/C][C]111.16[/C][C]111.304705882353[/C][C]-0.144705882352951[/C][/ROW]
[ROW][C]14[/C][C]111.17[/C][C]111.316470588235[/C][C]-0.146470588235294[/C][/ROW]
[ROW][C]15[/C][C]111.18[/C][C]111.344470588235[/C][C]-0.164470588235289[/C][/ROW]
[ROW][C]16[/C][C]111.19[/C][C]111.372470588235[/C][C]-0.182470588235298[/C][/ROW]
[ROW][C]17[/C][C]111.2[/C][C]111.400470588235[/C][C]-0.200470588235290[/C][/ROW]
[ROW][C]18[/C][C]111.21[/C][C]111.428470588235[/C][C]-0.218470588235300[/C][/ROW]
[ROW][C]19[/C][C]111.22[/C][C]111.276470588235[/C][C]-0.0564705882352936[/C][/ROW]
[ROW][C]20[/C][C]111.23[/C][C]111.286470588235[/C][C]-0.0564705882352909[/C][/ROW]
[ROW][C]21[/C][C]111.24[/C][C]111.296470588235[/C][C]-0.0564705882352994[/C][/ROW]
[ROW][C]22[/C][C]111.25[/C][C]111.306470588235[/C][C]-0.0564705882352937[/C][/ROW]
[ROW][C]23[/C][C]111.26[/C][C]111.316470588235[/C][C]-0.0564705882352908[/C][/ROW]
[ROW][C]24[/C][C]111.27[/C][C]111.326470588235[/C][C]-0.0564705882352996[/C][/ROW]
[ROW][C]25[/C][C]111.28[/C][C]111.368235294118[/C][C]-0.0882352941176518[/C][/ROW]
[ROW][C]26[/C][C]111.29[/C][C]111.38[/C][C]-0.0899999999999949[/C][/ROW]
[ROW][C]27[/C][C]111.3[/C][C]111.408[/C][C]-0.108000000000004[/C][/ROW]
[ROW][C]28[/C][C]111.31[/C][C]111.436[/C][C]-0.125999999999999[/C][/ROW]
[ROW][C]29[/C][C]111.32[/C][C]111.464[/C][C]-0.144000000000005[/C][/ROW]
[ROW][C]30[/C][C]111.33[/C][C]111.492[/C][C]-0.162000000000000[/C][/ROW]
[ROW][C]31[/C][C]111.34[/C][C]111.34[/C][C]5.66560687254025e-15[/C][/ROW]
[ROW][C]32[/C][C]111.35[/C][C]111.35[/C][C]-5.75234304633909e-15[/C][/ROW]
[ROW][C]33[/C][C]111.36[/C][C]111.36[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]111.37[/C][C]111.37[/C][C]5.64132074387658e-15[/C][/ROW]
[ROW][C]35[/C][C]111.38[/C][C]111.38[/C][C]-5.68989300120393e-15[/C][/ROW]
[ROW][C]36[/C][C]111.39[/C][C]111.39[/C][C]-2.56739074444567e-16[/C][/ROW]
[ROW][C]37[/C][C]111.4[/C][C]111.431764705882[/C][C]-0.0317647058823524[/C][/ROW]
[ROW][C]38[/C][C]111.41[/C][C]111.443529411765[/C][C]-0.0335294117647097[/C][/ROW]
[ROW][C]39[/C][C]111.42[/C][C]111.471529411765[/C][C]-0.0515294117647047[/C][/ROW]
[ROW][C]40[/C][C]111.43[/C][C]111.499529411765[/C][C]-0.0695294117646996[/C][/ROW]
[ROW][C]41[/C][C]111.44[/C][C]111.527529411765[/C][C]-0.087529411764706[/C][/ROW]
[ROW][C]42[/C][C]111.45[/C][C]111.555529411765[/C][C]-0.105529411764701[/C][/ROW]
[ROW][C]43[/C][C]111.46[/C][C]111.403529411765[/C][C]0.0564705882352908[/C][/ROW]
[ROW][C]44[/C][C]111.47[/C][C]111.413529411765[/C][C]0.0564705882352936[/C][/ROW]
[ROW][C]45[/C][C]111.48[/C][C]111.423529411765[/C][C]0.0564705882352994[/C][/ROW]
[ROW][C]46[/C][C]111.49[/C][C]111.433529411765[/C][C]0.0564705882352909[/C][/ROW]
[ROW][C]47[/C][C]111.5[/C][C]111.443529411765[/C][C]0.0564705882352937[/C][/ROW]
[ROW][C]48[/C][C]111.51[/C][C]111.453529411765[/C][C]0.0564705882352991[/C][/ROW]
[ROW][C]49[/C][C]111.52[/C][C]111.495294117647[/C][C]0.0247058823529328[/C][/ROW]
[ROW][C]50[/C][C]111.53[/C][C]111.507058823529[/C][C]0.0229411764705896[/C][/ROW]
[ROW][C]51[/C][C]111.54[/C][C]111.535058823529[/C][C]0.00494117647059468[/C][/ROW]
[ROW][C]52[/C][C]111.55[/C][C]111.563058823529[/C][C]-0.0130588235294145[/C][/ROW]
[ROW][C]53[/C][C]111.56[/C][C]111.591058823529[/C][C]-0.0310588235294067[/C][/ROW]
[ROW][C]54[/C][C]111.57[/C][C]111.619058823529[/C][C]-0.0490588235294159[/C][/ROW]
[ROW][C]55[/C][C]111.58[/C][C]111.467058823529[/C][C]0.112941176470590[/C][/ROW]
[ROW][C]56[/C][C]111.59[/C][C]111.477058823529[/C][C]0.112941176470593[/C][/ROW]
[ROW][C]57[/C][C]111.6[/C][C]111.487058823529[/C][C]0.112941176470585[/C][/ROW]
[ROW][C]58[/C][C]111.61[/C][C]111.497058823529[/C][C]0.112941176470590[/C][/ROW]
[ROW][C]59[/C][C]111.62[/C][C]111.507058823529[/C][C]0.112941176470593[/C][/ROW]
[ROW][C]60[/C][C]111.63[/C][C]111.517058823529[/C][C]0.112941176470584[/C][/ROW]
[ROW][C]61[/C][C]111.64[/C][C]111.558823529412[/C][C]0.0811764705882321[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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
1111.4111.2411764705880.158823529411790
2111.5111.2529411764710.247058823529409
3111.6111.2809411764710.319058823529404
4111.7111.3089411764710.391058823529412
5111.8111.3369411764710.463058823529409
6111.9111.3649411764710.535058823529417
7111.1111.212941176471-0.112941176470593
8111.11111.222941176471-0.112941176470590
9111.12111.232941176471-0.112941176470584
10111.13111.242941176471-0.112941176470593
11111.14111.252941176471-0.112941176470590
12111.15111.262941176471-0.112941176470585
13111.16111.304705882353-0.144705882352951
14111.17111.316470588235-0.146470588235294
15111.18111.344470588235-0.164470588235289
16111.19111.372470588235-0.182470588235298
17111.2111.400470588235-0.200470588235290
18111.21111.428470588235-0.218470588235300
19111.22111.276470588235-0.0564705882352936
20111.23111.286470588235-0.0564705882352909
21111.24111.296470588235-0.0564705882352994
22111.25111.306470588235-0.0564705882352937
23111.26111.316470588235-0.0564705882352908
24111.27111.326470588235-0.0564705882352996
25111.28111.368235294118-0.0882352941176518
26111.29111.38-0.0899999999999949
27111.3111.408-0.108000000000004
28111.31111.436-0.125999999999999
29111.32111.464-0.144000000000005
30111.33111.492-0.162000000000000
31111.34111.345.66560687254025e-15
32111.35111.35-5.75234304633909e-15
33111.36111.360
34111.37111.375.64132074387658e-15
35111.38111.38-5.68989300120393e-15
36111.39111.39-2.56739074444567e-16
37111.4111.431764705882-0.0317647058823524
38111.41111.443529411765-0.0335294117647097
39111.42111.471529411765-0.0515294117647047
40111.43111.499529411765-0.0695294117646996
41111.44111.527529411765-0.087529411764706
42111.45111.555529411765-0.105529411764701
43111.46111.4035294117650.0564705882352908
44111.47111.4135294117650.0564705882352936
45111.48111.4235294117650.0564705882352994
46111.49111.4335294117650.0564705882352909
47111.5111.4435294117650.0564705882352937
48111.51111.4535294117650.0564705882352991
49111.52111.4952941176470.0247058823529328
50111.53111.5070588235290.0229411764705896
51111.54111.5350588235290.00494117647059468
52111.55111.563058823529-0.0130588235294145
53111.56111.591058823529-0.0310588235294067
54111.57111.619058823529-0.0490588235294159
55111.58111.4670588235290.112941176470590
56111.59111.4770588235290.112941176470593
57111.6111.4870588235290.112941176470585
58111.61111.4970588235290.112941176470590
59111.62111.5070588235290.112941176470593
60111.63111.5170588235290.112941176470584
61111.64111.5588235294120.0811764705882321







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
16100
17100
18100
19100
20100
21100
22100
2311.99514737223241e-3139.97573686116206e-314
2418.55081090396699e-3064.27540545198349e-306
2518.34728714463905e-2914.17364357231952e-291
2612.53107192430004e-2891.26553596215002e-289
2719.24996927985933e-2634.62498463992967e-263
2811.80600591447304e-2529.03002957236519e-253
2914.5094638548793e-2362.25473192743965e-236
3012.29643585092949e-2401.14821792546475e-240
3112.09325831790545e-2181.04662915895272e-218
3213.54937182832621e-2011.77468591416310e-201
3312.46653027620546e-1861.23326513810273e-186
3412.93433837147492e-1771.46716918573746e-177
3513.94114146968869e-1701.97057073484435e-170
3611.03772924614298e-1615.18864623071491e-162
3714.00192806182619e-1392.00096403091309e-139
3814.19998818971376e-1322.09999409485688e-132
3912.64986203890171e-1141.32493101945086e-114
4014.60254732163907e-1032.30127366081953e-103
4114.24323627005003e-882.12161813502501e-88
4213.25256822186091e-761.62628411093046e-76
4312.17470625731146e-641.08735312865573e-64
4412.03791733501037e-541.01895866750518e-54
4516.30886377011875e-393.15443188505937e-39

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 1 & 0 & 0 \tabularnewline
17 & 1 & 0 & 0 \tabularnewline
18 & 1 & 0 & 0 \tabularnewline
19 & 1 & 0 & 0 \tabularnewline
20 & 1 & 0 & 0 \tabularnewline
21 & 1 & 0 & 0 \tabularnewline
22 & 1 & 0 & 0 \tabularnewline
23 & 1 & 1.99514737223241e-313 & 9.97573686116206e-314 \tabularnewline
24 & 1 & 8.55081090396699e-306 & 4.27540545198349e-306 \tabularnewline
25 & 1 & 8.34728714463905e-291 & 4.17364357231952e-291 \tabularnewline
26 & 1 & 2.53107192430004e-289 & 1.26553596215002e-289 \tabularnewline
27 & 1 & 9.24996927985933e-263 & 4.62498463992967e-263 \tabularnewline
28 & 1 & 1.80600591447304e-252 & 9.03002957236519e-253 \tabularnewline
29 & 1 & 4.5094638548793e-236 & 2.25473192743965e-236 \tabularnewline
30 & 1 & 2.29643585092949e-240 & 1.14821792546475e-240 \tabularnewline
31 & 1 & 2.09325831790545e-218 & 1.04662915895272e-218 \tabularnewline
32 & 1 & 3.54937182832621e-201 & 1.77468591416310e-201 \tabularnewline
33 & 1 & 2.46653027620546e-186 & 1.23326513810273e-186 \tabularnewline
34 & 1 & 2.93433837147492e-177 & 1.46716918573746e-177 \tabularnewline
35 & 1 & 3.94114146968869e-170 & 1.97057073484435e-170 \tabularnewline
36 & 1 & 1.03772924614298e-161 & 5.18864623071491e-162 \tabularnewline
37 & 1 & 4.00192806182619e-139 & 2.00096403091309e-139 \tabularnewline
38 & 1 & 4.19998818971376e-132 & 2.09999409485688e-132 \tabularnewline
39 & 1 & 2.64986203890171e-114 & 1.32493101945086e-114 \tabularnewline
40 & 1 & 4.60254732163907e-103 & 2.30127366081953e-103 \tabularnewline
41 & 1 & 4.24323627005003e-88 & 2.12161813502501e-88 \tabularnewline
42 & 1 & 3.25256822186091e-76 & 1.62628411093046e-76 \tabularnewline
43 & 1 & 2.17470625731146e-64 & 1.08735312865573e-64 \tabularnewline
44 & 1 & 2.03791733501037e-54 & 1.01895866750518e-54 \tabularnewline
45 & 1 & 6.30886377011875e-39 & 3.15443188505937e-39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&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]16[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]1.99514737223241e-313[/C][C]9.97573686116206e-314[/C][/ROW]
[ROW][C]24[/C][C]1[/C][C]8.55081090396699e-306[/C][C]4.27540545198349e-306[/C][/ROW]
[ROW][C]25[/C][C]1[/C][C]8.34728714463905e-291[/C][C]4.17364357231952e-291[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]2.53107192430004e-289[/C][C]1.26553596215002e-289[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]9.24996927985933e-263[/C][C]4.62498463992967e-263[/C][/ROW]
[ROW][C]28[/C][C]1[/C][C]1.80600591447304e-252[/C][C]9.03002957236519e-253[/C][/ROW]
[ROW][C]29[/C][C]1[/C][C]4.5094638548793e-236[/C][C]2.25473192743965e-236[/C][/ROW]
[ROW][C]30[/C][C]1[/C][C]2.29643585092949e-240[/C][C]1.14821792546475e-240[/C][/ROW]
[ROW][C]31[/C][C]1[/C][C]2.09325831790545e-218[/C][C]1.04662915895272e-218[/C][/ROW]
[ROW][C]32[/C][C]1[/C][C]3.54937182832621e-201[/C][C]1.77468591416310e-201[/C][/ROW]
[ROW][C]33[/C][C]1[/C][C]2.46653027620546e-186[/C][C]1.23326513810273e-186[/C][/ROW]
[ROW][C]34[/C][C]1[/C][C]2.93433837147492e-177[/C][C]1.46716918573746e-177[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]3.94114146968869e-170[/C][C]1.97057073484435e-170[/C][/ROW]
[ROW][C]36[/C][C]1[/C][C]1.03772924614298e-161[/C][C]5.18864623071491e-162[/C][/ROW]
[ROW][C]37[/C][C]1[/C][C]4.00192806182619e-139[/C][C]2.00096403091309e-139[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]4.19998818971376e-132[/C][C]2.09999409485688e-132[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]2.64986203890171e-114[/C][C]1.32493101945086e-114[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]4.60254732163907e-103[/C][C]2.30127366081953e-103[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]4.24323627005003e-88[/C][C]2.12161813502501e-88[/C][/ROW]
[ROW][C]42[/C][C]1[/C][C]3.25256822186091e-76[/C][C]1.62628411093046e-76[/C][/ROW]
[ROW][C]43[/C][C]1[/C][C]2.17470625731146e-64[/C][C]1.08735312865573e-64[/C][/ROW]
[ROW][C]44[/C][C]1[/C][C]2.03791733501037e-54[/C][C]1.01895866750518e-54[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]6.30886377011875e-39[/C][C]3.15443188505937e-39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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
16100
17100
18100
19100
20100
21100
22100
2311.99514737223241e-3139.97573686116206e-314
2418.55081090396699e-3064.27540545198349e-306
2518.34728714463905e-2914.17364357231952e-291
2612.53107192430004e-2891.26553596215002e-289
2719.24996927985933e-2634.62498463992967e-263
2811.80600591447304e-2529.03002957236519e-253
2914.5094638548793e-2362.25473192743965e-236
3012.29643585092949e-2401.14821792546475e-240
3112.09325831790545e-2181.04662915895272e-218
3213.54937182832621e-2011.77468591416310e-201
3312.46653027620546e-1861.23326513810273e-186
3412.93433837147492e-1771.46716918573746e-177
3513.94114146968869e-1701.97057073484435e-170
3611.03772924614298e-1615.18864623071491e-162
3714.00192806182619e-1392.00096403091309e-139
3814.19998818971376e-1322.09999409485688e-132
3912.64986203890171e-1141.32493101945086e-114
4014.60254732163907e-1032.30127366081953e-103
4114.24323627005003e-882.12161813502501e-88
4213.25256822186091e-761.62628411093046e-76
4312.17470625731146e-641.08735312865573e-64
4412.03791733501037e-541.01895866750518e-54
4516.30886377011875e-393.15443188505937e-39







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level301NOK
5% type I error level301NOK
10% type I error level301NOK

\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 & 30 & 1 & NOK \tabularnewline
5% type I error level & 30 & 1 & NOK \tabularnewline
10% type I error level & 30 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58193&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]30[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]30[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]30[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58193&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58193&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 level301NOK
5% type I error level301NOK
10% type I error level301NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}