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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 00:44:37 -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/t1258703141manp4suvu65045z.htm/, Retrieved Thu, 25 Apr 2024 16:48:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57978, Retrieved Thu, 25 Apr 2024 16:48:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 07:44:37] [2b679e8ec54382eeb0ec0b6bb527570a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.03	2
100.25	1.8
99.6	2.7
100.16	2.3
100.49	1.9
99.72	2
100.14	2.3
98.48	2.8
100.38	2.4
101.45	2.3
98.42	2.7
98.6	2.7
100.06	2.9
98.62	3
100.84	2.2
100.02	2.3
97.95	2.8
98.32	2.8
98.27	2.8
97.22	2.2
99.28	2.6
100.38	2.8
99.02	2.5
100.32	2.4
99.81	2.3
100.6	1.9
101.19	1.7
100.47	2
101.77	2.1
102.32	1.7
102.39	1.8
101.16	1.8
100.63	1.8
101.48	1.3
101.44	1.3
100.09	1.3
100.7	1.2
100.78	1.4
99.81	2.2
98.45	2.9
98.49	3.1
97.48	3.5
97.91	3.6
96.94	4.4
98.53	4.1
96.82	5.1
95.76	5.8
95.27	5.9
97.32	5.4
96.68	5.5
97.87	4.8
97.42	3.2
97.94	2.7
99.52	2.1
100.99	1.9
99.92	0.6
101.97	0.7
101.58	-0.2
99.54	-1
100.83	-1.7

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 101.473296893034 -0.89729709691884X[t] + 0.968511877494062M1[t] + 0.74987074493858M2[t] + 1.24112149625985M3[t] + 0.536858770135734M4[t] + 0.558163579518627M5[t] + 0.627684621148016M6[t] + 1.16477319828442M7[t] -0.123651702024567M8[t] + 1.26970716541995M9[t] + 1.41512009092609M10[t] -0.0756291577526306M11[t] -0.0152507513212727t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  101.473296893034 -0.89729709691884X[t] +  0.968511877494062M1[t] +  0.74987074493858M2[t] +  1.24112149625985M3[t] +  0.536858770135734M4[t] +  0.558163579518627M5[t] +  0.627684621148016M6[t] +  1.16477319828442M7[t] -0.123651702024567M8[t] +  1.26970716541995M9[t] +  1.41512009092609M10[t] -0.0756291577526306M11[t] -0.0152507513212727t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  101.473296893034 -0.89729709691884X[t] +  0.968511877494062M1[t] +  0.74987074493858M2[t] +  1.24112149625985M3[t] +  0.536858770135734M4[t] +  0.558163579518627M5[t] +  0.627684621148016M6[t] +  1.16477319828442M7[t] -0.123651702024567M8[t] +  1.26970716541995M9[t] +  1.41512009092609M10[t] -0.0756291577526306M11[t] -0.0152507513212727t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 101.473296893034 -0.89729709691884X[t] + 0.968511877494062M1[t] + 0.74987074493858M2[t] + 1.24112149625985M3[t] + 0.536858770135734M4[t] + 0.558163579518627M5[t] + 0.627684621148016M6[t] + 1.16477319828442M7[t] -0.123651702024567M8[t] + 1.26970716541995M9[t] + 1.41512009092609M10[t] -0.0756291577526306M11[t] -0.0152507513212727t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)101.4732968930340.556211182.436800
X-0.897297096918840.092424-9.708500
M10.9685118774940620.6405171.51210.1373540.068677
M20.749870744938580.6391961.17310.2467760.123388
M31.241121496259850.6383131.94440.057980.02899
M40.5368587701357340.6362330.84380.4031430.201572
M50.5581635795186270.6354190.87840.3842820.192141
M60.6276846211480160.6343170.98950.3275740.163787
M71.164773198284420.6340821.83690.0726840.036342
M8-0.1236517020245670.633154-0.19530.8460220.423011
M91.269707165419950.6327012.00680.0506690.025334
M101.415120090926090.6323232.2380.0301060.015053
M11-0.07562915775263060.63218-0.11960.9052950.452648
t-0.01525075132127270.007606-2.0050.0508660.025433

\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) & 101.473296893034 & 0.556211 & 182.4368 & 0 & 0 \tabularnewline
X & -0.89729709691884 & 0.092424 & -9.7085 & 0 & 0 \tabularnewline
M1 & 0.968511877494062 & 0.640517 & 1.5121 & 0.137354 & 0.068677 \tabularnewline
M2 & 0.74987074493858 & 0.639196 & 1.1731 & 0.246776 & 0.123388 \tabularnewline
M3 & 1.24112149625985 & 0.638313 & 1.9444 & 0.05798 & 0.02899 \tabularnewline
M4 & 0.536858770135734 & 0.636233 & 0.8438 & 0.403143 & 0.201572 \tabularnewline
M5 & 0.558163579518627 & 0.635419 & 0.8784 & 0.384282 & 0.192141 \tabularnewline
M6 & 0.627684621148016 & 0.634317 & 0.9895 & 0.327574 & 0.163787 \tabularnewline
M7 & 1.16477319828442 & 0.634082 & 1.8369 & 0.072684 & 0.036342 \tabularnewline
M8 & -0.123651702024567 & 0.633154 & -0.1953 & 0.846022 & 0.423011 \tabularnewline
M9 & 1.26970716541995 & 0.632701 & 2.0068 & 0.050669 & 0.025334 \tabularnewline
M10 & 1.41512009092609 & 0.632323 & 2.238 & 0.030106 & 0.015053 \tabularnewline
M11 & -0.0756291577526306 & 0.63218 & -0.1196 & 0.905295 & 0.452648 \tabularnewline
t & -0.0152507513212727 & 0.007606 & -2.005 & 0.050866 & 0.025433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&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]101.473296893034[/C][C]0.556211[/C][C]182.4368[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.89729709691884[/C][C]0.092424[/C][C]-9.7085[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.968511877494062[/C][C]0.640517[/C][C]1.5121[/C][C]0.137354[/C][C]0.068677[/C][/ROW]
[ROW][C]M2[/C][C]0.74987074493858[/C][C]0.639196[/C][C]1.1731[/C][C]0.246776[/C][C]0.123388[/C][/ROW]
[ROW][C]M3[/C][C]1.24112149625985[/C][C]0.638313[/C][C]1.9444[/C][C]0.05798[/C][C]0.02899[/C][/ROW]
[ROW][C]M4[/C][C]0.536858770135734[/C][C]0.636233[/C][C]0.8438[/C][C]0.403143[/C][C]0.201572[/C][/ROW]
[ROW][C]M5[/C][C]0.558163579518627[/C][C]0.635419[/C][C]0.8784[/C][C]0.384282[/C][C]0.192141[/C][/ROW]
[ROW][C]M6[/C][C]0.627684621148016[/C][C]0.634317[/C][C]0.9895[/C][C]0.327574[/C][C]0.163787[/C][/ROW]
[ROW][C]M7[/C][C]1.16477319828442[/C][C]0.634082[/C][C]1.8369[/C][C]0.072684[/C][C]0.036342[/C][/ROW]
[ROW][C]M8[/C][C]-0.123651702024567[/C][C]0.633154[/C][C]-0.1953[/C][C]0.846022[/C][C]0.423011[/C][/ROW]
[ROW][C]M9[/C][C]1.26970716541995[/C][C]0.632701[/C][C]2.0068[/C][C]0.050669[/C][C]0.025334[/C][/ROW]
[ROW][C]M10[/C][C]1.41512009092609[/C][C]0.632323[/C][C]2.238[/C][C]0.030106[/C][C]0.015053[/C][/ROW]
[ROW][C]M11[/C][C]-0.0756291577526306[/C][C]0.63218[/C][C]-0.1196[/C][C]0.905295[/C][C]0.452648[/C][/ROW]
[ROW][C]t[/C][C]-0.0152507513212727[/C][C]0.007606[/C][C]-2.005[/C][C]0.050866[/C][C]0.025433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)101.4732968930340.556211182.436800
X-0.897297096918840.092424-9.708500
M10.9685118774940620.6405171.51210.1373540.068677
M20.749870744938580.6391961.17310.2467760.123388
M31.241121496259850.6383131.94440.057980.02899
M40.5368587701357340.6362330.84380.4031430.201572
M50.5581635795186270.6354190.87840.3842820.192141
M60.6276846211480160.6343170.98950.3275740.163787
M71.164773198284420.6340821.83690.0726840.036342
M8-0.1236517020245670.633154-0.19530.8460220.423011
M91.269707165419950.6327012.00680.0506690.025334
M101.415120090926090.6323232.2380.0301060.015053
M11-0.07562915775263060.63218-0.11960.9052950.452648
t-0.01525075132127270.007606-2.0050.0508660.025433






Multiple Linear Regression - Regression Statistics
Multiple R0.843822817706935
R-squared0.712036947682871
Adjusted R-squared0.630656085071508
F-TEST (value)8.74943966965834
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.36955831120389e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.999274140497838
Sum Squared Residuals45.9332451619139

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.843822817706935 \tabularnewline
R-squared & 0.712036947682871 \tabularnewline
Adjusted R-squared & 0.630656085071508 \tabularnewline
F-TEST (value) & 8.74943966965834 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 1.36955831120389e-08 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.999274140497838 \tabularnewline
Sum Squared Residuals & 45.9332451619139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.843822817706935[/C][/ROW]
[ROW][C]R-squared[/C][C]0.712036947682871[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.630656085071508[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.74943966965834[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]1.36955831120389e-08[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.999274140497838[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]45.9332451619139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.843822817706935
R-squared0.712036947682871
Adjusted R-squared0.630656085071508
F-TEST (value)8.74943966965834
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.36955831120389e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.999274140497838
Sum Squared Residuals45.9332451619139






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1100.03100.631963825369-0.601963825368862
2100.25100.577531360876-0.327531360875884
399.6100.245963973649-0.645963973648927
4100.1699.8853693349710.274630665028931
5100.49100.2503422318000.239657768199771
699.72100.214882812416-0.494882812416457
7100.14100.467531509156-0.327531509155934
898.4898.7152073090663-0.235207309066252
9100.38100.452234263957-0.0722342639570395
10101.45100.6721261478340.777873852166214
1198.4298.8072073090663-0.387207309066256
1298.698.8675857154976-0.267585715497621
13100.0699.64138742228660.418612577713367
1498.6299.317765828718-0.697765828717993
15100.84100.5116035062530.328396493746934
16100.0299.70236031911580.317639680884203
1797.9599.259765828718-1.30976582871799
1898.3299.3140361190261-0.994036119026117
1998.2799.8358739448412-1.56587394484124
2097.2299.0705765513623-1.85057655136229
2199.28100.089765828718-0.809765828717994
22100.38100.0404685835190.339531416480898
2399.0298.80365771259480.216342287405244
24100.3298.9537658287181.366234171282
2599.8199.9967566645827-0.186756664582665
26100.6100.1217836194730.478216380526545
27101.19100.7772430388570.41275696114278
28100.4799.78854043233620.681459567663826
29101.7799.7048647807062.06513521929409
30102.32100.1180539097822.20194609021843
31102.39100.5501620259051.83983797409519
32101.1699.24648637427461.91351362572545
33100.63100.6245944903980.0054055096022002
34101.48101.2034052130420.276594786957919
35101.4499.6974052130421.74259478695791
36100.0999.75778361947340.332216380526557
37100.7100.800774455338-0.100774455338116
38100.78100.3874231520780.392576847922404
3999.81100.145585474543-0.335585474542523
4098.4598.797964029254-0.347964029253941
4198.4998.6245586679318-0.134558667931802
4297.4898.3199101194724-0.839910119472372
4397.9198.7520182355956-0.842018235595627
4496.9496.73050490643030.209495093569705
4598.5398.37780215162920.152197848370811
4696.8297.6106672288952-0.790667228895227
4795.7695.4765592610520.283440738947971
4895.2795.4472079577915-0.177207957791512
4997.3296.84911763242370.470882367576276
5096.6896.5254960388550.154503961144927
5197.8797.62960400669830.240395993301737
5297.4298.345765884323-0.925765884323018
5397.9498.800468490844-0.860468490844063
5499.5299.39311703930350.126882960696515
55100.99100.0944142845020.895585715497615
5699.9299.9572248588666-0.0372248588666119
57101.97101.2456032652980.724396734702024
58101.58102.183332826710-0.603332826709803
5999.54101.395170504245-1.85517050424487
60100.83102.083656878519-1.25365687851942

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.03 & 100.631963825369 & -0.601963825368862 \tabularnewline
2 & 100.25 & 100.577531360876 & -0.327531360875884 \tabularnewline
3 & 99.6 & 100.245963973649 & -0.645963973648927 \tabularnewline
4 & 100.16 & 99.885369334971 & 0.274630665028931 \tabularnewline
5 & 100.49 & 100.250342231800 & 0.239657768199771 \tabularnewline
6 & 99.72 & 100.214882812416 & -0.494882812416457 \tabularnewline
7 & 100.14 & 100.467531509156 & -0.327531509155934 \tabularnewline
8 & 98.48 & 98.7152073090663 & -0.235207309066252 \tabularnewline
9 & 100.38 & 100.452234263957 & -0.0722342639570395 \tabularnewline
10 & 101.45 & 100.672126147834 & 0.777873852166214 \tabularnewline
11 & 98.42 & 98.8072073090663 & -0.387207309066256 \tabularnewline
12 & 98.6 & 98.8675857154976 & -0.267585715497621 \tabularnewline
13 & 100.06 & 99.6413874222866 & 0.418612577713367 \tabularnewline
14 & 98.62 & 99.317765828718 & -0.697765828717993 \tabularnewline
15 & 100.84 & 100.511603506253 & 0.328396493746934 \tabularnewline
16 & 100.02 & 99.7023603191158 & 0.317639680884203 \tabularnewline
17 & 97.95 & 99.259765828718 & -1.30976582871799 \tabularnewline
18 & 98.32 & 99.3140361190261 & -0.994036119026117 \tabularnewline
19 & 98.27 & 99.8358739448412 & -1.56587394484124 \tabularnewline
20 & 97.22 & 99.0705765513623 & -1.85057655136229 \tabularnewline
21 & 99.28 & 100.089765828718 & -0.809765828717994 \tabularnewline
22 & 100.38 & 100.040468583519 & 0.339531416480898 \tabularnewline
23 & 99.02 & 98.8036577125948 & 0.216342287405244 \tabularnewline
24 & 100.32 & 98.953765828718 & 1.366234171282 \tabularnewline
25 & 99.81 & 99.9967566645827 & -0.186756664582665 \tabularnewline
26 & 100.6 & 100.121783619473 & 0.478216380526545 \tabularnewline
27 & 101.19 & 100.777243038857 & 0.41275696114278 \tabularnewline
28 & 100.47 & 99.7885404323362 & 0.681459567663826 \tabularnewline
29 & 101.77 & 99.704864780706 & 2.06513521929409 \tabularnewline
30 & 102.32 & 100.118053909782 & 2.20194609021843 \tabularnewline
31 & 102.39 & 100.550162025905 & 1.83983797409519 \tabularnewline
32 & 101.16 & 99.2464863742746 & 1.91351362572545 \tabularnewline
33 & 100.63 & 100.624594490398 & 0.0054055096022002 \tabularnewline
34 & 101.48 & 101.203405213042 & 0.276594786957919 \tabularnewline
35 & 101.44 & 99.697405213042 & 1.74259478695791 \tabularnewline
36 & 100.09 & 99.7577836194734 & 0.332216380526557 \tabularnewline
37 & 100.7 & 100.800774455338 & -0.100774455338116 \tabularnewline
38 & 100.78 & 100.387423152078 & 0.392576847922404 \tabularnewline
39 & 99.81 & 100.145585474543 & -0.335585474542523 \tabularnewline
40 & 98.45 & 98.797964029254 & -0.347964029253941 \tabularnewline
41 & 98.49 & 98.6245586679318 & -0.134558667931802 \tabularnewline
42 & 97.48 & 98.3199101194724 & -0.839910119472372 \tabularnewline
43 & 97.91 & 98.7520182355956 & -0.842018235595627 \tabularnewline
44 & 96.94 & 96.7305049064303 & 0.209495093569705 \tabularnewline
45 & 98.53 & 98.3778021516292 & 0.152197848370811 \tabularnewline
46 & 96.82 & 97.6106672288952 & -0.790667228895227 \tabularnewline
47 & 95.76 & 95.476559261052 & 0.283440738947971 \tabularnewline
48 & 95.27 & 95.4472079577915 & -0.177207957791512 \tabularnewline
49 & 97.32 & 96.8491176324237 & 0.470882367576276 \tabularnewline
50 & 96.68 & 96.525496038855 & 0.154503961144927 \tabularnewline
51 & 97.87 & 97.6296040066983 & 0.240395993301737 \tabularnewline
52 & 97.42 & 98.345765884323 & -0.925765884323018 \tabularnewline
53 & 97.94 & 98.800468490844 & -0.860468490844063 \tabularnewline
54 & 99.52 & 99.3931170393035 & 0.126882960696515 \tabularnewline
55 & 100.99 & 100.094414284502 & 0.895585715497615 \tabularnewline
56 & 99.92 & 99.9572248588666 & -0.0372248588666119 \tabularnewline
57 & 101.97 & 101.245603265298 & 0.724396734702024 \tabularnewline
58 & 101.58 & 102.183332826710 & -0.603332826709803 \tabularnewline
59 & 99.54 & 101.395170504245 & -1.85517050424487 \tabularnewline
60 & 100.83 & 102.083656878519 & -1.25365687851942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&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]100.03[/C][C]100.631963825369[/C][C]-0.601963825368862[/C][/ROW]
[ROW][C]2[/C][C]100.25[/C][C]100.577531360876[/C][C]-0.327531360875884[/C][/ROW]
[ROW][C]3[/C][C]99.6[/C][C]100.245963973649[/C][C]-0.645963973648927[/C][/ROW]
[ROW][C]4[/C][C]100.16[/C][C]99.885369334971[/C][C]0.274630665028931[/C][/ROW]
[ROW][C]5[/C][C]100.49[/C][C]100.250342231800[/C][C]0.239657768199771[/C][/ROW]
[ROW][C]6[/C][C]99.72[/C][C]100.214882812416[/C][C]-0.494882812416457[/C][/ROW]
[ROW][C]7[/C][C]100.14[/C][C]100.467531509156[/C][C]-0.327531509155934[/C][/ROW]
[ROW][C]8[/C][C]98.48[/C][C]98.7152073090663[/C][C]-0.235207309066252[/C][/ROW]
[ROW][C]9[/C][C]100.38[/C][C]100.452234263957[/C][C]-0.0722342639570395[/C][/ROW]
[ROW][C]10[/C][C]101.45[/C][C]100.672126147834[/C][C]0.777873852166214[/C][/ROW]
[ROW][C]11[/C][C]98.42[/C][C]98.8072073090663[/C][C]-0.387207309066256[/C][/ROW]
[ROW][C]12[/C][C]98.6[/C][C]98.8675857154976[/C][C]-0.267585715497621[/C][/ROW]
[ROW][C]13[/C][C]100.06[/C][C]99.6413874222866[/C][C]0.418612577713367[/C][/ROW]
[ROW][C]14[/C][C]98.62[/C][C]99.317765828718[/C][C]-0.697765828717993[/C][/ROW]
[ROW][C]15[/C][C]100.84[/C][C]100.511603506253[/C][C]0.328396493746934[/C][/ROW]
[ROW][C]16[/C][C]100.02[/C][C]99.7023603191158[/C][C]0.317639680884203[/C][/ROW]
[ROW][C]17[/C][C]97.95[/C][C]99.259765828718[/C][C]-1.30976582871799[/C][/ROW]
[ROW][C]18[/C][C]98.32[/C][C]99.3140361190261[/C][C]-0.994036119026117[/C][/ROW]
[ROW][C]19[/C][C]98.27[/C][C]99.8358739448412[/C][C]-1.56587394484124[/C][/ROW]
[ROW][C]20[/C][C]97.22[/C][C]99.0705765513623[/C][C]-1.85057655136229[/C][/ROW]
[ROW][C]21[/C][C]99.28[/C][C]100.089765828718[/C][C]-0.809765828717994[/C][/ROW]
[ROW][C]22[/C][C]100.38[/C][C]100.040468583519[/C][C]0.339531416480898[/C][/ROW]
[ROW][C]23[/C][C]99.02[/C][C]98.8036577125948[/C][C]0.216342287405244[/C][/ROW]
[ROW][C]24[/C][C]100.32[/C][C]98.953765828718[/C][C]1.366234171282[/C][/ROW]
[ROW][C]25[/C][C]99.81[/C][C]99.9967566645827[/C][C]-0.186756664582665[/C][/ROW]
[ROW][C]26[/C][C]100.6[/C][C]100.121783619473[/C][C]0.478216380526545[/C][/ROW]
[ROW][C]27[/C][C]101.19[/C][C]100.777243038857[/C][C]0.41275696114278[/C][/ROW]
[ROW][C]28[/C][C]100.47[/C][C]99.7885404323362[/C][C]0.681459567663826[/C][/ROW]
[ROW][C]29[/C][C]101.77[/C][C]99.704864780706[/C][C]2.06513521929409[/C][/ROW]
[ROW][C]30[/C][C]102.32[/C][C]100.118053909782[/C][C]2.20194609021843[/C][/ROW]
[ROW][C]31[/C][C]102.39[/C][C]100.550162025905[/C][C]1.83983797409519[/C][/ROW]
[ROW][C]32[/C][C]101.16[/C][C]99.2464863742746[/C][C]1.91351362572545[/C][/ROW]
[ROW][C]33[/C][C]100.63[/C][C]100.624594490398[/C][C]0.0054055096022002[/C][/ROW]
[ROW][C]34[/C][C]101.48[/C][C]101.203405213042[/C][C]0.276594786957919[/C][/ROW]
[ROW][C]35[/C][C]101.44[/C][C]99.697405213042[/C][C]1.74259478695791[/C][/ROW]
[ROW][C]36[/C][C]100.09[/C][C]99.7577836194734[/C][C]0.332216380526557[/C][/ROW]
[ROW][C]37[/C][C]100.7[/C][C]100.800774455338[/C][C]-0.100774455338116[/C][/ROW]
[ROW][C]38[/C][C]100.78[/C][C]100.387423152078[/C][C]0.392576847922404[/C][/ROW]
[ROW][C]39[/C][C]99.81[/C][C]100.145585474543[/C][C]-0.335585474542523[/C][/ROW]
[ROW][C]40[/C][C]98.45[/C][C]98.797964029254[/C][C]-0.347964029253941[/C][/ROW]
[ROW][C]41[/C][C]98.49[/C][C]98.6245586679318[/C][C]-0.134558667931802[/C][/ROW]
[ROW][C]42[/C][C]97.48[/C][C]98.3199101194724[/C][C]-0.839910119472372[/C][/ROW]
[ROW][C]43[/C][C]97.91[/C][C]98.7520182355956[/C][C]-0.842018235595627[/C][/ROW]
[ROW][C]44[/C][C]96.94[/C][C]96.7305049064303[/C][C]0.209495093569705[/C][/ROW]
[ROW][C]45[/C][C]98.53[/C][C]98.3778021516292[/C][C]0.152197848370811[/C][/ROW]
[ROW][C]46[/C][C]96.82[/C][C]97.6106672288952[/C][C]-0.790667228895227[/C][/ROW]
[ROW][C]47[/C][C]95.76[/C][C]95.476559261052[/C][C]0.283440738947971[/C][/ROW]
[ROW][C]48[/C][C]95.27[/C][C]95.4472079577915[/C][C]-0.177207957791512[/C][/ROW]
[ROW][C]49[/C][C]97.32[/C][C]96.8491176324237[/C][C]0.470882367576276[/C][/ROW]
[ROW][C]50[/C][C]96.68[/C][C]96.525496038855[/C][C]0.154503961144927[/C][/ROW]
[ROW][C]51[/C][C]97.87[/C][C]97.6296040066983[/C][C]0.240395993301737[/C][/ROW]
[ROW][C]52[/C][C]97.42[/C][C]98.345765884323[/C][C]-0.925765884323018[/C][/ROW]
[ROW][C]53[/C][C]97.94[/C][C]98.800468490844[/C][C]-0.860468490844063[/C][/ROW]
[ROW][C]54[/C][C]99.52[/C][C]99.3931170393035[/C][C]0.126882960696515[/C][/ROW]
[ROW][C]55[/C][C]100.99[/C][C]100.094414284502[/C][C]0.895585715497615[/C][/ROW]
[ROW][C]56[/C][C]99.92[/C][C]99.9572248588666[/C][C]-0.0372248588666119[/C][/ROW]
[ROW][C]57[/C][C]101.97[/C][C]101.245603265298[/C][C]0.724396734702024[/C][/ROW]
[ROW][C]58[/C][C]101.58[/C][C]102.183332826710[/C][C]-0.603332826709803[/C][/ROW]
[ROW][C]59[/C][C]99.54[/C][C]101.395170504245[/C][C]-1.85517050424487[/C][/ROW]
[ROW][C]60[/C][C]100.83[/C][C]102.083656878519[/C][C]-1.25365687851942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1100.03100.631963825369-0.601963825368862
2100.25100.577531360876-0.327531360875884
399.6100.245963973649-0.645963973648927
4100.1699.8853693349710.274630665028931
5100.49100.2503422318000.239657768199771
699.72100.214882812416-0.494882812416457
7100.14100.467531509156-0.327531509155934
898.4898.7152073090663-0.235207309066252
9100.38100.452234263957-0.0722342639570395
10101.45100.6721261478340.777873852166214
1198.4298.8072073090663-0.387207309066256
1298.698.8675857154976-0.267585715497621
13100.0699.64138742228660.418612577713367
1498.6299.317765828718-0.697765828717993
15100.84100.5116035062530.328396493746934
16100.0299.70236031911580.317639680884203
1797.9599.259765828718-1.30976582871799
1898.3299.3140361190261-0.994036119026117
1998.2799.8358739448412-1.56587394484124
2097.2299.0705765513623-1.85057655136229
2199.28100.089765828718-0.809765828717994
22100.38100.0404685835190.339531416480898
2399.0298.80365771259480.216342287405244
24100.3298.9537658287181.366234171282
2599.8199.9967566645827-0.186756664582665
26100.6100.1217836194730.478216380526545
27101.19100.7772430388570.41275696114278
28100.4799.78854043233620.681459567663826
29101.7799.7048647807062.06513521929409
30102.32100.1180539097822.20194609021843
31102.39100.5501620259051.83983797409519
32101.1699.24648637427461.91351362572545
33100.63100.6245944903980.0054055096022002
34101.48101.2034052130420.276594786957919
35101.4499.6974052130421.74259478695791
36100.0999.75778361947340.332216380526557
37100.7100.800774455338-0.100774455338116
38100.78100.3874231520780.392576847922404
3999.81100.145585474543-0.335585474542523
4098.4598.797964029254-0.347964029253941
4198.4998.6245586679318-0.134558667931802
4297.4898.3199101194724-0.839910119472372
4397.9198.7520182355956-0.842018235595627
4496.9496.73050490643030.209495093569705
4598.5398.37780215162920.152197848370811
4696.8297.6106672288952-0.790667228895227
4795.7695.4765592610520.283440738947971
4895.2795.4472079577915-0.177207957791512
4997.3296.84911763242370.470882367576276
5096.6896.5254960388550.154503961144927
5197.8797.62960400669830.240395993301737
5297.4298.345765884323-0.925765884323018
5397.9498.800468490844-0.860468490844063
5499.5299.39311703930350.126882960696515
55100.99100.0944142845020.895585715497615
5699.9299.9572248588666-0.0372248588666119
57101.97101.2456032652980.724396734702024
58101.58102.183332826710-0.603332826709803
5999.54101.395170504245-1.85517050424487
60100.83102.083656878519-1.25365687851942






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2712214346180690.5424428692361380.728778565381931
180.1561142038984860.3122284077969720.843885796101514
190.1771687499008180.3543374998016360.822831250099182
200.3903480235551960.7806960471103920.609651976444804
210.3678952746012370.7357905492024750.632104725398763
220.2602013500947690.5204027001895380.73979864990523
230.2428860731596310.4857721463192610.757113926840369
240.3156383184187790.6312766368375580.684361681581221
250.2625369519671220.5250739039342440.737463048032878
260.2269513761531160.4539027523062330.773048623846884
270.1618237853637180.3236475707274350.838176214636282
280.1062785693453580.2125571386907160.893721430654642
290.3126858705834880.6253717411669760.687314129416512
300.501239603778910.997520792442180.49876039622109
310.5385658016562290.9228683966875410.461434198343771
320.5909826683317060.8180346633365890.409017331668294
330.5825372187632220.8349255624735560.417462781236778
340.6267387118132890.7465225763734220.373261288186711
350.8125937989418160.3748124021163670.187406201058184
360.8593979103889360.2812041792221270.140602089611064
370.8157324247096540.3685351505806920.184267575290346
380.7875989512091530.4248020975816940.212401048790847
390.7050193963233220.5899612073533560.294980603676678
400.7243297040916170.5513405918167660.275670295908383
410.9295997898172040.1408004203655910.0704002101827955
420.8771884410995170.2456231178009660.122811558900483
430.7684365720394010.4631268559211970.231563427960599

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.271221434618069 & 0.542442869236138 & 0.728778565381931 \tabularnewline
18 & 0.156114203898486 & 0.312228407796972 & 0.843885796101514 \tabularnewline
19 & 0.177168749900818 & 0.354337499801636 & 0.822831250099182 \tabularnewline
20 & 0.390348023555196 & 0.780696047110392 & 0.609651976444804 \tabularnewline
21 & 0.367895274601237 & 0.735790549202475 & 0.632104725398763 \tabularnewline
22 & 0.260201350094769 & 0.520402700189538 & 0.73979864990523 \tabularnewline
23 & 0.242886073159631 & 0.485772146319261 & 0.757113926840369 \tabularnewline
24 & 0.315638318418779 & 0.631276636837558 & 0.684361681581221 \tabularnewline
25 & 0.262536951967122 & 0.525073903934244 & 0.737463048032878 \tabularnewline
26 & 0.226951376153116 & 0.453902752306233 & 0.773048623846884 \tabularnewline
27 & 0.161823785363718 & 0.323647570727435 & 0.838176214636282 \tabularnewline
28 & 0.106278569345358 & 0.212557138690716 & 0.893721430654642 \tabularnewline
29 & 0.312685870583488 & 0.625371741166976 & 0.687314129416512 \tabularnewline
30 & 0.50123960377891 & 0.99752079244218 & 0.49876039622109 \tabularnewline
31 & 0.538565801656229 & 0.922868396687541 & 0.461434198343771 \tabularnewline
32 & 0.590982668331706 & 0.818034663336589 & 0.409017331668294 \tabularnewline
33 & 0.582537218763222 & 0.834925562473556 & 0.417462781236778 \tabularnewline
34 & 0.626738711813289 & 0.746522576373422 & 0.373261288186711 \tabularnewline
35 & 0.812593798941816 & 0.374812402116367 & 0.187406201058184 \tabularnewline
36 & 0.859397910388936 & 0.281204179222127 & 0.140602089611064 \tabularnewline
37 & 0.815732424709654 & 0.368535150580692 & 0.184267575290346 \tabularnewline
38 & 0.787598951209153 & 0.424802097581694 & 0.212401048790847 \tabularnewline
39 & 0.705019396323322 & 0.589961207353356 & 0.294980603676678 \tabularnewline
40 & 0.724329704091617 & 0.551340591816766 & 0.275670295908383 \tabularnewline
41 & 0.929599789817204 & 0.140800420365591 & 0.0704002101827955 \tabularnewline
42 & 0.877188441099517 & 0.245623117800966 & 0.122811558900483 \tabularnewline
43 & 0.768436572039401 & 0.463126855921197 & 0.231563427960599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&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]0.271221434618069[/C][C]0.542442869236138[/C][C]0.728778565381931[/C][/ROW]
[ROW][C]18[/C][C]0.156114203898486[/C][C]0.312228407796972[/C][C]0.843885796101514[/C][/ROW]
[ROW][C]19[/C][C]0.177168749900818[/C][C]0.354337499801636[/C][C]0.822831250099182[/C][/ROW]
[ROW][C]20[/C][C]0.390348023555196[/C][C]0.780696047110392[/C][C]0.609651976444804[/C][/ROW]
[ROW][C]21[/C][C]0.367895274601237[/C][C]0.735790549202475[/C][C]0.632104725398763[/C][/ROW]
[ROW][C]22[/C][C]0.260201350094769[/C][C]0.520402700189538[/C][C]0.73979864990523[/C][/ROW]
[ROW][C]23[/C][C]0.242886073159631[/C][C]0.485772146319261[/C][C]0.757113926840369[/C][/ROW]
[ROW][C]24[/C][C]0.315638318418779[/C][C]0.631276636837558[/C][C]0.684361681581221[/C][/ROW]
[ROW][C]25[/C][C]0.262536951967122[/C][C]0.525073903934244[/C][C]0.737463048032878[/C][/ROW]
[ROW][C]26[/C][C]0.226951376153116[/C][C]0.453902752306233[/C][C]0.773048623846884[/C][/ROW]
[ROW][C]27[/C][C]0.161823785363718[/C][C]0.323647570727435[/C][C]0.838176214636282[/C][/ROW]
[ROW][C]28[/C][C]0.106278569345358[/C][C]0.212557138690716[/C][C]0.893721430654642[/C][/ROW]
[ROW][C]29[/C][C]0.312685870583488[/C][C]0.625371741166976[/C][C]0.687314129416512[/C][/ROW]
[ROW][C]30[/C][C]0.50123960377891[/C][C]0.99752079244218[/C][C]0.49876039622109[/C][/ROW]
[ROW][C]31[/C][C]0.538565801656229[/C][C]0.922868396687541[/C][C]0.461434198343771[/C][/ROW]
[ROW][C]32[/C][C]0.590982668331706[/C][C]0.818034663336589[/C][C]0.409017331668294[/C][/ROW]
[ROW][C]33[/C][C]0.582537218763222[/C][C]0.834925562473556[/C][C]0.417462781236778[/C][/ROW]
[ROW][C]34[/C][C]0.626738711813289[/C][C]0.746522576373422[/C][C]0.373261288186711[/C][/ROW]
[ROW][C]35[/C][C]0.812593798941816[/C][C]0.374812402116367[/C][C]0.187406201058184[/C][/ROW]
[ROW][C]36[/C][C]0.859397910388936[/C][C]0.281204179222127[/C][C]0.140602089611064[/C][/ROW]
[ROW][C]37[/C][C]0.815732424709654[/C][C]0.368535150580692[/C][C]0.184267575290346[/C][/ROW]
[ROW][C]38[/C][C]0.787598951209153[/C][C]0.424802097581694[/C][C]0.212401048790847[/C][/ROW]
[ROW][C]39[/C][C]0.705019396323322[/C][C]0.589961207353356[/C][C]0.294980603676678[/C][/ROW]
[ROW][C]40[/C][C]0.724329704091617[/C][C]0.551340591816766[/C][C]0.275670295908383[/C][/ROW]
[ROW][C]41[/C][C]0.929599789817204[/C][C]0.140800420365591[/C][C]0.0704002101827955[/C][/ROW]
[ROW][C]42[/C][C]0.877188441099517[/C][C]0.245623117800966[/C][C]0.122811558900483[/C][/ROW]
[ROW][C]43[/C][C]0.768436572039401[/C][C]0.463126855921197[/C][C]0.231563427960599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2712214346180690.5424428692361380.728778565381931
180.1561142038984860.3122284077969720.843885796101514
190.1771687499008180.3543374998016360.822831250099182
200.3903480235551960.7806960471103920.609651976444804
210.3678952746012370.7357905492024750.632104725398763
220.2602013500947690.5204027001895380.73979864990523
230.2428860731596310.4857721463192610.757113926840369
240.3156383184187790.6312766368375580.684361681581221
250.2625369519671220.5250739039342440.737463048032878
260.2269513761531160.4539027523062330.773048623846884
270.1618237853637180.3236475707274350.838176214636282
280.1062785693453580.2125571386907160.893721430654642
290.3126858705834880.6253717411669760.687314129416512
300.501239603778910.997520792442180.49876039622109
310.5385658016562290.9228683966875410.461434198343771
320.5909826683317060.8180346633365890.409017331668294
330.5825372187632220.8349255624735560.417462781236778
340.6267387118132890.7465225763734220.373261288186711
350.8125937989418160.3748124021163670.187406201058184
360.8593979103889360.2812041792221270.140602089611064
370.8157324247096540.3685351505806920.184267575290346
380.7875989512091530.4248020975816940.212401048790847
390.7050193963233220.5899612073533560.294980603676678
400.7243297040916170.5513405918167660.275670295908383
410.9295997898172040.1408004203655910.0704002101827955
420.8771884410995170.2456231178009660.122811558900483
430.7684365720394010.4631268559211970.231563427960599






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57978&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57978&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57978&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}