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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 07:38:51 -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/t1258727994fdvidnjrq336989.htm/, Retrieved Fri, 19 Apr 2024 22:43:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58218, Retrieved Fri, 19 Apr 2024 22:43:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Model 4] [2009-11-20 14:38:51] [865cd78857e928bd6e7d79509c6cdcc5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21,3	2533	21,8	19,2	20	20,3
21,5	2058	21,3	21,8	19,2	20
19,5	2160	21,5	21,3	21,8	19,2
19,5	2260	19,5	21,5	21,3	21,8
19,7	2498	19,5	19,5	21,5	21,3
18,7	2695	19,7	19,5	19,5	21,5
19,7	2799	18,7	19,7	19,5	19,5
20	2946	19,7	18,7	19,7	19,5
19,7	2930	20	19,7	18,7	19,7
19,2	2318	19,7	20	19,7	18,7
19,7	2540	19,2	19,7	20	19,7
22	2570	19,7	19,2	19,7	20
21,8	2669	22	19,7	19,2	19,7
22,8	2450	21,8	22	19,7	19,2
21	2842	22,8	21,8	22	19,7
25	3440	21	22,8	21,8	22
23,3	2678	25	21	22,8	21,8
25	2981	23,3	25	21	22,8
26,8	2260	25	23,3	25	21
25,3	2844	26,8	25	23,3	25
26,5	2546	25,3	26,8	25	23,3
27,8	2456	26,5	25,3	26,8	25
22	2295	27,8	26,5	25,3	26,8
22,3	2379	22	27,8	26,5	25,3
28	2479	22,3	22	27,8	26,5
25	2057	28	22,3	22	27,8
27,3	2280	25	28	22,3	22
25,8	2351	27,3	25	28	22,3
27,3	2276	25,8	27,3	25	28
23,5	2548	27,3	25,8	27,3	25
24,5	2311	23,5	27,3	25,8	27,3
18	2201	24,5	23,5	27,3	25,8
21,3	2725	18	24,5	23,5	27,3
21,8	2408	21,3	18	24,5	23,5
20,5	2139	21,8	21,3	18	24,5
22,3	1898	20,5	21,8	21,3	18
18,7	2537	22,3	20,5	21,8	21,3
22,3	2068	18,7	22,3	20,5	21,8
17,7	2063	22,3	18,7	22,3	20,5
19,7	2520	17,7	22,3	18,7	22,3
20,5	2434	19,7	17,7	22,3	18,7
18,5	2190	20,5	19,7	17,7	22,3
10	2794	18,5	20,5	19,7	17,7
14,2	2070	10	18,5	20,5	19,7
15,5	2615	14,2	10	18,5	20,5
16,5	2265	15,5	14,2	10	18,5
20,5	2139	16,5	15,5	14,2	10
15,7	2428	20,5	16,5	15,5	14,2
11,7	2137	15,7	20,5	16,5	15,5
7,5	1823	11,7	15,7	20,5	16,5
3,5	2063	7,5	11,7	15,7	20,5
4,5	1806	3,5	7,5	11,7	15,7
2,2	1758	4,5	3,5	7,5	11,7
5	2243	2,2	4,5	3,5	7,5
2,3	1993	5	2,2	4,5	3,5
6,1	1932	2,3	5	2,2	4,5
3,3	2465	6,1	2,3	5	2,2

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=58218&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=58218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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] = + 1.85422779475554 + 0.000604826557932779X[t] + 0.574485001754852Y1[t] + 0.391886275032236Y2[t] -0.0635822312445514Y3[t] -0.00547461318830385Y4[t] -0.301760548071200M1[t] -0.417100597659018M2[t] -1.99878180986883M3[t] + 0.351604644101707M4[t] + 0.316273377056073M5[t] -0.606367151252546M6[t] -1.53548312063179M7[t] -0.388501259503871M8[t] + 0.560018451568021M9[t] + 1.32513484904000M10[t] -0.155911104604277M11[t] -0.0496906557819444t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.85422779475554 +  0.000604826557932779X[t] +  0.574485001754852Y1[t] +  0.391886275032236Y2[t] -0.0635822312445514Y3[t] -0.00547461318830385Y4[t] -0.301760548071200M1[t] -0.417100597659018M2[t] -1.99878180986883M3[t] +  0.351604644101707M4[t] +  0.316273377056073M5[t] -0.606367151252546M6[t] -1.53548312063179M7[t] -0.388501259503871M8[t] +  0.560018451568021M9[t] +  1.32513484904000M10[t] -0.155911104604277M11[t] -0.0496906557819444t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.85422779475554 +  0.000604826557932779X[t] +  0.574485001754852Y1[t] +  0.391886275032236Y2[t] -0.0635822312445514Y3[t] -0.00547461318830385Y4[t] -0.301760548071200M1[t] -0.417100597659018M2[t] -1.99878180986883M3[t] +  0.351604644101707M4[t] +  0.316273377056073M5[t] -0.606367151252546M6[t] -1.53548312063179M7[t] -0.388501259503871M8[t] +  0.560018451568021M9[t] +  1.32513484904000M10[t] -0.155911104604277M11[t] -0.0496906557819444t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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] = + 1.85422779475554 + 0.000604826557932779X[t] + 0.574485001754852Y1[t] + 0.391886275032236Y2[t] -0.0635822312445514Y3[t] -0.00547461318830385Y4[t] -0.301760548071200M1[t] -0.417100597659018M2[t] -1.99878180986883M3[t] + 0.351604644101707M4[t] + 0.316273377056073M5[t] -0.606367151252546M6[t] -1.53548312063179M7[t] -0.388501259503871M8[t] + 0.560018451568021M9[t] + 1.32513484904000M10[t] -0.155911104604277M11[t] -0.0496906557819444t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.854227794755545.0740530.36540.7167630.358381
X0.0006048265579327790.0017560.34440.7323650.366183
Y10.5744850017548520.1640873.50110.0011770.000588
Y20.3918862750322360.189732.06550.0455670.022784
Y3-0.06358223124455140.19297-0.32950.7435460.371773
Y4-0.005474613188303850.167352-0.03270.974070.487035
M1-0.3017605480712002.062045-0.14630.8844060.442203
M2-0.4171005976590182.100274-0.19860.8436120.421806
M3-1.998781809868832.043168-0.97830.3339680.166984
M40.3516046441017072.1102330.16660.8685310.434265
M50.3162733770560732.1127330.14970.8817740.440887
M6-0.6063671512525462.127673-0.2850.7771590.38858
M7-1.535483120631792.048291-0.74960.4579690.228985
M8-0.3885012595038712.079945-0.18680.8527980.426399
M90.5600184515680212.2119550.25320.801460.40073
M101.325134849040002.2139380.59850.5529390.27647
M11-0.1559111046042772.17245-0.07180.9431540.471577
t-0.04969065578194440.034665-1.43350.1596950.079848

\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) & 1.85422779475554 & 5.074053 & 0.3654 & 0.716763 & 0.358381 \tabularnewline
X & 0.000604826557932779 & 0.001756 & 0.3444 & 0.732365 & 0.366183 \tabularnewline
Y1 & 0.574485001754852 & 0.164087 & 3.5011 & 0.001177 & 0.000588 \tabularnewline
Y2 & 0.391886275032236 & 0.18973 & 2.0655 & 0.045567 & 0.022784 \tabularnewline
Y3 & -0.0635822312445514 & 0.19297 & -0.3295 & 0.743546 & 0.371773 \tabularnewline
Y4 & -0.00547461318830385 & 0.167352 & -0.0327 & 0.97407 & 0.487035 \tabularnewline
M1 & -0.301760548071200 & 2.062045 & -0.1463 & 0.884406 & 0.442203 \tabularnewline
M2 & -0.417100597659018 & 2.100274 & -0.1986 & 0.843612 & 0.421806 \tabularnewline
M3 & -1.99878180986883 & 2.043168 & -0.9783 & 0.333968 & 0.166984 \tabularnewline
M4 & 0.351604644101707 & 2.110233 & 0.1666 & 0.868531 & 0.434265 \tabularnewline
M5 & 0.316273377056073 & 2.112733 & 0.1497 & 0.881774 & 0.440887 \tabularnewline
M6 & -0.606367151252546 & 2.127673 & -0.285 & 0.777159 & 0.38858 \tabularnewline
M7 & -1.53548312063179 & 2.048291 & -0.7496 & 0.457969 & 0.228985 \tabularnewline
M8 & -0.388501259503871 & 2.079945 & -0.1868 & 0.852798 & 0.426399 \tabularnewline
M9 & 0.560018451568021 & 2.211955 & 0.2532 & 0.80146 & 0.40073 \tabularnewline
M10 & 1.32513484904000 & 2.213938 & 0.5985 & 0.552939 & 0.27647 \tabularnewline
M11 & -0.155911104604277 & 2.17245 & -0.0718 & 0.943154 & 0.471577 \tabularnewline
t & -0.0496906557819444 & 0.034665 & -1.4335 & 0.159695 & 0.079848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&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]1.85422779475554[/C][C]5.074053[/C][C]0.3654[/C][C]0.716763[/C][C]0.358381[/C][/ROW]
[ROW][C]X[/C][C]0.000604826557932779[/C][C]0.001756[/C][C]0.3444[/C][C]0.732365[/C][C]0.366183[/C][/ROW]
[ROW][C]Y1[/C][C]0.574485001754852[/C][C]0.164087[/C][C]3.5011[/C][C]0.001177[/C][C]0.000588[/C][/ROW]
[ROW][C]Y2[/C][C]0.391886275032236[/C][C]0.18973[/C][C]2.0655[/C][C]0.045567[/C][C]0.022784[/C][/ROW]
[ROW][C]Y3[/C][C]-0.0635822312445514[/C][C]0.19297[/C][C]-0.3295[/C][C]0.743546[/C][C]0.371773[/C][/ROW]
[ROW][C]Y4[/C][C]-0.00547461318830385[/C][C]0.167352[/C][C]-0.0327[/C][C]0.97407[/C][C]0.487035[/C][/ROW]
[ROW][C]M1[/C][C]-0.301760548071200[/C][C]2.062045[/C][C]-0.1463[/C][C]0.884406[/C][C]0.442203[/C][/ROW]
[ROW][C]M2[/C][C]-0.417100597659018[/C][C]2.100274[/C][C]-0.1986[/C][C]0.843612[/C][C]0.421806[/C][/ROW]
[ROW][C]M3[/C][C]-1.99878180986883[/C][C]2.043168[/C][C]-0.9783[/C][C]0.333968[/C][C]0.166984[/C][/ROW]
[ROW][C]M4[/C][C]0.351604644101707[/C][C]2.110233[/C][C]0.1666[/C][C]0.868531[/C][C]0.434265[/C][/ROW]
[ROW][C]M5[/C][C]0.316273377056073[/C][C]2.112733[/C][C]0.1497[/C][C]0.881774[/C][C]0.440887[/C][/ROW]
[ROW][C]M6[/C][C]-0.606367151252546[/C][C]2.127673[/C][C]-0.285[/C][C]0.777159[/C][C]0.38858[/C][/ROW]
[ROW][C]M7[/C][C]-1.53548312063179[/C][C]2.048291[/C][C]-0.7496[/C][C]0.457969[/C][C]0.228985[/C][/ROW]
[ROW][C]M8[/C][C]-0.388501259503871[/C][C]2.079945[/C][C]-0.1868[/C][C]0.852798[/C][C]0.426399[/C][/ROW]
[ROW][C]M9[/C][C]0.560018451568021[/C][C]2.211955[/C][C]0.2532[/C][C]0.80146[/C][C]0.40073[/C][/ROW]
[ROW][C]M10[/C][C]1.32513484904000[/C][C]2.213938[/C][C]0.5985[/C][C]0.552939[/C][C]0.27647[/C][/ROW]
[ROW][C]M11[/C][C]-0.155911104604277[/C][C]2.17245[/C][C]-0.0718[/C][C]0.943154[/C][C]0.471577[/C][/ROW]
[ROW][C]t[/C][C]-0.0496906557819444[/C][C]0.034665[/C][C]-1.4335[/C][C]0.159695[/C][C]0.079848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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)1.854227794755545.0740530.36540.7167630.358381
X0.0006048265579327790.0017560.34440.7323650.366183
Y10.5744850017548520.1640873.50110.0011770.000588
Y20.3918862750322360.189732.06550.0455670.022784
Y3-0.06358223124455140.19297-0.32950.7435460.371773
Y4-0.005474613188303850.167352-0.03270.974070.487035
M1-0.3017605480712002.062045-0.14630.8844060.442203
M2-0.4171005976590182.100274-0.19860.8436120.421806
M3-1.998781809868832.043168-0.97830.3339680.166984
M40.3516046441017072.1102330.16660.8685310.434265
M50.3162733770560732.1127330.14970.8817740.440887
M6-0.6063671512525462.127673-0.2850.7771590.38858
M7-1.535483120631792.048291-0.74960.4579690.228985
M8-0.3885012595038712.079945-0.18680.8527980.426399
M90.5600184515680212.2119550.25320.801460.40073
M101.325134849040002.2139380.59850.5529390.27647
M11-0.1559111046042772.17245-0.07180.9431540.471577
t-0.04969065578194440.034665-1.43350.1596950.079848






Multiple Linear Regression - Regression Statistics
Multiple R0.933057841963762
R-squared0.870596936450073
Adjusted R-squared0.814190472851387
F-TEST (value)15.4343470749043
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value2.58504329053721e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.00902986975080
Sum Squared Residuals353.116169525049

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.933057841963762 \tabularnewline
R-squared & 0.870596936450073 \tabularnewline
Adjusted R-squared & 0.814190472851387 \tabularnewline
F-TEST (value) & 15.4343470749043 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 2.58504329053721e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.00902986975080 \tabularnewline
Sum Squared Residuals & 353.116169525049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.933057841963762[/C][/ROW]
[ROW][C]R-squared[/C][C]0.870596936450073[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.814190472851387[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.4343470749043[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]2.58504329053721e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.00902986975080[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]353.116169525049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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 R0.933057841963762
R-squared0.870596936450073
Adjusted R-squared0.814190472851387
F-TEST (value)15.4343470749043
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value2.58504329053721e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.00902986975080
Sum Squared Residuals353.116169525049






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.321.7000125084072-0.40001250840724
221.522.0318591711779-0.531859171177916
319.520.2201993642450-0.720199364244964
419.521.5283421910563-2.02834219105626
519.720.7935172992975-1.09351729929745
618.720.1813034873221-1.48130348732206
719.718.78024030381410.919759696185918
82020.1363232936499-0.136323293649880
919.721.6521942081785-1.95219420817849
1019.221.8845788603406-2.68457886034063
1119.720.0587560808267-0.358756080826719
122220.29185297516521.70814702483478
1321.821.55097174167850.249028258321539
1422.822.01087164331650.789128356683531
152120.96372309432610.0362769056738507
162522.98404328194792.01595671805215
1723.323.96820092533-0.66820092532999
182523.87902618849061.12097381150936
1926.822.53008282924914.26991717075089
2025.325.7670637555039-0.467063755503882
2126.526.230539338260.269460661740011
2227.826.86932842063320.930671579366772
232226.5438278108277-4.54382781082771
2422.323.8102060801691-1.51020608016915
252821.32941620100496.67058379899511
262524.66293902477340.337060975226573
2727.323.68941832873873.61058167126133
2825.825.8146523894295-0.0146523894294990
2927.325.88342080325921.41657919674085
3023.525.2196852407127-1.71968524071267
3124.522.58510286373511.91489713626494
321822.6140188772564-4.61401887725641
3321.320.72091137147570.579088628524328
3421.820.55036811125351.24963188874650
3520.520.8452102561284-0.345210256128447
3622.320.08054376234072.21945623765926
3718.720.5903402354798-1.89034023547980
3822.318.85881475720393.44118524279612
3917.717.7744431535285-0.0744431535284873
4019.719.33874599947750.36125400052248
4120.518.33881470602662.16118529397335
4218.518.7350360495159-0.235036049515885
431017.1841024400393-7.18410244003927
4414.212.11478914108902.08521085891104
4515.512.54783711198712.95216288801290
4616.515.99572460777270.504275392227346
4720.515.25220585221715.24779414778287
4815.718.1173971823249-2.41739718232489
4911.716.3292593134296-4.62925931342961
507.511.5355154035283-4.03551540352831
513.56.35221605916173-2.85221605916173
524.54.83421613808886-0.334216138088863
532.24.01604626608676-1.81604626608676
5452.684949033958742.31505096604126
552.32.220471563162470.0795284368375297
566.12.967804932500873.13219506749913
573.35.14851797009875-1.84851797009875

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 21.3 & 21.7000125084072 & -0.40001250840724 \tabularnewline
2 & 21.5 & 22.0318591711779 & -0.531859171177916 \tabularnewline
3 & 19.5 & 20.2201993642450 & -0.720199364244964 \tabularnewline
4 & 19.5 & 21.5283421910563 & -2.02834219105626 \tabularnewline
5 & 19.7 & 20.7935172992975 & -1.09351729929745 \tabularnewline
6 & 18.7 & 20.1813034873221 & -1.48130348732206 \tabularnewline
7 & 19.7 & 18.7802403038141 & 0.919759696185918 \tabularnewline
8 & 20 & 20.1363232936499 & -0.136323293649880 \tabularnewline
9 & 19.7 & 21.6521942081785 & -1.95219420817849 \tabularnewline
10 & 19.2 & 21.8845788603406 & -2.68457886034063 \tabularnewline
11 & 19.7 & 20.0587560808267 & -0.358756080826719 \tabularnewline
12 & 22 & 20.2918529751652 & 1.70814702483478 \tabularnewline
13 & 21.8 & 21.5509717416785 & 0.249028258321539 \tabularnewline
14 & 22.8 & 22.0108716433165 & 0.789128356683531 \tabularnewline
15 & 21 & 20.9637230943261 & 0.0362769056738507 \tabularnewline
16 & 25 & 22.9840432819479 & 2.01595671805215 \tabularnewline
17 & 23.3 & 23.96820092533 & -0.66820092532999 \tabularnewline
18 & 25 & 23.8790261884906 & 1.12097381150936 \tabularnewline
19 & 26.8 & 22.5300828292491 & 4.26991717075089 \tabularnewline
20 & 25.3 & 25.7670637555039 & -0.467063755503882 \tabularnewline
21 & 26.5 & 26.23053933826 & 0.269460661740011 \tabularnewline
22 & 27.8 & 26.8693284206332 & 0.930671579366772 \tabularnewline
23 & 22 & 26.5438278108277 & -4.54382781082771 \tabularnewline
24 & 22.3 & 23.8102060801691 & -1.51020608016915 \tabularnewline
25 & 28 & 21.3294162010049 & 6.67058379899511 \tabularnewline
26 & 25 & 24.6629390247734 & 0.337060975226573 \tabularnewline
27 & 27.3 & 23.6894183287387 & 3.61058167126133 \tabularnewline
28 & 25.8 & 25.8146523894295 & -0.0146523894294990 \tabularnewline
29 & 27.3 & 25.8834208032592 & 1.41657919674085 \tabularnewline
30 & 23.5 & 25.2196852407127 & -1.71968524071267 \tabularnewline
31 & 24.5 & 22.5851028637351 & 1.91489713626494 \tabularnewline
32 & 18 & 22.6140188772564 & -4.61401887725641 \tabularnewline
33 & 21.3 & 20.7209113714757 & 0.579088628524328 \tabularnewline
34 & 21.8 & 20.5503681112535 & 1.24963188874650 \tabularnewline
35 & 20.5 & 20.8452102561284 & -0.345210256128447 \tabularnewline
36 & 22.3 & 20.0805437623407 & 2.21945623765926 \tabularnewline
37 & 18.7 & 20.5903402354798 & -1.89034023547980 \tabularnewline
38 & 22.3 & 18.8588147572039 & 3.44118524279612 \tabularnewline
39 & 17.7 & 17.7744431535285 & -0.0744431535284873 \tabularnewline
40 & 19.7 & 19.3387459994775 & 0.36125400052248 \tabularnewline
41 & 20.5 & 18.3388147060266 & 2.16118529397335 \tabularnewline
42 & 18.5 & 18.7350360495159 & -0.235036049515885 \tabularnewline
43 & 10 & 17.1841024400393 & -7.18410244003927 \tabularnewline
44 & 14.2 & 12.1147891410890 & 2.08521085891104 \tabularnewline
45 & 15.5 & 12.5478371119871 & 2.95216288801290 \tabularnewline
46 & 16.5 & 15.9957246077727 & 0.504275392227346 \tabularnewline
47 & 20.5 & 15.2522058522171 & 5.24779414778287 \tabularnewline
48 & 15.7 & 18.1173971823249 & -2.41739718232489 \tabularnewline
49 & 11.7 & 16.3292593134296 & -4.62925931342961 \tabularnewline
50 & 7.5 & 11.5355154035283 & -4.03551540352831 \tabularnewline
51 & 3.5 & 6.35221605916173 & -2.85221605916173 \tabularnewline
52 & 4.5 & 4.83421613808886 & -0.334216138088863 \tabularnewline
53 & 2.2 & 4.01604626608676 & -1.81604626608676 \tabularnewline
54 & 5 & 2.68494903395874 & 2.31505096604126 \tabularnewline
55 & 2.3 & 2.22047156316247 & 0.0795284368375297 \tabularnewline
56 & 6.1 & 2.96780493250087 & 3.13219506749913 \tabularnewline
57 & 3.3 & 5.14851797009875 & -1.84851797009875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&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]21.3[/C][C]21.7000125084072[/C][C]-0.40001250840724[/C][/ROW]
[ROW][C]2[/C][C]21.5[/C][C]22.0318591711779[/C][C]-0.531859171177916[/C][/ROW]
[ROW][C]3[/C][C]19.5[/C][C]20.2201993642450[/C][C]-0.720199364244964[/C][/ROW]
[ROW][C]4[/C][C]19.5[/C][C]21.5283421910563[/C][C]-2.02834219105626[/C][/ROW]
[ROW][C]5[/C][C]19.7[/C][C]20.7935172992975[/C][C]-1.09351729929745[/C][/ROW]
[ROW][C]6[/C][C]18.7[/C][C]20.1813034873221[/C][C]-1.48130348732206[/C][/ROW]
[ROW][C]7[/C][C]19.7[/C][C]18.7802403038141[/C][C]0.919759696185918[/C][/ROW]
[ROW][C]8[/C][C]20[/C][C]20.1363232936499[/C][C]-0.136323293649880[/C][/ROW]
[ROW][C]9[/C][C]19.7[/C][C]21.6521942081785[/C][C]-1.95219420817849[/C][/ROW]
[ROW][C]10[/C][C]19.2[/C][C]21.8845788603406[/C][C]-2.68457886034063[/C][/ROW]
[ROW][C]11[/C][C]19.7[/C][C]20.0587560808267[/C][C]-0.358756080826719[/C][/ROW]
[ROW][C]12[/C][C]22[/C][C]20.2918529751652[/C][C]1.70814702483478[/C][/ROW]
[ROW][C]13[/C][C]21.8[/C][C]21.5509717416785[/C][C]0.249028258321539[/C][/ROW]
[ROW][C]14[/C][C]22.8[/C][C]22.0108716433165[/C][C]0.789128356683531[/C][/ROW]
[ROW][C]15[/C][C]21[/C][C]20.9637230943261[/C][C]0.0362769056738507[/C][/ROW]
[ROW][C]16[/C][C]25[/C][C]22.9840432819479[/C][C]2.01595671805215[/C][/ROW]
[ROW][C]17[/C][C]23.3[/C][C]23.96820092533[/C][C]-0.66820092532999[/C][/ROW]
[ROW][C]18[/C][C]25[/C][C]23.8790261884906[/C][C]1.12097381150936[/C][/ROW]
[ROW][C]19[/C][C]26.8[/C][C]22.5300828292491[/C][C]4.26991717075089[/C][/ROW]
[ROW][C]20[/C][C]25.3[/C][C]25.7670637555039[/C][C]-0.467063755503882[/C][/ROW]
[ROW][C]21[/C][C]26.5[/C][C]26.23053933826[/C][C]0.269460661740011[/C][/ROW]
[ROW][C]22[/C][C]27.8[/C][C]26.8693284206332[/C][C]0.930671579366772[/C][/ROW]
[ROW][C]23[/C][C]22[/C][C]26.5438278108277[/C][C]-4.54382781082771[/C][/ROW]
[ROW][C]24[/C][C]22.3[/C][C]23.8102060801691[/C][C]-1.51020608016915[/C][/ROW]
[ROW][C]25[/C][C]28[/C][C]21.3294162010049[/C][C]6.67058379899511[/C][/ROW]
[ROW][C]26[/C][C]25[/C][C]24.6629390247734[/C][C]0.337060975226573[/C][/ROW]
[ROW][C]27[/C][C]27.3[/C][C]23.6894183287387[/C][C]3.61058167126133[/C][/ROW]
[ROW][C]28[/C][C]25.8[/C][C]25.8146523894295[/C][C]-0.0146523894294990[/C][/ROW]
[ROW][C]29[/C][C]27.3[/C][C]25.8834208032592[/C][C]1.41657919674085[/C][/ROW]
[ROW][C]30[/C][C]23.5[/C][C]25.2196852407127[/C][C]-1.71968524071267[/C][/ROW]
[ROW][C]31[/C][C]24.5[/C][C]22.5851028637351[/C][C]1.91489713626494[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]22.6140188772564[/C][C]-4.61401887725641[/C][/ROW]
[ROW][C]33[/C][C]21.3[/C][C]20.7209113714757[/C][C]0.579088628524328[/C][/ROW]
[ROW][C]34[/C][C]21.8[/C][C]20.5503681112535[/C][C]1.24963188874650[/C][/ROW]
[ROW][C]35[/C][C]20.5[/C][C]20.8452102561284[/C][C]-0.345210256128447[/C][/ROW]
[ROW][C]36[/C][C]22.3[/C][C]20.0805437623407[/C][C]2.21945623765926[/C][/ROW]
[ROW][C]37[/C][C]18.7[/C][C]20.5903402354798[/C][C]-1.89034023547980[/C][/ROW]
[ROW][C]38[/C][C]22.3[/C][C]18.8588147572039[/C][C]3.44118524279612[/C][/ROW]
[ROW][C]39[/C][C]17.7[/C][C]17.7744431535285[/C][C]-0.0744431535284873[/C][/ROW]
[ROW][C]40[/C][C]19.7[/C][C]19.3387459994775[/C][C]0.36125400052248[/C][/ROW]
[ROW][C]41[/C][C]20.5[/C][C]18.3388147060266[/C][C]2.16118529397335[/C][/ROW]
[ROW][C]42[/C][C]18.5[/C][C]18.7350360495159[/C][C]-0.235036049515885[/C][/ROW]
[ROW][C]43[/C][C]10[/C][C]17.1841024400393[/C][C]-7.18410244003927[/C][/ROW]
[ROW][C]44[/C][C]14.2[/C][C]12.1147891410890[/C][C]2.08521085891104[/C][/ROW]
[ROW][C]45[/C][C]15.5[/C][C]12.5478371119871[/C][C]2.95216288801290[/C][/ROW]
[ROW][C]46[/C][C]16.5[/C][C]15.9957246077727[/C][C]0.504275392227346[/C][/ROW]
[ROW][C]47[/C][C]20.5[/C][C]15.2522058522171[/C][C]5.24779414778287[/C][/ROW]
[ROW][C]48[/C][C]15.7[/C][C]18.1173971823249[/C][C]-2.41739718232489[/C][/ROW]
[ROW][C]49[/C][C]11.7[/C][C]16.3292593134296[/C][C]-4.62925931342961[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]11.5355154035283[/C][C]-4.03551540352831[/C][/ROW]
[ROW][C]51[/C][C]3.5[/C][C]6.35221605916173[/C][C]-2.85221605916173[/C][/ROW]
[ROW][C]52[/C][C]4.5[/C][C]4.83421613808886[/C][C]-0.334216138088863[/C][/ROW]
[ROW][C]53[/C][C]2.2[/C][C]4.01604626608676[/C][C]-1.81604626608676[/C][/ROW]
[ROW][C]54[/C][C]5[/C][C]2.68494903395874[/C][C]2.31505096604126[/C][/ROW]
[ROW][C]55[/C][C]2.3[/C][C]2.22047156316247[/C][C]0.0795284368375297[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]2.96780493250087[/C][C]3.13219506749913[/C][/ROW]
[ROW][C]57[/C][C]3.3[/C][C]5.14851797009875[/C][C]-1.84851797009875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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
121.321.7000125084072-0.40001250840724
221.522.0318591711779-0.531859171177916
319.520.2201993642450-0.720199364244964
419.521.5283421910563-2.02834219105626
519.720.7935172992975-1.09351729929745
618.720.1813034873221-1.48130348732206
719.718.78024030381410.919759696185918
82020.1363232936499-0.136323293649880
919.721.6521942081785-1.95219420817849
1019.221.8845788603406-2.68457886034063
1119.720.0587560808267-0.358756080826719
122220.29185297516521.70814702483478
1321.821.55097174167850.249028258321539
1422.822.01087164331650.789128356683531
152120.96372309432610.0362769056738507
162522.98404328194792.01595671805215
1723.323.96820092533-0.66820092532999
182523.87902618849061.12097381150936
1926.822.53008282924914.26991717075089
2025.325.7670637555039-0.467063755503882
2126.526.230539338260.269460661740011
2227.826.86932842063320.930671579366772
232226.5438278108277-4.54382781082771
2422.323.8102060801691-1.51020608016915
252821.32941620100496.67058379899511
262524.66293902477340.337060975226573
2727.323.68941832873873.61058167126133
2825.825.8146523894295-0.0146523894294990
2927.325.88342080325921.41657919674085
3023.525.2196852407127-1.71968524071267
3124.522.58510286373511.91489713626494
321822.6140188772564-4.61401887725641
3321.320.72091137147570.579088628524328
3421.820.55036811125351.24963188874650
3520.520.8452102561284-0.345210256128447
3622.320.08054376234072.21945623765926
3718.720.5903402354798-1.89034023547980
3822.318.85881475720393.44118524279612
3917.717.7744431535285-0.0744431535284873
4019.719.33874599947750.36125400052248
4120.518.33881470602662.16118529397335
4218.518.7350360495159-0.235036049515885
431017.1841024400393-7.18410244003927
4414.212.11478914108902.08521085891104
4515.512.54783711198712.95216288801290
4616.515.99572460777270.504275392227346
4720.515.25220585221715.24779414778287
4815.718.1173971823249-2.41739718232489
4911.716.3292593134296-4.62925931342961
507.511.5355154035283-4.03551540352831
513.56.35221605916173-2.85221605916173
524.54.83421613808886-0.334216138088863
532.24.01604626608676-1.81604626608676
5452.684949033958742.31505096604126
552.32.220471563162470.0795284368375297
566.12.967804932500873.13219506749913
573.35.14851797009875-1.84851797009875






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.01057363766748340.02114727533496680.989426362332517
220.003011653434835570.006023306869671140.996988346565164
230.01162651710477910.02325303420955820.98837348289522
240.03596943301514460.07193886603028920.964030566984855
250.06455386129471930.1291077225894390.93544613870528
260.03158290650624750.0631658130124950.968417093493752
270.06101090952440620.1220218190488120.938989090475594
280.05400658345480450.1080131669096090.945993416545196
290.02705678006964620.05411356013929250.972943219930354
300.02874710657543860.05749421315087730.971252893424561
310.03737021782060930.07474043564121850.96262978217939
320.1522531976877070.3045063953754140.847746802312293
330.08687884123021340.1737576824604270.913121158769787
340.06285683055365730.1257136611073150.937143169446343
350.1280705718890050.2561411437780110.871929428110995
360.06859254913875630.1371850982775130.931407450861244

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0105736376674834 & 0.0211472753349668 & 0.989426362332517 \tabularnewline
22 & 0.00301165343483557 & 0.00602330686967114 & 0.996988346565164 \tabularnewline
23 & 0.0116265171047791 & 0.0232530342095582 & 0.98837348289522 \tabularnewline
24 & 0.0359694330151446 & 0.0719388660302892 & 0.964030566984855 \tabularnewline
25 & 0.0645538612947193 & 0.129107722589439 & 0.93544613870528 \tabularnewline
26 & 0.0315829065062475 & 0.063165813012495 & 0.968417093493752 \tabularnewline
27 & 0.0610109095244062 & 0.122021819048812 & 0.938989090475594 \tabularnewline
28 & 0.0540065834548045 & 0.108013166909609 & 0.945993416545196 \tabularnewline
29 & 0.0270567800696462 & 0.0541135601392925 & 0.972943219930354 \tabularnewline
30 & 0.0287471065754386 & 0.0574942131508773 & 0.971252893424561 \tabularnewline
31 & 0.0373702178206093 & 0.0747404356412185 & 0.96262978217939 \tabularnewline
32 & 0.152253197687707 & 0.304506395375414 & 0.847746802312293 \tabularnewline
33 & 0.0868788412302134 & 0.173757682460427 & 0.913121158769787 \tabularnewline
34 & 0.0628568305536573 & 0.125713661107315 & 0.937143169446343 \tabularnewline
35 & 0.128070571889005 & 0.256141143778011 & 0.871929428110995 \tabularnewline
36 & 0.0685925491387563 & 0.137185098277513 & 0.931407450861244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&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]21[/C][C]0.0105736376674834[/C][C]0.0211472753349668[/C][C]0.989426362332517[/C][/ROW]
[ROW][C]22[/C][C]0.00301165343483557[/C][C]0.00602330686967114[/C][C]0.996988346565164[/C][/ROW]
[ROW][C]23[/C][C]0.0116265171047791[/C][C]0.0232530342095582[/C][C]0.98837348289522[/C][/ROW]
[ROW][C]24[/C][C]0.0359694330151446[/C][C]0.0719388660302892[/C][C]0.964030566984855[/C][/ROW]
[ROW][C]25[/C][C]0.0645538612947193[/C][C]0.129107722589439[/C][C]0.93544613870528[/C][/ROW]
[ROW][C]26[/C][C]0.0315829065062475[/C][C]0.063165813012495[/C][C]0.968417093493752[/C][/ROW]
[ROW][C]27[/C][C]0.0610109095244062[/C][C]0.122021819048812[/C][C]0.938989090475594[/C][/ROW]
[ROW][C]28[/C][C]0.0540065834548045[/C][C]0.108013166909609[/C][C]0.945993416545196[/C][/ROW]
[ROW][C]29[/C][C]0.0270567800696462[/C][C]0.0541135601392925[/C][C]0.972943219930354[/C][/ROW]
[ROW][C]30[/C][C]0.0287471065754386[/C][C]0.0574942131508773[/C][C]0.971252893424561[/C][/ROW]
[ROW][C]31[/C][C]0.0373702178206093[/C][C]0.0747404356412185[/C][C]0.96262978217939[/C][/ROW]
[ROW][C]32[/C][C]0.152253197687707[/C][C]0.304506395375414[/C][C]0.847746802312293[/C][/ROW]
[ROW][C]33[/C][C]0.0868788412302134[/C][C]0.173757682460427[/C][C]0.913121158769787[/C][/ROW]
[ROW][C]34[/C][C]0.0628568305536573[/C][C]0.125713661107315[/C][C]0.937143169446343[/C][/ROW]
[ROW][C]35[/C][C]0.128070571889005[/C][C]0.256141143778011[/C][C]0.871929428110995[/C][/ROW]
[ROW][C]36[/C][C]0.0685925491387563[/C][C]0.137185098277513[/C][C]0.931407450861244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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
210.01057363766748340.02114727533496680.989426362332517
220.003011653434835570.006023306869671140.996988346565164
230.01162651710477910.02325303420955820.98837348289522
240.03596943301514460.07193886603028920.964030566984855
250.06455386129471930.1291077225894390.93544613870528
260.03158290650624750.0631658130124950.968417093493752
270.06101090952440620.1220218190488120.938989090475594
280.05400658345480450.1080131669096090.945993416545196
290.02705678006964620.05411356013929250.972943219930354
300.02874710657543860.05749421315087730.971252893424561
310.03737021782060930.07474043564121850.96262978217939
320.1522531976877070.3045063953754140.847746802312293
330.08687884123021340.1737576824604270.913121158769787
340.06285683055365730.1257136611073150.937143169446343
350.1280705718890050.2561411437780110.871929428110995
360.06859254913875630.1371850982775130.931407450861244






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0625NOK
5% type I error level30.1875NOK
10% type I error level80.5NOK

\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 & 1 & 0.0625 & NOK \tabularnewline
5% type I error level & 3 & 0.1875 & NOK \tabularnewline
10% type I error level & 8 & 0.5 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58218&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]1[/C][C]0.0625[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]3[/C][C]0.1875[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.5[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58218&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58218&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 level10.0625NOK
5% type I error level30.1875NOK
10% type I error level80.5NOK


Figures (Output of Computation)

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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')
}