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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 00:49:33 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258703435v2ajabyb0g2p8vj.htm/, Retrieved Fri, 19 Apr 2024 14:59:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57979, Retrieved Fri, 19 Apr 2024 14:59:00 +0000

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Estimated Impact

183

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] [] [2009-11-20 07:49:33] [2b679e8ec54382eeb0ec0b6bb527570a] [Current]
-    D        [Multiple Regression] [VerbeteringModel5] [2009-11-23 19:19:36] [9c2d53170eb755e9ae5fcf19d2174a32] 

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Dataseries X:

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Histogram

Boxplots

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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=57979&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=57979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 52.9237129088855 -0.456561313045817X[t] + 0.529784539853996Y1[t] + 0.00162859374509381Y2[t] + 0.211227162008023Y3[t] -0.268925741424594Y4[t] + 0.779715739410484M1[t] + 0.72084508465959M2[t] + 1.39416708889035M3[t] -0.251540990310942M4[t] + 1.76147716754322M5[t] + 1.11916991858972M6[t] -0.0997453594323863M7[t] + 0.207964494807340M8[t] + 1.42410413266541M9[t] + 1.02998559517508M10[t] + 1.50184215778441M11[t] -0.00838297611828369t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  52.9237129088855 -0.456561313045817X[t] +  0.529784539853996Y1[t] +  0.00162859374509381Y2[t] +  0.211227162008023Y3[t] -0.268925741424594Y4[t] +  0.779715739410484M1[t] +  0.72084508465959M2[t] +  1.39416708889035M3[t] -0.251540990310942M4[t] +  1.76147716754322M5[t] +  1.11916991858972M6[t] -0.0997453594323863M7[t] +  0.207964494807340M8[t] +  1.42410413266541M9[t] +  1.02998559517508M10[t] +  1.50184215778441M11[t] -0.00838297611828369t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57979&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  52.9237129088855 -0.456561313045817X[t] +  0.529784539853996Y1[t] +  0.00162859374509381Y2[t] +  0.211227162008023Y3[t] -0.268925741424594Y4[t] +  0.779715739410484M1[t] +  0.72084508465959M2[t] +  1.39416708889035M3[t] -0.251540990310942M4[t] +  1.76147716754322M5[t] +  1.11916991858972M6[t] -0.0997453594323863M7[t] +  0.207964494807340M8[t] +  1.42410413266541M9[t] +  1.02998559517508M10[t] +  1.50184215778441M11[t] -0.00838297611828369t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 52.9237129088855 -0.456561313045817X[t] + 0.529784539853996Y1[t] + 0.00162859374509381Y2[t] + 0.211227162008023Y3[t] -0.268925741424594Y4[t] + 0.779715739410484M1[t] + 0.72084508465959M2[t] + 1.39416708889035M3[t] -0.251540990310942M4[t] + 1.76147716754322M5[t] + 1.11916991858972M6[t] -0.0997453594323863M7[t] + 0.207964494807340M8[t] + 1.42410413266541M9[t] + 1.02998559517508M10[t] + 1.50184215778441M11[t] -0.00838297611828369t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	52.9237129088855	13.880394	3.8128	0.00049	0.000245
X	-0.456561313045817	0.136277	-3.3502	0.001834	0.000917
Y1	0.529784539853996	0.150924	3.5103	0.001171	0.000585
Y2	0.00162859374509381	0.169852	0.0096	0.9924	0.4962
Y3	0.211227162008023	0.165712	1.2747	0.210167	0.105083
Y4	-0.268925741424594	0.139164	-1.9324	0.060785	0.030393
M1	0.779715739410484	0.631015	1.2357	0.224172	0.112086
M2	0.72084508465959	0.604075	1.1933	0.240147	0.120074
M3	1.39416708889035	0.62547	2.229	0.031805	0.015902
M4	-0.251540990310942	0.599557	-0.4195	0.677181	0.33859
M5	1.76147716754322	0.654977	2.6894	0.010573	0.005287
M6	1.11916991858972	0.607961	1.8409	0.07346	0.03673
M7	-0.0997453594323863	0.66993	-0.1489	0.882428	0.441214
M8	0.207964494807340	0.660939	0.3147	0.754748	0.377374
M9	1.42410413266541	0.661141	2.154	0.037645	0.018823
M10	1.02998559517508	0.684813	1.504	0.140838	0.070419
M11	1.50184215778441	0.655248	2.292	0.027535	0.013767
t	-0.00838297611828369	0.008107	-1.0341	0.30764	0.15382

\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) & 52.9237129088855 & 13.880394 & 3.8128 & 0.00049 & 0.000245 \tabularnewline
X & -0.456561313045817 & 0.136277 & -3.3502 & 0.001834 & 0.000917 \tabularnewline
Y1 & 0.529784539853996 & 0.150924 & 3.5103 & 0.001171 & 0.000585 \tabularnewline
Y2 & 0.00162859374509381 & 0.169852 & 0.0096 & 0.9924 & 0.4962 \tabularnewline
Y3 & 0.211227162008023 & 0.165712 & 1.2747 & 0.210167 & 0.105083 \tabularnewline
Y4 & -0.268925741424594 & 0.139164 & -1.9324 & 0.060785 & 0.030393 \tabularnewline
M1 & 0.779715739410484 & 0.631015 & 1.2357 & 0.224172 & 0.112086 \tabularnewline
M2 & 0.72084508465959 & 0.604075 & 1.1933 & 0.240147 & 0.120074 \tabularnewline
M3 & 1.39416708889035 & 0.62547 & 2.229 & 0.031805 & 0.015902 \tabularnewline
M4 & -0.251540990310942 & 0.599557 & -0.4195 & 0.677181 & 0.33859 \tabularnewline
M5 & 1.76147716754322 & 0.654977 & 2.6894 & 0.010573 & 0.005287 \tabularnewline
M6 & 1.11916991858972 & 0.607961 & 1.8409 & 0.07346 & 0.03673 \tabularnewline
M7 & -0.0997453594323863 & 0.66993 & -0.1489 & 0.882428 & 0.441214 \tabularnewline
M8 & 0.207964494807340 & 0.660939 & 0.3147 & 0.754748 & 0.377374 \tabularnewline
M9 & 1.42410413266541 & 0.661141 & 2.154 & 0.037645 & 0.018823 \tabularnewline
M10 & 1.02998559517508 & 0.684813 & 1.504 & 0.140838 & 0.070419 \tabularnewline
M11 & 1.50184215778441 & 0.655248 & 2.292 & 0.027535 & 0.013767 \tabularnewline
t & -0.00838297611828369 & 0.008107 & -1.0341 & 0.30764 & 0.15382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57979&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]52.9237129088855[/C][C]13.880394[/C][C]3.8128[/C][C]0.00049[/C][C]0.000245[/C][/ROW]
[ROW][C]X[/C][C]-0.456561313045817[/C][C]0.136277[/C][C]-3.3502[/C][C]0.001834[/C][C]0.000917[/C][/ROW]
[ROW][C]Y1[/C][C]0.529784539853996[/C][C]0.150924[/C][C]3.5103[/C][C]0.001171[/C][C]0.000585[/C][/ROW]
[ROW][C]Y2[/C][C]0.00162859374509381[/C][C]0.169852[/C][C]0.0096[/C][C]0.9924[/C][C]0.4962[/C][/ROW]
[ROW][C]Y3[/C][C]0.211227162008023[/C][C]0.165712[/C][C]1.2747[/C][C]0.210167[/C][C]0.105083[/C][/ROW]
[ROW][C]Y4[/C][C]-0.268925741424594[/C][C]0.139164[/C][C]-1.9324[/C][C]0.060785[/C][C]0.030393[/C][/ROW]
[ROW][C]M1[/C][C]0.779715739410484[/C][C]0.631015[/C][C]1.2357[/C][C]0.224172[/C][C]0.112086[/C][/ROW]
[ROW][C]M2[/C][C]0.72084508465959[/C][C]0.604075[/C][C]1.1933[/C][C]0.240147[/C][C]0.120074[/C][/ROW]
[ROW][C]M3[/C][C]1.39416708889035[/C][C]0.62547[/C][C]2.229[/C][C]0.031805[/C][C]0.015902[/C][/ROW]
[ROW][C]M4[/C][C]-0.251540990310942[/C][C]0.599557[/C][C]-0.4195[/C][C]0.677181[/C][C]0.33859[/C][/ROW]
[ROW][C]M5[/C][C]1.76147716754322[/C][C]0.654977[/C][C]2.6894[/C][C]0.010573[/C][C]0.005287[/C][/ROW]
[ROW][C]M6[/C][C]1.11916991858972[/C][C]0.607961[/C][C]1.8409[/C][C]0.07346[/C][C]0.03673[/C][/ROW]
[ROW][C]M7[/C][C]-0.0997453594323863[/C][C]0.66993[/C][C]-0.1489[/C][C]0.882428[/C][C]0.441214[/C][/ROW]
[ROW][C]M8[/C][C]0.207964494807340[/C][C]0.660939[/C][C]0.3147[/C][C]0.754748[/C][C]0.377374[/C][/ROW]
[ROW][C]M9[/C][C]1.42410413266541[/C][C]0.661141[/C][C]2.154[/C][C]0.037645[/C][C]0.018823[/C][/ROW]
[ROW][C]M10[/C][C]1.02998559517508[/C][C]0.684813[/C][C]1.504[/C][C]0.140838[/C][C]0.070419[/C][/ROW]
[ROW][C]M11[/C][C]1.50184215778441[/C][C]0.655248[/C][C]2.292[/C][C]0.027535[/C][C]0.013767[/C][/ROW]
[ROW][C]t[/C][C]-0.00838297611828369[/C][C]0.008107[/C][C]-1.0341[/C][C]0.30764[/C][C]0.15382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	52.9237129088855	13.880394	3.8128	0.00049	0.000245
X	-0.456561313045817	0.136277	-3.3502	0.001834	0.000917
Y1	0.529784539853996	0.150924	3.5103	0.001171	0.000585
Y2	0.00162859374509381	0.169852	0.0096	0.9924	0.4962
Y3	0.211227162008023	0.165712	1.2747	0.210167	0.105083
Y4	-0.268925741424594	0.139164	-1.9324	0.060785	0.030393
M1	0.779715739410484	0.631015	1.2357	0.224172	0.112086
M2	0.72084508465959	0.604075	1.1933	0.240147	0.120074
M3	1.39416708889035	0.62547	2.229	0.031805	0.015902
M4	-0.251540990310942	0.599557	-0.4195	0.677181	0.33859
M5	1.76147716754322	0.654977	2.6894	0.010573	0.005287
M6	1.11916991858972	0.607961	1.8409	0.07346	0.03673
M7	-0.0997453594323863	0.66993	-0.1489	0.882428	0.441214
M8	0.207964494807340	0.660939	0.3147	0.754748	0.377374
M9	1.42410413266541	0.661141	2.154	0.037645	0.018823
M10	1.02998559517508	0.684813	1.504	0.140838	0.070419
M11	1.50184215778441	0.655248	2.292	0.027535	0.013767
t	-0.00838297611828369	0.008107	-1.0341	0.30764	0.15382

Multiple Linear Regression - Regression Statistics
Multiple R	0.904112399567176
R-squared	0.817419231051118
Adjusted R-squared	0.735738360731881
F-TEST (value)	10.0074745513406
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	2.72499856013297e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.871677777536568
Sum Squared Residuals	28.8732416183414

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.904112399567176 \tabularnewline
R-squared & 0.817419231051118 \tabularnewline
Adjusted R-squared & 0.735738360731881 \tabularnewline
F-TEST (value) & 10.0074745513406 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 2.72499856013297e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.871677777536568 \tabularnewline
Sum Squared Residuals & 28.8732416183414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57979&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.904112399567176[/C][/ROW]
[ROW][C]R-squared[/C][C]0.817419231051118[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.735738360731881[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.0074745513406[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]2.72499856013297e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.871677777536568[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]28.8732416183414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.904112399567176
R-squared	0.817419231051118
Adjusted R-squared	0.735738360731881
F-TEST (value)	10.0074745513406
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	2.72499856013297e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.871677777536568
Sum Squared Residuals	28.8732416183414

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	100.49	100.327887702781	0.162112297219314
2	99.72	100.194257532837	-0.474257532837242
3	100.14	100.607920449935	-0.467920449934754
4	98.48	98.865910775912	-0.385910775912100
5	100.38	99.9230217466653	0.456978253334675
6	101.45	100.617663041944	0.832336958055842
7	98.42	99.3141181480133	-0.894118148013252
8	98.6	98.8576888042644	-0.257688804264411
9	100.06	99.779613936163	0.280386063837036
10	98.62	99.1774660221021	-0.5574660221021
11	100.84	100.098542554186	0.741457445814154
12	100.02	99.9764228155368	0.043577184463196
13	97.95	99.3918683819685	-1.44186838196845
14	98.32	99.0828026740398	-0.762802674039766
15	98.27	99.1701693740367	-0.900169374036691
16	97.22	97.5474073418492	-0.32740734184915
17	99.28	99.4478931365246	-0.167893136524621
18	100.38	99.685472895083	0.694527104916929
19	99.02	98.9729186987735	0.0470813012264834
20	100.32	99.31668616935	1.00331383064994
21	99.81	100.934966827585	-1.12496682758545
22	100.6	99.8639296398403	0.736070360159702
23	101.19	101.476749011563	-0.286749011563036
24	100.47	99.686085634843	0.783914365156985
25	101.77	100.335299854558	1.43470014544176
26	102.32	101.050390753080	1.26960924691957
27	102.39	101.652422574590	0.737577425409654
28	101.16	100.504534008056	0.655465991943504
29	100.63	101.624219682587	-0.99421968258655
30	101.48	100.785897881166	0.694102118834376
31	101.44	99.7294191200466	1.71058087995335
32	100.09	100.227767187345	-0.137767187345252
33	100.7	101.087979438499	-0.387979438498780
34	100.78	100.678099663345	0.101900336655159
35	99.81	100.545300765718	-0.735300765718213
36	98.45	98.6936203162728	-0.24362031627277
37	98.49	98.5044075775133	-0.0144075775132797
38	97.48	98.0471015090648	-0.567101509064845
39	97.91	98.104956193221	-0.194956193220964
40	96.94	96.6859666547372	0.25403334526283
41	98.53	98.0902830587537	0.439716941246282
42	96.82	98.1862518815735	-1.36625188157353
43	95.76	95.415490193245	0.344509806754938
44	95.27	95.7015135892872	-0.431513589287205
45	97.32	96.0874397977528	1.23256020224719
46	96.68	96.9605046747128	-0.280504674712759
47	97.87	97.5894076685329	0.280592331467096
48	97.42	98.0038712333474	-0.583871233347412
49	97.94	98.0805364831793	-0.140536483179338
50	99.52	98.9854475309777	0.534552469022281
51	100.99	100.164531408217	0.825468591782755
52	99.92	100.116181219445	-0.196181219445085
53	101.97	101.704582375470	0.265417624530215
54	101.58	102.434714300234	-0.854714300233616
55	99.54	100.748053839922	-1.20805383992152
56	100.83	101.006344249753	-0.176344249753068

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.49 & 100.327887702781 & 0.162112297219314 \tabularnewline
2 & 99.72 & 100.194257532837 & -0.474257532837242 \tabularnewline
3 & 100.14 & 100.607920449935 & -0.467920449934754 \tabularnewline
4 & 98.48 & 98.865910775912 & -0.385910775912100 \tabularnewline
5 & 100.38 & 99.9230217466653 & 0.456978253334675 \tabularnewline
6 & 101.45 & 100.617663041944 & 0.832336958055842 \tabularnewline
7 & 98.42 & 99.3141181480133 & -0.894118148013252 \tabularnewline
8 & 98.6 & 98.8576888042644 & -0.257688804264411 \tabularnewline
9 & 100.06 & 99.779613936163 & 0.280386063837036 \tabularnewline
10 & 98.62 & 99.1774660221021 & -0.5574660221021 \tabularnewline
11 & 100.84 & 100.098542554186 & 0.741457445814154 \tabularnewline
12 & 100.02 & 99.9764228155368 & 0.043577184463196 \tabularnewline
13 & 97.95 & 99.3918683819685 & -1.44186838196845 \tabularnewline
14 & 98.32 & 99.0828026740398 & -0.762802674039766 \tabularnewline
15 & 98.27 & 99.1701693740367 & -0.900169374036691 \tabularnewline
16 & 97.22 & 97.5474073418492 & -0.32740734184915 \tabularnewline
17 & 99.28 & 99.4478931365246 & -0.167893136524621 \tabularnewline
18 & 100.38 & 99.685472895083 & 0.694527104916929 \tabularnewline
19 & 99.02 & 98.9729186987735 & 0.0470813012264834 \tabularnewline
20 & 100.32 & 99.31668616935 & 1.00331383064994 \tabularnewline
21 & 99.81 & 100.934966827585 & -1.12496682758545 \tabularnewline
22 & 100.6 & 99.8639296398403 & 0.736070360159702 \tabularnewline
23 & 101.19 & 101.476749011563 & -0.286749011563036 \tabularnewline
24 & 100.47 & 99.686085634843 & 0.783914365156985 \tabularnewline
25 & 101.77 & 100.335299854558 & 1.43470014544176 \tabularnewline
26 & 102.32 & 101.050390753080 & 1.26960924691957 \tabularnewline
27 & 102.39 & 101.652422574590 & 0.737577425409654 \tabularnewline
28 & 101.16 & 100.504534008056 & 0.655465991943504 \tabularnewline
29 & 100.63 & 101.624219682587 & -0.99421968258655 \tabularnewline
30 & 101.48 & 100.785897881166 & 0.694102118834376 \tabularnewline
31 & 101.44 & 99.7294191200466 & 1.71058087995335 \tabularnewline
32 & 100.09 & 100.227767187345 & -0.137767187345252 \tabularnewline
33 & 100.7 & 101.087979438499 & -0.387979438498780 \tabularnewline
34 & 100.78 & 100.678099663345 & 0.101900336655159 \tabularnewline
35 & 99.81 & 100.545300765718 & -0.735300765718213 \tabularnewline
36 & 98.45 & 98.6936203162728 & -0.24362031627277 \tabularnewline
37 & 98.49 & 98.5044075775133 & -0.0144075775132797 \tabularnewline
38 & 97.48 & 98.0471015090648 & -0.567101509064845 \tabularnewline
39 & 97.91 & 98.104956193221 & -0.194956193220964 \tabularnewline
40 & 96.94 & 96.6859666547372 & 0.25403334526283 \tabularnewline
41 & 98.53 & 98.0902830587537 & 0.439716941246282 \tabularnewline
42 & 96.82 & 98.1862518815735 & -1.36625188157353 \tabularnewline
43 & 95.76 & 95.415490193245 & 0.344509806754938 \tabularnewline
44 & 95.27 & 95.7015135892872 & -0.431513589287205 \tabularnewline
45 & 97.32 & 96.0874397977528 & 1.23256020224719 \tabularnewline
46 & 96.68 & 96.9605046747128 & -0.280504674712759 \tabularnewline
47 & 97.87 & 97.5894076685329 & 0.280592331467096 \tabularnewline
48 & 97.42 & 98.0038712333474 & -0.583871233347412 \tabularnewline
49 & 97.94 & 98.0805364831793 & -0.140536483179338 \tabularnewline
50 & 99.52 & 98.9854475309777 & 0.534552469022281 \tabularnewline
51 & 100.99 & 100.164531408217 & 0.825468591782755 \tabularnewline
52 & 99.92 & 100.116181219445 & -0.196181219445085 \tabularnewline
53 & 101.97 & 101.704582375470 & 0.265417624530215 \tabularnewline
54 & 101.58 & 102.434714300234 & -0.854714300233616 \tabularnewline
55 & 99.54 & 100.748053839922 & -1.20805383992152 \tabularnewline
56 & 100.83 & 101.006344249753 & -0.176344249753068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57979&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]100.49[/C][C]100.327887702781[/C][C]0.162112297219314[/C][/ROW]
[ROW][C]2[/C][C]99.72[/C][C]100.194257532837[/C][C]-0.474257532837242[/C][/ROW]
[ROW][C]3[/C][C]100.14[/C][C]100.607920449935[/C][C]-0.467920449934754[/C][/ROW]
[ROW][C]4[/C][C]98.48[/C][C]98.865910775912[/C][C]-0.385910775912100[/C][/ROW]
[ROW][C]5[/C][C]100.38[/C][C]99.9230217466653[/C][C]0.456978253334675[/C][/ROW]
[ROW][C]6[/C][C]101.45[/C][C]100.617663041944[/C][C]0.832336958055842[/C][/ROW]
[ROW][C]7[/C][C]98.42[/C][C]99.3141181480133[/C][C]-0.894118148013252[/C][/ROW]
[ROW][C]8[/C][C]98.6[/C][C]98.8576888042644[/C][C]-0.257688804264411[/C][/ROW]
[ROW][C]9[/C][C]100.06[/C][C]99.779613936163[/C][C]0.280386063837036[/C][/ROW]
[ROW][C]10[/C][C]98.62[/C][C]99.1774660221021[/C][C]-0.5574660221021[/C][/ROW]
[ROW][C]11[/C][C]100.84[/C][C]100.098542554186[/C][C]0.741457445814154[/C][/ROW]
[ROW][C]12[/C][C]100.02[/C][C]99.9764228155368[/C][C]0.043577184463196[/C][/ROW]
[ROW][C]13[/C][C]97.95[/C][C]99.3918683819685[/C][C]-1.44186838196845[/C][/ROW]
[ROW][C]14[/C][C]98.32[/C][C]99.0828026740398[/C][C]-0.762802674039766[/C][/ROW]
[ROW][C]15[/C][C]98.27[/C][C]99.1701693740367[/C][C]-0.900169374036691[/C][/ROW]
[ROW][C]16[/C][C]97.22[/C][C]97.5474073418492[/C][C]-0.32740734184915[/C][/ROW]
[ROW][C]17[/C][C]99.28[/C][C]99.4478931365246[/C][C]-0.167893136524621[/C][/ROW]
[ROW][C]18[/C][C]100.38[/C][C]99.685472895083[/C][C]0.694527104916929[/C][/ROW]
[ROW][C]19[/C][C]99.02[/C][C]98.9729186987735[/C][C]0.0470813012264834[/C][/ROW]
[ROW][C]20[/C][C]100.32[/C][C]99.31668616935[/C][C]1.00331383064994[/C][/ROW]
[ROW][C]21[/C][C]99.81[/C][C]100.934966827585[/C][C]-1.12496682758545[/C][/ROW]
[ROW][C]22[/C][C]100.6[/C][C]99.8639296398403[/C][C]0.736070360159702[/C][/ROW]
[ROW][C]23[/C][C]101.19[/C][C]101.476749011563[/C][C]-0.286749011563036[/C][/ROW]
[ROW][C]24[/C][C]100.47[/C][C]99.686085634843[/C][C]0.783914365156985[/C][/ROW]
[ROW][C]25[/C][C]101.77[/C][C]100.335299854558[/C][C]1.43470014544176[/C][/ROW]
[ROW][C]26[/C][C]102.32[/C][C]101.050390753080[/C][C]1.26960924691957[/C][/ROW]
[ROW][C]27[/C][C]102.39[/C][C]101.652422574590[/C][C]0.737577425409654[/C][/ROW]
[ROW][C]28[/C][C]101.16[/C][C]100.504534008056[/C][C]0.655465991943504[/C][/ROW]
[ROW][C]29[/C][C]100.63[/C][C]101.624219682587[/C][C]-0.99421968258655[/C][/ROW]
[ROW][C]30[/C][C]101.48[/C][C]100.785897881166[/C][C]0.694102118834376[/C][/ROW]
[ROW][C]31[/C][C]101.44[/C][C]99.7294191200466[/C][C]1.71058087995335[/C][/ROW]
[ROW][C]32[/C][C]100.09[/C][C]100.227767187345[/C][C]-0.137767187345252[/C][/ROW]
[ROW][C]33[/C][C]100.7[/C][C]101.087979438499[/C][C]-0.387979438498780[/C][/ROW]
[ROW][C]34[/C][C]100.78[/C][C]100.678099663345[/C][C]0.101900336655159[/C][/ROW]
[ROW][C]35[/C][C]99.81[/C][C]100.545300765718[/C][C]-0.735300765718213[/C][/ROW]
[ROW][C]36[/C][C]98.45[/C][C]98.6936203162728[/C][C]-0.24362031627277[/C][/ROW]
[ROW][C]37[/C][C]98.49[/C][C]98.5044075775133[/C][C]-0.0144075775132797[/C][/ROW]
[ROW][C]38[/C][C]97.48[/C][C]98.0471015090648[/C][C]-0.567101509064845[/C][/ROW]
[ROW][C]39[/C][C]97.91[/C][C]98.104956193221[/C][C]-0.194956193220964[/C][/ROW]
[ROW][C]40[/C][C]96.94[/C][C]96.6859666547372[/C][C]0.25403334526283[/C][/ROW]
[ROW][C]41[/C][C]98.53[/C][C]98.0902830587537[/C][C]0.439716941246282[/C][/ROW]
[ROW][C]42[/C][C]96.82[/C][C]98.1862518815735[/C][C]-1.36625188157353[/C][/ROW]
[ROW][C]43[/C][C]95.76[/C][C]95.415490193245[/C][C]0.344509806754938[/C][/ROW]
[ROW][C]44[/C][C]95.27[/C][C]95.7015135892872[/C][C]-0.431513589287205[/C][/ROW]
[ROW][C]45[/C][C]97.32[/C][C]96.0874397977528[/C][C]1.23256020224719[/C][/ROW]
[ROW][C]46[/C][C]96.68[/C][C]96.9605046747128[/C][C]-0.280504674712759[/C][/ROW]
[ROW][C]47[/C][C]97.87[/C][C]97.5894076685329[/C][C]0.280592331467096[/C][/ROW]
[ROW][C]48[/C][C]97.42[/C][C]98.0038712333474[/C][C]-0.583871233347412[/C][/ROW]
[ROW][C]49[/C][C]97.94[/C][C]98.0805364831793[/C][C]-0.140536483179338[/C][/ROW]
[ROW][C]50[/C][C]99.52[/C][C]98.9854475309777[/C][C]0.534552469022281[/C][/ROW]
[ROW][C]51[/C][C]100.99[/C][C]100.164531408217[/C][C]0.825468591782755[/C][/ROW]
[ROW][C]52[/C][C]99.92[/C][C]100.116181219445[/C][C]-0.196181219445085[/C][/ROW]
[ROW][C]53[/C][C]101.97[/C][C]101.704582375470[/C][C]0.265417624530215[/C][/ROW]
[ROW][C]54[/C][C]101.58[/C][C]102.434714300234[/C][C]-0.854714300233616[/C][/ROW]
[ROW][C]55[/C][C]99.54[/C][C]100.748053839922[/C][C]-1.20805383992152[/C][/ROW]
[ROW][C]56[/C][C]100.83[/C][C]101.006344249753[/C][C]-0.176344249753068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57979&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	100.49	100.327887702781	0.162112297219314
2	99.72	100.194257532837	-0.474257532837242
3	100.14	100.607920449935	-0.467920449934754
4	98.48	98.865910775912	-0.385910775912100
5	100.38	99.9230217466653	0.456978253334675
6	101.45	100.617663041944	0.832336958055842
7	98.42	99.3141181480133	-0.894118148013252
8	98.6	98.8576888042644	-0.257688804264411
9	100.06	99.779613936163	0.280386063837036
10	98.62	99.1774660221021	-0.5574660221021
11	100.84	100.098542554186	0.741457445814154
12	100.02	99.9764228155368	0.043577184463196
13	97.95	99.3918683819685	-1.44186838196845
14	98.32	99.0828026740398	-0.762802674039766
15	98.27	99.1701693740367	-0.900169374036691
16	97.22	97.5474073418492	-0.32740734184915
17	99.28	99.4478931365246	-0.167893136524621
18	100.38	99.685472895083	0.694527104916929
19	99.02	98.9729186987735	0.0470813012264834
20	100.32	99.31668616935	1.00331383064994
21	99.81	100.934966827585	-1.12496682758545
22	100.6	99.8639296398403	0.736070360159702
23	101.19	101.476749011563	-0.286749011563036
24	100.47	99.686085634843	0.783914365156985
25	101.77	100.335299854558	1.43470014544176
26	102.32	101.050390753080	1.26960924691957
27	102.39	101.652422574590	0.737577425409654
28	101.16	100.504534008056	0.655465991943504
29	100.63	101.624219682587	-0.99421968258655
30	101.48	100.785897881166	0.694102118834376
31	101.44	99.7294191200466	1.71058087995335
32	100.09	100.227767187345	-0.137767187345252
33	100.7	101.087979438499	-0.387979438498780
34	100.78	100.678099663345	0.101900336655159
35	99.81	100.545300765718	-0.735300765718213
36	98.45	98.6936203162728	-0.24362031627277
37	98.49	98.5044075775133	-0.0144075775132797
38	97.48	98.0471015090648	-0.567101509064845
39	97.91	98.104956193221	-0.194956193220964
40	96.94	96.6859666547372	0.25403334526283
41	98.53	98.0902830587537	0.439716941246282
42	96.82	98.1862518815735	-1.36625188157353
43	95.76	95.415490193245	0.344509806754938
44	95.27	95.7015135892872	-0.431513589287205
45	97.32	96.0874397977528	1.23256020224719
46	96.68	96.9605046747128	-0.280504674712759
47	97.87	97.5894076685329	0.280592331467096
48	97.42	98.0038712333474	-0.583871233347412
49	97.94	98.0805364831793	-0.140536483179338
50	99.52	98.9854475309777	0.534552469022281
51	100.99	100.164531408217	0.825468591782755
52	99.92	100.116181219445	-0.196181219445085
53	101.97	101.704582375470	0.265417624530215
54	101.58	102.434714300234	-0.854714300233616
55	99.54	100.748053839922	-1.20805383992152
56	100.83	101.006344249753	-0.176344249753068

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.593475660422072	0.813048679155856	0.406524339577928
22	0.473498161661901	0.946996323323802	0.526501838338099
23	0.445663568857683	0.891327137715367	0.554336431142317
24	0.416825557649025	0.83365111529805	0.583174442350975
25	0.583074056802449	0.833851886395102	0.416925943197551
26	0.58369702741661	0.832605945166779	0.416302972583389
27	0.482413061559585	0.96482612311917	0.517586938440415
28	0.418984965646474	0.837969931292949	0.581015034353526
29	0.609556527386277	0.780886945227447	0.390443472613723
30	0.614564307178687	0.770871385642627	0.385435692821313
31	0.725467682453386	0.549064635093227	0.274532317546614
32	0.777811566458133	0.444376867083734	0.222188433541867
33	0.7781744549891	0.4436510900218	0.2218255450109
34	0.674735376359363	0.650529247281274	0.325264623640637
35	0.495918592245693	0.991837184491385	0.504081407754307

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.593475660422072 & 0.813048679155856 & 0.406524339577928 \tabularnewline
22 & 0.473498161661901 & 0.946996323323802 & 0.526501838338099 \tabularnewline
23 & 0.445663568857683 & 0.891327137715367 & 0.554336431142317 \tabularnewline
24 & 0.416825557649025 & 0.83365111529805 & 0.583174442350975 \tabularnewline
25 & 0.583074056802449 & 0.833851886395102 & 0.416925943197551 \tabularnewline
26 & 0.58369702741661 & 0.832605945166779 & 0.416302972583389 \tabularnewline
27 & 0.482413061559585 & 0.96482612311917 & 0.517586938440415 \tabularnewline
28 & 0.418984965646474 & 0.837969931292949 & 0.581015034353526 \tabularnewline
29 & 0.609556527386277 & 0.780886945227447 & 0.390443472613723 \tabularnewline
30 & 0.614564307178687 & 0.770871385642627 & 0.385435692821313 \tabularnewline
31 & 0.725467682453386 & 0.549064635093227 & 0.274532317546614 \tabularnewline
32 & 0.777811566458133 & 0.444376867083734 & 0.222188433541867 \tabularnewline
33 & 0.7781744549891 & 0.4436510900218 & 0.2218255450109 \tabularnewline
34 & 0.674735376359363 & 0.650529247281274 & 0.325264623640637 \tabularnewline
35 & 0.495918592245693 & 0.991837184491385 & 0.504081407754307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57979&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]0.593475660422072[/C][C]0.813048679155856[/C][C]0.406524339577928[/C][/ROW]
[ROW][C]22[/C][C]0.473498161661901[/C][C]0.946996323323802[/C][C]0.526501838338099[/C][/ROW]
[ROW][C]23[/C][C]0.445663568857683[/C][C]0.891327137715367[/C][C]0.554336431142317[/C][/ROW]
[ROW][C]24[/C][C]0.416825557649025[/C][C]0.83365111529805[/C][C]0.583174442350975[/C][/ROW]
[ROW][C]25[/C][C]0.583074056802449[/C][C]0.833851886395102[/C][C]0.416925943197551[/C][/ROW]
[ROW][C]26[/C][C]0.58369702741661[/C][C]0.832605945166779[/C][C]0.416302972583389[/C][/ROW]
[ROW][C]27[/C][C]0.482413061559585[/C][C]0.96482612311917[/C][C]0.517586938440415[/C][/ROW]
[ROW][C]28[/C][C]0.418984965646474[/C][C]0.837969931292949[/C][C]0.581015034353526[/C][/ROW]
[ROW][C]29[/C][C]0.609556527386277[/C][C]0.780886945227447[/C][C]0.390443472613723[/C][/ROW]
[ROW][C]30[/C][C]0.614564307178687[/C][C]0.770871385642627[/C][C]0.385435692821313[/C][/ROW]
[ROW][C]31[/C][C]0.725467682453386[/C][C]0.549064635093227[/C][C]0.274532317546614[/C][/ROW]
[ROW][C]32[/C][C]0.777811566458133[/C][C]0.444376867083734[/C][C]0.222188433541867[/C][/ROW]
[ROW][C]33[/C][C]0.7781744549891[/C][C]0.4436510900218[/C][C]0.2218255450109[/C][/ROW]
[ROW][C]34[/C][C]0.674735376359363[/C][C]0.650529247281274[/C][C]0.325264623640637[/C][/ROW]
[ROW][C]35[/C][C]0.495918592245693[/C][C]0.991837184491385[/C][C]0.504081407754307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57979&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.593475660422072	0.813048679155856	0.406524339577928
22	0.473498161661901	0.946996323323802	0.526501838338099
23	0.445663568857683	0.891327137715367	0.554336431142317
24	0.416825557649025	0.83365111529805	0.583174442350975
25	0.583074056802449	0.833851886395102	0.416925943197551
26	0.58369702741661	0.832605945166779	0.416302972583389
27	0.482413061559585	0.96482612311917	0.517586938440415
28	0.418984965646474	0.837969931292949	0.581015034353526
29	0.609556527386277	0.780886945227447	0.390443472613723
30	0.614564307178687	0.770871385642627	0.385435692821313
31	0.725467682453386	0.549064635093227	0.274532317546614
32	0.777811566458133	0.444376867083734	0.222188433541867
33	0.7781744549891	0.4436510900218	0.2218255450109
34	0.674735376359363	0.650529247281274	0.325264623640637
35	0.495918592245693	0.991837184491385	0.504081407754307

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

\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=57979&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=57979&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57979&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

PNG link

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PDF link

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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code