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*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 23 Nov 2010 08:40:45 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/23/t1290501548rbpchrjiuxu31bn.htm/, Retrieved Wed, 24 Apr 2024 09:30:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98857, Retrieved Wed, 24 Apr 2024 09:30:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
F   PD  [Multiple Regression] [WS 7] [2010-11-20 16:26:00] [13c73ac943380855a1c72833078e44d2]
-   PD    [Multiple Regression] [WS 7 (1)] [2010-11-23 08:36:41] [717f3d787904f94c39256c5c1fc72d4c]
-   P         [Multiple Regression] [WS 7 (1)] [2010-11-23 08:40:45] [c1f1b5e209adb4577289f490325e36f2] [Current]
F   PD          [Multiple Regression] [WS 7 (1)] [2010-11-23 09:44:46] [717f3d787904f94c39256c5c1fc72d4c] 
F                 [Multiple Regression] [WS 7 (4)] [2010-11-23 10:16:31] [717f3d787904f94c39256c5c1fc72d4c] 

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Dataseries X:

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Histogram

Boxplots

1.39	1.08
1.34	1.12
1.33	1.12
1.3	1.16
1.28	1.16
1.29	1.16
1.29	1.16
1.28	1.15
1.27	1.17
1.26	1.16
1.29	1.19
1.36	1.13
1.33	1.14
1.35	1.13
1.31	1.16
1.3	1.17
1.32	1.14
1.33	1.14
1.36	1.11
1.35	1.12
1.4	1.08
1.41	1.07
1.4	1.09
1.4	1.08
1.4	1.08
1.41	1.08
1.4	1.09
1.39	1.08
1.41	1.07
1.42	1.07
1.43	1.07
1.42	1.08
1.42	1.07
1.43	1.06
1.43	1.06
1.43	1.06
1.46	1.04
1.47	1.03
1.47	1.03
1.46	1.04
1.47	1.03
1.49	1.02
1.5	1.01
1.47	1.03
1.48	1.02
1.49	1.01
1.49	1.02
1.5	1.01
1.48	1.02
1.46	1.03
1.43	1.04
1.44	1.04
1.43	1.03

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	39 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 39 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&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]39 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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	39 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
eu/us[t] = + 2.81747388264865 -1.31118267745398`us/ch`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
eu/us[t] =  +  2.81747388264865 -1.31118267745398`us/ch`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]eu/us[t] =  +  2.81747388264865 -1.31118267745398`us/ch`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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
eu/us[t] = + 2.81747388264865 -1.31118267745398`us/ch`[t] + 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)	2.81747388264865	0.039141	71.9828	0	0
`us/ch`	-1.31118267745398	0.03603	-36.3916	0	0

\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) & 2.81747388264865 & 0.039141 & 71.9828 & 0 & 0 \tabularnewline
`us/ch` & -1.31118267745398 & 0.03603 & -36.3916 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&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]2.81747388264865[/C][C]0.039141[/C][C]71.9828[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`us/ch`[/C][C]-1.31118267745398[/C][C]0.03603[/C][C]-36.3916[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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)	2.81747388264865	0.039141	71.9828	0	0
`us/ch`	-1.31118267745398	0.03603	-36.3916	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.981284059913598
R-squared	0.962918406240514
Adjusted R-squared	0.962191316166798
F-TEST (value)	1324.34541613258
F-TEST (DF numerator)	1
F-TEST (DF denominator)	51
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0136782808318764
Sum Squared Residuals	0.00954186369229955

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.981284059913598 \tabularnewline
R-squared & 0.962918406240514 \tabularnewline
Adjusted R-squared & 0.962191316166798 \tabularnewline
F-TEST (value) & 1324.34541613258 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 51 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0136782808318764 \tabularnewline
Sum Squared Residuals & 0.00954186369229955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.981284059913598[/C][/ROW]
[ROW][C]R-squared[/C][C]0.962918406240514[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.962191316166798[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1324.34541613258[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]51[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0136782808318764[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.00954186369229955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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	0.981284059913598
R-squared	0.962918406240514
Adjusted R-squared	0.962191316166798
F-TEST (value)	1324.34541613258
F-TEST (DF numerator)	1
F-TEST (DF denominator)	51
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0136782808318764
Sum Squared Residuals	0.00954186369229955

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.39	1.40139659099835	-0.0113965909983464
2	1.34	1.34894928390019	-0.008949283900191
3	1.33	1.34894928390019	-0.0189492839001910
4	1.3	1.29650197680203	0.00349802319796813
5	1.28	1.29650197680203	-0.0165019768020319
6	1.29	1.29650197680203	-0.00650197680203188
7	1.29	1.29650197680203	-0.00650197680203188
8	1.28	1.30961380357657	-0.0296138035765717
9	1.27	1.28339015002749	-0.0133901500274921
10	1.26	1.29650197680203	-0.0365019768020319
11	1.29	1.25716649647841	0.0328335035215877
12	1.36	1.33583745712565	0.0241625428743486
13	1.33	1.32272563035111	0.00727436964888843
14	1.35	1.33583745712565	0.0141625428743486
15	1.31	1.29650197680203	0.0134980231979681
16	1.3	1.28339015002749	0.0166098499725080
17	1.32	1.32272563035111	-0.00272563035111158
18	1.33	1.32272563035111	0.00727436964888843
19	1.36	1.36206111067473	-0.00206111067473081
20	1.35	1.34894928390019	0.00105071609980903
21	1.4	1.40139659099835	-0.00139659099835056
22	1.41	1.41450841777289	-0.00450841777289041
23	1.4	1.38828476422381	0.0117152357761893
24	1.4	1.40139659099835	-0.00139659099835056
25	1.4	1.40139659099835	-0.00139659099835056
26	1.41	1.40139659099835	0.00860340900164945
27	1.4	1.38828476422381	0.0117152357761893
28	1.39	1.40139659099835	-0.0113965909983506
29	1.41	1.41450841777289	-0.00450841777289041
30	1.42	1.41450841777289	0.0054915822271096
31	1.43	1.41450841777289	0.0154915822271096
32	1.42	1.40139659099835	0.0186034090016495
33	1.42	1.41450841777289	0.0054915822271096
34	1.43	1.42762024454743	0.00237975545256975
35	1.43	1.42762024454743	0.00237975545256975
36	1.43	1.42762024454743	0.00237975545256975
37	1.46	1.45384389809651	0.00615610190349007
38	1.47	1.46695572487105	0.00304427512895021
39	1.47	1.46695572487105	0.00304427512895021
40	1.46	1.45384389809651	0.00615610190349007
41	1.47	1.46695572487105	0.00304427512895021
42	1.49	1.48006755164559	0.00993244835441039
43	1.5	1.49317937842013	0.00682062157987055
44	1.47	1.46695572487105	0.00304427512895021
45	1.48	1.48006755164559	-6.75516455896238e-05
46	1.49	1.49317937842013	-0.00317937842012946
47	1.49	1.48006755164559	0.00993244835441039
48	1.5	1.49317937842013	0.00682062157987055
49	1.48	1.48006755164559	-6.75516455896238e-05
50	1.46	1.46695572487105	-0.0069557248710498
51	1.43	1.45384389809651	-0.0238438980965100
52	1.44	1.45384389809651	-0.0138438980965099
53	1.43	1.46695572487105	-0.0369557248710498

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.39 & 1.40139659099835 & -0.0113965909983464 \tabularnewline
2 & 1.34 & 1.34894928390019 & -0.008949283900191 \tabularnewline
3 & 1.33 & 1.34894928390019 & -0.0189492839001910 \tabularnewline
4 & 1.3 & 1.29650197680203 & 0.00349802319796813 \tabularnewline
5 & 1.28 & 1.29650197680203 & -0.0165019768020319 \tabularnewline
6 & 1.29 & 1.29650197680203 & -0.00650197680203188 \tabularnewline
7 & 1.29 & 1.29650197680203 & -0.00650197680203188 \tabularnewline
8 & 1.28 & 1.30961380357657 & -0.0296138035765717 \tabularnewline
9 & 1.27 & 1.28339015002749 & -0.0133901500274921 \tabularnewline
10 & 1.26 & 1.29650197680203 & -0.0365019768020319 \tabularnewline
11 & 1.29 & 1.25716649647841 & 0.0328335035215877 \tabularnewline
12 & 1.36 & 1.33583745712565 & 0.0241625428743486 \tabularnewline
13 & 1.33 & 1.32272563035111 & 0.00727436964888843 \tabularnewline
14 & 1.35 & 1.33583745712565 & 0.0141625428743486 \tabularnewline
15 & 1.31 & 1.29650197680203 & 0.0134980231979681 \tabularnewline
16 & 1.3 & 1.28339015002749 & 0.0166098499725080 \tabularnewline
17 & 1.32 & 1.32272563035111 & -0.00272563035111158 \tabularnewline
18 & 1.33 & 1.32272563035111 & 0.00727436964888843 \tabularnewline
19 & 1.36 & 1.36206111067473 & -0.00206111067473081 \tabularnewline
20 & 1.35 & 1.34894928390019 & 0.00105071609980903 \tabularnewline
21 & 1.4 & 1.40139659099835 & -0.00139659099835056 \tabularnewline
22 & 1.41 & 1.41450841777289 & -0.00450841777289041 \tabularnewline
23 & 1.4 & 1.38828476422381 & 0.0117152357761893 \tabularnewline
24 & 1.4 & 1.40139659099835 & -0.00139659099835056 \tabularnewline
25 & 1.4 & 1.40139659099835 & -0.00139659099835056 \tabularnewline
26 & 1.41 & 1.40139659099835 & 0.00860340900164945 \tabularnewline
27 & 1.4 & 1.38828476422381 & 0.0117152357761893 \tabularnewline
28 & 1.39 & 1.40139659099835 & -0.0113965909983506 \tabularnewline
29 & 1.41 & 1.41450841777289 & -0.00450841777289041 \tabularnewline
30 & 1.42 & 1.41450841777289 & 0.0054915822271096 \tabularnewline
31 & 1.43 & 1.41450841777289 & 0.0154915822271096 \tabularnewline
32 & 1.42 & 1.40139659099835 & 0.0186034090016495 \tabularnewline
33 & 1.42 & 1.41450841777289 & 0.0054915822271096 \tabularnewline
34 & 1.43 & 1.42762024454743 & 0.00237975545256975 \tabularnewline
35 & 1.43 & 1.42762024454743 & 0.00237975545256975 \tabularnewline
36 & 1.43 & 1.42762024454743 & 0.00237975545256975 \tabularnewline
37 & 1.46 & 1.45384389809651 & 0.00615610190349007 \tabularnewline
38 & 1.47 & 1.46695572487105 & 0.00304427512895021 \tabularnewline
39 & 1.47 & 1.46695572487105 & 0.00304427512895021 \tabularnewline
40 & 1.46 & 1.45384389809651 & 0.00615610190349007 \tabularnewline
41 & 1.47 & 1.46695572487105 & 0.00304427512895021 \tabularnewline
42 & 1.49 & 1.48006755164559 & 0.00993244835441039 \tabularnewline
43 & 1.5 & 1.49317937842013 & 0.00682062157987055 \tabularnewline
44 & 1.47 & 1.46695572487105 & 0.00304427512895021 \tabularnewline
45 & 1.48 & 1.48006755164559 & -6.75516455896238e-05 \tabularnewline
46 & 1.49 & 1.49317937842013 & -0.00317937842012946 \tabularnewline
47 & 1.49 & 1.48006755164559 & 0.00993244835441039 \tabularnewline
48 & 1.5 & 1.49317937842013 & 0.00682062157987055 \tabularnewline
49 & 1.48 & 1.48006755164559 & -6.75516455896238e-05 \tabularnewline
50 & 1.46 & 1.46695572487105 & -0.0069557248710498 \tabularnewline
51 & 1.43 & 1.45384389809651 & -0.0238438980965100 \tabularnewline
52 & 1.44 & 1.45384389809651 & -0.0138438980965099 \tabularnewline
53 & 1.43 & 1.46695572487105 & -0.0369557248710498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&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]1.39[/C][C]1.40139659099835[/C][C]-0.0113965909983464[/C][/ROW]
[ROW][C]2[/C][C]1.34[/C][C]1.34894928390019[/C][C]-0.008949283900191[/C][/ROW]
[ROW][C]3[/C][C]1.33[/C][C]1.34894928390019[/C][C]-0.0189492839001910[/C][/ROW]
[ROW][C]4[/C][C]1.3[/C][C]1.29650197680203[/C][C]0.00349802319796813[/C][/ROW]
[ROW][C]5[/C][C]1.28[/C][C]1.29650197680203[/C][C]-0.0165019768020319[/C][/ROW]
[ROW][C]6[/C][C]1.29[/C][C]1.29650197680203[/C][C]-0.00650197680203188[/C][/ROW]
[ROW][C]7[/C][C]1.29[/C][C]1.29650197680203[/C][C]-0.00650197680203188[/C][/ROW]
[ROW][C]8[/C][C]1.28[/C][C]1.30961380357657[/C][C]-0.0296138035765717[/C][/ROW]
[ROW][C]9[/C][C]1.27[/C][C]1.28339015002749[/C][C]-0.0133901500274921[/C][/ROW]
[ROW][C]10[/C][C]1.26[/C][C]1.29650197680203[/C][C]-0.0365019768020319[/C][/ROW]
[ROW][C]11[/C][C]1.29[/C][C]1.25716649647841[/C][C]0.0328335035215877[/C][/ROW]
[ROW][C]12[/C][C]1.36[/C][C]1.33583745712565[/C][C]0.0241625428743486[/C][/ROW]
[ROW][C]13[/C][C]1.33[/C][C]1.32272563035111[/C][C]0.00727436964888843[/C][/ROW]
[ROW][C]14[/C][C]1.35[/C][C]1.33583745712565[/C][C]0.0141625428743486[/C][/ROW]
[ROW][C]15[/C][C]1.31[/C][C]1.29650197680203[/C][C]0.0134980231979681[/C][/ROW]
[ROW][C]16[/C][C]1.3[/C][C]1.28339015002749[/C][C]0.0166098499725080[/C][/ROW]
[ROW][C]17[/C][C]1.32[/C][C]1.32272563035111[/C][C]-0.00272563035111158[/C][/ROW]
[ROW][C]18[/C][C]1.33[/C][C]1.32272563035111[/C][C]0.00727436964888843[/C][/ROW]
[ROW][C]19[/C][C]1.36[/C][C]1.36206111067473[/C][C]-0.00206111067473081[/C][/ROW]
[ROW][C]20[/C][C]1.35[/C][C]1.34894928390019[/C][C]0.00105071609980903[/C][/ROW]
[ROW][C]21[/C][C]1.4[/C][C]1.40139659099835[/C][C]-0.00139659099835056[/C][/ROW]
[ROW][C]22[/C][C]1.41[/C][C]1.41450841777289[/C][C]-0.00450841777289041[/C][/ROW]
[ROW][C]23[/C][C]1.4[/C][C]1.38828476422381[/C][C]0.0117152357761893[/C][/ROW]
[ROW][C]24[/C][C]1.4[/C][C]1.40139659099835[/C][C]-0.00139659099835056[/C][/ROW]
[ROW][C]25[/C][C]1.4[/C][C]1.40139659099835[/C][C]-0.00139659099835056[/C][/ROW]
[ROW][C]26[/C][C]1.41[/C][C]1.40139659099835[/C][C]0.00860340900164945[/C][/ROW]
[ROW][C]27[/C][C]1.4[/C][C]1.38828476422381[/C][C]0.0117152357761893[/C][/ROW]
[ROW][C]28[/C][C]1.39[/C][C]1.40139659099835[/C][C]-0.0113965909983506[/C][/ROW]
[ROW][C]29[/C][C]1.41[/C][C]1.41450841777289[/C][C]-0.00450841777289041[/C][/ROW]
[ROW][C]30[/C][C]1.42[/C][C]1.41450841777289[/C][C]0.0054915822271096[/C][/ROW]
[ROW][C]31[/C][C]1.43[/C][C]1.41450841777289[/C][C]0.0154915822271096[/C][/ROW]
[ROW][C]32[/C][C]1.42[/C][C]1.40139659099835[/C][C]0.0186034090016495[/C][/ROW]
[ROW][C]33[/C][C]1.42[/C][C]1.41450841777289[/C][C]0.0054915822271096[/C][/ROW]
[ROW][C]34[/C][C]1.43[/C][C]1.42762024454743[/C][C]0.00237975545256975[/C][/ROW]
[ROW][C]35[/C][C]1.43[/C][C]1.42762024454743[/C][C]0.00237975545256975[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.42762024454743[/C][C]0.00237975545256975[/C][/ROW]
[ROW][C]37[/C][C]1.46[/C][C]1.45384389809651[/C][C]0.00615610190349007[/C][/ROW]
[ROW][C]38[/C][C]1.47[/C][C]1.46695572487105[/C][C]0.00304427512895021[/C][/ROW]
[ROW][C]39[/C][C]1.47[/C][C]1.46695572487105[/C][C]0.00304427512895021[/C][/ROW]
[ROW][C]40[/C][C]1.46[/C][C]1.45384389809651[/C][C]0.00615610190349007[/C][/ROW]
[ROW][C]41[/C][C]1.47[/C][C]1.46695572487105[/C][C]0.00304427512895021[/C][/ROW]
[ROW][C]42[/C][C]1.49[/C][C]1.48006755164559[/C][C]0.00993244835441039[/C][/ROW]
[ROW][C]43[/C][C]1.5[/C][C]1.49317937842013[/C][C]0.00682062157987055[/C][/ROW]
[ROW][C]44[/C][C]1.47[/C][C]1.46695572487105[/C][C]0.00304427512895021[/C][/ROW]
[ROW][C]45[/C][C]1.48[/C][C]1.48006755164559[/C][C]-6.75516455896238e-05[/C][/ROW]
[ROW][C]46[/C][C]1.49[/C][C]1.49317937842013[/C][C]-0.00317937842012946[/C][/ROW]
[ROW][C]47[/C][C]1.49[/C][C]1.48006755164559[/C][C]0.00993244835441039[/C][/ROW]
[ROW][C]48[/C][C]1.5[/C][C]1.49317937842013[/C][C]0.00682062157987055[/C][/ROW]
[ROW][C]49[/C][C]1.48[/C][C]1.48006755164559[/C][C]-6.75516455896238e-05[/C][/ROW]
[ROW][C]50[/C][C]1.46[/C][C]1.46695572487105[/C][C]-0.0069557248710498[/C][/ROW]
[ROW][C]51[/C][C]1.43[/C][C]1.45384389809651[/C][C]-0.0238438980965100[/C][/ROW]
[ROW][C]52[/C][C]1.44[/C][C]1.45384389809651[/C][C]-0.0138438980965099[/C][/ROW]
[ROW][C]53[/C][C]1.43[/C][C]1.46695572487105[/C][C]-0.0369557248710498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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	1.39	1.40139659099835	-0.0113965909983464
2	1.34	1.34894928390019	-0.008949283900191
3	1.33	1.34894928390019	-0.0189492839001910
4	1.3	1.29650197680203	0.00349802319796813
5	1.28	1.29650197680203	-0.0165019768020319
6	1.29	1.29650197680203	-0.00650197680203188
7	1.29	1.29650197680203	-0.00650197680203188
8	1.28	1.30961380357657	-0.0296138035765717
9	1.27	1.28339015002749	-0.0133901500274921
10	1.26	1.29650197680203	-0.0365019768020319
11	1.29	1.25716649647841	0.0328335035215877
12	1.36	1.33583745712565	0.0241625428743486
13	1.33	1.32272563035111	0.00727436964888843
14	1.35	1.33583745712565	0.0141625428743486
15	1.31	1.29650197680203	0.0134980231979681
16	1.3	1.28339015002749	0.0166098499725080
17	1.32	1.32272563035111	-0.00272563035111158
18	1.33	1.32272563035111	0.00727436964888843
19	1.36	1.36206111067473	-0.00206111067473081
20	1.35	1.34894928390019	0.00105071609980903
21	1.4	1.40139659099835	-0.00139659099835056
22	1.41	1.41450841777289	-0.00450841777289041
23	1.4	1.38828476422381	0.0117152357761893
24	1.4	1.40139659099835	-0.00139659099835056
25	1.4	1.40139659099835	-0.00139659099835056
26	1.41	1.40139659099835	0.00860340900164945
27	1.4	1.38828476422381	0.0117152357761893
28	1.39	1.40139659099835	-0.0113965909983506
29	1.41	1.41450841777289	-0.00450841777289041
30	1.42	1.41450841777289	0.0054915822271096
31	1.43	1.41450841777289	0.0154915822271096
32	1.42	1.40139659099835	0.0186034090016495
33	1.42	1.41450841777289	0.0054915822271096
34	1.43	1.42762024454743	0.00237975545256975
35	1.43	1.42762024454743	0.00237975545256975
36	1.43	1.42762024454743	0.00237975545256975
37	1.46	1.45384389809651	0.00615610190349007
38	1.47	1.46695572487105	0.00304427512895021
39	1.47	1.46695572487105	0.00304427512895021
40	1.46	1.45384389809651	0.00615610190349007
41	1.47	1.46695572487105	0.00304427512895021
42	1.49	1.48006755164559	0.00993244835441039
43	1.5	1.49317937842013	0.00682062157987055
44	1.47	1.46695572487105	0.00304427512895021
45	1.48	1.48006755164559	-6.75516455896238e-05
46	1.49	1.49317937842013	-0.00317937842012946
47	1.49	1.48006755164559	0.00993244835441039
48	1.5	1.49317937842013	0.00682062157987055
49	1.48	1.48006755164559	-6.75516455896238e-05
50	1.46	1.46695572487105	-0.0069557248710498
51	1.43	1.45384389809651	-0.0238438980965100
52	1.44	1.45384389809651	-0.0138438980965099
53	1.43	1.46695572487105	-0.0369557248710498

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.313746225999553	0.627492451999106	0.686253774000447
6	0.171315934096949	0.342631868193897	0.828684065903051
7	0.0861208821893242	0.172241764378648	0.913879117810676
8	0.323557837045587	0.647115674091173	0.676442162954413
9	0.250287600178877	0.500575200357754	0.749712399821123
10	0.770540113343542	0.458919773312915	0.229459886656458
11	0.99286726981463	0.0142654603707388	0.00713273018536942
12	0.999377884814268	0.00124423037146334	0.000622115185731669
13	0.999106550553382	0.00178689889323586	0.000893449446617928
14	0.999241171114927	0.00151765777014608	0.000758828885073039
15	0.999027748391961	0.00194450321607752	0.000972251608038762
16	0.998932287373444	0.00213542525311212	0.00106771262655606
17	0.998095215270129	0.00380956945974258	0.00190478472987129
18	0.996853023402968	0.00629395319406446	0.00314697659703223
19	0.9947004238804	0.0105991522392001	0.00529957611960006
20	0.991219366892004	0.0175612662159911	0.00878063310799553
21	0.986140138887108	0.0277197222257835	0.0138598611128917
22	0.979106094989216	0.0417878100215682	0.0208939050107841
23	0.97582740015438	0.048345199691239	0.0241725998456195
24	0.962979384696863	0.0740412306062742	0.0370206153031371
25	0.945407859700664	0.109184280598672	0.0545921402993361
26	0.927741832422426	0.144516335155148	0.0722581675775742
27	0.91317636560864	0.173647268782719	0.0868236343913595
28	0.9131423906896	0.173715218620799	0.0868576093103997
29	0.888092116677861	0.223815766644278	0.111907883322139
30	0.847476785926414	0.305046428147173	0.152523214073586
31	0.843273341621624	0.313453316756752	0.156726658378376
32	0.87567110067609	0.248657798647822	0.124328899323911
33	0.84223770201654	0.31552459596692	0.15776229798346
34	0.794987995870136	0.410024008259729	0.205012004129864
35	0.750126923054113	0.499746153891774	0.249873076945887
36	0.736044946847992	0.527910106304015	0.263955053152008
37	0.732474096266359	0.535051807467281	0.267525903733641
38	0.672850581656471	0.654298836687058	0.327149418343529
39	0.611288518268456	0.777422963463088	0.388711481731544
40	0.697699373021766	0.604601253956468	0.302300626978234
41	0.676607795578726	0.646784408842547	0.323392204421274
42	0.651887027883729	0.696225944232542	0.348112972116271
43	0.543684817525358	0.912630364949285	0.456315182474642
44	0.559887307457068	0.880225385085864	0.440112692542932
45	0.445737403924325	0.891474807848651	0.554262596075675
46	0.38487677793764	0.76975355587528	0.61512322206236
47	0.36648118615386	0.73296237230772	0.63351881384614
48	0.234382347510309	0.468764695020617	0.765617652489691

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.313746225999553 & 0.627492451999106 & 0.686253774000447 \tabularnewline
6 & 0.171315934096949 & 0.342631868193897 & 0.828684065903051 \tabularnewline
7 & 0.0861208821893242 & 0.172241764378648 & 0.913879117810676 \tabularnewline
8 & 0.323557837045587 & 0.647115674091173 & 0.676442162954413 \tabularnewline
9 & 0.250287600178877 & 0.500575200357754 & 0.749712399821123 \tabularnewline
10 & 0.770540113343542 & 0.458919773312915 & 0.229459886656458 \tabularnewline
11 & 0.99286726981463 & 0.0142654603707388 & 0.00713273018536942 \tabularnewline
12 & 0.999377884814268 & 0.00124423037146334 & 0.000622115185731669 \tabularnewline
13 & 0.999106550553382 & 0.00178689889323586 & 0.000893449446617928 \tabularnewline
14 & 0.999241171114927 & 0.00151765777014608 & 0.000758828885073039 \tabularnewline
15 & 0.999027748391961 & 0.00194450321607752 & 0.000972251608038762 \tabularnewline
16 & 0.998932287373444 & 0.00213542525311212 & 0.00106771262655606 \tabularnewline
17 & 0.998095215270129 & 0.00380956945974258 & 0.00190478472987129 \tabularnewline
18 & 0.996853023402968 & 0.00629395319406446 & 0.00314697659703223 \tabularnewline
19 & 0.9947004238804 & 0.0105991522392001 & 0.00529957611960006 \tabularnewline
20 & 0.991219366892004 & 0.0175612662159911 & 0.00878063310799553 \tabularnewline
21 & 0.986140138887108 & 0.0277197222257835 & 0.0138598611128917 \tabularnewline
22 & 0.979106094989216 & 0.0417878100215682 & 0.0208939050107841 \tabularnewline
23 & 0.97582740015438 & 0.048345199691239 & 0.0241725998456195 \tabularnewline
24 & 0.962979384696863 & 0.0740412306062742 & 0.0370206153031371 \tabularnewline
25 & 0.945407859700664 & 0.109184280598672 & 0.0545921402993361 \tabularnewline
26 & 0.927741832422426 & 0.144516335155148 & 0.0722581675775742 \tabularnewline
27 & 0.91317636560864 & 0.173647268782719 & 0.0868236343913595 \tabularnewline
28 & 0.9131423906896 & 0.173715218620799 & 0.0868576093103997 \tabularnewline
29 & 0.888092116677861 & 0.223815766644278 & 0.111907883322139 \tabularnewline
30 & 0.847476785926414 & 0.305046428147173 & 0.152523214073586 \tabularnewline
31 & 0.843273341621624 & 0.313453316756752 & 0.156726658378376 \tabularnewline
32 & 0.87567110067609 & 0.248657798647822 & 0.124328899323911 \tabularnewline
33 & 0.84223770201654 & 0.31552459596692 & 0.15776229798346 \tabularnewline
34 & 0.794987995870136 & 0.410024008259729 & 0.205012004129864 \tabularnewline
35 & 0.750126923054113 & 0.499746153891774 & 0.249873076945887 \tabularnewline
36 & 0.736044946847992 & 0.527910106304015 & 0.263955053152008 \tabularnewline
37 & 0.732474096266359 & 0.535051807467281 & 0.267525903733641 \tabularnewline
38 & 0.672850581656471 & 0.654298836687058 & 0.327149418343529 \tabularnewline
39 & 0.611288518268456 & 0.777422963463088 & 0.388711481731544 \tabularnewline
40 & 0.697699373021766 & 0.604601253956468 & 0.302300626978234 \tabularnewline
41 & 0.676607795578726 & 0.646784408842547 & 0.323392204421274 \tabularnewline
42 & 0.651887027883729 & 0.696225944232542 & 0.348112972116271 \tabularnewline
43 & 0.543684817525358 & 0.912630364949285 & 0.456315182474642 \tabularnewline
44 & 0.559887307457068 & 0.880225385085864 & 0.440112692542932 \tabularnewline
45 & 0.445737403924325 & 0.891474807848651 & 0.554262596075675 \tabularnewline
46 & 0.38487677793764 & 0.76975355587528 & 0.61512322206236 \tabularnewline
47 & 0.36648118615386 & 0.73296237230772 & 0.63351881384614 \tabularnewline
48 & 0.234382347510309 & 0.468764695020617 & 0.765617652489691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&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]5[/C][C]0.313746225999553[/C][C]0.627492451999106[/C][C]0.686253774000447[/C][/ROW]
[ROW][C]6[/C][C]0.171315934096949[/C][C]0.342631868193897[/C][C]0.828684065903051[/C][/ROW]
[ROW][C]7[/C][C]0.0861208821893242[/C][C]0.172241764378648[/C][C]0.913879117810676[/C][/ROW]
[ROW][C]8[/C][C]0.323557837045587[/C][C]0.647115674091173[/C][C]0.676442162954413[/C][/ROW]
[ROW][C]9[/C][C]0.250287600178877[/C][C]0.500575200357754[/C][C]0.749712399821123[/C][/ROW]
[ROW][C]10[/C][C]0.770540113343542[/C][C]0.458919773312915[/C][C]0.229459886656458[/C][/ROW]
[ROW][C]11[/C][C]0.99286726981463[/C][C]0.0142654603707388[/C][C]0.00713273018536942[/C][/ROW]
[ROW][C]12[/C][C]0.999377884814268[/C][C]0.00124423037146334[/C][C]0.000622115185731669[/C][/ROW]
[ROW][C]13[/C][C]0.999106550553382[/C][C]0.00178689889323586[/C][C]0.000893449446617928[/C][/ROW]
[ROW][C]14[/C][C]0.999241171114927[/C][C]0.00151765777014608[/C][C]0.000758828885073039[/C][/ROW]
[ROW][C]15[/C][C]0.999027748391961[/C][C]0.00194450321607752[/C][C]0.000972251608038762[/C][/ROW]
[ROW][C]16[/C][C]0.998932287373444[/C][C]0.00213542525311212[/C][C]0.00106771262655606[/C][/ROW]
[ROW][C]17[/C][C]0.998095215270129[/C][C]0.00380956945974258[/C][C]0.00190478472987129[/C][/ROW]
[ROW][C]18[/C][C]0.996853023402968[/C][C]0.00629395319406446[/C][C]0.00314697659703223[/C][/ROW]
[ROW][C]19[/C][C]0.9947004238804[/C][C]0.0105991522392001[/C][C]0.00529957611960006[/C][/ROW]
[ROW][C]20[/C][C]0.991219366892004[/C][C]0.0175612662159911[/C][C]0.00878063310799553[/C][/ROW]
[ROW][C]21[/C][C]0.986140138887108[/C][C]0.0277197222257835[/C][C]0.0138598611128917[/C][/ROW]
[ROW][C]22[/C][C]0.979106094989216[/C][C]0.0417878100215682[/C][C]0.0208939050107841[/C][/ROW]
[ROW][C]23[/C][C]0.97582740015438[/C][C]0.048345199691239[/C][C]0.0241725998456195[/C][/ROW]
[ROW][C]24[/C][C]0.962979384696863[/C][C]0.0740412306062742[/C][C]0.0370206153031371[/C][/ROW]
[ROW][C]25[/C][C]0.945407859700664[/C][C]0.109184280598672[/C][C]0.0545921402993361[/C][/ROW]
[ROW][C]26[/C][C]0.927741832422426[/C][C]0.144516335155148[/C][C]0.0722581675775742[/C][/ROW]
[ROW][C]27[/C][C]0.91317636560864[/C][C]0.173647268782719[/C][C]0.0868236343913595[/C][/ROW]
[ROW][C]28[/C][C]0.9131423906896[/C][C]0.173715218620799[/C][C]0.0868576093103997[/C][/ROW]
[ROW][C]29[/C][C]0.888092116677861[/C][C]0.223815766644278[/C][C]0.111907883322139[/C][/ROW]
[ROW][C]30[/C][C]0.847476785926414[/C][C]0.305046428147173[/C][C]0.152523214073586[/C][/ROW]
[ROW][C]31[/C][C]0.843273341621624[/C][C]0.313453316756752[/C][C]0.156726658378376[/C][/ROW]
[ROW][C]32[/C][C]0.87567110067609[/C][C]0.248657798647822[/C][C]0.124328899323911[/C][/ROW]
[ROW][C]33[/C][C]0.84223770201654[/C][C]0.31552459596692[/C][C]0.15776229798346[/C][/ROW]
[ROW][C]34[/C][C]0.794987995870136[/C][C]0.410024008259729[/C][C]0.205012004129864[/C][/ROW]
[ROW][C]35[/C][C]0.750126923054113[/C][C]0.499746153891774[/C][C]0.249873076945887[/C][/ROW]
[ROW][C]36[/C][C]0.736044946847992[/C][C]0.527910106304015[/C][C]0.263955053152008[/C][/ROW]
[ROW][C]37[/C][C]0.732474096266359[/C][C]0.535051807467281[/C][C]0.267525903733641[/C][/ROW]
[ROW][C]38[/C][C]0.672850581656471[/C][C]0.654298836687058[/C][C]0.327149418343529[/C][/ROW]
[ROW][C]39[/C][C]0.611288518268456[/C][C]0.777422963463088[/C][C]0.388711481731544[/C][/ROW]
[ROW][C]40[/C][C]0.697699373021766[/C][C]0.604601253956468[/C][C]0.302300626978234[/C][/ROW]
[ROW][C]41[/C][C]0.676607795578726[/C][C]0.646784408842547[/C][C]0.323392204421274[/C][/ROW]
[ROW][C]42[/C][C]0.651887027883729[/C][C]0.696225944232542[/C][C]0.348112972116271[/C][/ROW]
[ROW][C]43[/C][C]0.543684817525358[/C][C]0.912630364949285[/C][C]0.456315182474642[/C][/ROW]
[ROW][C]44[/C][C]0.559887307457068[/C][C]0.880225385085864[/C][C]0.440112692542932[/C][/ROW]
[ROW][C]45[/C][C]0.445737403924325[/C][C]0.891474807848651[/C][C]0.554262596075675[/C][/ROW]
[ROW][C]46[/C][C]0.38487677793764[/C][C]0.76975355587528[/C][C]0.61512322206236[/C][/ROW]
[ROW][C]47[/C][C]0.36648118615386[/C][C]0.73296237230772[/C][C]0.63351881384614[/C][/ROW]
[ROW][C]48[/C][C]0.234382347510309[/C][C]0.468764695020617[/C][C]0.765617652489691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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
5	0.313746225999553	0.627492451999106	0.686253774000447
6	0.171315934096949	0.342631868193897	0.828684065903051
7	0.0861208821893242	0.172241764378648	0.913879117810676
8	0.323557837045587	0.647115674091173	0.676442162954413
9	0.250287600178877	0.500575200357754	0.749712399821123
10	0.770540113343542	0.458919773312915	0.229459886656458
11	0.99286726981463	0.0142654603707388	0.00713273018536942
12	0.999377884814268	0.00124423037146334	0.000622115185731669
13	0.999106550553382	0.00178689889323586	0.000893449446617928
14	0.999241171114927	0.00151765777014608	0.000758828885073039
15	0.999027748391961	0.00194450321607752	0.000972251608038762
16	0.998932287373444	0.00213542525311212	0.00106771262655606
17	0.998095215270129	0.00380956945974258	0.00190478472987129
18	0.996853023402968	0.00629395319406446	0.00314697659703223
19	0.9947004238804	0.0105991522392001	0.00529957611960006
20	0.991219366892004	0.0175612662159911	0.00878063310799553
21	0.986140138887108	0.0277197222257835	0.0138598611128917
22	0.979106094989216	0.0417878100215682	0.0208939050107841
23	0.97582740015438	0.048345199691239	0.0241725998456195
24	0.962979384696863	0.0740412306062742	0.0370206153031371
25	0.945407859700664	0.109184280598672	0.0545921402993361
26	0.927741832422426	0.144516335155148	0.0722581675775742
27	0.91317636560864	0.173647268782719	0.0868236343913595
28	0.9131423906896	0.173715218620799	0.0868576093103997
29	0.888092116677861	0.223815766644278	0.111907883322139
30	0.847476785926414	0.305046428147173	0.152523214073586
31	0.843273341621624	0.313453316756752	0.156726658378376
32	0.87567110067609	0.248657798647822	0.124328899323911
33	0.84223770201654	0.31552459596692	0.15776229798346
34	0.794987995870136	0.410024008259729	0.205012004129864
35	0.750126923054113	0.499746153891774	0.249873076945887
36	0.736044946847992	0.527910106304015	0.263955053152008
37	0.732474096266359	0.535051807467281	0.267525903733641
38	0.672850581656471	0.654298836687058	0.327149418343529
39	0.611288518268456	0.777422963463088	0.388711481731544
40	0.697699373021766	0.604601253956468	0.302300626978234
41	0.676607795578726	0.646784408842547	0.323392204421274
42	0.651887027883729	0.696225944232542	0.348112972116271
43	0.543684817525358	0.912630364949285	0.456315182474642
44	0.559887307457068	0.880225385085864	0.440112692542932
45	0.445737403924325	0.891474807848651	0.554262596075675
46	0.38487677793764	0.76975355587528	0.61512322206236
47	0.36648118615386	0.73296237230772	0.63351881384614
48	0.234382347510309	0.468764695020617	0.765617652489691

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.159090909090909	NOK
5% type I error level	13	0.295454545454545	NOK
10% type I error level	14	0.318181818181818	NOK

\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 & 7 & 0.159090909090909 & NOK \tabularnewline
5% type I error level & 13 & 0.295454545454545 & NOK \tabularnewline
10% type I error level & 14 & 0.318181818181818 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98857&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]7[/C][C]0.159090909090909[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]0.295454545454545[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]14[/C][C]0.318181818181818[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98857&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98857&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	7	0.159090909090909	NOK
5% type I error level	13	0.295454545454545	NOK
10% type I error level	14	0.318181818181818	NOK

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

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code