Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 19 Nov 2009 12:31:56 -0700

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/2009/Nov/19/t1258659292ovn42x6atb29k99.htm/, Retrieved Thu, 25 Apr 2024 04:11:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57913, Retrieved Thu, 25 Apr 2024 04:11:56 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [Multiple regression] [2009-11-19 19:11:31] [e3c32faf833f030d3b397185b633f75f]
-   P       [Multiple Regression] [Multiple regression] [2009-11-19 19:20:52] [e3c32faf833f030d3b397185b633f75f]
-    D          [Multiple Regression] [Multiple regression] [2009-11-19 19:31:56] [4996e0131d5120d29a6e9a8dccb25dc3] [Current]
-   PD            [Multiple Regression] [Multiple regression] [2009-11-19 19:50:16] [e3c32faf833f030d3b397185b633f75f] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

22	591	19	19	18	19
23	589	22	19	19	18
20	584	23	22	19	19
14	573	20	23	22	19
14	567	14	20	23	22
14	569	14	14	20	23
15	621	14	14	14	20
11	629	15	14	14	14
17	628	11	15	14	14
16	612	17	11	15	14
20	595	16	17	11	15
24	597	20	16	17	11
23	593	24	20	16	17
20	590	23	24	20	16
21	580	20	23	24	20
19	574	21	20	23	24
23	573	19	21	20	23
23	573	23	19	21	20
23	620	23	23	19	21
23	626	23	23	23	19
27	620	23	23	23	23
26	588	27	23	23	23
17	566	26	27	23	23
24	557	17	26	27	23
26	561	24	17	26	27
24	549	26	24	17	26
27	532	24	26	24	17
27	526	27	24	26	24
26	511	27	27	24	26
24	499	26	27	27	24
23	555	24	26	27	27
23	565	23	24	26	27
24	542	23	23	24	26
17	527	24	23	23	24
21	510	17	24	23	23
19	514	21	17	24	23
22	517	19	21	17	24
22	508	22	19	21	17
18	493	22	22	19	21
16	490	18	22	22	19
14	469	16	18	22	22
12	478	14	16	18	22
14	528	12	14	16	18
16	534	14	12	14	16
8	518	16	14	12	14
3	506	8	16	14	12
0	502	3	8	16	14
5	516	0	3	8	16
1	528	5	0	3	8
1	533	1	5	0	3
3	536	1	1	5	0
6	537	3	1	1	5
7	524	6	3	1	1
8	536	7	6	3	1
14	587	8	7	6	3
14	597	14	8	7	6
13	581	14	14	8	7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
y[t] = -37.9811272503563 + 0.0670198079699449x[t] + 0.682921562538848y1[t] + 0.119179732248385y2[t] + 0.150514391120164y3[t] + 0.0814757034058975y4[t] -1.58003334572513M1[t] -2.61700254763576M2[t] -2.23468565236653M3[t] -3.49583107087434M4[t] -1.40348894920972M5[t] -2.27169803811806M6[t] -3.62374782576128M7[t] -5.63694467436919M8[t] -4.37543160126942M9[t] -6.46479144004884M10[t] -4.23386625939827M11[t] + 0.109731952455411t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  -37.9811272503563 +  0.0670198079699449x[t] +  0.682921562538848y1[t] +  0.119179732248385y2[t] +  0.150514391120164y3[t] +  0.0814757034058975y4[t] -1.58003334572513M1[t] -2.61700254763576M2[t] -2.23468565236653M3[t] -3.49583107087434M4[t] -1.40348894920972M5[t] -2.27169803811806M6[t] -3.62374782576128M7[t] -5.63694467436919M8[t] -4.37543160126942M9[t] -6.46479144004884M10[t] -4.23386625939827M11[t] +  0.109731952455411t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  -37.9811272503563 +  0.0670198079699449x[t] +  0.682921562538848y1[t] +  0.119179732248385y2[t] +  0.150514391120164y3[t] +  0.0814757034058975y4[t] -1.58003334572513M1[t] -2.61700254763576M2[t] -2.23468565236653M3[t] -3.49583107087434M4[t] -1.40348894920972M5[t] -2.27169803811806M6[t] -3.62374782576128M7[t] -5.63694467436919M8[t] -4.37543160126942M9[t] -6.46479144004884M10[t] -4.23386625939827M11[t] +  0.109731952455411t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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] = -37.9811272503563 + 0.0670198079699449x[t] + 0.682921562538848y1[t] + 0.119179732248385y2[t] + 0.150514391120164y3[t] + 0.0814757034058975y4[t] -1.58003334572513M1[t] -2.61700254763576M2[t] -2.23468565236653M3[t] -3.49583107087434M4[t] -1.40348894920972M5[t] -2.27169803811806M6[t] -3.62374782576128M7[t] -5.63694467436919M8[t] -4.37543160126942M9[t] -6.46479144004884M10[t] -4.23386625939827M11[t] + 0.109731952455411t + 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)	-37.9811272503563	17.518128	-2.1681	0.036314	0.018157
x	0.0670198079699449	0.026158	2.5621	0.01438	0.00719
y1	0.682921562538848	0.154769	4.4125	7.8e-05	3.9e-05
y2	0.119179732248385	0.188236	0.6331	0.530338	0.265169
y3	0.150514391120164	0.191686	0.7852	0.437074	0.218537
y4	0.0814757034058975	0.16312	0.4995	0.620246	0.310123
M1	-1.58003334572513	2.338083	-0.6758	0.503167	0.251584
M2	-2.61700254763576	2.407656	-1.087	0.283731	0.141866
M3	-2.23468565236653	2.333619	-0.9576	0.344161	0.17208
M4	-3.49583107087434	2.23898	-1.5614	0.12652	0.06326
M5	-1.40348894920972	2.285549	-0.6141	0.542734	0.271367
M6	-2.27169803811806	2.263027	-1.0038	0.321648	0.160824
M7	-3.62374782576128	2.392632	-1.5145	0.137951	0.068976
M8	-5.63694467436919	2.422322	-2.3271	0.025245	0.012623
M9	-4.37543160126942	2.395629	-1.8264	0.075449	0.037724
M10	-6.46479144004884	2.339435	-2.7634	0.008685	0.004343
M11	-4.23386625939827	2.375336	-1.7824	0.082466	0.041233
t	0.109731952455411	0.065306	1.6803	0.100897	0.050449

\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) & -37.9811272503563 & 17.518128 & -2.1681 & 0.036314 & 0.018157 \tabularnewline
x & 0.0670198079699449 & 0.026158 & 2.5621 & 0.01438 & 0.00719 \tabularnewline
y1 & 0.682921562538848 & 0.154769 & 4.4125 & 7.8e-05 & 3.9e-05 \tabularnewline
y2 & 0.119179732248385 & 0.188236 & 0.6331 & 0.530338 & 0.265169 \tabularnewline
y3 & 0.150514391120164 & 0.191686 & 0.7852 & 0.437074 & 0.218537 \tabularnewline
y4 & 0.0814757034058975 & 0.16312 & 0.4995 & 0.620246 & 0.310123 \tabularnewline
M1 & -1.58003334572513 & 2.338083 & -0.6758 & 0.503167 & 0.251584 \tabularnewline
M2 & -2.61700254763576 & 2.407656 & -1.087 & 0.283731 & 0.141866 \tabularnewline
M3 & -2.23468565236653 & 2.333619 & -0.9576 & 0.344161 & 0.17208 \tabularnewline
M4 & -3.49583107087434 & 2.23898 & -1.5614 & 0.12652 & 0.06326 \tabularnewline
M5 & -1.40348894920972 & 2.285549 & -0.6141 & 0.542734 & 0.271367 \tabularnewline
M6 & -2.27169803811806 & 2.263027 & -1.0038 & 0.321648 & 0.160824 \tabularnewline
M7 & -3.62374782576128 & 2.392632 & -1.5145 & 0.137951 & 0.068976 \tabularnewline
M8 & -5.63694467436919 & 2.422322 & -2.3271 & 0.025245 & 0.012623 \tabularnewline
M9 & -4.37543160126942 & 2.395629 & -1.8264 & 0.075449 & 0.037724 \tabularnewline
M10 & -6.46479144004884 & 2.339435 & -2.7634 & 0.008685 & 0.004343 \tabularnewline
M11 & -4.23386625939827 & 2.375336 & -1.7824 & 0.082466 & 0.041233 \tabularnewline
t & 0.109731952455411 & 0.065306 & 1.6803 & 0.100897 & 0.050449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&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]-37.9811272503563[/C][C]17.518128[/C][C]-2.1681[/C][C]0.036314[/C][C]0.018157[/C][/ROW]
[ROW][C]x[/C][C]0.0670198079699449[/C][C]0.026158[/C][C]2.5621[/C][C]0.01438[/C][C]0.00719[/C][/ROW]
[ROW][C]y1[/C][C]0.682921562538848[/C][C]0.154769[/C][C]4.4125[/C][C]7.8e-05[/C][C]3.9e-05[/C][/ROW]
[ROW][C]y2[/C][C]0.119179732248385[/C][C]0.188236[/C][C]0.6331[/C][C]0.530338[/C][C]0.265169[/C][/ROW]
[ROW][C]y3[/C][C]0.150514391120164[/C][C]0.191686[/C][C]0.7852[/C][C]0.437074[/C][C]0.218537[/C][/ROW]
[ROW][C]y4[/C][C]0.0814757034058975[/C][C]0.16312[/C][C]0.4995[/C][C]0.620246[/C][C]0.310123[/C][/ROW]
[ROW][C]M1[/C][C]-1.58003334572513[/C][C]2.338083[/C][C]-0.6758[/C][C]0.503167[/C][C]0.251584[/C][/ROW]
[ROW][C]M2[/C][C]-2.61700254763576[/C][C]2.407656[/C][C]-1.087[/C][C]0.283731[/C][C]0.141866[/C][/ROW]
[ROW][C]M3[/C][C]-2.23468565236653[/C][C]2.333619[/C][C]-0.9576[/C][C]0.344161[/C][C]0.17208[/C][/ROW]
[ROW][C]M4[/C][C]-3.49583107087434[/C][C]2.23898[/C][C]-1.5614[/C][C]0.12652[/C][C]0.06326[/C][/ROW]
[ROW][C]M5[/C][C]-1.40348894920972[/C][C]2.285549[/C][C]-0.6141[/C][C]0.542734[/C][C]0.271367[/C][/ROW]
[ROW][C]M6[/C][C]-2.27169803811806[/C][C]2.263027[/C][C]-1.0038[/C][C]0.321648[/C][C]0.160824[/C][/ROW]
[ROW][C]M7[/C][C]-3.62374782576128[/C][C]2.392632[/C][C]-1.5145[/C][C]0.137951[/C][C]0.068976[/C][/ROW]
[ROW][C]M8[/C][C]-5.63694467436919[/C][C]2.422322[/C][C]-2.3271[/C][C]0.025245[/C][C]0.012623[/C][/ROW]
[ROW][C]M9[/C][C]-4.37543160126942[/C][C]2.395629[/C][C]-1.8264[/C][C]0.075449[/C][C]0.037724[/C][/ROW]
[ROW][C]M10[/C][C]-6.46479144004884[/C][C]2.339435[/C][C]-2.7634[/C][C]0.008685[/C][C]0.004343[/C][/ROW]
[ROW][C]M11[/C][C]-4.23386625939827[/C][C]2.375336[/C][C]-1.7824[/C][C]0.082466[/C][C]0.041233[/C][/ROW]
[ROW][C]t[/C][C]0.109731952455411[/C][C]0.065306[/C][C]1.6803[/C][C]0.100897[/C][C]0.050449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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)	-37.9811272503563	17.518128	-2.1681	0.036314	0.018157
x	0.0670198079699449	0.026158	2.5621	0.01438	0.00719
y1	0.682921562538848	0.154769	4.4125	7.8e-05	3.9e-05
y2	0.119179732248385	0.188236	0.6331	0.530338	0.265169
y3	0.150514391120164	0.191686	0.7852	0.437074	0.218537
y4	0.0814757034058975	0.16312	0.4995	0.620246	0.310123
M1	-1.58003334572513	2.338083	-0.6758	0.503167	0.251584
M2	-2.61700254763576	2.407656	-1.087	0.283731	0.141866
M3	-2.23468565236653	2.333619	-0.9576	0.344161	0.17208
M4	-3.49583107087434	2.23898	-1.5614	0.12652	0.06326
M5	-1.40348894920972	2.285549	-0.6141	0.542734	0.271367
M6	-2.27169803811806	2.263027	-1.0038	0.321648	0.160824
M7	-3.62374782576128	2.392632	-1.5145	0.137951	0.068976
M8	-5.63694467436919	2.422322	-2.3271	0.025245	0.012623
M9	-4.37543160126942	2.395629	-1.8264	0.075449	0.037724
M10	-6.46479144004884	2.339435	-2.7634	0.008685	0.004343
M11	-4.23386625939827	2.375336	-1.7824	0.082466	0.041233
t	0.109731952455411	0.065306	1.6803	0.100897	0.050449

Multiple Linear Regression - Regression Statistics
Multiple R	0.932188746251565
R-squared	0.868975858638064
Adjusted R-squared	0.811862771377733
F-TEST (value)	15.2150041316647
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	3.25228732833693e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.21930628543235
Sum Squared Residuals	404.193385417546

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.932188746251565 \tabularnewline
R-squared & 0.868975858638064 \tabularnewline
Adjusted R-squared & 0.811862771377733 \tabularnewline
F-TEST (value) & 15.2150041316647 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 3.25228732833693e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.21930628543235 \tabularnewline
Sum Squared Residuals & 404.193385417546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.932188746251565[/C][/ROW]
[ROW][C]R-squared[/C][C]0.868975858638064[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.811862771377733[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.2150041316647[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]3.25228732833693e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.21930628543235[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]404.193385417546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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	0.932188746251565
R-squared	0.868975858638064
Adjusted R-squared	0.811862771377733
F-TEST (value)	15.2150041316647
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	3.25228732833693e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.21930628543235
Sum Squared Residuals	404.193385417546

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	22	19.6544998724439	2.34550012755607
2	23	20.7110263823796	2.28897361762041
3	20	21.9899126529444	-1.98991265294441
4	14	18.6232395172149	-4.62323951721494
5	14	16.3630676728749	-2.36306767287492
6	14	14.6534842889170	-0.65348428891698
7	15	15.7486830112276	-0.748683011227628
8	11	14.5754439209382	-3.57544392093815
9	17	13.2671626206164	3.73283737938362
10	16	13.9865426441330	2.01345735586703
11	20	14.6994380116266	5.30056198837341
12	24	22.3667658904246	1.63323410957544
13	23	24.1751302737392	-1.17513027373922
14	20	23.3612128279036	-3.36121282790361
15	21	21.9430795541681	-0.943079554168122
16	19	20.8903180285932	-1.89031802859317
17	23	21.2456900251476	1.75430997485245
18	23	22.8866269552557	0.113373044744275
19	23	25.0514059448144	-2.05140594481443
20	23	23.9891660541505	-0.989166054150464
21	27	25.2841950455096	1.71580495449044
22	26	23.8916195543027	2.10838044569729
23	17	24.5516382785246	-7.5516382785246
24	24	22.6286419880314	1.37135801196859
25	26	25.3096415966814	0.690358403318623
26	24	24.3421626789158	-0.342162678915839
27	27	22.8877105377586	4.11228946224144
28	27	24.0159421530879	2.98405784691213
29	26	25.4321809289754	0.567819071024645
30	24	23.4751363008929	0.524863699107063
31	23	24.7453319649136	-1.74533196491365
32	23	22.4402697303048	0.559730269695181
33	24	21.7683749546567	2.23162504534334
34	17	19.1529057133904	-2.15290571339037
35	21	15.6114792020778	5.38852079792216
36	19	22.2710991613482	-3.27109916134816
37	22	19.1406079614689	2.85939203853113
38	22	19.4523253040433	2.5476746959567
39	18	19.3214902603472	-1.32149026034718
40	16	15.5259228867782	0.474077113221756
41	14	14.7224460496759	-0.722446049675899
42	12	12.3608870308974	-0.360887030897355
43	14	12.2384254087684	1.76157459123160
44	16	11.4005828319644	4.59941716803562
45	8	12.8397333305228	-4.83973333052278
46	3	4.96893208817396	-1.96893208817396
47	0	3.13744450777096	-3.13744450777096
48	5	4.73349296019588	0.266507039804116
49	1	5.7201202956666	-4.7201202956666
50	1	2.13327280675766	-1.13327280675766
51	3	2.85780699478172	0.142193005218279
52	6	2.94457741432579	3.05542258567421
53	7	6.23661532332627	0.763384676673734
54	8	7.623865424037	0.376134575962994
55	14	11.2161536702759	2.7838463297241
56	14	14.5945374626422	-0.594537462642183
57	13	15.8405340486946	-2.84053404869461

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 22 & 19.6544998724439 & 2.34550012755607 \tabularnewline
2 & 23 & 20.7110263823796 & 2.28897361762041 \tabularnewline
3 & 20 & 21.9899126529444 & -1.98991265294441 \tabularnewline
4 & 14 & 18.6232395172149 & -4.62323951721494 \tabularnewline
5 & 14 & 16.3630676728749 & -2.36306767287492 \tabularnewline
6 & 14 & 14.6534842889170 & -0.65348428891698 \tabularnewline
7 & 15 & 15.7486830112276 & -0.748683011227628 \tabularnewline
8 & 11 & 14.5754439209382 & -3.57544392093815 \tabularnewline
9 & 17 & 13.2671626206164 & 3.73283737938362 \tabularnewline
10 & 16 & 13.9865426441330 & 2.01345735586703 \tabularnewline
11 & 20 & 14.6994380116266 & 5.30056198837341 \tabularnewline
12 & 24 & 22.3667658904246 & 1.63323410957544 \tabularnewline
13 & 23 & 24.1751302737392 & -1.17513027373922 \tabularnewline
14 & 20 & 23.3612128279036 & -3.36121282790361 \tabularnewline
15 & 21 & 21.9430795541681 & -0.943079554168122 \tabularnewline
16 & 19 & 20.8903180285932 & -1.89031802859317 \tabularnewline
17 & 23 & 21.2456900251476 & 1.75430997485245 \tabularnewline
18 & 23 & 22.8866269552557 & 0.113373044744275 \tabularnewline
19 & 23 & 25.0514059448144 & -2.05140594481443 \tabularnewline
20 & 23 & 23.9891660541505 & -0.989166054150464 \tabularnewline
21 & 27 & 25.2841950455096 & 1.71580495449044 \tabularnewline
22 & 26 & 23.8916195543027 & 2.10838044569729 \tabularnewline
23 & 17 & 24.5516382785246 & -7.5516382785246 \tabularnewline
24 & 24 & 22.6286419880314 & 1.37135801196859 \tabularnewline
25 & 26 & 25.3096415966814 & 0.690358403318623 \tabularnewline
26 & 24 & 24.3421626789158 & -0.342162678915839 \tabularnewline
27 & 27 & 22.8877105377586 & 4.11228946224144 \tabularnewline
28 & 27 & 24.0159421530879 & 2.98405784691213 \tabularnewline
29 & 26 & 25.4321809289754 & 0.567819071024645 \tabularnewline
30 & 24 & 23.4751363008929 & 0.524863699107063 \tabularnewline
31 & 23 & 24.7453319649136 & -1.74533196491365 \tabularnewline
32 & 23 & 22.4402697303048 & 0.559730269695181 \tabularnewline
33 & 24 & 21.7683749546567 & 2.23162504534334 \tabularnewline
34 & 17 & 19.1529057133904 & -2.15290571339037 \tabularnewline
35 & 21 & 15.6114792020778 & 5.38852079792216 \tabularnewline
36 & 19 & 22.2710991613482 & -3.27109916134816 \tabularnewline
37 & 22 & 19.1406079614689 & 2.85939203853113 \tabularnewline
38 & 22 & 19.4523253040433 & 2.5476746959567 \tabularnewline
39 & 18 & 19.3214902603472 & -1.32149026034718 \tabularnewline
40 & 16 & 15.5259228867782 & 0.474077113221756 \tabularnewline
41 & 14 & 14.7224460496759 & -0.722446049675899 \tabularnewline
42 & 12 & 12.3608870308974 & -0.360887030897355 \tabularnewline
43 & 14 & 12.2384254087684 & 1.76157459123160 \tabularnewline
44 & 16 & 11.4005828319644 & 4.59941716803562 \tabularnewline
45 & 8 & 12.8397333305228 & -4.83973333052278 \tabularnewline
46 & 3 & 4.96893208817396 & -1.96893208817396 \tabularnewline
47 & 0 & 3.13744450777096 & -3.13744450777096 \tabularnewline
48 & 5 & 4.73349296019588 & 0.266507039804116 \tabularnewline
49 & 1 & 5.7201202956666 & -4.7201202956666 \tabularnewline
50 & 1 & 2.13327280675766 & -1.13327280675766 \tabularnewline
51 & 3 & 2.85780699478172 & 0.142193005218279 \tabularnewline
52 & 6 & 2.94457741432579 & 3.05542258567421 \tabularnewline
53 & 7 & 6.23661532332627 & 0.763384676673734 \tabularnewline
54 & 8 & 7.623865424037 & 0.376134575962994 \tabularnewline
55 & 14 & 11.2161536702759 & 2.7838463297241 \tabularnewline
56 & 14 & 14.5945374626422 & -0.594537462642183 \tabularnewline
57 & 13 & 15.8405340486946 & -2.84053404869461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&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]22[/C][C]19.6544998724439[/C][C]2.34550012755607[/C][/ROW]
[ROW][C]2[/C][C]23[/C][C]20.7110263823796[/C][C]2.28897361762041[/C][/ROW]
[ROW][C]3[/C][C]20[/C][C]21.9899126529444[/C][C]-1.98991265294441[/C][/ROW]
[ROW][C]4[/C][C]14[/C][C]18.6232395172149[/C][C]-4.62323951721494[/C][/ROW]
[ROW][C]5[/C][C]14[/C][C]16.3630676728749[/C][C]-2.36306767287492[/C][/ROW]
[ROW][C]6[/C][C]14[/C][C]14.6534842889170[/C][C]-0.65348428891698[/C][/ROW]
[ROW][C]7[/C][C]15[/C][C]15.7486830112276[/C][C]-0.748683011227628[/C][/ROW]
[ROW][C]8[/C][C]11[/C][C]14.5754439209382[/C][C]-3.57544392093815[/C][/ROW]
[ROW][C]9[/C][C]17[/C][C]13.2671626206164[/C][C]3.73283737938362[/C][/ROW]
[ROW][C]10[/C][C]16[/C][C]13.9865426441330[/C][C]2.01345735586703[/C][/ROW]
[ROW][C]11[/C][C]20[/C][C]14.6994380116266[/C][C]5.30056198837341[/C][/ROW]
[ROW][C]12[/C][C]24[/C][C]22.3667658904246[/C][C]1.63323410957544[/C][/ROW]
[ROW][C]13[/C][C]23[/C][C]24.1751302737392[/C][C]-1.17513027373922[/C][/ROW]
[ROW][C]14[/C][C]20[/C][C]23.3612128279036[/C][C]-3.36121282790361[/C][/ROW]
[ROW][C]15[/C][C]21[/C][C]21.9430795541681[/C][C]-0.943079554168122[/C][/ROW]
[ROW][C]16[/C][C]19[/C][C]20.8903180285932[/C][C]-1.89031802859317[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]21.2456900251476[/C][C]1.75430997485245[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]22.8866269552557[/C][C]0.113373044744275[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]25.0514059448144[/C][C]-2.05140594481443[/C][/ROW]
[ROW][C]20[/C][C]23[/C][C]23.9891660541505[/C][C]-0.989166054150464[/C][/ROW]
[ROW][C]21[/C][C]27[/C][C]25.2841950455096[/C][C]1.71580495449044[/C][/ROW]
[ROW][C]22[/C][C]26[/C][C]23.8916195543027[/C][C]2.10838044569729[/C][/ROW]
[ROW][C]23[/C][C]17[/C][C]24.5516382785246[/C][C]-7.5516382785246[/C][/ROW]
[ROW][C]24[/C][C]24[/C][C]22.6286419880314[/C][C]1.37135801196859[/C][/ROW]
[ROW][C]25[/C][C]26[/C][C]25.3096415966814[/C][C]0.690358403318623[/C][/ROW]
[ROW][C]26[/C][C]24[/C][C]24.3421626789158[/C][C]-0.342162678915839[/C][/ROW]
[ROW][C]27[/C][C]27[/C][C]22.8877105377586[/C][C]4.11228946224144[/C][/ROW]
[ROW][C]28[/C][C]27[/C][C]24.0159421530879[/C][C]2.98405784691213[/C][/ROW]
[ROW][C]29[/C][C]26[/C][C]25.4321809289754[/C][C]0.567819071024645[/C][/ROW]
[ROW][C]30[/C][C]24[/C][C]23.4751363008929[/C][C]0.524863699107063[/C][/ROW]
[ROW][C]31[/C][C]23[/C][C]24.7453319649136[/C][C]-1.74533196491365[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]22.4402697303048[/C][C]0.559730269695181[/C][/ROW]
[ROW][C]33[/C][C]24[/C][C]21.7683749546567[/C][C]2.23162504534334[/C][/ROW]
[ROW][C]34[/C][C]17[/C][C]19.1529057133904[/C][C]-2.15290571339037[/C][/ROW]
[ROW][C]35[/C][C]21[/C][C]15.6114792020778[/C][C]5.38852079792216[/C][/ROW]
[ROW][C]36[/C][C]19[/C][C]22.2710991613482[/C][C]-3.27109916134816[/C][/ROW]
[ROW][C]37[/C][C]22[/C][C]19.1406079614689[/C][C]2.85939203853113[/C][/ROW]
[ROW][C]38[/C][C]22[/C][C]19.4523253040433[/C][C]2.5476746959567[/C][/ROW]
[ROW][C]39[/C][C]18[/C][C]19.3214902603472[/C][C]-1.32149026034718[/C][/ROW]
[ROW][C]40[/C][C]16[/C][C]15.5259228867782[/C][C]0.474077113221756[/C][/ROW]
[ROW][C]41[/C][C]14[/C][C]14.7224460496759[/C][C]-0.722446049675899[/C][/ROW]
[ROW][C]42[/C][C]12[/C][C]12.3608870308974[/C][C]-0.360887030897355[/C][/ROW]
[ROW][C]43[/C][C]14[/C][C]12.2384254087684[/C][C]1.76157459123160[/C][/ROW]
[ROW][C]44[/C][C]16[/C][C]11.4005828319644[/C][C]4.59941716803562[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]12.8397333305228[/C][C]-4.83973333052278[/C][/ROW]
[ROW][C]46[/C][C]3[/C][C]4.96893208817396[/C][C]-1.96893208817396[/C][/ROW]
[ROW][C]47[/C][C]0[/C][C]3.13744450777096[/C][C]-3.13744450777096[/C][/ROW]
[ROW][C]48[/C][C]5[/C][C]4.73349296019588[/C][C]0.266507039804116[/C][/ROW]
[ROW][C]49[/C][C]1[/C][C]5.7201202956666[/C][C]-4.7201202956666[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]2.13327280675766[/C][C]-1.13327280675766[/C][/ROW]
[ROW][C]51[/C][C]3[/C][C]2.85780699478172[/C][C]0.142193005218279[/C][/ROW]
[ROW][C]52[/C][C]6[/C][C]2.94457741432579[/C][C]3.05542258567421[/C][/ROW]
[ROW][C]53[/C][C]7[/C][C]6.23661532332627[/C][C]0.763384676673734[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]7.623865424037[/C][C]0.376134575962994[/C][/ROW]
[ROW][C]55[/C][C]14[/C][C]11.2161536702759[/C][C]2.7838463297241[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]14.5945374626422[/C][C]-0.594537462642183[/C][/ROW]
[ROW][C]57[/C][C]13[/C][C]15.8405340486946[/C][C]-2.84053404869461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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	22	19.6544998724439	2.34550012755607
2	23	20.7110263823796	2.28897361762041
3	20	21.9899126529444	-1.98991265294441
4	14	18.6232395172149	-4.62323951721494
5	14	16.3630676728749	-2.36306767287492
6	14	14.6534842889170	-0.65348428891698
7	15	15.7486830112276	-0.748683011227628
8	11	14.5754439209382	-3.57544392093815
9	17	13.2671626206164	3.73283737938362
10	16	13.9865426441330	2.01345735586703
11	20	14.6994380116266	5.30056198837341
12	24	22.3667658904246	1.63323410957544
13	23	24.1751302737392	-1.17513027373922
14	20	23.3612128279036	-3.36121282790361
15	21	21.9430795541681	-0.943079554168122
16	19	20.8903180285932	-1.89031802859317
17	23	21.2456900251476	1.75430997485245
18	23	22.8866269552557	0.113373044744275
19	23	25.0514059448144	-2.05140594481443
20	23	23.9891660541505	-0.989166054150464
21	27	25.2841950455096	1.71580495449044
22	26	23.8916195543027	2.10838044569729
23	17	24.5516382785246	-7.5516382785246
24	24	22.6286419880314	1.37135801196859
25	26	25.3096415966814	0.690358403318623
26	24	24.3421626789158	-0.342162678915839
27	27	22.8877105377586	4.11228946224144
28	27	24.0159421530879	2.98405784691213
29	26	25.4321809289754	0.567819071024645
30	24	23.4751363008929	0.524863699107063
31	23	24.7453319649136	-1.74533196491365
32	23	22.4402697303048	0.559730269695181
33	24	21.7683749546567	2.23162504534334
34	17	19.1529057133904	-2.15290571339037
35	21	15.6114792020778	5.38852079792216
36	19	22.2710991613482	-3.27109916134816
37	22	19.1406079614689	2.85939203853113
38	22	19.4523253040433	2.5476746959567
39	18	19.3214902603472	-1.32149026034718
40	16	15.5259228867782	0.474077113221756
41	14	14.7224460496759	-0.722446049675899
42	12	12.3608870308974	-0.360887030897355
43	14	12.2384254087684	1.76157459123160
44	16	11.4005828319644	4.59941716803562
45	8	12.8397333305228	-4.83973333052278
46	3	4.96893208817396	-1.96893208817396
47	0	3.13744450777096	-3.13744450777096
48	5	4.73349296019588	0.266507039804116
49	1	5.7201202956666	-4.7201202956666
50	1	2.13327280675766	-1.13327280675766
51	3	2.85780699478172	0.142193005218279
52	6	2.94457741432579	3.05542258567421
53	7	6.23661532332627	0.763384676673734
54	8	7.623865424037	0.376134575962994
55	14	11.2161536702759	2.7838463297241
56	14	14.5945374626422	-0.594537462642183
57	13	15.8405340486946	-2.84053404869461

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.152681842250322	0.305363684500643	0.847318157749678
22	0.389023526356137	0.778047052712274	0.610976473643863
23	0.575435573959904	0.849128852080193	0.424564426040096
24	0.470033147153822	0.940066294307644	0.529966852846178
25	0.540925438542755	0.918149122914491	0.459074561457245
26	0.439256771975076	0.878513543950151	0.560743228024924
27	0.656521126852212	0.686957746295576	0.343478873147788
28	0.593939835848916	0.812120328302168	0.406060164151084
29	0.486900792385123	0.973801584770246	0.513099207614877
30	0.363962108957986	0.727924217915972	0.636037891042014
31	0.405954710759082	0.811909421518164	0.594045289240918
32	0.588352971148111	0.823294057703777	0.411647028851888
33	0.474235138563298	0.948470277126595	0.525764861436702
34	0.533988409766375	0.932023180467251	0.466011590233625
35	0.408220643014274	0.816441286028547	0.591779356985726
36	0.719930271047051	0.560139457905898	0.280069728952949

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.152681842250322 & 0.305363684500643 & 0.847318157749678 \tabularnewline
22 & 0.389023526356137 & 0.778047052712274 & 0.610976473643863 \tabularnewline
23 & 0.575435573959904 & 0.849128852080193 & 0.424564426040096 \tabularnewline
24 & 0.470033147153822 & 0.940066294307644 & 0.529966852846178 \tabularnewline
25 & 0.540925438542755 & 0.918149122914491 & 0.459074561457245 \tabularnewline
26 & 0.439256771975076 & 0.878513543950151 & 0.560743228024924 \tabularnewline
27 & 0.656521126852212 & 0.686957746295576 & 0.343478873147788 \tabularnewline
28 & 0.593939835848916 & 0.812120328302168 & 0.406060164151084 \tabularnewline
29 & 0.486900792385123 & 0.973801584770246 & 0.513099207614877 \tabularnewline
30 & 0.363962108957986 & 0.727924217915972 & 0.636037891042014 \tabularnewline
31 & 0.405954710759082 & 0.811909421518164 & 0.594045289240918 \tabularnewline
32 & 0.588352971148111 & 0.823294057703777 & 0.411647028851888 \tabularnewline
33 & 0.474235138563298 & 0.948470277126595 & 0.525764861436702 \tabularnewline
34 & 0.533988409766375 & 0.932023180467251 & 0.466011590233625 \tabularnewline
35 & 0.408220643014274 & 0.816441286028547 & 0.591779356985726 \tabularnewline
36 & 0.719930271047051 & 0.560139457905898 & 0.280069728952949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57913&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]0.152681842250322[/C][C]0.305363684500643[/C][C]0.847318157749678[/C][/ROW]
[ROW][C]22[/C][C]0.389023526356137[/C][C]0.778047052712274[/C][C]0.610976473643863[/C][/ROW]
[ROW][C]23[/C][C]0.575435573959904[/C][C]0.849128852080193[/C][C]0.424564426040096[/C][/ROW]
[ROW][C]24[/C][C]0.470033147153822[/C][C]0.940066294307644[/C][C]0.529966852846178[/C][/ROW]
[ROW][C]25[/C][C]0.540925438542755[/C][C]0.918149122914491[/C][C]0.459074561457245[/C][/ROW]
[ROW][C]26[/C][C]0.439256771975076[/C][C]0.878513543950151[/C][C]0.560743228024924[/C][/ROW]
[ROW][C]27[/C][C]0.656521126852212[/C][C]0.686957746295576[/C][C]0.343478873147788[/C][/ROW]
[ROW][C]28[/C][C]0.593939835848916[/C][C]0.812120328302168[/C][C]0.406060164151084[/C][/ROW]
[ROW][C]29[/C][C]0.486900792385123[/C][C]0.973801584770246[/C][C]0.513099207614877[/C][/ROW]
[ROW][C]30[/C][C]0.363962108957986[/C][C]0.727924217915972[/C][C]0.636037891042014[/C][/ROW]
[ROW][C]31[/C][C]0.405954710759082[/C][C]0.811909421518164[/C][C]0.594045289240918[/C][/ROW]
[ROW][C]32[/C][C]0.588352971148111[/C][C]0.823294057703777[/C][C]0.411647028851888[/C][/ROW]
[ROW][C]33[/C][C]0.474235138563298[/C][C]0.948470277126595[/C][C]0.525764861436702[/C][/ROW]
[ROW][C]34[/C][C]0.533988409766375[/C][C]0.932023180467251[/C][C]0.466011590233625[/C][/ROW]
[ROW][C]35[/C][C]0.408220643014274[/C][C]0.816441286028547[/C][C]0.591779356985726[/C][/ROW]
[ROW][C]36[/C][C]0.719930271047051[/C][C]0.560139457905898[/C][C]0.280069728952949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57913&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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	0.152681842250322	0.305363684500643	0.847318157749678
22	0.389023526356137	0.778047052712274	0.610976473643863
23	0.575435573959904	0.849128852080193	0.424564426040096
24	0.470033147153822	0.940066294307644	0.529966852846178
25	0.540925438542755	0.918149122914491	0.459074561457245
26	0.439256771975076	0.878513543950151	0.560743228024924
27	0.656521126852212	0.686957746295576	0.343478873147788
28	0.593939835848916	0.812120328302168	0.406060164151084
29	0.486900792385123	0.973801584770246	0.513099207614877
30	0.363962108957986	0.727924217915972	0.636037891042014
31	0.405954710759082	0.811909421518164	0.594045289240918
32	0.588352971148111	0.823294057703777	0.411647028851888
33	0.474235138563298	0.948470277126595	0.525764861436702
34	0.533988409766375	0.932023180467251	0.466011590233625
35	0.408220643014274	0.816441286028547	0.591779356985726
36	0.719930271047051	0.560139457905898	0.280069728952949

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=57913&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=57913&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57913&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

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

Figure 10

PNG link

Postscript link

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