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

Tue, 23 Nov 2010 15:40:07 +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/t1290526709yqmtlz68h8kbhei.htm/, Retrieved Tue, 16 Apr 2024 16:20:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=99299, Retrieved Tue, 16 Apr 2024 16:20:00 +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

163

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

-       [Multiple Regression] [] [2010-11-23 15:40:07] [059f61fa4455ecc8020fda045e7124df] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

97,3	332,9
90,45	341,6
80,64	333,4
80,58	348,2
75,82	344,7
85,59	344,7
89,35	329,3
89,42	323,5
104,73	323,2
95,32	317,4
89,27	330,1
90,44	329,2
86,97	334,9
79,98	315,8
81,22	315,4
87,35	319,6
83,64	317,3
82,22	313,8
94,4	315,8
102,18	311,3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	11 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 11 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99299&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]11 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99299&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99299&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	11 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation
Colombia[t] = + 115.126449876048 -0.0749892159053702USA[t] + 2.04744931475523M1[t] -5.26249460795268M2[t] -9.86994823634578M3[t] -6.12255068524476M4[t] -10.5750194113703M5[t] -6.53125053920473M6[t] + 0.936321714229291M7[t] + 4.47512725231664M8[t] + 13.8400647045678M9[t] + 3.99512725231663M10[t] -1.10250970568517M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Colombia[t] =  +  115.126449876048 -0.0749892159053702USA[t] +  2.04744931475523M1[t] -5.26249460795268M2[t] -9.86994823634578M3[t] -6.12255068524476M4[t] -10.5750194113703M5[t] -6.53125053920473M6[t] +  0.936321714229291M7[t] +  4.47512725231664M8[t] +  13.8400647045678M9[t] +  3.99512725231663M10[t] -1.10250970568517M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99299&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Colombia[t] =  +  115.126449876048 -0.0749892159053702USA[t] +  2.04744931475523M1[t] -5.26249460795268M2[t] -9.86994823634578M3[t] -6.12255068524476M4[t] -10.5750194113703M5[t] -6.53125053920473M6[t] +  0.936321714229291M7[t] +  4.47512725231664M8[t] +  13.8400647045678M9[t] +  3.99512725231663M10[t] -1.10250970568517M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99299&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99299&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
Colombia[t] = + 115.126449876048 -0.0749892159053702USA[t] + 2.04744931475523M1[t] -5.26249460795268M2[t] -9.86994823634578M3[t] -6.12255068524476M4[t] -10.5750194113703M5[t] -6.53125053920473M6[t] + 0.936321714229291M7[t] + 4.47512725231664M8[t] + 13.8400647045678M9[t] + 3.99512725231663M10[t] -1.10250970568517M11[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)	115.126449876048	45.322843	2.5401	0.038656	0.019328
USA	-0.0749892159053702	0.13647	-0.5495	0.59975	0.299875
M1	2.04744931475523	7.3596	0.2782	0.788896	0.394448
M2	-5.26249460795268	7.331914	-0.7178	0.496159	0.24808
M3	-9.86994823634578	7.360802	-1.3409	0.221836	0.110918
M4	-6.12255068524476	7.3596	-0.8319	0.432918	0.216459
M5	-10.5750194113703	7.335711	-1.4416	0.19262	0.09631
M6	-6.53125053920473	7.3316	-0.8908	0.402597	0.201298
M7	0.936321714229291	7.387551	0.1267	0.902707	0.451354
M8	4.47512725231664	7.506365	0.5962	0.569825	0.284912
M9	13.8400647045678	8.505305	1.6272	0.147714	0.073857
M10	3.99512725231663	8.617595	0.4636	0.657004	0.328502
M11	-1.10250970568517	8.46669	-0.1302	0.900058	0.450029

\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) & 115.126449876048 & 45.322843 & 2.5401 & 0.038656 & 0.019328 \tabularnewline
USA & -0.0749892159053702 & 0.13647 & -0.5495 & 0.59975 & 0.299875 \tabularnewline
M1 & 2.04744931475523 & 7.3596 & 0.2782 & 0.788896 & 0.394448 \tabularnewline
M2 & -5.26249460795268 & 7.331914 & -0.7178 & 0.496159 & 0.24808 \tabularnewline
M3 & -9.86994823634578 & 7.360802 & -1.3409 & 0.221836 & 0.110918 \tabularnewline
M4 & -6.12255068524476 & 7.3596 & -0.8319 & 0.432918 & 0.216459 \tabularnewline
M5 & -10.5750194113703 & 7.335711 & -1.4416 & 0.19262 & 0.09631 \tabularnewline
M6 & -6.53125053920473 & 7.3316 & -0.8908 & 0.402597 & 0.201298 \tabularnewline
M7 & 0.936321714229291 & 7.387551 & 0.1267 & 0.902707 & 0.451354 \tabularnewline
M8 & 4.47512725231664 & 7.506365 & 0.5962 & 0.569825 & 0.284912 \tabularnewline
M9 & 13.8400647045678 & 8.505305 & 1.6272 & 0.147714 & 0.073857 \tabularnewline
M10 & 3.99512725231663 & 8.617595 & 0.4636 & 0.657004 & 0.328502 \tabularnewline
M11 & -1.10250970568517 & 8.46669 & -0.1302 & 0.900058 & 0.450029 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99299&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]115.126449876048[/C][C]45.322843[/C][C]2.5401[/C][C]0.038656[/C][C]0.019328[/C][/ROW]
[ROW][C]USA[/C][C]-0.0749892159053702[/C][C]0.13647[/C][C]-0.5495[/C][C]0.59975[/C][C]0.299875[/C][/ROW]
[ROW][C]M1[/C][C]2.04744931475523[/C][C]7.3596[/C][C]0.2782[/C][C]0.788896[/C][C]0.394448[/C][/ROW]
[ROW][C]M2[/C][C]-5.26249460795268[/C][C]7.331914[/C][C]-0.7178[/C][C]0.496159[/C][C]0.24808[/C][/ROW]
[ROW][C]M3[/C][C]-9.86994823634578[/C][C]7.360802[/C][C]-1.3409[/C][C]0.221836[/C][C]0.110918[/C][/ROW]
[ROW][C]M4[/C][C]-6.12255068524476[/C][C]7.3596[/C][C]-0.8319[/C][C]0.432918[/C][C]0.216459[/C][/ROW]
[ROW][C]M5[/C][C]-10.5750194113703[/C][C]7.335711[/C][C]-1.4416[/C][C]0.19262[/C][C]0.09631[/C][/ROW]
[ROW][C]M6[/C][C]-6.53125053920473[/C][C]7.3316[/C][C]-0.8908[/C][C]0.402597[/C][C]0.201298[/C][/ROW]
[ROW][C]M7[/C][C]0.936321714229291[/C][C]7.387551[/C][C]0.1267[/C][C]0.902707[/C][C]0.451354[/C][/ROW]
[ROW][C]M8[/C][C]4.47512725231664[/C][C]7.506365[/C][C]0.5962[/C][C]0.569825[/C][C]0.284912[/C][/ROW]
[ROW][C]M9[/C][C]13.8400647045678[/C][C]8.505305[/C][C]1.6272[/C][C]0.147714[/C][C]0.073857[/C][/ROW]
[ROW][C]M10[/C][C]3.99512725231663[/C][C]8.617595[/C][C]0.4636[/C][C]0.657004[/C][C]0.328502[/C][/ROW]
[ROW][C]M11[/C][C]-1.10250970568517[/C][C]8.46669[/C][C]-0.1302[/C][C]0.900058[/C][C]0.450029[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99299&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99299&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)	115.126449876048	45.322843	2.5401	0.038656	0.019328
USA	-0.0749892159053702	0.13647	-0.5495	0.59975	0.299875
M1	2.04744931475523	7.3596	0.2782	0.788896	0.394448
M2	-5.26249460795268	7.331914	-0.7178	0.496159	0.24808
M3	-9.86994823634578	7.360802	-1.3409	0.221836	0.110918
M4	-6.12255068524476	7.3596	-0.8319	0.432918	0.216459
M5	-10.5750194113703	7.335711	-1.4416	0.19262	0.09631
M6	-6.53125053920473	7.3316	-0.8908	0.402597	0.201298
M7	0.936321714229291	7.387551	0.1267	0.902707	0.451354
M8	4.47512725231664	7.506365	0.5962	0.569825	0.284912
M9	13.8400647045678	8.505305	1.6272	0.147714	0.073857
M10	3.99512725231663	8.617595	0.4636	0.657004	0.328502
M11	-1.10250970568517	8.46669	-0.1302	0.900058	0.450029

Multiple Linear Regression - Regression Statistics
Multiple R	0.879155360716646
R-squared	0.772914148276816
Adjusted R-squared	0.383624116751357
F-TEST (value)	1.98544551795508
F-TEST (DF numerator)	12
F-TEST (DF denominator)	7
p-value	0.185023599667774
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.98622383985848
Sum Squared Residuals	250.84413102623

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.879155360716646 \tabularnewline
R-squared & 0.772914148276816 \tabularnewline
Adjusted R-squared & 0.383624116751357 \tabularnewline
F-TEST (value) & 1.98544551795508 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 7 \tabularnewline
p-value & 0.185023599667774 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.98622383985848 \tabularnewline
Sum Squared Residuals & 250.84413102623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99299&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.879155360716646[/C][/ROW]
[ROW][C]R-squared[/C][C]0.772914148276816[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.383624116751357[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.98544551795508[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]7[/C][/ROW]
[ROW][C]p-value[/C][C]0.185023599667774[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.98622383985848[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]250.84413102623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99299&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99299&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	0.879155360716646
R-squared	0.772914148276816
Adjusted R-squared	0.383624116751357
F-TEST (value)	1.98544551795508
F-TEST (DF numerator)	12
F-TEST (DF denominator)	7
p-value	0.185023599667774
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.98622383985848
Sum Squared Residuals	250.84413102623

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	97.3	92.2099892159054	5.09001078409462
2	90.45	84.2476391148207	6.20236088517927
3	80.64	80.2550970568517	0.384902943148332
4	80.58	82.8926542125532	-2.31265421255320
5	75.82	78.7026477420964	-2.88264774209643
6	85.59	82.746416614262	2.84358338573797
7	89.35	91.3688227926388	-2.01882279263876
8	89.42	95.3425657829772	-5.92256578297725
9	104.73	104.73	1.93963768657657e-16
10	95.32	95.32	1.93963768657657e-16
11	89.27	89.27	-1.91545997813014e-15
12	90.44	90.44	5.27030676045204e-16
13	86.97	92.0600107840946	-5.09001078409462
14	79.98	86.1823608851793	-6.20236088517927
15	81.22	81.6049029431483	-0.38490294314833
16	87.35	85.0373457874468	2.31265421255321
17	83.64	80.7573522579036	2.88264774209643
18	82.22	85.063583385738	-2.84358338573797
19	94.4	92.3811772073612	2.01882279263876
20	102.18	96.2574342170228	5.92256578297724

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 97.3 & 92.2099892159054 & 5.09001078409462 \tabularnewline
2 & 90.45 & 84.2476391148207 & 6.20236088517927 \tabularnewline
3 & 80.64 & 80.2550970568517 & 0.384902943148332 \tabularnewline
4 & 80.58 & 82.8926542125532 & -2.31265421255320 \tabularnewline
5 & 75.82 & 78.7026477420964 & -2.88264774209643 \tabularnewline
6 & 85.59 & 82.746416614262 & 2.84358338573797 \tabularnewline
7 & 89.35 & 91.3688227926388 & -2.01882279263876 \tabularnewline
8 & 89.42 & 95.3425657829772 & -5.92256578297725 \tabularnewline
9 & 104.73 & 104.73 & 1.93963768657657e-16 \tabularnewline
10 & 95.32 & 95.32 & 1.93963768657657e-16 \tabularnewline
11 & 89.27 & 89.27 & -1.91545997813014e-15 \tabularnewline
12 & 90.44 & 90.44 & 5.27030676045204e-16 \tabularnewline
13 & 86.97 & 92.0600107840946 & -5.09001078409462 \tabularnewline
14 & 79.98 & 86.1823608851793 & -6.20236088517927 \tabularnewline
15 & 81.22 & 81.6049029431483 & -0.38490294314833 \tabularnewline
16 & 87.35 & 85.0373457874468 & 2.31265421255321 \tabularnewline
17 & 83.64 & 80.7573522579036 & 2.88264774209643 \tabularnewline
18 & 82.22 & 85.063583385738 & -2.84358338573797 \tabularnewline
19 & 94.4 & 92.3811772073612 & 2.01882279263876 \tabularnewline
20 & 102.18 & 96.2574342170228 & 5.92256578297724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=99299&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]97.3[/C][C]92.2099892159054[/C][C]5.09001078409462[/C][/ROW]
[ROW][C]2[/C][C]90.45[/C][C]84.2476391148207[/C][C]6.20236088517927[/C][/ROW]
[ROW][C]3[/C][C]80.64[/C][C]80.2550970568517[/C][C]0.384902943148332[/C][/ROW]
[ROW][C]4[/C][C]80.58[/C][C]82.8926542125532[/C][C]-2.31265421255320[/C][/ROW]
[ROW][C]5[/C][C]75.82[/C][C]78.7026477420964[/C][C]-2.88264774209643[/C][/ROW]
[ROW][C]6[/C][C]85.59[/C][C]82.746416614262[/C][C]2.84358338573797[/C][/ROW]
[ROW][C]7[/C][C]89.35[/C][C]91.3688227926388[/C][C]-2.01882279263876[/C][/ROW]
[ROW][C]8[/C][C]89.42[/C][C]95.3425657829772[/C][C]-5.92256578297725[/C][/ROW]
[ROW][C]9[/C][C]104.73[/C][C]104.73[/C][C]1.93963768657657e-16[/C][/ROW]
[ROW][C]10[/C][C]95.32[/C][C]95.32[/C][C]1.93963768657657e-16[/C][/ROW]
[ROW][C]11[/C][C]89.27[/C][C]89.27[/C][C]-1.91545997813014e-15[/C][/ROW]
[ROW][C]12[/C][C]90.44[/C][C]90.44[/C][C]5.27030676045204e-16[/C][/ROW]
[ROW][C]13[/C][C]86.97[/C][C]92.0600107840946[/C][C]-5.09001078409462[/C][/ROW]
[ROW][C]14[/C][C]79.98[/C][C]86.1823608851793[/C][C]-6.20236088517927[/C][/ROW]
[ROW][C]15[/C][C]81.22[/C][C]81.6049029431483[/C][C]-0.38490294314833[/C][/ROW]
[ROW][C]16[/C][C]87.35[/C][C]85.0373457874468[/C][C]2.31265421255321[/C][/ROW]
[ROW][C]17[/C][C]83.64[/C][C]80.7573522579036[/C][C]2.88264774209643[/C][/ROW]
[ROW][C]18[/C][C]82.22[/C][C]85.063583385738[/C][C]-2.84358338573797[/C][/ROW]
[ROW][C]19[/C][C]94.4[/C][C]92.3811772073612[/C][C]2.01882279263876[/C][/ROW]
[ROW][C]20[/C][C]102.18[/C][C]96.2574342170228[/C][C]5.92256578297724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=99299&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=99299&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	97.3	92.2099892159054	5.09001078409462
2	90.45	84.2476391148207	6.20236088517927
3	80.64	80.2550970568517	0.384902943148332
4	80.58	82.8926542125532	-2.31265421255320
5	75.82	78.7026477420964	-2.88264774209643
6	85.59	82.746416614262	2.84358338573797
7	89.35	91.3688227926388	-2.01882279263876
8	89.42	95.3425657829772	-5.92256578297725
9	104.73	104.73	1.93963768657657e-16
10	95.32	95.32	1.93963768657657e-16
11	89.27	89.27	-1.91545997813014e-15
12	90.44	90.44	5.27030676045204e-16
13	86.97	92.0600107840946	-5.09001078409462
14	79.98	86.1823608851793	-6.20236088517927
15	81.22	81.6049029431483	-0.38490294314833
16	87.35	85.0373457874468	2.31265421255321
17	83.64	80.7573522579036	2.88264774209643
18	82.22	85.063583385738	-2.84358338573797
19	94.4	92.3811772073612	2.01882279263876
20	102.18	96.2574342170228	5.92256578297724

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 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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