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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 19 Nov 2007 03:58:58 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/19/t1195469844tv6bdcb7qb9wd64.htm/, Retrieved Fri, 03 May 2024 06:17:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5702, Retrieved Fri, 03 May 2024 06:17:43 +0000

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Estimated Impact

204

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

-       [Multiple Regression] [Vraag 3 Case seat...] [2007-11-19 10:58:58] [4a507cbea0acb4f2b617b46f2010fec1] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	10 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 10 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5702&T=0

[TABLE]
[ROW][C]Summary of compuational 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]10 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5702&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5702&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	10 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 9.57547231270359 + 1.04177524429967x[t] -0.266776149113282M1[t] -0.59633731451321M2[t] -1.05222312703583M3[t] -1.03975389069852M4[t] -0.647284654361202M5[t] -0.714815418023887M6[t] -0.862346181686573M7[t] -1.36987694534926M8[t] -1.47740770901194M9[t] -1.36493847267463M10[t] -0.192469236337315M11[t] -0.0124692363373145t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  9.57547231270359 +  1.04177524429967x[t] -0.266776149113282M1[t] -0.59633731451321M2[t] -1.05222312703583M3[t] -1.03975389069852M4[t] -0.647284654361202M5[t] -0.714815418023887M6[t] -0.862346181686573M7[t] -1.36987694534926M8[t] -1.47740770901194M9[t] -1.36493847267463M10[t] -0.192469236337315M11[t] -0.0124692363373145t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5702&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  9.57547231270359 +  1.04177524429967x[t] -0.266776149113282M1[t] -0.59633731451321M2[t] -1.05222312703583M3[t] -1.03975389069852M4[t] -0.647284654361202M5[t] -0.714815418023887M6[t] -0.862346181686573M7[t] -1.36987694534926M8[t] -1.47740770901194M9[t] -1.36493847267463M10[t] -0.192469236337315M11[t] -0.0124692363373145t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5702&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5702&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] = + 9.57547231270359 + 1.04177524429967x[t] -0.266776149113282M1[t] -0.59633731451321M2[t] -1.05222312703583M3[t] -1.03975389069852M4[t] -0.647284654361202M5[t] -0.714815418023887M6[t] -0.862346181686573M7[t] -1.36987694534926M8[t] -1.47740770901194M9[t] -1.36493847267463M10[t] -0.192469236337315M11[t] -0.0124692363373145t + 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)	9.57547231270359	0.189209	50.6078	0	0
x	1.04177524429967	0.164053	6.3502	0	0
M1	-0.266776149113282	0.218526	-1.2208	0.228252	0.114126
M2	-0.59633731451321	0.229267	-2.6011	0.012387	0.006193
M3	-1.05222312703583	0.23042	-4.5665	3.6e-05	1.8e-05
M4	-1.03975389069852	0.22985	-4.5236	4.1e-05	2.1e-05
M5	-0.647284654361202	0.229345	-2.8223	0.006967	0.003484
M6	-0.714815418023887	0.228907	-3.1227	0.003064	0.001532
M7	-0.862346181686573	0.228536	-3.7733	0.000451	0.000225
M8	-1.36987694534926	0.228232	-6.0021	0	0
M9	-1.47740770901194	0.227995	-6.48	0	0
M10	-1.36493847267463	0.227826	-5.9912	0	0
M11	-0.192469236337315	0.227724	-0.8452	0.402289	0.201144
t	-0.0124692363373145	0.003929	-3.1733	0.002657	0.001329

\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) & 9.57547231270359 & 0.189209 & 50.6078 & 0 & 0 \tabularnewline
x & 1.04177524429967 & 0.164053 & 6.3502 & 0 & 0 \tabularnewline
M1 & -0.266776149113282 & 0.218526 & -1.2208 & 0.228252 & 0.114126 \tabularnewline
M2 & -0.59633731451321 & 0.229267 & -2.6011 & 0.012387 & 0.006193 \tabularnewline
M3 & -1.05222312703583 & 0.23042 & -4.5665 & 3.6e-05 & 1.8e-05 \tabularnewline
M4 & -1.03975389069852 & 0.22985 & -4.5236 & 4.1e-05 & 2.1e-05 \tabularnewline
M5 & -0.647284654361202 & 0.229345 & -2.8223 & 0.006967 & 0.003484 \tabularnewline
M6 & -0.714815418023887 & 0.228907 & -3.1227 & 0.003064 & 0.001532 \tabularnewline
M7 & -0.862346181686573 & 0.228536 & -3.7733 & 0.000451 & 0.000225 \tabularnewline
M8 & -1.36987694534926 & 0.228232 & -6.0021 & 0 & 0 \tabularnewline
M9 & -1.47740770901194 & 0.227995 & -6.48 & 0 & 0 \tabularnewline
M10 & -1.36493847267463 & 0.227826 & -5.9912 & 0 & 0 \tabularnewline
M11 & -0.192469236337315 & 0.227724 & -0.8452 & 0.402289 & 0.201144 \tabularnewline
t & -0.0124692363373145 & 0.003929 & -3.1733 & 0.002657 & 0.001329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5702&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]9.57547231270359[/C][C]0.189209[/C][C]50.6078[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]1.04177524429967[/C][C]0.164053[/C][C]6.3502[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.266776149113282[/C][C]0.218526[/C][C]-1.2208[/C][C]0.228252[/C][C]0.114126[/C][/ROW]
[ROW][C]M2[/C][C]-0.59633731451321[/C][C]0.229267[/C][C]-2.6011[/C][C]0.012387[/C][C]0.006193[/C][/ROW]
[ROW][C]M3[/C][C]-1.05222312703583[/C][C]0.23042[/C][C]-4.5665[/C][C]3.6e-05[/C][C]1.8e-05[/C][/ROW]
[ROW][C]M4[/C][C]-1.03975389069852[/C][C]0.22985[/C][C]-4.5236[/C][C]4.1e-05[/C][C]2.1e-05[/C][/ROW]
[ROW][C]M5[/C][C]-0.647284654361202[/C][C]0.229345[/C][C]-2.8223[/C][C]0.006967[/C][C]0.003484[/C][/ROW]
[ROW][C]M6[/C][C]-0.714815418023887[/C][C]0.228907[/C][C]-3.1227[/C][C]0.003064[/C][C]0.001532[/C][/ROW]
[ROW][C]M7[/C][C]-0.862346181686573[/C][C]0.228536[/C][C]-3.7733[/C][C]0.000451[/C][C]0.000225[/C][/ROW]
[ROW][C]M8[/C][C]-1.36987694534926[/C][C]0.228232[/C][C]-6.0021[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-1.47740770901194[/C][C]0.227995[/C][C]-6.48[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-1.36493847267463[/C][C]0.227826[/C][C]-5.9912[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-0.192469236337315[/C][C]0.227724[/C][C]-0.8452[/C][C]0.402289[/C][C]0.201144[/C][/ROW]
[ROW][C]t[/C][C]-0.0124692363373145[/C][C]0.003929[/C][C]-3.1733[/C][C]0.002657[/C][C]0.001329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5702&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5702&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)	9.57547231270359	0.189209	50.6078	0	0
x	1.04177524429967	0.164053	6.3502	0	0
M1	-0.266776149113282	0.218526	-1.2208	0.228252	0.114126
M2	-0.59633731451321	0.229267	-2.6011	0.012387	0.006193
M3	-1.05222312703583	0.23042	-4.5665	3.6e-05	1.8e-05
M4	-1.03975389069852	0.22985	-4.5236	4.1e-05	2.1e-05
M5	-0.647284654361202	0.229345	-2.8223	0.006967	0.003484
M6	-0.714815418023887	0.228907	-3.1227	0.003064	0.001532
M7	-0.862346181686573	0.228536	-3.7733	0.000451	0.000225
M8	-1.36987694534926	0.228232	-6.0021	0	0
M9	-1.47740770901194	0.227995	-6.48	0	0
M10	-1.36493847267463	0.227826	-5.9912	0	0
M11	-0.192469236337315	0.227724	-0.8452	0.402289	0.201144
t	-0.0124692363373145	0.003929	-3.1733	0.002657	0.001329

Multiple Linear Regression - Regression Statistics
Multiple R	0.86239729601255
R-squared	0.743729096169758
Adjusted R-squared	0.672845654684797
F-TEST (value)	10.4922825499035
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	6.5846827990157e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.360009378495489
Sum Squared Residuals	6.09151737242127

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.86239729601255 \tabularnewline
R-squared & 0.743729096169758 \tabularnewline
Adjusted R-squared & 0.672845654684797 \tabularnewline
F-TEST (value) & 10.4922825499035 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 6.5846827990157e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.360009378495489 \tabularnewline
Sum Squared Residuals & 6.09151737242127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5702&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.86239729601255[/C][/ROW]
[ROW][C]R-squared[/C][C]0.743729096169758[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.672845654684797[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.4922825499035[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]6.5846827990157e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.360009378495489[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.09151737242127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5702&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5702&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	0.86239729601255
R-squared	0.743729096169758
Adjusted R-squared	0.672845654684797
F-TEST (value)	10.4922825499035
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	6.5846827990157e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.360009378495489
Sum Squared Residuals	6.09151737242127

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.5	9.29622692725298	-0.796226927252981
2	8.6	8.95419652551574	-0.354196525515745
3	8.5	8.48584147665581	0.0141585233441906
4	8.5	8.48584147665581	0.0141585233441908
5	9	8.86584147665581	0.134158523344190
6	9	8.78584147665581	0.214158523344191
7	8.8	8.62584147665581	0.174158523344192
8	8	8.10584147665581	-0.105841476655810
9	7.9	7.98584147665581	-0.085841476655809
10	8.1	8.08584147665581	0.0141585233441907
11	9.3	9.24584147665581	0.0541585233441909
12	9.4	9.42584147665581	-0.0258414766558089
13	9.4	9.14659609120521	0.253403908794787
14	9.3	8.80456568946797	0.495434310532031
15	9	9.3779858849077	-0.377985884907709
16	9.1	9.3779858849077	-0.277985884907710
17	9.7	9.7579858849077	-0.0579858849077093
18	9.7	9.6779858849077	0.0220141150922907
19	9.6	9.5179858849077	0.0820141150922907
20	8.3	8.99798588490771	-0.697985884907708
21	8.2	8.8779858849077	-0.67798588490771
22	8.4	8.9779858849077	-0.577985884907708
23	10.6	10.1379858849077	0.462014115092291
24	10.9	10.3179858849077	0.582014115092291
25	10.9	10.0387404994571	0.861259500542887
26	9.6	9.69671009771987	-0.0967100977198696
27	9.3	9.22835504885994	0.0716449511400656
28	9.3	9.22835504885994	0.0716449511400656
29	9.6	9.60835504885993	-0.00835504885993503
30	9.5	9.52835504885993	-0.0283550488599347
31	9.5	9.36835504885993	0.131644951140065
32	9	8.84835504885993	0.151644951140065
33	8.9	8.72835504885994	0.171644951140066
34	9	8.82835504885993	0.171644951140065
35	10.1	9.98835504885994	0.111644951140065
36	10.2	10.1683550488599	0.0316449511400643
37	10.2	9.88910966340934	0.310890336590661
38	9.5	9.5470792616721	-0.0470792616720952
39	9.3	9.07872421281216	0.22127578718784
40	9.3	9.07872421281216	0.221275787187840
41	9.4	9.45872421281216	-0.0587242128121602
42	9.3	9.37872421281216	-0.0787242128121599
43	9.1	9.21872421281216	-0.118724212812161
44	9	8.69872421281216	0.301275787187839
45	8.9	8.57872421281216	0.32127578718784
46	9	8.67872421281216	0.321275787187839
47	9.8	9.83872421281216	-0.0387242128121598
48	10	10.0187242128122	-0.0187242128121607
49	9.8	9.73947882736156	0.0605211726384363
50	9.4	9.39744842562432	0.00255157437567918
51	9	8.92909337676439	0.070906623235613
52	8.9	8.92909337676439	-0.0290933767643866
53	9.3	9.30909337676439	-0.00909337676438587
54	9.1	9.22909337676439	-0.129093376764387
55	8.8	9.06909337676439	-0.269093376764386
56	8.9	8.54909337676439	0.350906623235614
57	8.7	8.42909337676439	0.270906623235613
58	8.6	8.52909337676439	0.0709066232356131
59	9.1	9.68909337676439	-0.589093376764387
60	9.3	9.86909337676439	-0.569093376764386
61	8.9	9.5898479913138	-0.68984799131379

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.5 & 9.29622692725298 & -0.796226927252981 \tabularnewline
2 & 8.6 & 8.95419652551574 & -0.354196525515745 \tabularnewline
3 & 8.5 & 8.48584147665581 & 0.0141585233441906 \tabularnewline
4 & 8.5 & 8.48584147665581 & 0.0141585233441908 \tabularnewline
5 & 9 & 8.86584147665581 & 0.134158523344190 \tabularnewline
6 & 9 & 8.78584147665581 & 0.214158523344191 \tabularnewline
7 & 8.8 & 8.62584147665581 & 0.174158523344192 \tabularnewline
8 & 8 & 8.10584147665581 & -0.105841476655810 \tabularnewline
9 & 7.9 & 7.98584147665581 & -0.085841476655809 \tabularnewline
10 & 8.1 & 8.08584147665581 & 0.0141585233441907 \tabularnewline
11 & 9.3 & 9.24584147665581 & 0.0541585233441909 \tabularnewline
12 & 9.4 & 9.42584147665581 & -0.0258414766558089 \tabularnewline
13 & 9.4 & 9.14659609120521 & 0.253403908794787 \tabularnewline
14 & 9.3 & 8.80456568946797 & 0.495434310532031 \tabularnewline
15 & 9 & 9.3779858849077 & -0.377985884907709 \tabularnewline
16 & 9.1 & 9.3779858849077 & -0.277985884907710 \tabularnewline
17 & 9.7 & 9.7579858849077 & -0.0579858849077093 \tabularnewline
18 & 9.7 & 9.6779858849077 & 0.0220141150922907 \tabularnewline
19 & 9.6 & 9.5179858849077 & 0.0820141150922907 \tabularnewline
20 & 8.3 & 8.99798588490771 & -0.697985884907708 \tabularnewline
21 & 8.2 & 8.8779858849077 & -0.67798588490771 \tabularnewline
22 & 8.4 & 8.9779858849077 & -0.577985884907708 \tabularnewline
23 & 10.6 & 10.1379858849077 & 0.462014115092291 \tabularnewline
24 & 10.9 & 10.3179858849077 & 0.582014115092291 \tabularnewline
25 & 10.9 & 10.0387404994571 & 0.861259500542887 \tabularnewline
26 & 9.6 & 9.69671009771987 & -0.0967100977198696 \tabularnewline
27 & 9.3 & 9.22835504885994 & 0.0716449511400656 \tabularnewline
28 & 9.3 & 9.22835504885994 & 0.0716449511400656 \tabularnewline
29 & 9.6 & 9.60835504885993 & -0.00835504885993503 \tabularnewline
30 & 9.5 & 9.52835504885993 & -0.0283550488599347 \tabularnewline
31 & 9.5 & 9.36835504885993 & 0.131644951140065 \tabularnewline
32 & 9 & 8.84835504885993 & 0.151644951140065 \tabularnewline
33 & 8.9 & 8.72835504885994 & 0.171644951140066 \tabularnewline
34 & 9 & 8.82835504885993 & 0.171644951140065 \tabularnewline
35 & 10.1 & 9.98835504885994 & 0.111644951140065 \tabularnewline
36 & 10.2 & 10.1683550488599 & 0.0316449511400643 \tabularnewline
37 & 10.2 & 9.88910966340934 & 0.310890336590661 \tabularnewline
38 & 9.5 & 9.5470792616721 & -0.0470792616720952 \tabularnewline
39 & 9.3 & 9.07872421281216 & 0.22127578718784 \tabularnewline
40 & 9.3 & 9.07872421281216 & 0.221275787187840 \tabularnewline
41 & 9.4 & 9.45872421281216 & -0.0587242128121602 \tabularnewline
42 & 9.3 & 9.37872421281216 & -0.0787242128121599 \tabularnewline
43 & 9.1 & 9.21872421281216 & -0.118724212812161 \tabularnewline
44 & 9 & 8.69872421281216 & 0.301275787187839 \tabularnewline
45 & 8.9 & 8.57872421281216 & 0.32127578718784 \tabularnewline
46 & 9 & 8.67872421281216 & 0.321275787187839 \tabularnewline
47 & 9.8 & 9.83872421281216 & -0.0387242128121598 \tabularnewline
48 & 10 & 10.0187242128122 & -0.0187242128121607 \tabularnewline
49 & 9.8 & 9.73947882736156 & 0.0605211726384363 \tabularnewline
50 & 9.4 & 9.39744842562432 & 0.00255157437567918 \tabularnewline
51 & 9 & 8.92909337676439 & 0.070906623235613 \tabularnewline
52 & 8.9 & 8.92909337676439 & -0.0290933767643866 \tabularnewline
53 & 9.3 & 9.30909337676439 & -0.00909337676438587 \tabularnewline
54 & 9.1 & 9.22909337676439 & -0.129093376764387 \tabularnewline
55 & 8.8 & 9.06909337676439 & -0.269093376764386 \tabularnewline
56 & 8.9 & 8.54909337676439 & 0.350906623235614 \tabularnewline
57 & 8.7 & 8.42909337676439 & 0.270906623235613 \tabularnewline
58 & 8.6 & 8.52909337676439 & 0.0709066232356131 \tabularnewline
59 & 9.1 & 9.68909337676439 & -0.589093376764387 \tabularnewline
60 & 9.3 & 9.86909337676439 & -0.569093376764386 \tabularnewline
61 & 8.9 & 9.5898479913138 & -0.68984799131379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5702&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]8.5[/C][C]9.29622692725298[/C][C]-0.796226927252981[/C][/ROW]
[ROW][C]2[/C][C]8.6[/C][C]8.95419652551574[/C][C]-0.354196525515745[/C][/ROW]
[ROW][C]3[/C][C]8.5[/C][C]8.48584147665581[/C][C]0.0141585233441906[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.48584147665581[/C][C]0.0141585233441908[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]8.86584147665581[/C][C]0.134158523344190[/C][/ROW]
[ROW][C]6[/C][C]9[/C][C]8.78584147665581[/C][C]0.214158523344191[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.62584147665581[/C][C]0.174158523344192[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]8.10584147665581[/C][C]-0.105841476655810[/C][/ROW]
[ROW][C]9[/C][C]7.9[/C][C]7.98584147665581[/C][C]-0.085841476655809[/C][/ROW]
[ROW][C]10[/C][C]8.1[/C][C]8.08584147665581[/C][C]0.0141585233441907[/C][/ROW]
[ROW][C]11[/C][C]9.3[/C][C]9.24584147665581[/C][C]0.0541585233441909[/C][/ROW]
[ROW][C]12[/C][C]9.4[/C][C]9.42584147665581[/C][C]-0.0258414766558089[/C][/ROW]
[ROW][C]13[/C][C]9.4[/C][C]9.14659609120521[/C][C]0.253403908794787[/C][/ROW]
[ROW][C]14[/C][C]9.3[/C][C]8.80456568946797[/C][C]0.495434310532031[/C][/ROW]
[ROW][C]15[/C][C]9[/C][C]9.3779858849077[/C][C]-0.377985884907709[/C][/ROW]
[ROW][C]16[/C][C]9.1[/C][C]9.3779858849077[/C][C]-0.277985884907710[/C][/ROW]
[ROW][C]17[/C][C]9.7[/C][C]9.7579858849077[/C][C]-0.0579858849077093[/C][/ROW]
[ROW][C]18[/C][C]9.7[/C][C]9.6779858849077[/C][C]0.0220141150922907[/C][/ROW]
[ROW][C]19[/C][C]9.6[/C][C]9.5179858849077[/C][C]0.0820141150922907[/C][/ROW]
[ROW][C]20[/C][C]8.3[/C][C]8.99798588490771[/C][C]-0.697985884907708[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]8.8779858849077[/C][C]-0.67798588490771[/C][/ROW]
[ROW][C]22[/C][C]8.4[/C][C]8.9779858849077[/C][C]-0.577985884907708[/C][/ROW]
[ROW][C]23[/C][C]10.6[/C][C]10.1379858849077[/C][C]0.462014115092291[/C][/ROW]
[ROW][C]24[/C][C]10.9[/C][C]10.3179858849077[/C][C]0.582014115092291[/C][/ROW]
[ROW][C]25[/C][C]10.9[/C][C]10.0387404994571[/C][C]0.861259500542887[/C][/ROW]
[ROW][C]26[/C][C]9.6[/C][C]9.69671009771987[/C][C]-0.0967100977198696[/C][/ROW]
[ROW][C]27[/C][C]9.3[/C][C]9.22835504885994[/C][C]0.0716449511400656[/C][/ROW]
[ROW][C]28[/C][C]9.3[/C][C]9.22835504885994[/C][C]0.0716449511400656[/C][/ROW]
[ROW][C]29[/C][C]9.6[/C][C]9.60835504885993[/C][C]-0.00835504885993503[/C][/ROW]
[ROW][C]30[/C][C]9.5[/C][C]9.52835504885993[/C][C]-0.0283550488599347[/C][/ROW]
[ROW][C]31[/C][C]9.5[/C][C]9.36835504885993[/C][C]0.131644951140065[/C][/ROW]
[ROW][C]32[/C][C]9[/C][C]8.84835504885993[/C][C]0.151644951140065[/C][/ROW]
[ROW][C]33[/C][C]8.9[/C][C]8.72835504885994[/C][C]0.171644951140066[/C][/ROW]
[ROW][C]34[/C][C]9[/C][C]8.82835504885993[/C][C]0.171644951140065[/C][/ROW]
[ROW][C]35[/C][C]10.1[/C][C]9.98835504885994[/C][C]0.111644951140065[/C][/ROW]
[ROW][C]36[/C][C]10.2[/C][C]10.1683550488599[/C][C]0.0316449511400643[/C][/ROW]
[ROW][C]37[/C][C]10.2[/C][C]9.88910966340934[/C][C]0.310890336590661[/C][/ROW]
[ROW][C]38[/C][C]9.5[/C][C]9.5470792616721[/C][C]-0.0470792616720952[/C][/ROW]
[ROW][C]39[/C][C]9.3[/C][C]9.07872421281216[/C][C]0.22127578718784[/C][/ROW]
[ROW][C]40[/C][C]9.3[/C][C]9.07872421281216[/C][C]0.221275787187840[/C][/ROW]
[ROW][C]41[/C][C]9.4[/C][C]9.45872421281216[/C][C]-0.0587242128121602[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]9.37872421281216[/C][C]-0.0787242128121599[/C][/ROW]
[ROW][C]43[/C][C]9.1[/C][C]9.21872421281216[/C][C]-0.118724212812161[/C][/ROW]
[ROW][C]44[/C][C]9[/C][C]8.69872421281216[/C][C]0.301275787187839[/C][/ROW]
[ROW][C]45[/C][C]8.9[/C][C]8.57872421281216[/C][C]0.32127578718784[/C][/ROW]
[ROW][C]46[/C][C]9[/C][C]8.67872421281216[/C][C]0.321275787187839[/C][/ROW]
[ROW][C]47[/C][C]9.8[/C][C]9.83872421281216[/C][C]-0.0387242128121598[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]10.0187242128122[/C][C]-0.0187242128121607[/C][/ROW]
[ROW][C]49[/C][C]9.8[/C][C]9.73947882736156[/C][C]0.0605211726384363[/C][/ROW]
[ROW][C]50[/C][C]9.4[/C][C]9.39744842562432[/C][C]0.00255157437567918[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]8.92909337676439[/C][C]0.070906623235613[/C][/ROW]
[ROW][C]52[/C][C]8.9[/C][C]8.92909337676439[/C][C]-0.0290933767643866[/C][/ROW]
[ROW][C]53[/C][C]9.3[/C][C]9.30909337676439[/C][C]-0.00909337676438587[/C][/ROW]
[ROW][C]54[/C][C]9.1[/C][C]9.22909337676439[/C][C]-0.129093376764387[/C][/ROW]
[ROW][C]55[/C][C]8.8[/C][C]9.06909337676439[/C][C]-0.269093376764386[/C][/ROW]
[ROW][C]56[/C][C]8.9[/C][C]8.54909337676439[/C][C]0.350906623235614[/C][/ROW]
[ROW][C]57[/C][C]8.7[/C][C]8.42909337676439[/C][C]0.270906623235613[/C][/ROW]
[ROW][C]58[/C][C]8.6[/C][C]8.52909337676439[/C][C]0.0709066232356131[/C][/ROW]
[ROW][C]59[/C][C]9.1[/C][C]9.68909337676439[/C][C]-0.589093376764387[/C][/ROW]
[ROW][C]60[/C][C]9.3[/C][C]9.86909337676439[/C][C]-0.569093376764386[/C][/ROW]
[ROW][C]61[/C][C]8.9[/C][C]9.5898479913138[/C][C]-0.68984799131379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5702&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5702&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	8.5	9.29622692725298	-0.796226927252981
2	8.6	8.95419652551574	-0.354196525515745
3	8.5	8.48584147665581	0.0141585233441906
4	8.5	8.48584147665581	0.0141585233441908
5	9	8.86584147665581	0.134158523344190
6	9	8.78584147665581	0.214158523344191
7	8.8	8.62584147665581	0.174158523344192
8	8	8.10584147665581	-0.105841476655810
9	7.9	7.98584147665581	-0.085841476655809
10	8.1	8.08584147665581	0.0141585233441907
11	9.3	9.24584147665581	0.0541585233441909
12	9.4	9.42584147665581	-0.0258414766558089
13	9.4	9.14659609120521	0.253403908794787
14	9.3	8.80456568946797	0.495434310532031
15	9	9.3779858849077	-0.377985884907709
16	9.1	9.3779858849077	-0.277985884907710
17	9.7	9.7579858849077	-0.0579858849077093
18	9.7	9.6779858849077	0.0220141150922907
19	9.6	9.5179858849077	0.0820141150922907
20	8.3	8.99798588490771	-0.697985884907708
21	8.2	8.8779858849077	-0.67798588490771
22	8.4	8.9779858849077	-0.577985884907708
23	10.6	10.1379858849077	0.462014115092291
24	10.9	10.3179858849077	0.582014115092291
25	10.9	10.0387404994571	0.861259500542887
26	9.6	9.69671009771987	-0.0967100977198696
27	9.3	9.22835504885994	0.0716449511400656
28	9.3	9.22835504885994	0.0716449511400656
29	9.6	9.60835504885993	-0.00835504885993503
30	9.5	9.52835504885993	-0.0283550488599347
31	9.5	9.36835504885993	0.131644951140065
32	9	8.84835504885993	0.151644951140065
33	8.9	8.72835504885994	0.171644951140066
34	9	8.82835504885993	0.171644951140065
35	10.1	9.98835504885994	0.111644951140065
36	10.2	10.1683550488599	0.0316449511400643
37	10.2	9.88910966340934	0.310890336590661
38	9.5	9.5470792616721	-0.0470792616720952
39	9.3	9.07872421281216	0.22127578718784
40	9.3	9.07872421281216	0.221275787187840
41	9.4	9.45872421281216	-0.0587242128121602
42	9.3	9.37872421281216	-0.0787242128121599
43	9.1	9.21872421281216	-0.118724212812161
44	9	8.69872421281216	0.301275787187839
45	8.9	8.57872421281216	0.32127578718784
46	9	8.67872421281216	0.321275787187839
47	9.8	9.83872421281216	-0.0387242128121598
48	10	10.0187242128122	-0.0187242128121607
49	9.8	9.73947882736156	0.0605211726384363
50	9.4	9.39744842562432	0.00255157437567918
51	9	8.92909337676439	0.070906623235613
52	8.9	8.92909337676439	-0.0290933767643866
53	9.3	9.30909337676439	-0.00909337676438587
54	9.1	9.22909337676439	-0.129093376764387
55	8.8	9.06909337676439	-0.269093376764386
56	8.9	8.54909337676439	0.350906623235614
57	8.7	8.42909337676439	0.270906623235613
58	8.6	8.52909337676439	0.0709066232356131
59	9.1	9.68909337676439	-0.589093376764387
60	9.3	9.86909337676439	-0.569093376764386
61	8.9	9.5898479913138	-0.68984799131379

Figure 1

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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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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)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code