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Author

*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 18 Dec 2007 09:04:38 -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/2007/Dec/18/t1197993802kh6ck8usdflehx5.htm/, Retrieved Sat, 04 May 2024 12:11:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4546, Retrieved Sat, 04 May 2024 12:11:50 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

162

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

-       [Multiple Regression] [brood met trend m...] [2007-12-18 16:04:38] [7eb5b05bf0841f2a6d4b99da83be8d69] [Current]

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1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,5
1,43	0	0,51
1,43	0	0,51
1,43	0	0,5
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,51
1,43	0	0,52
1,43	0	0,52
1,44	0	0,52
1,48	0	0,53
1,48	0	0,53
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,52
1,48	0	0,53
1,48	0	0,53
1,48	0	0,53
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,54
1,48	0	0,53
1,48	0	0,53
1,48	0	0,53
1,48	0	0,53
1,48	0	0,53
1,57	0	0,54
1,58	0	0,55
1,58	0	0,55
1,58	0	0,55
1,58	0	0,55
1,59	1	0,55
1,6	1	0,55
1,6	1	0,55
1,61	1	0,55
1,61	1	0,56
1,61	1	0,56
1,62	1	0,56
1,63	1	0,56
1,63	1	0,56
1,64	1	0,55
1,64	1	0,56
1,64	1	0,55
1,64	1	0,55
1,64	1	0,56
1,65	1	0,55
1,65	1	0,55
1,65	1	0,55
1,65	1	0,55

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 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 & 6 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=4546&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]6 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=4546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4546&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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 1.01583420916727 + 0.074205333797495x1[t] + 0.782453795876532x2[t] + 0.00164324049146559t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  1.01583420916727 +  0.074205333797495x1[t] +  0.782453795876532x2[t] +  0.00164324049146559t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4546&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  1.01583420916727 +  0.074205333797495x1[t] +  0.782453795876532x2[t] +  0.00164324049146559t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4546&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] = + 1.01583420916727 + 0.074205333797495x1[t] + 0.782453795876532x2[t] + 0.00164324049146559t + 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)	1.01583420916727	0.19569	5.191	2e-06	1e-06
x1	0.074205333797495	0.008458	8.7732	0	0
x2	0.782453795876532	0.387913	2.0171	0.047637	0.023818
t	0.00164324049146559	0.000339	4.8501	8e-06	4e-06

\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) & 1.01583420916727 & 0.19569 & 5.191 & 2e-06 & 1e-06 \tabularnewline
x1 & 0.074205333797495 & 0.008458 & 8.7732 & 0 & 0 \tabularnewline
x2 & 0.782453795876532 & 0.387913 & 2.0171 & 0.047637 & 0.023818 \tabularnewline
t & 0.00164324049146559 & 0.000339 & 4.8501 & 8e-06 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4546&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]1.01583420916727[/C][C]0.19569[/C][C]5.191[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]x1[/C][C]0.074205333797495[/C][C]0.008458[/C][C]8.7732[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x2[/C][C]0.782453795876532[/C][C]0.387913[/C][C]2.0171[/C][C]0.047637[/C][C]0.023818[/C][/ROW]
[ROW][C]t[/C][C]0.00164324049146559[/C][C]0.000339[/C][C]4.8501[/C][C]8e-06[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4546&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4546&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)	1.01583420916727	0.19569	5.191	2e-06	1e-06
x1	0.074205333797495	0.008458	8.7732	0	0
x2	0.782453795876532	0.387913	2.0171	0.047637	0.023818
t	0.00164324049146559	0.000339	4.8501	8e-06	4e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.966096496623152
R-squared	0.933342440787529
Adjusted R-squared	0.93040166611639
F-TEST (value)	317.379787695945
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0204509693490157
Sum Squared Residuals	0.0284404660173777

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.966096496623152 \tabularnewline
R-squared & 0.933342440787529 \tabularnewline
Adjusted R-squared & 0.93040166611639 \tabularnewline
F-TEST (value) & 317.379787695945 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 68 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0204509693490157 \tabularnewline
Sum Squared Residuals & 0.0284404660173777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4546&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.966096496623152[/C][/ROW]
[ROW][C]R-squared[/C][C]0.933342440787529[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.93040166611639[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]317.379787695945[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]68[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0204509693490157[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0284404660173777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4546&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4546&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	0.966096496623152
R-squared	0.933342440787529
Adjusted R-squared	0.93040166611639
F-TEST (value)	317.379787695945
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0204509693490157
Sum Squared Residuals	0.0284404660173777

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.43	1.41652888555577	0.0134711144442342
2	1.43	1.41817212604723	0.0118278739527655
3	1.43	1.4198153665387	0.0101846334613000
4	1.43	1.42145860703017	0.00854139296983443
5	1.43	1.42310184752163	0.00689815247836882
6	1.43	1.42474508801310	0.00525491198690322
7	1.43	1.42638832850456	0.00361167149543763
8	1.43	1.42803156899603	0.00196843100397204
9	1.43	1.42185027152873	0.00814972847127176
10	1.43	1.43131804997896	-0.00131804997895915
11	1.43	1.43296129047042	-0.00296129047042474
12	1.43	1.42677999300312	0.00322000699687498
13	1.43	1.43624777145336	-0.00624777145335593
14	1.43	1.43789101194482	-0.00789101194482152
15	1.43	1.43953425243629	-0.00953425243628712
16	1.43	1.44117749292775	-0.0111774929277527
17	1.43	1.45064527137798	-0.0206452713779836
18	1.43	1.45228851186945	-0.0222885118694492
19	1.44	1.45393175236091	-0.0139317523609148
20	1.48	1.46339953081115	0.0166004691888543
21	1.48	1.46504277130261	0.0149572286973887
22	1.48	1.45886147383531	0.0211385261646885
23	1.48	1.46050471432678	0.0194952856732229
24	1.48	1.46214795481824	0.0178520451817573
25	1.48	1.46379119530971	0.0162088046902917
26	1.48	1.46543443580117	0.0145655641988261
27	1.48	1.46707767629264	0.0129223237073605
28	1.48	1.46872091678411	0.0112790832158949
29	1.48	1.47036415727557	0.00963584272442931
30	1.48	1.47200739776704	0.00799260223296372
31	1.48	1.47365063825850	0.00634936174149813
32	1.48	1.48311841670873	-0.00311841670873279
33	1.48	1.48476165720020	-0.00476165720019838
34	1.48	1.48640489769166	-0.00640489769166398
35	1.48	1.49587267614189	-0.0158726761418949
36	1.48	1.49751591663336	-0.0175159166333605
37	1.48	1.49915915712483	-0.0191591571248261
38	1.48	1.50080239761629	-0.0208023976162917
39	1.48	1.50244563810776	-0.0224456381077573
40	1.48	1.50408887859922	-0.0240888785992229
41	1.48	1.50573211909069	-0.0257321190906884
42	1.48	1.50737535958215	-0.0273753595821540
43	1.48	1.50901860007362	-0.0290186000736196
44	1.48	1.51066184056509	-0.0306618405650852
45	1.48	1.50448054309779	-0.0244805430977855
46	1.48	1.50612378358925	-0.0261237835892511
47	1.48	1.50776702408072	-0.0277670240807167
48	1.48	1.50941026457218	-0.0294102645721823
49	1.48	1.51105350506365	-0.0310535050636479
50	1.57	1.52052128351388	0.0494787164861213
51	1.58	1.52998906196411	0.0500109380358904
52	1.58	1.53163230245558	0.0483676975444248
53	1.58	1.53327554294704	0.0467244570529592
54	1.58	1.53491878343851	0.0450812165614936
55	1.59	1.61076735772747	-0.0207673577274670
56	1.6	1.61241059821893	-0.0124105982189325
57	1.6	1.61405383871040	-0.0140538387103981
58	1.61	1.61569707920186	-0.00569707920186373
59	1.61	1.62516485765209	-0.0151648576520946
60	1.61	1.62680809814356	-0.0168080981435602
61	1.62	1.62845133863503	-0.00845133863502581
62	1.63	1.63009457912649	-9.45791264916076e-05
63	1.63	1.63173781961796	-0.0017378196179572
64	1.64	1.62555652215066	0.0144434778493425
65	1.64	1.63502430060089	0.00497569939911162
66	1.64	1.62884300313359	0.0111569968664113
67	1.64	1.63048624362505	0.00951375637494576
68	1.64	1.63995402207529	4.59779247148431e-05
69	1.65	1.63377272460799	0.0162272753920146
70	1.65	1.63541596509945	0.0145840349005490
71	1.65	1.63705920559092	0.0129407944090834
72	1.65	1.63870244608238	0.0112975539176178

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.43 & 1.41652888555577 & 0.0134711144442342 \tabularnewline
2 & 1.43 & 1.41817212604723 & 0.0118278739527655 \tabularnewline
3 & 1.43 & 1.4198153665387 & 0.0101846334613000 \tabularnewline
4 & 1.43 & 1.42145860703017 & 0.00854139296983443 \tabularnewline
5 & 1.43 & 1.42310184752163 & 0.00689815247836882 \tabularnewline
6 & 1.43 & 1.42474508801310 & 0.00525491198690322 \tabularnewline
7 & 1.43 & 1.42638832850456 & 0.00361167149543763 \tabularnewline
8 & 1.43 & 1.42803156899603 & 0.00196843100397204 \tabularnewline
9 & 1.43 & 1.42185027152873 & 0.00814972847127176 \tabularnewline
10 & 1.43 & 1.43131804997896 & -0.00131804997895915 \tabularnewline
11 & 1.43 & 1.43296129047042 & -0.00296129047042474 \tabularnewline
12 & 1.43 & 1.42677999300312 & 0.00322000699687498 \tabularnewline
13 & 1.43 & 1.43624777145336 & -0.00624777145335593 \tabularnewline
14 & 1.43 & 1.43789101194482 & -0.00789101194482152 \tabularnewline
15 & 1.43 & 1.43953425243629 & -0.00953425243628712 \tabularnewline
16 & 1.43 & 1.44117749292775 & -0.0111774929277527 \tabularnewline
17 & 1.43 & 1.45064527137798 & -0.0206452713779836 \tabularnewline
18 & 1.43 & 1.45228851186945 & -0.0222885118694492 \tabularnewline
19 & 1.44 & 1.45393175236091 & -0.0139317523609148 \tabularnewline
20 & 1.48 & 1.46339953081115 & 0.0166004691888543 \tabularnewline
21 & 1.48 & 1.46504277130261 & 0.0149572286973887 \tabularnewline
22 & 1.48 & 1.45886147383531 & 0.0211385261646885 \tabularnewline
23 & 1.48 & 1.46050471432678 & 0.0194952856732229 \tabularnewline
24 & 1.48 & 1.46214795481824 & 0.0178520451817573 \tabularnewline
25 & 1.48 & 1.46379119530971 & 0.0162088046902917 \tabularnewline
26 & 1.48 & 1.46543443580117 & 0.0145655641988261 \tabularnewline
27 & 1.48 & 1.46707767629264 & 0.0129223237073605 \tabularnewline
28 & 1.48 & 1.46872091678411 & 0.0112790832158949 \tabularnewline
29 & 1.48 & 1.47036415727557 & 0.00963584272442931 \tabularnewline
30 & 1.48 & 1.47200739776704 & 0.00799260223296372 \tabularnewline
31 & 1.48 & 1.47365063825850 & 0.00634936174149813 \tabularnewline
32 & 1.48 & 1.48311841670873 & -0.00311841670873279 \tabularnewline
33 & 1.48 & 1.48476165720020 & -0.00476165720019838 \tabularnewline
34 & 1.48 & 1.48640489769166 & -0.00640489769166398 \tabularnewline
35 & 1.48 & 1.49587267614189 & -0.0158726761418949 \tabularnewline
36 & 1.48 & 1.49751591663336 & -0.0175159166333605 \tabularnewline
37 & 1.48 & 1.49915915712483 & -0.0191591571248261 \tabularnewline
38 & 1.48 & 1.50080239761629 & -0.0208023976162917 \tabularnewline
39 & 1.48 & 1.50244563810776 & -0.0224456381077573 \tabularnewline
40 & 1.48 & 1.50408887859922 & -0.0240888785992229 \tabularnewline
41 & 1.48 & 1.50573211909069 & -0.0257321190906884 \tabularnewline
42 & 1.48 & 1.50737535958215 & -0.0273753595821540 \tabularnewline
43 & 1.48 & 1.50901860007362 & -0.0290186000736196 \tabularnewline
44 & 1.48 & 1.51066184056509 & -0.0306618405650852 \tabularnewline
45 & 1.48 & 1.50448054309779 & -0.0244805430977855 \tabularnewline
46 & 1.48 & 1.50612378358925 & -0.0261237835892511 \tabularnewline
47 & 1.48 & 1.50776702408072 & -0.0277670240807167 \tabularnewline
48 & 1.48 & 1.50941026457218 & -0.0294102645721823 \tabularnewline
49 & 1.48 & 1.51105350506365 & -0.0310535050636479 \tabularnewline
50 & 1.57 & 1.52052128351388 & 0.0494787164861213 \tabularnewline
51 & 1.58 & 1.52998906196411 & 0.0500109380358904 \tabularnewline
52 & 1.58 & 1.53163230245558 & 0.0483676975444248 \tabularnewline
53 & 1.58 & 1.53327554294704 & 0.0467244570529592 \tabularnewline
54 & 1.58 & 1.53491878343851 & 0.0450812165614936 \tabularnewline
55 & 1.59 & 1.61076735772747 & -0.0207673577274670 \tabularnewline
56 & 1.6 & 1.61241059821893 & -0.0124105982189325 \tabularnewline
57 & 1.6 & 1.61405383871040 & -0.0140538387103981 \tabularnewline
58 & 1.61 & 1.61569707920186 & -0.00569707920186373 \tabularnewline
59 & 1.61 & 1.62516485765209 & -0.0151648576520946 \tabularnewline
60 & 1.61 & 1.62680809814356 & -0.0168080981435602 \tabularnewline
61 & 1.62 & 1.62845133863503 & -0.00845133863502581 \tabularnewline
62 & 1.63 & 1.63009457912649 & -9.45791264916076e-05 \tabularnewline
63 & 1.63 & 1.63173781961796 & -0.0017378196179572 \tabularnewline
64 & 1.64 & 1.62555652215066 & 0.0144434778493425 \tabularnewline
65 & 1.64 & 1.63502430060089 & 0.00497569939911162 \tabularnewline
66 & 1.64 & 1.62884300313359 & 0.0111569968664113 \tabularnewline
67 & 1.64 & 1.63048624362505 & 0.00951375637494576 \tabularnewline
68 & 1.64 & 1.63995402207529 & 4.59779247148431e-05 \tabularnewline
69 & 1.65 & 1.63377272460799 & 0.0162272753920146 \tabularnewline
70 & 1.65 & 1.63541596509945 & 0.0145840349005490 \tabularnewline
71 & 1.65 & 1.63705920559092 & 0.0129407944090834 \tabularnewline
72 & 1.65 & 1.63870244608238 & 0.0112975539176178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4546&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]1.43[/C][C]1.41652888555577[/C][C]0.0134711144442342[/C][/ROW]
[ROW][C]2[/C][C]1.43[/C][C]1.41817212604723[/C][C]0.0118278739527655[/C][/ROW]
[ROW][C]3[/C][C]1.43[/C][C]1.4198153665387[/C][C]0.0101846334613000[/C][/ROW]
[ROW][C]4[/C][C]1.43[/C][C]1.42145860703017[/C][C]0.00854139296983443[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.42310184752163[/C][C]0.00689815247836882[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.42474508801310[/C][C]0.00525491198690322[/C][/ROW]
[ROW][C]7[/C][C]1.43[/C][C]1.42638832850456[/C][C]0.00361167149543763[/C][/ROW]
[ROW][C]8[/C][C]1.43[/C][C]1.42803156899603[/C][C]0.00196843100397204[/C][/ROW]
[ROW][C]9[/C][C]1.43[/C][C]1.42185027152873[/C][C]0.00814972847127176[/C][/ROW]
[ROW][C]10[/C][C]1.43[/C][C]1.43131804997896[/C][C]-0.00131804997895915[/C][/ROW]
[ROW][C]11[/C][C]1.43[/C][C]1.43296129047042[/C][C]-0.00296129047042474[/C][/ROW]
[ROW][C]12[/C][C]1.43[/C][C]1.42677999300312[/C][C]0.00322000699687498[/C][/ROW]
[ROW][C]13[/C][C]1.43[/C][C]1.43624777145336[/C][C]-0.00624777145335593[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43789101194482[/C][C]-0.00789101194482152[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.43953425243629[/C][C]-0.00953425243628712[/C][/ROW]
[ROW][C]16[/C][C]1.43[/C][C]1.44117749292775[/C][C]-0.0111774929277527[/C][/ROW]
[ROW][C]17[/C][C]1.43[/C][C]1.45064527137798[/C][C]-0.0206452713779836[/C][/ROW]
[ROW][C]18[/C][C]1.43[/C][C]1.45228851186945[/C][C]-0.0222885118694492[/C][/ROW]
[ROW][C]19[/C][C]1.44[/C][C]1.45393175236091[/C][C]-0.0139317523609148[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.46339953081115[/C][C]0.0166004691888543[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.46504277130261[/C][C]0.0149572286973887[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.45886147383531[/C][C]0.0211385261646885[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.46050471432678[/C][C]0.0194952856732229[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.46214795481824[/C][C]0.0178520451817573[/C][/ROW]
[ROW][C]25[/C][C]1.48[/C][C]1.46379119530971[/C][C]0.0162088046902917[/C][/ROW]
[ROW][C]26[/C][C]1.48[/C][C]1.46543443580117[/C][C]0.0145655641988261[/C][/ROW]
[ROW][C]27[/C][C]1.48[/C][C]1.46707767629264[/C][C]0.0129223237073605[/C][/ROW]
[ROW][C]28[/C][C]1.48[/C][C]1.46872091678411[/C][C]0.0112790832158949[/C][/ROW]
[ROW][C]29[/C][C]1.48[/C][C]1.47036415727557[/C][C]0.00963584272442931[/C][/ROW]
[ROW][C]30[/C][C]1.48[/C][C]1.47200739776704[/C][C]0.00799260223296372[/C][/ROW]
[ROW][C]31[/C][C]1.48[/C][C]1.47365063825850[/C][C]0.00634936174149813[/C][/ROW]
[ROW][C]32[/C][C]1.48[/C][C]1.48311841670873[/C][C]-0.00311841670873279[/C][/ROW]
[ROW][C]33[/C][C]1.48[/C][C]1.48476165720020[/C][C]-0.00476165720019838[/C][/ROW]
[ROW][C]34[/C][C]1.48[/C][C]1.48640489769166[/C][C]-0.00640489769166398[/C][/ROW]
[ROW][C]35[/C][C]1.48[/C][C]1.49587267614189[/C][C]-0.0158726761418949[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.49751591663336[/C][C]-0.0175159166333605[/C][/ROW]
[ROW][C]37[/C][C]1.48[/C][C]1.49915915712483[/C][C]-0.0191591571248261[/C][/ROW]
[ROW][C]38[/C][C]1.48[/C][C]1.50080239761629[/C][C]-0.0208023976162917[/C][/ROW]
[ROW][C]39[/C][C]1.48[/C][C]1.50244563810776[/C][C]-0.0224456381077573[/C][/ROW]
[ROW][C]40[/C][C]1.48[/C][C]1.50408887859922[/C][C]-0.0240888785992229[/C][/ROW]
[ROW][C]41[/C][C]1.48[/C][C]1.50573211909069[/C][C]-0.0257321190906884[/C][/ROW]
[ROW][C]42[/C][C]1.48[/C][C]1.50737535958215[/C][C]-0.0273753595821540[/C][/ROW]
[ROW][C]43[/C][C]1.48[/C][C]1.50901860007362[/C][C]-0.0290186000736196[/C][/ROW]
[ROW][C]44[/C][C]1.48[/C][C]1.51066184056509[/C][C]-0.0306618405650852[/C][/ROW]
[ROW][C]45[/C][C]1.48[/C][C]1.50448054309779[/C][C]-0.0244805430977855[/C][/ROW]
[ROW][C]46[/C][C]1.48[/C][C]1.50612378358925[/C][C]-0.0261237835892511[/C][/ROW]
[ROW][C]47[/C][C]1.48[/C][C]1.50776702408072[/C][C]-0.0277670240807167[/C][/ROW]
[ROW][C]48[/C][C]1.48[/C][C]1.50941026457218[/C][C]-0.0294102645721823[/C][/ROW]
[ROW][C]49[/C][C]1.48[/C][C]1.51105350506365[/C][C]-0.0310535050636479[/C][/ROW]
[ROW][C]50[/C][C]1.57[/C][C]1.52052128351388[/C][C]0.0494787164861213[/C][/ROW]
[ROW][C]51[/C][C]1.58[/C][C]1.52998906196411[/C][C]0.0500109380358904[/C][/ROW]
[ROW][C]52[/C][C]1.58[/C][C]1.53163230245558[/C][C]0.0483676975444248[/C][/ROW]
[ROW][C]53[/C][C]1.58[/C][C]1.53327554294704[/C][C]0.0467244570529592[/C][/ROW]
[ROW][C]54[/C][C]1.58[/C][C]1.53491878343851[/C][C]0.0450812165614936[/C][/ROW]
[ROW][C]55[/C][C]1.59[/C][C]1.61076735772747[/C][C]-0.0207673577274670[/C][/ROW]
[ROW][C]56[/C][C]1.6[/C][C]1.61241059821893[/C][C]-0.0124105982189325[/C][/ROW]
[ROW][C]57[/C][C]1.6[/C][C]1.61405383871040[/C][C]-0.0140538387103981[/C][/ROW]
[ROW][C]58[/C][C]1.61[/C][C]1.61569707920186[/C][C]-0.00569707920186373[/C][/ROW]
[ROW][C]59[/C][C]1.61[/C][C]1.62516485765209[/C][C]-0.0151648576520946[/C][/ROW]
[ROW][C]60[/C][C]1.61[/C][C]1.62680809814356[/C][C]-0.0168080981435602[/C][/ROW]
[ROW][C]61[/C][C]1.62[/C][C]1.62845133863503[/C][C]-0.00845133863502581[/C][/ROW]
[ROW][C]62[/C][C]1.63[/C][C]1.63009457912649[/C][C]-9.45791264916076e-05[/C][/ROW]
[ROW][C]63[/C][C]1.63[/C][C]1.63173781961796[/C][C]-0.0017378196179572[/C][/ROW]
[ROW][C]64[/C][C]1.64[/C][C]1.62555652215066[/C][C]0.0144434778493425[/C][/ROW]
[ROW][C]65[/C][C]1.64[/C][C]1.63502430060089[/C][C]0.00497569939911162[/C][/ROW]
[ROW][C]66[/C][C]1.64[/C][C]1.62884300313359[/C][C]0.0111569968664113[/C][/ROW]
[ROW][C]67[/C][C]1.64[/C][C]1.63048624362505[/C][C]0.00951375637494576[/C][/ROW]
[ROW][C]68[/C][C]1.64[/C][C]1.63995402207529[/C][C]4.59779247148431e-05[/C][/ROW]
[ROW][C]69[/C][C]1.65[/C][C]1.63377272460799[/C][C]0.0162272753920146[/C][/ROW]
[ROW][C]70[/C][C]1.65[/C][C]1.63541596509945[/C][C]0.0145840349005490[/C][/ROW]
[ROW][C]71[/C][C]1.65[/C][C]1.63705920559092[/C][C]0.0129407944090834[/C][/ROW]
[ROW][C]72[/C][C]1.65[/C][C]1.63870244608238[/C][C]0.0112975539176178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4546&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4546&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.43	1.41652888555577	0.0134711144442342
2	1.43	1.41817212604723	0.0118278739527655
3	1.43	1.4198153665387	0.0101846334613000
4	1.43	1.42145860703017	0.00854139296983443
5	1.43	1.42310184752163	0.00689815247836882
6	1.43	1.42474508801310	0.00525491198690322
7	1.43	1.42638832850456	0.00361167149543763
8	1.43	1.42803156899603	0.00196843100397204
9	1.43	1.42185027152873	0.00814972847127176
10	1.43	1.43131804997896	-0.00131804997895915
11	1.43	1.43296129047042	-0.00296129047042474
12	1.43	1.42677999300312	0.00322000699687498
13	1.43	1.43624777145336	-0.00624777145335593
14	1.43	1.43789101194482	-0.00789101194482152
15	1.43	1.43953425243629	-0.00953425243628712
16	1.43	1.44117749292775	-0.0111774929277527
17	1.43	1.45064527137798	-0.0206452713779836
18	1.43	1.45228851186945	-0.0222885118694492
19	1.44	1.45393175236091	-0.0139317523609148
20	1.48	1.46339953081115	0.0166004691888543
21	1.48	1.46504277130261	0.0149572286973887
22	1.48	1.45886147383531	0.0211385261646885
23	1.48	1.46050471432678	0.0194952856732229
24	1.48	1.46214795481824	0.0178520451817573
25	1.48	1.46379119530971	0.0162088046902917
26	1.48	1.46543443580117	0.0145655641988261
27	1.48	1.46707767629264	0.0129223237073605
28	1.48	1.46872091678411	0.0112790832158949
29	1.48	1.47036415727557	0.00963584272442931
30	1.48	1.47200739776704	0.00799260223296372
31	1.48	1.47365063825850	0.00634936174149813
32	1.48	1.48311841670873	-0.00311841670873279
33	1.48	1.48476165720020	-0.00476165720019838
34	1.48	1.48640489769166	-0.00640489769166398
35	1.48	1.49587267614189	-0.0158726761418949
36	1.48	1.49751591663336	-0.0175159166333605
37	1.48	1.49915915712483	-0.0191591571248261
38	1.48	1.50080239761629	-0.0208023976162917
39	1.48	1.50244563810776	-0.0224456381077573
40	1.48	1.50408887859922	-0.0240888785992229
41	1.48	1.50573211909069	-0.0257321190906884
42	1.48	1.50737535958215	-0.0273753595821540
43	1.48	1.50901860007362	-0.0290186000736196
44	1.48	1.51066184056509	-0.0306618405650852
45	1.48	1.50448054309779	-0.0244805430977855
46	1.48	1.50612378358925	-0.0261237835892511
47	1.48	1.50776702408072	-0.0277670240807167
48	1.48	1.50941026457218	-0.0294102645721823
49	1.48	1.51105350506365	-0.0310535050636479
50	1.57	1.52052128351388	0.0494787164861213
51	1.58	1.52998906196411	0.0500109380358904
52	1.58	1.53163230245558	0.0483676975444248
53	1.58	1.53327554294704	0.0467244570529592
54	1.58	1.53491878343851	0.0450812165614936
55	1.59	1.61076735772747	-0.0207673577274670
56	1.6	1.61241059821893	-0.0124105982189325
57	1.6	1.61405383871040	-0.0140538387103981
58	1.61	1.61569707920186	-0.00569707920186373
59	1.61	1.62516485765209	-0.0151648576520946
60	1.61	1.62680809814356	-0.0168080981435602
61	1.62	1.62845133863503	-0.00845133863502581
62	1.63	1.63009457912649	-9.45791264916076e-05
63	1.63	1.63173781961796	-0.0017378196179572
64	1.64	1.62555652215066	0.0144434778493425
65	1.64	1.63502430060089	0.00497569939911162
66	1.64	1.62884300313359	0.0111569968664113
67	1.64	1.63048624362505	0.00951375637494576
68	1.64	1.63995402207529	4.59779247148431e-05
69	1.65	1.63377272460799	0.0162272753920146
70	1.65	1.63541596509945	0.0145840349005490
71	1.65	1.63705920559092	0.0129407944090834
72	1.65	1.63870244608238	0.0112975539176178

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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