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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 18 Dec 2007 14:03:51 -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/Dec/18/t1198010852zb3ibmcnoeihkp2.htm/, Retrieved Sat, 04 May 2024 12:38:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4610, Retrieved Sat, 04 May 2024 12:38:42 +0000

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No (this computation is public)

User-defined keywords

PRM

Estimated Impact

220

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

-       [Multiple Regression] [Paper - Regressio...] [2007-12-18 21:03:51] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]
-    D    [Multiple Regression] [Paper - Regressio...] [2008-12-28 14:19:15] [c29178f7f550574a75dc881e636e0923] 

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10,51	7,63	-15,57	16,07
-1,02	-1,52	-7	-8,58
-2,68	5,71	-2,08	5,08
-9,75	13,19	6,06	0,09
3,64	-5,5	3,1	3,83
9,5	1,77	-7,28	5,82
-0,33	1,97	11,93	37,12
-0,99	-5,61	-15,18	-0,46
3,16	-7,32	-4,97	-3,63
4,27	-1,09	-3,06	-3,88
-2,97	-0,1	5,18	4,62
-7,49	-9,4	-2,3	-12,97
0,33	-6,39	-1,86	3,2
-2,57	-2,03	-8,75	-5,75
4,07	0,9	-8,02	-0,57
5,31	7,57	4,8	-7,16
-8,09	-2,19	3,9	-18,05
5,29	3,59	-11,31	15,63
7,38	-1,69	4,26	-18,68
-6,12	-1,54	-6,89	-0,7
-3,38	13,36	4,13	2,59
-8,61	-3,66	4,25	2,57
2,58	0,61	-5,92	0,36
10,02	9,25	-2,62	32,56
7,08	11,03	-5,12	8,53
-2,75	-3,5	-6,19	1,42
3,42	-6,56	1,58	3,53
-1,6	5,55	6,93	0,9
0,65	16,5	1,3	-1,1
2,86	-0,09	0,7	13,32
-3,52	-10,19	18,15	-33,59
5,65	-1,56	-13,63	-0,85
4,31	3,62	-8,97	42,09
-4,39	-3,46	-3,48	-6,25
-5,85	-0,84	0,13	-11,08
-5,47	-1,75	0,16	-29,29
-2,3	-5,59	-1,28	-11,17
-0,14	-4,31	-8,46	13,92
8,08	8,29	-2,92	13,54
-7,43	-14,07	0,15	-16,49
0,02	-4,08	3,87	-9,38
-2,47	3,96	7,71	-2,84
-2,11	-2,54	-4,12	-2,88
7,87	24,36	-2,74	6,18
4,66	11,73	3,19	3,71
3,6	3,82	-6,22	3,18
-3,64	-2,98	1,25	-4,18
7,26	7,46	4,24	13,6
-7,62	-6,39	0,15	4,82
13,83	11,7	-2,06	10,05
1,28	2,36	2,14	9,69
-0,32	-7,48	-1,68	-13,63
-2,9	-2,54	5,03	2,81
4,92	-2,31	2,25	2,39
11,99	10,86	-6,58	9,12
10,06	-2,11	-2,85	14,21
-2,22	3,41	5,04	3,49
3,97	11,2	4,44	5,51
0,56	-1,21	-0,68	-6,15
3,34	5,82	-2,51	2,72
-2,86	-2,61	2,36	-11,12
4,38	-1,54	-6,32	-4,7
1,43	-5,42	-3,82	1,82
-0,49	11,6	2,17	-10,44
-1,23	-9,07	4,14	6,04

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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4610&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4610&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4610&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Producten[t] = + 0.344236397106684 + 0.244312093866000Machines[t] -0.240781863201269Electronica[t] + 0.120843814609541Medisch[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Producten[t] =  +  0.344236397106684 +  0.244312093866000Machines[t] -0.240781863201269Electronica[t] +  0.120843814609541Medisch[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4610&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Producten[t] =  +  0.344236397106684 +  0.244312093866000Machines[t] -0.240781863201269Electronica[t] +  0.120843814609541Medisch[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4610&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4610&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
Producten[t] = + 0.344236397106684 + 0.244312093866000Machines[t] -0.240781863201269Electronica[t] + 0.120843814609541Medisch[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)	0.344236397106684	0.56443	0.6099	0.544204	0.272102
Machines	0.244312093866000	0.082765	2.9519	0.004478	0.002239
Electronica	-0.240781863201269	0.093352	-2.5793	0.012327	0.006164
Medisch	0.120843814609541	0.048547	2.4892	0.015545	0.007773

\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) & 0.344236397106684 & 0.56443 & 0.6099 & 0.544204 & 0.272102 \tabularnewline
Machines & 0.244312093866000 & 0.082765 & 2.9519 & 0.004478 & 0.002239 \tabularnewline
Electronica & -0.240781863201269 & 0.093352 & -2.5793 & 0.012327 & 0.006164 \tabularnewline
Medisch & 0.120843814609541 & 0.048547 & 2.4892 & 0.015545 & 0.007773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4610&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]0.344236397106684[/C][C]0.56443[/C][C]0.6099[/C][C]0.544204[/C][C]0.272102[/C][/ROW]
[ROW][C]Machines[/C][C]0.244312093866000[/C][C]0.082765[/C][C]2.9519[/C][C]0.004478[/C][C]0.002239[/C][/ROW]
[ROW][C]Electronica[/C][C]-0.240781863201269[/C][C]0.093352[/C][C]-2.5793[/C][C]0.012327[/C][C]0.006164[/C][/ROW]
[ROW][C]Medisch[/C][C]0.120843814609541[/C][C]0.048547[/C][C]2.4892[/C][C]0.015545[/C][C]0.007773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4610&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4610&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)	0.344236397106684	0.56443	0.6099	0.544204	0.272102
Machines	0.244312093866000	0.082765	2.9519	0.004478	0.002239
Electronica	-0.240781863201269	0.093352	-2.5793	0.012327	0.006164
Medisch	0.120843814609541	0.048547	2.4892	0.015545	0.007773

Multiple Linear Regression - Regression Statistics
Multiple R	0.60496196371144
R-squared	0.365978977537602
Adjusted R-squared	0.334797615777156
F-TEST (value)	11.7371069406550
F-TEST (DF numerator)	3
F-TEST (DF denominator)	61
p-value	3.60802363918999e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.43887068411695
Sum Squared Residuals	1201.91794996908

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.60496196371144 \tabularnewline
R-squared & 0.365978977537602 \tabularnewline
Adjusted R-squared & 0.334797615777156 \tabularnewline
F-TEST (value) & 11.7371069406550 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 61 \tabularnewline
p-value & 3.60802363918999e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.43887068411695 \tabularnewline
Sum Squared Residuals & 1201.91794996908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4610&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.60496196371144[/C][/ROW]
[ROW][C]R-squared[/C][C]0.365978977537602[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.334797615777156[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]11.7371069406550[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]61[/C][/ROW]
[ROW][C]p-value[/C][C]3.60802363918999e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.43887068411695[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1201.91794996908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4610&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4610&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	0.60496196371144
R-squared	0.365978977537602
Adjusted R-squared	0.334797615777156
F-TEST (value)	11.7371069406550
F-TEST (DF numerator)	3
F-TEST (DF denominator)	61
p-value	3.60802363918999e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.43887068411695
Sum Squared Residuals	1201.91794996908

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	10.51	7.89927138412336	2.61072861587664
2	-1.02	0.621515127489391	-1.64151512748939
3	-2.68	2.85397130675664	-5.53397130675664
4	-9.75	2.11845076751440	-11.8684507675144
5	3.64	-1.28307208512571	4.92307208512571
6	9.5	3.23287176838227	6.26712823161773
7	-0.33	2.43872599233773	-2.76872599233773
8	-0.99	2.5731260791933	-3.56312607919330
9	3.16	-0.686105316914764	3.84610531691476
10	4.27	0.345854715503608	3.92414528449639
11	-2.97	-0.369146440166408	-2.60085355983359
12	-7.49	-2.96584327535655	-4.52415672464345
13	0.33	-0.382363410392165	0.712363410392165
14	-2.57	1.26027221556495	-3.83027221556495
15	4.07	2.42630685013282	1.64369314986718
16	5.31	0.172684291701903	5.1373157082981
17	-8.09	-3.31108720864702	-4.77891279135298
18	5.29	5.83334850923911	-0.543348509239105
19	7.38	-3.35174423567049	10.7317442356705
20	-6.12	1.54239213978311	-7.66239213978311
21	-3.38	2.92680235597392	-6.30680235597392
22	-8.61	-1.26270018150175	-7.34729981849825
23	2.58	1.96219917777589	0.617800822224108
24	10.02	7.16964635064117	2.85035364935883
25	7.08	5.30259967065855	1.77740032934145
26	-2.75	1.15118201853709	-3.90118201853709
27	3.42	-1.2123076169406	4.6323076169406
28	-1.6	0.140309639226780	-1.74030963922678
29	0.65	3.92944132766354	-3.27944132766354
30	2.86	1.76334061501694	1.09665938498306
31	-3.52	-10.5746383892254	7.05463838922537
32	5.65	3.14224908369091	2.50775091630909
33	4.31	8.47477564673257	-4.16477564673257
34	-4.39	-0.418436405038891	-3.97156359496111
35	-5.85	-1.23123686983064	-4.61876313016936
36	-5.47	-3.66135019518448	-1.80864980481552
37	-2.3	-2.06309283189521	-0.236907168104795
38	-0.14	3.01041173459177	-3.15041173459177
39	8.08	4.70889194561672	3.37110805438328
40	-7.43	-5.12206654597946	-2.30793345402054
41	0.02	-2.717897737493	2.737897737493
42	-2.47	-0.887912309956835	-1.58208769004317
43	-2.11	0.367674769000795	-2.47767476900079
44	7.87	7.7022360831409	0.167763916859109
45	4.66	2.89025366674422	1.76974633325578
46	3.6	3.15945511524504	0.440544884754961
47	-3.64	-1.18991811668346	-2.45008188331654
48	7.26	2.78936539606342	4.47063460393658
49	-7.62	-0.670567975759259	-6.94943202424074
50	13.83	4.91317887035939	8.91682112964061
51	1.28	1.57651631494618	-0.296516314946182
52	-0.32	-2.72580572796091	2.40580572796091
53	-2.9	-1.14787797416253	-1.75212202583747
54	4.92	-0.473067015009828	5.39306701500983
55	11.99	5.68390598559481	6.30609401440519
56	10.06	2.23215679477462	7.82784320522538
57	-2.22	0.385544959642648	-2.60554495964265
58	3.97	2.67730979429082	1.29269020570918
59	0.56	-0.53083902934299	1.09083902934299
60	3.34	2.69919043577994	0.640809564220057
61	-2.86	-2.20544658349667	-0.654553416503333
62	4.38	0.921771219320221	3.45822878067978
63	1.43	0.159787308371176	1.27021269162882
64	-0.49	1.39415061828193	-1.88415061828193
65	-1.23	-2.13861456766956	0.908614567669563

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10.51 & 7.89927138412336 & 2.61072861587664 \tabularnewline
2 & -1.02 & 0.621515127489391 & -1.64151512748939 \tabularnewline
3 & -2.68 & 2.85397130675664 & -5.53397130675664 \tabularnewline
4 & -9.75 & 2.11845076751440 & -11.8684507675144 \tabularnewline
5 & 3.64 & -1.28307208512571 & 4.92307208512571 \tabularnewline
6 & 9.5 & 3.23287176838227 & 6.26712823161773 \tabularnewline
7 & -0.33 & 2.43872599233773 & -2.76872599233773 \tabularnewline
8 & -0.99 & 2.5731260791933 & -3.56312607919330 \tabularnewline
9 & 3.16 & -0.686105316914764 & 3.84610531691476 \tabularnewline
10 & 4.27 & 0.345854715503608 & 3.92414528449639 \tabularnewline
11 & -2.97 & -0.369146440166408 & -2.60085355983359 \tabularnewline
12 & -7.49 & -2.96584327535655 & -4.52415672464345 \tabularnewline
13 & 0.33 & -0.382363410392165 & 0.712363410392165 \tabularnewline
14 & -2.57 & 1.26027221556495 & -3.83027221556495 \tabularnewline
15 & 4.07 & 2.42630685013282 & 1.64369314986718 \tabularnewline
16 & 5.31 & 0.172684291701903 & 5.1373157082981 \tabularnewline
17 & -8.09 & -3.31108720864702 & -4.77891279135298 \tabularnewline
18 & 5.29 & 5.83334850923911 & -0.543348509239105 \tabularnewline
19 & 7.38 & -3.35174423567049 & 10.7317442356705 \tabularnewline
20 & -6.12 & 1.54239213978311 & -7.66239213978311 \tabularnewline
21 & -3.38 & 2.92680235597392 & -6.30680235597392 \tabularnewline
22 & -8.61 & -1.26270018150175 & -7.34729981849825 \tabularnewline
23 & 2.58 & 1.96219917777589 & 0.617800822224108 \tabularnewline
24 & 10.02 & 7.16964635064117 & 2.85035364935883 \tabularnewline
25 & 7.08 & 5.30259967065855 & 1.77740032934145 \tabularnewline
26 & -2.75 & 1.15118201853709 & -3.90118201853709 \tabularnewline
27 & 3.42 & -1.2123076169406 & 4.6323076169406 \tabularnewline
28 & -1.6 & 0.140309639226780 & -1.74030963922678 \tabularnewline
29 & 0.65 & 3.92944132766354 & -3.27944132766354 \tabularnewline
30 & 2.86 & 1.76334061501694 & 1.09665938498306 \tabularnewline
31 & -3.52 & -10.5746383892254 & 7.05463838922537 \tabularnewline
32 & 5.65 & 3.14224908369091 & 2.50775091630909 \tabularnewline
33 & 4.31 & 8.47477564673257 & -4.16477564673257 \tabularnewline
34 & -4.39 & -0.418436405038891 & -3.97156359496111 \tabularnewline
35 & -5.85 & -1.23123686983064 & -4.61876313016936 \tabularnewline
36 & -5.47 & -3.66135019518448 & -1.80864980481552 \tabularnewline
37 & -2.3 & -2.06309283189521 & -0.236907168104795 \tabularnewline
38 & -0.14 & 3.01041173459177 & -3.15041173459177 \tabularnewline
39 & 8.08 & 4.70889194561672 & 3.37110805438328 \tabularnewline
40 & -7.43 & -5.12206654597946 & -2.30793345402054 \tabularnewline
41 & 0.02 & -2.717897737493 & 2.737897737493 \tabularnewline
42 & -2.47 & -0.887912309956835 & -1.58208769004317 \tabularnewline
43 & -2.11 & 0.367674769000795 & -2.47767476900079 \tabularnewline
44 & 7.87 & 7.7022360831409 & 0.167763916859109 \tabularnewline
45 & 4.66 & 2.89025366674422 & 1.76974633325578 \tabularnewline
46 & 3.6 & 3.15945511524504 & 0.440544884754961 \tabularnewline
47 & -3.64 & -1.18991811668346 & -2.45008188331654 \tabularnewline
48 & 7.26 & 2.78936539606342 & 4.47063460393658 \tabularnewline
49 & -7.62 & -0.670567975759259 & -6.94943202424074 \tabularnewline
50 & 13.83 & 4.91317887035939 & 8.91682112964061 \tabularnewline
51 & 1.28 & 1.57651631494618 & -0.296516314946182 \tabularnewline
52 & -0.32 & -2.72580572796091 & 2.40580572796091 \tabularnewline
53 & -2.9 & -1.14787797416253 & -1.75212202583747 \tabularnewline
54 & 4.92 & -0.473067015009828 & 5.39306701500983 \tabularnewline
55 & 11.99 & 5.68390598559481 & 6.30609401440519 \tabularnewline
56 & 10.06 & 2.23215679477462 & 7.82784320522538 \tabularnewline
57 & -2.22 & 0.385544959642648 & -2.60554495964265 \tabularnewline
58 & 3.97 & 2.67730979429082 & 1.29269020570918 \tabularnewline
59 & 0.56 & -0.53083902934299 & 1.09083902934299 \tabularnewline
60 & 3.34 & 2.69919043577994 & 0.640809564220057 \tabularnewline
61 & -2.86 & -2.20544658349667 & -0.654553416503333 \tabularnewline
62 & 4.38 & 0.921771219320221 & 3.45822878067978 \tabularnewline
63 & 1.43 & 0.159787308371176 & 1.27021269162882 \tabularnewline
64 & -0.49 & 1.39415061828193 & -1.88415061828193 \tabularnewline
65 & -1.23 & -2.13861456766956 & 0.908614567669563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4610&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]10.51[/C][C]7.89927138412336[/C][C]2.61072861587664[/C][/ROW]
[ROW][C]2[/C][C]-1.02[/C][C]0.621515127489391[/C][C]-1.64151512748939[/C][/ROW]
[ROW][C]3[/C][C]-2.68[/C][C]2.85397130675664[/C][C]-5.53397130675664[/C][/ROW]
[ROW][C]4[/C][C]-9.75[/C][C]2.11845076751440[/C][C]-11.8684507675144[/C][/ROW]
[ROW][C]5[/C][C]3.64[/C][C]-1.28307208512571[/C][C]4.92307208512571[/C][/ROW]
[ROW][C]6[/C][C]9.5[/C][C]3.23287176838227[/C][C]6.26712823161773[/C][/ROW]
[ROW][C]7[/C][C]-0.33[/C][C]2.43872599233773[/C][C]-2.76872599233773[/C][/ROW]
[ROW][C]8[/C][C]-0.99[/C][C]2.5731260791933[/C][C]-3.56312607919330[/C][/ROW]
[ROW][C]9[/C][C]3.16[/C][C]-0.686105316914764[/C][C]3.84610531691476[/C][/ROW]
[ROW][C]10[/C][C]4.27[/C][C]0.345854715503608[/C][C]3.92414528449639[/C][/ROW]
[ROW][C]11[/C][C]-2.97[/C][C]-0.369146440166408[/C][C]-2.60085355983359[/C][/ROW]
[ROW][C]12[/C][C]-7.49[/C][C]-2.96584327535655[/C][C]-4.52415672464345[/C][/ROW]
[ROW][C]13[/C][C]0.33[/C][C]-0.382363410392165[/C][C]0.712363410392165[/C][/ROW]
[ROW][C]14[/C][C]-2.57[/C][C]1.26027221556495[/C][C]-3.83027221556495[/C][/ROW]
[ROW][C]15[/C][C]4.07[/C][C]2.42630685013282[/C][C]1.64369314986718[/C][/ROW]
[ROW][C]16[/C][C]5.31[/C][C]0.172684291701903[/C][C]5.1373157082981[/C][/ROW]
[ROW][C]17[/C][C]-8.09[/C][C]-3.31108720864702[/C][C]-4.77891279135298[/C][/ROW]
[ROW][C]18[/C][C]5.29[/C][C]5.83334850923911[/C][C]-0.543348509239105[/C][/ROW]
[ROW][C]19[/C][C]7.38[/C][C]-3.35174423567049[/C][C]10.7317442356705[/C][/ROW]
[ROW][C]20[/C][C]-6.12[/C][C]1.54239213978311[/C][C]-7.66239213978311[/C][/ROW]
[ROW][C]21[/C][C]-3.38[/C][C]2.92680235597392[/C][C]-6.30680235597392[/C][/ROW]
[ROW][C]22[/C][C]-8.61[/C][C]-1.26270018150175[/C][C]-7.34729981849825[/C][/ROW]
[ROW][C]23[/C][C]2.58[/C][C]1.96219917777589[/C][C]0.617800822224108[/C][/ROW]
[ROW][C]24[/C][C]10.02[/C][C]7.16964635064117[/C][C]2.85035364935883[/C][/ROW]
[ROW][C]25[/C][C]7.08[/C][C]5.30259967065855[/C][C]1.77740032934145[/C][/ROW]
[ROW][C]26[/C][C]-2.75[/C][C]1.15118201853709[/C][C]-3.90118201853709[/C][/ROW]
[ROW][C]27[/C][C]3.42[/C][C]-1.2123076169406[/C][C]4.6323076169406[/C][/ROW]
[ROW][C]28[/C][C]-1.6[/C][C]0.140309639226780[/C][C]-1.74030963922678[/C][/ROW]
[ROW][C]29[/C][C]0.65[/C][C]3.92944132766354[/C][C]-3.27944132766354[/C][/ROW]
[ROW][C]30[/C][C]2.86[/C][C]1.76334061501694[/C][C]1.09665938498306[/C][/ROW]
[ROW][C]31[/C][C]-3.52[/C][C]-10.5746383892254[/C][C]7.05463838922537[/C][/ROW]
[ROW][C]32[/C][C]5.65[/C][C]3.14224908369091[/C][C]2.50775091630909[/C][/ROW]
[ROW][C]33[/C][C]4.31[/C][C]8.47477564673257[/C][C]-4.16477564673257[/C][/ROW]
[ROW][C]34[/C][C]-4.39[/C][C]-0.418436405038891[/C][C]-3.97156359496111[/C][/ROW]
[ROW][C]35[/C][C]-5.85[/C][C]-1.23123686983064[/C][C]-4.61876313016936[/C][/ROW]
[ROW][C]36[/C][C]-5.47[/C][C]-3.66135019518448[/C][C]-1.80864980481552[/C][/ROW]
[ROW][C]37[/C][C]-2.3[/C][C]-2.06309283189521[/C][C]-0.236907168104795[/C][/ROW]
[ROW][C]38[/C][C]-0.14[/C][C]3.01041173459177[/C][C]-3.15041173459177[/C][/ROW]
[ROW][C]39[/C][C]8.08[/C][C]4.70889194561672[/C][C]3.37110805438328[/C][/ROW]
[ROW][C]40[/C][C]-7.43[/C][C]-5.12206654597946[/C][C]-2.30793345402054[/C][/ROW]
[ROW][C]41[/C][C]0.02[/C][C]-2.717897737493[/C][C]2.737897737493[/C][/ROW]
[ROW][C]42[/C][C]-2.47[/C][C]-0.887912309956835[/C][C]-1.58208769004317[/C][/ROW]
[ROW][C]43[/C][C]-2.11[/C][C]0.367674769000795[/C][C]-2.47767476900079[/C][/ROW]
[ROW][C]44[/C][C]7.87[/C][C]7.7022360831409[/C][C]0.167763916859109[/C][/ROW]
[ROW][C]45[/C][C]4.66[/C][C]2.89025366674422[/C][C]1.76974633325578[/C][/ROW]
[ROW][C]46[/C][C]3.6[/C][C]3.15945511524504[/C][C]0.440544884754961[/C][/ROW]
[ROW][C]47[/C][C]-3.64[/C][C]-1.18991811668346[/C][C]-2.45008188331654[/C][/ROW]
[ROW][C]48[/C][C]7.26[/C][C]2.78936539606342[/C][C]4.47063460393658[/C][/ROW]
[ROW][C]49[/C][C]-7.62[/C][C]-0.670567975759259[/C][C]-6.94943202424074[/C][/ROW]
[ROW][C]50[/C][C]13.83[/C][C]4.91317887035939[/C][C]8.91682112964061[/C][/ROW]
[ROW][C]51[/C][C]1.28[/C][C]1.57651631494618[/C][C]-0.296516314946182[/C][/ROW]
[ROW][C]52[/C][C]-0.32[/C][C]-2.72580572796091[/C][C]2.40580572796091[/C][/ROW]
[ROW][C]53[/C][C]-2.9[/C][C]-1.14787797416253[/C][C]-1.75212202583747[/C][/ROW]
[ROW][C]54[/C][C]4.92[/C][C]-0.473067015009828[/C][C]5.39306701500983[/C][/ROW]
[ROW][C]55[/C][C]11.99[/C][C]5.68390598559481[/C][C]6.30609401440519[/C][/ROW]
[ROW][C]56[/C][C]10.06[/C][C]2.23215679477462[/C][C]7.82784320522538[/C][/ROW]
[ROW][C]57[/C][C]-2.22[/C][C]0.385544959642648[/C][C]-2.60554495964265[/C][/ROW]
[ROW][C]58[/C][C]3.97[/C][C]2.67730979429082[/C][C]1.29269020570918[/C][/ROW]
[ROW][C]59[/C][C]0.56[/C][C]-0.53083902934299[/C][C]1.09083902934299[/C][/ROW]
[ROW][C]60[/C][C]3.34[/C][C]2.69919043577994[/C][C]0.640809564220057[/C][/ROW]
[ROW][C]61[/C][C]-2.86[/C][C]-2.20544658349667[/C][C]-0.654553416503333[/C][/ROW]
[ROW][C]62[/C][C]4.38[/C][C]0.921771219320221[/C][C]3.45822878067978[/C][/ROW]
[ROW][C]63[/C][C]1.43[/C][C]0.159787308371176[/C][C]1.27021269162882[/C][/ROW]
[ROW][C]64[/C][C]-0.49[/C][C]1.39415061828193[/C][C]-1.88415061828193[/C][/ROW]
[ROW][C]65[/C][C]-1.23[/C][C]-2.13861456766956[/C][C]0.908614567669563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4610&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4610&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	10.51	7.89927138412336	2.61072861587664
2	-1.02	0.621515127489391	-1.64151512748939
3	-2.68	2.85397130675664	-5.53397130675664
4	-9.75	2.11845076751440	-11.8684507675144
5	3.64	-1.28307208512571	4.92307208512571
6	9.5	3.23287176838227	6.26712823161773
7	-0.33	2.43872599233773	-2.76872599233773
8	-0.99	2.5731260791933	-3.56312607919330
9	3.16	-0.686105316914764	3.84610531691476
10	4.27	0.345854715503608	3.92414528449639
11	-2.97	-0.369146440166408	-2.60085355983359
12	-7.49	-2.96584327535655	-4.52415672464345
13	0.33	-0.382363410392165	0.712363410392165
14	-2.57	1.26027221556495	-3.83027221556495
15	4.07	2.42630685013282	1.64369314986718
16	5.31	0.172684291701903	5.1373157082981
17	-8.09	-3.31108720864702	-4.77891279135298
18	5.29	5.83334850923911	-0.543348509239105
19	7.38	-3.35174423567049	10.7317442356705
20	-6.12	1.54239213978311	-7.66239213978311
21	-3.38	2.92680235597392	-6.30680235597392
22	-8.61	-1.26270018150175	-7.34729981849825
23	2.58	1.96219917777589	0.617800822224108
24	10.02	7.16964635064117	2.85035364935883
25	7.08	5.30259967065855	1.77740032934145
26	-2.75	1.15118201853709	-3.90118201853709
27	3.42	-1.2123076169406	4.6323076169406
28	-1.6	0.140309639226780	-1.74030963922678
29	0.65	3.92944132766354	-3.27944132766354
30	2.86	1.76334061501694	1.09665938498306
31	-3.52	-10.5746383892254	7.05463838922537
32	5.65	3.14224908369091	2.50775091630909
33	4.31	8.47477564673257	-4.16477564673257
34	-4.39	-0.418436405038891	-3.97156359496111
35	-5.85	-1.23123686983064	-4.61876313016936
36	-5.47	-3.66135019518448	-1.80864980481552
37	-2.3	-2.06309283189521	-0.236907168104795
38	-0.14	3.01041173459177	-3.15041173459177
39	8.08	4.70889194561672	3.37110805438328
40	-7.43	-5.12206654597946	-2.30793345402054
41	0.02	-2.717897737493	2.737897737493
42	-2.47	-0.887912309956835	-1.58208769004317
43	-2.11	0.367674769000795	-2.47767476900079
44	7.87	7.7022360831409	0.167763916859109
45	4.66	2.89025366674422	1.76974633325578
46	3.6	3.15945511524504	0.440544884754961
47	-3.64	-1.18991811668346	-2.45008188331654
48	7.26	2.78936539606342	4.47063460393658
49	-7.62	-0.670567975759259	-6.94943202424074
50	13.83	4.91317887035939	8.91682112964061
51	1.28	1.57651631494618	-0.296516314946182
52	-0.32	-2.72580572796091	2.40580572796091
53	-2.9	-1.14787797416253	-1.75212202583747
54	4.92	-0.473067015009828	5.39306701500983
55	11.99	5.68390598559481	6.30609401440519
56	10.06	2.23215679477462	7.82784320522538
57	-2.22	0.385544959642648	-2.60554495964265
58	3.97	2.67730979429082	1.29269020570918
59	0.56	-0.53083902934299	1.09083902934299
60	3.34	2.69919043577994	0.640809564220057
61	-2.86	-2.20544658349667	-0.654553416503333
62	4.38	0.921771219320221	3.45822878067978
63	1.43	0.159787308371176	1.27021269162882
64	-0.49	1.39415061828193	-1.88415061828193
65	-1.23	-2.13861456766956	0.908614567669563

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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 = No Linear Trend ;

Parameters (R input):

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

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

library(lattice)
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