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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 09:47:50 -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/t1197995456h4owqevtfip9w7p.htm/, Retrieved Sat, 04 May 2024 07:13:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4550, Retrieved Sat, 04 May 2024 07:13:22 +0000

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No (this computation is public)

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Estimated Impact

192

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

-       [Multiple Regression] [brood met vier du...] [2007-12-18 16:47:50] [7eb5b05bf0841f2a6d4b99da83be8d69] [Current]

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1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,5
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,5
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,51
1,43	0	0	0	0	0,52
1,43	0	0	0	0	0,52
1,44	0	0	0	0	0,52
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,52
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,54
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,48	1	0	0	0	0,53
1,57	1	1	0	0	0,54
1,58	1	1	0	0	0,55
1,58	1	1	0	0	0,55
1,58	1	1	0	0	0,55
1,58	1	1	0	0	0,55
1,59	1	1	0	0	0,55
1,6	1	1	1	1	0,55
1,6	1	1	1	2	0,55
1,61	1	1	1	3	0,55
1,61	1	1	1	4	0,56
1,61	1	1	1	5	0,56
1,62	1	1	1	6	0,56
1,63	1	1	1	7	0,56
1,63	1	1	1	8	0,56
1,64	1	1	1	9	0,55
1,64	1	1	1	10	0,56
1,64	1	1	1	11	0,55
1,64	1	1	1	12	0,55
1,64	1	1	1	13	0,56
1,65	1	1	1	14	0,55
1,65	1	1	1	15	0,55
1,65	1	1	1	16	0,55
1,65	1	1	1	17	0,55

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=4550&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=4550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4550&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
y[t] = + 1.39151998080862 + 0.0478035703125428x1[t] + 0.09846595983763x2[t] + 0.0184894550635091x3[t] + 0.00344250663472741x4[t] + 0.0762561542764317x5[t] + 7.5561481834617e-06t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  1.39151998080862 +  0.0478035703125428x1[t] +  0.09846595983763x2[t] +  0.0184894550635091x3[t] +  0.00344250663472741x4[t] +  0.0762561542764317x5[t] +  7.5561481834617e-06t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4550&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  1.39151998080862 +  0.0478035703125428x1[t] +  0.09846595983763x2[t] +  0.0184894550635091x3[t] +  0.00344250663472741x4[t] +  0.0762561542764317x5[t] +  7.5561481834617e-06t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4550&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] = + 1.39151998080862 + 0.0478035703125428x1[t] + 0.09846595983763x2[t] + 0.0184894550635091x3[t] + 0.00344250663472741x4[t] + 0.0762561542764317x5[t] + 7.5561481834617e-06t + 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)	1.39151998080862	0.035335	39.3812	0	0
x1	0.0478035703125428	0.001804	26.4999	0	0
x2	0.09846595983763	0.001897	51.9142	0	0
x3	0.0184894550635091	0.002149	8.6037	0	0
x4	0.00344250663472741	0.000179	19.2291	0	0
x5	0.0762561542764317	0.069938	1.0903	0.279592	0.139796
t	7.5561481834617e-06	7.2e-05	0.1056	0.916194	0.458097

\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) & 1.39151998080862 & 0.035335 & 39.3812 & 0 & 0 \tabularnewline
x1 & 0.0478035703125428 & 0.001804 & 26.4999 & 0 & 0 \tabularnewline
x2 & 0.09846595983763 & 0.001897 & 51.9142 & 0 & 0 \tabularnewline
x3 & 0.0184894550635091 & 0.002149 & 8.6037 & 0 & 0 \tabularnewline
x4 & 0.00344250663472741 & 0.000179 & 19.2291 & 0 & 0 \tabularnewline
x5 & 0.0762561542764317 & 0.069938 & 1.0903 & 0.279592 & 0.139796 \tabularnewline
t & 7.5561481834617e-06 & 7.2e-05 & 0.1056 & 0.916194 & 0.458097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4550&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]1.39151998080862[/C][C]0.035335[/C][C]39.3812[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x1[/C][C]0.0478035703125428[/C][C]0.001804[/C][C]26.4999[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x2[/C][C]0.09846595983763[/C][C]0.001897[/C][C]51.9142[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x3[/C][C]0.0184894550635091[/C][C]0.002149[/C][C]8.6037[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x4[/C][C]0.00344250663472741[/C][C]0.000179[/C][C]19.2291[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x5[/C][C]0.0762561542764317[/C][C]0.069938[/C][C]1.0903[/C][C]0.279592[/C][C]0.139796[/C][/ROW]
[ROW][C]t[/C][C]7.5561481834617e-06[/C][C]7.2e-05[/C][C]0.1056[/C][C]0.916194[/C][C]0.458097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4550&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4550&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)	1.39151998080862	0.035335	39.3812	0	0
x1	0.0478035703125428	0.001804	26.4999	0	0
x2	0.09846595983763	0.001897	51.9142	0	0
x3	0.0184894550635091	0.002149	8.6037	0	0
x4	0.00344250663472741	0.000179	19.2291	0	0
x5	0.0762561542764317	0.069938	1.0903	0.279592	0.139796
t	7.5561481834617e-06	7.2e-05	0.1056	0.916194	0.458097

Multiple Linear Regression - Regression Statistics
Multiple R	0.999212635065156
R-squared	0.998425890073853
Adjusted R-squared	0.998280587619131
F-TEST (value)	6871.36285473646
F-TEST (DF numerator)	6
F-TEST (DF denominator)	65
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00321443391090483
Sum Squared Residuals	0.000671618048892368

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999212635065156 \tabularnewline
R-squared & 0.998425890073853 \tabularnewline
Adjusted R-squared & 0.998280587619131 \tabularnewline
F-TEST (value) & 6871.36285473646 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 65 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.00321443391090483 \tabularnewline
Sum Squared Residuals & 0.000671618048892368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4550&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999212635065156[/C][/ROW]
[ROW][C]R-squared[/C][C]0.998425890073853[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.998280587619131[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6871.36285473646[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]65[/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]0.00321443391090483[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.000671618048892368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4550&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4550&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	0.999212635065156
R-squared	0.998425890073853
Adjusted R-squared	0.998280587619131
F-TEST (value)	6871.36285473646
F-TEST (DF numerator)	6
F-TEST (DF denominator)	65
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00321443391090483
Sum Squared Residuals	0.000671618048892368

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.43	1.43041817563778	-0.00041817563777877
2	1.43	1.43042573178597	-0.000425731785965638
3	1.43	1.43043328793415	-0.000433287934149580
4	1.43	1.43044084408233	-0.000440844082332907
5	1.43	1.43044840023052	-0.000448400230516382
6	1.43	1.4304559563787	-0.000455956378699815
7	1.43	1.43046351252688	-0.000463512526883277
8	1.43	1.43047106867507	-0.000471068675066738
9	1.43	1.42971606328049	0.000283936719514118
10	1.43	1.43048618097143	-0.000486180971433661
11	1.43	1.43049373711962	-0.000493737119617123
12	1.43	1.42973873172504	0.000261268274963733
13	1.43	1.43050884941598	-0.000508849415984046
14	1.43	1.43051640556417	-0.000516405564167508
15	1.43	1.43052396171235	-0.000523961712350969
16	1.43	1.43053151786053	-0.000531517860534431
17	1.43	1.43130163555148	-0.00130163555148221
18	1.43	1.43130919169967	-0.00130919169966567
19	1.44	1.43131674784785	0.00868325215215088
20	1.48	1.47989043585134	0.000109564148660195
21	1.48	1.47989799199952	0.000102008000476733
22	1.48	1.47914298660494	0.000857013395057588
23	1.48	1.47915054275313	0.000849457246874127
24	1.48	1.47915809890131	0.000841901098690665
25	1.48	1.47916565504949	0.000834344950507203
26	1.48	1.47917321119768	0.000826788802323742
27	1.48	1.47918076734586	0.00081923265414028
28	1.48	1.47918832349404	0.000811676505956818
29	1.48	1.47919587964223	0.000804120357773356
30	1.48	1.47920343579041	0.000796564209589895
31	1.48	1.47921099193859	0.000789008061406433
32	1.48	1.47998110962954	1.88903704586545e-05
33	1.48	1.47998866577772	1.13342222751928e-05
34	1.48	1.47999622192591	3.77807409173111e-06
35	1.48	1.48076633961686	-0.000766339616856048
36	1.48	1.48077389576504	-0.00077389576503951
37	1.48	1.48078145191322	-0.000781451913222971
38	1.48	1.48078900806141	-0.000789008061406433
39	1.48	1.48079656420959	-0.000796564209589895
40	1.48	1.48080412035777	-0.000804120357773356
41	1.48	1.48081167650596	-0.000811676505956818
42	1.48	1.48081923265414	-0.00081923265414028
43	1.48	1.48082678880232	-0.000826788802323741
44	1.48	1.48083434495051	-0.000834344950507203
45	1.48	1.48007933955593	-7.93395559263474e-05
46	1.48	1.48008689570411	-8.68957041098091e-05
47	1.48	1.48009445185229	-9.44518522932708e-05
48	1.48	1.48010200800048	-0.000102008000476732
49	1.48	1.48010956414866	-0.000109564148660194
50	1.57	1.57934564167724	-0.00934564167723776
51	1.58	1.58011575936819	-0.000115759368185527
52	1.58	1.58012331551637	-0.000123315516368989
53	1.58	1.58013087166455	-0.000130871664552451
54	1.58	1.58013842781274	-0.000138427812735912
55	1.59	1.58014598396092	0.00985401603908064
56	1.6	1.60208550180734	-0.00208550180733934
57	1.6	1.60553556459025	-0.00553556459025022
58	1.61	1.60898562737316	0.00101437262683892
59	1.61	1.61319825169884	-0.00319825169883627
60	1.61	1.61664831448175	-0.00664831448174715
61	1.62	1.62009837726466	-9.83772646580127e-05
62	1.63	1.62354844004757	0.0064515599524309
63	1.63	1.62699850283048	0.00300149716952003
64	1.64	1.62968600407063	0.0103139959293735
65	1.64	1.6338986283963	0.00610137160369828
66	1.64	1.63658612963645	0.00341387036355172
67	1.64	1.64003619241936	-3.61924193591546e-05
68	1.64	1.64424881674503	-0.00424881674503435
69	1.65	1.64693631798518	0.00306368201481911
70	1.65	1.65038638076809	-0.000386380768091772
71	1.65	1.65383644355100	-0.00383644355100264
72	1.65	1.65728650633391	-0.00728650633391352

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.43 & 1.43041817563778 & -0.00041817563777877 \tabularnewline
2 & 1.43 & 1.43042573178597 & -0.000425731785965638 \tabularnewline
3 & 1.43 & 1.43043328793415 & -0.000433287934149580 \tabularnewline
4 & 1.43 & 1.43044084408233 & -0.000440844082332907 \tabularnewline
5 & 1.43 & 1.43044840023052 & -0.000448400230516382 \tabularnewline
6 & 1.43 & 1.4304559563787 & -0.000455956378699815 \tabularnewline
7 & 1.43 & 1.43046351252688 & -0.000463512526883277 \tabularnewline
8 & 1.43 & 1.43047106867507 & -0.000471068675066738 \tabularnewline
9 & 1.43 & 1.42971606328049 & 0.000283936719514118 \tabularnewline
10 & 1.43 & 1.43048618097143 & -0.000486180971433661 \tabularnewline
11 & 1.43 & 1.43049373711962 & -0.000493737119617123 \tabularnewline
12 & 1.43 & 1.42973873172504 & 0.000261268274963733 \tabularnewline
13 & 1.43 & 1.43050884941598 & -0.000508849415984046 \tabularnewline
14 & 1.43 & 1.43051640556417 & -0.000516405564167508 \tabularnewline
15 & 1.43 & 1.43052396171235 & -0.000523961712350969 \tabularnewline
16 & 1.43 & 1.43053151786053 & -0.000531517860534431 \tabularnewline
17 & 1.43 & 1.43130163555148 & -0.00130163555148221 \tabularnewline
18 & 1.43 & 1.43130919169967 & -0.00130919169966567 \tabularnewline
19 & 1.44 & 1.43131674784785 & 0.00868325215215088 \tabularnewline
20 & 1.48 & 1.47989043585134 & 0.000109564148660195 \tabularnewline
21 & 1.48 & 1.47989799199952 & 0.000102008000476733 \tabularnewline
22 & 1.48 & 1.47914298660494 & 0.000857013395057588 \tabularnewline
23 & 1.48 & 1.47915054275313 & 0.000849457246874127 \tabularnewline
24 & 1.48 & 1.47915809890131 & 0.000841901098690665 \tabularnewline
25 & 1.48 & 1.47916565504949 & 0.000834344950507203 \tabularnewline
26 & 1.48 & 1.47917321119768 & 0.000826788802323742 \tabularnewline
27 & 1.48 & 1.47918076734586 & 0.00081923265414028 \tabularnewline
28 & 1.48 & 1.47918832349404 & 0.000811676505956818 \tabularnewline
29 & 1.48 & 1.47919587964223 & 0.000804120357773356 \tabularnewline
30 & 1.48 & 1.47920343579041 & 0.000796564209589895 \tabularnewline
31 & 1.48 & 1.47921099193859 & 0.000789008061406433 \tabularnewline
32 & 1.48 & 1.47998110962954 & 1.88903704586545e-05 \tabularnewline
33 & 1.48 & 1.47998866577772 & 1.13342222751928e-05 \tabularnewline
34 & 1.48 & 1.47999622192591 & 3.77807409173111e-06 \tabularnewline
35 & 1.48 & 1.48076633961686 & -0.000766339616856048 \tabularnewline
36 & 1.48 & 1.48077389576504 & -0.00077389576503951 \tabularnewline
37 & 1.48 & 1.48078145191322 & -0.000781451913222971 \tabularnewline
38 & 1.48 & 1.48078900806141 & -0.000789008061406433 \tabularnewline
39 & 1.48 & 1.48079656420959 & -0.000796564209589895 \tabularnewline
40 & 1.48 & 1.48080412035777 & -0.000804120357773356 \tabularnewline
41 & 1.48 & 1.48081167650596 & -0.000811676505956818 \tabularnewline
42 & 1.48 & 1.48081923265414 & -0.00081923265414028 \tabularnewline
43 & 1.48 & 1.48082678880232 & -0.000826788802323741 \tabularnewline
44 & 1.48 & 1.48083434495051 & -0.000834344950507203 \tabularnewline
45 & 1.48 & 1.48007933955593 & -7.93395559263474e-05 \tabularnewline
46 & 1.48 & 1.48008689570411 & -8.68957041098091e-05 \tabularnewline
47 & 1.48 & 1.48009445185229 & -9.44518522932708e-05 \tabularnewline
48 & 1.48 & 1.48010200800048 & -0.000102008000476732 \tabularnewline
49 & 1.48 & 1.48010956414866 & -0.000109564148660194 \tabularnewline
50 & 1.57 & 1.57934564167724 & -0.00934564167723776 \tabularnewline
51 & 1.58 & 1.58011575936819 & -0.000115759368185527 \tabularnewline
52 & 1.58 & 1.58012331551637 & -0.000123315516368989 \tabularnewline
53 & 1.58 & 1.58013087166455 & -0.000130871664552451 \tabularnewline
54 & 1.58 & 1.58013842781274 & -0.000138427812735912 \tabularnewline
55 & 1.59 & 1.58014598396092 & 0.00985401603908064 \tabularnewline
56 & 1.6 & 1.60208550180734 & -0.00208550180733934 \tabularnewline
57 & 1.6 & 1.60553556459025 & -0.00553556459025022 \tabularnewline
58 & 1.61 & 1.60898562737316 & 0.00101437262683892 \tabularnewline
59 & 1.61 & 1.61319825169884 & -0.00319825169883627 \tabularnewline
60 & 1.61 & 1.61664831448175 & -0.00664831448174715 \tabularnewline
61 & 1.62 & 1.62009837726466 & -9.83772646580127e-05 \tabularnewline
62 & 1.63 & 1.62354844004757 & 0.0064515599524309 \tabularnewline
63 & 1.63 & 1.62699850283048 & 0.00300149716952003 \tabularnewline
64 & 1.64 & 1.62968600407063 & 0.0103139959293735 \tabularnewline
65 & 1.64 & 1.6338986283963 & 0.00610137160369828 \tabularnewline
66 & 1.64 & 1.63658612963645 & 0.00341387036355172 \tabularnewline
67 & 1.64 & 1.64003619241936 & -3.61924193591546e-05 \tabularnewline
68 & 1.64 & 1.64424881674503 & -0.00424881674503435 \tabularnewline
69 & 1.65 & 1.64693631798518 & 0.00306368201481911 \tabularnewline
70 & 1.65 & 1.65038638076809 & -0.000386380768091772 \tabularnewline
71 & 1.65 & 1.65383644355100 & -0.00383644355100264 \tabularnewline
72 & 1.65 & 1.65728650633391 & -0.00728650633391352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4550&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]1.43041817563778[/C][C]-0.00041817563777877[/C][/ROW]
[ROW][C]2[/C][C]1.43[/C][C]1.43042573178597[/C][C]-0.000425731785965638[/C][/ROW]
[ROW][C]3[/C][C]1.43[/C][C]1.43043328793415[/C][C]-0.000433287934149580[/C][/ROW]
[ROW][C]4[/C][C]1.43[/C][C]1.43044084408233[/C][C]-0.000440844082332907[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.43044840023052[/C][C]-0.000448400230516382[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.4304559563787[/C][C]-0.000455956378699815[/C][/ROW]
[ROW][C]7[/C][C]1.43[/C][C]1.43046351252688[/C][C]-0.000463512526883277[/C][/ROW]
[ROW][C]8[/C][C]1.43[/C][C]1.43047106867507[/C][C]-0.000471068675066738[/C][/ROW]
[ROW][C]9[/C][C]1.43[/C][C]1.42971606328049[/C][C]0.000283936719514118[/C][/ROW]
[ROW][C]10[/C][C]1.43[/C][C]1.43048618097143[/C][C]-0.000486180971433661[/C][/ROW]
[ROW][C]11[/C][C]1.43[/C][C]1.43049373711962[/C][C]-0.000493737119617123[/C][/ROW]
[ROW][C]12[/C][C]1.43[/C][C]1.42973873172504[/C][C]0.000261268274963733[/C][/ROW]
[ROW][C]13[/C][C]1.43[/C][C]1.43050884941598[/C][C]-0.000508849415984046[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43051640556417[/C][C]-0.000516405564167508[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.43052396171235[/C][C]-0.000523961712350969[/C][/ROW]
[ROW][C]16[/C][C]1.43[/C][C]1.43053151786053[/C][C]-0.000531517860534431[/C][/ROW]
[ROW][C]17[/C][C]1.43[/C][C]1.43130163555148[/C][C]-0.00130163555148221[/C][/ROW]
[ROW][C]18[/C][C]1.43[/C][C]1.43130919169967[/C][C]-0.00130919169966567[/C][/ROW]
[ROW][C]19[/C][C]1.44[/C][C]1.43131674784785[/C][C]0.00868325215215088[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.47989043585134[/C][C]0.000109564148660195[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.47989799199952[/C][C]0.000102008000476733[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.47914298660494[/C][C]0.000857013395057588[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.47915054275313[/C][C]0.000849457246874127[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.47915809890131[/C][C]0.000841901098690665[/C][/ROW]
[ROW][C]25[/C][C]1.48[/C][C]1.47916565504949[/C][C]0.000834344950507203[/C][/ROW]
[ROW][C]26[/C][C]1.48[/C][C]1.47917321119768[/C][C]0.000826788802323742[/C][/ROW]
[ROW][C]27[/C][C]1.48[/C][C]1.47918076734586[/C][C]0.00081923265414028[/C][/ROW]
[ROW][C]28[/C][C]1.48[/C][C]1.47918832349404[/C][C]0.000811676505956818[/C][/ROW]
[ROW][C]29[/C][C]1.48[/C][C]1.47919587964223[/C][C]0.000804120357773356[/C][/ROW]
[ROW][C]30[/C][C]1.48[/C][C]1.47920343579041[/C][C]0.000796564209589895[/C][/ROW]
[ROW][C]31[/C][C]1.48[/C][C]1.47921099193859[/C][C]0.000789008061406433[/C][/ROW]
[ROW][C]32[/C][C]1.48[/C][C]1.47998110962954[/C][C]1.88903704586545e-05[/C][/ROW]
[ROW][C]33[/C][C]1.48[/C][C]1.47998866577772[/C][C]1.13342222751928e-05[/C][/ROW]
[ROW][C]34[/C][C]1.48[/C][C]1.47999622192591[/C][C]3.77807409173111e-06[/C][/ROW]
[ROW][C]35[/C][C]1.48[/C][C]1.48076633961686[/C][C]-0.000766339616856048[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.48077389576504[/C][C]-0.00077389576503951[/C][/ROW]
[ROW][C]37[/C][C]1.48[/C][C]1.48078145191322[/C][C]-0.000781451913222971[/C][/ROW]
[ROW][C]38[/C][C]1.48[/C][C]1.48078900806141[/C][C]-0.000789008061406433[/C][/ROW]
[ROW][C]39[/C][C]1.48[/C][C]1.48079656420959[/C][C]-0.000796564209589895[/C][/ROW]
[ROW][C]40[/C][C]1.48[/C][C]1.48080412035777[/C][C]-0.000804120357773356[/C][/ROW]
[ROW][C]41[/C][C]1.48[/C][C]1.48081167650596[/C][C]-0.000811676505956818[/C][/ROW]
[ROW][C]42[/C][C]1.48[/C][C]1.48081923265414[/C][C]-0.00081923265414028[/C][/ROW]
[ROW][C]43[/C][C]1.48[/C][C]1.48082678880232[/C][C]-0.000826788802323741[/C][/ROW]
[ROW][C]44[/C][C]1.48[/C][C]1.48083434495051[/C][C]-0.000834344950507203[/C][/ROW]
[ROW][C]45[/C][C]1.48[/C][C]1.48007933955593[/C][C]-7.93395559263474e-05[/C][/ROW]
[ROW][C]46[/C][C]1.48[/C][C]1.48008689570411[/C][C]-8.68957041098091e-05[/C][/ROW]
[ROW][C]47[/C][C]1.48[/C][C]1.48009445185229[/C][C]-9.44518522932708e-05[/C][/ROW]
[ROW][C]48[/C][C]1.48[/C][C]1.48010200800048[/C][C]-0.000102008000476732[/C][/ROW]
[ROW][C]49[/C][C]1.48[/C][C]1.48010956414866[/C][C]-0.000109564148660194[/C][/ROW]
[ROW][C]50[/C][C]1.57[/C][C]1.57934564167724[/C][C]-0.00934564167723776[/C][/ROW]
[ROW][C]51[/C][C]1.58[/C][C]1.58011575936819[/C][C]-0.000115759368185527[/C][/ROW]
[ROW][C]52[/C][C]1.58[/C][C]1.58012331551637[/C][C]-0.000123315516368989[/C][/ROW]
[ROW][C]53[/C][C]1.58[/C][C]1.58013087166455[/C][C]-0.000130871664552451[/C][/ROW]
[ROW][C]54[/C][C]1.58[/C][C]1.58013842781274[/C][C]-0.000138427812735912[/C][/ROW]
[ROW][C]55[/C][C]1.59[/C][C]1.58014598396092[/C][C]0.00985401603908064[/C][/ROW]
[ROW][C]56[/C][C]1.6[/C][C]1.60208550180734[/C][C]-0.00208550180733934[/C][/ROW]
[ROW][C]57[/C][C]1.6[/C][C]1.60553556459025[/C][C]-0.00553556459025022[/C][/ROW]
[ROW][C]58[/C][C]1.61[/C][C]1.60898562737316[/C][C]0.00101437262683892[/C][/ROW]
[ROW][C]59[/C][C]1.61[/C][C]1.61319825169884[/C][C]-0.00319825169883627[/C][/ROW]
[ROW][C]60[/C][C]1.61[/C][C]1.61664831448175[/C][C]-0.00664831448174715[/C][/ROW]
[ROW][C]61[/C][C]1.62[/C][C]1.62009837726466[/C][C]-9.83772646580127e-05[/C][/ROW]
[ROW][C]62[/C][C]1.63[/C][C]1.62354844004757[/C][C]0.0064515599524309[/C][/ROW]
[ROW][C]63[/C][C]1.63[/C][C]1.62699850283048[/C][C]0.00300149716952003[/C][/ROW]
[ROW][C]64[/C][C]1.64[/C][C]1.62968600407063[/C][C]0.0103139959293735[/C][/ROW]
[ROW][C]65[/C][C]1.64[/C][C]1.6338986283963[/C][C]0.00610137160369828[/C][/ROW]
[ROW][C]66[/C][C]1.64[/C][C]1.63658612963645[/C][C]0.00341387036355172[/C][/ROW]
[ROW][C]67[/C][C]1.64[/C][C]1.64003619241936[/C][C]-3.61924193591546e-05[/C][/ROW]
[ROW][C]68[/C][C]1.64[/C][C]1.64424881674503[/C][C]-0.00424881674503435[/C][/ROW]
[ROW][C]69[/C][C]1.65[/C][C]1.64693631798518[/C][C]0.00306368201481911[/C][/ROW]
[ROW][C]70[/C][C]1.65[/C][C]1.65038638076809[/C][C]-0.000386380768091772[/C][/ROW]
[ROW][C]71[/C][C]1.65[/C][C]1.65383644355100[/C][C]-0.00383644355100264[/C][/ROW]
[ROW][C]72[/C][C]1.65[/C][C]1.65728650633391[/C][C]-0.00728650633391352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4550&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4550&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	1.43041817563778	-0.00041817563777877
2	1.43	1.43042573178597	-0.000425731785965638
3	1.43	1.43043328793415	-0.000433287934149580
4	1.43	1.43044084408233	-0.000440844082332907
5	1.43	1.43044840023052	-0.000448400230516382
6	1.43	1.4304559563787	-0.000455956378699815
7	1.43	1.43046351252688	-0.000463512526883277
8	1.43	1.43047106867507	-0.000471068675066738
9	1.43	1.42971606328049	0.000283936719514118
10	1.43	1.43048618097143	-0.000486180971433661
11	1.43	1.43049373711962	-0.000493737119617123
12	1.43	1.42973873172504	0.000261268274963733
13	1.43	1.43050884941598	-0.000508849415984046
14	1.43	1.43051640556417	-0.000516405564167508
15	1.43	1.43052396171235	-0.000523961712350969
16	1.43	1.43053151786053	-0.000531517860534431
17	1.43	1.43130163555148	-0.00130163555148221
18	1.43	1.43130919169967	-0.00130919169966567
19	1.44	1.43131674784785	0.00868325215215088
20	1.48	1.47989043585134	0.000109564148660195
21	1.48	1.47989799199952	0.000102008000476733
22	1.48	1.47914298660494	0.000857013395057588
23	1.48	1.47915054275313	0.000849457246874127
24	1.48	1.47915809890131	0.000841901098690665
25	1.48	1.47916565504949	0.000834344950507203
26	1.48	1.47917321119768	0.000826788802323742
27	1.48	1.47918076734586	0.00081923265414028
28	1.48	1.47918832349404	0.000811676505956818
29	1.48	1.47919587964223	0.000804120357773356
30	1.48	1.47920343579041	0.000796564209589895
31	1.48	1.47921099193859	0.000789008061406433
32	1.48	1.47998110962954	1.88903704586545e-05
33	1.48	1.47998866577772	1.13342222751928e-05
34	1.48	1.47999622192591	3.77807409173111e-06
35	1.48	1.48076633961686	-0.000766339616856048
36	1.48	1.48077389576504	-0.00077389576503951
37	1.48	1.48078145191322	-0.000781451913222971
38	1.48	1.48078900806141	-0.000789008061406433
39	1.48	1.48079656420959	-0.000796564209589895
40	1.48	1.48080412035777	-0.000804120357773356
41	1.48	1.48081167650596	-0.000811676505956818
42	1.48	1.48081923265414	-0.00081923265414028
43	1.48	1.48082678880232	-0.000826788802323741
44	1.48	1.48083434495051	-0.000834344950507203
45	1.48	1.48007933955593	-7.93395559263474e-05
46	1.48	1.48008689570411	-8.68957041098091e-05
47	1.48	1.48009445185229	-9.44518522932708e-05
48	1.48	1.48010200800048	-0.000102008000476732
49	1.48	1.48010956414866	-0.000109564148660194
50	1.57	1.57934564167724	-0.00934564167723776
51	1.58	1.58011575936819	-0.000115759368185527
52	1.58	1.58012331551637	-0.000123315516368989
53	1.58	1.58013087166455	-0.000130871664552451
54	1.58	1.58013842781274	-0.000138427812735912
55	1.59	1.58014598396092	0.00985401603908064
56	1.6	1.60208550180734	-0.00208550180733934
57	1.6	1.60553556459025	-0.00553556459025022
58	1.61	1.60898562737316	0.00101437262683892
59	1.61	1.61319825169884	-0.00319825169883627
60	1.61	1.61664831448175	-0.00664831448174715
61	1.62	1.62009837726466	-9.83772646580127e-05
62	1.63	1.62354844004757	0.0064515599524309
63	1.63	1.62699850283048	0.00300149716952003
64	1.64	1.62968600407063	0.0103139959293735
65	1.64	1.6338986283963	0.00610137160369828
66	1.64	1.63658612963645	0.00341387036355172
67	1.64	1.64003619241936	-3.61924193591546e-05
68	1.64	1.64424881674503	-0.00424881674503435
69	1.65	1.64693631798518	0.00306368201481911
70	1.65	1.65038638076809	-0.000386380768091772
71	1.65	1.65383644355100	-0.00383644355100264
72	1.65	1.65728650633391	-0.00728650633391352

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