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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 17 Nov 2007 11:22:13 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/17/t119532370472pnpgf3d75vzp8.htm/, Retrieved Wed, 08 May 2024 08:44:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5541, Retrieved Wed, 08 May 2024 08:44:42 +0000

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No (this computation is public)

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Estimated Impact

247

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

-       [Multiple Regression] [mult regr] [2007-11-17 18:22:13] [079615521100262cd8b5675a0217a3b1] [Current]

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95,90	96,92	95,86
96,06	96,06	96,02
96,31	96,59	96,34
96,34	96,67	96,84
96,49	97,27	96,73
96,22	96,38	96,34
96,53	96,47	96,60
96,50	96,05	96,64
96,77	96,76	97,20
96,66	96,51	97,50
96,58	96,55	96,99
96,63	95,97	97,08
97,06	97,00	97,55
97,73	97,46	98,42
98,01	97,90	98,78
97,76	98,42	97,49
97,49	98,54	96,99
97,77	99,00	97,16
97,96	98,94	97,29
98,23	99,02	97,80
98,51	100,07	98,12
98,19	98,72	98,03
98,37	98,73	98,11
98,31	98,04	98,07
98,60	99,08	98,21
98,97	99,22	98,48
99,11	99,57	98,83
99,64	100,44	99,20
100,03	100,84	99,88
99,98	100,75	99,71
100,32	100,49	100,03
100,44	99,98	100,60
100,51	99,96	100,85
101,00	99,76	101,96
100,88	100,11	101,40
100,55	99,79	100,81
100,83	100,29	100,66
101,51	101,12	101,55
102,16	102,65	102,23
102,39	102,71	102,90
102,54	103,39	102,68
102,85	102,80	103,41
103,47	102,07	104,62
103,57	102,15	104,93
103,69	101,21	105,88
103,50	101,27	105,18
103,47	101,86	104,54
103,45	101,65	104,58
103,48	101,94	104,34
103,93	102,62	104,66
103,89	102,71	104,73
104,40	103,39	105,44
104,79	104,51	105,72
104,77	104,09	105,68
105,13	104,29	105,90
105,26	104,57	105,97
104,96	105,39	105,21
104,75	105,15	104,75
105,01	106,13	104,89
105,15	105,46	105,26
105,20	106,47	104,84
105,77	106,62	105,47
105,78	106,52	105,40
106,26	108,04	105,73
106,13	107,15	105,72
106,12	107,32	105,63
106,57	107,76	105,97
106,44	107,26	105,92
106,54	107,89	106,32

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=5541&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=5541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5541&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
x[t] = + 0.80040639255172 + 0.379659939126742y[t] + 0.611032021039155z[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
x[t] =  +  0.80040639255172 +  0.379659939126742y[t] +  0.611032021039155z[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5541&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]x[t] =  +  0.80040639255172 +  0.379659939126742y[t] +  0.611032021039155z[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5541&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
x[t] = + 0.80040639255172 + 0.379659939126742y[t] + 0.611032021039155z[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)	0.80040639255172	0.653634	1.2245	0.225098	0.112549
y	0.379659939126742	0.015551	24.4133	0	0
z	0.611032021039155	0.015164	40.2942	0	0

\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) & 0.80040639255172 & 0.653634 & 1.2245 & 0.225098 & 0.112549 \tabularnewline
y & 0.379659939126742 & 0.015551 & 24.4133 & 0 & 0 \tabularnewline
z & 0.611032021039155 & 0.015164 & 40.2942 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5541&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]0.80040639255172[/C][C]0.653634[/C][C]1.2245[/C][C]0.225098[/C][C]0.112549[/C][/ROW]
[ROW][C]y[/C][C]0.379659939126742[/C][C]0.015551[/C][C]24.4133[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]z[/C][C]0.611032021039155[/C][C]0.015164[/C][C]40.2942[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5541&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5541&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)	0.80040639255172	0.653634	1.2245	0.225098	0.112549
y	0.379659939126742	0.015551	24.4133	0	0
z	0.611032021039155	0.015164	40.2942	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.998619183453074
R-squared	0.997240273560485
Adjusted R-squared	0.99715664548656
F-TEST (value)	11924.7069406202
F-TEST (DF numerator)	2
F-TEST (DF denominator)	66
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.186084686163247
Sum Squared Residuals	2.28541568801528

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.998619183453074 \tabularnewline
R-squared & 0.997240273560485 \tabularnewline
Adjusted R-squared & 0.99715664548656 \tabularnewline
F-TEST (value) & 11924.7069406202 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 66 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.186084686163247 \tabularnewline
Sum Squared Residuals & 2.28541568801528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5541&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.998619183453074[/C][/ROW]
[ROW][C]R-squared[/C][C]0.997240273560485[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.99715664548656[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]11924.7069406202[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]66[/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]0.186084686163247[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.28541568801528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5541&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5541&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	0.998619183453074
R-squared	0.997240273560485
Adjusted R-squared	0.99715664548656
F-TEST (value)	11924.7069406202
F-TEST (DF numerator)	2
F-TEST (DF denominator)	66
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.186084686163247
Sum Squared Residuals	2.28541568801528

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	95.9	96.1705772295294	-0.270577229529418
2	96.06	95.9418348052463	0.118165194753693
3	96.31	96.338584819716	-0.0285848197160194
4	96.34	96.6744736253657	-0.334473625365734
5	96.49	96.8350560665275	-0.345056066527479
6	96.22	96.2588562324994	-0.0388562324994034
7	96.53	96.451893952491	0.0781060475090164
8	96.5	96.3168780588993	0.183121941100678
9	96.77	96.9286145474612	-0.158614547461245
10	96.66	97.0170091689913	-0.357009168991304
11	96.58	96.7205692358264	-0.140569235826396
12	96.63	96.5553593530264	0.074640646973585
13	97.06	97.2335941402154	-0.173594140215355
14	97.73	97.9398355705177	-0.209835570517721
15	98.01	98.3268574713076	-0.316857471307586
16	97.76	97.736049332513	0.0239506674870234
17	97.49	97.4760925146886	0.0139074853113800
18	97.77	97.7546115302636	0.0153884697364248
19	97.96	97.811266096651	0.148733903348932
20	98.23	98.1532652225112	0.0767347774888395
21	98.51	98.7474384053268	-0.237438405326772
22	98.19	98.1799046056122	0.0100953943878467
23	98.37	98.2325837666865	0.137416233313453
24	98.31	97.9461771278475	0.363822872152472
25	98.6	98.4265679474848	0.173432052515173
26	98.97	98.6446989846431	0.325301015356855
27	99.11	98.9914411707012	0.118558829298797
28	99.64	99.547827165526	0.0921728344740407
29	100.03	100.115192915483	-0.085192915483279
30	99.98	99.9771480773852	0.00285192261478946
31	100.32	100.073966739945	0.246033260055199
32	100.44	100.228628422982	0.211371577017525
33	100.51	100.373793229460	0.136206770540282
34	101	100.976106784988	0.0238932150121592
35	100.88	100.766809831900	0.113190168099716
36	100.55	100.284809758967	0.265190241033377
37	100.83	100.382984925374	0.447015074625884
38	101.51	101.241921173574	0.268078826425846
39	102.16	102.238302654745	-0.0783026547447078
40	102.39	102.670473705189	-0.280473705188539
41	102.54	102.794215419166	-0.254215419166107
42	102.85	103.01626943044	-0.166269430439917
43	103.47	103.478466420335	-0.00846642033477176
44	103.57	103.698259141987	-0.128259141987061
45	103.69	103.921859219195	-0.231859219195105
46	103.5	103.516916400815	-0.0169164008153062
47	103.47	103.349855271435	0.120144728564973
48	103.45	103.29456796506	0.155432034940029
49	103.48	103.258021662357	0.221978337642672
50	103.93	103.711720667696	0.218279332303962
51	103.89	103.788662303690	0.101337696309808
52	104.4	104.480663797234	-0.0806637972341706
53	104.79	105.076971894947	-0.286971894947087
54	104.77	104.893073439672	-0.123073439672304
55	105.13	105.103432472126	0.0265675278737328
56	105.26	105.252509496554	0.00749050344552279
57	104.96	105.099446310649	-0.139446310648659
58	104.75	104.727253195580	0.0227468044197707
59	105.01	105.18486441887	-0.174864418869910
60	105.15	105.156574107439	-0.00657410743948088
61	105.2	105.283397197121	-0.083397197121049
62	105.77	105.725296361245	0.0447036387552654
63	105.78	105.644558125859	0.135441874140684
64	106.26	106.423281800275	-0.163281800274884
65	106.13	106.079274134242	0.0507258657583022
66	106.12	106.088823442000	0.0311765580002959
67	106.57	106.463624702369	0.106375297631199
68	106.44	106.243243131753	0.19675686824653
69	106.54	106.726841701819	-0.186841701818964

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 95.9 & 96.1705772295294 & -0.270577229529418 \tabularnewline
2 & 96.06 & 95.9418348052463 & 0.118165194753693 \tabularnewline
3 & 96.31 & 96.338584819716 & -0.0285848197160194 \tabularnewline
4 & 96.34 & 96.6744736253657 & -0.334473625365734 \tabularnewline
5 & 96.49 & 96.8350560665275 & -0.345056066527479 \tabularnewline
6 & 96.22 & 96.2588562324994 & -0.0388562324994034 \tabularnewline
7 & 96.53 & 96.451893952491 & 0.0781060475090164 \tabularnewline
8 & 96.5 & 96.3168780588993 & 0.183121941100678 \tabularnewline
9 & 96.77 & 96.9286145474612 & -0.158614547461245 \tabularnewline
10 & 96.66 & 97.0170091689913 & -0.357009168991304 \tabularnewline
11 & 96.58 & 96.7205692358264 & -0.140569235826396 \tabularnewline
12 & 96.63 & 96.5553593530264 & 0.074640646973585 \tabularnewline
13 & 97.06 & 97.2335941402154 & -0.173594140215355 \tabularnewline
14 & 97.73 & 97.9398355705177 & -0.209835570517721 \tabularnewline
15 & 98.01 & 98.3268574713076 & -0.316857471307586 \tabularnewline
16 & 97.76 & 97.736049332513 & 0.0239506674870234 \tabularnewline
17 & 97.49 & 97.4760925146886 & 0.0139074853113800 \tabularnewline
18 & 97.77 & 97.7546115302636 & 0.0153884697364248 \tabularnewline
19 & 97.96 & 97.811266096651 & 0.148733903348932 \tabularnewline
20 & 98.23 & 98.1532652225112 & 0.0767347774888395 \tabularnewline
21 & 98.51 & 98.7474384053268 & -0.237438405326772 \tabularnewline
22 & 98.19 & 98.1799046056122 & 0.0100953943878467 \tabularnewline
23 & 98.37 & 98.2325837666865 & 0.137416233313453 \tabularnewline
24 & 98.31 & 97.9461771278475 & 0.363822872152472 \tabularnewline
25 & 98.6 & 98.4265679474848 & 0.173432052515173 \tabularnewline
26 & 98.97 & 98.6446989846431 & 0.325301015356855 \tabularnewline
27 & 99.11 & 98.9914411707012 & 0.118558829298797 \tabularnewline
28 & 99.64 & 99.547827165526 & 0.0921728344740407 \tabularnewline
29 & 100.03 & 100.115192915483 & -0.085192915483279 \tabularnewline
30 & 99.98 & 99.9771480773852 & 0.00285192261478946 \tabularnewline
31 & 100.32 & 100.073966739945 & 0.246033260055199 \tabularnewline
32 & 100.44 & 100.228628422982 & 0.211371577017525 \tabularnewline
33 & 100.51 & 100.373793229460 & 0.136206770540282 \tabularnewline
34 & 101 & 100.976106784988 & 0.0238932150121592 \tabularnewline
35 & 100.88 & 100.766809831900 & 0.113190168099716 \tabularnewline
36 & 100.55 & 100.284809758967 & 0.265190241033377 \tabularnewline
37 & 100.83 & 100.382984925374 & 0.447015074625884 \tabularnewline
38 & 101.51 & 101.241921173574 & 0.268078826425846 \tabularnewline
39 & 102.16 & 102.238302654745 & -0.0783026547447078 \tabularnewline
40 & 102.39 & 102.670473705189 & -0.280473705188539 \tabularnewline
41 & 102.54 & 102.794215419166 & -0.254215419166107 \tabularnewline
42 & 102.85 & 103.01626943044 & -0.166269430439917 \tabularnewline
43 & 103.47 & 103.478466420335 & -0.00846642033477176 \tabularnewline
44 & 103.57 & 103.698259141987 & -0.128259141987061 \tabularnewline
45 & 103.69 & 103.921859219195 & -0.231859219195105 \tabularnewline
46 & 103.5 & 103.516916400815 & -0.0169164008153062 \tabularnewline
47 & 103.47 & 103.349855271435 & 0.120144728564973 \tabularnewline
48 & 103.45 & 103.29456796506 & 0.155432034940029 \tabularnewline
49 & 103.48 & 103.258021662357 & 0.221978337642672 \tabularnewline
50 & 103.93 & 103.711720667696 & 0.218279332303962 \tabularnewline
51 & 103.89 & 103.788662303690 & 0.101337696309808 \tabularnewline
52 & 104.4 & 104.480663797234 & -0.0806637972341706 \tabularnewline
53 & 104.79 & 105.076971894947 & -0.286971894947087 \tabularnewline
54 & 104.77 & 104.893073439672 & -0.123073439672304 \tabularnewline
55 & 105.13 & 105.103432472126 & 0.0265675278737328 \tabularnewline
56 & 105.26 & 105.252509496554 & 0.00749050344552279 \tabularnewline
57 & 104.96 & 105.099446310649 & -0.139446310648659 \tabularnewline
58 & 104.75 & 104.727253195580 & 0.0227468044197707 \tabularnewline
59 & 105.01 & 105.18486441887 & -0.174864418869910 \tabularnewline
60 & 105.15 & 105.156574107439 & -0.00657410743948088 \tabularnewline
61 & 105.2 & 105.283397197121 & -0.083397197121049 \tabularnewline
62 & 105.77 & 105.725296361245 & 0.0447036387552654 \tabularnewline
63 & 105.78 & 105.644558125859 & 0.135441874140684 \tabularnewline
64 & 106.26 & 106.423281800275 & -0.163281800274884 \tabularnewline
65 & 106.13 & 106.079274134242 & 0.0507258657583022 \tabularnewline
66 & 106.12 & 106.088823442000 & 0.0311765580002959 \tabularnewline
67 & 106.57 & 106.463624702369 & 0.106375297631199 \tabularnewline
68 & 106.44 & 106.243243131753 & 0.19675686824653 \tabularnewline
69 & 106.54 & 106.726841701819 & -0.186841701818964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5541&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]95.9[/C][C]96.1705772295294[/C][C]-0.270577229529418[/C][/ROW]
[ROW][C]2[/C][C]96.06[/C][C]95.9418348052463[/C][C]0.118165194753693[/C][/ROW]
[ROW][C]3[/C][C]96.31[/C][C]96.338584819716[/C][C]-0.0285848197160194[/C][/ROW]
[ROW][C]4[/C][C]96.34[/C][C]96.6744736253657[/C][C]-0.334473625365734[/C][/ROW]
[ROW][C]5[/C][C]96.49[/C][C]96.8350560665275[/C][C]-0.345056066527479[/C][/ROW]
[ROW][C]6[/C][C]96.22[/C][C]96.2588562324994[/C][C]-0.0388562324994034[/C][/ROW]
[ROW][C]7[/C][C]96.53[/C][C]96.451893952491[/C][C]0.0781060475090164[/C][/ROW]
[ROW][C]8[/C][C]96.5[/C][C]96.3168780588993[/C][C]0.183121941100678[/C][/ROW]
[ROW][C]9[/C][C]96.77[/C][C]96.9286145474612[/C][C]-0.158614547461245[/C][/ROW]
[ROW][C]10[/C][C]96.66[/C][C]97.0170091689913[/C][C]-0.357009168991304[/C][/ROW]
[ROW][C]11[/C][C]96.58[/C][C]96.7205692358264[/C][C]-0.140569235826396[/C][/ROW]
[ROW][C]12[/C][C]96.63[/C][C]96.5553593530264[/C][C]0.074640646973585[/C][/ROW]
[ROW][C]13[/C][C]97.06[/C][C]97.2335941402154[/C][C]-0.173594140215355[/C][/ROW]
[ROW][C]14[/C][C]97.73[/C][C]97.9398355705177[/C][C]-0.209835570517721[/C][/ROW]
[ROW][C]15[/C][C]98.01[/C][C]98.3268574713076[/C][C]-0.316857471307586[/C][/ROW]
[ROW][C]16[/C][C]97.76[/C][C]97.736049332513[/C][C]0.0239506674870234[/C][/ROW]
[ROW][C]17[/C][C]97.49[/C][C]97.4760925146886[/C][C]0.0139074853113800[/C][/ROW]
[ROW][C]18[/C][C]97.77[/C][C]97.7546115302636[/C][C]0.0153884697364248[/C][/ROW]
[ROW][C]19[/C][C]97.96[/C][C]97.811266096651[/C][C]0.148733903348932[/C][/ROW]
[ROW][C]20[/C][C]98.23[/C][C]98.1532652225112[/C][C]0.0767347774888395[/C][/ROW]
[ROW][C]21[/C][C]98.51[/C][C]98.7474384053268[/C][C]-0.237438405326772[/C][/ROW]
[ROW][C]22[/C][C]98.19[/C][C]98.1799046056122[/C][C]0.0100953943878467[/C][/ROW]
[ROW][C]23[/C][C]98.37[/C][C]98.2325837666865[/C][C]0.137416233313453[/C][/ROW]
[ROW][C]24[/C][C]98.31[/C][C]97.9461771278475[/C][C]0.363822872152472[/C][/ROW]
[ROW][C]25[/C][C]98.6[/C][C]98.4265679474848[/C][C]0.173432052515173[/C][/ROW]
[ROW][C]26[/C][C]98.97[/C][C]98.6446989846431[/C][C]0.325301015356855[/C][/ROW]
[ROW][C]27[/C][C]99.11[/C][C]98.9914411707012[/C][C]0.118558829298797[/C][/ROW]
[ROW][C]28[/C][C]99.64[/C][C]99.547827165526[/C][C]0.0921728344740407[/C][/ROW]
[ROW][C]29[/C][C]100.03[/C][C]100.115192915483[/C][C]-0.085192915483279[/C][/ROW]
[ROW][C]30[/C][C]99.98[/C][C]99.9771480773852[/C][C]0.00285192261478946[/C][/ROW]
[ROW][C]31[/C][C]100.32[/C][C]100.073966739945[/C][C]0.246033260055199[/C][/ROW]
[ROW][C]32[/C][C]100.44[/C][C]100.228628422982[/C][C]0.211371577017525[/C][/ROW]
[ROW][C]33[/C][C]100.51[/C][C]100.373793229460[/C][C]0.136206770540282[/C][/ROW]
[ROW][C]34[/C][C]101[/C][C]100.976106784988[/C][C]0.0238932150121592[/C][/ROW]
[ROW][C]35[/C][C]100.88[/C][C]100.766809831900[/C][C]0.113190168099716[/C][/ROW]
[ROW][C]36[/C][C]100.55[/C][C]100.284809758967[/C][C]0.265190241033377[/C][/ROW]
[ROW][C]37[/C][C]100.83[/C][C]100.382984925374[/C][C]0.447015074625884[/C][/ROW]
[ROW][C]38[/C][C]101.51[/C][C]101.241921173574[/C][C]0.268078826425846[/C][/ROW]
[ROW][C]39[/C][C]102.16[/C][C]102.238302654745[/C][C]-0.0783026547447078[/C][/ROW]
[ROW][C]40[/C][C]102.39[/C][C]102.670473705189[/C][C]-0.280473705188539[/C][/ROW]
[ROW][C]41[/C][C]102.54[/C][C]102.794215419166[/C][C]-0.254215419166107[/C][/ROW]
[ROW][C]42[/C][C]102.85[/C][C]103.01626943044[/C][C]-0.166269430439917[/C][/ROW]
[ROW][C]43[/C][C]103.47[/C][C]103.478466420335[/C][C]-0.00846642033477176[/C][/ROW]
[ROW][C]44[/C][C]103.57[/C][C]103.698259141987[/C][C]-0.128259141987061[/C][/ROW]
[ROW][C]45[/C][C]103.69[/C][C]103.921859219195[/C][C]-0.231859219195105[/C][/ROW]
[ROW][C]46[/C][C]103.5[/C][C]103.516916400815[/C][C]-0.0169164008153062[/C][/ROW]
[ROW][C]47[/C][C]103.47[/C][C]103.349855271435[/C][C]0.120144728564973[/C][/ROW]
[ROW][C]48[/C][C]103.45[/C][C]103.29456796506[/C][C]0.155432034940029[/C][/ROW]
[ROW][C]49[/C][C]103.48[/C][C]103.258021662357[/C][C]0.221978337642672[/C][/ROW]
[ROW][C]50[/C][C]103.93[/C][C]103.711720667696[/C][C]0.218279332303962[/C][/ROW]
[ROW][C]51[/C][C]103.89[/C][C]103.788662303690[/C][C]0.101337696309808[/C][/ROW]
[ROW][C]52[/C][C]104.4[/C][C]104.480663797234[/C][C]-0.0806637972341706[/C][/ROW]
[ROW][C]53[/C][C]104.79[/C][C]105.076971894947[/C][C]-0.286971894947087[/C][/ROW]
[ROW][C]54[/C][C]104.77[/C][C]104.893073439672[/C][C]-0.123073439672304[/C][/ROW]
[ROW][C]55[/C][C]105.13[/C][C]105.103432472126[/C][C]0.0265675278737328[/C][/ROW]
[ROW][C]56[/C][C]105.26[/C][C]105.252509496554[/C][C]0.00749050344552279[/C][/ROW]
[ROW][C]57[/C][C]104.96[/C][C]105.099446310649[/C][C]-0.139446310648659[/C][/ROW]
[ROW][C]58[/C][C]104.75[/C][C]104.727253195580[/C][C]0.0227468044197707[/C][/ROW]
[ROW][C]59[/C][C]105.01[/C][C]105.18486441887[/C][C]-0.174864418869910[/C][/ROW]
[ROW][C]60[/C][C]105.15[/C][C]105.156574107439[/C][C]-0.00657410743948088[/C][/ROW]
[ROW][C]61[/C][C]105.2[/C][C]105.283397197121[/C][C]-0.083397197121049[/C][/ROW]
[ROW][C]62[/C][C]105.77[/C][C]105.725296361245[/C][C]0.0447036387552654[/C][/ROW]
[ROW][C]63[/C][C]105.78[/C][C]105.644558125859[/C][C]0.135441874140684[/C][/ROW]
[ROW][C]64[/C][C]106.26[/C][C]106.423281800275[/C][C]-0.163281800274884[/C][/ROW]
[ROW][C]65[/C][C]106.13[/C][C]106.079274134242[/C][C]0.0507258657583022[/C][/ROW]
[ROW][C]66[/C][C]106.12[/C][C]106.088823442000[/C][C]0.0311765580002959[/C][/ROW]
[ROW][C]67[/C][C]106.57[/C][C]106.463624702369[/C][C]0.106375297631199[/C][/ROW]
[ROW][C]68[/C][C]106.44[/C][C]106.243243131753[/C][C]0.19675686824653[/C][/ROW]
[ROW][C]69[/C][C]106.54[/C][C]106.726841701819[/C][C]-0.186841701818964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5541&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5541&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	95.9	96.1705772295294	-0.270577229529418
2	96.06	95.9418348052463	0.118165194753693
3	96.31	96.338584819716	-0.0285848197160194
4	96.34	96.6744736253657	-0.334473625365734
5	96.49	96.8350560665275	-0.345056066527479
6	96.22	96.2588562324994	-0.0388562324994034
7	96.53	96.451893952491	0.0781060475090164
8	96.5	96.3168780588993	0.183121941100678
9	96.77	96.9286145474612	-0.158614547461245
10	96.66	97.0170091689913	-0.357009168991304
11	96.58	96.7205692358264	-0.140569235826396
12	96.63	96.5553593530264	0.074640646973585
13	97.06	97.2335941402154	-0.173594140215355
14	97.73	97.9398355705177	-0.209835570517721
15	98.01	98.3268574713076	-0.316857471307586
16	97.76	97.736049332513	0.0239506674870234
17	97.49	97.4760925146886	0.0139074853113800
18	97.77	97.7546115302636	0.0153884697364248
19	97.96	97.811266096651	0.148733903348932
20	98.23	98.1532652225112	0.0767347774888395
21	98.51	98.7474384053268	-0.237438405326772
22	98.19	98.1799046056122	0.0100953943878467
23	98.37	98.2325837666865	0.137416233313453
24	98.31	97.9461771278475	0.363822872152472
25	98.6	98.4265679474848	0.173432052515173
26	98.97	98.6446989846431	0.325301015356855
27	99.11	98.9914411707012	0.118558829298797
28	99.64	99.547827165526	0.0921728344740407
29	100.03	100.115192915483	-0.085192915483279
30	99.98	99.9771480773852	0.00285192261478946
31	100.32	100.073966739945	0.246033260055199
32	100.44	100.228628422982	0.211371577017525
33	100.51	100.373793229460	0.136206770540282
34	101	100.976106784988	0.0238932150121592
35	100.88	100.766809831900	0.113190168099716
36	100.55	100.284809758967	0.265190241033377
37	100.83	100.382984925374	0.447015074625884
38	101.51	101.241921173574	0.268078826425846
39	102.16	102.238302654745	-0.0783026547447078
40	102.39	102.670473705189	-0.280473705188539
41	102.54	102.794215419166	-0.254215419166107
42	102.85	103.01626943044	-0.166269430439917
43	103.47	103.478466420335	-0.00846642033477176
44	103.57	103.698259141987	-0.128259141987061
45	103.69	103.921859219195	-0.231859219195105
46	103.5	103.516916400815	-0.0169164008153062
47	103.47	103.349855271435	0.120144728564973
48	103.45	103.29456796506	0.155432034940029
49	103.48	103.258021662357	0.221978337642672
50	103.93	103.711720667696	0.218279332303962
51	103.89	103.788662303690	0.101337696309808
52	104.4	104.480663797234	-0.0806637972341706
53	104.79	105.076971894947	-0.286971894947087
54	104.77	104.893073439672	-0.123073439672304
55	105.13	105.103432472126	0.0265675278737328
56	105.26	105.252509496554	0.00749050344552279
57	104.96	105.099446310649	-0.139446310648659
58	104.75	104.727253195580	0.0227468044197707
59	105.01	105.18486441887	-0.174864418869910
60	105.15	105.156574107439	-0.00657410743948088
61	105.2	105.283397197121	-0.083397197121049
62	105.77	105.725296361245	0.0447036387552654
63	105.78	105.644558125859	0.135441874140684
64	106.26	106.423281800275	-0.163281800274884
65	106.13	106.079274134242	0.0507258657583022
66	106.12	106.088823442000	0.0311765580002959
67	106.57	106.463624702369	0.106375297631199
68	106.44	106.243243131753	0.19675686824653
69	106.54	106.726841701819	-0.186841701818964

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 = 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