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*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 21 Dec 2008 07:45:31 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229870785almhnvrl9pngmy4.htm/, Retrieved Fri, 09 May 2025 16:25:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35615, Retrieved Fri, 09 May 2025 16:25:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

341

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Multiple Regression] [The Seatbelt Law ...] [2008-11-15 12:00:57] [93834488277b53a4510bfd06084ae13b]
-   PD    [Multiple Regression] [] [2008-11-15 18:50:27] [93834488277b53a4510bfd06084ae13b]
-    D        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:45:31] [07b7cf1321bc38017c2c7efcf91ca696] [Current]
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:09:11] [85841a4a203c2f9589565c024425a91b] 
- RMPD            [ARIMA Forecasting] [Paper - Arima for...] [2008-12-21 19:50:13] [85841a4a203c2f9589565c024425a91b] 
-   PD              [ARIMA Forecasting] [arima forecast gas] [2008-12-22 17:09:25] [44a98561a4b3e6ab8cd5a857b48b0914] 
- RMPD            [ARIMA Forecasting] [Paper - Arima for...] [2008-12-21 20:01:58] [85841a4a203c2f9589565c024425a91b] 
- R PD            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:36:38] [85841a4a203c2f9589565c024425a91b] 
- R  D            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:38:40] [85841a4a203c2f9589565c024425a91b] 
- R PD            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:39:51] [85841a4a203c2f9589565c024425a91b] 
-   PD              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:06:36] [85841a4a203c2f9589565c024425a91b] 
-    D              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:08:28] [85841a4a203c2f9589565c024425a91b] 
-   PD              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:11:46] [85841a4a203c2f9589565c024425a91b] 
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:49:26] [85841a4a203c2f9589565c024425a91b] 
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:50:56] [85841a4a203c2f9589565c024425a91b] 

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Dataseries X:

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Histogram

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20.7246301	0
21.44580352	0
22.09413114	0
21.53321848	0
23.3470789	0
23.5656163	0
26.42117166	0
25.21193138	0
26.43574082	0
29.33500366	0
29.40056488	0
33.05013946	0
28.38072368	0
26.0059506	0
29.31314992	0
30.36212944	0
35.74543406	0
36.15337054	0
34.20838768	0
37.90895432	0
38.70297354	0
42.11944156	0
42.16314904	0
39.79566054	0
37.36261082	0
38.3533137	0
42.60022384	0
41.24529196	0
42.15586446	0
46.94183352	0
47.42990038	0
47.0583868	0
50.18347162	0
50.12519498	0
43.22669772	0
40.04333626	0
40.37114236	0
42.2141411	0
36.99838182	0
39.74466848	0
42.68035422	0
46.2935059	0
46.97097184	0
48.72655562	0
52.36884562	0
50.05234918	0
54.03701444	0
57.78128856	0
64.71620872	0
63.4122689	0
64.3592643	0
66.02743312	0
72.13919574	0
76.60464328	0
86.97060062	0
93.48301514	0
95.58825876	0
81.88596378	1
70.5511573	1
50.38015528	1
36.24807008	1

Summary of computational 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 computational 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=35615&T=0

[TABLE]
[ROW][C]Summary of computational 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=35615&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35615&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 computational 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
Olie[t] = + 43.7138699824561 + 16.0524666275439Dumivariabele[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Olie[t] =  +  43.7138699824561 +  16.0524666275439Dumivariabele[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35615&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Olie[t] =  +  43.7138699824561 +  16.0524666275439Dumivariabele[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35615&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35615&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
Olie[t] = + 43.7138699824561 + 16.0524666275439Dumivariabele[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)	43.7138699824561	2.324501	18.8057	0	0
Dumivariabele	16.0524666275439	9.077467	1.7684	0.082166	0.041083

\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) & 43.7138699824561 & 2.324501 & 18.8057 & 0 & 0 \tabularnewline
Dumivariabele & 16.0524666275439 & 9.077467 & 1.7684 & 0.082166 & 0.041083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35615&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]43.7138699824561[/C][C]2.324501[/C][C]18.8057[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Dumivariabele[/C][C]16.0524666275439[/C][C]9.077467[/C][C]1.7684[/C][C]0.082166[/C][C]0.041083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35615&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35615&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)	43.7138699824561	2.324501	18.8057	0	0
Dumivariabele	16.0524666275439	9.077467	1.7684	0.082166	0.041083

Multiple Linear Regression - Regression Statistics
Multiple R	0.224355255896349
R-squared	0.0503352808483162
Adjusted R-squared	0.0342392686593046
F-TEST (value)	3.12718953348451
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	0.0821659618270217
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.549598283773
Sum Squared Residuals	18171.3155953867

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.224355255896349 \tabularnewline
R-squared & 0.0503352808483162 \tabularnewline
Adjusted R-squared & 0.0342392686593046 \tabularnewline
F-TEST (value) & 3.12718953348451 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 0.0821659618270217 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 17.549598283773 \tabularnewline
Sum Squared Residuals & 18171.3155953867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35615&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.224355255896349[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0503352808483162[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.0342392686593046[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.12718953348451[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]0.0821659618270217[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]17.549598283773[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]18171.3155953867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35615&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35615&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	0.224355255896349
R-squared	0.0503352808483162
Adjusted R-squared	0.0342392686593046
F-TEST (value)	3.12718953348451
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	0.0821659618270217
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.549598283773
Sum Squared Residuals	18171.3155953867

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	20.7246301	43.7138699824561	-22.9892398824561
2	21.44580352	43.7138699824561	-22.2680664624561
3	22.09413114	43.7138699824561	-21.6197388424561
4	21.53321848	43.7138699824561	-22.1806515024561
5	23.3470789	43.7138699824561	-20.3667910824561
6	23.5656163	43.7138699824561	-20.1482536824561
7	26.42117166	43.7138699824561	-17.2926983224561
8	25.21193138	43.7138699824561	-18.5019386024561
9	26.43574082	43.7138699824561	-17.2781291624561
10	29.33500366	43.7138699824561	-14.3788663224561
11	29.40056488	43.7138699824561	-14.3133051024561
12	33.05013946	43.7138699824561	-10.6637305224561
13	28.38072368	43.7138699824561	-15.3331463024561
14	26.0059506	43.7138699824561	-17.7079193824561
15	29.31314992	43.7138699824561	-14.4007200624561
16	30.36212944	43.7138699824561	-13.3517405424561
17	35.74543406	43.7138699824561	-7.96843592245614
18	36.15337054	43.7138699824561	-7.56049944245614
19	34.20838768	43.7138699824561	-9.50548230245614
20	37.90895432	43.7138699824561	-5.80491566245614
21	38.70297354	43.7138699824561	-5.01089644245614
22	42.11944156	43.7138699824561	-1.59442842245614
23	42.16314904	43.7138699824561	-1.55072094245614
24	39.79566054	43.7138699824561	-3.91820944245614
25	37.36261082	43.7138699824561	-6.35125916245614
26	38.3533137	43.7138699824561	-5.36055628245614
27	42.60022384	43.7138699824561	-1.11364614245614
28	41.24529196	43.7138699824561	-2.46857802245614
29	42.15586446	43.7138699824561	-1.55800552245614
30	46.94183352	43.7138699824561	3.22796353754386
31	47.42990038	43.7138699824561	3.71603039754386
32	47.0583868	43.7138699824561	3.34451681754386
33	50.18347162	43.7138699824561	6.46960163754386
34	50.12519498	43.7138699824561	6.41132499754386
35	43.22669772	43.7138699824561	-0.487172262456142
36	40.04333626	43.7138699824561	-3.67053372245614
37	40.37114236	43.7138699824561	-3.34272762245614
38	42.2141411	43.7138699824561	-1.49972888245614
39	36.99838182	43.7138699824561	-6.71548816245614
40	39.74466848	43.7138699824561	-3.96920150245614
41	42.68035422	43.7138699824561	-1.03351576245614
42	46.2935059	43.7138699824561	2.57963591754386
43	46.97097184	43.7138699824561	3.25710185754386
44	48.72655562	43.7138699824561	5.01268563754386
45	52.36884562	43.7138699824561	8.65497563754386
46	50.05234918	43.7138699824561	6.33847919754386
47	54.03701444	43.7138699824561	10.3231444575439
48	57.78128856	43.7138699824561	14.0674185775439
49	64.71620872	43.7138699824561	21.0023387375439
50	63.4122689	43.7138699824561	19.6983989175439
51	64.3592643	43.7138699824561	20.6453943175439
52	66.02743312	43.7138699824561	22.3135631375439
53	72.13919574	43.7138699824561	28.4253257575439
54	76.60464328	43.7138699824561	32.8907732975439
55	86.97060062	43.7138699824561	43.2567306375439
56	93.48301514	43.7138699824561	49.7691451575439
57	95.58825876	43.7138699824561	51.8743887775439
58	81.88596378	59.76633661	22.11962717
59	70.5511573	59.76633661	10.78482069
60	50.38015528	59.76633661	-9.38618133
61	36.24807008	59.76633661	-23.51826653

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 20.7246301 & 43.7138699824561 & -22.9892398824561 \tabularnewline
2 & 21.44580352 & 43.7138699824561 & -22.2680664624561 \tabularnewline
3 & 22.09413114 & 43.7138699824561 & -21.6197388424561 \tabularnewline
4 & 21.53321848 & 43.7138699824561 & -22.1806515024561 \tabularnewline
5 & 23.3470789 & 43.7138699824561 & -20.3667910824561 \tabularnewline
6 & 23.5656163 & 43.7138699824561 & -20.1482536824561 \tabularnewline
7 & 26.42117166 & 43.7138699824561 & -17.2926983224561 \tabularnewline
8 & 25.21193138 & 43.7138699824561 & -18.5019386024561 \tabularnewline
9 & 26.43574082 & 43.7138699824561 & -17.2781291624561 \tabularnewline
10 & 29.33500366 & 43.7138699824561 & -14.3788663224561 \tabularnewline
11 & 29.40056488 & 43.7138699824561 & -14.3133051024561 \tabularnewline
12 & 33.05013946 & 43.7138699824561 & -10.6637305224561 \tabularnewline
13 & 28.38072368 & 43.7138699824561 & -15.3331463024561 \tabularnewline
14 & 26.0059506 & 43.7138699824561 & -17.7079193824561 \tabularnewline
15 & 29.31314992 & 43.7138699824561 & -14.4007200624561 \tabularnewline
16 & 30.36212944 & 43.7138699824561 & -13.3517405424561 \tabularnewline
17 & 35.74543406 & 43.7138699824561 & -7.96843592245614 \tabularnewline
18 & 36.15337054 & 43.7138699824561 & -7.56049944245614 \tabularnewline
19 & 34.20838768 & 43.7138699824561 & -9.50548230245614 \tabularnewline
20 & 37.90895432 & 43.7138699824561 & -5.80491566245614 \tabularnewline
21 & 38.70297354 & 43.7138699824561 & -5.01089644245614 \tabularnewline
22 & 42.11944156 & 43.7138699824561 & -1.59442842245614 \tabularnewline
23 & 42.16314904 & 43.7138699824561 & -1.55072094245614 \tabularnewline
24 & 39.79566054 & 43.7138699824561 & -3.91820944245614 \tabularnewline
25 & 37.36261082 & 43.7138699824561 & -6.35125916245614 \tabularnewline
26 & 38.3533137 & 43.7138699824561 & -5.36055628245614 \tabularnewline
27 & 42.60022384 & 43.7138699824561 & -1.11364614245614 \tabularnewline
28 & 41.24529196 & 43.7138699824561 & -2.46857802245614 \tabularnewline
29 & 42.15586446 & 43.7138699824561 & -1.55800552245614 \tabularnewline
30 & 46.94183352 & 43.7138699824561 & 3.22796353754386 \tabularnewline
31 & 47.42990038 & 43.7138699824561 & 3.71603039754386 \tabularnewline
32 & 47.0583868 & 43.7138699824561 & 3.34451681754386 \tabularnewline
33 & 50.18347162 & 43.7138699824561 & 6.46960163754386 \tabularnewline
34 & 50.12519498 & 43.7138699824561 & 6.41132499754386 \tabularnewline
35 & 43.22669772 & 43.7138699824561 & -0.487172262456142 \tabularnewline
36 & 40.04333626 & 43.7138699824561 & -3.67053372245614 \tabularnewline
37 & 40.37114236 & 43.7138699824561 & -3.34272762245614 \tabularnewline
38 & 42.2141411 & 43.7138699824561 & -1.49972888245614 \tabularnewline
39 & 36.99838182 & 43.7138699824561 & -6.71548816245614 \tabularnewline
40 & 39.74466848 & 43.7138699824561 & -3.96920150245614 \tabularnewline
41 & 42.68035422 & 43.7138699824561 & -1.03351576245614 \tabularnewline
42 & 46.2935059 & 43.7138699824561 & 2.57963591754386 \tabularnewline
43 & 46.97097184 & 43.7138699824561 & 3.25710185754386 \tabularnewline
44 & 48.72655562 & 43.7138699824561 & 5.01268563754386 \tabularnewline
45 & 52.36884562 & 43.7138699824561 & 8.65497563754386 \tabularnewline
46 & 50.05234918 & 43.7138699824561 & 6.33847919754386 \tabularnewline
47 & 54.03701444 & 43.7138699824561 & 10.3231444575439 \tabularnewline
48 & 57.78128856 & 43.7138699824561 & 14.0674185775439 \tabularnewline
49 & 64.71620872 & 43.7138699824561 & 21.0023387375439 \tabularnewline
50 & 63.4122689 & 43.7138699824561 & 19.6983989175439 \tabularnewline
51 & 64.3592643 & 43.7138699824561 & 20.6453943175439 \tabularnewline
52 & 66.02743312 & 43.7138699824561 & 22.3135631375439 \tabularnewline
53 & 72.13919574 & 43.7138699824561 & 28.4253257575439 \tabularnewline
54 & 76.60464328 & 43.7138699824561 & 32.8907732975439 \tabularnewline
55 & 86.97060062 & 43.7138699824561 & 43.2567306375439 \tabularnewline
56 & 93.48301514 & 43.7138699824561 & 49.7691451575439 \tabularnewline
57 & 95.58825876 & 43.7138699824561 & 51.8743887775439 \tabularnewline
58 & 81.88596378 & 59.76633661 & 22.11962717 \tabularnewline
59 & 70.5511573 & 59.76633661 & 10.78482069 \tabularnewline
60 & 50.38015528 & 59.76633661 & -9.38618133 \tabularnewline
61 & 36.24807008 & 59.76633661 & -23.51826653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35615&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]20.7246301[/C][C]43.7138699824561[/C][C]-22.9892398824561[/C][/ROW]
[ROW][C]2[/C][C]21.44580352[/C][C]43.7138699824561[/C][C]-22.2680664624561[/C][/ROW]
[ROW][C]3[/C][C]22.09413114[/C][C]43.7138699824561[/C][C]-21.6197388424561[/C][/ROW]
[ROW][C]4[/C][C]21.53321848[/C][C]43.7138699824561[/C][C]-22.1806515024561[/C][/ROW]
[ROW][C]5[/C][C]23.3470789[/C][C]43.7138699824561[/C][C]-20.3667910824561[/C][/ROW]
[ROW][C]6[/C][C]23.5656163[/C][C]43.7138699824561[/C][C]-20.1482536824561[/C][/ROW]
[ROW][C]7[/C][C]26.42117166[/C][C]43.7138699824561[/C][C]-17.2926983224561[/C][/ROW]
[ROW][C]8[/C][C]25.21193138[/C][C]43.7138699824561[/C][C]-18.5019386024561[/C][/ROW]
[ROW][C]9[/C][C]26.43574082[/C][C]43.7138699824561[/C][C]-17.2781291624561[/C][/ROW]
[ROW][C]10[/C][C]29.33500366[/C][C]43.7138699824561[/C][C]-14.3788663224561[/C][/ROW]
[ROW][C]11[/C][C]29.40056488[/C][C]43.7138699824561[/C][C]-14.3133051024561[/C][/ROW]
[ROW][C]12[/C][C]33.05013946[/C][C]43.7138699824561[/C][C]-10.6637305224561[/C][/ROW]
[ROW][C]13[/C][C]28.38072368[/C][C]43.7138699824561[/C][C]-15.3331463024561[/C][/ROW]
[ROW][C]14[/C][C]26.0059506[/C][C]43.7138699824561[/C][C]-17.7079193824561[/C][/ROW]
[ROW][C]15[/C][C]29.31314992[/C][C]43.7138699824561[/C][C]-14.4007200624561[/C][/ROW]
[ROW][C]16[/C][C]30.36212944[/C][C]43.7138699824561[/C][C]-13.3517405424561[/C][/ROW]
[ROW][C]17[/C][C]35.74543406[/C][C]43.7138699824561[/C][C]-7.96843592245614[/C][/ROW]
[ROW][C]18[/C][C]36.15337054[/C][C]43.7138699824561[/C][C]-7.56049944245614[/C][/ROW]
[ROW][C]19[/C][C]34.20838768[/C][C]43.7138699824561[/C][C]-9.50548230245614[/C][/ROW]
[ROW][C]20[/C][C]37.90895432[/C][C]43.7138699824561[/C][C]-5.80491566245614[/C][/ROW]
[ROW][C]21[/C][C]38.70297354[/C][C]43.7138699824561[/C][C]-5.01089644245614[/C][/ROW]
[ROW][C]22[/C][C]42.11944156[/C][C]43.7138699824561[/C][C]-1.59442842245614[/C][/ROW]
[ROW][C]23[/C][C]42.16314904[/C][C]43.7138699824561[/C][C]-1.55072094245614[/C][/ROW]
[ROW][C]24[/C][C]39.79566054[/C][C]43.7138699824561[/C][C]-3.91820944245614[/C][/ROW]
[ROW][C]25[/C][C]37.36261082[/C][C]43.7138699824561[/C][C]-6.35125916245614[/C][/ROW]
[ROW][C]26[/C][C]38.3533137[/C][C]43.7138699824561[/C][C]-5.36055628245614[/C][/ROW]
[ROW][C]27[/C][C]42.60022384[/C][C]43.7138699824561[/C][C]-1.11364614245614[/C][/ROW]
[ROW][C]28[/C][C]41.24529196[/C][C]43.7138699824561[/C][C]-2.46857802245614[/C][/ROW]
[ROW][C]29[/C][C]42.15586446[/C][C]43.7138699824561[/C][C]-1.55800552245614[/C][/ROW]
[ROW][C]30[/C][C]46.94183352[/C][C]43.7138699824561[/C][C]3.22796353754386[/C][/ROW]
[ROW][C]31[/C][C]47.42990038[/C][C]43.7138699824561[/C][C]3.71603039754386[/C][/ROW]
[ROW][C]32[/C][C]47.0583868[/C][C]43.7138699824561[/C][C]3.34451681754386[/C][/ROW]
[ROW][C]33[/C][C]50.18347162[/C][C]43.7138699824561[/C][C]6.46960163754386[/C][/ROW]
[ROW][C]34[/C][C]50.12519498[/C][C]43.7138699824561[/C][C]6.41132499754386[/C][/ROW]
[ROW][C]35[/C][C]43.22669772[/C][C]43.7138699824561[/C][C]-0.487172262456142[/C][/ROW]
[ROW][C]36[/C][C]40.04333626[/C][C]43.7138699824561[/C][C]-3.67053372245614[/C][/ROW]
[ROW][C]37[/C][C]40.37114236[/C][C]43.7138699824561[/C][C]-3.34272762245614[/C][/ROW]
[ROW][C]38[/C][C]42.2141411[/C][C]43.7138699824561[/C][C]-1.49972888245614[/C][/ROW]
[ROW][C]39[/C][C]36.99838182[/C][C]43.7138699824561[/C][C]-6.71548816245614[/C][/ROW]
[ROW][C]40[/C][C]39.74466848[/C][C]43.7138699824561[/C][C]-3.96920150245614[/C][/ROW]
[ROW][C]41[/C][C]42.68035422[/C][C]43.7138699824561[/C][C]-1.03351576245614[/C][/ROW]
[ROW][C]42[/C][C]46.2935059[/C][C]43.7138699824561[/C][C]2.57963591754386[/C][/ROW]
[ROW][C]43[/C][C]46.97097184[/C][C]43.7138699824561[/C][C]3.25710185754386[/C][/ROW]
[ROW][C]44[/C][C]48.72655562[/C][C]43.7138699824561[/C][C]5.01268563754386[/C][/ROW]
[ROW][C]45[/C][C]52.36884562[/C][C]43.7138699824561[/C][C]8.65497563754386[/C][/ROW]
[ROW][C]46[/C][C]50.05234918[/C][C]43.7138699824561[/C][C]6.33847919754386[/C][/ROW]
[ROW][C]47[/C][C]54.03701444[/C][C]43.7138699824561[/C][C]10.3231444575439[/C][/ROW]
[ROW][C]48[/C][C]57.78128856[/C][C]43.7138699824561[/C][C]14.0674185775439[/C][/ROW]
[ROW][C]49[/C][C]64.71620872[/C][C]43.7138699824561[/C][C]21.0023387375439[/C][/ROW]
[ROW][C]50[/C][C]63.4122689[/C][C]43.7138699824561[/C][C]19.6983989175439[/C][/ROW]
[ROW][C]51[/C][C]64.3592643[/C][C]43.7138699824561[/C][C]20.6453943175439[/C][/ROW]
[ROW][C]52[/C][C]66.02743312[/C][C]43.7138699824561[/C][C]22.3135631375439[/C][/ROW]
[ROW][C]53[/C][C]72.13919574[/C][C]43.7138699824561[/C][C]28.4253257575439[/C][/ROW]
[ROW][C]54[/C][C]76.60464328[/C][C]43.7138699824561[/C][C]32.8907732975439[/C][/ROW]
[ROW][C]55[/C][C]86.97060062[/C][C]43.7138699824561[/C][C]43.2567306375439[/C][/ROW]
[ROW][C]56[/C][C]93.48301514[/C][C]43.7138699824561[/C][C]49.7691451575439[/C][/ROW]
[ROW][C]57[/C][C]95.58825876[/C][C]43.7138699824561[/C][C]51.8743887775439[/C][/ROW]
[ROW][C]58[/C][C]81.88596378[/C][C]59.76633661[/C][C]22.11962717[/C][/ROW]
[ROW][C]59[/C][C]70.5511573[/C][C]59.76633661[/C][C]10.78482069[/C][/ROW]
[ROW][C]60[/C][C]50.38015528[/C][C]59.76633661[/C][C]-9.38618133[/C][/ROW]
[ROW][C]61[/C][C]36.24807008[/C][C]59.76633661[/C][C]-23.51826653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35615&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35615&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	20.7246301	43.7138699824561	-22.9892398824561
2	21.44580352	43.7138699824561	-22.2680664624561
3	22.09413114	43.7138699824561	-21.6197388424561
4	21.53321848	43.7138699824561	-22.1806515024561
5	23.3470789	43.7138699824561	-20.3667910824561
6	23.5656163	43.7138699824561	-20.1482536824561
7	26.42117166	43.7138699824561	-17.2926983224561
8	25.21193138	43.7138699824561	-18.5019386024561
9	26.43574082	43.7138699824561	-17.2781291624561
10	29.33500366	43.7138699824561	-14.3788663224561
11	29.40056488	43.7138699824561	-14.3133051024561
12	33.05013946	43.7138699824561	-10.6637305224561
13	28.38072368	43.7138699824561	-15.3331463024561
14	26.0059506	43.7138699824561	-17.7079193824561
15	29.31314992	43.7138699824561	-14.4007200624561
16	30.36212944	43.7138699824561	-13.3517405424561
17	35.74543406	43.7138699824561	-7.96843592245614
18	36.15337054	43.7138699824561	-7.56049944245614
19	34.20838768	43.7138699824561	-9.50548230245614
20	37.90895432	43.7138699824561	-5.80491566245614
21	38.70297354	43.7138699824561	-5.01089644245614
22	42.11944156	43.7138699824561	-1.59442842245614
23	42.16314904	43.7138699824561	-1.55072094245614
24	39.79566054	43.7138699824561	-3.91820944245614
25	37.36261082	43.7138699824561	-6.35125916245614
26	38.3533137	43.7138699824561	-5.36055628245614
27	42.60022384	43.7138699824561	-1.11364614245614
28	41.24529196	43.7138699824561	-2.46857802245614
29	42.15586446	43.7138699824561	-1.55800552245614
30	46.94183352	43.7138699824561	3.22796353754386
31	47.42990038	43.7138699824561	3.71603039754386
32	47.0583868	43.7138699824561	3.34451681754386
33	50.18347162	43.7138699824561	6.46960163754386
34	50.12519498	43.7138699824561	6.41132499754386
35	43.22669772	43.7138699824561	-0.487172262456142
36	40.04333626	43.7138699824561	-3.67053372245614
37	40.37114236	43.7138699824561	-3.34272762245614
38	42.2141411	43.7138699824561	-1.49972888245614
39	36.99838182	43.7138699824561	-6.71548816245614
40	39.74466848	43.7138699824561	-3.96920150245614
41	42.68035422	43.7138699824561	-1.03351576245614
42	46.2935059	43.7138699824561	2.57963591754386
43	46.97097184	43.7138699824561	3.25710185754386
44	48.72655562	43.7138699824561	5.01268563754386
45	52.36884562	43.7138699824561	8.65497563754386
46	50.05234918	43.7138699824561	6.33847919754386
47	54.03701444	43.7138699824561	10.3231444575439
48	57.78128856	43.7138699824561	14.0674185775439
49	64.71620872	43.7138699824561	21.0023387375439
50	63.4122689	43.7138699824561	19.6983989175439
51	64.3592643	43.7138699824561	20.6453943175439
52	66.02743312	43.7138699824561	22.3135631375439
53	72.13919574	43.7138699824561	28.4253257575439
54	76.60464328	43.7138699824561	32.8907732975439
55	86.97060062	43.7138699824561	43.2567306375439
56	93.48301514	43.7138699824561	49.7691451575439
57	95.58825876	43.7138699824561	51.8743887775439
58	81.88596378	59.76633661	22.11962717
59	70.5511573	59.76633661	10.78482069
60	50.38015528	59.76633661	-9.38618133
61	36.24807008	59.76633661	-23.51826653

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