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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 29 Nov 2010 10:32:18 +0000

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/2010/Nov/29/t1291026891shbqlfqc4bz4zwk.htm/, Retrieved Fri, 09 May 2025 16:14:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102815, Retrieved Fri, 09 May 2025 16:14:18 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

309

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]
-  M D    [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 10:32:18] [99c051a77087383325372ff23bc64341] [Current]
-    D      [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 10:57:26] [d946de7cca328fbcf207448a112523ab] 
-           [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 20:25:47] [3635fb7041b1998c5a1332cf9de22bce] 
-    D        [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 20:46:24] [3635fb7041b1998c5a1332cf9de22bce] 
F               [Multiple Regression] [WS 8, Multiple Re...] [2010-11-29 23:13:27] [8081b8996d5947580de3eb171e82db4f] 
-               [Multiple Regression] [WS 8, Multiple Re...] [2010-11-29 23:45:10] [8081b8996d5947580de3eb171e82db4f] 
-               [Multiple Regression] [Workshop 8 Multip...] [2010-11-30 14:40:24] [a9e130f95bad0a0597234e75c6380c5a] 
- R  D            [Multiple Regression] [WS8 Multiple Line...] [2011-11-29 11:55:04] [d0cddc92c01af61bef0226b9e5ade9b3] 
- R  D            [Multiple Regression] [WS8 - Mini-tutori...] [2011-11-29 13:55:48] [74be16979710d4c4e7c6647856088456] 
-                   [Multiple Regression] [Paper - Deel 2 - ...] [2011-12-20 11:10:35] [95a4a8598e82ac3272c4dca488d0ba38] 
-                     [Multiple Regression] [Paper Deel 4 Mult...] [2012-12-19 19:15:09] [d5c5f9d2d41487720068c665b8e94d36] 
-                   [Multiple Regression] [Paper - Deel 2 - ...] [2011-12-20 11:27:34] [95a4a8598e82ac3272c4dca488d0ba38] 
-  M                [Multiple Regression] [WS8 02] [2012-11-26 12:32:24] [527264e3173c1bca10b2a11a99a7175d] 
-  M                [Multiple Regression] [WS 8 03] [2012-11-26 12:48:33] [527264e3173c1bca10b2a11a99a7175d] 
-  M                [Multiple Regression] [WS 8 04] [2012-11-26 12:54:59] [527264e3173c1bca10b2a11a99a7175d] 
- R               [Multiple Regression] [] [2011-11-29 15:37:27] [06f5daa9a1979410bf169cb7a41fb3eb] 
- R PD          [Multiple Regression] [Paper Multiple Re...] [2010-12-18 18:58:17] [3635fb7041b1998c5a1332cf9de22bce] 
- R PD          [Multiple Regression] [Paper Multiple Li...] [2010-12-19 12:08:20] [8081b8996d5947580de3eb171e82db4f] 
- R PD          [Multiple Regression] [Paper Multiple Li...] [2010-12-19 12:08:20] [8081b8996d5947580de3eb171e82db4f] 
- R PD          [Multiple Regression] [Paper, MR poging 2] [2010-12-19 20:57:32] [3635fb7041b1998c5a1332cf9de22bce] 
-   P             [Multiple Regression] [Multiple Regression] [2010-12-22 08:41:16] [8081b8996d5947580de3eb171e82db4f] 
-                 [Multiple Regression] [Paper Multiple Li...] [2010-12-22 08:59:09] [d946de7cca328fbcf207448a112523ab] 
-                 [Multiple Regression] [Paper Multiple Li...] [2010-12-22 08:59:09] [d946de7cca328fbcf207448a112523ab] 
-   PD            [Multiple Regression] [paper] [2011-12-17 16:04:09] [43239ed98a62e091c70785d80176537f] 
- R  D            [Multiple Regression] [] [2011-12-23 10:56:39] [74be16979710d4c4e7c6647856088456] 
-   P               [Multiple Regression] [] [2011-12-23 11:07:47] [74be16979710d4c4e7c6647856088456] 
- R  D          [Multiple Regression] [] [2011-11-25 08:48:38] [46896e8a404bb9354f2d070359621409] 
- R  D          [Multiple Regression] [] [2011-11-25 16:05:07] [b1eb71d4db1ceb5d347df987feb4a25e] 
- RM D          [Exponential Smoothing] [] [2011-11-25 17:03:34] [b1eb71d4db1ceb5d347df987feb4a25e] 
- R PD            [Exponential Smoothing] [] [2011-12-09 17:07:28] [b1eb71d4db1ceb5d347df987feb4a25e] 
- RM            [Multiple Regression] [] [2011-11-29 11:57:11] [74be16979710d4c4e7c6647856088456] 
- R             [Multiple Regression] [Multiple regression] [2011-11-29 14:51:37] [c505444e07acba7694d29053ca5d114e] 
- RMPD          [Decomposition by Loess] [ws8by loes Monthl...] [2011-11-29 21:04:41] [43a0606d8103c0ba382f0586f4417c48] 
- RM            [Multiple Regression] [] [2012-11-27 21:43:17] [74be16979710d4c4e7c6647856088456] 
-    D      [Multiple Regression] [] [2010-12-07 10:51:05] [74be16979710d4c4e7c6647856088456] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102815&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]7 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=102815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102815&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	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 10.7769305310332 -0.00142148930178946V2[t] -0.126224441924607M1[t] -1.42498067086984M2[t] -1.00092731366402M3[t] -1.60708946602567M4[t] -1.97763090471127M5[t] -2.03046948444693M6[t] -1.95539175083042M7[t] -1.73814736322608M8[t] -2.06285463383341M9[t] -1.45685064599854M10[t] -1.57828494644998M11[t] -0.0356402673962946t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  10.7769305310332 -0.00142148930178946V2[t] -0.126224441924607M1[t] -1.42498067086984M2[t] -1.00092731366402M3[t] -1.60708946602567M4[t] -1.97763090471127M5[t] -2.03046948444693M6[t] -1.95539175083042M7[t] -1.73814736322608M8[t] -2.06285463383341M9[t] -1.45685064599854M10[t] -1.57828494644998M11[t] -0.0356402673962946t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102815&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  10.7769305310332 -0.00142148930178946V2[t] -0.126224441924607M1[t] -1.42498067086984M2[t] -1.00092731366402M3[t] -1.60708946602567M4[t] -1.97763090471127M5[t] -2.03046948444693M6[t] -1.95539175083042M7[t] -1.73814736322608M8[t] -2.06285463383341M9[t] -1.45685064599854M10[t] -1.57828494644998M11[t] -0.0356402673962946t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102815&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] = + 10.7769305310332 -0.00142148930178946V2[t] -0.126224441924607M1[t] -1.42498067086984M2[t] -1.00092731366402M3[t] -1.60708946602567M4[t] -1.97763090471127M5[t] -2.03046948444693M6[t] -1.95539175083042M7[t] -1.73814736322608M8[t] -2.06285463383341M9[t] -1.45685064599854M10[t] -1.57828494644998M11[t] -0.0356402673962946t + 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)	10.7769305310332	0.247092	43.6151	0	0
V2	-0.00142148930178946	0.000243	-5.8504	0.000162	8.1e-05
M1	-0.126224441924607	0.255499	-0.494	0.631955	0.315978
M2	-1.42498067086984	0.259282	-5.4959	0.000263	0.000132
M3	-1.00092731366402	0.252254	-3.9679	0.002652	0.001326
M4	-1.60708946602567	0.25074	-6.4094	7.7e-05	3.9e-05
M5	-1.97763090471127	0.245652	-8.0505	1.1e-05	6e-06
M6	-2.03046948444693	0.242539	-8.3717	8e-06	4e-06
M7	-1.95539175083042	0.243953	-8.0155	1.2e-05	6e-06
M8	-1.73814736322608	0.247601	-7.02	3.6e-05	1.8e-05
M9	-2.06285463383341	0.237094	-8.7006	6e-06	3e-06
M10	-1.45685064599854	0.237092	-6.1447	0.000109	5.5e-05
M11	-1.57828494644998	0.236018	-6.6871	5.5e-05	2.7e-05
t	-0.0356402673962946	0.008022	-4.4426	0.001249	0.000625

\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) & 10.7769305310332 & 0.247092 & 43.6151 & 0 & 0 \tabularnewline
V2 & -0.00142148930178946 & 0.000243 & -5.8504 & 0.000162 & 8.1e-05 \tabularnewline
M1 & -0.126224441924607 & 0.255499 & -0.494 & 0.631955 & 0.315978 \tabularnewline
M2 & -1.42498067086984 & 0.259282 & -5.4959 & 0.000263 & 0.000132 \tabularnewline
M3 & -1.00092731366402 & 0.252254 & -3.9679 & 0.002652 & 0.001326 \tabularnewline
M4 & -1.60708946602567 & 0.25074 & -6.4094 & 7.7e-05 & 3.9e-05 \tabularnewline
M5 & -1.97763090471127 & 0.245652 & -8.0505 & 1.1e-05 & 6e-06 \tabularnewline
M6 & -2.03046948444693 & 0.242539 & -8.3717 & 8e-06 & 4e-06 \tabularnewline
M7 & -1.95539175083042 & 0.243953 & -8.0155 & 1.2e-05 & 6e-06 \tabularnewline
M8 & -1.73814736322608 & 0.247601 & -7.02 & 3.6e-05 & 1.8e-05 \tabularnewline
M9 & -2.06285463383341 & 0.237094 & -8.7006 & 6e-06 & 3e-06 \tabularnewline
M10 & -1.45685064599854 & 0.237092 & -6.1447 & 0.000109 & 5.5e-05 \tabularnewline
M11 & -1.57828494644998 & 0.236018 & -6.6871 & 5.5e-05 & 2.7e-05 \tabularnewline
t & -0.0356402673962946 & 0.008022 & -4.4426 & 0.001249 & 0.000625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102815&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]10.7769305310332[/C][C]0.247092[/C][C]43.6151[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]V2[/C][C]-0.00142148930178946[/C][C]0.000243[/C][C]-5.8504[/C][C]0.000162[/C][C]8.1e-05[/C][/ROW]
[ROW][C]M1[/C][C]-0.126224441924607[/C][C]0.255499[/C][C]-0.494[/C][C]0.631955[/C][C]0.315978[/C][/ROW]
[ROW][C]M2[/C][C]-1.42498067086984[/C][C]0.259282[/C][C]-5.4959[/C][C]0.000263[/C][C]0.000132[/C][/ROW]
[ROW][C]M3[/C][C]-1.00092731366402[/C][C]0.252254[/C][C]-3.9679[/C][C]0.002652[/C][C]0.001326[/C][/ROW]
[ROW][C]M4[/C][C]-1.60708946602567[/C][C]0.25074[/C][C]-6.4094[/C][C]7.7e-05[/C][C]3.9e-05[/C][/ROW]
[ROW][C]M5[/C][C]-1.97763090471127[/C][C]0.245652[/C][C]-8.0505[/C][C]1.1e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]M6[/C][C]-2.03046948444693[/C][C]0.242539[/C][C]-8.3717[/C][C]8e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M7[/C][C]-1.95539175083042[/C][C]0.243953[/C][C]-8.0155[/C][C]1.2e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]M8[/C][C]-1.73814736322608[/C][C]0.247601[/C][C]-7.02[/C][C]3.6e-05[/C][C]1.8e-05[/C][/ROW]
[ROW][C]M9[/C][C]-2.06285463383341[/C][C]0.237094[/C][C]-8.7006[/C][C]6e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M10[/C][C]-1.45685064599854[/C][C]0.237092[/C][C]-6.1447[/C][C]0.000109[/C][C]5.5e-05[/C][/ROW]
[ROW][C]M11[/C][C]-1.57828494644998[/C][C]0.236018[/C][C]-6.6871[/C][C]5.5e-05[/C][C]2.7e-05[/C][/ROW]
[ROW][C]t[/C][C]-0.0356402673962946[/C][C]0.008022[/C][C]-4.4426[/C][C]0.001249[/C][C]0.000625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102815&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102815&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)	10.7769305310332	0.247092	43.6151	0	0
V2	-0.00142148930178946	0.000243	-5.8504	0.000162	8.1e-05
M1	-0.126224441924607	0.255499	-0.494	0.631955	0.315978
M2	-1.42498067086984	0.259282	-5.4959	0.000263	0.000132
M3	-1.00092731366402	0.252254	-3.9679	0.002652	0.001326
M4	-1.60708946602567	0.25074	-6.4094	7.7e-05	3.9e-05
M5	-1.97763090471127	0.245652	-8.0505	1.1e-05	6e-06
M6	-2.03046948444693	0.242539	-8.3717	8e-06	4e-06
M7	-1.95539175083042	0.243953	-8.0155	1.2e-05	6e-06
M8	-1.73814736322608	0.247601	-7.02	3.6e-05	1.8e-05
M9	-2.06285463383341	0.237094	-8.7006	6e-06	3e-06
M10	-1.45685064599854	0.237092	-6.1447	0.000109	5.5e-05
M11	-1.57828494644998	0.236018	-6.6871	5.5e-05	2.7e-05
t	-0.0356402673962946	0.008022	-4.4426	0.001249	0.000625

Multiple Linear Regression - Regression Statistics
Multiple R	0.979886770587539
R-squared	0.960178083172476
Adjusted R-squared	0.908409591296696
F-TEST (value)	18.5475382492586
F-TEST (DF numerator)	13
F-TEST (DF denominator)	10
p-value	2.8662040530536e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.235764201915993
Sum Squared Residuals	0.555847589050849

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.979886770587539 \tabularnewline
R-squared & 0.960178083172476 \tabularnewline
Adjusted R-squared & 0.908409591296696 \tabularnewline
F-TEST (value) & 18.5475382492586 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 10 \tabularnewline
p-value & 2.8662040530536e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.235764201915993 \tabularnewline
Sum Squared Residuals & 0.555847589050849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102815&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.979886770587539[/C][/ROW]
[ROW][C]R-squared[/C][C]0.960178083172476[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.908409591296696[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]18.5475382492586[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]10[/C][/ROW]
[ROW][C]p-value[/C][C]2.8662040530536e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.235764201915993[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.555847589050849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102815&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102815&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	0.979886770587539
R-squared	0.960178083172476
Adjusted R-squared	0.908409591296696
F-TEST (value)	18.5475382492586
F-TEST (DF numerator)	13
F-TEST (DF denominator)	10
p-value	2.8662040530536e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.235764201915993
Sum Squared Residuals	0.555847589050849

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	9	9.32008906778208	-0.320089067782082
2	8	7.9800066142334	0.0199933857665987
3	9	9.02656925077145	-0.0265692507714503
4	9	8.86807319362192	0.131926806378075
5	8	7.95015533889582	0.0498446611041782
6	8	8.20567690279692	-0.205676902796923
7	8	8.02620501654156	-0.0262050165415588
8	8	7.86523021501835	0.134769784981654
9	8	8.07916435493766	-0.0791643549376605
10	8	8.04113065421035	-0.0411306542103476
11	8	7.91817182960556	0.0818281703944409
12	10	9.71952756158493	0.280472438415074
13	10	9.67991093221792	0.320089067782082
14	8	8.0199933857666	-0.0199933857665987
15	8	7.97343074922855	0.0265692507714503
16	8	8.13192680637808	-0.131926806378075
17	8	8.04984466110418	-0.0498446611041783
18	7	6.79432309720308	0.205676902796923
19	8	7.97379498345844	0.0262050165415587
20	7	7.13476978498165	-0.134769784981654
21	7	6.92083564506234	0.0791643549376605
22	8	7.95886934578965	0.0411306542103477
23	8	8.08182817039444	-0.081828170394441
24	9	9.28047243841507	-0.280472438415074

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9 & 9.32008906778208 & -0.320089067782082 \tabularnewline
2 & 8 & 7.9800066142334 & 0.0199933857665987 \tabularnewline
3 & 9 & 9.02656925077145 & -0.0265692507714503 \tabularnewline
4 & 9 & 8.86807319362192 & 0.131926806378075 \tabularnewline
5 & 8 & 7.95015533889582 & 0.0498446611041782 \tabularnewline
6 & 8 & 8.20567690279692 & -0.205676902796923 \tabularnewline
7 & 8 & 8.02620501654156 & -0.0262050165415588 \tabularnewline
8 & 8 & 7.86523021501835 & 0.134769784981654 \tabularnewline
9 & 8 & 8.07916435493766 & -0.0791643549376605 \tabularnewline
10 & 8 & 8.04113065421035 & -0.0411306542103476 \tabularnewline
11 & 8 & 7.91817182960556 & 0.0818281703944409 \tabularnewline
12 & 10 & 9.71952756158493 & 0.280472438415074 \tabularnewline
13 & 10 & 9.67991093221792 & 0.320089067782082 \tabularnewline
14 & 8 & 8.0199933857666 & -0.0199933857665987 \tabularnewline
15 & 8 & 7.97343074922855 & 0.0265692507714503 \tabularnewline
16 & 8 & 8.13192680637808 & -0.131926806378075 \tabularnewline
17 & 8 & 8.04984466110418 & -0.0498446611041783 \tabularnewline
18 & 7 & 6.79432309720308 & 0.205676902796923 \tabularnewline
19 & 8 & 7.97379498345844 & 0.0262050165415587 \tabularnewline
20 & 7 & 7.13476978498165 & -0.134769784981654 \tabularnewline
21 & 7 & 6.92083564506234 & 0.0791643549376605 \tabularnewline
22 & 8 & 7.95886934578965 & 0.0411306542103477 \tabularnewline
23 & 8 & 8.08182817039444 & -0.081828170394441 \tabularnewline
24 & 9 & 9.28047243841507 & -0.280472438415074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102815&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]9[/C][C]9.32008906778208[/C][C]-0.320089067782082[/C][/ROW]
[ROW][C]2[/C][C]8[/C][C]7.9800066142334[/C][C]0.0199933857665987[/C][/ROW]
[ROW][C]3[/C][C]9[/C][C]9.02656925077145[/C][C]-0.0265692507714503[/C][/ROW]
[ROW][C]4[/C][C]9[/C][C]8.86807319362192[/C][C]0.131926806378075[/C][/ROW]
[ROW][C]5[/C][C]8[/C][C]7.95015533889582[/C][C]0.0498446611041782[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]8.20567690279692[/C][C]-0.205676902796923[/C][/ROW]
[ROW][C]7[/C][C]8[/C][C]8.02620501654156[/C][C]-0.0262050165415588[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]7.86523021501835[/C][C]0.134769784981654[/C][/ROW]
[ROW][C]9[/C][C]8[/C][C]8.07916435493766[/C][C]-0.0791643549376605[/C][/ROW]
[ROW][C]10[/C][C]8[/C][C]8.04113065421035[/C][C]-0.0411306542103476[/C][/ROW]
[ROW][C]11[/C][C]8[/C][C]7.91817182960556[/C][C]0.0818281703944409[/C][/ROW]
[ROW][C]12[/C][C]10[/C][C]9.71952756158493[/C][C]0.280472438415074[/C][/ROW]
[ROW][C]13[/C][C]10[/C][C]9.67991093221792[/C][C]0.320089067782082[/C][/ROW]
[ROW][C]14[/C][C]8[/C][C]8.0199933857666[/C][C]-0.0199933857665987[/C][/ROW]
[ROW][C]15[/C][C]8[/C][C]7.97343074922855[/C][C]0.0265692507714503[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]8.13192680637808[/C][C]-0.131926806378075[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]8.04984466110418[/C][C]-0.0498446611041783[/C][/ROW]
[ROW][C]18[/C][C]7[/C][C]6.79432309720308[/C][C]0.205676902796923[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]7.97379498345844[/C][C]0.0262050165415587[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]7.13476978498165[/C][C]-0.134769784981654[/C][/ROW]
[ROW][C]21[/C][C]7[/C][C]6.92083564506234[/C][C]0.0791643549376605[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]7.95886934578965[/C][C]0.0411306542103477[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.08182817039444[/C][C]-0.081828170394441[/C][/ROW]
[ROW][C]24[/C][C]9[/C][C]9.28047243841507[/C][C]-0.280472438415074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102815&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102815&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	9	9.32008906778208	-0.320089067782082
2	8	7.9800066142334	0.0199933857665987
3	9	9.02656925077145	-0.0265692507714503
4	9	8.86807319362192	0.131926806378075
5	8	7.95015533889582	0.0498446611041782
6	8	8.20567690279692	-0.205676902796923
7	8	8.02620501654156	-0.0262050165415588
8	8	7.86523021501835	0.134769784981654
9	8	8.07916435493766	-0.0791643549376605
10	8	8.04113065421035	-0.0411306542103476
11	8	7.91817182960556	0.0818281703944409
12	10	9.71952756158493	0.280472438415074
13	10	9.67991093221792	0.320089067782082
14	8	8.0199933857666	-0.0199933857665987
15	8	7.97343074922855	0.0265692507714503
16	8	8.13192680637808	-0.131926806378075
17	8	8.04984466110418	-0.0498446611041783
18	7	6.79432309720308	0.205676902796923
19	8	7.97379498345844	0.0262050165415587
20	7	7.13476978498165	-0.134769784981654
21	7	6.92083564506234	0.0791643549376605
22	8	7.95886934578965	0.0411306542103477
23	8	8.08182817039444	-0.081828170394441
24	9	9.28047243841507	-0.280472438415074

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 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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