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Author

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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 15 Nov 2008 11:50:27 -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/Nov/15/t12267752251sy0a47pgbol2b1.htm/, Retrieved Fri, 09 May 2025 15:02:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24945, Retrieved Fri, 09 May 2025 15:02:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

418

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] [4127a50d3937d4bda99dae34ed7ecdc5] [Current]
F   P         [Multiple Regression] [Q3 - Consumptiepr...] [2008-11-15 21:54:28] [93834488277b53a4510bfd06084ae13b] 
F    D        [Multiple Regression] [q3 ] [2008-11-19 14:12:05] [44a98561a4b3e6ab8cd5a857b48b0914] 
F   P           [Multiple Regression] [q3 dummie+trend] [2008-11-19 14:18:31] [44a98561a4b3e6ab8cd5a857b48b0914] 
-   PD        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:42:00] [85841a4a203c2f9589565c024425a91b] 
-    D        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:45:31] [85841a4a203c2f9589565c024425a91b] 
-   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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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24945&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24945&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	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation
Consumptieprijsindex[t] = + 2.57222222222222 -1.12222222222222Dumivariabele[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Consumptieprijsindex[t] =  +  2.57222222222222 -1.12222222222222Dumivariabele[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24945&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Consumptieprijsindex[t] =  +  2.57222222222222 -1.12222222222222Dumivariabele[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24945&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
Consumptieprijsindex[t] = + 2.57222222222222 -1.12222222222222Dumivariabele[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)	2.57222222222222	0.054281	47.3868	0	0
Dumivariabele	-1.12222222222222	0.085826	-13.0755	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) & 2.57222222222222 & 0.054281 & 47.3868 & 0 & 0 \tabularnewline
Dumivariabele & -1.12222222222222 & 0.085826 & -13.0755 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24945&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]2.57222222222222[/C][C]0.054281[/C][C]47.3868[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Dumivariabele[/C][C]-1.12222222222222[/C][C]0.085826[/C][C]-13.0755[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24945&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24945&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)	2.57222222222222	0.054281	47.3868	0	0
Dumivariabele	-1.12222222222222	0.085826	-13.0755	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.864112313268198
R-squared	0.746690089941716
Adjusted R-squared	0.742322677699332
F-TEST (value)	170.968538919993
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.325688189738078
Sum Squared Residuals	6.15222222222223

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.864112313268198 \tabularnewline
R-squared & 0.746690089941716 \tabularnewline
Adjusted R-squared & 0.742322677699332 \tabularnewline
F-TEST (value) & 170.968538919993 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.325688189738078 \tabularnewline
Sum Squared Residuals & 6.15222222222223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24945&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.864112313268198[/C][/ROW]
[ROW][C]R-squared[/C][C]0.746690089941716[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.742322677699332[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]170.968538919993[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/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]0.325688189738078[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.15222222222223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24945&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24945&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	0.864112313268198
R-squared	0.746690089941716
Adjusted R-squared	0.742322677699332
F-TEST (value)	170.968538919993
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.325688189738078
Sum Squared Residuals	6.15222222222223

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2.2	2.57222222222223	-0.372222222222226
2	2.3	2.57222222222222	-0.272222222222222
3	2.1	2.57222222222222	-0.472222222222222
4	2.8	2.57222222222222	0.227777777777778
5	3.1	2.57222222222222	0.527777777777778
6	2.9	2.57222222222222	0.327777777777778
7	2.6	2.57222222222222	0.0277777777777780
8	2.7	2.57222222222222	0.127777777777778
9	2.3	2.57222222222222	-0.272222222222222
10	2.3	2.57222222222222	-0.272222222222222
11	2.1	2.57222222222222	-0.472222222222222
12	2.2	2.57222222222222	-0.372222222222222
13	2.9	2.57222222222222	0.327777777777778
14	2.6	2.57222222222222	0.0277777777777780
15	2.7	2.57222222222222	0.127777777777778
16	1.8	1.45	0.35
17	1.3	1.45	-0.15
18	0.9	1.45	-0.55
19	1.3	1.45	-0.15
20	1.3	1.45	-0.15
21	1.3	1.45	-0.15
22	1.3	1.45	-0.15
23	1.1	1.45	-0.35
24	1.4	1.45	-0.0500000000000001
25	1.2	1.45	-0.25
26	1.7	1.45	0.25
27	1.8	1.45	0.35
28	1.5	1.45	0.05
29	1	1.45	-0.45
30	1.6	1.45	0.15
31	1.5	1.45	0.05
32	1.8	1.45	0.35
33	1.8	1.45	0.35
34	1.6	1.45	0.15
35	1.9	1.45	0.45
36	1.7	1.45	0.25
37	1.6	1.45	0.15
38	1.3	1.45	-0.15
39	1.1	1.45	-0.35
40	1.9	2.57222222222222	-0.672222222222222
41	2.6	2.57222222222222	0.0277777777777780
42	2.3	2.57222222222222	-0.272222222222222
43	2.4	2.57222222222222	-0.172222222222222
44	2.2	2.57222222222222	-0.372222222222222
45	2	2.57222222222222	-0.572222222222222
46	2.9	2.57222222222222	0.327777777777778
47	2.6	2.57222222222222	0.0277777777777780
48	2.3	2.57222222222222	-0.272222222222222
49	2.3	2.57222222222222	-0.272222222222222
50	2.6	2.57222222222222	0.0277777777777780
51	3.1	2.57222222222222	0.527777777777778
52	2.8	2.57222222222222	0.227777777777778
53	2.5	2.57222222222222	-0.0722222222222221
54	2.9	2.57222222222222	0.327777777777778
55	3.1	2.57222222222222	0.527777777777778
56	3.1	2.57222222222222	0.527777777777778
57	3.2	2.57222222222222	0.627777777777778
58	2.5	2.57222222222222	-0.0722222222222221
59	2.6	2.57222222222222	0.0277777777777780
60	2.9	2.57222222222222	0.327777777777778

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.2 & 2.57222222222223 & -0.372222222222226 \tabularnewline
2 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
3 & 2.1 & 2.57222222222222 & -0.472222222222222 \tabularnewline
4 & 2.8 & 2.57222222222222 & 0.227777777777778 \tabularnewline
5 & 3.1 & 2.57222222222222 & 0.527777777777778 \tabularnewline
6 & 2.9 & 2.57222222222222 & 0.327777777777778 \tabularnewline
7 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
8 & 2.7 & 2.57222222222222 & 0.127777777777778 \tabularnewline
9 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
10 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
11 & 2.1 & 2.57222222222222 & -0.472222222222222 \tabularnewline
12 & 2.2 & 2.57222222222222 & -0.372222222222222 \tabularnewline
13 & 2.9 & 2.57222222222222 & 0.327777777777778 \tabularnewline
14 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
15 & 2.7 & 2.57222222222222 & 0.127777777777778 \tabularnewline
16 & 1.8 & 1.45 & 0.35 \tabularnewline
17 & 1.3 & 1.45 & -0.15 \tabularnewline
18 & 0.9 & 1.45 & -0.55 \tabularnewline
19 & 1.3 & 1.45 & -0.15 \tabularnewline
20 & 1.3 & 1.45 & -0.15 \tabularnewline
21 & 1.3 & 1.45 & -0.15 \tabularnewline
22 & 1.3 & 1.45 & -0.15 \tabularnewline
23 & 1.1 & 1.45 & -0.35 \tabularnewline
24 & 1.4 & 1.45 & -0.0500000000000001 \tabularnewline
25 & 1.2 & 1.45 & -0.25 \tabularnewline
26 & 1.7 & 1.45 & 0.25 \tabularnewline
27 & 1.8 & 1.45 & 0.35 \tabularnewline
28 & 1.5 & 1.45 & 0.05 \tabularnewline
29 & 1 & 1.45 & -0.45 \tabularnewline
30 & 1.6 & 1.45 & 0.15 \tabularnewline
31 & 1.5 & 1.45 & 0.05 \tabularnewline
32 & 1.8 & 1.45 & 0.35 \tabularnewline
33 & 1.8 & 1.45 & 0.35 \tabularnewline
34 & 1.6 & 1.45 & 0.15 \tabularnewline
35 & 1.9 & 1.45 & 0.45 \tabularnewline
36 & 1.7 & 1.45 & 0.25 \tabularnewline
37 & 1.6 & 1.45 & 0.15 \tabularnewline
38 & 1.3 & 1.45 & -0.15 \tabularnewline
39 & 1.1 & 1.45 & -0.35 \tabularnewline
40 & 1.9 & 2.57222222222222 & -0.672222222222222 \tabularnewline
41 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
42 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
43 & 2.4 & 2.57222222222222 & -0.172222222222222 \tabularnewline
44 & 2.2 & 2.57222222222222 & -0.372222222222222 \tabularnewline
45 & 2 & 2.57222222222222 & -0.572222222222222 \tabularnewline
46 & 2.9 & 2.57222222222222 & 0.327777777777778 \tabularnewline
47 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
48 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
49 & 2.3 & 2.57222222222222 & -0.272222222222222 \tabularnewline
50 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
51 & 3.1 & 2.57222222222222 & 0.527777777777778 \tabularnewline
52 & 2.8 & 2.57222222222222 & 0.227777777777778 \tabularnewline
53 & 2.5 & 2.57222222222222 & -0.0722222222222221 \tabularnewline
54 & 2.9 & 2.57222222222222 & 0.327777777777778 \tabularnewline
55 & 3.1 & 2.57222222222222 & 0.527777777777778 \tabularnewline
56 & 3.1 & 2.57222222222222 & 0.527777777777778 \tabularnewline
57 & 3.2 & 2.57222222222222 & 0.627777777777778 \tabularnewline
58 & 2.5 & 2.57222222222222 & -0.0722222222222221 \tabularnewline
59 & 2.6 & 2.57222222222222 & 0.0277777777777780 \tabularnewline
60 & 2.9 & 2.57222222222222 & 0.327777777777778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24945&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]2.2[/C][C]2.57222222222223[/C][C]-0.372222222222226[/C][/ROW]
[ROW][C]2[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]3[/C][C]2.1[/C][C]2.57222222222222[/C][C]-0.472222222222222[/C][/ROW]
[ROW][C]4[/C][C]2.8[/C][C]2.57222222222222[/C][C]0.227777777777778[/C][/ROW]
[ROW][C]5[/C][C]3.1[/C][C]2.57222222222222[/C][C]0.527777777777778[/C][/ROW]
[ROW][C]6[/C][C]2.9[/C][C]2.57222222222222[/C][C]0.327777777777778[/C][/ROW]
[ROW][C]7[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]8[/C][C]2.7[/C][C]2.57222222222222[/C][C]0.127777777777778[/C][/ROW]
[ROW][C]9[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]10[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]11[/C][C]2.1[/C][C]2.57222222222222[/C][C]-0.472222222222222[/C][/ROW]
[ROW][C]12[/C][C]2.2[/C][C]2.57222222222222[/C][C]-0.372222222222222[/C][/ROW]
[ROW][C]13[/C][C]2.9[/C][C]2.57222222222222[/C][C]0.327777777777778[/C][/ROW]
[ROW][C]14[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]15[/C][C]2.7[/C][C]2.57222222222222[/C][C]0.127777777777778[/C][/ROW]
[ROW][C]16[/C][C]1.8[/C][C]1.45[/C][C]0.35[/C][/ROW]
[ROW][C]17[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]18[/C][C]0.9[/C][C]1.45[/C][C]-0.55[/C][/ROW]
[ROW][C]19[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]20[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]22[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]23[/C][C]1.1[/C][C]1.45[/C][C]-0.35[/C][/ROW]
[ROW][C]24[/C][C]1.4[/C][C]1.45[/C][C]-0.0500000000000001[/C][/ROW]
[ROW][C]25[/C][C]1.2[/C][C]1.45[/C][C]-0.25[/C][/ROW]
[ROW][C]26[/C][C]1.7[/C][C]1.45[/C][C]0.25[/C][/ROW]
[ROW][C]27[/C][C]1.8[/C][C]1.45[/C][C]0.35[/C][/ROW]
[ROW][C]28[/C][C]1.5[/C][C]1.45[/C][C]0.05[/C][/ROW]
[ROW][C]29[/C][C]1[/C][C]1.45[/C][C]-0.45[/C][/ROW]
[ROW][C]30[/C][C]1.6[/C][C]1.45[/C][C]0.15[/C][/ROW]
[ROW][C]31[/C][C]1.5[/C][C]1.45[/C][C]0.05[/C][/ROW]
[ROW][C]32[/C][C]1.8[/C][C]1.45[/C][C]0.35[/C][/ROW]
[ROW][C]33[/C][C]1.8[/C][C]1.45[/C][C]0.35[/C][/ROW]
[ROW][C]34[/C][C]1.6[/C][C]1.45[/C][C]0.15[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.45[/C][C]0.45[/C][/ROW]
[ROW][C]36[/C][C]1.7[/C][C]1.45[/C][C]0.25[/C][/ROW]
[ROW][C]37[/C][C]1.6[/C][C]1.45[/C][C]0.15[/C][/ROW]
[ROW][C]38[/C][C]1.3[/C][C]1.45[/C][C]-0.15[/C][/ROW]
[ROW][C]39[/C][C]1.1[/C][C]1.45[/C][C]-0.35[/C][/ROW]
[ROW][C]40[/C][C]1.9[/C][C]2.57222222222222[/C][C]-0.672222222222222[/C][/ROW]
[ROW][C]41[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]42[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]43[/C][C]2.4[/C][C]2.57222222222222[/C][C]-0.172222222222222[/C][/ROW]
[ROW][C]44[/C][C]2.2[/C][C]2.57222222222222[/C][C]-0.372222222222222[/C][/ROW]
[ROW][C]45[/C][C]2[/C][C]2.57222222222222[/C][C]-0.572222222222222[/C][/ROW]
[ROW][C]46[/C][C]2.9[/C][C]2.57222222222222[/C][C]0.327777777777778[/C][/ROW]
[ROW][C]47[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]48[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]49[/C][C]2.3[/C][C]2.57222222222222[/C][C]-0.272222222222222[/C][/ROW]
[ROW][C]50[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]51[/C][C]3.1[/C][C]2.57222222222222[/C][C]0.527777777777778[/C][/ROW]
[ROW][C]52[/C][C]2.8[/C][C]2.57222222222222[/C][C]0.227777777777778[/C][/ROW]
[ROW][C]53[/C][C]2.5[/C][C]2.57222222222222[/C][C]-0.0722222222222221[/C][/ROW]
[ROW][C]54[/C][C]2.9[/C][C]2.57222222222222[/C][C]0.327777777777778[/C][/ROW]
[ROW][C]55[/C][C]3.1[/C][C]2.57222222222222[/C][C]0.527777777777778[/C][/ROW]
[ROW][C]56[/C][C]3.1[/C][C]2.57222222222222[/C][C]0.527777777777778[/C][/ROW]
[ROW][C]57[/C][C]3.2[/C][C]2.57222222222222[/C][C]0.627777777777778[/C][/ROW]
[ROW][C]58[/C][C]2.5[/C][C]2.57222222222222[/C][C]-0.0722222222222221[/C][/ROW]
[ROW][C]59[/C][C]2.6[/C][C]2.57222222222222[/C][C]0.0277777777777780[/C][/ROW]
[ROW][C]60[/C][C]2.9[/C][C]2.57222222222222[/C][C]0.327777777777778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24945&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24945&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	2.2	2.57222222222223	-0.372222222222226
2	2.3	2.57222222222222	-0.272222222222222
3	2.1	2.57222222222222	-0.472222222222222
4	2.8	2.57222222222222	0.227777777777778
5	3.1	2.57222222222222	0.527777777777778
6	2.9	2.57222222222222	0.327777777777778
7	2.6	2.57222222222222	0.0277777777777780
8	2.7	2.57222222222222	0.127777777777778
9	2.3	2.57222222222222	-0.272222222222222
10	2.3	2.57222222222222	-0.272222222222222
11	2.1	2.57222222222222	-0.472222222222222
12	2.2	2.57222222222222	-0.372222222222222
13	2.9	2.57222222222222	0.327777777777778
14	2.6	2.57222222222222	0.0277777777777780
15	2.7	2.57222222222222	0.127777777777778
16	1.8	1.45	0.35
17	1.3	1.45	-0.15
18	0.9	1.45	-0.55
19	1.3	1.45	-0.15
20	1.3	1.45	-0.15
21	1.3	1.45	-0.15
22	1.3	1.45	-0.15
23	1.1	1.45	-0.35
24	1.4	1.45	-0.0500000000000001
25	1.2	1.45	-0.25
26	1.7	1.45	0.25
27	1.8	1.45	0.35
28	1.5	1.45	0.05
29	1	1.45	-0.45
30	1.6	1.45	0.15
31	1.5	1.45	0.05
32	1.8	1.45	0.35
33	1.8	1.45	0.35
34	1.6	1.45	0.15
35	1.9	1.45	0.45
36	1.7	1.45	0.25
37	1.6	1.45	0.15
38	1.3	1.45	-0.15
39	1.1	1.45	-0.35
40	1.9	2.57222222222222	-0.672222222222222
41	2.6	2.57222222222222	0.0277777777777780
42	2.3	2.57222222222222	-0.272222222222222
43	2.4	2.57222222222222	-0.172222222222222
44	2.2	2.57222222222222	-0.372222222222222
45	2	2.57222222222222	-0.572222222222222
46	2.9	2.57222222222222	0.327777777777778
47	2.6	2.57222222222222	0.0277777777777780
48	2.3	2.57222222222222	-0.272222222222222
49	2.3	2.57222222222222	-0.272222222222222
50	2.6	2.57222222222222	0.0277777777777780
51	3.1	2.57222222222222	0.527777777777778
52	2.8	2.57222222222222	0.227777777777778
53	2.5	2.57222222222222	-0.0722222222222221
54	2.9	2.57222222222222	0.327777777777778
55	3.1	2.57222222222222	0.527777777777778
56	3.1	2.57222222222222	0.527777777777778
57	3.2	2.57222222222222	0.627777777777778
58	2.5	2.57222222222222	-0.0722222222222221
59	2.6	2.57222222222222	0.0277777777777780
60	2.9	2.57222222222222	0.327777777777778

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