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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 17 Nov 2007 08:07:38 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/17/t1195311739gp3gf3ybeak2zmo.htm/, Retrieved Wed, 08 May 2024 11:38:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5534, Retrieved Wed, 08 May 2024 11:38:08 +0000

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Original text written by user:

met maandseizonaliteit

IsPrivate?

No (this computation is public)

User-defined keywords

s0650921

Estimated Impact

266

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

-       [Multiple Regression] [multiple regressi...] [2007-11-17 15:07:38] [1232d415564adb2a600743f77b12553a] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5534&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5534&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5534&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 111.713076923077 + 7.47932692307695x[t] -10.3282692307694M1[t] -12.2482692307693M2[t] -0.524134615384614M3[t] -11.4641346153846M4[t] -11.9241346153846M5[t] -2.98000000000001M6[t] -15.8800000000000M7[t] -11.9M8[t] + 4.69999999999999M9[t] + 2.93999999999999M10[t] -1.98000000000001M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  111.713076923077 +  7.47932692307695x[t] -10.3282692307694M1[t] -12.2482692307693M2[t] -0.524134615384614M3[t] -11.4641346153846M4[t] -11.9241346153846M5[t] -2.98000000000001M6[t] -15.8800000000000M7[t] -11.9M8[t] +  4.69999999999999M9[t] +  2.93999999999999M10[t] -1.98000000000001M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5534&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  111.713076923077 +  7.47932692307695x[t] -10.3282692307694M1[t] -12.2482692307693M2[t] -0.524134615384614M3[t] -11.4641346153846M4[t] -11.9241346153846M5[t] -2.98000000000001M6[t] -15.8800000000000M7[t] -11.9M8[t] +  4.69999999999999M9[t] +  2.93999999999999M10[t] -1.98000000000001M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5534&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5534&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] = + 111.713076923077 + 7.47932692307695x[t] -10.3282692307694M1[t] -12.2482692307693M2[t] -0.524134615384614M3[t] -11.4641346153846M4[t] -11.9241346153846M5[t] -2.98000000000001M6[t] -15.8800000000000M7[t] -11.9M8[t] + 4.69999999999999M9[t] + 2.93999999999999M10[t] -1.98000000000001M11[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)	111.713076923077	3.026443	36.9123	0	0
x	7.47932692307695	0.917525	8.1516	0	0
M1	-10.3282692307694	3.760734	-2.7463	0.008514	0.004257
M2	-12.2482692307693	3.760734	-3.2569	0.002094	0.001047
M3	-0.524134615384614	3.747279	-0.1399	0.88936	0.44468
M4	-11.4641346153846	3.747279	-3.0593	0.003658	0.001829
M5	-11.9241346153846	3.747279	-3.1821	0.002592	0.001296
M6	-2.98000000000001	3.742783	-0.7962	0.42992	0.21496
M7	-15.8800000000000	3.742783	-4.2428	0.000103	5.1e-05
M8	-11.9	3.742783	-3.1795	0.002611	0.001306
M9	4.69999999999999	3.742783	1.2557	0.215414	0.107707
M10	2.93999999999999	3.742783	0.7855	0.436096	0.218048
M11	-1.98000000000001	3.742783	-0.529	0.599283	0.299641

\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) & 111.713076923077 & 3.026443 & 36.9123 & 0 & 0 \tabularnewline
x & 7.47932692307695 & 0.917525 & 8.1516 & 0 & 0 \tabularnewline
M1 & -10.3282692307694 & 3.760734 & -2.7463 & 0.008514 & 0.004257 \tabularnewline
M2 & -12.2482692307693 & 3.760734 & -3.2569 & 0.002094 & 0.001047 \tabularnewline
M3 & -0.524134615384614 & 3.747279 & -0.1399 & 0.88936 & 0.44468 \tabularnewline
M4 & -11.4641346153846 & 3.747279 & -3.0593 & 0.003658 & 0.001829 \tabularnewline
M5 & -11.9241346153846 & 3.747279 & -3.1821 & 0.002592 & 0.001296 \tabularnewline
M6 & -2.98000000000001 & 3.742783 & -0.7962 & 0.42992 & 0.21496 \tabularnewline
M7 & -15.8800000000000 & 3.742783 & -4.2428 & 0.000103 & 5.1e-05 \tabularnewline
M8 & -11.9 & 3.742783 & -3.1795 & 0.002611 & 0.001306 \tabularnewline
M9 & 4.69999999999999 & 3.742783 & 1.2557 & 0.215414 & 0.107707 \tabularnewline
M10 & 2.93999999999999 & 3.742783 & 0.7855 & 0.436096 & 0.218048 \tabularnewline
M11 & -1.98000000000001 & 3.742783 & -0.529 & 0.599283 & 0.299641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5534&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]111.713076923077[/C][C]3.026443[/C][C]36.9123[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]7.47932692307695[/C][C]0.917525[/C][C]8.1516[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-10.3282692307694[/C][C]3.760734[/C][C]-2.7463[/C][C]0.008514[/C][C]0.004257[/C][/ROW]
[ROW][C]M2[/C][C]-12.2482692307693[/C][C]3.760734[/C][C]-3.2569[/C][C]0.002094[/C][C]0.001047[/C][/ROW]
[ROW][C]M3[/C][C]-0.524134615384614[/C][C]3.747279[/C][C]-0.1399[/C][C]0.88936[/C][C]0.44468[/C][/ROW]
[ROW][C]M4[/C][C]-11.4641346153846[/C][C]3.747279[/C][C]-3.0593[/C][C]0.003658[/C][C]0.001829[/C][/ROW]
[ROW][C]M5[/C][C]-11.9241346153846[/C][C]3.747279[/C][C]-3.1821[/C][C]0.002592[/C][C]0.001296[/C][/ROW]
[ROW][C]M6[/C][C]-2.98000000000001[/C][C]3.742783[/C][C]-0.7962[/C][C]0.42992[/C][C]0.21496[/C][/ROW]
[ROW][C]M7[/C][C]-15.8800000000000[/C][C]3.742783[/C][C]-4.2428[/C][C]0.000103[/C][C]5.1e-05[/C][/ROW]
[ROW][C]M8[/C][C]-11.9[/C][C]3.742783[/C][C]-3.1795[/C][C]0.002611[/C][C]0.001306[/C][/ROW]
[ROW][C]M9[/C][C]4.69999999999999[/C][C]3.742783[/C][C]1.2557[/C][C]0.215414[/C][C]0.107707[/C][/ROW]
[ROW][C]M10[/C][C]2.93999999999999[/C][C]3.742783[/C][C]0.7855[/C][C]0.436096[/C][C]0.218048[/C][/ROW]
[ROW][C]M11[/C][C]-1.98000000000001[/C][C]3.742783[/C][C]-0.529[/C][C]0.599283[/C][C]0.299641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5534&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5534&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)	111.713076923077	3.026443	36.9123	0	0
x	7.47932692307695	0.917525	8.1516	0	0
M1	-10.3282692307694	3.760734	-2.7463	0.008514	0.004257
M2	-12.2482692307693	3.760734	-3.2569	0.002094	0.001047
M3	-0.524134615384614	3.747279	-0.1399	0.88936	0.44468
M4	-11.4641346153846	3.747279	-3.0593	0.003658	0.001829
M5	-11.9241346153846	3.747279	-3.1821	0.002592	0.001296
M6	-2.98000000000001	3.742783	-0.7962	0.42992	0.21496
M7	-15.8800000000000	3.742783	-4.2428	0.000103	5.1e-05
M8	-11.9	3.742783	-3.1795	0.002611	0.001306
M9	4.69999999999999	3.742783	1.2557	0.215414	0.107707
M10	2.93999999999999	3.742783	0.7855	0.436096	0.218048
M11	-1.98000000000001	3.742783	-0.529	0.599283	0.299641

Multiple Linear Regression - Regression Statistics
Multiple R	0.877616207306407
R-squared	0.770210207326883
Adjusted R-squared	0.711540473027364
F-TEST (value)	13.1278966322708
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	3.05591107974124e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.91786013143165
Sum Squared Residuals	1645.99022115385

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.877616207306407 \tabularnewline
R-squared & 0.770210207326883 \tabularnewline
Adjusted R-squared & 0.711540473027364 \tabularnewline
F-TEST (value) & 13.1278966322708 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 3.05591107974124e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.91786013143165 \tabularnewline
Sum Squared Residuals & 1645.99022115385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5534&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.877616207306407[/C][/ROW]
[ROW][C]R-squared[/C][C]0.770210207326883[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.711540473027364[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.1278966322708[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]3.05591107974124e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.91786013143165[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1645.99022115385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5534&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5534&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	0.877616207306407
R-squared	0.770210207326883
Adjusted R-squared	0.711540473027364
F-TEST (value)	13.1278966322708
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	3.05591107974124e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.91786013143165
Sum Squared Residuals	1645.99022115385

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	99.9	101.384807692308	-1.48480769230812
2	98.2	99.4648076923077	-1.26480769230774
3	104.5	111.188942307692	-6.68894230769227
4	100.8	100.248942307692	0.55105769230774
5	101.5	99.7889423076923	1.71105769230773
6	103.9	108.733076923077	-4.83307692307689
7	99.6	95.833076923077	3.76692307692307
8	98.4	99.8130769230769	-1.41307692307689
9	112.7	116.413076923077	-3.7130769230769
10	118.4	114.653076923077	3.7469230769231
11	108.1	109.733076923077	-1.63307692307690
12	105.4	111.713076923077	-6.3130769230769
13	114.6	101.384807692308	13.2151923076924
14	106.9	99.4648076923077	7.43519230769235
15	115.9	118.668269230769	-2.76826923076923
16	109.8	107.728269230769	2.07173076923077
17	101.8	107.268269230769	-5.46826923076923
18	114.2	123.691730769231	-9.49173076923078
19	110.8	110.791730769231	0.00826923076922678
20	108.4	114.771730769231	-6.37173076923078
21	127.5	131.371730769231	-3.87173076923078
22	128.6	129.611730769231	-1.01173076923078
23	116.6	124.691730769231	-8.09173076923078
24	127.4	126.671730769231	0.728269230769223
25	105	116.343461538461	-11.3434615384614
26	108.3	114.423461538462	-6.12346153846154
27	125	126.147596153846	-1.14759615384617
28	111.6	115.207596153846	-3.60759615384617
29	106.5	114.747596153846	-8.24759615384617
30	130.3	123.691730769231	6.60826923076923
31	115	110.791730769231	4.20826923076923
32	116.1	114.771730769231	1.32826923076922
33	134	131.371730769231	2.62826923076922
34	126.5	129.611730769231	-3.11173076923077
35	125.8	124.691730769231	1.10826923076923
36	136.4	126.671730769231	9.72826923076922
37	114.9	116.343461538461	-1.44346153846144
38	110.9	114.423461538462	-3.52346153846153
39	125.5	126.147596153846	-0.647596153846172
40	116.8	115.207596153846	1.59240384615383
41	116.8	114.747596153846	2.05240384615383
42	125.5	123.691730769231	1.80826923076922
43	104.2	110.791730769231	-6.59173076923076
44	115.1	114.771730769231	0.328269230769217
45	132.8	131.371730769231	1.42826923076923
46	123.3	129.611730769231	-6.31173076923078
47	124.8	124.691730769231	0.108269230769227
48	122	126.671730769231	-4.67173076923079
49	117.4	116.343461538461	1.05653846153857
50	117.9	114.423461538462	3.47653846153847
51	137.4	126.147596153846	11.2524038461538
52	114.6	115.207596153846	-0.607596153846170
53	124.7	114.747596153846	9.95240384615384
54	129.6	123.691730769231	5.90826923076921
55	109.4	110.791730769231	-1.39173076923076
56	120.9	114.771730769231	6.12826923076923
57	134.9	131.371730769231	3.52826923076923
58	136.3	129.611730769231	6.68826923076923
59	133.2	124.691730769231	8.50826923076922
60	127.2	126.671730769231	0.52826923076922

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 99.9 & 101.384807692308 & -1.48480769230812 \tabularnewline
2 & 98.2 & 99.4648076923077 & -1.26480769230774 \tabularnewline
3 & 104.5 & 111.188942307692 & -6.68894230769227 \tabularnewline
4 & 100.8 & 100.248942307692 & 0.55105769230774 \tabularnewline
5 & 101.5 & 99.7889423076923 & 1.71105769230773 \tabularnewline
6 & 103.9 & 108.733076923077 & -4.83307692307689 \tabularnewline
7 & 99.6 & 95.833076923077 & 3.76692307692307 \tabularnewline
8 & 98.4 & 99.8130769230769 & -1.41307692307689 \tabularnewline
9 & 112.7 & 116.413076923077 & -3.7130769230769 \tabularnewline
10 & 118.4 & 114.653076923077 & 3.7469230769231 \tabularnewline
11 & 108.1 & 109.733076923077 & -1.63307692307690 \tabularnewline
12 & 105.4 & 111.713076923077 & -6.3130769230769 \tabularnewline
13 & 114.6 & 101.384807692308 & 13.2151923076924 \tabularnewline
14 & 106.9 & 99.4648076923077 & 7.43519230769235 \tabularnewline
15 & 115.9 & 118.668269230769 & -2.76826923076923 \tabularnewline
16 & 109.8 & 107.728269230769 & 2.07173076923077 \tabularnewline
17 & 101.8 & 107.268269230769 & -5.46826923076923 \tabularnewline
18 & 114.2 & 123.691730769231 & -9.49173076923078 \tabularnewline
19 & 110.8 & 110.791730769231 & 0.00826923076922678 \tabularnewline
20 & 108.4 & 114.771730769231 & -6.37173076923078 \tabularnewline
21 & 127.5 & 131.371730769231 & -3.87173076923078 \tabularnewline
22 & 128.6 & 129.611730769231 & -1.01173076923078 \tabularnewline
23 & 116.6 & 124.691730769231 & -8.09173076923078 \tabularnewline
24 & 127.4 & 126.671730769231 & 0.728269230769223 \tabularnewline
25 & 105 & 116.343461538461 & -11.3434615384614 \tabularnewline
26 & 108.3 & 114.423461538462 & -6.12346153846154 \tabularnewline
27 & 125 & 126.147596153846 & -1.14759615384617 \tabularnewline
28 & 111.6 & 115.207596153846 & -3.60759615384617 \tabularnewline
29 & 106.5 & 114.747596153846 & -8.24759615384617 \tabularnewline
30 & 130.3 & 123.691730769231 & 6.60826923076923 \tabularnewline
31 & 115 & 110.791730769231 & 4.20826923076923 \tabularnewline
32 & 116.1 & 114.771730769231 & 1.32826923076922 \tabularnewline
33 & 134 & 131.371730769231 & 2.62826923076922 \tabularnewline
34 & 126.5 & 129.611730769231 & -3.11173076923077 \tabularnewline
35 & 125.8 & 124.691730769231 & 1.10826923076923 \tabularnewline
36 & 136.4 & 126.671730769231 & 9.72826923076922 \tabularnewline
37 & 114.9 & 116.343461538461 & -1.44346153846144 \tabularnewline
38 & 110.9 & 114.423461538462 & -3.52346153846153 \tabularnewline
39 & 125.5 & 126.147596153846 & -0.647596153846172 \tabularnewline
40 & 116.8 & 115.207596153846 & 1.59240384615383 \tabularnewline
41 & 116.8 & 114.747596153846 & 2.05240384615383 \tabularnewline
42 & 125.5 & 123.691730769231 & 1.80826923076922 \tabularnewline
43 & 104.2 & 110.791730769231 & -6.59173076923076 \tabularnewline
44 & 115.1 & 114.771730769231 & 0.328269230769217 \tabularnewline
45 & 132.8 & 131.371730769231 & 1.42826923076923 \tabularnewline
46 & 123.3 & 129.611730769231 & -6.31173076923078 \tabularnewline
47 & 124.8 & 124.691730769231 & 0.108269230769227 \tabularnewline
48 & 122 & 126.671730769231 & -4.67173076923079 \tabularnewline
49 & 117.4 & 116.343461538461 & 1.05653846153857 \tabularnewline
50 & 117.9 & 114.423461538462 & 3.47653846153847 \tabularnewline
51 & 137.4 & 126.147596153846 & 11.2524038461538 \tabularnewline
52 & 114.6 & 115.207596153846 & -0.607596153846170 \tabularnewline
53 & 124.7 & 114.747596153846 & 9.95240384615384 \tabularnewline
54 & 129.6 & 123.691730769231 & 5.90826923076921 \tabularnewline
55 & 109.4 & 110.791730769231 & -1.39173076923076 \tabularnewline
56 & 120.9 & 114.771730769231 & 6.12826923076923 \tabularnewline
57 & 134.9 & 131.371730769231 & 3.52826923076923 \tabularnewline
58 & 136.3 & 129.611730769231 & 6.68826923076923 \tabularnewline
59 & 133.2 & 124.691730769231 & 8.50826923076922 \tabularnewline
60 & 127.2 & 126.671730769231 & 0.52826923076922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5534&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]99.9[/C][C]101.384807692308[/C][C]-1.48480769230812[/C][/ROW]
[ROW][C]2[/C][C]98.2[/C][C]99.4648076923077[/C][C]-1.26480769230774[/C][/ROW]
[ROW][C]3[/C][C]104.5[/C][C]111.188942307692[/C][C]-6.68894230769227[/C][/ROW]
[ROW][C]4[/C][C]100.8[/C][C]100.248942307692[/C][C]0.55105769230774[/C][/ROW]
[ROW][C]5[/C][C]101.5[/C][C]99.7889423076923[/C][C]1.71105769230773[/C][/ROW]
[ROW][C]6[/C][C]103.9[/C][C]108.733076923077[/C][C]-4.83307692307689[/C][/ROW]
[ROW][C]7[/C][C]99.6[/C][C]95.833076923077[/C][C]3.76692307692307[/C][/ROW]
[ROW][C]8[/C][C]98.4[/C][C]99.8130769230769[/C][C]-1.41307692307689[/C][/ROW]
[ROW][C]9[/C][C]112.7[/C][C]116.413076923077[/C][C]-3.7130769230769[/C][/ROW]
[ROW][C]10[/C][C]118.4[/C][C]114.653076923077[/C][C]3.7469230769231[/C][/ROW]
[ROW][C]11[/C][C]108.1[/C][C]109.733076923077[/C][C]-1.63307692307690[/C][/ROW]
[ROW][C]12[/C][C]105.4[/C][C]111.713076923077[/C][C]-6.3130769230769[/C][/ROW]
[ROW][C]13[/C][C]114.6[/C][C]101.384807692308[/C][C]13.2151923076924[/C][/ROW]
[ROW][C]14[/C][C]106.9[/C][C]99.4648076923077[/C][C]7.43519230769235[/C][/ROW]
[ROW][C]15[/C][C]115.9[/C][C]118.668269230769[/C][C]-2.76826923076923[/C][/ROW]
[ROW][C]16[/C][C]109.8[/C][C]107.728269230769[/C][C]2.07173076923077[/C][/ROW]
[ROW][C]17[/C][C]101.8[/C][C]107.268269230769[/C][C]-5.46826923076923[/C][/ROW]
[ROW][C]18[/C][C]114.2[/C][C]123.691730769231[/C][C]-9.49173076923078[/C][/ROW]
[ROW][C]19[/C][C]110.8[/C][C]110.791730769231[/C][C]0.00826923076922678[/C][/ROW]
[ROW][C]20[/C][C]108.4[/C][C]114.771730769231[/C][C]-6.37173076923078[/C][/ROW]
[ROW][C]21[/C][C]127.5[/C][C]131.371730769231[/C][C]-3.87173076923078[/C][/ROW]
[ROW][C]22[/C][C]128.6[/C][C]129.611730769231[/C][C]-1.01173076923078[/C][/ROW]
[ROW][C]23[/C][C]116.6[/C][C]124.691730769231[/C][C]-8.09173076923078[/C][/ROW]
[ROW][C]24[/C][C]127.4[/C][C]126.671730769231[/C][C]0.728269230769223[/C][/ROW]
[ROW][C]25[/C][C]105[/C][C]116.343461538461[/C][C]-11.3434615384614[/C][/ROW]
[ROW][C]26[/C][C]108.3[/C][C]114.423461538462[/C][C]-6.12346153846154[/C][/ROW]
[ROW][C]27[/C][C]125[/C][C]126.147596153846[/C][C]-1.14759615384617[/C][/ROW]
[ROW][C]28[/C][C]111.6[/C][C]115.207596153846[/C][C]-3.60759615384617[/C][/ROW]
[ROW][C]29[/C][C]106.5[/C][C]114.747596153846[/C][C]-8.24759615384617[/C][/ROW]
[ROW][C]30[/C][C]130.3[/C][C]123.691730769231[/C][C]6.60826923076923[/C][/ROW]
[ROW][C]31[/C][C]115[/C][C]110.791730769231[/C][C]4.20826923076923[/C][/ROW]
[ROW][C]32[/C][C]116.1[/C][C]114.771730769231[/C][C]1.32826923076922[/C][/ROW]
[ROW][C]33[/C][C]134[/C][C]131.371730769231[/C][C]2.62826923076922[/C][/ROW]
[ROW][C]34[/C][C]126.5[/C][C]129.611730769231[/C][C]-3.11173076923077[/C][/ROW]
[ROW][C]35[/C][C]125.8[/C][C]124.691730769231[/C][C]1.10826923076923[/C][/ROW]
[ROW][C]36[/C][C]136.4[/C][C]126.671730769231[/C][C]9.72826923076922[/C][/ROW]
[ROW][C]37[/C][C]114.9[/C][C]116.343461538461[/C][C]-1.44346153846144[/C][/ROW]
[ROW][C]38[/C][C]110.9[/C][C]114.423461538462[/C][C]-3.52346153846153[/C][/ROW]
[ROW][C]39[/C][C]125.5[/C][C]126.147596153846[/C][C]-0.647596153846172[/C][/ROW]
[ROW][C]40[/C][C]116.8[/C][C]115.207596153846[/C][C]1.59240384615383[/C][/ROW]
[ROW][C]41[/C][C]116.8[/C][C]114.747596153846[/C][C]2.05240384615383[/C][/ROW]
[ROW][C]42[/C][C]125.5[/C][C]123.691730769231[/C][C]1.80826923076922[/C][/ROW]
[ROW][C]43[/C][C]104.2[/C][C]110.791730769231[/C][C]-6.59173076923076[/C][/ROW]
[ROW][C]44[/C][C]115.1[/C][C]114.771730769231[/C][C]0.328269230769217[/C][/ROW]
[ROW][C]45[/C][C]132.8[/C][C]131.371730769231[/C][C]1.42826923076923[/C][/ROW]
[ROW][C]46[/C][C]123.3[/C][C]129.611730769231[/C][C]-6.31173076923078[/C][/ROW]
[ROW][C]47[/C][C]124.8[/C][C]124.691730769231[/C][C]0.108269230769227[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]126.671730769231[/C][C]-4.67173076923079[/C][/ROW]
[ROW][C]49[/C][C]117.4[/C][C]116.343461538461[/C][C]1.05653846153857[/C][/ROW]
[ROW][C]50[/C][C]117.9[/C][C]114.423461538462[/C][C]3.47653846153847[/C][/ROW]
[ROW][C]51[/C][C]137.4[/C][C]126.147596153846[/C][C]11.2524038461538[/C][/ROW]
[ROW][C]52[/C][C]114.6[/C][C]115.207596153846[/C][C]-0.607596153846170[/C][/ROW]
[ROW][C]53[/C][C]124.7[/C][C]114.747596153846[/C][C]9.95240384615384[/C][/ROW]
[ROW][C]54[/C][C]129.6[/C][C]123.691730769231[/C][C]5.90826923076921[/C][/ROW]
[ROW][C]55[/C][C]109.4[/C][C]110.791730769231[/C][C]-1.39173076923076[/C][/ROW]
[ROW][C]56[/C][C]120.9[/C][C]114.771730769231[/C][C]6.12826923076923[/C][/ROW]
[ROW][C]57[/C][C]134.9[/C][C]131.371730769231[/C][C]3.52826923076923[/C][/ROW]
[ROW][C]58[/C][C]136.3[/C][C]129.611730769231[/C][C]6.68826923076923[/C][/ROW]
[ROW][C]59[/C][C]133.2[/C][C]124.691730769231[/C][C]8.50826923076922[/C][/ROW]
[ROW][C]60[/C][C]127.2[/C][C]126.671730769231[/C][C]0.52826923076922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5534&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5534&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	99.9	101.384807692308	-1.48480769230812
2	98.2	99.4648076923077	-1.26480769230774
3	104.5	111.188942307692	-6.68894230769227
4	100.8	100.248942307692	0.55105769230774
5	101.5	99.7889423076923	1.71105769230773
6	103.9	108.733076923077	-4.83307692307689
7	99.6	95.833076923077	3.76692307692307
8	98.4	99.8130769230769	-1.41307692307689
9	112.7	116.413076923077	-3.7130769230769
10	118.4	114.653076923077	3.7469230769231
11	108.1	109.733076923077	-1.63307692307690
12	105.4	111.713076923077	-6.3130769230769
13	114.6	101.384807692308	13.2151923076924
14	106.9	99.4648076923077	7.43519230769235
15	115.9	118.668269230769	-2.76826923076923
16	109.8	107.728269230769	2.07173076923077
17	101.8	107.268269230769	-5.46826923076923
18	114.2	123.691730769231	-9.49173076923078
19	110.8	110.791730769231	0.00826923076922678
20	108.4	114.771730769231	-6.37173076923078
21	127.5	131.371730769231	-3.87173076923078
22	128.6	129.611730769231	-1.01173076923078
23	116.6	124.691730769231	-8.09173076923078
24	127.4	126.671730769231	0.728269230769223
25	105	116.343461538461	-11.3434615384614
26	108.3	114.423461538462	-6.12346153846154
27	125	126.147596153846	-1.14759615384617
28	111.6	115.207596153846	-3.60759615384617
29	106.5	114.747596153846	-8.24759615384617
30	130.3	123.691730769231	6.60826923076923
31	115	110.791730769231	4.20826923076923
32	116.1	114.771730769231	1.32826923076922
33	134	131.371730769231	2.62826923076922
34	126.5	129.611730769231	-3.11173076923077
35	125.8	124.691730769231	1.10826923076923
36	136.4	126.671730769231	9.72826923076922
37	114.9	116.343461538461	-1.44346153846144
38	110.9	114.423461538462	-3.52346153846153
39	125.5	126.147596153846	-0.647596153846172
40	116.8	115.207596153846	1.59240384615383
41	116.8	114.747596153846	2.05240384615383
42	125.5	123.691730769231	1.80826923076922
43	104.2	110.791730769231	-6.59173076923076
44	115.1	114.771730769231	0.328269230769217
45	132.8	131.371730769231	1.42826923076923
46	123.3	129.611730769231	-6.31173076923078
47	124.8	124.691730769231	0.108269230769227
48	122	126.671730769231	-4.67173076923079
49	117.4	116.343461538461	1.05653846153857
50	117.9	114.423461538462	3.47653846153847
51	137.4	126.147596153846	11.2524038461538
52	114.6	115.207596153846	-0.607596153846170
53	124.7	114.747596153846	9.95240384615384
54	129.6	123.691730769231	5.90826923076921
55	109.4	110.791730769231	-1.39173076923076
56	120.9	114.771730769231	6.12826923076923
57	134.9	131.371730769231	3.52826923076923
58	136.3	129.611730769231	6.68826923076923
59	133.2	124.691730769231	8.50826923076922
60	127.2	126.671730769231	0.52826923076922

Figure 1

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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