Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 12 Dec 2007 13:04:52 -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/2007/Dec/12/t1197489011k4o4o1prb18n84d.htm/, Retrieved Thu, 02 May 2024 21:15:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3268, Retrieved Thu, 02 May 2024 21:15:24 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

s0650062

Estimated Impact

187

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

-       [Multiple Regression] [inflatie paper] [2007-12-12 20:04:52] [85ebbca709d200023cfec93009cd575f] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=3268&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=3268&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3268&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] = + 1.85434782608696 + 0.554347826086957x[t] -0.0990579710144927M1[t] -0.247246376811593M2[t] -0.135434782608695M3[t] -0.183623188405796M4[t] -0.091811594202898M5[t] -0.159999999999999M6[t] -0.108188405797101M7[t] -0.136376811594202M8[t] -0.124565217391304M9[t] -0.172753623188405M10[t] -0.100942028985506M11[t] + 0.00818840579710145t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  1.85434782608696 +  0.554347826086957x[t] -0.0990579710144927M1[t] -0.247246376811593M2[t] -0.135434782608695M3[t] -0.183623188405796M4[t] -0.091811594202898M5[t] -0.159999999999999M6[t] -0.108188405797101M7[t] -0.136376811594202M8[t] -0.124565217391304M9[t] -0.172753623188405M10[t] -0.100942028985506M11[t] +  0.00818840579710145t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3268&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  1.85434782608696 +  0.554347826086957x[t] -0.0990579710144927M1[t] -0.247246376811593M2[t] -0.135434782608695M3[t] -0.183623188405796M4[t] -0.091811594202898M5[t] -0.159999999999999M6[t] -0.108188405797101M7[t] -0.136376811594202M8[t] -0.124565217391304M9[t] -0.172753623188405M10[t] -0.100942028985506M11[t] +  0.00818840579710145t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3268&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3268&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] = + 1.85434782608696 + 0.554347826086957x[t] -0.0990579710144927M1[t] -0.247246376811593M2[t] -0.135434782608695M3[t] -0.183623188405796M4[t] -0.091811594202898M5[t] -0.159999999999999M6[t] -0.108188405797101M7[t] -0.136376811594202M8[t] -0.124565217391304M9[t] -0.172753623188405M10[t] -0.100942028985506M11[t] + 0.00818840579710145t + 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)	1.85434782608696	0.323788	5.727	1e-06	0
x	0.554347826086957	0.670306	0.827	0.412502	0.206251
M1	-0.0990579710144927	0.394375	-0.2512	0.802796	0.401398
M2	-0.247246376811593	0.394138	-0.6273	0.533558	0.266779
M3	-0.135434782608695	0.393953	-0.3438	0.732575	0.366288
M4	-0.183623188405796	0.393821	-0.4663	0.64323	0.321615
M5	-0.091811594202898	0.393742	-0.2332	0.816658	0.408329
M6	-0.159999999999999	0.393715	-0.4064	0.686344	0.343172
M7	-0.108188405797101	0.393742	-0.2748	0.784723	0.392362
M8	-0.136376811594202	0.393821	-0.3463	0.730703	0.365351
M9	-0.124565217391304	0.393953	-0.3162	0.753286	0.376643
M10	-0.172753623188405	0.394138	-0.4383	0.663215	0.331607
M11	-0.100942028985506	0.394375	-0.256	0.799127	0.399564
t	0.00818840579710145	0.004561	1.7954	0.079166	0.039583

\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) & 1.85434782608696 & 0.323788 & 5.727 & 1e-06 & 0 \tabularnewline
x & 0.554347826086957 & 0.670306 & 0.827 & 0.412502 & 0.206251 \tabularnewline
M1 & -0.0990579710144927 & 0.394375 & -0.2512 & 0.802796 & 0.401398 \tabularnewline
M2 & -0.247246376811593 & 0.394138 & -0.6273 & 0.533558 & 0.266779 \tabularnewline
M3 & -0.135434782608695 & 0.393953 & -0.3438 & 0.732575 & 0.366288 \tabularnewline
M4 & -0.183623188405796 & 0.393821 & -0.4663 & 0.64323 & 0.321615 \tabularnewline
M5 & -0.091811594202898 & 0.393742 & -0.2332 & 0.816658 & 0.408329 \tabularnewline
M6 & -0.159999999999999 & 0.393715 & -0.4064 & 0.686344 & 0.343172 \tabularnewline
M7 & -0.108188405797101 & 0.393742 & -0.2748 & 0.784723 & 0.392362 \tabularnewline
M8 & -0.136376811594202 & 0.393821 & -0.3463 & 0.730703 & 0.365351 \tabularnewline
M9 & -0.124565217391304 & 0.393953 & -0.3162 & 0.753286 & 0.376643 \tabularnewline
M10 & -0.172753623188405 & 0.394138 & -0.4383 & 0.663215 & 0.331607 \tabularnewline
M11 & -0.100942028985506 & 0.394375 & -0.256 & 0.799127 & 0.399564 \tabularnewline
t & 0.00818840579710145 & 0.004561 & 1.7954 & 0.079166 & 0.039583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3268&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]1.85434782608696[/C][C]0.323788[/C][C]5.727[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]0.554347826086957[/C][C]0.670306[/C][C]0.827[/C][C]0.412502[/C][C]0.206251[/C][/ROW]
[ROW][C]M1[/C][C]-0.0990579710144927[/C][C]0.394375[/C][C]-0.2512[/C][C]0.802796[/C][C]0.401398[/C][/ROW]
[ROW][C]M2[/C][C]-0.247246376811593[/C][C]0.394138[/C][C]-0.6273[/C][C]0.533558[/C][C]0.266779[/C][/ROW]
[ROW][C]M3[/C][C]-0.135434782608695[/C][C]0.393953[/C][C]-0.3438[/C][C]0.732575[/C][C]0.366288[/C][/ROW]
[ROW][C]M4[/C][C]-0.183623188405796[/C][C]0.393821[/C][C]-0.4663[/C][C]0.64323[/C][C]0.321615[/C][/ROW]
[ROW][C]M5[/C][C]-0.091811594202898[/C][C]0.393742[/C][C]-0.2332[/C][C]0.816658[/C][C]0.408329[/C][/ROW]
[ROW][C]M6[/C][C]-0.159999999999999[/C][C]0.393715[/C][C]-0.4064[/C][C]0.686344[/C][C]0.343172[/C][/ROW]
[ROW][C]M7[/C][C]-0.108188405797101[/C][C]0.393742[/C][C]-0.2748[/C][C]0.784723[/C][C]0.392362[/C][/ROW]
[ROW][C]M8[/C][C]-0.136376811594202[/C][C]0.393821[/C][C]-0.3463[/C][C]0.730703[/C][C]0.365351[/C][/ROW]
[ROW][C]M9[/C][C]-0.124565217391304[/C][C]0.393953[/C][C]-0.3162[/C][C]0.753286[/C][C]0.376643[/C][/ROW]
[ROW][C]M10[/C][C]-0.172753623188405[/C][C]0.394138[/C][C]-0.4383[/C][C]0.663215[/C][C]0.331607[/C][/ROW]
[ROW][C]M11[/C][C]-0.100942028985506[/C][C]0.394375[/C][C]-0.256[/C][C]0.799127[/C][C]0.399564[/C][/ROW]
[ROW][C]t[/C][C]0.00818840579710145[/C][C]0.004561[/C][C]1.7954[/C][C]0.079166[/C][C]0.039583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3268&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3268&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)	1.85434782608696	0.323788	5.727	1e-06	0
x	0.554347826086957	0.670306	0.827	0.412502	0.206251
M1	-0.0990579710144927	0.394375	-0.2512	0.802796	0.401398
M2	-0.247246376811593	0.394138	-0.6273	0.533558	0.266779
M3	-0.135434782608695	0.393953	-0.3438	0.732575	0.366288
M4	-0.183623188405796	0.393821	-0.4663	0.64323	0.321615
M5	-0.091811594202898	0.393742	-0.2332	0.816658	0.408329
M6	-0.159999999999999	0.393715	-0.4064	0.686344	0.343172
M7	-0.108188405797101	0.393742	-0.2748	0.784723	0.392362
M8	-0.136376811594202	0.393821	-0.3463	0.730703	0.365351
M9	-0.124565217391304	0.393953	-0.3162	0.753286	0.376643
M10	-0.172753623188405	0.394138	-0.4383	0.663215	0.331607
M11	-0.100942028985506	0.394375	-0.256	0.799127	0.399564
t	0.00818840579710145	0.004561	1.7954	0.079166	0.039583

Multiple Linear Regression - Regression Statistics
Multiple R	0.350389114316179
R-squared	0.122772531431276
Adjusted R-squared	-0.125139579251189
F-TEST (value)	0.495226034312328
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.915973912243563
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.586916262709505
Sum Squared Residuals	15.8456521739130

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.350389114316179 \tabularnewline
R-squared & 0.122772531431276 \tabularnewline
Adjusted R-squared & -0.125139579251189 \tabularnewline
F-TEST (value) & 0.495226034312328 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.915973912243563 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.586916262709505 \tabularnewline
Sum Squared Residuals & 15.8456521739130 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3268&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.350389114316179[/C][/ROW]
[ROW][C]R-squared[/C][C]0.122772531431276[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.125139579251189[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.495226034312328[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.915973912243563[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.586916262709505[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]15.8456521739130[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3268&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3268&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	0.350389114316179
R-squared	0.122772531431276
Adjusted R-squared	-0.125139579251189
F-TEST (value)	0.495226034312328
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.915973912243563
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.586916262709505
Sum Squared Residuals	15.8456521739130

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.3	1.76347826086957	-0.463478260869569
2	1.2	1.62347826086957	-0.423478260869565
3	1.6	1.74347826086957	-0.143478260869565
4	1.7	1.70347826086957	-0.00347826086956534
5	1.5	1.80347826086957	-0.303478260869566
6	0.9	1.74347826086957	-0.843478260869565
7	1.5	1.80347826086956	-0.303478260869565
8	1.4	1.78347826086956	-0.383478260869565
9	1.6	1.80347826086957	-0.203478260869565
10	1.7	1.76347826086956	-0.063478260869565
11	1.4	1.84347826086957	-0.443478260869565
12	1.8	1.95260869565217	-0.152608695652173
13	1.7	1.86173913043478	-0.161739130434782
14	1.4	1.72173913043478	-0.321739130434783
15	1.2	1.84173913043478	-0.641739130434783
16	1	1.80173913043478	-0.801739130434783
17	1.7	1.90173913043478	-0.201739130434782
18	2.4	1.84173913043478	0.558260869565217
19	2	1.90173913043478	0.0982608695652175
20	2.1	1.88173913043478	0.218260869565218
21	2	1.90173913043478	0.0982608695652175
22	1.8	1.86173913043478	-0.0617391304347827
23	2.7	1.94173913043478	0.758260869565217
24	2.3	2.05086956521739	0.249130434782609
25	1.9	1.96	-0.0599999999999992
26	2	1.82	0.180000000000000
27	2.3	1.94	0.36
28	2.8	1.9	0.9
29	2.4	2	0.4
30	2.3	1.94	0.36
31	2.7	2	0.7
32	2.7	1.98	0.72
33	2.9	2	0.9
34	3	1.96	1.04
35	2.2	2.04	0.16
36	2.3	2.14913043478261	0.150869565217392
37	2.8	2.05826086956522	0.741739130434783
38	2.8	1.91826086956522	0.881739130434783
39	2.8	2.03826086956522	0.761739130434782
40	2.2	1.99826086956522	0.201739130434783
41	2.6	2.09826086956522	0.501739130434782
42	2.8	2.03826086956522	0.761739130434782
43	2.5	2.09826086956522	0.401739130434783
44	2.4	2.07826086956522	0.321739130434782
45	2.3	2.09826086956522	0.201739130434783
46	1.9	2.05826086956522	-0.158260869565218
47	1.7	2.13826086956522	-0.438260869565218
48	2	2.24739130434783	-0.247391304347825
49	2.1	2.15652173913043	-0.0565217391304339
50	1.7	2.01652173913044	-0.316521739130435
51	1.8	2.13652173913043	-0.336521739130435
52	1.8	2.09652173913044	-0.296521739130435
53	1.8	2.19652173913043	-0.396521739130435
54	1.3	2.13652173913044	-0.836521739130435
55	1.3	2.19652173913044	-0.896521739130435
56	1.3	2.17652173913044	-0.876521739130435
57	1.2	2.19652173913044	-0.996521739130435
58	1.4	2.15652173913044	-0.756521739130435
59	2.2	2.23652173913043	-0.0365217391304347
60	2.9	2.9	-6.2450045135165e-17

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.3 & 1.76347826086957 & -0.463478260869569 \tabularnewline
2 & 1.2 & 1.62347826086957 & -0.423478260869565 \tabularnewline
3 & 1.6 & 1.74347826086957 & -0.143478260869565 \tabularnewline
4 & 1.7 & 1.70347826086957 & -0.00347826086956534 \tabularnewline
5 & 1.5 & 1.80347826086957 & -0.303478260869566 \tabularnewline
6 & 0.9 & 1.74347826086957 & -0.843478260869565 \tabularnewline
7 & 1.5 & 1.80347826086956 & -0.303478260869565 \tabularnewline
8 & 1.4 & 1.78347826086956 & -0.383478260869565 \tabularnewline
9 & 1.6 & 1.80347826086957 & -0.203478260869565 \tabularnewline
10 & 1.7 & 1.76347826086956 & -0.063478260869565 \tabularnewline
11 & 1.4 & 1.84347826086957 & -0.443478260869565 \tabularnewline
12 & 1.8 & 1.95260869565217 & -0.152608695652173 \tabularnewline
13 & 1.7 & 1.86173913043478 & -0.161739130434782 \tabularnewline
14 & 1.4 & 1.72173913043478 & -0.321739130434783 \tabularnewline
15 & 1.2 & 1.84173913043478 & -0.641739130434783 \tabularnewline
16 & 1 & 1.80173913043478 & -0.801739130434783 \tabularnewline
17 & 1.7 & 1.90173913043478 & -0.201739130434782 \tabularnewline
18 & 2.4 & 1.84173913043478 & 0.558260869565217 \tabularnewline
19 & 2 & 1.90173913043478 & 0.0982608695652175 \tabularnewline
20 & 2.1 & 1.88173913043478 & 0.218260869565218 \tabularnewline
21 & 2 & 1.90173913043478 & 0.0982608695652175 \tabularnewline
22 & 1.8 & 1.86173913043478 & -0.0617391304347827 \tabularnewline
23 & 2.7 & 1.94173913043478 & 0.758260869565217 \tabularnewline
24 & 2.3 & 2.05086956521739 & 0.249130434782609 \tabularnewline
25 & 1.9 & 1.96 & -0.0599999999999992 \tabularnewline
26 & 2 & 1.82 & 0.180000000000000 \tabularnewline
27 & 2.3 & 1.94 & 0.36 \tabularnewline
28 & 2.8 & 1.9 & 0.9 \tabularnewline
29 & 2.4 & 2 & 0.4 \tabularnewline
30 & 2.3 & 1.94 & 0.36 \tabularnewline
31 & 2.7 & 2 & 0.7 \tabularnewline
32 & 2.7 & 1.98 & 0.72 \tabularnewline
33 & 2.9 & 2 & 0.9 \tabularnewline
34 & 3 & 1.96 & 1.04 \tabularnewline
35 & 2.2 & 2.04 & 0.16 \tabularnewline
36 & 2.3 & 2.14913043478261 & 0.150869565217392 \tabularnewline
37 & 2.8 & 2.05826086956522 & 0.741739130434783 \tabularnewline
38 & 2.8 & 1.91826086956522 & 0.881739130434783 \tabularnewline
39 & 2.8 & 2.03826086956522 & 0.761739130434782 \tabularnewline
40 & 2.2 & 1.99826086956522 & 0.201739130434783 \tabularnewline
41 & 2.6 & 2.09826086956522 & 0.501739130434782 \tabularnewline
42 & 2.8 & 2.03826086956522 & 0.761739130434782 \tabularnewline
43 & 2.5 & 2.09826086956522 & 0.401739130434783 \tabularnewline
44 & 2.4 & 2.07826086956522 & 0.321739130434782 \tabularnewline
45 & 2.3 & 2.09826086956522 & 0.201739130434783 \tabularnewline
46 & 1.9 & 2.05826086956522 & -0.158260869565218 \tabularnewline
47 & 1.7 & 2.13826086956522 & -0.438260869565218 \tabularnewline
48 & 2 & 2.24739130434783 & -0.247391304347825 \tabularnewline
49 & 2.1 & 2.15652173913043 & -0.0565217391304339 \tabularnewline
50 & 1.7 & 2.01652173913044 & -0.316521739130435 \tabularnewline
51 & 1.8 & 2.13652173913043 & -0.336521739130435 \tabularnewline
52 & 1.8 & 2.09652173913044 & -0.296521739130435 \tabularnewline
53 & 1.8 & 2.19652173913043 & -0.396521739130435 \tabularnewline
54 & 1.3 & 2.13652173913044 & -0.836521739130435 \tabularnewline
55 & 1.3 & 2.19652173913044 & -0.896521739130435 \tabularnewline
56 & 1.3 & 2.17652173913044 & -0.876521739130435 \tabularnewline
57 & 1.2 & 2.19652173913044 & -0.996521739130435 \tabularnewline
58 & 1.4 & 2.15652173913044 & -0.756521739130435 \tabularnewline
59 & 2.2 & 2.23652173913043 & -0.0365217391304347 \tabularnewline
60 & 2.9 & 2.9 & -6.2450045135165e-17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3268&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]1.3[/C][C]1.76347826086957[/C][C]-0.463478260869569[/C][/ROW]
[ROW][C]2[/C][C]1.2[/C][C]1.62347826086957[/C][C]-0.423478260869565[/C][/ROW]
[ROW][C]3[/C][C]1.6[/C][C]1.74347826086957[/C][C]-0.143478260869565[/C][/ROW]
[ROW][C]4[/C][C]1.7[/C][C]1.70347826086957[/C][C]-0.00347826086956534[/C][/ROW]
[ROW][C]5[/C][C]1.5[/C][C]1.80347826086957[/C][C]-0.303478260869566[/C][/ROW]
[ROW][C]6[/C][C]0.9[/C][C]1.74347826086957[/C][C]-0.843478260869565[/C][/ROW]
[ROW][C]7[/C][C]1.5[/C][C]1.80347826086956[/C][C]-0.303478260869565[/C][/ROW]
[ROW][C]8[/C][C]1.4[/C][C]1.78347826086956[/C][C]-0.383478260869565[/C][/ROW]
[ROW][C]9[/C][C]1.6[/C][C]1.80347826086957[/C][C]-0.203478260869565[/C][/ROW]
[ROW][C]10[/C][C]1.7[/C][C]1.76347826086956[/C][C]-0.063478260869565[/C][/ROW]
[ROW][C]11[/C][C]1.4[/C][C]1.84347826086957[/C][C]-0.443478260869565[/C][/ROW]
[ROW][C]12[/C][C]1.8[/C][C]1.95260869565217[/C][C]-0.152608695652173[/C][/ROW]
[ROW][C]13[/C][C]1.7[/C][C]1.86173913043478[/C][C]-0.161739130434782[/C][/ROW]
[ROW][C]14[/C][C]1.4[/C][C]1.72173913043478[/C][C]-0.321739130434783[/C][/ROW]
[ROW][C]15[/C][C]1.2[/C][C]1.84173913043478[/C][C]-0.641739130434783[/C][/ROW]
[ROW][C]16[/C][C]1[/C][C]1.80173913043478[/C][C]-0.801739130434783[/C][/ROW]
[ROW][C]17[/C][C]1.7[/C][C]1.90173913043478[/C][C]-0.201739130434782[/C][/ROW]
[ROW][C]18[/C][C]2.4[/C][C]1.84173913043478[/C][C]0.558260869565217[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]1.90173913043478[/C][C]0.0982608695652175[/C][/ROW]
[ROW][C]20[/C][C]2.1[/C][C]1.88173913043478[/C][C]0.218260869565218[/C][/ROW]
[ROW][C]21[/C][C]2[/C][C]1.90173913043478[/C][C]0.0982608695652175[/C][/ROW]
[ROW][C]22[/C][C]1.8[/C][C]1.86173913043478[/C][C]-0.0617391304347827[/C][/ROW]
[ROW][C]23[/C][C]2.7[/C][C]1.94173913043478[/C][C]0.758260869565217[/C][/ROW]
[ROW][C]24[/C][C]2.3[/C][C]2.05086956521739[/C][C]0.249130434782609[/C][/ROW]
[ROW][C]25[/C][C]1.9[/C][C]1.96[/C][C]-0.0599999999999992[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.82[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]27[/C][C]2.3[/C][C]1.94[/C][C]0.36[/C][/ROW]
[ROW][C]28[/C][C]2.8[/C][C]1.9[/C][C]0.9[/C][/ROW]
[ROW][C]29[/C][C]2.4[/C][C]2[/C][C]0.4[/C][/ROW]
[ROW][C]30[/C][C]2.3[/C][C]1.94[/C][C]0.36[/C][/ROW]
[ROW][C]31[/C][C]2.7[/C][C]2[/C][C]0.7[/C][/ROW]
[ROW][C]32[/C][C]2.7[/C][C]1.98[/C][C]0.72[/C][/ROW]
[ROW][C]33[/C][C]2.9[/C][C]2[/C][C]0.9[/C][/ROW]
[ROW][C]34[/C][C]3[/C][C]1.96[/C][C]1.04[/C][/ROW]
[ROW][C]35[/C][C]2.2[/C][C]2.04[/C][C]0.16[/C][/ROW]
[ROW][C]36[/C][C]2.3[/C][C]2.14913043478261[/C][C]0.150869565217392[/C][/ROW]
[ROW][C]37[/C][C]2.8[/C][C]2.05826086956522[/C][C]0.741739130434783[/C][/ROW]
[ROW][C]38[/C][C]2.8[/C][C]1.91826086956522[/C][C]0.881739130434783[/C][/ROW]
[ROW][C]39[/C][C]2.8[/C][C]2.03826086956522[/C][C]0.761739130434782[/C][/ROW]
[ROW][C]40[/C][C]2.2[/C][C]1.99826086956522[/C][C]0.201739130434783[/C][/ROW]
[ROW][C]41[/C][C]2.6[/C][C]2.09826086956522[/C][C]0.501739130434782[/C][/ROW]
[ROW][C]42[/C][C]2.8[/C][C]2.03826086956522[/C][C]0.761739130434782[/C][/ROW]
[ROW][C]43[/C][C]2.5[/C][C]2.09826086956522[/C][C]0.401739130434783[/C][/ROW]
[ROW][C]44[/C][C]2.4[/C][C]2.07826086956522[/C][C]0.321739130434782[/C][/ROW]
[ROW][C]45[/C][C]2.3[/C][C]2.09826086956522[/C][C]0.201739130434783[/C][/ROW]
[ROW][C]46[/C][C]1.9[/C][C]2.05826086956522[/C][C]-0.158260869565218[/C][/ROW]
[ROW][C]47[/C][C]1.7[/C][C]2.13826086956522[/C][C]-0.438260869565218[/C][/ROW]
[ROW][C]48[/C][C]2[/C][C]2.24739130434783[/C][C]-0.247391304347825[/C][/ROW]
[ROW][C]49[/C][C]2.1[/C][C]2.15652173913043[/C][C]-0.0565217391304339[/C][/ROW]
[ROW][C]50[/C][C]1.7[/C][C]2.01652173913044[/C][C]-0.316521739130435[/C][/ROW]
[ROW][C]51[/C][C]1.8[/C][C]2.13652173913043[/C][C]-0.336521739130435[/C][/ROW]
[ROW][C]52[/C][C]1.8[/C][C]2.09652173913044[/C][C]-0.296521739130435[/C][/ROW]
[ROW][C]53[/C][C]1.8[/C][C]2.19652173913043[/C][C]-0.396521739130435[/C][/ROW]
[ROW][C]54[/C][C]1.3[/C][C]2.13652173913044[/C][C]-0.836521739130435[/C][/ROW]
[ROW][C]55[/C][C]1.3[/C][C]2.19652173913044[/C][C]-0.896521739130435[/C][/ROW]
[ROW][C]56[/C][C]1.3[/C][C]2.17652173913044[/C][C]-0.876521739130435[/C][/ROW]
[ROW][C]57[/C][C]1.2[/C][C]2.19652173913044[/C][C]-0.996521739130435[/C][/ROW]
[ROW][C]58[/C][C]1.4[/C][C]2.15652173913044[/C][C]-0.756521739130435[/C][/ROW]
[ROW][C]59[/C][C]2.2[/C][C]2.23652173913043[/C][C]-0.0365217391304347[/C][/ROW]
[ROW][C]60[/C][C]2.9[/C][C]2.9[/C][C]-6.2450045135165e-17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3268&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3268&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	1.3	1.76347826086957	-0.463478260869569
2	1.2	1.62347826086957	-0.423478260869565
3	1.6	1.74347826086957	-0.143478260869565
4	1.7	1.70347826086957	-0.00347826086956534
5	1.5	1.80347826086957	-0.303478260869566
6	0.9	1.74347826086957	-0.843478260869565
7	1.5	1.80347826086956	-0.303478260869565
8	1.4	1.78347826086956	-0.383478260869565
9	1.6	1.80347826086957	-0.203478260869565
10	1.7	1.76347826086956	-0.063478260869565
11	1.4	1.84347826086957	-0.443478260869565
12	1.8	1.95260869565217	-0.152608695652173
13	1.7	1.86173913043478	-0.161739130434782
14	1.4	1.72173913043478	-0.321739130434783
15	1.2	1.84173913043478	-0.641739130434783
16	1	1.80173913043478	-0.801739130434783
17	1.7	1.90173913043478	-0.201739130434782
18	2.4	1.84173913043478	0.558260869565217
19	2	1.90173913043478	0.0982608695652175
20	2.1	1.88173913043478	0.218260869565218
21	2	1.90173913043478	0.0982608695652175
22	1.8	1.86173913043478	-0.0617391304347827
23	2.7	1.94173913043478	0.758260869565217
24	2.3	2.05086956521739	0.249130434782609
25	1.9	1.96	-0.0599999999999992
26	2	1.82	0.180000000000000
27	2.3	1.94	0.36
28	2.8	1.9	0.9
29	2.4	2	0.4
30	2.3	1.94	0.36
31	2.7	2	0.7
32	2.7	1.98	0.72
33	2.9	2	0.9
34	3	1.96	1.04
35	2.2	2.04	0.16
36	2.3	2.14913043478261	0.150869565217392
37	2.8	2.05826086956522	0.741739130434783
38	2.8	1.91826086956522	0.881739130434783
39	2.8	2.03826086956522	0.761739130434782
40	2.2	1.99826086956522	0.201739130434783
41	2.6	2.09826086956522	0.501739130434782
42	2.8	2.03826086956522	0.761739130434782
43	2.5	2.09826086956522	0.401739130434783
44	2.4	2.07826086956522	0.321739130434782
45	2.3	2.09826086956522	0.201739130434783
46	1.9	2.05826086956522	-0.158260869565218
47	1.7	2.13826086956522	-0.438260869565218
48	2	2.24739130434783	-0.247391304347825
49	2.1	2.15652173913043	-0.0565217391304339
50	1.7	2.01652173913044	-0.316521739130435
51	1.8	2.13652173913043	-0.336521739130435
52	1.8	2.09652173913044	-0.296521739130435
53	1.8	2.19652173913043	-0.396521739130435
54	1.3	2.13652173913044	-0.836521739130435
55	1.3	2.19652173913044	-0.896521739130435
56	1.3	2.17652173913044	-0.876521739130435
57	1.2	2.19652173913044	-0.996521739130435
58	1.4	2.15652173913044	-0.756521739130435
59	2.2	2.23652173913043	-0.0365217391304347
60	2.9	2.9	-6.2450045135165e-17

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

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