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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 07 Dec 2007 04:48:32 -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/Dec/07/t119702731594n6flk7t618046.htm/, Retrieved Sun, 28 Apr 2024 22:37:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2766, Retrieved Sun, 28 Apr 2024 22:37:29 +0000

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Estimated Impact

207

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

-       [Multiple Regression] [tijdreeks 4: outl...] [2007-12-07 11:48:32] [c34baf302affc2b9b7cce5b975b1f71e] [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=2766&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=2766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2766&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
x[t] = + 90.5447115384615 -25.7745192307692y[t] -4.96431490384618M1[t] -7.6396875M2[t] -6.47527644230769M3[t] -1.73564903846153M4[t] -2.79602163461538M5[t] -8.95639423076922M6[t] -4.54176682692307M7[t] -3.57713942307692M8[t] -5.38751201923077M9[t] -2.67288461538462M10[t] + 4.16037259615385M11[t] + 0.835372596153847t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
x[t] =  +  90.5447115384615 -25.7745192307692y[t] -4.96431490384618M1[t] -7.6396875M2[t] -6.47527644230769M3[t] -1.73564903846153M4[t] -2.79602163461538M5[t] -8.95639423076922M6[t] -4.54176682692307M7[t] -3.57713942307692M8[t] -5.38751201923077M9[t] -2.67288461538462M10[t] +  4.16037259615385M11[t] +  0.835372596153847t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2766&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]x[t] =  +  90.5447115384615 -25.7745192307692y[t] -4.96431490384618M1[t] -7.6396875M2[t] -6.47527644230769M3[t] -1.73564903846153M4[t] -2.79602163461538M5[t] -8.95639423076922M6[t] -4.54176682692307M7[t] -3.57713942307692M8[t] -5.38751201923077M9[t] -2.67288461538462M10[t] +  4.16037259615385M11[t] +  0.835372596153847t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2766&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
x[t] = + 90.5447115384615 -25.7745192307692y[t] -4.96431490384618M1[t] -7.6396875M2[t] -6.47527644230769M3[t] -1.73564903846153M4[t] -2.79602163461538M5[t] -8.95639423076922M6[t] -4.54176682692307M7[t] -3.57713942307692M8[t] -5.38751201923077M9[t] -2.67288461538462M10[t] + 4.16037259615385M11[t] + 0.835372596153847t + 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)	90.5447115384615	5.943837	15.2334	0	0
y	-25.7745192307692	5.860702	-4.3979	9.3e-05	4.6e-05
M1	-4.96431490384618	6.79567	-0.7305	0.469805	0.234903
M2	-7.6396875	6.791382	-1.1249	0.268072	0.134036
M3	-6.47527644230769	7.201539	-0.8992	0.374547	0.187273
M4	-1.73564903846153	7.189155	-0.2414	0.810595	0.405297
M5	-2.79602163461538	7.182397	-0.3893	0.699356	0.349678
M6	-8.95639423076922	7.181282	-1.2472	0.220382	0.110191
M7	-4.54176682692307	7.185812	-0.632	0.53135	0.265675
M8	-3.57713942307692	7.195977	-0.4971	0.622139	0.31107
M9	-5.38751201923077	7.211752	-0.747	0.459887	0.229944
M10	-2.67288461538462	7.233101	-0.3695	0.713894	0.356947
M11	4.16037259615385	7.146441	0.5822	0.564087	0.282044
t	0.835372596153847	0.201369	4.1485	0.000195	9.8e-05

\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) & 90.5447115384615 & 5.943837 & 15.2334 & 0 & 0 \tabularnewline
y & -25.7745192307692 & 5.860702 & -4.3979 & 9.3e-05 & 4.6e-05 \tabularnewline
M1 & -4.96431490384618 & 6.79567 & -0.7305 & 0.469805 & 0.234903 \tabularnewline
M2 & -7.6396875 & 6.791382 & -1.1249 & 0.268072 & 0.134036 \tabularnewline
M3 & -6.47527644230769 & 7.201539 & -0.8992 & 0.374547 & 0.187273 \tabularnewline
M4 & -1.73564903846153 & 7.189155 & -0.2414 & 0.810595 & 0.405297 \tabularnewline
M5 & -2.79602163461538 & 7.182397 & -0.3893 & 0.699356 & 0.349678 \tabularnewline
M6 & -8.95639423076922 & 7.181282 & -1.2472 & 0.220382 & 0.110191 \tabularnewline
M7 & -4.54176682692307 & 7.185812 & -0.632 & 0.53135 & 0.265675 \tabularnewline
M8 & -3.57713942307692 & 7.195977 & -0.4971 & 0.622139 & 0.31107 \tabularnewline
M9 & -5.38751201923077 & 7.211752 & -0.747 & 0.459887 & 0.229944 \tabularnewline
M10 & -2.67288461538462 & 7.233101 & -0.3695 & 0.713894 & 0.356947 \tabularnewline
M11 & 4.16037259615385 & 7.146441 & 0.5822 & 0.564087 & 0.282044 \tabularnewline
t & 0.835372596153847 & 0.201369 & 4.1485 & 0.000195 & 9.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2766&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]90.5447115384615[/C][C]5.943837[/C][C]15.2334[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]y[/C][C]-25.7745192307692[/C][C]5.860702[/C][C]-4.3979[/C][C]9.3e-05[/C][C]4.6e-05[/C][/ROW]
[ROW][C]M1[/C][C]-4.96431490384618[/C][C]6.79567[/C][C]-0.7305[/C][C]0.469805[/C][C]0.234903[/C][/ROW]
[ROW][C]M2[/C][C]-7.6396875[/C][C]6.791382[/C][C]-1.1249[/C][C]0.268072[/C][C]0.134036[/C][/ROW]
[ROW][C]M3[/C][C]-6.47527644230769[/C][C]7.201539[/C][C]-0.8992[/C][C]0.374547[/C][C]0.187273[/C][/ROW]
[ROW][C]M4[/C][C]-1.73564903846153[/C][C]7.189155[/C][C]-0.2414[/C][C]0.810595[/C][C]0.405297[/C][/ROW]
[ROW][C]M5[/C][C]-2.79602163461538[/C][C]7.182397[/C][C]-0.3893[/C][C]0.699356[/C][C]0.349678[/C][/ROW]
[ROW][C]M6[/C][C]-8.95639423076922[/C][C]7.181282[/C][C]-1.2472[/C][C]0.220382[/C][C]0.110191[/C][/ROW]
[ROW][C]M7[/C][C]-4.54176682692307[/C][C]7.185812[/C][C]-0.632[/C][C]0.53135[/C][C]0.265675[/C][/ROW]
[ROW][C]M8[/C][C]-3.57713942307692[/C][C]7.195977[/C][C]-0.4971[/C][C]0.622139[/C][C]0.31107[/C][/ROW]
[ROW][C]M9[/C][C]-5.38751201923077[/C][C]7.211752[/C][C]-0.747[/C][C]0.459887[/C][C]0.229944[/C][/ROW]
[ROW][C]M10[/C][C]-2.67288461538462[/C][C]7.233101[/C][C]-0.3695[/C][C]0.713894[/C][C]0.356947[/C][/ROW]
[ROW][C]M11[/C][C]4.16037259615385[/C][C]7.146441[/C][C]0.5822[/C][C]0.564087[/C][C]0.282044[/C][/ROW]
[ROW][C]t[/C][C]0.835372596153847[/C][C]0.201369[/C][C]4.1485[/C][C]0.000195[/C][C]9.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2766&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)	90.5447115384615	5.943837	15.2334	0	0
y	-25.7745192307692	5.860702	-4.3979	9.3e-05	4.6e-05
M1	-4.96431490384618	6.79567	-0.7305	0.469805	0.234903
M2	-7.6396875	6.791382	-1.1249	0.268072	0.134036
M3	-6.47527644230769	7.201539	-0.8992	0.374547	0.187273
M4	-1.73564903846153	7.189155	-0.2414	0.810595	0.405297
M5	-2.79602163461538	7.182397	-0.3893	0.699356	0.349678
M6	-8.95639423076922	7.181282	-1.2472	0.220382	0.110191
M7	-4.54176682692307	7.185812	-0.632	0.53135	0.265675
M8	-3.57713942307692	7.195977	-0.4971	0.622139	0.31107
M9	-5.38751201923077	7.211752	-0.747	0.459887	0.229944
M10	-2.67288461538462	7.233101	-0.3695	0.713894	0.356947
M11	4.16037259615385	7.146441	0.5822	0.564087	0.282044
t	0.835372596153847	0.201369	4.1485	0.000195	9.8e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.64626567666583
R-squared	0.417659324836343
Adjusted R-squared	0.207369636582801
F-TEST (value)	1.98611414713202
F-TEST (DF numerator)	13
F-TEST (DF denominator)	36
p-value	0.0521115636155549
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.1025803605435
Sum Squared Residuals	3674.23667788462

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.64626567666583 \tabularnewline
R-squared & 0.417659324836343 \tabularnewline
Adjusted R-squared & 0.207369636582801 \tabularnewline
F-TEST (value) & 1.98611414713202 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 36 \tabularnewline
p-value & 0.0521115636155549 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 10.1025803605435 \tabularnewline
Sum Squared Residuals & 3674.23667788462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2766&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.64626567666583[/C][/ROW]
[ROW][C]R-squared[/C][C]0.417659324836343[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.207369636582801[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.98611414713202[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]0.0521115636155549[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]10.1025803605435[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3674.23667788462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2766&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2766&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	0.64626567666583
R-squared	0.417659324836343
Adjusted R-squared	0.207369636582801
F-TEST (value)	1.98611414713202
F-TEST (DF numerator)	13
F-TEST (DF denominator)	36
p-value	0.0521115636155549
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.1025803605435
Sum Squared Residuals	3674.23667788462

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	85	86.4157692307693	-1.41576923076932
2	87.6	84.5757692307692	3.02423076923075
3	88.6	86.5755528846154	2.02444711538463
4	95	92.1505528846154	2.84944711538461
5	96.3	91.9255528846154	4.37444711538463
6	83.3	86.6005528846154	-3.30055288461539
7	96.9	91.8505528846154	5.04944711538463
8	103.4	93.6505528846154	9.74944711538462
9	99.3	92.6755528846154	6.62444711538462
10	103.8	96.2255528846154	7.57444711538462
11	113.4	103.894182692308	9.50581730769231
12	111.5	100.569182692308	10.9308173076923
13	114.2	96.4402403846154	17.7597596153847
14	90.6	94.6002403846154	-4.00024038461537
15	90.8	96.6000240384615	-5.80002403846155
16	96.4	102.175024038462	-5.77502403846153
17	90	101.950024038462	-11.9500240384615
18	92.1	96.6250240384615	-4.52502403846154
19	97.2	101.875024038462	-4.67502403846154
20	95.1	103.675024038462	-8.57502403846154
21	88.5	102.700024038462	-14.2000240384615
22	91	106.250024038462	-15.2500240384615
23	90.5	88.1441346153846	2.35586538461539
24	75	84.8191346153846	-9.81913461538461
25	66.3	80.6901923076923	-14.3901923076923
26	66	78.8501923076923	-12.8501923076923
27	68.4	80.8499759615385	-12.4499759615385
28	70.6	86.4249759615385	-15.8249759615385
29	83.9	86.1999759615385	-2.29997596153846
30	90.1	80.8749759615385	9.22502403846154
31	90.6	86.1249759615385	4.47502403846153
32	87.1	87.9249759615385	-0.824975961538458
33	90.8	86.9499759615385	3.85002403846154
34	94.1	90.4999759615385	3.60002403846154
35	99.8	98.1686057692308	1.63139423076923
36	96.8	94.8436057692308	1.95639423076923
37	87	90.7146634615384	-3.71466346153844
38	96.3	88.8746634615385	7.42533653846154
39	107.1	90.8744471153846	16.2255528846154
40	115.2	96.4494471153846	18.7505528846154
41	106.1	96.2244471153846	9.87555288461537
42	89.5	90.8994471153846	-1.39944711538461
43	91.3	96.1494471153846	-4.84944711538463
44	97.6	97.9494471153846	-0.349447115384619
45	100.7	96.9744471153846	3.72555288461538
46	104.6	100.524447115385	4.07555288461538
47	94.7	108.193076923077	-13.4930769230769
48	101.8	104.868076923077	-3.06807692307693
49	102.5	100.739134615385	1.76086538461539
50	105.3	98.8991346153846	6.40086538461538

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 85 & 86.4157692307693 & -1.41576923076932 \tabularnewline
2 & 87.6 & 84.5757692307692 & 3.02423076923075 \tabularnewline
3 & 88.6 & 86.5755528846154 & 2.02444711538463 \tabularnewline
4 & 95 & 92.1505528846154 & 2.84944711538461 \tabularnewline
5 & 96.3 & 91.9255528846154 & 4.37444711538463 \tabularnewline
6 & 83.3 & 86.6005528846154 & -3.30055288461539 \tabularnewline
7 & 96.9 & 91.8505528846154 & 5.04944711538463 \tabularnewline
8 & 103.4 & 93.6505528846154 & 9.74944711538462 \tabularnewline
9 & 99.3 & 92.6755528846154 & 6.62444711538462 \tabularnewline
10 & 103.8 & 96.2255528846154 & 7.57444711538462 \tabularnewline
11 & 113.4 & 103.894182692308 & 9.50581730769231 \tabularnewline
12 & 111.5 & 100.569182692308 & 10.9308173076923 \tabularnewline
13 & 114.2 & 96.4402403846154 & 17.7597596153847 \tabularnewline
14 & 90.6 & 94.6002403846154 & -4.00024038461537 \tabularnewline
15 & 90.8 & 96.6000240384615 & -5.80002403846155 \tabularnewline
16 & 96.4 & 102.175024038462 & -5.77502403846153 \tabularnewline
17 & 90 & 101.950024038462 & -11.9500240384615 \tabularnewline
18 & 92.1 & 96.6250240384615 & -4.52502403846154 \tabularnewline
19 & 97.2 & 101.875024038462 & -4.67502403846154 \tabularnewline
20 & 95.1 & 103.675024038462 & -8.57502403846154 \tabularnewline
21 & 88.5 & 102.700024038462 & -14.2000240384615 \tabularnewline
22 & 91 & 106.250024038462 & -15.2500240384615 \tabularnewline
23 & 90.5 & 88.1441346153846 & 2.35586538461539 \tabularnewline
24 & 75 & 84.8191346153846 & -9.81913461538461 \tabularnewline
25 & 66.3 & 80.6901923076923 & -14.3901923076923 \tabularnewline
26 & 66 & 78.8501923076923 & -12.8501923076923 \tabularnewline
27 & 68.4 & 80.8499759615385 & -12.4499759615385 \tabularnewline
28 & 70.6 & 86.4249759615385 & -15.8249759615385 \tabularnewline
29 & 83.9 & 86.1999759615385 & -2.29997596153846 \tabularnewline
30 & 90.1 & 80.8749759615385 & 9.22502403846154 \tabularnewline
31 & 90.6 & 86.1249759615385 & 4.47502403846153 \tabularnewline
32 & 87.1 & 87.9249759615385 & -0.824975961538458 \tabularnewline
33 & 90.8 & 86.9499759615385 & 3.85002403846154 \tabularnewline
34 & 94.1 & 90.4999759615385 & 3.60002403846154 \tabularnewline
35 & 99.8 & 98.1686057692308 & 1.63139423076923 \tabularnewline
36 & 96.8 & 94.8436057692308 & 1.95639423076923 \tabularnewline
37 & 87 & 90.7146634615384 & -3.71466346153844 \tabularnewline
38 & 96.3 & 88.8746634615385 & 7.42533653846154 \tabularnewline
39 & 107.1 & 90.8744471153846 & 16.2255528846154 \tabularnewline
40 & 115.2 & 96.4494471153846 & 18.7505528846154 \tabularnewline
41 & 106.1 & 96.2244471153846 & 9.87555288461537 \tabularnewline
42 & 89.5 & 90.8994471153846 & -1.39944711538461 \tabularnewline
43 & 91.3 & 96.1494471153846 & -4.84944711538463 \tabularnewline
44 & 97.6 & 97.9494471153846 & -0.349447115384619 \tabularnewline
45 & 100.7 & 96.9744471153846 & 3.72555288461538 \tabularnewline
46 & 104.6 & 100.524447115385 & 4.07555288461538 \tabularnewline
47 & 94.7 & 108.193076923077 & -13.4930769230769 \tabularnewline
48 & 101.8 & 104.868076923077 & -3.06807692307693 \tabularnewline
49 & 102.5 & 100.739134615385 & 1.76086538461539 \tabularnewline
50 & 105.3 & 98.8991346153846 & 6.40086538461538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2766&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]85[/C][C]86.4157692307693[/C][C]-1.41576923076932[/C][/ROW]
[ROW][C]2[/C][C]87.6[/C][C]84.5757692307692[/C][C]3.02423076923075[/C][/ROW]
[ROW][C]3[/C][C]88.6[/C][C]86.5755528846154[/C][C]2.02444711538463[/C][/ROW]
[ROW][C]4[/C][C]95[/C][C]92.1505528846154[/C][C]2.84944711538461[/C][/ROW]
[ROW][C]5[/C][C]96.3[/C][C]91.9255528846154[/C][C]4.37444711538463[/C][/ROW]
[ROW][C]6[/C][C]83.3[/C][C]86.6005528846154[/C][C]-3.30055288461539[/C][/ROW]
[ROW][C]7[/C][C]96.9[/C][C]91.8505528846154[/C][C]5.04944711538463[/C][/ROW]
[ROW][C]8[/C][C]103.4[/C][C]93.6505528846154[/C][C]9.74944711538462[/C][/ROW]
[ROW][C]9[/C][C]99.3[/C][C]92.6755528846154[/C][C]6.62444711538462[/C][/ROW]
[ROW][C]10[/C][C]103.8[/C][C]96.2255528846154[/C][C]7.57444711538462[/C][/ROW]
[ROW][C]11[/C][C]113.4[/C][C]103.894182692308[/C][C]9.50581730769231[/C][/ROW]
[ROW][C]12[/C][C]111.5[/C][C]100.569182692308[/C][C]10.9308173076923[/C][/ROW]
[ROW][C]13[/C][C]114.2[/C][C]96.4402403846154[/C][C]17.7597596153847[/C][/ROW]
[ROW][C]14[/C][C]90.6[/C][C]94.6002403846154[/C][C]-4.00024038461537[/C][/ROW]
[ROW][C]15[/C][C]90.8[/C][C]96.6000240384615[/C][C]-5.80002403846155[/C][/ROW]
[ROW][C]16[/C][C]96.4[/C][C]102.175024038462[/C][C]-5.77502403846153[/C][/ROW]
[ROW][C]17[/C][C]90[/C][C]101.950024038462[/C][C]-11.9500240384615[/C][/ROW]
[ROW][C]18[/C][C]92.1[/C][C]96.6250240384615[/C][C]-4.52502403846154[/C][/ROW]
[ROW][C]19[/C][C]97.2[/C][C]101.875024038462[/C][C]-4.67502403846154[/C][/ROW]
[ROW][C]20[/C][C]95.1[/C][C]103.675024038462[/C][C]-8.57502403846154[/C][/ROW]
[ROW][C]21[/C][C]88.5[/C][C]102.700024038462[/C][C]-14.2000240384615[/C][/ROW]
[ROW][C]22[/C][C]91[/C][C]106.250024038462[/C][C]-15.2500240384615[/C][/ROW]
[ROW][C]23[/C][C]90.5[/C][C]88.1441346153846[/C][C]2.35586538461539[/C][/ROW]
[ROW][C]24[/C][C]75[/C][C]84.8191346153846[/C][C]-9.81913461538461[/C][/ROW]
[ROW][C]25[/C][C]66.3[/C][C]80.6901923076923[/C][C]-14.3901923076923[/C][/ROW]
[ROW][C]26[/C][C]66[/C][C]78.8501923076923[/C][C]-12.8501923076923[/C][/ROW]
[ROW][C]27[/C][C]68.4[/C][C]80.8499759615385[/C][C]-12.4499759615385[/C][/ROW]
[ROW][C]28[/C][C]70.6[/C][C]86.4249759615385[/C][C]-15.8249759615385[/C][/ROW]
[ROW][C]29[/C][C]83.9[/C][C]86.1999759615385[/C][C]-2.29997596153846[/C][/ROW]
[ROW][C]30[/C][C]90.1[/C][C]80.8749759615385[/C][C]9.22502403846154[/C][/ROW]
[ROW][C]31[/C][C]90.6[/C][C]86.1249759615385[/C][C]4.47502403846153[/C][/ROW]
[ROW][C]32[/C][C]87.1[/C][C]87.9249759615385[/C][C]-0.824975961538458[/C][/ROW]
[ROW][C]33[/C][C]90.8[/C][C]86.9499759615385[/C][C]3.85002403846154[/C][/ROW]
[ROW][C]34[/C][C]94.1[/C][C]90.4999759615385[/C][C]3.60002403846154[/C][/ROW]
[ROW][C]35[/C][C]99.8[/C][C]98.1686057692308[/C][C]1.63139423076923[/C][/ROW]
[ROW][C]36[/C][C]96.8[/C][C]94.8436057692308[/C][C]1.95639423076923[/C][/ROW]
[ROW][C]37[/C][C]87[/C][C]90.7146634615384[/C][C]-3.71466346153844[/C][/ROW]
[ROW][C]38[/C][C]96.3[/C][C]88.8746634615385[/C][C]7.42533653846154[/C][/ROW]
[ROW][C]39[/C][C]107.1[/C][C]90.8744471153846[/C][C]16.2255528846154[/C][/ROW]
[ROW][C]40[/C][C]115.2[/C][C]96.4494471153846[/C][C]18.7505528846154[/C][/ROW]
[ROW][C]41[/C][C]106.1[/C][C]96.2244471153846[/C][C]9.87555288461537[/C][/ROW]
[ROW][C]42[/C][C]89.5[/C][C]90.8994471153846[/C][C]-1.39944711538461[/C][/ROW]
[ROW][C]43[/C][C]91.3[/C][C]96.1494471153846[/C][C]-4.84944711538463[/C][/ROW]
[ROW][C]44[/C][C]97.6[/C][C]97.9494471153846[/C][C]-0.349447115384619[/C][/ROW]
[ROW][C]45[/C][C]100.7[/C][C]96.9744471153846[/C][C]3.72555288461538[/C][/ROW]
[ROW][C]46[/C][C]104.6[/C][C]100.524447115385[/C][C]4.07555288461538[/C][/ROW]
[ROW][C]47[/C][C]94.7[/C][C]108.193076923077[/C][C]-13.4930769230769[/C][/ROW]
[ROW][C]48[/C][C]101.8[/C][C]104.868076923077[/C][C]-3.06807692307693[/C][/ROW]
[ROW][C]49[/C][C]102.5[/C][C]100.739134615385[/C][C]1.76086538461539[/C][/ROW]
[ROW][C]50[/C][C]105.3[/C][C]98.8991346153846[/C][C]6.40086538461538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2766&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2766&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	85	86.4157692307693	-1.41576923076932
2	87.6	84.5757692307692	3.02423076923075
3	88.6	86.5755528846154	2.02444711538463
4	95	92.1505528846154	2.84944711538461
5	96.3	91.9255528846154	4.37444711538463
6	83.3	86.6005528846154	-3.30055288461539
7	96.9	91.8505528846154	5.04944711538463
8	103.4	93.6505528846154	9.74944711538462
9	99.3	92.6755528846154	6.62444711538462
10	103.8	96.2255528846154	7.57444711538462
11	113.4	103.894182692308	9.50581730769231
12	111.5	100.569182692308	10.9308173076923
13	114.2	96.4402403846154	17.7597596153847
14	90.6	94.6002403846154	-4.00024038461537
15	90.8	96.6000240384615	-5.80002403846155
16	96.4	102.175024038462	-5.77502403846153
17	90	101.950024038462	-11.9500240384615
18	92.1	96.6250240384615	-4.52502403846154
19	97.2	101.875024038462	-4.67502403846154
20	95.1	103.675024038462	-8.57502403846154
21	88.5	102.700024038462	-14.2000240384615
22	91	106.250024038462	-15.2500240384615
23	90.5	88.1441346153846	2.35586538461539
24	75	84.8191346153846	-9.81913461538461
25	66.3	80.6901923076923	-14.3901923076923
26	66	78.8501923076923	-12.8501923076923
27	68.4	80.8499759615385	-12.4499759615385
28	70.6	86.4249759615385	-15.8249759615385
29	83.9	86.1999759615385	-2.29997596153846
30	90.1	80.8749759615385	9.22502403846154
31	90.6	86.1249759615385	4.47502403846153
32	87.1	87.9249759615385	-0.824975961538458
33	90.8	86.9499759615385	3.85002403846154
34	94.1	90.4999759615385	3.60002403846154
35	99.8	98.1686057692308	1.63139423076923
36	96.8	94.8436057692308	1.95639423076923
37	87	90.7146634615384	-3.71466346153844
38	96.3	88.8746634615385	7.42533653846154
39	107.1	90.8744471153846	16.2255528846154
40	115.2	96.4494471153846	18.7505528846154
41	106.1	96.2244471153846	9.87555288461537
42	89.5	90.8994471153846	-1.39944711538461
43	91.3	96.1494471153846	-4.84944711538463
44	97.6	97.9494471153846	-0.349447115384619
45	100.7	96.9744471153846	3.72555288461538
46	104.6	100.524447115385	4.07555288461538
47	94.7	108.193076923077	-13.4930769230769
48	101.8	104.868076923077	-3.06807692307693
49	102.5	100.739134615385	1.76086538461539
50	105.3	98.8991346153846	6.40086538461538

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code