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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 23 Nov 2008 13:07:48 -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/2008/Nov/23/t1227470924pytkmqgx1m8l54p.htm/, Retrieved Sun, 19 May 2024 08:55:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25332, Retrieved Sun, 19 May 2024 08:55:57 +0000

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Estimated Impact

155

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

F     [Multiple Regression] [] [2007-11-19 19:55:31] [b731da8b544846036771bbf9bf2f34ce]
-    D  [Multiple Regression] [9/11 op prijs diesel] [2008-11-23 20:03:30] [8b0d202c3a0c4ea223fd8b8e731dacd8]
-   PD      [Multiple Regression] [9/11 en prijs die...] [2008-11-23 20:07:48] [9ba97de59bb4d2edf0cfeac4ca7d2b73] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25332&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25332&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 0.76161379310345 -0.160982758620690x[t] + 0.0084152298850578M1[t] -0.0310385057471264M2[t] -0.0293543103448277M3[t] -0.0116701149425288M4[t] -0.00598591954022995M5[t] -0.0163017241379312M6[t] -0.0166175287356323M7[t] -0.0149333333333335M8[t] -0.0112491379310346M9[t] + 0.0326316091954023M10[t] + 0.0283158045977011M11[t] + 0.00631580459770114t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  0.76161379310345 -0.160982758620690x[t] +  0.0084152298850578M1[t] -0.0310385057471264M2[t] -0.0293543103448277M3[t] -0.0116701149425288M4[t] -0.00598591954022995M5[t] -0.0163017241379312M6[t] -0.0166175287356323M7[t] -0.0149333333333335M8[t] -0.0112491379310346M9[t] +  0.0326316091954023M10[t] +  0.0283158045977011M11[t] +  0.00631580459770114t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25332&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  0.76161379310345 -0.160982758620690x[t] +  0.0084152298850578M1[t] -0.0310385057471264M2[t] -0.0293543103448277M3[t] -0.0116701149425288M4[t] -0.00598591954022995M5[t] -0.0163017241379312M6[t] -0.0166175287356323M7[t] -0.0149333333333335M8[t] -0.0112491379310346M9[t] +  0.0326316091954023M10[t] +  0.0283158045977011M11[t] +  0.00631580459770114t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25332&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] = + 0.76161379310345 -0.160982758620690x[t] + 0.0084152298850578M1[t] -0.0310385057471264M2[t] -0.0293543103448277M3[t] -0.0116701149425288M4[t] -0.00598591954022995M5[t] -0.0163017241379312M6[t] -0.0166175287356323M7[t] -0.0149333333333335M8[t] -0.0112491379310346M9[t] + 0.0326316091954023M10[t] + 0.0283158045977011M11[t] + 0.00631580459770114t + 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)	0.76161379310345	0.036716	20.7436	0	0
x	-0.160982758620690	0.029493	-5.4584	2e-06	1e-06
M1	0.0084152298850578	0.038289	0.2198	0.826992	0.413496
M2	-0.0310385057471264	0.040121	-0.7736	0.443031	0.221515
M3	-0.0293543103448277	0.040092	-0.7322	0.467704	0.233852
M4	-0.0116701149425288	0.040072	-0.2912	0.77216	0.38608
M5	-0.00598591954022995	0.040061	-0.1494	0.88186	0.44093
M6	-0.0163017241379312	0.040058	-0.407	0.685887	0.342943
M7	-0.0166175287356323	0.040063	-0.4148	0.680187	0.340093
M8	-0.0149333333333335	0.040077	-0.3726	0.71111	0.355555
M9	-0.0112491379310346	0.0401	-0.2805	0.780302	0.390151
M10	0.0326316091954023	0.039801	0.8199	0.416425	0.208213
M11	0.0283158045977011	0.039788	0.7117	0.480186	0.240093
t	0.00631580459770114	0.000585	10.789	0	0

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.76161379310345 & 0.036716 & 20.7436 & 0 & 0 \tabularnewline
x & -0.160982758620690 & 0.029493 & -5.4584 & 2e-06 & 1e-06 \tabularnewline
M1 & 0.0084152298850578 & 0.038289 & 0.2198 & 0.826992 & 0.413496 \tabularnewline
M2 & -0.0310385057471264 & 0.040121 & -0.7736 & 0.443031 & 0.221515 \tabularnewline
M3 & -0.0293543103448277 & 0.040092 & -0.7322 & 0.467704 & 0.233852 \tabularnewline
M4 & -0.0116701149425288 & 0.040072 & -0.2912 & 0.77216 & 0.38608 \tabularnewline
M5 & -0.00598591954022995 & 0.040061 & -0.1494 & 0.88186 & 0.44093 \tabularnewline
M6 & -0.0163017241379312 & 0.040058 & -0.407 & 0.685887 & 0.342943 \tabularnewline
M7 & -0.0166175287356323 & 0.040063 & -0.4148 & 0.680187 & 0.340093 \tabularnewline
M8 & -0.0149333333333335 & 0.040077 & -0.3726 & 0.71111 & 0.355555 \tabularnewline
M9 & -0.0112491379310346 & 0.0401 & -0.2805 & 0.780302 & 0.390151 \tabularnewline
M10 & 0.0326316091954023 & 0.039801 & 0.8199 & 0.416425 & 0.208213 \tabularnewline
M11 & 0.0283158045977011 & 0.039788 & 0.7117 & 0.480186 & 0.240093 \tabularnewline
t & 0.00631580459770114 & 0.000585 & 10.789 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25332&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]0.76161379310345[/C][C]0.036716[/C][C]20.7436[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]-0.160982758620690[/C][C]0.029493[/C][C]-5.4584[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M1[/C][C]0.0084152298850578[/C][C]0.038289[/C][C]0.2198[/C][C]0.826992[/C][C]0.413496[/C][/ROW]
[ROW][C]M2[/C][C]-0.0310385057471264[/C][C]0.040121[/C][C]-0.7736[/C][C]0.443031[/C][C]0.221515[/C][/ROW]
[ROW][C]M3[/C][C]-0.0293543103448277[/C][C]0.040092[/C][C]-0.7322[/C][C]0.467704[/C][C]0.233852[/C][/ROW]
[ROW][C]M4[/C][C]-0.0116701149425288[/C][C]0.040072[/C][C]-0.2912[/C][C]0.77216[/C][C]0.38608[/C][/ROW]
[ROW][C]M5[/C][C]-0.00598591954022995[/C][C]0.040061[/C][C]-0.1494[/C][C]0.88186[/C][C]0.44093[/C][/ROW]
[ROW][C]M6[/C][C]-0.0163017241379312[/C][C]0.040058[/C][C]-0.407[/C][C]0.685887[/C][C]0.342943[/C][/ROW]
[ROW][C]M7[/C][C]-0.0166175287356323[/C][C]0.040063[/C][C]-0.4148[/C][C]0.680187[/C][C]0.340093[/C][/ROW]
[ROW][C]M8[/C][C]-0.0149333333333335[/C][C]0.040077[/C][C]-0.3726[/C][C]0.71111[/C][C]0.355555[/C][/ROW]
[ROW][C]M9[/C][C]-0.0112491379310346[/C][C]0.0401[/C][C]-0.2805[/C][C]0.780302[/C][C]0.390151[/C][/ROW]
[ROW][C]M10[/C][C]0.0326316091954023[/C][C]0.039801[/C][C]0.8199[/C][C]0.416425[/C][C]0.208213[/C][/ROW]
[ROW][C]M11[/C][C]0.0283158045977011[/C][C]0.039788[/C][C]0.7117[/C][C]0.480186[/C][C]0.240093[/C][/ROW]
[ROW][C]t[/C][C]0.00631580459770114[/C][C]0.000585[/C][C]10.789[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25332&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25332&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)	0.76161379310345	0.036716	20.7436	0	0
x	-0.160982758620690	0.029493	-5.4584	2e-06	1e-06
M1	0.0084152298850578	0.038289	0.2198	0.826992	0.413496
M2	-0.0310385057471264	0.040121	-0.7736	0.443031	0.221515
M3	-0.0293543103448277	0.040092	-0.7322	0.467704	0.233852
M4	-0.0116701149425288	0.040072	-0.2912	0.77216	0.38608
M5	-0.00598591954022995	0.040061	-0.1494	0.88186	0.44093
M6	-0.0163017241379312	0.040058	-0.407	0.685887	0.342943
M7	-0.0166175287356323	0.040063	-0.4148	0.680187	0.340093
M8	-0.0149333333333335	0.040077	-0.3726	0.71111	0.355555
M9	-0.0112491379310346	0.0401	-0.2805	0.780302	0.390151
M10	0.0326316091954023	0.039801	0.8199	0.416425	0.208213
M11	0.0283158045977011	0.039788	0.7117	0.480186	0.240093
t	0.00631580459770114	0.000585	10.789	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.855163567900384
R-squared	0.731304727864114
Adjusted R-squared	0.656984758975465
F-TEST (value)	9.83994932720975
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	1.83569648370963e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0629031210770387
Sum Squared Residuals	0.185969724137932

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.855163567900384 \tabularnewline
R-squared & 0.731304727864114 \tabularnewline
Adjusted R-squared & 0.656984758975465 \tabularnewline
F-TEST (value) & 9.83994932720975 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 1.83569648370963e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0629031210770387 \tabularnewline
Sum Squared Residuals & 0.185969724137932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25332&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.855163567900384[/C][/ROW]
[ROW][C]R-squared[/C][C]0.731304727864114[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.656984758975465[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]9.83994932720975[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]1.83569648370963e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0629031210770387[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.185969724137932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25332&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25332&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	0.855163567900384
R-squared	0.731304727864114
Adjusted R-squared	0.656984758975465
F-TEST (value)	9.83994932720975
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	1.83569648370963e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0629031210770387
Sum Squared Residuals	0.185969724137932

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.84	0.776344827586205	0.0636551724137951
2	0.76	0.743206896551724	0.0167931034482763
3	0.77	0.751206896551724	0.0187931034482756
4	0.76	0.775206896551724	-0.0152068965517243
5	0.77	0.787206896551724	-0.0172068965517245
6	0.78	0.783206896551724	-0.00320689655172441
7	0.79	0.789206896551724	0.000793103448275535
8	0.78	0.797206896551724	-0.0172068965517244
9	0.76	0.807206896551725	-0.0472068965517245
10	0.78	0.696420689655172	0.0835793103448276
11	0.76	0.698420689655172	0.0615793103448276
12	0.74	0.676420689655172	0.0635793103448275
13	0.73	0.691151724137931	0.0388482758620685
14	0.72	0.658013793103448	0.0619862068965519
15	0.71	0.666013793103448	0.0439862068965518
16	0.73	0.690013793103448	0.0399862068965517
17	0.75	0.702013793103448	0.0479862068965518
18	0.75	0.698013793103448	0.0519862068965517
19	0.72	0.704013793103448	0.0159862068965518
20	0.72	0.712013793103448	0.0079862068965517
21	0.72	0.722013793103448	-0.00201379310344828
22	0.74	0.772210344827586	-0.0322103448275863
23	0.78	0.774210344827586	0.00578965517241375
24	0.74	0.752210344827586	-0.0122103448275863
25	0.74	0.766941379310345	-0.0269413793103453
26	0.75	0.733803448275862	0.0161965517241377
27	0.78	0.741803448275862	0.038196551724138
28	0.81	0.765803448275862	0.044196551724138
29	0.75	0.777803448275862	-0.027803448275862
30	0.7	0.773803448275862	-0.073803448275862
31	0.71	0.779803448275862	-0.069803448275862
32	0.71	0.787803448275862	-0.077803448275862
33	0.73	0.797803448275862	-0.067803448275862
34	0.74	0.848	-0.108
35	0.74	0.85	-0.11
36	0.75	0.828	-0.078
37	0.74	0.842731034482759	-0.102731034482759
38	0.74	0.809593103448276	-0.069593103448276
39	0.73	0.817593103448276	-0.0875931034482758
40	0.76	0.841593103448276	-0.0815931034482758
41	0.8	0.853593103448276	-0.0535931034482758
42	0.83	0.849593103448276	-0.0195931034482758
43	0.81	0.855593103448276	-0.0455931034482757
44	0.83	0.863593103448276	-0.0335931034482758
45	0.88	0.873593103448276	0.00640689655172419
46	0.89	0.923789655172414	-0.0337896551724138
47	0.93	0.925789655172414	0.00421034482758626
48	0.91	0.903789655172414	0.00621034482758623
49	0.9	0.918520689655173	-0.0185206896551727
50	0.86	0.88538275862069	-0.0253827586206899
51	0.88	0.89338275862069	-0.0133827586206895
52	0.93	0.91738275862069	0.0126172413793105
53	0.98	0.92938275862069	0.0506172413793105
54	0.97	0.92538275862069	0.0446172413793105
55	1.03	0.93138275862069	0.0986172413793105
56	1.06	0.93938275862069	0.120617241379311
57	1.06	0.94938275862069	0.110617241379311
58	1.09	0.999579310344827	0.0904206896551725
59	1.04	1.00157931034483	0.0384206896551726
60	1	0.979579310344827	0.0204206896551725
61	1.04	0.994310344827587	0.0456896551724135

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 0.84 & 0.776344827586205 & 0.0636551724137951 \tabularnewline
2 & 0.76 & 0.743206896551724 & 0.0167931034482763 \tabularnewline
3 & 0.77 & 0.751206896551724 & 0.0187931034482756 \tabularnewline
4 & 0.76 & 0.775206896551724 & -0.0152068965517243 \tabularnewline
5 & 0.77 & 0.787206896551724 & -0.0172068965517245 \tabularnewline
6 & 0.78 & 0.783206896551724 & -0.00320689655172441 \tabularnewline
7 & 0.79 & 0.789206896551724 & 0.000793103448275535 \tabularnewline
8 & 0.78 & 0.797206896551724 & -0.0172068965517244 \tabularnewline
9 & 0.76 & 0.807206896551725 & -0.0472068965517245 \tabularnewline
10 & 0.78 & 0.696420689655172 & 0.0835793103448276 \tabularnewline
11 & 0.76 & 0.698420689655172 & 0.0615793103448276 \tabularnewline
12 & 0.74 & 0.676420689655172 & 0.0635793103448275 \tabularnewline
13 & 0.73 & 0.691151724137931 & 0.0388482758620685 \tabularnewline
14 & 0.72 & 0.658013793103448 & 0.0619862068965519 \tabularnewline
15 & 0.71 & 0.666013793103448 & 0.0439862068965518 \tabularnewline
16 & 0.73 & 0.690013793103448 & 0.0399862068965517 \tabularnewline
17 & 0.75 & 0.702013793103448 & 0.0479862068965518 \tabularnewline
18 & 0.75 & 0.698013793103448 & 0.0519862068965517 \tabularnewline
19 & 0.72 & 0.704013793103448 & 0.0159862068965518 \tabularnewline
20 & 0.72 & 0.712013793103448 & 0.0079862068965517 \tabularnewline
21 & 0.72 & 0.722013793103448 & -0.00201379310344828 \tabularnewline
22 & 0.74 & 0.772210344827586 & -0.0322103448275863 \tabularnewline
23 & 0.78 & 0.774210344827586 & 0.00578965517241375 \tabularnewline
24 & 0.74 & 0.752210344827586 & -0.0122103448275863 \tabularnewline
25 & 0.74 & 0.766941379310345 & -0.0269413793103453 \tabularnewline
26 & 0.75 & 0.733803448275862 & 0.0161965517241377 \tabularnewline
27 & 0.78 & 0.741803448275862 & 0.038196551724138 \tabularnewline
28 & 0.81 & 0.765803448275862 & 0.044196551724138 \tabularnewline
29 & 0.75 & 0.777803448275862 & -0.027803448275862 \tabularnewline
30 & 0.7 & 0.773803448275862 & -0.073803448275862 \tabularnewline
31 & 0.71 & 0.779803448275862 & -0.069803448275862 \tabularnewline
32 & 0.71 & 0.787803448275862 & -0.077803448275862 \tabularnewline
33 & 0.73 & 0.797803448275862 & -0.067803448275862 \tabularnewline
34 & 0.74 & 0.848 & -0.108 \tabularnewline
35 & 0.74 & 0.85 & -0.11 \tabularnewline
36 & 0.75 & 0.828 & -0.078 \tabularnewline
37 & 0.74 & 0.842731034482759 & -0.102731034482759 \tabularnewline
38 & 0.74 & 0.809593103448276 & -0.069593103448276 \tabularnewline
39 & 0.73 & 0.817593103448276 & -0.0875931034482758 \tabularnewline
40 & 0.76 & 0.841593103448276 & -0.0815931034482758 \tabularnewline
41 & 0.8 & 0.853593103448276 & -0.0535931034482758 \tabularnewline
42 & 0.83 & 0.849593103448276 & -0.0195931034482758 \tabularnewline
43 & 0.81 & 0.855593103448276 & -0.0455931034482757 \tabularnewline
44 & 0.83 & 0.863593103448276 & -0.0335931034482758 \tabularnewline
45 & 0.88 & 0.873593103448276 & 0.00640689655172419 \tabularnewline
46 & 0.89 & 0.923789655172414 & -0.0337896551724138 \tabularnewline
47 & 0.93 & 0.925789655172414 & 0.00421034482758626 \tabularnewline
48 & 0.91 & 0.903789655172414 & 0.00621034482758623 \tabularnewline
49 & 0.9 & 0.918520689655173 & -0.0185206896551727 \tabularnewline
50 & 0.86 & 0.88538275862069 & -0.0253827586206899 \tabularnewline
51 & 0.88 & 0.89338275862069 & -0.0133827586206895 \tabularnewline
52 & 0.93 & 0.91738275862069 & 0.0126172413793105 \tabularnewline
53 & 0.98 & 0.92938275862069 & 0.0506172413793105 \tabularnewline
54 & 0.97 & 0.92538275862069 & 0.0446172413793105 \tabularnewline
55 & 1.03 & 0.93138275862069 & 0.0986172413793105 \tabularnewline
56 & 1.06 & 0.93938275862069 & 0.120617241379311 \tabularnewline
57 & 1.06 & 0.94938275862069 & 0.110617241379311 \tabularnewline
58 & 1.09 & 0.999579310344827 & 0.0904206896551725 \tabularnewline
59 & 1.04 & 1.00157931034483 & 0.0384206896551726 \tabularnewline
60 & 1 & 0.979579310344827 & 0.0204206896551725 \tabularnewline
61 & 1.04 & 0.994310344827587 & 0.0456896551724135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25332&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]0.84[/C][C]0.776344827586205[/C][C]0.0636551724137951[/C][/ROW]
[ROW][C]2[/C][C]0.76[/C][C]0.743206896551724[/C][C]0.0167931034482763[/C][/ROW]
[ROW][C]3[/C][C]0.77[/C][C]0.751206896551724[/C][C]0.0187931034482756[/C][/ROW]
[ROW][C]4[/C][C]0.76[/C][C]0.775206896551724[/C][C]-0.0152068965517243[/C][/ROW]
[ROW][C]5[/C][C]0.77[/C][C]0.787206896551724[/C][C]-0.0172068965517245[/C][/ROW]
[ROW][C]6[/C][C]0.78[/C][C]0.783206896551724[/C][C]-0.00320689655172441[/C][/ROW]
[ROW][C]7[/C][C]0.79[/C][C]0.789206896551724[/C][C]0.000793103448275535[/C][/ROW]
[ROW][C]8[/C][C]0.78[/C][C]0.797206896551724[/C][C]-0.0172068965517244[/C][/ROW]
[ROW][C]9[/C][C]0.76[/C][C]0.807206896551725[/C][C]-0.0472068965517245[/C][/ROW]
[ROW][C]10[/C][C]0.78[/C][C]0.696420689655172[/C][C]0.0835793103448276[/C][/ROW]
[ROW][C]11[/C][C]0.76[/C][C]0.698420689655172[/C][C]0.0615793103448276[/C][/ROW]
[ROW][C]12[/C][C]0.74[/C][C]0.676420689655172[/C][C]0.0635793103448275[/C][/ROW]
[ROW][C]13[/C][C]0.73[/C][C]0.691151724137931[/C][C]0.0388482758620685[/C][/ROW]
[ROW][C]14[/C][C]0.72[/C][C]0.658013793103448[/C][C]0.0619862068965519[/C][/ROW]
[ROW][C]15[/C][C]0.71[/C][C]0.666013793103448[/C][C]0.0439862068965518[/C][/ROW]
[ROW][C]16[/C][C]0.73[/C][C]0.690013793103448[/C][C]0.0399862068965517[/C][/ROW]
[ROW][C]17[/C][C]0.75[/C][C]0.702013793103448[/C][C]0.0479862068965518[/C][/ROW]
[ROW][C]18[/C][C]0.75[/C][C]0.698013793103448[/C][C]0.0519862068965517[/C][/ROW]
[ROW][C]19[/C][C]0.72[/C][C]0.704013793103448[/C][C]0.0159862068965518[/C][/ROW]
[ROW][C]20[/C][C]0.72[/C][C]0.712013793103448[/C][C]0.0079862068965517[/C][/ROW]
[ROW][C]21[/C][C]0.72[/C][C]0.722013793103448[/C][C]-0.00201379310344828[/C][/ROW]
[ROW][C]22[/C][C]0.74[/C][C]0.772210344827586[/C][C]-0.0322103448275863[/C][/ROW]
[ROW][C]23[/C][C]0.78[/C][C]0.774210344827586[/C][C]0.00578965517241375[/C][/ROW]
[ROW][C]24[/C][C]0.74[/C][C]0.752210344827586[/C][C]-0.0122103448275863[/C][/ROW]
[ROW][C]25[/C][C]0.74[/C][C]0.766941379310345[/C][C]-0.0269413793103453[/C][/ROW]
[ROW][C]26[/C][C]0.75[/C][C]0.733803448275862[/C][C]0.0161965517241377[/C][/ROW]
[ROW][C]27[/C][C]0.78[/C][C]0.741803448275862[/C][C]0.038196551724138[/C][/ROW]
[ROW][C]28[/C][C]0.81[/C][C]0.765803448275862[/C][C]0.044196551724138[/C][/ROW]
[ROW][C]29[/C][C]0.75[/C][C]0.777803448275862[/C][C]-0.027803448275862[/C][/ROW]
[ROW][C]30[/C][C]0.7[/C][C]0.773803448275862[/C][C]-0.073803448275862[/C][/ROW]
[ROW][C]31[/C][C]0.71[/C][C]0.779803448275862[/C][C]-0.069803448275862[/C][/ROW]
[ROW][C]32[/C][C]0.71[/C][C]0.787803448275862[/C][C]-0.077803448275862[/C][/ROW]
[ROW][C]33[/C][C]0.73[/C][C]0.797803448275862[/C][C]-0.067803448275862[/C][/ROW]
[ROW][C]34[/C][C]0.74[/C][C]0.848[/C][C]-0.108[/C][/ROW]
[ROW][C]35[/C][C]0.74[/C][C]0.85[/C][C]-0.11[/C][/ROW]
[ROW][C]36[/C][C]0.75[/C][C]0.828[/C][C]-0.078[/C][/ROW]
[ROW][C]37[/C][C]0.74[/C][C]0.842731034482759[/C][C]-0.102731034482759[/C][/ROW]
[ROW][C]38[/C][C]0.74[/C][C]0.809593103448276[/C][C]-0.069593103448276[/C][/ROW]
[ROW][C]39[/C][C]0.73[/C][C]0.817593103448276[/C][C]-0.0875931034482758[/C][/ROW]
[ROW][C]40[/C][C]0.76[/C][C]0.841593103448276[/C][C]-0.0815931034482758[/C][/ROW]
[ROW][C]41[/C][C]0.8[/C][C]0.853593103448276[/C][C]-0.0535931034482758[/C][/ROW]
[ROW][C]42[/C][C]0.83[/C][C]0.849593103448276[/C][C]-0.0195931034482758[/C][/ROW]
[ROW][C]43[/C][C]0.81[/C][C]0.855593103448276[/C][C]-0.0455931034482757[/C][/ROW]
[ROW][C]44[/C][C]0.83[/C][C]0.863593103448276[/C][C]-0.0335931034482758[/C][/ROW]
[ROW][C]45[/C][C]0.88[/C][C]0.873593103448276[/C][C]0.00640689655172419[/C][/ROW]
[ROW][C]46[/C][C]0.89[/C][C]0.923789655172414[/C][C]-0.0337896551724138[/C][/ROW]
[ROW][C]47[/C][C]0.93[/C][C]0.925789655172414[/C][C]0.00421034482758626[/C][/ROW]
[ROW][C]48[/C][C]0.91[/C][C]0.903789655172414[/C][C]0.00621034482758623[/C][/ROW]
[ROW][C]49[/C][C]0.9[/C][C]0.918520689655173[/C][C]-0.0185206896551727[/C][/ROW]
[ROW][C]50[/C][C]0.86[/C][C]0.88538275862069[/C][C]-0.0253827586206899[/C][/ROW]
[ROW][C]51[/C][C]0.88[/C][C]0.89338275862069[/C][C]-0.0133827586206895[/C][/ROW]
[ROW][C]52[/C][C]0.93[/C][C]0.91738275862069[/C][C]0.0126172413793105[/C][/ROW]
[ROW][C]53[/C][C]0.98[/C][C]0.92938275862069[/C][C]0.0506172413793105[/C][/ROW]
[ROW][C]54[/C][C]0.97[/C][C]0.92538275862069[/C][C]0.0446172413793105[/C][/ROW]
[ROW][C]55[/C][C]1.03[/C][C]0.93138275862069[/C][C]0.0986172413793105[/C][/ROW]
[ROW][C]56[/C][C]1.06[/C][C]0.93938275862069[/C][C]0.120617241379311[/C][/ROW]
[ROW][C]57[/C][C]1.06[/C][C]0.94938275862069[/C][C]0.110617241379311[/C][/ROW]
[ROW][C]58[/C][C]1.09[/C][C]0.999579310344827[/C][C]0.0904206896551725[/C][/ROW]
[ROW][C]59[/C][C]1.04[/C][C]1.00157931034483[/C][C]0.0384206896551726[/C][/ROW]
[ROW][C]60[/C][C]1[/C][C]0.979579310344827[/C][C]0.0204206896551725[/C][/ROW]
[ROW][C]61[/C][C]1.04[/C][C]0.994310344827587[/C][C]0.0456896551724135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25332&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25332&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	0.84	0.776344827586205	0.0636551724137951
2	0.76	0.743206896551724	0.0167931034482763
3	0.77	0.751206896551724	0.0187931034482756
4	0.76	0.775206896551724	-0.0152068965517243
5	0.77	0.787206896551724	-0.0172068965517245
6	0.78	0.783206896551724	-0.00320689655172441
7	0.79	0.789206896551724	0.000793103448275535
8	0.78	0.797206896551724	-0.0172068965517244
9	0.76	0.807206896551725	-0.0472068965517245
10	0.78	0.696420689655172	0.0835793103448276
11	0.76	0.698420689655172	0.0615793103448276
12	0.74	0.676420689655172	0.0635793103448275
13	0.73	0.691151724137931	0.0388482758620685
14	0.72	0.658013793103448	0.0619862068965519
15	0.71	0.666013793103448	0.0439862068965518
16	0.73	0.690013793103448	0.0399862068965517
17	0.75	0.702013793103448	0.0479862068965518
18	0.75	0.698013793103448	0.0519862068965517
19	0.72	0.704013793103448	0.0159862068965518
20	0.72	0.712013793103448	0.0079862068965517
21	0.72	0.722013793103448	-0.00201379310344828
22	0.74	0.772210344827586	-0.0322103448275863
23	0.78	0.774210344827586	0.00578965517241375
24	0.74	0.752210344827586	-0.0122103448275863
25	0.74	0.766941379310345	-0.0269413793103453
26	0.75	0.733803448275862	0.0161965517241377
27	0.78	0.741803448275862	0.038196551724138
28	0.81	0.765803448275862	0.044196551724138
29	0.75	0.777803448275862	-0.027803448275862
30	0.7	0.773803448275862	-0.073803448275862
31	0.71	0.779803448275862	-0.069803448275862
32	0.71	0.787803448275862	-0.077803448275862
33	0.73	0.797803448275862	-0.067803448275862
34	0.74	0.848	-0.108
35	0.74	0.85	-0.11
36	0.75	0.828	-0.078
37	0.74	0.842731034482759	-0.102731034482759
38	0.74	0.809593103448276	-0.069593103448276
39	0.73	0.817593103448276	-0.0875931034482758
40	0.76	0.841593103448276	-0.0815931034482758
41	0.8	0.853593103448276	-0.0535931034482758
42	0.83	0.849593103448276	-0.0195931034482758
43	0.81	0.855593103448276	-0.0455931034482757
44	0.83	0.863593103448276	-0.0335931034482758
45	0.88	0.873593103448276	0.00640689655172419
46	0.89	0.923789655172414	-0.0337896551724138
47	0.93	0.925789655172414	0.00421034482758626
48	0.91	0.903789655172414	0.00621034482758623
49	0.9	0.918520689655173	-0.0185206896551727
50	0.86	0.88538275862069	-0.0253827586206899
51	0.88	0.89338275862069	-0.0133827586206895
52	0.93	0.91738275862069	0.0126172413793105
53	0.98	0.92938275862069	0.0506172413793105
54	0.97	0.92538275862069	0.0446172413793105
55	1.03	0.93138275862069	0.0986172413793105
56	1.06	0.93938275862069	0.120617241379311
57	1.06	0.94938275862069	0.110617241379311
58	1.09	0.999579310344827	0.0904206896551725
59	1.04	1.00157931034483	0.0384206896551726
60	1	0.979579310344827	0.0204206896551725
61	1.04	0.994310344827587	0.0456896551724135

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