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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 22 Nov 2007 09:59:43 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/22/t11957513350njysa5uza3bn5y.htm/, Retrieved Thu, 02 May 2024 22:40:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6078, Retrieved Thu, 02 May 2024 22:40:41 +0000

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Estimated Impact

208

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

-       [Multiple Regression] [The seatbelt law q3] [2007-11-22 16:59:43] [89d26cd0a44959d9c8b169f34617598a] [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=6078&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=6078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6078&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] = + 7.68021390374331 + 0.363636363636362x[t] -0.0545751633986933M1[t] -0.233392751039809M2[t] -0.134598930481283M3[t] + 0.0714676173499709M4[t] + 0.0175341651812232M5[t] -0.169126559714794M6[t] -0.70306001188354M7[t] -0.704266191325014M8[t] -0.69819964349376M9[t] -0.14486036838978M10[t] -0.0187938205585262M11[t] + 0.0139334521687463t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  7.68021390374331 +  0.363636363636362x[t] -0.0545751633986933M1[t] -0.233392751039809M2[t] -0.134598930481283M3[t] +  0.0714676173499709M4[t] +  0.0175341651812232M5[t] -0.169126559714794M6[t] -0.70306001188354M7[t] -0.704266191325014M8[t] -0.69819964349376M9[t] -0.14486036838978M10[t] -0.0187938205585262M11[t] +  0.0139334521687463t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6078&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  7.68021390374331 +  0.363636363636362x[t] -0.0545751633986933M1[t] -0.233392751039809M2[t] -0.134598930481283M3[t] +  0.0714676173499709M4[t] +  0.0175341651812232M5[t] -0.169126559714794M6[t] -0.70306001188354M7[t] -0.704266191325014M8[t] -0.69819964349376M9[t] -0.14486036838978M10[t] -0.0187938205585262M11[t] +  0.0139334521687463t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6078&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] = + 7.68021390374331 + 0.363636363636362x[t] -0.0545751633986933M1[t] -0.233392751039809M2[t] -0.134598930481283M3[t] + 0.0714676173499709M4[t] + 0.0175341651812232M5[t] -0.169126559714794M6[t] -0.70306001188354M7[t] -0.704266191325014M8[t] -0.69819964349376M9[t] -0.14486036838978M10[t] -0.0187938205585262M11[t] + 0.0139334521687463t + 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)	7.68021390374331	0.177372	43.3	0	0
x	0.363636363636362	0.10566	3.4416	0.001224	0.000612
M1	-0.0545751633986933	0.20579	-0.2652	0.792016	0.396008
M2	-0.233392751039809	0.218064	-1.0703	0.289953	0.144977
M3	-0.134598930481283	0.215556	-0.6244	0.535368	0.267684
M4	0.0714676173499709	0.215256	0.332	0.741356	0.370678
M5	0.0175341651812232	0.21499	0.0816	0.935344	0.467672
M6	-0.169126559714794	0.216485	-0.7812	0.43858	0.21929
M7	-0.70306001188354	0.216177	-3.2522	0.002122	0.001061
M8	-0.704266191325014	0.214404	-3.2848	0.001933	0.000966
M9	-0.69819964349376	0.21428	-3.2584	0.002085	0.001043
M10	-0.14486036838978	0.215461	-0.6723	0.504668	0.252334
M11	-0.0187938205585262	0.215293	-0.0873	0.930809	0.465404
t	0.0139334521687463	0.002761	5.0472	7e-06	4e-06

\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) & 7.68021390374331 & 0.177372 & 43.3 & 0 & 0 \tabularnewline
x & 0.363636363636362 & 0.10566 & 3.4416 & 0.001224 & 0.000612 \tabularnewline
M1 & -0.0545751633986933 & 0.20579 & -0.2652 & 0.792016 & 0.396008 \tabularnewline
M2 & -0.233392751039809 & 0.218064 & -1.0703 & 0.289953 & 0.144977 \tabularnewline
M3 & -0.134598930481283 & 0.215556 & -0.6244 & 0.535368 & 0.267684 \tabularnewline
M4 & 0.0714676173499709 & 0.215256 & 0.332 & 0.741356 & 0.370678 \tabularnewline
M5 & 0.0175341651812232 & 0.21499 & 0.0816 & 0.935344 & 0.467672 \tabularnewline
M6 & -0.169126559714794 & 0.216485 & -0.7812 & 0.43858 & 0.21929 \tabularnewline
M7 & -0.70306001188354 & 0.216177 & -3.2522 & 0.002122 & 0.001061 \tabularnewline
M8 & -0.704266191325014 & 0.214404 & -3.2848 & 0.001933 & 0.000966 \tabularnewline
M9 & -0.69819964349376 & 0.21428 & -3.2584 & 0.002085 & 0.001043 \tabularnewline
M10 & -0.14486036838978 & 0.215461 & -0.6723 & 0.504668 & 0.252334 \tabularnewline
M11 & -0.0187938205585262 & 0.215293 & -0.0873 & 0.930809 & 0.465404 \tabularnewline
t & 0.0139334521687463 & 0.002761 & 5.0472 & 7e-06 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6078&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]7.68021390374331[/C][C]0.177372[/C][C]43.3[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]0.363636363636362[/C][C]0.10566[/C][C]3.4416[/C][C]0.001224[/C][C]0.000612[/C][/ROW]
[ROW][C]M1[/C][C]-0.0545751633986933[/C][C]0.20579[/C][C]-0.2652[/C][C]0.792016[/C][C]0.396008[/C][/ROW]
[ROW][C]M2[/C][C]-0.233392751039809[/C][C]0.218064[/C][C]-1.0703[/C][C]0.289953[/C][C]0.144977[/C][/ROW]
[ROW][C]M3[/C][C]-0.134598930481283[/C][C]0.215556[/C][C]-0.6244[/C][C]0.535368[/C][C]0.267684[/C][/ROW]
[ROW][C]M4[/C][C]0.0714676173499709[/C][C]0.215256[/C][C]0.332[/C][C]0.741356[/C][C]0.370678[/C][/ROW]
[ROW][C]M5[/C][C]0.0175341651812232[/C][C]0.21499[/C][C]0.0816[/C][C]0.935344[/C][C]0.467672[/C][/ROW]
[ROW][C]M6[/C][C]-0.169126559714794[/C][C]0.216485[/C][C]-0.7812[/C][C]0.43858[/C][C]0.21929[/C][/ROW]
[ROW][C]M7[/C][C]-0.70306001188354[/C][C]0.216177[/C][C]-3.2522[/C][C]0.002122[/C][C]0.001061[/C][/ROW]
[ROW][C]M8[/C][C]-0.704266191325014[/C][C]0.214404[/C][C]-3.2848[/C][C]0.001933[/C][C]0.000966[/C][/ROW]
[ROW][C]M9[/C][C]-0.69819964349376[/C][C]0.21428[/C][C]-3.2584[/C][C]0.002085[/C][C]0.001043[/C][/ROW]
[ROW][C]M10[/C][C]-0.14486036838978[/C][C]0.215461[/C][C]-0.6723[/C][C]0.504668[/C][C]0.252334[/C][/ROW]
[ROW][C]M11[/C][C]-0.0187938205585262[/C][C]0.215293[/C][C]-0.0873[/C][C]0.930809[/C][C]0.465404[/C][/ROW]
[ROW][C]t[/C][C]0.0139334521687463[/C][C]0.002761[/C][C]5.0472[/C][C]7e-06[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6078&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)	7.68021390374331	0.177372	43.3	0	0
x	0.363636363636362	0.10566	3.4416	0.001224	0.000612
M1	-0.0545751633986933	0.20579	-0.2652	0.792016	0.396008
M2	-0.233392751039809	0.218064	-1.0703	0.289953	0.144977
M3	-0.134598930481283	0.215556	-0.6244	0.535368	0.267684
M4	0.0714676173499709	0.215256	0.332	0.741356	0.370678
M5	0.0175341651812232	0.21499	0.0816	0.935344	0.467672
M6	-0.169126559714794	0.216485	-0.7812	0.43858	0.21929
M7	-0.70306001188354	0.216177	-3.2522	0.002122	0.001061
M8	-0.704266191325014	0.214404	-3.2848	0.001933	0.000966
M9	-0.69819964349376	0.21428	-3.2584	0.002085	0.001043
M10	-0.14486036838978	0.215461	-0.6723	0.504668	0.252334
M11	-0.0187938205585262	0.215293	-0.0873	0.930809	0.465404
t	0.0139334521687463	0.002761	5.0472	7e-06	4e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.832574434891245
R-squared	0.693180189634476
Adjusted R-squared	0.608315135703587
F-TEST (value)	8.1680286234069
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	3.14613436414035e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.338552981283977
Sum Squared Residuals	5.38705169340464

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.832574434891245 \tabularnewline
R-squared & 0.693180189634476 \tabularnewline
Adjusted R-squared & 0.608315135703587 \tabularnewline
F-TEST (value) & 8.1680286234069 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 3.14613436414035e-08 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.338552981283977 \tabularnewline
Sum Squared Residuals & 5.38705169340464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6078&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.832574434891245[/C][/ROW]
[ROW][C]R-squared[/C][C]0.693180189634476[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.608315135703587[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.1680286234069[/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]3.14613436414035e-08[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.338552981283977[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5.38705169340464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6078&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	0.832574434891245
R-squared	0.693180189634476
Adjusted R-squared	0.608315135703587
F-TEST (value)	8.1680286234069
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	3.14613436414035e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.338552981283977
Sum Squared Residuals	5.38705169340464

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.8	8.00320855614973	-0.203208556149734
2	7.4	7.83832442067736	-0.438324420677364
3	7.4	7.58741532976827	-0.187415329768271
4	7.5	7.80741532976827	-0.307415329768272
5	7.4	7.76741532976827	-0.36741532976827
6	7.4	7.594688057041	-0.194688057040999
7	7	7.074688057041	-0.0746880570409974
8	6.9	7.08741532976827	-0.187415329768271
9	6.9	7.10741532976827	-0.207415329768272
10	7.6	7.674688057041	-0.0746880570409988
11	7.7	7.814688057041	-0.114688057040998
12	7.6	7.84741532976827	-0.247415329768271
13	8.2	7.80677361853832	0.393226381461676
14	8	7.64188948306595	0.358110516934046
15	8.1	7.75461675579323	0.345383244206773
16	8.3	7.97461675579323	0.325383244206774
17	8.2	7.93461675579323	0.265383244206773
18	8.1	8.12552584670232	-0.0255258467023171
19	7.7	7.60552584670232	0.0944741532976826
20	7.6	7.61825311942959	-0.0182531194295898
21	7.7	7.63825311942959	0.0617468805704104
22	8.2	8.20552584670232	-0.00552584670231735
23	8.4	8.34552584670232	0.0544741532976839
24	8.4	8.37825311942959	0.0217468805704113
25	8.6	8.33761140819964	0.262388591800357
26	8.4	8.17272727272727	0.227272727272728
27	8.5	8.28545454545455	0.214545454545455
28	8.7	8.50545454545454	0.194545454545454
29	8.7	8.46545454545454	0.234545454545455
30	8.6	8.29272727272727	0.307272727272727
31	7.4	7.77272727272727	-0.372727272727273
32	7.3	7.78545454545455	-0.485454545454545
33	7.4	7.80545454545455	-0.405454545454545
34	9	8.37272727272727	0.627272727272728
35	9.2	8.51272727272727	0.687272727272727
36	9.2	8.54545454545454	0.654545454545454
37	8.5	8.5048128342246	-0.00481283422459798
38	8.3	8.33992869875223	-0.0399286987522274
39	8.3	8.4526559714795	-0.152655971479500
40	8.6	8.6726559714795	-0.0726559714795008
41	8.6	8.6326559714795	-0.0326559714795006
42	8.5	8.45992869875223	0.040071301247772
43	8.1	7.93992869875223	0.160071301247771
44	8.1	7.9526559714795	0.147344028520499
45	8	7.9726559714795	0.0273440285204990
46	8.6	8.53992869875223	0.0600713012477719
47	8.7	8.67992869875223	0.0200713012477715
48	8.7	8.7126559714795	-0.0126559714795011
49	8.6	8.67201426024955	-0.072014260249554
50	8.4	8.50713012477718	-0.107130124777183
51	8.4	8.61985739750446	-0.219857397504456
52	8.7	8.83985739750446	-0.139857397504457
53	8.7	8.79985739750446	-0.0998573975044566
54	8.5	8.62713012477718	-0.127130124777184
55	8.3	8.10713012477718	0.192869875222816
56	8.3	7.75622103386809	0.543778966131907
57	8.3	7.7762210338681	0.523778966131907
58	8.1	8.70713012477718	-0.607130124777184
59	8.2	8.84713012477718	-0.647130124777184
60	8.1	8.5162210338681	-0.416221033868093
61	8.1	8.47557932263815	-0.375579322638147

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.8 & 8.00320855614973 & -0.203208556149734 \tabularnewline
2 & 7.4 & 7.83832442067736 & -0.438324420677364 \tabularnewline
3 & 7.4 & 7.58741532976827 & -0.187415329768271 \tabularnewline
4 & 7.5 & 7.80741532976827 & -0.307415329768272 \tabularnewline
5 & 7.4 & 7.76741532976827 & -0.36741532976827 \tabularnewline
6 & 7.4 & 7.594688057041 & -0.194688057040999 \tabularnewline
7 & 7 & 7.074688057041 & -0.0746880570409974 \tabularnewline
8 & 6.9 & 7.08741532976827 & -0.187415329768271 \tabularnewline
9 & 6.9 & 7.10741532976827 & -0.207415329768272 \tabularnewline
10 & 7.6 & 7.674688057041 & -0.0746880570409988 \tabularnewline
11 & 7.7 & 7.814688057041 & -0.114688057040998 \tabularnewline
12 & 7.6 & 7.84741532976827 & -0.247415329768271 \tabularnewline
13 & 8.2 & 7.80677361853832 & 0.393226381461676 \tabularnewline
14 & 8 & 7.64188948306595 & 0.358110516934046 \tabularnewline
15 & 8.1 & 7.75461675579323 & 0.345383244206773 \tabularnewline
16 & 8.3 & 7.97461675579323 & 0.325383244206774 \tabularnewline
17 & 8.2 & 7.93461675579323 & 0.265383244206773 \tabularnewline
18 & 8.1 & 8.12552584670232 & -0.0255258467023171 \tabularnewline
19 & 7.7 & 7.60552584670232 & 0.0944741532976826 \tabularnewline
20 & 7.6 & 7.61825311942959 & -0.0182531194295898 \tabularnewline
21 & 7.7 & 7.63825311942959 & 0.0617468805704104 \tabularnewline
22 & 8.2 & 8.20552584670232 & -0.00552584670231735 \tabularnewline
23 & 8.4 & 8.34552584670232 & 0.0544741532976839 \tabularnewline
24 & 8.4 & 8.37825311942959 & 0.0217468805704113 \tabularnewline
25 & 8.6 & 8.33761140819964 & 0.262388591800357 \tabularnewline
26 & 8.4 & 8.17272727272727 & 0.227272727272728 \tabularnewline
27 & 8.5 & 8.28545454545455 & 0.214545454545455 \tabularnewline
28 & 8.7 & 8.50545454545454 & 0.194545454545454 \tabularnewline
29 & 8.7 & 8.46545454545454 & 0.234545454545455 \tabularnewline
30 & 8.6 & 8.29272727272727 & 0.307272727272727 \tabularnewline
31 & 7.4 & 7.77272727272727 & -0.372727272727273 \tabularnewline
32 & 7.3 & 7.78545454545455 & -0.485454545454545 \tabularnewline
33 & 7.4 & 7.80545454545455 & -0.405454545454545 \tabularnewline
34 & 9 & 8.37272727272727 & 0.627272727272728 \tabularnewline
35 & 9.2 & 8.51272727272727 & 0.687272727272727 \tabularnewline
36 & 9.2 & 8.54545454545454 & 0.654545454545454 \tabularnewline
37 & 8.5 & 8.5048128342246 & -0.00481283422459798 \tabularnewline
38 & 8.3 & 8.33992869875223 & -0.0399286987522274 \tabularnewline
39 & 8.3 & 8.4526559714795 & -0.152655971479500 \tabularnewline
40 & 8.6 & 8.6726559714795 & -0.0726559714795008 \tabularnewline
41 & 8.6 & 8.6326559714795 & -0.0326559714795006 \tabularnewline
42 & 8.5 & 8.45992869875223 & 0.040071301247772 \tabularnewline
43 & 8.1 & 7.93992869875223 & 0.160071301247771 \tabularnewline
44 & 8.1 & 7.9526559714795 & 0.147344028520499 \tabularnewline
45 & 8 & 7.9726559714795 & 0.0273440285204990 \tabularnewline
46 & 8.6 & 8.53992869875223 & 0.0600713012477719 \tabularnewline
47 & 8.7 & 8.67992869875223 & 0.0200713012477715 \tabularnewline
48 & 8.7 & 8.7126559714795 & -0.0126559714795011 \tabularnewline
49 & 8.6 & 8.67201426024955 & -0.072014260249554 \tabularnewline
50 & 8.4 & 8.50713012477718 & -0.107130124777183 \tabularnewline
51 & 8.4 & 8.61985739750446 & -0.219857397504456 \tabularnewline
52 & 8.7 & 8.83985739750446 & -0.139857397504457 \tabularnewline
53 & 8.7 & 8.79985739750446 & -0.0998573975044566 \tabularnewline
54 & 8.5 & 8.62713012477718 & -0.127130124777184 \tabularnewline
55 & 8.3 & 8.10713012477718 & 0.192869875222816 \tabularnewline
56 & 8.3 & 7.75622103386809 & 0.543778966131907 \tabularnewline
57 & 8.3 & 7.7762210338681 & 0.523778966131907 \tabularnewline
58 & 8.1 & 8.70713012477718 & -0.607130124777184 \tabularnewline
59 & 8.2 & 8.84713012477718 & -0.647130124777184 \tabularnewline
60 & 8.1 & 8.5162210338681 & -0.416221033868093 \tabularnewline
61 & 8.1 & 8.47557932263815 & -0.375579322638147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6078&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]7.8[/C][C]8.00320855614973[/C][C]-0.203208556149734[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]7.83832442067736[/C][C]-0.438324420677364[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]7.58741532976827[/C][C]-0.187415329768271[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]7.80741532976827[/C][C]-0.307415329768272[/C][/ROW]
[ROW][C]5[/C][C]7.4[/C][C]7.76741532976827[/C][C]-0.36741532976827[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]7.594688057041[/C][C]-0.194688057040999[/C][/ROW]
[ROW][C]7[/C][C]7[/C][C]7.074688057041[/C][C]-0.0746880570409974[/C][/ROW]
[ROW][C]8[/C][C]6.9[/C][C]7.08741532976827[/C][C]-0.187415329768271[/C][/ROW]
[ROW][C]9[/C][C]6.9[/C][C]7.10741532976827[/C][C]-0.207415329768272[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.674688057041[/C][C]-0.0746880570409988[/C][/ROW]
[ROW][C]11[/C][C]7.7[/C][C]7.814688057041[/C][C]-0.114688057040998[/C][/ROW]
[ROW][C]12[/C][C]7.6[/C][C]7.84741532976827[/C][C]-0.247415329768271[/C][/ROW]
[ROW][C]13[/C][C]8.2[/C][C]7.80677361853832[/C][C]0.393226381461676[/C][/ROW]
[ROW][C]14[/C][C]8[/C][C]7.64188948306595[/C][C]0.358110516934046[/C][/ROW]
[ROW][C]15[/C][C]8.1[/C][C]7.75461675579323[/C][C]0.345383244206773[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]7.97461675579323[/C][C]0.325383244206774[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]7.93461675579323[/C][C]0.265383244206773[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.12552584670232[/C][C]-0.0255258467023171[/C][/ROW]
[ROW][C]19[/C][C]7.7[/C][C]7.60552584670232[/C][C]0.0944741532976826[/C][/ROW]
[ROW][C]20[/C][C]7.6[/C][C]7.61825311942959[/C][C]-0.0182531194295898[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.63825311942959[/C][C]0.0617468805704104[/C][/ROW]
[ROW][C]22[/C][C]8.2[/C][C]8.20552584670232[/C][C]-0.00552584670231735[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]8.34552584670232[/C][C]0.0544741532976839[/C][/ROW]
[ROW][C]24[/C][C]8.4[/C][C]8.37825311942959[/C][C]0.0217468805704113[/C][/ROW]
[ROW][C]25[/C][C]8.6[/C][C]8.33761140819964[/C][C]0.262388591800357[/C][/ROW]
[ROW][C]26[/C][C]8.4[/C][C]8.17272727272727[/C][C]0.227272727272728[/C][/ROW]
[ROW][C]27[/C][C]8.5[/C][C]8.28545454545455[/C][C]0.214545454545455[/C][/ROW]
[ROW][C]28[/C][C]8.7[/C][C]8.50545454545454[/C][C]0.194545454545454[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.46545454545454[/C][C]0.234545454545455[/C][/ROW]
[ROW][C]30[/C][C]8.6[/C][C]8.29272727272727[/C][C]0.307272727272727[/C][/ROW]
[ROW][C]31[/C][C]7.4[/C][C]7.77272727272727[/C][C]-0.372727272727273[/C][/ROW]
[ROW][C]32[/C][C]7.3[/C][C]7.78545454545455[/C][C]-0.485454545454545[/C][/ROW]
[ROW][C]33[/C][C]7.4[/C][C]7.80545454545455[/C][C]-0.405454545454545[/C][/ROW]
[ROW][C]34[/C][C]9[/C][C]8.37272727272727[/C][C]0.627272727272728[/C][/ROW]
[ROW][C]35[/C][C]9.2[/C][C]8.51272727272727[/C][C]0.687272727272727[/C][/ROW]
[ROW][C]36[/C][C]9.2[/C][C]8.54545454545454[/C][C]0.654545454545454[/C][/ROW]
[ROW][C]37[/C][C]8.5[/C][C]8.5048128342246[/C][C]-0.00481283422459798[/C][/ROW]
[ROW][C]38[/C][C]8.3[/C][C]8.33992869875223[/C][C]-0.0399286987522274[/C][/ROW]
[ROW][C]39[/C][C]8.3[/C][C]8.4526559714795[/C][C]-0.152655971479500[/C][/ROW]
[ROW][C]40[/C][C]8.6[/C][C]8.6726559714795[/C][C]-0.0726559714795008[/C][/ROW]
[ROW][C]41[/C][C]8.6[/C][C]8.6326559714795[/C][C]-0.0326559714795006[/C][/ROW]
[ROW][C]42[/C][C]8.5[/C][C]8.45992869875223[/C][C]0.040071301247772[/C][/ROW]
[ROW][C]43[/C][C]8.1[/C][C]7.93992869875223[/C][C]0.160071301247771[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]7.9526559714795[/C][C]0.147344028520499[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]7.9726559714795[/C][C]0.0273440285204990[/C][/ROW]
[ROW][C]46[/C][C]8.6[/C][C]8.53992869875223[/C][C]0.0600713012477719[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.67992869875223[/C][C]0.0200713012477715[/C][/ROW]
[ROW][C]48[/C][C]8.7[/C][C]8.7126559714795[/C][C]-0.0126559714795011[/C][/ROW]
[ROW][C]49[/C][C]8.6[/C][C]8.67201426024955[/C][C]-0.072014260249554[/C][/ROW]
[ROW][C]50[/C][C]8.4[/C][C]8.50713012477718[/C][C]-0.107130124777183[/C][/ROW]
[ROW][C]51[/C][C]8.4[/C][C]8.61985739750446[/C][C]-0.219857397504456[/C][/ROW]
[ROW][C]52[/C][C]8.7[/C][C]8.83985739750446[/C][C]-0.139857397504457[/C][/ROW]
[ROW][C]53[/C][C]8.7[/C][C]8.79985739750446[/C][C]-0.0998573975044566[/C][/ROW]
[ROW][C]54[/C][C]8.5[/C][C]8.62713012477718[/C][C]-0.127130124777184[/C][/ROW]
[ROW][C]55[/C][C]8.3[/C][C]8.10713012477718[/C][C]0.192869875222816[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]7.75622103386809[/C][C]0.543778966131907[/C][/ROW]
[ROW][C]57[/C][C]8.3[/C][C]7.7762210338681[/C][C]0.523778966131907[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8.70713012477718[/C][C]-0.607130124777184[/C][/ROW]
[ROW][C]59[/C][C]8.2[/C][C]8.84713012477718[/C][C]-0.647130124777184[/C][/ROW]
[ROW][C]60[/C][C]8.1[/C][C]8.5162210338681[/C][C]-0.416221033868093[/C][/ROW]
[ROW][C]61[/C][C]8.1[/C][C]8.47557932263815[/C][C]-0.375579322638147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6078&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6078&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	7.8	8.00320855614973	-0.203208556149734
2	7.4	7.83832442067736	-0.438324420677364
3	7.4	7.58741532976827	-0.187415329768271
4	7.5	7.80741532976827	-0.307415329768272
5	7.4	7.76741532976827	-0.36741532976827
6	7.4	7.594688057041	-0.194688057040999
7	7	7.074688057041	-0.0746880570409974
8	6.9	7.08741532976827	-0.187415329768271
9	6.9	7.10741532976827	-0.207415329768272
10	7.6	7.674688057041	-0.0746880570409988
11	7.7	7.814688057041	-0.114688057040998
12	7.6	7.84741532976827	-0.247415329768271
13	8.2	7.80677361853832	0.393226381461676
14	8	7.64188948306595	0.358110516934046
15	8.1	7.75461675579323	0.345383244206773
16	8.3	7.97461675579323	0.325383244206774
17	8.2	7.93461675579323	0.265383244206773
18	8.1	8.12552584670232	-0.0255258467023171
19	7.7	7.60552584670232	0.0944741532976826
20	7.6	7.61825311942959	-0.0182531194295898
21	7.7	7.63825311942959	0.0617468805704104
22	8.2	8.20552584670232	-0.00552584670231735
23	8.4	8.34552584670232	0.0544741532976839
24	8.4	8.37825311942959	0.0217468805704113
25	8.6	8.33761140819964	0.262388591800357
26	8.4	8.17272727272727	0.227272727272728
27	8.5	8.28545454545455	0.214545454545455
28	8.7	8.50545454545454	0.194545454545454
29	8.7	8.46545454545454	0.234545454545455
30	8.6	8.29272727272727	0.307272727272727
31	7.4	7.77272727272727	-0.372727272727273
32	7.3	7.78545454545455	-0.485454545454545
33	7.4	7.80545454545455	-0.405454545454545
34	9	8.37272727272727	0.627272727272728
35	9.2	8.51272727272727	0.687272727272727
36	9.2	8.54545454545454	0.654545454545454
37	8.5	8.5048128342246	-0.00481283422459798
38	8.3	8.33992869875223	-0.0399286987522274
39	8.3	8.4526559714795	-0.152655971479500
40	8.6	8.6726559714795	-0.0726559714795008
41	8.6	8.6326559714795	-0.0326559714795006
42	8.5	8.45992869875223	0.040071301247772
43	8.1	7.93992869875223	0.160071301247771
44	8.1	7.9526559714795	0.147344028520499
45	8	7.9726559714795	0.0273440285204990
46	8.6	8.53992869875223	0.0600713012477719
47	8.7	8.67992869875223	0.0200713012477715
48	8.7	8.7126559714795	-0.0126559714795011
49	8.6	8.67201426024955	-0.072014260249554
50	8.4	8.50713012477718	-0.107130124777183
51	8.4	8.61985739750446	-0.219857397504456
52	8.7	8.83985739750446	-0.139857397504457
53	8.7	8.79985739750446	-0.0998573975044566
54	8.5	8.62713012477718	-0.127130124777184
55	8.3	8.10713012477718	0.192869875222816
56	8.3	7.75622103386809	0.543778966131907
57	8.3	7.7762210338681	0.523778966131907
58	8.1	8.70713012477718	-0.607130124777184
59	8.2	8.84713012477718	-0.647130124777184
60	8.1	8.5162210338681	-0.416221033868093
61	8.1	8.47557932263815	-0.375579322638147

Figure 1

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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