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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 11 Dec 2008 04:59:09 -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/Dec/11/t1228996821ouozkuzy675hhx2.htm/, Retrieved Fri, 17 May 2024 02:02:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32175, Retrieved Fri, 17 May 2024 02:02:38 +0000

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Original text written by user:

In samenwerking met Katrien Bourdiaudhy, St�phanie Claes en Kevin Engels

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

222

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Multiple Regression] [Q1 Case: the Seat...] [2008-11-19 13:07:53] [c993f605b206b366f754f7f8c1fcc291]
-   PD    [Multiple Regression] [Q3 seatbelt case] [2008-11-30 21:48:04] [7173087adebe3e3a714c80ea2417b3eb]
-    D      [Multiple Regression] [Multiple Linear R...] [2008-12-11 11:30:21] [c993f605b206b366f754f7f8c1fcc291]
-   P           [Multiple Regression] [Multiple Regressi...] [2008-12-11 11:59:09] [70ba55c7ff8e068610dc28fc16e6d1e2] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32175&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32175&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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 7.31533125 + 0.006171875x[t] -0.866765625M1[t] + 0.449634375000001M2[t] -0.492565624999999M3[t] -0.290965624999999M4[t] + 0.577200000000001M5[t] -0.861399999999998M6[t] -0.764199999999999M7[t] -0.6466M8[t] -0.0615999999999992M9[t] -1.2034M10[t] -0.410199999999999M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  7.31533125 +  0.006171875x[t] -0.866765625M1[t] +  0.449634375000001M2[t] -0.492565624999999M3[t] -0.290965624999999M4[t] +  0.577200000000001M5[t] -0.861399999999998M6[t] -0.764199999999999M7[t] -0.6466M8[t] -0.0615999999999992M9[t] -1.2034M10[t] -0.410199999999999M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32175&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  7.31533125 +  0.006171875x[t] -0.866765625M1[t] +  0.449634375000001M2[t] -0.492565624999999M3[t] -0.290965624999999M4[t] +  0.577200000000001M5[t] -0.861399999999998M6[t] -0.764199999999999M7[t] -0.6466M8[t] -0.0615999999999992M9[t] -1.2034M10[t] -0.410199999999999M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32175&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] = + 7.31533125 + 0.006171875x[t] -0.866765625M1[t] + 0.449634375000001M2[t] -0.492565624999999M3[t] -0.290965624999999M4[t] + 0.577200000000001M5[t] -0.861399999999998M6[t] -0.764199999999999M7[t] -0.6466M8[t] -0.0615999999999992M9[t] -1.2034M10[t] -0.410199999999999M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	7.31533125	0.425973	17.1732	0	0
x	0.006171875	0.258284	0.0239	0.981037	0.490518
M1	-0.866765625	0.586709	-1.4773	0.146256	0.073128
M2	0.449634375000001	0.586709	0.7664	0.44729	0.223645
M3	-0.492565624999999	0.586709	-0.8395	0.405417	0.202708
M4	-0.290965624999999	0.586709	-0.4959	0.622256	0.311128
M5	0.577200000000001	0.584431	0.9876	0.328392	0.164196
M6	-0.861399999999998	0.584431	-1.4739	0.147172	0.073586
M7	-0.764199999999999	0.584431	-1.3076	0.19737	0.098685
M8	-0.6466	0.584431	-1.1064	0.274195	0.137097
M9	-0.0615999999999992	0.584431	-0.1054	0.916506	0.458253
M10	-1.2034	0.584431	-2.0591	0.04505	0.022525
M11	-0.410199999999999	0.584431	-0.7019	0.486215	0.243108

\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) & 7.31533125 & 0.425973 & 17.1732 & 0 & 0 \tabularnewline
x & 0.006171875 & 0.258284 & 0.0239 & 0.981037 & 0.490518 \tabularnewline
M1 & -0.866765625 & 0.586709 & -1.4773 & 0.146256 & 0.073128 \tabularnewline
M2 & 0.449634375000001 & 0.586709 & 0.7664 & 0.44729 & 0.223645 \tabularnewline
M3 & -0.492565624999999 & 0.586709 & -0.8395 & 0.405417 & 0.202708 \tabularnewline
M4 & -0.290965624999999 & 0.586709 & -0.4959 & 0.622256 & 0.311128 \tabularnewline
M5 & 0.577200000000001 & 0.584431 & 0.9876 & 0.328392 & 0.164196 \tabularnewline
M6 & -0.861399999999998 & 0.584431 & -1.4739 & 0.147172 & 0.073586 \tabularnewline
M7 & -0.764199999999999 & 0.584431 & -1.3076 & 0.19737 & 0.098685 \tabularnewline
M8 & -0.6466 & 0.584431 & -1.1064 & 0.274195 & 0.137097 \tabularnewline
M9 & -0.0615999999999992 & 0.584431 & -0.1054 & 0.916506 & 0.458253 \tabularnewline
M10 & -1.2034 & 0.584431 & -2.0591 & 0.04505 & 0.022525 \tabularnewline
M11 & -0.410199999999999 & 0.584431 & -0.7019 & 0.486215 & 0.243108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32175&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]7.31533125[/C][C]0.425973[/C][C]17.1732[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]0.006171875[/C][C]0.258284[/C][C]0.0239[/C][C]0.981037[/C][C]0.490518[/C][/ROW]
[ROW][C]M1[/C][C]-0.866765625[/C][C]0.586709[/C][C]-1.4773[/C][C]0.146256[/C][C]0.073128[/C][/ROW]
[ROW][C]M2[/C][C]0.449634375000001[/C][C]0.586709[/C][C]0.7664[/C][C]0.44729[/C][C]0.223645[/C][/ROW]
[ROW][C]M3[/C][C]-0.492565624999999[/C][C]0.586709[/C][C]-0.8395[/C][C]0.405417[/C][C]0.202708[/C][/ROW]
[ROW][C]M4[/C][C]-0.290965624999999[/C][C]0.586709[/C][C]-0.4959[/C][C]0.622256[/C][C]0.311128[/C][/ROW]
[ROW][C]M5[/C][C]0.577200000000001[/C][C]0.584431[/C][C]0.9876[/C][C]0.328392[/C][C]0.164196[/C][/ROW]
[ROW][C]M6[/C][C]-0.861399999999998[/C][C]0.584431[/C][C]-1.4739[/C][C]0.147172[/C][C]0.073586[/C][/ROW]
[ROW][C]M7[/C][C]-0.764199999999999[/C][C]0.584431[/C][C]-1.3076[/C][C]0.19737[/C][C]0.098685[/C][/ROW]
[ROW][C]M8[/C][C]-0.6466[/C][C]0.584431[/C][C]-1.1064[/C][C]0.274195[/C][C]0.137097[/C][/ROW]
[ROW][C]M9[/C][C]-0.0615999999999992[/C][C]0.584431[/C][C]-0.1054[/C][C]0.916506[/C][C]0.458253[/C][/ROW]
[ROW][C]M10[/C][C]-1.2034[/C][C]0.584431[/C][C]-2.0591[/C][C]0.04505[/C][C]0.022525[/C][/ROW]
[ROW][C]M11[/C][C]-0.410199999999999[/C][C]0.584431[/C][C]-0.7019[/C][C]0.486215[/C][C]0.243108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32175&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)	7.31533125	0.425973	17.1732	0	0
x	0.006171875	0.258284	0.0239	0.981037	0.490518
M1	-0.866765625	0.586709	-1.4773	0.146256	0.073128
M2	0.449634375000001	0.586709	0.7664	0.44729	0.223645
M3	-0.492565624999999	0.586709	-0.8395	0.405417	0.202708
M4	-0.290965624999999	0.586709	-0.4959	0.622256	0.311128
M5	0.577200000000001	0.584431	0.9876	0.328392	0.164196
M6	-0.861399999999998	0.584431	-1.4739	0.147172	0.073586
M7	-0.764199999999999	0.584431	-1.3076	0.19737	0.098685
M8	-0.6466	0.584431	-1.1064	0.274195	0.137097
M9	-0.0615999999999992	0.584431	-0.1054	0.916506	0.458253
M10	-1.2034	0.584431	-2.0591	0.04505	0.022525
M11	-0.410199999999999	0.584431	-0.7019	0.486215	0.243108

Multiple Linear Regression - Regression Statistics
Multiple R	0.536051580390871
R-squared	0.28735129683955
Adjusted R-squared	0.105398436458159
F-TEST (value)	1.57926232232477
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	0.13072387664634
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.924065766539892
Sum Squared Residuals	40.133184421875

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.536051580390871 \tabularnewline
R-squared & 0.28735129683955 \tabularnewline
Adjusted R-squared & 0.105398436458159 \tabularnewline
F-TEST (value) & 1.57926232232477 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.13072387664634 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.924065766539892 \tabularnewline
Sum Squared Residuals & 40.133184421875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32175&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.536051580390871[/C][/ROW]
[ROW][C]R-squared[/C][C]0.28735129683955[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.105398436458159[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.57926232232477[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.13072387664634[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.924065766539892[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]40.133184421875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32175&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32175&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	0.536051580390871
R-squared	0.28735129683955
Adjusted R-squared	0.105398436458159
F-TEST (value)	1.57926232232477
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	0.13072387664634
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.924065766539892
Sum Squared Residuals	40.133184421875

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	5.014	6.448565625	-1.43456562500001
2	6.153	7.764965625	-1.61196562500000
3	6.441	6.822765625	-0.381765625000001
4	5.584	7.024365625	-1.440365625
5	6.427	7.89253125	-1.46553125
6	6.062	6.45393125	-0.391931250000000
7	5.589	6.55113125	-0.96213125
8	6.216	6.66873125	-0.452731250000001
9	5.809	7.25373125	-1.44473125
10	4.989	6.11193125	-1.12293125000000
11	6.706	6.90513125	-0.199131250000000
12	7.174	7.31533125	-0.141331249999998
13	6.122	6.448565625	-0.326565624999999
14	8.075	7.764965625	0.310034374999999
15	6.292	6.822765625	-0.530765625
16	6.337	7.024365625	-0.687365625
17	8.576	7.89253125	0.68346875
18	6.077	6.45393125	-0.37693125
19	5.931	6.55113125	-0.62013125
20	6.288	6.66873125	-0.380731250000000
21	7.167	7.25373125	-0.0867312500000003
22	6.054	6.11193125	-0.05793125
23	6.468	6.90513125	-0.43713125
24	6.401	7.31533125	-0.91433125
25	6.927	6.448565625	0.478434375000001
26	7.914	7.764965625	0.149034374999999
27	7.728	6.822765625	0.905234375
28	8.699	7.024365625	1.674634375
29	8.522	7.89253125	0.62946875
30	6.481	6.45393125	0.0270687499999994
31	7.502	6.55113125	0.95086875
32	7.778	6.66873125	1.10926875
33	7.424	7.25373125	0.170268750000000
34	6.941	6.11193125	0.82906875
35	8.574	6.90513125	1.66886875
36	9.169	7.31533125	1.85366875
37	7.701	6.448565625	1.252434375
38	9.035	7.764965625	1.270034375
39	7.158	6.822765625	0.335234375000001
40	8.195	7.024365625	1.170634375
41	8.124	7.898703125	0.225296875000000
42	7.073	6.460103125	0.612896875
43	7.017	6.557303125	0.459696875
44	7.39	6.674903125	0.715096875
45	7.776	7.259903125	0.516096875
46	6.197	6.118103125	0.0788968749999997
47	6.889	6.911303125	-0.0223031249999998
48	7.087	7.321503125	-0.234503124999999
49	6.485	6.4547375	0.0302625000000019
50	7.654	7.7711375	-0.117137500000001
51	6.501	6.8289375	-0.327937499999999
52	6.313	7.0305375	-0.717537500
53	7.826	7.898703125	-0.0727031250000006
54	6.589	6.460103125	0.128896875
55	6.729	6.557303125	0.171696875
56	5.684	6.674903125	-0.990903125
57	8.105	7.259903125	0.845096875
58	6.391	6.118103125	0.272896875000000
59	5.901	6.911303125	-1.010303125
60	6.758	7.321503125	-0.563503124999999

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 5.014 & 6.448565625 & -1.43456562500001 \tabularnewline
2 & 6.153 & 7.764965625 & -1.61196562500000 \tabularnewline
3 & 6.441 & 6.822765625 & -0.381765625000001 \tabularnewline
4 & 5.584 & 7.024365625 & -1.440365625 \tabularnewline
5 & 6.427 & 7.89253125 & -1.46553125 \tabularnewline
6 & 6.062 & 6.45393125 & -0.391931250000000 \tabularnewline
7 & 5.589 & 6.55113125 & -0.96213125 \tabularnewline
8 & 6.216 & 6.66873125 & -0.452731250000001 \tabularnewline
9 & 5.809 & 7.25373125 & -1.44473125 \tabularnewline
10 & 4.989 & 6.11193125 & -1.12293125000000 \tabularnewline
11 & 6.706 & 6.90513125 & -0.199131250000000 \tabularnewline
12 & 7.174 & 7.31533125 & -0.141331249999998 \tabularnewline
13 & 6.122 & 6.448565625 & -0.326565624999999 \tabularnewline
14 & 8.075 & 7.764965625 & 0.310034374999999 \tabularnewline
15 & 6.292 & 6.822765625 & -0.530765625 \tabularnewline
16 & 6.337 & 7.024365625 & -0.687365625 \tabularnewline
17 & 8.576 & 7.89253125 & 0.68346875 \tabularnewline
18 & 6.077 & 6.45393125 & -0.37693125 \tabularnewline
19 & 5.931 & 6.55113125 & -0.62013125 \tabularnewline
20 & 6.288 & 6.66873125 & -0.380731250000000 \tabularnewline
21 & 7.167 & 7.25373125 & -0.0867312500000003 \tabularnewline
22 & 6.054 & 6.11193125 & -0.05793125 \tabularnewline
23 & 6.468 & 6.90513125 & -0.43713125 \tabularnewline
24 & 6.401 & 7.31533125 & -0.91433125 \tabularnewline
25 & 6.927 & 6.448565625 & 0.478434375000001 \tabularnewline
26 & 7.914 & 7.764965625 & 0.149034374999999 \tabularnewline
27 & 7.728 & 6.822765625 & 0.905234375 \tabularnewline
28 & 8.699 & 7.024365625 & 1.674634375 \tabularnewline
29 & 8.522 & 7.89253125 & 0.62946875 \tabularnewline
30 & 6.481 & 6.45393125 & 0.0270687499999994 \tabularnewline
31 & 7.502 & 6.55113125 & 0.95086875 \tabularnewline
32 & 7.778 & 6.66873125 & 1.10926875 \tabularnewline
33 & 7.424 & 7.25373125 & 0.170268750000000 \tabularnewline
34 & 6.941 & 6.11193125 & 0.82906875 \tabularnewline
35 & 8.574 & 6.90513125 & 1.66886875 \tabularnewline
36 & 9.169 & 7.31533125 & 1.85366875 \tabularnewline
37 & 7.701 & 6.448565625 & 1.252434375 \tabularnewline
38 & 9.035 & 7.764965625 & 1.270034375 \tabularnewline
39 & 7.158 & 6.822765625 & 0.335234375000001 \tabularnewline
40 & 8.195 & 7.024365625 & 1.170634375 \tabularnewline
41 & 8.124 & 7.898703125 & 0.225296875000000 \tabularnewline
42 & 7.073 & 6.460103125 & 0.612896875 \tabularnewline
43 & 7.017 & 6.557303125 & 0.459696875 \tabularnewline
44 & 7.39 & 6.674903125 & 0.715096875 \tabularnewline
45 & 7.776 & 7.259903125 & 0.516096875 \tabularnewline
46 & 6.197 & 6.118103125 & 0.0788968749999997 \tabularnewline
47 & 6.889 & 6.911303125 & -0.0223031249999998 \tabularnewline
48 & 7.087 & 7.321503125 & -0.234503124999999 \tabularnewline
49 & 6.485 & 6.4547375 & 0.0302625000000019 \tabularnewline
50 & 7.654 & 7.7711375 & -0.117137500000001 \tabularnewline
51 & 6.501 & 6.8289375 & -0.327937499999999 \tabularnewline
52 & 6.313 & 7.0305375 & -0.717537500 \tabularnewline
53 & 7.826 & 7.898703125 & -0.0727031250000006 \tabularnewline
54 & 6.589 & 6.460103125 & 0.128896875 \tabularnewline
55 & 6.729 & 6.557303125 & 0.171696875 \tabularnewline
56 & 5.684 & 6.674903125 & -0.990903125 \tabularnewline
57 & 8.105 & 7.259903125 & 0.845096875 \tabularnewline
58 & 6.391 & 6.118103125 & 0.272896875000000 \tabularnewline
59 & 5.901 & 6.911303125 & -1.010303125 \tabularnewline
60 & 6.758 & 7.321503125 & -0.563503124999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32175&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]5.014[/C][C]6.448565625[/C][C]-1.43456562500001[/C][/ROW]
[ROW][C]2[/C][C]6.153[/C][C]7.764965625[/C][C]-1.61196562500000[/C][/ROW]
[ROW][C]3[/C][C]6.441[/C][C]6.822765625[/C][C]-0.381765625000001[/C][/ROW]
[ROW][C]4[/C][C]5.584[/C][C]7.024365625[/C][C]-1.440365625[/C][/ROW]
[ROW][C]5[/C][C]6.427[/C][C]7.89253125[/C][C]-1.46553125[/C][/ROW]
[ROW][C]6[/C][C]6.062[/C][C]6.45393125[/C][C]-0.391931250000000[/C][/ROW]
[ROW][C]7[/C][C]5.589[/C][C]6.55113125[/C][C]-0.96213125[/C][/ROW]
[ROW][C]8[/C][C]6.216[/C][C]6.66873125[/C][C]-0.452731250000001[/C][/ROW]
[ROW][C]9[/C][C]5.809[/C][C]7.25373125[/C][C]-1.44473125[/C][/ROW]
[ROW][C]10[/C][C]4.989[/C][C]6.11193125[/C][C]-1.12293125000000[/C][/ROW]
[ROW][C]11[/C][C]6.706[/C][C]6.90513125[/C][C]-0.199131250000000[/C][/ROW]
[ROW][C]12[/C][C]7.174[/C][C]7.31533125[/C][C]-0.141331249999998[/C][/ROW]
[ROW][C]13[/C][C]6.122[/C][C]6.448565625[/C][C]-0.326565624999999[/C][/ROW]
[ROW][C]14[/C][C]8.075[/C][C]7.764965625[/C][C]0.310034374999999[/C][/ROW]
[ROW][C]15[/C][C]6.292[/C][C]6.822765625[/C][C]-0.530765625[/C][/ROW]
[ROW][C]16[/C][C]6.337[/C][C]7.024365625[/C][C]-0.687365625[/C][/ROW]
[ROW][C]17[/C][C]8.576[/C][C]7.89253125[/C][C]0.68346875[/C][/ROW]
[ROW][C]18[/C][C]6.077[/C][C]6.45393125[/C][C]-0.37693125[/C][/ROW]
[ROW][C]19[/C][C]5.931[/C][C]6.55113125[/C][C]-0.62013125[/C][/ROW]
[ROW][C]20[/C][C]6.288[/C][C]6.66873125[/C][C]-0.380731250000000[/C][/ROW]
[ROW][C]21[/C][C]7.167[/C][C]7.25373125[/C][C]-0.0867312500000003[/C][/ROW]
[ROW][C]22[/C][C]6.054[/C][C]6.11193125[/C][C]-0.05793125[/C][/ROW]
[ROW][C]23[/C][C]6.468[/C][C]6.90513125[/C][C]-0.43713125[/C][/ROW]
[ROW][C]24[/C][C]6.401[/C][C]7.31533125[/C][C]-0.91433125[/C][/ROW]
[ROW][C]25[/C][C]6.927[/C][C]6.448565625[/C][C]0.478434375000001[/C][/ROW]
[ROW][C]26[/C][C]7.914[/C][C]7.764965625[/C][C]0.149034374999999[/C][/ROW]
[ROW][C]27[/C][C]7.728[/C][C]6.822765625[/C][C]0.905234375[/C][/ROW]
[ROW][C]28[/C][C]8.699[/C][C]7.024365625[/C][C]1.674634375[/C][/ROW]
[ROW][C]29[/C][C]8.522[/C][C]7.89253125[/C][C]0.62946875[/C][/ROW]
[ROW][C]30[/C][C]6.481[/C][C]6.45393125[/C][C]0.0270687499999994[/C][/ROW]
[ROW][C]31[/C][C]7.502[/C][C]6.55113125[/C][C]0.95086875[/C][/ROW]
[ROW][C]32[/C][C]7.778[/C][C]6.66873125[/C][C]1.10926875[/C][/ROW]
[ROW][C]33[/C][C]7.424[/C][C]7.25373125[/C][C]0.170268750000000[/C][/ROW]
[ROW][C]34[/C][C]6.941[/C][C]6.11193125[/C][C]0.82906875[/C][/ROW]
[ROW][C]35[/C][C]8.574[/C][C]6.90513125[/C][C]1.66886875[/C][/ROW]
[ROW][C]36[/C][C]9.169[/C][C]7.31533125[/C][C]1.85366875[/C][/ROW]
[ROW][C]37[/C][C]7.701[/C][C]6.448565625[/C][C]1.252434375[/C][/ROW]
[ROW][C]38[/C][C]9.035[/C][C]7.764965625[/C][C]1.270034375[/C][/ROW]
[ROW][C]39[/C][C]7.158[/C][C]6.822765625[/C][C]0.335234375000001[/C][/ROW]
[ROW][C]40[/C][C]8.195[/C][C]7.024365625[/C][C]1.170634375[/C][/ROW]
[ROW][C]41[/C][C]8.124[/C][C]7.898703125[/C][C]0.225296875000000[/C][/ROW]
[ROW][C]42[/C][C]7.073[/C][C]6.460103125[/C][C]0.612896875[/C][/ROW]
[ROW][C]43[/C][C]7.017[/C][C]6.557303125[/C][C]0.459696875[/C][/ROW]
[ROW][C]44[/C][C]7.39[/C][C]6.674903125[/C][C]0.715096875[/C][/ROW]
[ROW][C]45[/C][C]7.776[/C][C]7.259903125[/C][C]0.516096875[/C][/ROW]
[ROW][C]46[/C][C]6.197[/C][C]6.118103125[/C][C]0.0788968749999997[/C][/ROW]
[ROW][C]47[/C][C]6.889[/C][C]6.911303125[/C][C]-0.0223031249999998[/C][/ROW]
[ROW][C]48[/C][C]7.087[/C][C]7.321503125[/C][C]-0.234503124999999[/C][/ROW]
[ROW][C]49[/C][C]6.485[/C][C]6.4547375[/C][C]0.0302625000000019[/C][/ROW]
[ROW][C]50[/C][C]7.654[/C][C]7.7711375[/C][C]-0.117137500000001[/C][/ROW]
[ROW][C]51[/C][C]6.501[/C][C]6.8289375[/C][C]-0.327937499999999[/C][/ROW]
[ROW][C]52[/C][C]6.313[/C][C]7.0305375[/C][C]-0.717537500[/C][/ROW]
[ROW][C]53[/C][C]7.826[/C][C]7.898703125[/C][C]-0.0727031250000006[/C][/ROW]
[ROW][C]54[/C][C]6.589[/C][C]6.460103125[/C][C]0.128896875[/C][/ROW]
[ROW][C]55[/C][C]6.729[/C][C]6.557303125[/C][C]0.171696875[/C][/ROW]
[ROW][C]56[/C][C]5.684[/C][C]6.674903125[/C][C]-0.990903125[/C][/ROW]
[ROW][C]57[/C][C]8.105[/C][C]7.259903125[/C][C]0.845096875[/C][/ROW]
[ROW][C]58[/C][C]6.391[/C][C]6.118103125[/C][C]0.272896875000000[/C][/ROW]
[ROW][C]59[/C][C]5.901[/C][C]6.911303125[/C][C]-1.010303125[/C][/ROW]
[ROW][C]60[/C][C]6.758[/C][C]7.321503125[/C][C]-0.563503124999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32175&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32175&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	5.014	6.448565625	-1.43456562500001
2	6.153	7.764965625	-1.61196562500000
3	6.441	6.822765625	-0.381765625000001
4	5.584	7.024365625	-1.440365625
5	6.427	7.89253125	-1.46553125
6	6.062	6.45393125	-0.391931250000000
7	5.589	6.55113125	-0.96213125
8	6.216	6.66873125	-0.452731250000001
9	5.809	7.25373125	-1.44473125
10	4.989	6.11193125	-1.12293125000000
11	6.706	6.90513125	-0.199131250000000
12	7.174	7.31533125	-0.141331249999998
13	6.122	6.448565625	-0.326565624999999
14	8.075	7.764965625	0.310034374999999
15	6.292	6.822765625	-0.530765625
16	6.337	7.024365625	-0.687365625
17	8.576	7.89253125	0.68346875
18	6.077	6.45393125	-0.37693125
19	5.931	6.55113125	-0.62013125
20	6.288	6.66873125	-0.380731250000000
21	7.167	7.25373125	-0.0867312500000003
22	6.054	6.11193125	-0.05793125
23	6.468	6.90513125	-0.43713125
24	6.401	7.31533125	-0.91433125
25	6.927	6.448565625	0.478434375000001
26	7.914	7.764965625	0.149034374999999
27	7.728	6.822765625	0.905234375
28	8.699	7.024365625	1.674634375
29	8.522	7.89253125	0.62946875
30	6.481	6.45393125	0.0270687499999994
31	7.502	6.55113125	0.95086875
32	7.778	6.66873125	1.10926875
33	7.424	7.25373125	0.170268750000000
34	6.941	6.11193125	0.82906875
35	8.574	6.90513125	1.66886875
36	9.169	7.31533125	1.85366875
37	7.701	6.448565625	1.252434375
38	9.035	7.764965625	1.270034375
39	7.158	6.822765625	0.335234375000001
40	8.195	7.024365625	1.170634375
41	8.124	7.898703125	0.225296875000000
42	7.073	6.460103125	0.612896875
43	7.017	6.557303125	0.459696875
44	7.39	6.674903125	0.715096875
45	7.776	7.259903125	0.516096875
46	6.197	6.118103125	0.0788968749999997
47	6.889	6.911303125	-0.0223031249999998
48	7.087	7.321503125	-0.234503124999999
49	6.485	6.4547375	0.0302625000000019
50	7.654	7.7711375	-0.117137500000001
51	6.501	6.8289375	-0.327937499999999
52	6.313	7.0305375	-0.717537500
53	7.826	7.898703125	-0.0727031250000006
54	6.589	6.460103125	0.128896875
55	6.729	6.557303125	0.171696875
56	5.684	6.674903125	-0.990903125
57	8.105	7.259903125	0.845096875
58	6.391	6.118103125	0.272896875000000
59	5.901	6.911303125	-1.010303125
60	6.758	7.321503125	-0.563503124999999

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 = No Linear Trend ;

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code