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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 18 Dec 2007 10:41:09 -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/2007/Dec/18/t1197998658z72dduuh7vbwu9w.htm/, Retrieved Sat, 04 May 2024 18:59:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14392, Retrieved Sat, 04 May 2024 18:59:15 +0000

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Estimated Impact

176

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

-       [Multiple Regression] [werkloosheid en i...] [2007-12-18 17:41:09] [151d9b972bcbe57745b80028e4bf0c5f] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14392&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]2 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=14392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14392&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
werkl[t] = + 11.2733558593295 -0.00898720362548001Iprod[t] + 0.109752313169581M1[t] + 0.222885921711642M2[t] + 0.139503708067787M3[t] -0.128586371679523M4[t] -0.502276293141087M5[t] -0.151493643504616M6[t] -0.49851200356862M7[t] + 0.0682543790177037M8[t] + 0.547008063529259M9[t] -0.202961986883062M10[t] -0.37961074167442M11[t] -0.00281201299111269t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
werkl[t] =  +  11.2733558593295 -0.00898720362548001Iprod[t] +  0.109752313169581M1[t] +  0.222885921711642M2[t] +  0.139503708067787M3[t] -0.128586371679523M4[t] -0.502276293141087M5[t] -0.151493643504616M6[t] -0.49851200356862M7[t] +  0.0682543790177037M8[t] +  0.547008063529259M9[t] -0.202961986883062M10[t] -0.37961074167442M11[t] -0.00281201299111269t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14392&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]werkl[t] =  +  11.2733558593295 -0.00898720362548001Iprod[t] +  0.109752313169581M1[t] +  0.222885921711642M2[t] +  0.139503708067787M3[t] -0.128586371679523M4[t] -0.502276293141087M5[t] -0.151493643504616M6[t] -0.49851200356862M7[t] +  0.0682543790177037M8[t] +  0.547008063529259M9[t] -0.202961986883062M10[t] -0.37961074167442M11[t] -0.00281201299111269t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14392&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
werkl[t] = + 11.2733558593295 -0.00898720362548001Iprod[t] + 0.109752313169581M1[t] + 0.222885921711642M2[t] + 0.139503708067787M3[t] -0.128586371679523M4[t] -0.502276293141087M5[t] -0.151493643504616M6[t] -0.49851200356862M7[t] + 0.0682543790177037M8[t] + 0.547008063529259M9[t] -0.202961986883062M10[t] -0.37961074167442M11[t] -0.00281201299111269t + 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)	11.2733558593295	1.620446	6.9569	0	0
Iprod	-0.00898720362548001	0.00492	-1.8267	0.074237	0.037119
M1	0.109752313169581	0.264388	0.4151	0.679986	0.339993
M2	0.222885921711642	0.278508	0.8003	0.42766	0.21383
M3	0.139503708067787	0.28873	0.4832	0.631272	0.315636
M4	-0.128586371679523	0.320183	-0.4016	0.689836	0.344918
M5	-0.502276293141087	0.308896	-1.626	0.110774	0.055387
M6	-0.151493643504616	0.271472	-0.558	0.579519	0.289759
M7	-0.49851200356862	0.286829	-1.738	0.0889	0.04445
M8	0.0682543790177037	0.287268	0.2376	0.813248	0.406624
M9	0.547008063529259	0.269667	2.0285	0.048326	0.024163
M10	-0.202961986883062	0.405014	-0.5011	0.618674	0.309337
M11	-0.37961074167442	0.407526	-0.9315	0.356459	0.178229
t	-0.00281201299111269	0.004808	-0.5849	0.561474	0.280737

\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) & 11.2733558593295 & 1.620446 & 6.9569 & 0 & 0 \tabularnewline
Iprod & -0.00898720362548001 & 0.00492 & -1.8267 & 0.074237 & 0.037119 \tabularnewline
M1 & 0.109752313169581 & 0.264388 & 0.4151 & 0.679986 & 0.339993 \tabularnewline
M2 & 0.222885921711642 & 0.278508 & 0.8003 & 0.42766 & 0.21383 \tabularnewline
M3 & 0.139503708067787 & 0.28873 & 0.4832 & 0.631272 & 0.315636 \tabularnewline
M4 & -0.128586371679523 & 0.320183 & -0.4016 & 0.689836 & 0.344918 \tabularnewline
M5 & -0.502276293141087 & 0.308896 & -1.626 & 0.110774 & 0.055387 \tabularnewline
M6 & -0.151493643504616 & 0.271472 & -0.558 & 0.579519 & 0.289759 \tabularnewline
M7 & -0.49851200356862 & 0.286829 & -1.738 & 0.0889 & 0.04445 \tabularnewline
M8 & 0.0682543790177037 & 0.287268 & 0.2376 & 0.813248 & 0.406624 \tabularnewline
M9 & 0.547008063529259 & 0.269667 & 2.0285 & 0.048326 & 0.024163 \tabularnewline
M10 & -0.202961986883062 & 0.405014 & -0.5011 & 0.618674 & 0.309337 \tabularnewline
M11 & -0.37961074167442 & 0.407526 & -0.9315 & 0.356459 & 0.178229 \tabularnewline
t & -0.00281201299111269 & 0.004808 & -0.5849 & 0.561474 & 0.280737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14392&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]11.2733558593295[/C][C]1.620446[/C][C]6.9569[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Iprod[/C][C]-0.00898720362548001[/C][C]0.00492[/C][C]-1.8267[/C][C]0.074237[/C][C]0.037119[/C][/ROW]
[ROW][C]M1[/C][C]0.109752313169581[/C][C]0.264388[/C][C]0.4151[/C][C]0.679986[/C][C]0.339993[/C][/ROW]
[ROW][C]M2[/C][C]0.222885921711642[/C][C]0.278508[/C][C]0.8003[/C][C]0.42766[/C][C]0.21383[/C][/ROW]
[ROW][C]M3[/C][C]0.139503708067787[/C][C]0.28873[/C][C]0.4832[/C][C]0.631272[/C][C]0.315636[/C][/ROW]
[ROW][C]M4[/C][C]-0.128586371679523[/C][C]0.320183[/C][C]-0.4016[/C][C]0.689836[/C][C]0.344918[/C][/ROW]
[ROW][C]M5[/C][C]-0.502276293141087[/C][C]0.308896[/C][C]-1.626[/C][C]0.110774[/C][C]0.055387[/C][/ROW]
[ROW][C]M6[/C][C]-0.151493643504616[/C][C]0.271472[/C][C]-0.558[/C][C]0.579519[/C][C]0.289759[/C][/ROW]
[ROW][C]M7[/C][C]-0.49851200356862[/C][C]0.286829[/C][C]-1.738[/C][C]0.0889[/C][C]0.04445[/C][/ROW]
[ROW][C]M8[/C][C]0.0682543790177037[/C][C]0.287268[/C][C]0.2376[/C][C]0.813248[/C][C]0.406624[/C][/ROW]
[ROW][C]M9[/C][C]0.547008063529259[/C][C]0.269667[/C][C]2.0285[/C][C]0.048326[/C][C]0.024163[/C][/ROW]
[ROW][C]M10[/C][C]-0.202961986883062[/C][C]0.405014[/C][C]-0.5011[/C][C]0.618674[/C][C]0.309337[/C][/ROW]
[ROW][C]M11[/C][C]-0.37961074167442[/C][C]0.407526[/C][C]-0.9315[/C][C]0.356459[/C][C]0.178229[/C][/ROW]
[ROW][C]t[/C][C]-0.00281201299111269[/C][C]0.004808[/C][C]-0.5849[/C][C]0.561474[/C][C]0.280737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14392&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)	11.2733558593295	1.620446	6.9569	0	0
Iprod	-0.00898720362548001	0.00492	-1.8267	0.074237	0.037119
M1	0.109752313169581	0.264388	0.4151	0.679986	0.339993
M2	0.222885921711642	0.278508	0.8003	0.42766	0.21383
M3	0.139503708067787	0.28873	0.4832	0.631272	0.315636
M4	-0.128586371679523	0.320183	-0.4016	0.689836	0.344918
M5	-0.502276293141087	0.308896	-1.626	0.110774	0.055387
M6	-0.151493643504616	0.271472	-0.558	0.579519	0.289759
M7	-0.49851200356862	0.286829	-1.738	0.0889	0.04445
M8	0.0682543790177037	0.287268	0.2376	0.813248	0.406624
M9	0.547008063529259	0.269667	2.0285	0.048326	0.024163
M10	-0.202961986883062	0.405014	-0.5011	0.618674	0.309337
M11	-0.37961074167442	0.407526	-0.9315	0.356459	0.178229
t	-0.00281201299111269	0.004808	-0.5849	0.561474	0.280737

Multiple Linear Regression - Regression Statistics
Multiple R	0.657206628108399
R-squared	0.431920552029611
Adjusted R-squared	0.271376360211893
F-TEST (value)	2.69035302454300
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.00676045586162599
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.414257639036294
Sum Squared Residuals	7.89403200899652

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.657206628108399 \tabularnewline
R-squared & 0.431920552029611 \tabularnewline
Adjusted R-squared & 0.271376360211893 \tabularnewline
F-TEST (value) & 2.69035302454300 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.00676045586162599 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.414257639036294 \tabularnewline
Sum Squared Residuals & 7.89403200899652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14392&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.657206628108399[/C][/ROW]
[ROW][C]R-squared[/C][C]0.431920552029611[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.271376360211893[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.69035302454300[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.00676045586162599[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.414257639036294[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7.89403200899652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14392&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14392&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	0.657206628108399
R-squared	0.431920552029611
Adjusted R-squared	0.271376360211893
F-TEST (value)	2.69035302454300
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.00676045586162599
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.414257639036294
Sum Squared Residuals	7.89403200899652

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.1	8.15389005796068	-0.0538900579606841
2	8.3	8.75311553073769	-0.453115530737686
3	8.2	8.72893300911853	-0.528933009118533
4	8.1	8.40770257607742	-0.307702576077421
5	7.7	8.01861855654907	-0.318618556549072
6	7.6	8.12752957675666	-0.527529576756662
7	7.7	7.89003924902005	-0.190039249020046
8	8.2	8.56184006212102	-0.361840062121017
9	8.4	8.8193926855423	-0.419392685542295
10	8.4	8.48900919253642	-0.0890091925364214
11	8.6	8.52883619321566	0.0711638067843368
12	8.4	8.22170872599994	0.178291274000059
13	8.5	8.30438357638961	0.195616423610387
14	8.7	8.6681443141791	0.0318556858209007
15	8.7	8.47590108476347	0.224098915236533
16	8.6	8.49977927094079	0.100220729059211
17	7.4	8.0199244947951	-0.619924494795091
18	7.3	7.83046035463675	-0.530460354636745
19	7.4	7.77990386231011	-0.379903862310113
20	9	8.55236135601646	0.44763864398354
21	9.2	8.50794393762161	0.692056062378389
22	9.2	8.42201238322879	0.777987616771206
23	8.5	8.25782986160964	0.242170138390362
24	8.3	7.98665120889584	0.313348791104163
25	8.3	8.20323539330516	0.0967646066948395
26	8.6	8.45825096722634	0.141749032773661
27	8.6	8.33251304463926	0.267486955360741
28	8.5	8.33661938284052	0.163380617159476
29	8.1	7.92506735424848	0.174932645751524
30	8.1	7.87670231101017	0.223297688989835
31	8	7.77042515620556	0.229574843794443
32	8.6	8.44851701184436	0.151482988155635
33	8.7	8.478693383541	0.221306616459001
34	8.7	8.53835452788096	0.161645472119042
35	8.6	8.2204908242661	0.379509175733905
36	8.4	8.00143795258008	0.398562047419923
37	8.4	8.38158924297314	0.0184107570268628
38	8.7	8.37867207284304	0.321327927156961
39	8.7	8.40751405261421	0.292485947385785
40	8.5	8.21390191105492	0.286098088945080
41	8.3	7.75022410143509	0.549775898564914
42	8.3	7.59670877577866	0.703291224221341
43	8.3	7.81756583294152	0.482434167058476
44	8.1	8.0400064647685	0.0599935352315046
45	8.2	8.35327975066775	-0.153279750667751
46	8.1	8.39856136920694	-0.298561369206942
47	8.1	8.07620406377934	0.0237959362206616
48	7.9	7.8868089640574	0.0131910359425956
49	7.7	7.9569017293714	-0.256901729371404
50	8.1	8.14181711501384	-0.0418171150138374
51	8	8.25513880886453	-0.255138808864526
52	7.7	7.94199685908635	-0.241996859086347
53	7.8	7.58616549297227	0.213834507027725
54	7.6	7.46859898181777	0.131401018182232
55	7.4	7.54206589952276	-0.14206589952276
56	7.7	7.99727510524966	-0.297275105249663
57	7.8	8.14069024262735	-0.340690242627345
58	7.5	8.05206252714688	-0.552062527146885
59	7.2	7.91663905712927	-0.716639057129265
60	7	7.90339314846674	-0.90339314846674

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.1 & 8.15389005796068 & -0.0538900579606841 \tabularnewline
2 & 8.3 & 8.75311553073769 & -0.453115530737686 \tabularnewline
3 & 8.2 & 8.72893300911853 & -0.528933009118533 \tabularnewline
4 & 8.1 & 8.40770257607742 & -0.307702576077421 \tabularnewline
5 & 7.7 & 8.01861855654907 & -0.318618556549072 \tabularnewline
6 & 7.6 & 8.12752957675666 & -0.527529576756662 \tabularnewline
7 & 7.7 & 7.89003924902005 & -0.190039249020046 \tabularnewline
8 & 8.2 & 8.56184006212102 & -0.361840062121017 \tabularnewline
9 & 8.4 & 8.8193926855423 & -0.419392685542295 \tabularnewline
10 & 8.4 & 8.48900919253642 & -0.0890091925364214 \tabularnewline
11 & 8.6 & 8.52883619321566 & 0.0711638067843368 \tabularnewline
12 & 8.4 & 8.22170872599994 & 0.178291274000059 \tabularnewline
13 & 8.5 & 8.30438357638961 & 0.195616423610387 \tabularnewline
14 & 8.7 & 8.6681443141791 & 0.0318556858209007 \tabularnewline
15 & 8.7 & 8.47590108476347 & 0.224098915236533 \tabularnewline
16 & 8.6 & 8.49977927094079 & 0.100220729059211 \tabularnewline
17 & 7.4 & 8.0199244947951 & -0.619924494795091 \tabularnewline
18 & 7.3 & 7.83046035463675 & -0.530460354636745 \tabularnewline
19 & 7.4 & 7.77990386231011 & -0.379903862310113 \tabularnewline
20 & 9 & 8.55236135601646 & 0.44763864398354 \tabularnewline
21 & 9.2 & 8.50794393762161 & 0.692056062378389 \tabularnewline
22 & 9.2 & 8.42201238322879 & 0.777987616771206 \tabularnewline
23 & 8.5 & 8.25782986160964 & 0.242170138390362 \tabularnewline
24 & 8.3 & 7.98665120889584 & 0.313348791104163 \tabularnewline
25 & 8.3 & 8.20323539330516 & 0.0967646066948395 \tabularnewline
26 & 8.6 & 8.45825096722634 & 0.141749032773661 \tabularnewline
27 & 8.6 & 8.33251304463926 & 0.267486955360741 \tabularnewline
28 & 8.5 & 8.33661938284052 & 0.163380617159476 \tabularnewline
29 & 8.1 & 7.92506735424848 & 0.174932645751524 \tabularnewline
30 & 8.1 & 7.87670231101017 & 0.223297688989835 \tabularnewline
31 & 8 & 7.77042515620556 & 0.229574843794443 \tabularnewline
32 & 8.6 & 8.44851701184436 & 0.151482988155635 \tabularnewline
33 & 8.7 & 8.478693383541 & 0.221306616459001 \tabularnewline
34 & 8.7 & 8.53835452788096 & 0.161645472119042 \tabularnewline
35 & 8.6 & 8.2204908242661 & 0.379509175733905 \tabularnewline
36 & 8.4 & 8.00143795258008 & 0.398562047419923 \tabularnewline
37 & 8.4 & 8.38158924297314 & 0.0184107570268628 \tabularnewline
38 & 8.7 & 8.37867207284304 & 0.321327927156961 \tabularnewline
39 & 8.7 & 8.40751405261421 & 0.292485947385785 \tabularnewline
40 & 8.5 & 8.21390191105492 & 0.286098088945080 \tabularnewline
41 & 8.3 & 7.75022410143509 & 0.549775898564914 \tabularnewline
42 & 8.3 & 7.59670877577866 & 0.703291224221341 \tabularnewline
43 & 8.3 & 7.81756583294152 & 0.482434167058476 \tabularnewline
44 & 8.1 & 8.0400064647685 & 0.0599935352315046 \tabularnewline
45 & 8.2 & 8.35327975066775 & -0.153279750667751 \tabularnewline
46 & 8.1 & 8.39856136920694 & -0.298561369206942 \tabularnewline
47 & 8.1 & 8.07620406377934 & 0.0237959362206616 \tabularnewline
48 & 7.9 & 7.8868089640574 & 0.0131910359425956 \tabularnewline
49 & 7.7 & 7.9569017293714 & -0.256901729371404 \tabularnewline
50 & 8.1 & 8.14181711501384 & -0.0418171150138374 \tabularnewline
51 & 8 & 8.25513880886453 & -0.255138808864526 \tabularnewline
52 & 7.7 & 7.94199685908635 & -0.241996859086347 \tabularnewline
53 & 7.8 & 7.58616549297227 & 0.213834507027725 \tabularnewline
54 & 7.6 & 7.46859898181777 & 0.131401018182232 \tabularnewline
55 & 7.4 & 7.54206589952276 & -0.14206589952276 \tabularnewline
56 & 7.7 & 7.99727510524966 & -0.297275105249663 \tabularnewline
57 & 7.8 & 8.14069024262735 & -0.340690242627345 \tabularnewline
58 & 7.5 & 8.05206252714688 & -0.552062527146885 \tabularnewline
59 & 7.2 & 7.91663905712927 & -0.716639057129265 \tabularnewline
60 & 7 & 7.90339314846674 & -0.90339314846674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14392&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]8.1[/C][C]8.15389005796068[/C][C]-0.0538900579606841[/C][/ROW]
[ROW][C]2[/C][C]8.3[/C][C]8.75311553073769[/C][C]-0.453115530737686[/C][/ROW]
[ROW][C]3[/C][C]8.2[/C][C]8.72893300911853[/C][C]-0.528933009118533[/C][/ROW]
[ROW][C]4[/C][C]8.1[/C][C]8.40770257607742[/C][C]-0.307702576077421[/C][/ROW]
[ROW][C]5[/C][C]7.7[/C][C]8.01861855654907[/C][C]-0.318618556549072[/C][/ROW]
[ROW][C]6[/C][C]7.6[/C][C]8.12752957675666[/C][C]-0.527529576756662[/C][/ROW]
[ROW][C]7[/C][C]7.7[/C][C]7.89003924902005[/C][C]-0.190039249020046[/C][/ROW]
[ROW][C]8[/C][C]8.2[/C][C]8.56184006212102[/C][C]-0.361840062121017[/C][/ROW]
[ROW][C]9[/C][C]8.4[/C][C]8.8193926855423[/C][C]-0.419392685542295[/C][/ROW]
[ROW][C]10[/C][C]8.4[/C][C]8.48900919253642[/C][C]-0.0890091925364214[/C][/ROW]
[ROW][C]11[/C][C]8.6[/C][C]8.52883619321566[/C][C]0.0711638067843368[/C][/ROW]
[ROW][C]12[/C][C]8.4[/C][C]8.22170872599994[/C][C]0.178291274000059[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.30438357638961[/C][C]0.195616423610387[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.6681443141791[/C][C]0.0318556858209007[/C][/ROW]
[ROW][C]15[/C][C]8.7[/C][C]8.47590108476347[/C][C]0.224098915236533[/C][/ROW]
[ROW][C]16[/C][C]8.6[/C][C]8.49977927094079[/C][C]0.100220729059211[/C][/ROW]
[ROW][C]17[/C][C]7.4[/C][C]8.0199244947951[/C][C]-0.619924494795091[/C][/ROW]
[ROW][C]18[/C][C]7.3[/C][C]7.83046035463675[/C][C]-0.530460354636745[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]7.77990386231011[/C][C]-0.379903862310113[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]8.55236135601646[/C][C]0.44763864398354[/C][/ROW]
[ROW][C]21[/C][C]9.2[/C][C]8.50794393762161[/C][C]0.692056062378389[/C][/ROW]
[ROW][C]22[/C][C]9.2[/C][C]8.42201238322879[/C][C]0.777987616771206[/C][/ROW]
[ROW][C]23[/C][C]8.5[/C][C]8.25782986160964[/C][C]0.242170138390362[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]7.98665120889584[/C][C]0.313348791104163[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.20323539330516[/C][C]0.0967646066948395[/C][/ROW]
[ROW][C]26[/C][C]8.6[/C][C]8.45825096722634[/C][C]0.141749032773661[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.33251304463926[/C][C]0.267486955360741[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.33661938284052[/C][C]0.163380617159476[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]7.92506735424848[/C][C]0.174932645751524[/C][/ROW]
[ROW][C]30[/C][C]8.1[/C][C]7.87670231101017[/C][C]0.223297688989835[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]7.77042515620556[/C][C]0.229574843794443[/C][/ROW]
[ROW][C]32[/C][C]8.6[/C][C]8.44851701184436[/C][C]0.151482988155635[/C][/ROW]
[ROW][C]33[/C][C]8.7[/C][C]8.478693383541[/C][C]0.221306616459001[/C][/ROW]
[ROW][C]34[/C][C]8.7[/C][C]8.53835452788096[/C][C]0.161645472119042[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.2204908242661[/C][C]0.379509175733905[/C][/ROW]
[ROW][C]36[/C][C]8.4[/C][C]8.00143795258008[/C][C]0.398562047419923[/C][/ROW]
[ROW][C]37[/C][C]8.4[/C][C]8.38158924297314[/C][C]0.0184107570268628[/C][/ROW]
[ROW][C]38[/C][C]8.7[/C][C]8.37867207284304[/C][C]0.321327927156961[/C][/ROW]
[ROW][C]39[/C][C]8.7[/C][C]8.40751405261421[/C][C]0.292485947385785[/C][/ROW]
[ROW][C]40[/C][C]8.5[/C][C]8.21390191105492[/C][C]0.286098088945080[/C][/ROW]
[ROW][C]41[/C][C]8.3[/C][C]7.75022410143509[/C][C]0.549775898564914[/C][/ROW]
[ROW][C]42[/C][C]8.3[/C][C]7.59670877577866[/C][C]0.703291224221341[/C][/ROW]
[ROW][C]43[/C][C]8.3[/C][C]7.81756583294152[/C][C]0.482434167058476[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]8.0400064647685[/C][C]0.0599935352315046[/C][/ROW]
[ROW][C]45[/C][C]8.2[/C][C]8.35327975066775[/C][C]-0.153279750667751[/C][/ROW]
[ROW][C]46[/C][C]8.1[/C][C]8.39856136920694[/C][C]-0.298561369206942[/C][/ROW]
[ROW][C]47[/C][C]8.1[/C][C]8.07620406377934[/C][C]0.0237959362206616[/C][/ROW]
[ROW][C]48[/C][C]7.9[/C][C]7.8868089640574[/C][C]0.0131910359425956[/C][/ROW]
[ROW][C]49[/C][C]7.7[/C][C]7.9569017293714[/C][C]-0.256901729371404[/C][/ROW]
[ROW][C]50[/C][C]8.1[/C][C]8.14181711501384[/C][C]-0.0418171150138374[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.25513880886453[/C][C]-0.255138808864526[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.94199685908635[/C][C]-0.241996859086347[/C][/ROW]
[ROW][C]53[/C][C]7.8[/C][C]7.58616549297227[/C][C]0.213834507027725[/C][/ROW]
[ROW][C]54[/C][C]7.6[/C][C]7.46859898181777[/C][C]0.131401018182232[/C][/ROW]
[ROW][C]55[/C][C]7.4[/C][C]7.54206589952276[/C][C]-0.14206589952276[/C][/ROW]
[ROW][C]56[/C][C]7.7[/C][C]7.99727510524966[/C][C]-0.297275105249663[/C][/ROW]
[ROW][C]57[/C][C]7.8[/C][C]8.14069024262735[/C][C]-0.340690242627345[/C][/ROW]
[ROW][C]58[/C][C]7.5[/C][C]8.05206252714688[/C][C]-0.552062527146885[/C][/ROW]
[ROW][C]59[/C][C]7.2[/C][C]7.91663905712927[/C][C]-0.716639057129265[/C][/ROW]
[ROW][C]60[/C][C]7[/C][C]7.90339314846674[/C][C]-0.90339314846674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14392&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14392&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	8.1	8.15389005796068	-0.0538900579606841
2	8.3	8.75311553073769	-0.453115530737686
3	8.2	8.72893300911853	-0.528933009118533
4	8.1	8.40770257607742	-0.307702576077421
5	7.7	8.01861855654907	-0.318618556549072
6	7.6	8.12752957675666	-0.527529576756662
7	7.7	7.89003924902005	-0.190039249020046
8	8.2	8.56184006212102	-0.361840062121017
9	8.4	8.8193926855423	-0.419392685542295
10	8.4	8.48900919253642	-0.0890091925364214
11	8.6	8.52883619321566	0.0711638067843368
12	8.4	8.22170872599994	0.178291274000059
13	8.5	8.30438357638961	0.195616423610387
14	8.7	8.6681443141791	0.0318556858209007
15	8.7	8.47590108476347	0.224098915236533
16	8.6	8.49977927094079	0.100220729059211
17	7.4	8.0199244947951	-0.619924494795091
18	7.3	7.83046035463675	-0.530460354636745
19	7.4	7.77990386231011	-0.379903862310113
20	9	8.55236135601646	0.44763864398354
21	9.2	8.50794393762161	0.692056062378389
22	9.2	8.42201238322879	0.777987616771206
23	8.5	8.25782986160964	0.242170138390362
24	8.3	7.98665120889584	0.313348791104163
25	8.3	8.20323539330516	0.0967646066948395
26	8.6	8.45825096722634	0.141749032773661
27	8.6	8.33251304463926	0.267486955360741
28	8.5	8.33661938284052	0.163380617159476
29	8.1	7.92506735424848	0.174932645751524
30	8.1	7.87670231101017	0.223297688989835
31	8	7.77042515620556	0.229574843794443
32	8.6	8.44851701184436	0.151482988155635
33	8.7	8.478693383541	0.221306616459001
34	8.7	8.53835452788096	0.161645472119042
35	8.6	8.2204908242661	0.379509175733905
36	8.4	8.00143795258008	0.398562047419923
37	8.4	8.38158924297314	0.0184107570268628
38	8.7	8.37867207284304	0.321327927156961
39	8.7	8.40751405261421	0.292485947385785
40	8.5	8.21390191105492	0.286098088945080
41	8.3	7.75022410143509	0.549775898564914
42	8.3	7.59670877577866	0.703291224221341
43	8.3	7.81756583294152	0.482434167058476
44	8.1	8.0400064647685	0.0599935352315046
45	8.2	8.35327975066775	-0.153279750667751
46	8.1	8.39856136920694	-0.298561369206942
47	8.1	8.07620406377934	0.0237959362206616
48	7.9	7.8868089640574	0.0131910359425956
49	7.7	7.9569017293714	-0.256901729371404
50	8.1	8.14181711501384	-0.0418171150138374
51	8	8.25513880886453	-0.255138808864526
52	7.7	7.94199685908635	-0.241996859086347
53	7.8	7.58616549297227	0.213834507027725
54	7.6	7.46859898181777	0.131401018182232
55	7.4	7.54206589952276	-0.14206589952276
56	7.7	7.99727510524966	-0.297275105249663
57	7.8	8.14069024262735	-0.340690242627345
58	7.5	8.05206252714688	-0.552062527146885
59	7.2	7.91663905712927	-0.716639057129265
60	7	7.90339314846674	-0.90339314846674

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Figure 3

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Figure 7

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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