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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 16 Dec 2008 12:46:15 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/16/t1229456934kyb1jf0ojre5de8.htm/, Retrieved Wed, 15 May 2024 22:57:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34154, Retrieved Wed, 15 May 2024 22:57:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact216

Tree of Dependent Computations

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]
-    D    [Multiple Regression] [Paper] [2008-12-16 19:46:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RM D      [Multiple Regression] [] [2009-12-16 17:12:08] [74be16979710d4c4e7c6647856088456]
- RM D      [Multiple Regression] [] [2009-12-16 17:12:08] [ff47dd0689925b5f8d992b55e66ceb45]
-   PD        [Multiple Regression] [] [2009-12-16 18:35:32] [ff47dd0689925b5f8d992b55e66ceb45]
-   PD        [Multiple Regression] [] [2009-12-16 18:39:45] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [Standard Deviation-Mean Plot] [] [2009-12-17 10:57:54] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [Univariate Data Series] [] [2009-12-17 14:09:52] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [Univariate Data Series] [] [2009-12-17 14:09:52] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [Univariate Data Series] [] [2009-12-17 14:09:52] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [Standard Deviation-Mean Plot] [] [2009-12-17 14:23:16] [ff47dd0689925b5f8d992b55e66ceb45]
- RMPD        [(Partial) Autocorrelation Function] [] [2009-12-17 14:49:59] [ff47dd0689925b5f8d992b55e66ceb45]
-    D          [(Partial) Autocorrelation Function] [] [2009-12-17 15:21:07] [ff47dd0689925b5f8d992b55e66ceb45]
-    D          [(Partial) Autocorrelation Function] [] [2009-12-17 15:36:19] [ff47dd0689925b5f8d992b55e66ceb45]
- RM D          [Variance Reduction Matrix] [] [2009-12-17 15:44:00] [ff47dd0689925b5f8d992b55e66ceb45]
- RM D          [Variance Reduction Matrix] [] [2009-12-17 15:44:00] [ff47dd0689925b5f8d992b55e66ceb45]
-    D          [(Partial) Autocorrelation Function] [] [2009-12-17 15:46:35] [ff47dd0689925b5f8d992b55e66ceb45]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87.0	0
96.3	0
107.1	0
115.2	0
106.1	0
89.5	0
91.3	0
97.6	0
100.7	0
104.6	0
94.7	0
101.8	0
102.5	0
105.3	0
110.3	1
109.8	1
117.3	1
118.8	1
131.3	1
125.9	1
133.1	1
147.0	1
145.8	1
164.4	1
149.8	1
137.7	1
151.7	1
156.8	1
180.0	1
180.4	1
170.4	1
191.6	1
199.5	1
218.2	1
217.5	1
205.0	1
194.0	1
199.3	1
219.3	1
211.1	1
215.2	1
240.2	1
242.2	1
240.7	1
255.4	1
253.0	1
218.2	1
203.7	1
205.6	1
215.6	1
188.5	1
202.9	1
214.0	1
230.3	1
230.0	1
241.0	1
259.6	1
247.8	1
270.3	1
289.7	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34154&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34154&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 82.6574825174825 + 3.81678321678324X[t] -11.61831002331M1[t] -11.5363403263403M2[t] -10.7377272727273M3[t] -9.93575757575757M4[t] -5.5537878787879M5[t] -3.21181818181818M6[t] -4.98984848484848M7[t] -1.64787878787879M8[t] + 5.67409090909092M9[t] + 7.1560606060606M10[t] -0.641969696969688M11[t] + 2.97803030303030t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  82.6574825174825 +  3.81678321678324X[t] -11.61831002331M1[t] -11.5363403263403M2[t] -10.7377272727273M3[t] -9.93575757575757M4[t] -5.5537878787879M5[t] -3.21181818181818M6[t] -4.98984848484848M7[t] -1.64787878787879M8[t] +  5.67409090909092M9[t] +  7.1560606060606M10[t] -0.641969696969688M11[t] +  2.97803030303030t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34154&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  82.6574825174825 +  3.81678321678324X[t] -11.61831002331M1[t] -11.5363403263403M2[t] -10.7377272727273M3[t] -9.93575757575757M4[t] -5.5537878787879M5[t] -3.21181818181818M6[t] -4.98984848484848M7[t] -1.64787878787879M8[t] +  5.67409090909092M9[t] +  7.1560606060606M10[t] -0.641969696969688M11[t] +  2.97803030303030t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34154&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 82.6574825174825 + 3.81678321678324X[t] -11.61831002331M1[t] -11.5363403263403M2[t] -10.7377272727273M3[t] -9.93575757575757M4[t] -5.5537878787879M5[t] -3.21181818181818M6[t] -4.98984848484848M7[t] -1.64787878787879M8[t] + 5.67409090909092M9[t] + 7.1560606060606M10[t] -0.641969696969688M11[t] + 2.97803030303030t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)82.657482517482510.6788017.740300
X3.816783216783249.2481130.41270.6817370.340868
M1-11.6183100233112.881285-0.9020.3717810.18589
M2-11.536340326340312.86329-0.89680.3744730.187236
M3-10.737727272727312.932211-0.83030.4106530.205326
M4-9.9357575757575712.898334-0.77030.4450520.222526
M5-5.553787878787912.868368-0.43160.668060.33403
M6-3.2118181818181812.842341-0.25010.8036270.401813
M7-4.9898484848484812.820276-0.38920.6989130.349456
M8-1.6478787878787912.802196-0.12870.8981420.449071
M95.6740909090909212.7881150.44370.6593390.32967
M107.156060606060612.7780480.560.5781780.289089
M11-0.64196969696968812.772004-0.05030.960130.480065
t2.978030303030300.22688113.12600

\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) & 82.6574825174825 & 10.678801 & 7.7403 & 0 & 0 \tabularnewline
X & 3.81678321678324 & 9.248113 & 0.4127 & 0.681737 & 0.340868 \tabularnewline
M1 & -11.61831002331 & 12.881285 & -0.902 & 0.371781 & 0.18589 \tabularnewline
M2 & -11.5363403263403 & 12.86329 & -0.8968 & 0.374473 & 0.187236 \tabularnewline
M3 & -10.7377272727273 & 12.932211 & -0.8303 & 0.410653 & 0.205326 \tabularnewline
M4 & -9.93575757575757 & 12.898334 & -0.7703 & 0.445052 & 0.222526 \tabularnewline
M5 & -5.5537878787879 & 12.868368 & -0.4316 & 0.66806 & 0.33403 \tabularnewline
M6 & -3.21181818181818 & 12.842341 & -0.2501 & 0.803627 & 0.401813 \tabularnewline
M7 & -4.98984848484848 & 12.820276 & -0.3892 & 0.698913 & 0.349456 \tabularnewline
M8 & -1.64787878787879 & 12.802196 & -0.1287 & 0.898142 & 0.449071 \tabularnewline
M9 & 5.67409090909092 & 12.788115 & 0.4437 & 0.659339 & 0.32967 \tabularnewline
M10 & 7.1560606060606 & 12.778048 & 0.56 & 0.578178 & 0.289089 \tabularnewline
M11 & -0.641969696969688 & 12.772004 & -0.0503 & 0.96013 & 0.480065 \tabularnewline
t & 2.97803030303030 & 0.226881 & 13.126 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34154&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]82.6574825174825[/C][C]10.678801[/C][C]7.7403[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]3.81678321678324[/C][C]9.248113[/C][C]0.4127[/C][C]0.681737[/C][C]0.340868[/C][/ROW]
[ROW][C]M1[/C][C]-11.61831002331[/C][C]12.881285[/C][C]-0.902[/C][C]0.371781[/C][C]0.18589[/C][/ROW]
[ROW][C]M2[/C][C]-11.5363403263403[/C][C]12.86329[/C][C]-0.8968[/C][C]0.374473[/C][C]0.187236[/C][/ROW]
[ROW][C]M3[/C][C]-10.7377272727273[/C][C]12.932211[/C][C]-0.8303[/C][C]0.410653[/C][C]0.205326[/C][/ROW]
[ROW][C]M4[/C][C]-9.93575757575757[/C][C]12.898334[/C][C]-0.7703[/C][C]0.445052[/C][C]0.222526[/C][/ROW]
[ROW][C]M5[/C][C]-5.5537878787879[/C][C]12.868368[/C][C]-0.4316[/C][C]0.66806[/C][C]0.33403[/C][/ROW]
[ROW][C]M6[/C][C]-3.21181818181818[/C][C]12.842341[/C][C]-0.2501[/C][C]0.803627[/C][C]0.401813[/C][/ROW]
[ROW][C]M7[/C][C]-4.98984848484848[/C][C]12.820276[/C][C]-0.3892[/C][C]0.698913[/C][C]0.349456[/C][/ROW]
[ROW][C]M8[/C][C]-1.64787878787879[/C][C]12.802196[/C][C]-0.1287[/C][C]0.898142[/C][C]0.449071[/C][/ROW]
[ROW][C]M9[/C][C]5.67409090909092[/C][C]12.788115[/C][C]0.4437[/C][C]0.659339[/C][C]0.32967[/C][/ROW]
[ROW][C]M10[/C][C]7.1560606060606[/C][C]12.778048[/C][C]0.56[/C][C]0.578178[/C][C]0.289089[/C][/ROW]
[ROW][C]M11[/C][C]-0.641969696969688[/C][C]12.772004[/C][C]-0.0503[/C][C]0.96013[/C][C]0.480065[/C][/ROW]
[ROW][C]t[/C][C]2.97803030303030[/C][C]0.226881[/C][C]13.126[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34154&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)82.657482517482510.6788017.740300
X3.816783216783249.2481130.41270.6817370.340868
M1-11.6183100233112.881285-0.9020.3717810.18589
M2-11.536340326340312.86329-0.89680.3744730.187236
M3-10.737727272727312.932211-0.83030.4106530.205326
M4-9.9357575757575712.898334-0.77030.4450520.222526
M5-5.553787878787912.868368-0.43160.668060.33403
M6-3.2118181818181812.842341-0.25010.8036270.401813
M7-4.9898484848484812.820276-0.38920.6989130.349456
M8-1.6478787878787912.802196-0.12870.8981420.449071
M95.6740909090909212.7881150.44370.6593390.32967
M107.156060606060612.7780480.560.5781780.289089
M11-0.64196969696968812.772004-0.05030.960130.480065
t2.978030303030300.22688113.12600






Multiple Linear Regression - Regression Statistics
Multiple R0.950628485445134
R-squared0.90369451733971
Adjusted R-squared0.876477750500931
F-TEST (value)33.2035955149583
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation20.1911251798702
Sum Squared Residuals18753.3506573427

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.950628485445134 \tabularnewline
R-squared & 0.90369451733971 \tabularnewline
Adjusted R-squared & 0.876477750500931 \tabularnewline
F-TEST (value) & 33.2035955149583 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 20.1911251798702 \tabularnewline
Sum Squared Residuals & 18753.3506573427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34154&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.950628485445134[/C][/ROW]
[ROW][C]R-squared[/C][C]0.90369451733971[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.876477750500931[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]33.2035955149583[/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[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]20.1911251798702[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]18753.3506573427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34154&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34154&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.950628485445134
R-squared0.90369451733971
Adjusted R-squared0.876477750500931
F-TEST (value)33.2035955149583
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation20.1911251798702
Sum Squared Residuals18753.3506573427






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18774.017202797202812.9827972027972
296.377.077202797202819.2227972027972
3107.180.853846153846126.2461538461539
4115.284.633846153846130.5661538461539
5106.191.993846153846114.1061538461539
689.597.3138461538462-7.81384615384616
791.398.5138461538461-7.21384615384614
897.6104.833846153846-7.23384615384613
9100.7115.133846153846-14.4338461538462
10104.6119.593846153846-14.9938461538462
1194.7114.773846153846-20.0738461538461
12101.8118.393846153846-16.5938461538462
13102.5109.753566433566-7.25356643356643
14105.3112.813566433566-7.51356643356636
15110.3120.406993006993-10.106993006993
16109.8124.186993006993-14.3869930069930
17117.3131.546993006993-14.246993006993
18118.8136.866993006993-18.0669930069931
19131.3138.066993006993-6.76699300699301
20125.9144.386993006993-18.4869930069930
21133.1154.686993006993-21.5869930069930
22147159.146993006993-12.146993006993
23145.8154.326993006993-8.52699300699299
24164.4157.9469930069936.45300699300698
25149.8149.3067132867130.493286713286695
26137.7152.366713286713-14.6667132867133
27151.7156.143356643357-4.44335664335666
28156.8159.923356643357-3.12335664335662
29180167.28335664335712.7166433566434
30180.4172.6033566433577.79664335664337
31170.4173.803356643357-3.40335664335665
32191.6180.12335664335711.4766433566434
33199.5190.4233566433579.07664335664334
34218.2194.88335664335723.3166433566433
35217.5190.06335664335727.4366433566433
36205193.68335664335711.3166433566433
37194185.0430769230778.95692307692305
38199.3188.10307692307711.1969230769231
39219.3191.87972027972027.4202797202797
40211.1195.65972027972015.4402797202797
41215.2203.01972027972012.1802797202797
42240.2208.33972027972031.8602797202797
43242.2209.53972027972032.6602797202797
44240.7215.85972027972024.8402797202797
45255.4226.15972027972029.2402797202797
46253230.61972027972022.3802797202797
47218.2225.799720279720-7.5997202797203
48203.7229.419720279720-25.7197202797203
49205.6220.779440559441-15.1794405594406
50215.6223.839440559441-8.23944055944058
51188.5227.616083916084-39.1160839160839
52202.9231.396083916084-28.4960839160839
53214238.756083916084-24.7560839160839
54230.3244.076083916084-13.7760839160839
55230245.276083916084-15.2760839160839
56241251.596083916084-10.5960839160839
57259.6261.896083916084-2.29608391608390
58247.8266.356083916084-18.5560839160839
59270.3261.5360839160848.76391608391608
60289.7265.15608391608424.5439160839161

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 87 & 74.0172027972028 & 12.9827972027972 \tabularnewline
2 & 96.3 & 77.0772027972028 & 19.2227972027972 \tabularnewline
3 & 107.1 & 80.8538461538461 & 26.2461538461539 \tabularnewline
4 & 115.2 & 84.6338461538461 & 30.5661538461539 \tabularnewline
5 & 106.1 & 91.9938461538461 & 14.1061538461539 \tabularnewline
6 & 89.5 & 97.3138461538462 & -7.81384615384616 \tabularnewline
7 & 91.3 & 98.5138461538461 & -7.21384615384614 \tabularnewline
8 & 97.6 & 104.833846153846 & -7.23384615384613 \tabularnewline
9 & 100.7 & 115.133846153846 & -14.4338461538462 \tabularnewline
10 & 104.6 & 119.593846153846 & -14.9938461538462 \tabularnewline
11 & 94.7 & 114.773846153846 & -20.0738461538461 \tabularnewline
12 & 101.8 & 118.393846153846 & -16.5938461538462 \tabularnewline
13 & 102.5 & 109.753566433566 & -7.25356643356643 \tabularnewline
14 & 105.3 & 112.813566433566 & -7.51356643356636 \tabularnewline
15 & 110.3 & 120.406993006993 & -10.106993006993 \tabularnewline
16 & 109.8 & 124.186993006993 & -14.3869930069930 \tabularnewline
17 & 117.3 & 131.546993006993 & -14.246993006993 \tabularnewline
18 & 118.8 & 136.866993006993 & -18.0669930069931 \tabularnewline
19 & 131.3 & 138.066993006993 & -6.76699300699301 \tabularnewline
20 & 125.9 & 144.386993006993 & -18.4869930069930 \tabularnewline
21 & 133.1 & 154.686993006993 & -21.5869930069930 \tabularnewline
22 & 147 & 159.146993006993 & -12.146993006993 \tabularnewline
23 & 145.8 & 154.326993006993 & -8.52699300699299 \tabularnewline
24 & 164.4 & 157.946993006993 & 6.45300699300698 \tabularnewline
25 & 149.8 & 149.306713286713 & 0.493286713286695 \tabularnewline
26 & 137.7 & 152.366713286713 & -14.6667132867133 \tabularnewline
27 & 151.7 & 156.143356643357 & -4.44335664335666 \tabularnewline
28 & 156.8 & 159.923356643357 & -3.12335664335662 \tabularnewline
29 & 180 & 167.283356643357 & 12.7166433566434 \tabularnewline
30 & 180.4 & 172.603356643357 & 7.79664335664337 \tabularnewline
31 & 170.4 & 173.803356643357 & -3.40335664335665 \tabularnewline
32 & 191.6 & 180.123356643357 & 11.4766433566434 \tabularnewline
33 & 199.5 & 190.423356643357 & 9.07664335664334 \tabularnewline
34 & 218.2 & 194.883356643357 & 23.3166433566433 \tabularnewline
35 & 217.5 & 190.063356643357 & 27.4366433566433 \tabularnewline
36 & 205 & 193.683356643357 & 11.3166433566433 \tabularnewline
37 & 194 & 185.043076923077 & 8.95692307692305 \tabularnewline
38 & 199.3 & 188.103076923077 & 11.1969230769231 \tabularnewline
39 & 219.3 & 191.879720279720 & 27.4202797202797 \tabularnewline
40 & 211.1 & 195.659720279720 & 15.4402797202797 \tabularnewline
41 & 215.2 & 203.019720279720 & 12.1802797202797 \tabularnewline
42 & 240.2 & 208.339720279720 & 31.8602797202797 \tabularnewline
43 & 242.2 & 209.539720279720 & 32.6602797202797 \tabularnewline
44 & 240.7 & 215.859720279720 & 24.8402797202797 \tabularnewline
45 & 255.4 & 226.159720279720 & 29.2402797202797 \tabularnewline
46 & 253 & 230.619720279720 & 22.3802797202797 \tabularnewline
47 & 218.2 & 225.799720279720 & -7.5997202797203 \tabularnewline
48 & 203.7 & 229.419720279720 & -25.7197202797203 \tabularnewline
49 & 205.6 & 220.779440559441 & -15.1794405594406 \tabularnewline
50 & 215.6 & 223.839440559441 & -8.23944055944058 \tabularnewline
51 & 188.5 & 227.616083916084 & -39.1160839160839 \tabularnewline
52 & 202.9 & 231.396083916084 & -28.4960839160839 \tabularnewline
53 & 214 & 238.756083916084 & -24.7560839160839 \tabularnewline
54 & 230.3 & 244.076083916084 & -13.7760839160839 \tabularnewline
55 & 230 & 245.276083916084 & -15.2760839160839 \tabularnewline
56 & 241 & 251.596083916084 & -10.5960839160839 \tabularnewline
57 & 259.6 & 261.896083916084 & -2.29608391608390 \tabularnewline
58 & 247.8 & 266.356083916084 & -18.5560839160839 \tabularnewline
59 & 270.3 & 261.536083916084 & 8.76391608391608 \tabularnewline
60 & 289.7 & 265.156083916084 & 24.5439160839161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34154&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]87[/C][C]74.0172027972028[/C][C]12.9827972027972[/C][/ROW]
[ROW][C]2[/C][C]96.3[/C][C]77.0772027972028[/C][C]19.2227972027972[/C][/ROW]
[ROW][C]3[/C][C]107.1[/C][C]80.8538461538461[/C][C]26.2461538461539[/C][/ROW]
[ROW][C]4[/C][C]115.2[/C][C]84.6338461538461[/C][C]30.5661538461539[/C][/ROW]
[ROW][C]5[/C][C]106.1[/C][C]91.9938461538461[/C][C]14.1061538461539[/C][/ROW]
[ROW][C]6[/C][C]89.5[/C][C]97.3138461538462[/C][C]-7.81384615384616[/C][/ROW]
[ROW][C]7[/C][C]91.3[/C][C]98.5138461538461[/C][C]-7.21384615384614[/C][/ROW]
[ROW][C]8[/C][C]97.6[/C][C]104.833846153846[/C][C]-7.23384615384613[/C][/ROW]
[ROW][C]9[/C][C]100.7[/C][C]115.133846153846[/C][C]-14.4338461538462[/C][/ROW]
[ROW][C]10[/C][C]104.6[/C][C]119.593846153846[/C][C]-14.9938461538462[/C][/ROW]
[ROW][C]11[/C][C]94.7[/C][C]114.773846153846[/C][C]-20.0738461538461[/C][/ROW]
[ROW][C]12[/C][C]101.8[/C][C]118.393846153846[/C][C]-16.5938461538462[/C][/ROW]
[ROW][C]13[/C][C]102.5[/C][C]109.753566433566[/C][C]-7.25356643356643[/C][/ROW]
[ROW][C]14[/C][C]105.3[/C][C]112.813566433566[/C][C]-7.51356643356636[/C][/ROW]
[ROW][C]15[/C][C]110.3[/C][C]120.406993006993[/C][C]-10.106993006993[/C][/ROW]
[ROW][C]16[/C][C]109.8[/C][C]124.186993006993[/C][C]-14.3869930069930[/C][/ROW]
[ROW][C]17[/C][C]117.3[/C][C]131.546993006993[/C][C]-14.246993006993[/C][/ROW]
[ROW][C]18[/C][C]118.8[/C][C]136.866993006993[/C][C]-18.0669930069931[/C][/ROW]
[ROW][C]19[/C][C]131.3[/C][C]138.066993006993[/C][C]-6.76699300699301[/C][/ROW]
[ROW][C]20[/C][C]125.9[/C][C]144.386993006993[/C][C]-18.4869930069930[/C][/ROW]
[ROW][C]21[/C][C]133.1[/C][C]154.686993006993[/C][C]-21.5869930069930[/C][/ROW]
[ROW][C]22[/C][C]147[/C][C]159.146993006993[/C][C]-12.146993006993[/C][/ROW]
[ROW][C]23[/C][C]145.8[/C][C]154.326993006993[/C][C]-8.52699300699299[/C][/ROW]
[ROW][C]24[/C][C]164.4[/C][C]157.946993006993[/C][C]6.45300699300698[/C][/ROW]
[ROW][C]25[/C][C]149.8[/C][C]149.306713286713[/C][C]0.493286713286695[/C][/ROW]
[ROW][C]26[/C][C]137.7[/C][C]152.366713286713[/C][C]-14.6667132867133[/C][/ROW]
[ROW][C]27[/C][C]151.7[/C][C]156.143356643357[/C][C]-4.44335664335666[/C][/ROW]
[ROW][C]28[/C][C]156.8[/C][C]159.923356643357[/C][C]-3.12335664335662[/C][/ROW]
[ROW][C]29[/C][C]180[/C][C]167.283356643357[/C][C]12.7166433566434[/C][/ROW]
[ROW][C]30[/C][C]180.4[/C][C]172.603356643357[/C][C]7.79664335664337[/C][/ROW]
[ROW][C]31[/C][C]170.4[/C][C]173.803356643357[/C][C]-3.40335664335665[/C][/ROW]
[ROW][C]32[/C][C]191.6[/C][C]180.123356643357[/C][C]11.4766433566434[/C][/ROW]
[ROW][C]33[/C][C]199.5[/C][C]190.423356643357[/C][C]9.07664335664334[/C][/ROW]
[ROW][C]34[/C][C]218.2[/C][C]194.883356643357[/C][C]23.3166433566433[/C][/ROW]
[ROW][C]35[/C][C]217.5[/C][C]190.063356643357[/C][C]27.4366433566433[/C][/ROW]
[ROW][C]36[/C][C]205[/C][C]193.683356643357[/C][C]11.3166433566433[/C][/ROW]
[ROW][C]37[/C][C]194[/C][C]185.043076923077[/C][C]8.95692307692305[/C][/ROW]
[ROW][C]38[/C][C]199.3[/C][C]188.103076923077[/C][C]11.1969230769231[/C][/ROW]
[ROW][C]39[/C][C]219.3[/C][C]191.879720279720[/C][C]27.4202797202797[/C][/ROW]
[ROW][C]40[/C][C]211.1[/C][C]195.659720279720[/C][C]15.4402797202797[/C][/ROW]
[ROW][C]41[/C][C]215.2[/C][C]203.019720279720[/C][C]12.1802797202797[/C][/ROW]
[ROW][C]42[/C][C]240.2[/C][C]208.339720279720[/C][C]31.8602797202797[/C][/ROW]
[ROW][C]43[/C][C]242.2[/C][C]209.539720279720[/C][C]32.6602797202797[/C][/ROW]
[ROW][C]44[/C][C]240.7[/C][C]215.859720279720[/C][C]24.8402797202797[/C][/ROW]
[ROW][C]45[/C][C]255.4[/C][C]226.159720279720[/C][C]29.2402797202797[/C][/ROW]
[ROW][C]46[/C][C]253[/C][C]230.619720279720[/C][C]22.3802797202797[/C][/ROW]
[ROW][C]47[/C][C]218.2[/C][C]225.799720279720[/C][C]-7.5997202797203[/C][/ROW]
[ROW][C]48[/C][C]203.7[/C][C]229.419720279720[/C][C]-25.7197202797203[/C][/ROW]
[ROW][C]49[/C][C]205.6[/C][C]220.779440559441[/C][C]-15.1794405594406[/C][/ROW]
[ROW][C]50[/C][C]215.6[/C][C]223.839440559441[/C][C]-8.23944055944058[/C][/ROW]
[ROW][C]51[/C][C]188.5[/C][C]227.616083916084[/C][C]-39.1160839160839[/C][/ROW]
[ROW][C]52[/C][C]202.9[/C][C]231.396083916084[/C][C]-28.4960839160839[/C][/ROW]
[ROW][C]53[/C][C]214[/C][C]238.756083916084[/C][C]-24.7560839160839[/C][/ROW]
[ROW][C]54[/C][C]230.3[/C][C]244.076083916084[/C][C]-13.7760839160839[/C][/ROW]
[ROW][C]55[/C][C]230[/C][C]245.276083916084[/C][C]-15.2760839160839[/C][/ROW]
[ROW][C]56[/C][C]241[/C][C]251.596083916084[/C][C]-10.5960839160839[/C][/ROW]
[ROW][C]57[/C][C]259.6[/C][C]261.896083916084[/C][C]-2.29608391608390[/C][/ROW]
[ROW][C]58[/C][C]247.8[/C][C]266.356083916084[/C][C]-18.5560839160839[/C][/ROW]
[ROW][C]59[/C][C]270.3[/C][C]261.536083916084[/C][C]8.76391608391608[/C][/ROW]
[ROW][C]60[/C][C]289.7[/C][C]265.156083916084[/C][C]24.5439160839161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34154&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34154&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18774.017202797202812.9827972027972
296.377.077202797202819.2227972027972
3107.180.853846153846126.2461538461539
4115.284.633846153846130.5661538461539
5106.191.993846153846114.1061538461539
689.597.3138461538462-7.81384615384616
791.398.5138461538461-7.21384615384614
897.6104.833846153846-7.23384615384613
9100.7115.133846153846-14.4338461538462
10104.6119.593846153846-14.9938461538462
1194.7114.773846153846-20.0738461538461
12101.8118.393846153846-16.5938461538462
13102.5109.753566433566-7.25356643356643
14105.3112.813566433566-7.51356643356636
15110.3120.406993006993-10.106993006993
16109.8124.186993006993-14.3869930069930
17117.3131.546993006993-14.246993006993
18118.8136.866993006993-18.0669930069931
19131.3138.066993006993-6.76699300699301
20125.9144.386993006993-18.4869930069930
21133.1154.686993006993-21.5869930069930
22147159.146993006993-12.146993006993
23145.8154.326993006993-8.52699300699299
24164.4157.9469930069936.45300699300698
25149.8149.3067132867130.493286713286695
26137.7152.366713286713-14.6667132867133
27151.7156.143356643357-4.44335664335666
28156.8159.923356643357-3.12335664335662
29180167.28335664335712.7166433566434
30180.4172.6033566433577.79664335664337
31170.4173.803356643357-3.40335664335665
32191.6180.12335664335711.4766433566434
33199.5190.4233566433579.07664335664334
34218.2194.88335664335723.3166433566433
35217.5190.06335664335727.4366433566433
36205193.68335664335711.3166433566433
37194185.0430769230778.95692307692305
38199.3188.10307692307711.1969230769231
39219.3191.87972027972027.4202797202797
40211.1195.65972027972015.4402797202797
41215.2203.01972027972012.1802797202797
42240.2208.33972027972031.8602797202797
43242.2209.53972027972032.6602797202797
44240.7215.85972027972024.8402797202797
45255.4226.15972027972029.2402797202797
46253230.61972027972022.3802797202797
47218.2225.799720279720-7.5997202797203
48203.7229.419720279720-25.7197202797203
49205.6220.779440559441-15.1794405594406
50215.6223.839440559441-8.23944055944058
51188.5227.616083916084-39.1160839160839
52202.9231.396083916084-28.4960839160839
53214238.756083916084-24.7560839160839
54230.3244.076083916084-13.7760839160839
55230245.276083916084-15.2760839160839
56241251.596083916084-10.5960839160839
57259.6261.896083916084-2.29608391608390
58247.8266.356083916084-18.5560839160839
59270.3261.5360839160848.76391608391608
60289.7265.15608391608424.5439160839161


Figures (Output of Computation)

Figure 1
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Figure 2
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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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Input Parameters & R Code

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')