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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 16 Dec 2009 10:12:08 -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/2009/Dec/16/t1260983688i6927q7dwlsen28.htm/, Retrieved Tue, 30 Apr 2024 17:44:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68485, Retrieved Tue, 30 Apr 2024 17:44:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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] [74be16979710d4c4e7c6647856088456]
- RM D      [Multiple Regression] [] [2009-12-16 17:12:08] [208e60166df5802f3c494097313a670f] [Current]
-   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 
19	0
18	0
19	0
19	0
22	0
23	0
20	0
14	0
14	0
14	0
15	0
11	0
17	0
16	0
20	0
24	0
23	0
20	0
21	0
19	0
23	0
23	0
23	0
23	0
27	0
26	0
17	0
24	0
26	0
24	0
27	0
27	0
26	0
24	0
23	0
23	0
24	1
17	1
21	1
19	1
22	1
22	1
18	1
16	1
14	1
12	1
14	1
16	1
8	1
3	1
0	1
5	1
1	1
1	1
3	1
6	1
7	1
8	1
14	1
14	1
13	1
15	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68485&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]4 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=68485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68485&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
consumentenvertrouwen[t] = + 19.9166666666667 -10.3452380952381`financiële_crisis`[t] + 1.85972222222223M1[t] -0.351984126984132M2[t] -1.59464285714286M3[t] + 1.16031746031746M4[t] + 1.71527777777778M5[t] + 0.870238095238092M6[t] + 0.62519841269841M7[t] -0.819841269841272M8[t] -0.464880952380954M9[t] -1.10992063492063M10[t] + 0.44503968253968M11[t] + 0.0450396825396822t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
consumentenvertrouwen[t] =  +  19.9166666666667 -10.3452380952381`financiële_crisis`[t] +  1.85972222222223M1[t] -0.351984126984132M2[t] -1.59464285714286M3[t] +  1.16031746031746M4[t] +  1.71527777777778M5[t] +  0.870238095238092M6[t] +  0.62519841269841M7[t] -0.819841269841272M8[t] -0.464880952380954M9[t] -1.10992063492063M10[t] +  0.44503968253968M11[t] +  0.0450396825396822t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68485&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]consumentenvertrouwen[t] =  +  19.9166666666667 -10.3452380952381`financiële_crisis`[t] +  1.85972222222223M1[t] -0.351984126984132M2[t] -1.59464285714286M3[t] +  1.16031746031746M4[t] +  1.71527777777778M5[t] +  0.870238095238092M6[t] +  0.62519841269841M7[t] -0.819841269841272M8[t] -0.464880952380954M9[t] -1.10992063492063M10[t] +  0.44503968253968M11[t] +  0.0450396825396822t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68485&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
consumentenvertrouwen[t] = + 19.9166666666667 -10.3452380952381`financiële_crisis`[t] + 1.85972222222223M1[t] -0.351984126984132M2[t] -1.59464285714286M3[t] + 1.16031746031746M4[t] + 1.71527777777778M5[t] + 0.870238095238092M6[t] + 0.62519841269841M7[t] -0.819841269841272M8[t] -0.464880952380954M9[t] -1.10992063492063M10[t] + 0.44503968253968M11[t] + 0.0450396825396822t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)19.91666666666673.5167265.66341e-060
`financiële_crisis`-10.34523809523813.192629-3.24040.0021710.001086
M11.859722222222233.8074740.48840.6274620.313731
M2-0.3519841269841323.791701-0.09280.9264250.463212
M3-1.594642857142863.982264-0.40040.6906120.345306
M41.160317460317463.9654410.29260.7710830.385542
M51.715277777777783.9505380.43420.6660970.333049
M60.8702380952380923.9375760.2210.8260230.413012
M70.625198412698413.9265750.15920.8741620.437081
M8-0.8198412698412723.917551-0.20930.835120.41756
M9-0.4648809523809543.910518-0.11890.9058670.452933
M10-1.109920634920633.905487-0.28420.7774830.388742
M110.445039682539683.9024650.1140.9096810.454841
t0.04503968253968220.0886840.50790.6138730.306937

\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) & 19.9166666666667 & 3.516726 & 5.6634 & 1e-06 & 0 \tabularnewline
`financiële_crisis` & -10.3452380952381 & 3.192629 & -3.2404 & 0.002171 & 0.001086 \tabularnewline
M1 & 1.85972222222223 & 3.807474 & 0.4884 & 0.627462 & 0.313731 \tabularnewline
M2 & -0.351984126984132 & 3.791701 & -0.0928 & 0.926425 & 0.463212 \tabularnewline
M3 & -1.59464285714286 & 3.982264 & -0.4004 & 0.690612 & 0.345306 \tabularnewline
M4 & 1.16031746031746 & 3.965441 & 0.2926 & 0.771083 & 0.385542 \tabularnewline
M5 & 1.71527777777778 & 3.950538 & 0.4342 & 0.666097 & 0.333049 \tabularnewline
M6 & 0.870238095238092 & 3.937576 & 0.221 & 0.826023 & 0.413012 \tabularnewline
M7 & 0.62519841269841 & 3.926575 & 0.1592 & 0.874162 & 0.437081 \tabularnewline
M8 & -0.819841269841272 & 3.917551 & -0.2093 & 0.83512 & 0.41756 \tabularnewline
M9 & -0.464880952380954 & 3.910518 & -0.1189 & 0.905867 & 0.452933 \tabularnewline
M10 & -1.10992063492063 & 3.905487 & -0.2842 & 0.777483 & 0.388742 \tabularnewline
M11 & 0.44503968253968 & 3.902465 & 0.114 & 0.909681 & 0.454841 \tabularnewline
t & 0.0450396825396822 & 0.088684 & 0.5079 & 0.613873 & 0.306937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68485&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]19.9166666666667[/C][C]3.516726[/C][C]5.6634[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]`financiële_crisis`[/C][C]-10.3452380952381[/C][C]3.192629[/C][C]-3.2404[/C][C]0.002171[/C][C]0.001086[/C][/ROW]
[ROW][C]M1[/C][C]1.85972222222223[/C][C]3.807474[/C][C]0.4884[/C][C]0.627462[/C][C]0.313731[/C][/ROW]
[ROW][C]M2[/C][C]-0.351984126984132[/C][C]3.791701[/C][C]-0.0928[/C][C]0.926425[/C][C]0.463212[/C][/ROW]
[ROW][C]M3[/C][C]-1.59464285714286[/C][C]3.982264[/C][C]-0.4004[/C][C]0.690612[/C][C]0.345306[/C][/ROW]
[ROW][C]M4[/C][C]1.16031746031746[/C][C]3.965441[/C][C]0.2926[/C][C]0.771083[/C][C]0.385542[/C][/ROW]
[ROW][C]M5[/C][C]1.71527777777778[/C][C]3.950538[/C][C]0.4342[/C][C]0.666097[/C][C]0.333049[/C][/ROW]
[ROW][C]M6[/C][C]0.870238095238092[/C][C]3.937576[/C][C]0.221[/C][C]0.826023[/C][C]0.413012[/C][/ROW]
[ROW][C]M7[/C][C]0.62519841269841[/C][C]3.926575[/C][C]0.1592[/C][C]0.874162[/C][C]0.437081[/C][/ROW]
[ROW][C]M8[/C][C]-0.819841269841272[/C][C]3.917551[/C][C]-0.2093[/C][C]0.83512[/C][C]0.41756[/C][/ROW]
[ROW][C]M9[/C][C]-0.464880952380954[/C][C]3.910518[/C][C]-0.1189[/C][C]0.905867[/C][C]0.452933[/C][/ROW]
[ROW][C]M10[/C][C]-1.10992063492063[/C][C]3.905487[/C][C]-0.2842[/C][C]0.777483[/C][C]0.388742[/C][/ROW]
[ROW][C]M11[/C][C]0.44503968253968[/C][C]3.902465[/C][C]0.114[/C][C]0.909681[/C][C]0.454841[/C][/ROW]
[ROW][C]t[/C][C]0.0450396825396822[/C][C]0.088684[/C][C]0.5079[/C][C]0.613873[/C][C]0.306937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68485&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)19.91666666666673.5167265.66341e-060
`financiële_crisis`-10.34523809523813.192629-3.24040.0021710.001086
M11.859722222222233.8074740.48840.6274620.313731
M2-0.3519841269841323.791701-0.09280.9264250.463212
M3-1.594642857142863.982264-0.40040.6906120.345306
M41.160317460317463.9654410.29260.7710830.385542
M51.715277777777783.9505380.43420.6660970.333049
M60.8702380952380923.9375760.2210.8260230.413012
M70.625198412698413.9265750.15920.8741620.437081
M8-0.8198412698412723.917551-0.20930.835120.41756
M9-0.4648809523809543.910518-0.11890.9058670.452933
M10-1.109920634920633.905487-0.28420.7774830.388742
M110.445039682539683.9024650.1140.9096810.454841
t0.04503968253968220.0886840.50790.6138730.306937






Multiple Linear Regression - Regression Statistics
Multiple R0.640966321583416
R-squared0.410837825404175
Adjusted R-squared0.251273069784472
F-TEST (value)2.57474041688342
F-TEST (DF numerator)13
F-TEST (DF denominator)48
p-value0.00874013524307227
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.16874562768215
Sum Squared Residuals1826.56428571429

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.640966321583416 \tabularnewline
R-squared & 0.410837825404175 \tabularnewline
Adjusted R-squared & 0.251273069784472 \tabularnewline
F-TEST (value) & 2.57474041688342 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.00874013524307227 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.16874562768215 \tabularnewline
Sum Squared Residuals & 1826.56428571429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68485&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.640966321583416[/C][/ROW]
[ROW][C]R-squared[/C][C]0.410837825404175[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.251273069784472[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.57474041688342[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.00874013524307227[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]6.16874562768215[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1826.56428571429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68485&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 R0.640966321583416
R-squared0.410837825404175
Adjusted R-squared0.251273069784472
F-TEST (value)2.57474041688342
F-TEST (DF numerator)13
F-TEST (DF denominator)48
p-value0.00874013524307227
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.16874562768215
Sum Squared Residuals1826.56428571429






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11921.8214285714285-2.82142857142852
21819.6547619047619-1.65476190476191
31918.45714285714290.542857142857136
41921.2571428571429-2.25714285714286
52221.85714285714290.142857142857144
62321.05714285714291.94285714285714
72020.8571428571429-0.857142857142862
81419.4571428571429-5.45714285714286
91419.8571428571429-5.85714285714287
101419.2571428571429-5.25714285714286
111520.8571428571429-5.85714285714286
121120.4571428571429-9.45714285714287
131722.3619047619048-5.36190476190477
141620.1952380952381-4.19523809523809
152018.99761904761911.00238095238095
162421.79761904761912.20238095238095
172322.39761904761900.60238095238095
182021.5976190476190-1.59761904761905
192121.3976190476190-0.397619047619046
201919.9976190476191-0.997619047619049
212320.39761904761902.60238095238095
222319.79761904761903.20238095238095
232321.39761904761901.60238095238095
242320.99761904761912.00238095238095
252722.90238095238104.09761904761903
262620.73571428571435.26428571428572
271719.5380952380952-2.53809523809524
282422.33809523809521.66190476190476
292622.93809523809523.06190476190476
302422.13809523809521.86190476190476
312721.93809523809525.06190476190477
322720.53809523809526.46190476190476
332620.93809523809525.06190476190477
342420.33809523809523.66190476190476
352321.93809523809521.06190476190476
362321.53809523809521.46190476190476
372413.097619047619110.9023809523809
381710.93095238095246.06904761904762
39219.7333333333333311.2666666666667
401912.53333333333336.46666666666667
412213.13333333333338.86666666666667
422212.33333333333339.66666666666667
431812.13333333333335.86666666666667
441610.73333333333335.26666666666666
451411.13333333333332.86666666666667
461210.53333333333331.46666666666667
471412.13333333333331.86666666666667
481611.73333333333334.26666666666666
49813.6380952380953-5.63809523809525
50311.4714285714286-8.47142857142857
51010.2738095238095-10.2738095238095
52513.0738095238095-8.07380952380952
53113.6738095238095-12.6738095238095
54112.8738095238095-11.8738095238095
55312.6738095238095-9.67380952380952
56611.2738095238095-5.27380952380952
57711.6738095238095-4.67380952380952
58811.0738095238095-3.07380952380952
591412.67380952380951.32619047619048
601412.27380952380951.72619047619048
611314.1785714285714-1.17857142857144
621512.01190476190482.98809523809524

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 19 & 21.8214285714285 & -2.82142857142852 \tabularnewline
2 & 18 & 19.6547619047619 & -1.65476190476191 \tabularnewline
3 & 19 & 18.4571428571429 & 0.542857142857136 \tabularnewline
4 & 19 & 21.2571428571429 & -2.25714285714286 \tabularnewline
5 & 22 & 21.8571428571429 & 0.142857142857144 \tabularnewline
6 & 23 & 21.0571428571429 & 1.94285714285714 \tabularnewline
7 & 20 & 20.8571428571429 & -0.857142857142862 \tabularnewline
8 & 14 & 19.4571428571429 & -5.45714285714286 \tabularnewline
9 & 14 & 19.8571428571429 & -5.85714285714287 \tabularnewline
10 & 14 & 19.2571428571429 & -5.25714285714286 \tabularnewline
11 & 15 & 20.8571428571429 & -5.85714285714286 \tabularnewline
12 & 11 & 20.4571428571429 & -9.45714285714287 \tabularnewline
13 & 17 & 22.3619047619048 & -5.36190476190477 \tabularnewline
14 & 16 & 20.1952380952381 & -4.19523809523809 \tabularnewline
15 & 20 & 18.9976190476191 & 1.00238095238095 \tabularnewline
16 & 24 & 21.7976190476191 & 2.20238095238095 \tabularnewline
17 & 23 & 22.3976190476190 & 0.60238095238095 \tabularnewline
18 & 20 & 21.5976190476190 & -1.59761904761905 \tabularnewline
19 & 21 & 21.3976190476190 & -0.397619047619046 \tabularnewline
20 & 19 & 19.9976190476191 & -0.997619047619049 \tabularnewline
21 & 23 & 20.3976190476190 & 2.60238095238095 \tabularnewline
22 & 23 & 19.7976190476190 & 3.20238095238095 \tabularnewline
23 & 23 & 21.3976190476190 & 1.60238095238095 \tabularnewline
24 & 23 & 20.9976190476191 & 2.00238095238095 \tabularnewline
25 & 27 & 22.9023809523810 & 4.09761904761903 \tabularnewline
26 & 26 & 20.7357142857143 & 5.26428571428572 \tabularnewline
27 & 17 & 19.5380952380952 & -2.53809523809524 \tabularnewline
28 & 24 & 22.3380952380952 & 1.66190476190476 \tabularnewline
29 & 26 & 22.9380952380952 & 3.06190476190476 \tabularnewline
30 & 24 & 22.1380952380952 & 1.86190476190476 \tabularnewline
31 & 27 & 21.9380952380952 & 5.06190476190477 \tabularnewline
32 & 27 & 20.5380952380952 & 6.46190476190476 \tabularnewline
33 & 26 & 20.9380952380952 & 5.06190476190477 \tabularnewline
34 & 24 & 20.3380952380952 & 3.66190476190476 \tabularnewline
35 & 23 & 21.9380952380952 & 1.06190476190476 \tabularnewline
36 & 23 & 21.5380952380952 & 1.46190476190476 \tabularnewline
37 & 24 & 13.0976190476191 & 10.9023809523809 \tabularnewline
38 & 17 & 10.9309523809524 & 6.06904761904762 \tabularnewline
39 & 21 & 9.73333333333333 & 11.2666666666667 \tabularnewline
40 & 19 & 12.5333333333333 & 6.46666666666667 \tabularnewline
41 & 22 & 13.1333333333333 & 8.86666666666667 \tabularnewline
42 & 22 & 12.3333333333333 & 9.66666666666667 \tabularnewline
43 & 18 & 12.1333333333333 & 5.86666666666667 \tabularnewline
44 & 16 & 10.7333333333333 & 5.26666666666666 \tabularnewline
45 & 14 & 11.1333333333333 & 2.86666666666667 \tabularnewline
46 & 12 & 10.5333333333333 & 1.46666666666667 \tabularnewline
47 & 14 & 12.1333333333333 & 1.86666666666667 \tabularnewline
48 & 16 & 11.7333333333333 & 4.26666666666666 \tabularnewline
49 & 8 & 13.6380952380953 & -5.63809523809525 \tabularnewline
50 & 3 & 11.4714285714286 & -8.47142857142857 \tabularnewline
51 & 0 & 10.2738095238095 & -10.2738095238095 \tabularnewline
52 & 5 & 13.0738095238095 & -8.07380952380952 \tabularnewline
53 & 1 & 13.6738095238095 & -12.6738095238095 \tabularnewline
54 & 1 & 12.8738095238095 & -11.8738095238095 \tabularnewline
55 & 3 & 12.6738095238095 & -9.67380952380952 \tabularnewline
56 & 6 & 11.2738095238095 & -5.27380952380952 \tabularnewline
57 & 7 & 11.6738095238095 & -4.67380952380952 \tabularnewline
58 & 8 & 11.0738095238095 & -3.07380952380952 \tabularnewline
59 & 14 & 12.6738095238095 & 1.32619047619048 \tabularnewline
60 & 14 & 12.2738095238095 & 1.72619047619048 \tabularnewline
61 & 13 & 14.1785714285714 & -1.17857142857144 \tabularnewline
62 & 15 & 12.0119047619048 & 2.98809523809524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68485&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]19[/C][C]21.8214285714285[/C][C]-2.82142857142852[/C][/ROW]
[ROW][C]2[/C][C]18[/C][C]19.6547619047619[/C][C]-1.65476190476191[/C][/ROW]
[ROW][C]3[/C][C]19[/C][C]18.4571428571429[/C][C]0.542857142857136[/C][/ROW]
[ROW][C]4[/C][C]19[/C][C]21.2571428571429[/C][C]-2.25714285714286[/C][/ROW]
[ROW][C]5[/C][C]22[/C][C]21.8571428571429[/C][C]0.142857142857144[/C][/ROW]
[ROW][C]6[/C][C]23[/C][C]21.0571428571429[/C][C]1.94285714285714[/C][/ROW]
[ROW][C]7[/C][C]20[/C][C]20.8571428571429[/C][C]-0.857142857142862[/C][/ROW]
[ROW][C]8[/C][C]14[/C][C]19.4571428571429[/C][C]-5.45714285714286[/C][/ROW]
[ROW][C]9[/C][C]14[/C][C]19.8571428571429[/C][C]-5.85714285714287[/C][/ROW]
[ROW][C]10[/C][C]14[/C][C]19.2571428571429[/C][C]-5.25714285714286[/C][/ROW]
[ROW][C]11[/C][C]15[/C][C]20.8571428571429[/C][C]-5.85714285714286[/C][/ROW]
[ROW][C]12[/C][C]11[/C][C]20.4571428571429[/C][C]-9.45714285714287[/C][/ROW]
[ROW][C]13[/C][C]17[/C][C]22.3619047619048[/C][C]-5.36190476190477[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]20.1952380952381[/C][C]-4.19523809523809[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]18.9976190476191[/C][C]1.00238095238095[/C][/ROW]
[ROW][C]16[/C][C]24[/C][C]21.7976190476191[/C][C]2.20238095238095[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]22.3976190476190[/C][C]0.60238095238095[/C][/ROW]
[ROW][C]18[/C][C]20[/C][C]21.5976190476190[/C][C]-1.59761904761905[/C][/ROW]
[ROW][C]19[/C][C]21[/C][C]21.3976190476190[/C][C]-0.397619047619046[/C][/ROW]
[ROW][C]20[/C][C]19[/C][C]19.9976190476191[/C][C]-0.997619047619049[/C][/ROW]
[ROW][C]21[/C][C]23[/C][C]20.3976190476190[/C][C]2.60238095238095[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]19.7976190476190[/C][C]3.20238095238095[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]21.3976190476190[/C][C]1.60238095238095[/C][/ROW]
[ROW][C]24[/C][C]23[/C][C]20.9976190476191[/C][C]2.00238095238095[/C][/ROW]
[ROW][C]25[/C][C]27[/C][C]22.9023809523810[/C][C]4.09761904761903[/C][/ROW]
[ROW][C]26[/C][C]26[/C][C]20.7357142857143[/C][C]5.26428571428572[/C][/ROW]
[ROW][C]27[/C][C]17[/C][C]19.5380952380952[/C][C]-2.53809523809524[/C][/ROW]
[ROW][C]28[/C][C]24[/C][C]22.3380952380952[/C][C]1.66190476190476[/C][/ROW]
[ROW][C]29[/C][C]26[/C][C]22.9380952380952[/C][C]3.06190476190476[/C][/ROW]
[ROW][C]30[/C][C]24[/C][C]22.1380952380952[/C][C]1.86190476190476[/C][/ROW]
[ROW][C]31[/C][C]27[/C][C]21.9380952380952[/C][C]5.06190476190477[/C][/ROW]
[ROW][C]32[/C][C]27[/C][C]20.5380952380952[/C][C]6.46190476190476[/C][/ROW]
[ROW][C]33[/C][C]26[/C][C]20.9380952380952[/C][C]5.06190476190477[/C][/ROW]
[ROW][C]34[/C][C]24[/C][C]20.3380952380952[/C][C]3.66190476190476[/C][/ROW]
[ROW][C]35[/C][C]23[/C][C]21.9380952380952[/C][C]1.06190476190476[/C][/ROW]
[ROW][C]36[/C][C]23[/C][C]21.5380952380952[/C][C]1.46190476190476[/C][/ROW]
[ROW][C]37[/C][C]24[/C][C]13.0976190476191[/C][C]10.9023809523809[/C][/ROW]
[ROW][C]38[/C][C]17[/C][C]10.9309523809524[/C][C]6.06904761904762[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]9.73333333333333[/C][C]11.2666666666667[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]12.5333333333333[/C][C]6.46666666666667[/C][/ROW]
[ROW][C]41[/C][C]22[/C][C]13.1333333333333[/C][C]8.86666666666667[/C][/ROW]
[ROW][C]42[/C][C]22[/C][C]12.3333333333333[/C][C]9.66666666666667[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]12.1333333333333[/C][C]5.86666666666667[/C][/ROW]
[ROW][C]44[/C][C]16[/C][C]10.7333333333333[/C][C]5.26666666666666[/C][/ROW]
[ROW][C]45[/C][C]14[/C][C]11.1333333333333[/C][C]2.86666666666667[/C][/ROW]
[ROW][C]46[/C][C]12[/C][C]10.5333333333333[/C][C]1.46666666666667[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]12.1333333333333[/C][C]1.86666666666667[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]11.7333333333333[/C][C]4.26666666666666[/C][/ROW]
[ROW][C]49[/C][C]8[/C][C]13.6380952380953[/C][C]-5.63809523809525[/C][/ROW]
[ROW][C]50[/C][C]3[/C][C]11.4714285714286[/C][C]-8.47142857142857[/C][/ROW]
[ROW][C]51[/C][C]0[/C][C]10.2738095238095[/C][C]-10.2738095238095[/C][/ROW]
[ROW][C]52[/C][C]5[/C][C]13.0738095238095[/C][C]-8.07380952380952[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]13.6738095238095[/C][C]-12.6738095238095[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]12.8738095238095[/C][C]-11.8738095238095[/C][/ROW]
[ROW][C]55[/C][C]3[/C][C]12.6738095238095[/C][C]-9.67380952380952[/C][/ROW]
[ROW][C]56[/C][C]6[/C][C]11.2738095238095[/C][C]-5.27380952380952[/C][/ROW]
[ROW][C]57[/C][C]7[/C][C]11.6738095238095[/C][C]-4.67380952380952[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]11.0738095238095[/C][C]-3.07380952380952[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]12.6738095238095[/C][C]1.32619047619048[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]12.2738095238095[/C][C]1.72619047619048[/C][/ROW]
[ROW][C]61[/C][C]13[/C][C]14.1785714285714[/C][C]-1.17857142857144[/C][/ROW]
[ROW][C]62[/C][C]15[/C][C]12.0119047619048[/C][C]2.98809523809524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68485&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68485&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
11921.8214285714285-2.82142857142852
21819.6547619047619-1.65476190476191
31918.45714285714290.542857142857136
41921.2571428571429-2.25714285714286
52221.85714285714290.142857142857144
62321.05714285714291.94285714285714
72020.8571428571429-0.857142857142862
81419.4571428571429-5.45714285714286
91419.8571428571429-5.85714285714287
101419.2571428571429-5.25714285714286
111520.8571428571429-5.85714285714286
121120.4571428571429-9.45714285714287
131722.3619047619048-5.36190476190477
141620.1952380952381-4.19523809523809
152018.99761904761911.00238095238095
162421.79761904761912.20238095238095
172322.39761904761900.60238095238095
182021.5976190476190-1.59761904761905
192121.3976190476190-0.397619047619046
201919.9976190476191-0.997619047619049
212320.39761904761902.60238095238095
222319.79761904761903.20238095238095
232321.39761904761901.60238095238095
242320.99761904761912.00238095238095
252722.90238095238104.09761904761903
262620.73571428571435.26428571428572
271719.5380952380952-2.53809523809524
282422.33809523809521.66190476190476
292622.93809523809523.06190476190476
302422.13809523809521.86190476190476
312721.93809523809525.06190476190477
322720.53809523809526.46190476190476
332620.93809523809525.06190476190477
342420.33809523809523.66190476190476
352321.93809523809521.06190476190476
362321.53809523809521.46190476190476
372413.097619047619110.9023809523809
381710.93095238095246.06904761904762
39219.7333333333333311.2666666666667
401912.53333333333336.46666666666667
412213.13333333333338.86666666666667
422212.33333333333339.66666666666667
431812.13333333333335.86666666666667
441610.73333333333335.26666666666666
451411.13333333333332.86666666666667
461210.53333333333331.46666666666667
471412.13333333333331.86666666666667
481611.73333333333334.26666666666666
49813.6380952380953-5.63809523809525
50311.4714285714286-8.47142857142857
51010.2738095238095-10.2738095238095
52513.0738095238095-8.07380952380952
53113.6738095238095-12.6738095238095
54112.8738095238095-11.8738095238095
55312.6738095238095-9.67380952380952
56611.2738095238095-5.27380952380952
57711.6738095238095-4.67380952380952
58811.0738095238095-3.07380952380952
591412.67380952380951.32619047619048
601412.27380952380951.72619047619048
611314.1785714285714-1.17857142857144
621512.01190476190482.98809523809524


Figures (Output of Computation)

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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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')