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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Moduleesteq.wasp
Title produced by softwareEstimate Equation
Date of computationTue, 16 Nov 2010 10:03:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t12899029738xcitl833pjmpxm.htm/, Retrieved Mon, 12 May 2025 21:16:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95346, Retrieved Mon, 12 May 2025 21:16:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Linear Regression Graphical Model Validation] [Colombia Coffee -...] [2008-02-26 10:22:06] [74be16979710d4c4e7c6647856088456]
-  M D  [Linear Regression Graphical Model Validation] [workshop 6 tutorial] [2010-11-12 10:13:29] [87d60b8864dc39f7ed759c345edfb471]
-    D    [Linear Regression Graphical Model Validation] [workshop 6 mini-t...] [2010-11-12 14:05:27] [87d60b8864dc39f7ed759c345edfb471]
- RMPD      [Multiple Regression] [] [2010-11-16 08:42:30] [5b5e2f42cf221276958b46f2b8444c18]
-   P         [Multiple Regression] [] [2010-11-16 08:50:28] [5b5e2f42cf221276958b46f2b8444c18]
-    D          [Multiple Regression] [] [2010-11-16 09:22:57] [5b5e2f42cf221276958b46f2b8444c18]
F RMP               [Estimate Equation] [] [2010-11-16 10:03:08] [6b67b7c8c7d0a997c30f007387afbdb8] [Current]
Feedback Forum
2010-11-20 17:01:04 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply] 
Uit de omschrijving van de hypothese en van de beschikbare gegevens blijkt opnieuw dat student enkelvoudige lineaire regressie wil onderzoeken en hiervoor een model wil opstellen.
Echter werd opnieuw gebruik gemaakt van de softwaremodule voor meervoudige regressie. De student zal dus een keuze moeten maken tussen beiden en aanpassingen moeten doen in ofwel de gebruikte softwaremodule ofwel de geformuleerde hypothese.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25	15
19	0
18	3
24	2
18	3
32	12
23	3
23	0
23	12
25	15
24	0
22	10
30	20
25	20
17	2
30	3
25	16
25	4
26	2
23	4
19	0
19	0
35	15
21	9
25	1
23	15
20	5
23	4
19	15
24	4
17	12
27	2
27	4
18	2
24	4
22	8
26	30
23	6
26	6
25	7
14	4
20	17
26	5
18	0
22	3
25	4
29	15
21	0
25	8
24	10
22	4
22	0
32	6
23	11
31	10
18	0
23	0
19	0
26	0
14	0
27	0
20	0
22	7
24	4
32	12
25	6
21	12
21	10
28	9
24	0
23	16
24	2
21	0
13	0
21	1
17	10
29	14
25	12
16	12
25	12
20	5
25	0
21	4
23	3
21	0
26	3
19	0
20	12
21	12
19	15
14	0
22	8
14	6
20	14
19	5
29	10
25	16
21	4
22	0
15	8
22	12
19	6
28	4
25	20
17	0
21	13
19	0
27	0
29	0
22	0
19	10
20	6
16	16
24	6
17	0
21	4
22	9
26	17
17	12
17	3
19	8
19	3
17	0
27	10
25	3
19	0
16	8
15	0
24	4
15	13
20	12
29	16
19	20
29	20
24	14
24	12
21	15
23	9
23	4
22	8
26	0
22	13
29	0
21	21
22	0
20	1
21	16
18	12
18	2

Tables (Output of Computation)





Multiple Linear Regression - Estimated Regression Equation
Sport[t] = +0.32028128863504 Perf[t] -0.17647464519623 + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Sport[t] = +0.32028128863504 Perf[t] -0.17647464519623 + e[t] \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=95346&T=0

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW]
Sport[t] = +0.32028128863504 Perf[t] -0.17647464519623 + e[t][/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=95346&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95346&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:

Multiple Linear Regression - Estimated Regression Equation
Sport[t] = +0.32028128863504 Perf[t] -0.17647464519623 + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-value
Perf[t]0.3202810.1200392.6681440.0084830.004242
Constant-0.1764752.724153-0.0647810.9484360.474218
VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value
%Perf[t]1.0253320.3842870.065920.9475310.473766
%Constant-0.0253320.391039-2.4925060.0137940.006897
VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value
S-Perf[t]0.2149220.0805512.6681440.0084830.004242
S-Constant00010.5
*Notecomputed against deterministic endogenous series
VariablePartial Correlation
Perf[t]0.214922
Constant-0.005343
Critical Values (alpha = 5%)
1-tail CV at 5%1.65
2-tail CV at 5%1.96

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ordinary Least Squares \tabularnewline
VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-value \tabularnewline Perf[t]0.3202810.1200392.6681440.0084830.004242 \tabularnewline Constant-0.1764752.724153-0.0647810.9484360.474218 \tabularnewline \tabularnewline VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value \tabularnewline %Perf[t]1.0253320.3842870.065920.9475310.473766 \tabularnewline %Constant-0.0253320.391039-2.4925060.0137940.006897 \tabularnewline VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value \tabularnewline S-Perf[t]0.2149220.0805512.6681440.0084830.004242 \tabularnewline S-Constant00010.5 \tabularnewline *Notecomputed against deterministic endogenous series \tabularnewline VariablePartial Correlation \tabularnewline Perf[t]0.214922 \tabularnewline Constant-0.005343 \tabularnewline Critical Values (alpha = 5%) \tabularnewline 1-tail CV at 5%1.65 \tabularnewline 2-tail CV at 5%1.96 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=95346&T=1

[TABLE]

[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]

[ROW]
Variable[/C]Parameter[/C]S.E.[/C]T-STATH0: parameter = 0[/C]2-tail p-value[/C]1-tail p-value[/C][/ROW] [ROW][C]Perf[t][/C]0.320281[/C]0.120039[/C]2.668144[/C]0.008483[/C]0.004242[/C][/ROW] [ROW][C]Constant[/C]-0.176475[/C]2.724153[/C]-0.064781[/C]0.948436[/C]0.474218[/C][/ROW] [ROW][C][/C][/ROW] [ROW]Variable[/C]Elasticity[/C]S.E.*[/C]T-STATH0: |elast| = 1[/C]2-tail p-value[/C]1-tail p-value[/C][/ROW] [ROW][C]%Perf[t][/C]1.025332[/C]0.384287[/C]0.06592[/C]0.947531[/C]0.473766[/C][/ROW] [ROW][C]%Constant[/C]-0.025332[/C]0.391039[/C]-2.492506[/C]0.013794[/C]0.006897[/C][/ROW] [ROW]Variable[/C]Stand. Coeff.[/C]S.E.*[/C]T-STATH0: coeff = 0[/C]2-tail p-value[/C]1-tail p-value[/C][/ROW] [ROW][C]S-Perf[t][/C]0.214922[/C]0.080551[/C]2.668144[/C]0.008483[/C]0.004242[/C][/ROW] [ROW][C]S-Constant[/C]0[/C]0[/C]0[/C]1[/C]0.5[/C][/ROW] [ROW][C]*Note[/C]computed against deterministic endogenous series[/C][/ROW] [ROW]Variable[/C]Partial Correlation[/C][/ROW] [ROW][C]Perf[t][/C]0.214922[/C][/ROW] [ROW][C]Constant[/C]-0.005343[/C][/ROW] [ROW][C]Critical Values (alpha = 5%)[/C][/ROW] [ROW][C]1-tail CV at 5%[/C]1.65[/C][/ROW] [ROW][C]2-tail CV at 5%[/C]1.96[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=95346&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95346&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 - Ordinary Least Squares
VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-value
Perf[t]0.3202810.1200392.6681440.0084830.004242
Constant-0.1764752.724153-0.0647810.9484360.474218
VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value
%Perf[t]1.0253320.3842870.065920.9475310.473766
%Constant-0.0253320.391039-2.4925060.0137940.006897
VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value
S-Perf[t]0.2149220.0805512.6681440.0084830.004242
S-Constant00010.5
*Notecomputed against deterministic endogenous series
VariablePartial Correlation
Perf[t]0.214922
Constant-0.005343
Critical Values (alpha = 5%)
1-tail CV at 5%1.65
2-tail CV at 5%1.96






Multiple Linear Regression - Regression Statistics
Multiple R0.214922
R-squared0.046192
Adjusted R-squared0.039703
F-TEST7.118995
Observations149
Degrees of Freedom147
Multiple Linear Regression - Residual Statistics
Standard Error6.152988
Sum Squared Errors5565.312286
Log Likelihood-481.138816
Durbin-Watson1.806237
Von Neumann Ratio1.818441
# e[t] > 067
# e[t] < 082
# Runs72
Stand. Normal Runs Statistic-0.455932

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Regression Statistics \tabularnewline

Multiple R
0.214922 \tabularnewline R-squared0.046192 \tabularnewline Adjusted R-squared0.039703 \tabularnewline F-TEST7.118995 \tabularnewline Observations149 \tabularnewline Degrees of Freedom147 \tabularnewline Multiple Linear Regression - Residual Statistics \tabularnewline Standard Error6.152988 \tabularnewline Sum Squared Errors5565.312286 \tabularnewline Log Likelihood-481.138816 \tabularnewline Durbin-Watson1.806237 \tabularnewline Von Neumann Ratio1.818441 \tabularnewline # e[t] > 067 \tabularnewline # e[t] < 082 \tabularnewline # Runs72 \tabularnewline Stand. Normal Runs Statistic-0.455932 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=95346&T=2

[TABLE]

[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]

[ROW][C]Multiple R[/C]
0.214922[/C][/ROW] [ROW][C]R-squared[/C]0.046192[/C][/ROW] [ROW][C]Adjusted R-squared[/C]0.039703[/C][/ROW] [ROW][C]F-TEST[/C]7.118995[/C][/ROW] [ROW][C]Observations[/C]149[/C][/ROW] [ROW][C]Degrees of Freedom[/C]147[/C][/ROW] [ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW] [ROW][C]Standard Error[/C]6.152988[/C][/ROW] [ROW][C]Sum Squared Errors[/C]5565.312286[/C][/ROW] [ROW][C]Log Likelihood[/C]-481.138816[/C][/ROW] [ROW][C]Durbin-Watson[/C]1.806237[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]1.818441[/C][/ROW] [ROW][C]# e[t] > 0[/C]67[/C][/ROW] [ROW][C]# e[t] < 0[/C]82[/C][/ROW] [ROW][C]# Runs[/C]72[/C][/ROW] [ROW][C]Stand. Normal Runs Statistic[/C]-0.455932[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=95346&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95346&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 - Regression Statistics
Multiple R0.214922
R-squared0.046192
Adjusted R-squared0.039703
F-TEST7.118995
Observations149
Degrees of Freedom147
Multiple Linear Regression - Residual Statistics
Standard Error6.152988
Sum Squared Errors5565.312286
Log Likelihood-481.138816
Durbin-Watson1.806237
Von Neumann Ratio1.818441
# e[t] > 067
# e[t] < 082
# Runs72
Stand. Normal Runs Statistic-0.455932






Multiple Linear Regression - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error38.367445
Akaike (1973) Log Information Criterion3.647208
Akaike (1974) Information Criterion38.367383
Schwarz (1978) Log Criterion3.687529
Schwarz (1978) Criterion39.946024
Craven-Wahba (1979) Generalized Cross Validation38.374359
Hannan-Quinn (1979) Criterion39.001092
Rice (1984) Criterion38.381464
Shibata (1981) Criterion38.353803

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ad Hoc Selection Test Statistics \tabularnewline

Akaike (1969) Final Prediction Error
38.367445 \tabularnewline Akaike (1973) Log Information Criterion3.647208 \tabularnewline Akaike (1974) Information Criterion38.367383 \tabularnewline Schwarz (1978) Log Criterion3.687529 \tabularnewline Schwarz (1978) Criterion39.946024 \tabularnewline Craven-Wahba (1979) Generalized Cross Validation38.374359 \tabularnewline Hannan-Quinn (1979) Criterion39.001092 \tabularnewline Rice (1984) Criterion38.381464 \tabularnewline Shibata (1981) Criterion38.353803 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=95346&T=3

[TABLE]

[ROW][C]Multiple Linear Regression - Ad Hoc Selection Test Statistics[/C][/ROW]

[ROW][C]Akaike (1969) Final Prediction Error[/C]
38.367445[/C][/ROW] [ROW][C]Akaike (1973) Log Information Criterion[/C]3.647208[/C][/ROW] [ROW][C]Akaike (1974) Information Criterion[/C]38.367383[/C][/ROW] [ROW][C]Schwarz (1978) Log Criterion[/C]3.687529[/C][/ROW] [ROW][C]Schwarz (1978) Criterion[/C]39.946024[/C][/ROW] [ROW][C]Craven-Wahba (1979) Generalized Cross Validation[/C]38.374359[/C][/ROW] [ROW][C]Hannan-Quinn (1979) Criterion[/C]39.001092[/C][/ROW] [ROW][C]Rice (1984) Criterion[/C]38.381464[/C][/ROW] [ROW][C]Shibata (1981) Criterion[/C]38.353803[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=95346&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95346&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 - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error38.367445
Akaike (1973) Log Information Criterion3.647208
Akaike (1974) Information Criterion38.367383
Schwarz (1978) Log Criterion3.687529
Schwarz (1978) Criterion39.946024
Craven-Wahba (1979) Generalized Cross Validation38.374359
Hannan-Quinn (1979) Criterion39.001092
Rice (1984) Criterion38.381464
Shibata (1981) Criterion38.353803






Multiple Linear Regression - Analysis of Variance
ANOVADFSum of SquaresMean Square
Regression1269.519929269.519929
Residual1475565.31228637.859267
Total1485834.83221539.424541991656
F-TEST7.118995
p-value0.008483

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Analysis of Variance \tabularnewline

ANOVA & DF & Sum of Squares & Mean Square \tabularnewline

Regression
1269.519929269.519929 \tabularnewline Residual1475565.31228637.859267 \tabularnewline Total1485834.83221539.424541991656 \tabularnewline F-TEST7.118995 \tabularnewline p-value0.008483 \tabularnewline
\hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=95346&T=4

[TABLE]

[ROW][C]Multiple Linear Regression - Analysis of Variance[/C][/ROW]

[ROW][C]ANOVA[/C][C]DF[/C][C]Sum of Squares[/C][C]Mean Square[/C][/ROW]

[ROW][C]Regression[/C]
1[/C]269.519929[/C]269.519929[/C][/ROW] [ROW][C]Residual[/C]147[/C]5565.312286[/C]37.859267[/C][/ROW] [ROW][C]Total[/C]148[/C]5834.832215[/C]39.424541991656[/C][/ROW] [ROW][C]F-TEST[/C]7.118995[/C][/ROW] [ROW][C]p-value[/C]0.008483[/C][/ROW]
[/TABLE] Source: https://freestatistics.org/blog/index.php?pk=95346&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95346&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 - Analysis of Variance
ANOVADFSum of SquaresMean Square
Regression1269.519929269.519929
Residual1475565.31228637.859267
Total1485834.83221539.424541991656
F-TEST7.118995
p-value0.008483


Figures (Output of Computation)

Input Parameters & R Code

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