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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Moduleesteq.wasp
Title produced by softwareEstimate Equation
Date of computationFri, 22 May 2009 00:44:12 -0600
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/May/22/t12429750037nbtgvk8zr394n0.htm/, Retrieved Sun, 05 May 2024 13:10:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40279, Retrieved Sun, 05 May 2024 13:10:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPortland John Ross Condos Housing Affordability
Estimated Impact223

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Estimate Equation] [Linear regression...] [2009-05-22 06:44:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
638	170000
631	172000
636	198850
640	199000
633	199950
781	201300
637	225000
639	234000
791	234900
639	249000
791	279000
793	279000
829	279900
773	284900
790	289900
920	299000
1061	329000
1205	339500
1205	349000
1207	379000
1207	389000
1207	389000
1205	399000
1205	399000
1207	419000
1207	429000
1207	429000
1210	479000
1210	479000
1207	479000
1207	479000
1207	579000
1873	599000
1827	647000
1826	649000
2133	649000
1468	675000
1928	699000
1831	709000
1831	729000
1833	769000
1894	819000
1938	819000

Tables (Output of Computation)





Multiple Linear Regression - Estimated Regression Equation
Sq.ft.[t] = +0.0022346258508251 Price[t] +237.35339830648 + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Sq.ft.[t] = +0.0022346258508251 Price[t] +237.35339830648 + e[t] \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=40279&T=0

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW]
Sq.ft.[t] = +0.0022346258508251 Price[t] +237.35339830648 + e[t][/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=40279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40279&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
Sq.ft.[t] = +0.0022346258508251 Price[t] +237.35339830648 + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-value
Price[t]0.0022350.00011519.38378600
Constant237.35339853.8061994.4112657.3E-53.6E-5
VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value
%Price[t]0.8002970.041287-4.836941.9E-59.0E-6
%Constant0.1997030.045271-17.67791600
VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value
S-Price[t]0.9495340.04898619.38378600
S-Constant00010.5
*Notecomputed against deterministic endogenous series
VariablePartial Correlation
Price[t]0.949534
Constant0.567325
Critical Values (alpha = 5%)
1-tail CV at 5%1.69
2-tail CV at 5%2.02

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ordinary Least Squares \tabularnewline
VariableParameterS.E.T-STATH0: parameter = 02-tail p-value1-tail p-value \tabularnewline Price[t]0.0022350.00011519.38378600 \tabularnewline Constant237.35339853.8061994.4112657.3E-53.6E-5 \tabularnewline \tabularnewline VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value \tabularnewline %Price[t]0.8002970.041287-4.836941.9E-59.0E-6 \tabularnewline %Constant0.1997030.045271-17.67791600 \tabularnewline VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value \tabularnewline S-Price[t]0.9495340.04898619.38378600 \tabularnewline S-Constant00010.5 \tabularnewline *Notecomputed against deterministic endogenous series \tabularnewline VariablePartial Correlation \tabularnewline Price[t]0.949534 \tabularnewline Constant0.567325 \tabularnewline Critical Values (alpha = 5%) \tabularnewline 1-tail CV at 5%1.69 \tabularnewline 2-tail CV at 5%2.02 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=40279&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]Price[t][/C]0.002235[/C]0.000115[/C]19.383786[/C]0[/C]0[/C][/ROW] [ROW][C]Constant[/C]237.353398[/C]53.806199[/C]4.411265[/C]7.3E-5[/C]3.6E-5[/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]%Price[t][/C]0.800297[/C]0.041287[/C]-4.83694[/C]1.9E-5[/C]9.0E-6[/C][/ROW] [ROW][C]%Constant[/C]0.199703[/C]0.045271[/C]-17.677916[/C]0[/C]0[/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-Price[t][/C]0.949534[/C]0.048986[/C]19.383786[/C]0[/C]0[/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]Price[t][/C]0.949534[/C][/ROW] [ROW][C]Constant[/C]0.567325[/C][/ROW] [ROW][C]Critical Values (alpha = 5%)[/C][/ROW] [ROW][C]1-tail CV at 5%[/C]1.69[/C][/ROW] [ROW][C]2-tail CV at 5%[/C]2.02[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=40279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40279&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
Price[t]0.0022350.00011519.38378600
Constant237.35339853.8061994.4112657.3E-53.6E-5
VariableElasticityS.E.*T-STATH0: |elast| = 12-tail p-value1-tail p-value
%Price[t]0.8002970.041287-4.836941.9E-59.0E-6
%Constant0.1997030.045271-17.67791600
VariableStand. Coeff.S.E.*T-STATH0: coeff = 02-tail p-value1-tail p-value
S-Price[t]0.9495340.04898619.38378600
S-Constant00010.5
*Notecomputed against deterministic endogenous series
VariablePartial Correlation
Price[t]0.949534
Constant0.567325
Critical Values (alpha = 5%)
1-tail CV at 5%1.69
2-tail CV at 5%2.02






Multiple Linear Regression - Regression Statistics
Multiple R0.949534
R-squared0.901615
Adjusted R-squared0.899216
F-TEST375.731178
Observations43
Degrees of Freedom41
Multiple Linear Regression - Residual Statistics
Standard Error144.731669
Sum Squared Errors858837.499402
Log Likelihood-273.910257
Durbin-Watson1.693645
Von Neumann Ratio1.73397
# e[t] > 022
# e[t] < 021
# Runs12
Stand. Normal Runs Statistic-3.239495

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Regression Statistics \tabularnewline

Multiple R
0.949534 \tabularnewline R-squared0.901615 \tabularnewline Adjusted R-squared0.899216 \tabularnewline F-TEST375.731178 \tabularnewline Observations43 \tabularnewline Degrees of Freedom41 \tabularnewline Multiple Linear Regression - Residual Statistics \tabularnewline Standard Error144.731669 \tabularnewline Sum Squared Errors858837.499402 \tabularnewline Log Likelihood-273.910257 \tabularnewline Durbin-Watson1.693645 \tabularnewline Von Neumann Ratio1.73397 \tabularnewline # e[t] > 022 \tabularnewline # e[t] < 021 \tabularnewline # Runs12 \tabularnewline Stand. Normal Runs Statistic-3.239495 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=40279&T=2

[TABLE]

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

[ROW][C]Multiple R[/C]
0.949534[/C][/ROW] [ROW][C]R-squared[/C]0.901615[/C][/ROW] [ROW][C]Adjusted R-squared[/C]0.899216[/C][/ROW] [ROW][C]F-TEST[/C]375.731178[/C][/ROW] [ROW][C]Observations[/C]43[/C][/ROW] [ROW][C]Degrees of Freedom[/C]41[/C][/ROW] [ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW] [ROW][C]Standard Error[/C]144.731669[/C][/ROW] [ROW][C]Sum Squared Errors[/C]858837.499402[/C][/ROW] [ROW][C]Log Likelihood[/C]-273.910257[/C][/ROW] [ROW][C]Durbin-Watson[/C]1.693645[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]1.73397[/C][/ROW] [ROW][C]# e[t] > 0[/C]22[/C][/ROW] [ROW][C]# e[t] < 0[/C]21[/C][/ROW] [ROW][C]# Runs[/C]12[/C][/ROW] [ROW][C]Stand. Normal Runs Statistic[/C]-3.239495[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=40279&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40279&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 R0.949534
R-squared0.901615
Adjusted R-squared0.899216
F-TEST375.731178
Observations43
Degrees of Freedom41
Multiple Linear Regression - Residual Statistics
Standard Error144.731669
Sum Squared Errors858837.499402
Log Likelihood-273.910257
Durbin-Watson1.693645
Von Neumann Ratio1.73397
# e[t] > 022
# e[t] < 021
# Runs12
Stand. Normal Runs Statistic-3.239495






Multiple Linear Regression - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error21921.547064
Akaike (1973) Log Information Criterion9.995158
Akaike (1974) Information Criterion21920.074703
Schwarz (1978) Log Criterion10.077074
Schwarz (1978) Criterion23791.280655
Craven-Wahba (1979) Generalized Cross Validation21969.073453
Hannan-Quinn (1979) Criterion22592.343464
Rice (1984) Criterion22021.474344
Shibata (1981) Criterion21830.915344

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ad Hoc Selection Test Statistics \tabularnewline

Akaike (1969) Final Prediction Error
21921.547064 \tabularnewline Akaike (1973) Log Information Criterion9.995158 \tabularnewline Akaike (1974) Information Criterion21920.074703 \tabularnewline Schwarz (1978) Log Criterion10.077074 \tabularnewline Schwarz (1978) Criterion23791.280655 \tabularnewline Craven-Wahba (1979) Generalized Cross Validation21969.073453 \tabularnewline Hannan-Quinn (1979) Criterion22592.343464 \tabularnewline Rice (1984) Criterion22021.474344 \tabularnewline Shibata (1981) Criterion21830.915344 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=40279&T=3

[TABLE]

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

[ROW][C]Akaike (1969) Final Prediction Error[/C]
21921.547064[/C][/ROW] [ROW][C]Akaike (1973) Log Information Criterion[/C]9.995158[/C][/ROW] [ROW][C]Akaike (1974) Information Criterion[/C]21920.074703[/C][/ROW] [ROW][C]Schwarz (1978) Log Criterion[/C]10.077074[/C][/ROW] [ROW][C]Schwarz (1978) Criterion[/C]23791.280655[/C][/ROW] [ROW][C]Craven-Wahba (1979) Generalized Cross Validation[/C]21969.073453[/C][/ROW] [ROW][C]Hannan-Quinn (1979) Criterion[/C]22592.343464[/C][/ROW] [ROW][C]Rice (1984) Criterion[/C]22021.474344[/C][/ROW] [ROW][C]Shibata (1981) Criterion[/C]21830.915344[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=40279&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40279&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 Error21921.547064
Akaike (1973) Log Information Criterion9.995158
Akaike (1974) Information Criterion21920.074703
Schwarz (1978) Log Criterion10.077074
Schwarz (1978) Criterion23791.280655
Craven-Wahba (1979) Generalized Cross Validation21969.073453
Hannan-Quinn (1979) Criterion22592.343464
Rice (1984) Criterion22021.474344
Shibata (1981) Criterion21830.915344






Multiple Linear Regression - Analysis of Variance
ANOVADFSum of SquaresMean Square
Regression17870537.1982737870537.198273
Residual41858837.49940220947.256083
Total428729374.697674207842.25470653
F-TEST375.731178
p-value0

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Analysis of Variance \tabularnewline

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

Regression
17870537.1982737870537.198273 \tabularnewline Residual41858837.49940220947.256083 \tabularnewline Total428729374.697674207842.25470653 \tabularnewline F-TEST375.731178 \tabularnewline p-value0 \tabularnewline
\hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=40279&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]7870537.198273[/C]7870537.198273[/C][/ROW] [ROW][C]Residual[/C]41[/C]858837.499402[/C]20947.256083[/C][/ROW] [ROW][C]Total[/C]42[/C]8729374.697674[/C]207842.25470653[/C][/ROW] [ROW][C]F-TEST[/C]375.731178[/C][/ROW] [ROW][C]p-value[/C]0[/C][/ROW]
[/TABLE] Source: https://freestatistics.org/blog/index.php?pk=40279&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40279&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
Regression17870537.1982737870537.198273
Residual41858837.49940220947.256083
Total428729374.697674207842.25470653
F-TEST375.731178
p-value0


Figures (Output of Computation)

Input Parameters & R Code

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