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Inclusion of standard error in regression equation

multiplicative treatment effects with standard errorsLinear Equation System with Random CoefficientsConstructing the OLS standard error by hand to avoid regressionGeneralized $R^2$ for average modelStandard error of the sampling distribution of the meanStandard error of regression coefficient without raw dataIntution behind variance of OLS slope and intercept estimators in simple linear regression being independent of $y_i$'sMultivariate Regression with Uniform ErrorsSandwich standard errors versus typical standard error estimationCalculating standard error of coefficients in segmented regression

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;

2

$begingroup$

$$
beginalignat14
P =
11&.32
&+ 0&.71 ,textPASN
&+ 1&.54 ,textDIS
&- 1&.02 ,textDIS^2
&+ 3&.44 ,textFUEL
&+ 1&.36 ,textFIRST
&+ 1&.12 ,textBIS \[-25px]
(5&.16)
& (0&.11)
& (1&.91)
& (0&.41)
& (1&.17)
& (0&.91)
& (0&.52)
endalignat \[25px]
R^2 = 0.56;
~~ textRSS = 211.22;
~~ textRRleft(1,textd.f.right) = 9.48;
~~ Wleft(1right) = 17.11
$$

I often see that standard errors are displayed under the regression equation but I don't really understand the purpose of it. Are those the standard errors of the estimated slope coefficient? And how does the inclusion of this information help with the statistical analyses? Thanks

regression normal-distribution regression-coefficients standard-error

share|cite|improve this question

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

$endgroup$

add a comment | 

2

$begingroup$

$$
beginalignat14
P =
11&.32
&+ 0&.71 ,textPASN
&+ 1&.54 ,textDIS
&- 1&.02 ,textDIS^2
&+ 3&.44 ,textFUEL
&+ 1&.36 ,textFIRST
&+ 1&.12 ,textBIS \[-25px]
(5&.16)
& (0&.11)
& (1&.91)
& (0&.41)
& (1&.17)
& (0&.91)
& (0&.52)
endalignat \[25px]
R^2 = 0.56;
~~ textRSS = 211.22;
~~ textRRleft(1,textd.f.right) = 9.48;
~~ Wleft(1right) = 17.11
$$

I often see that standard errors are displayed under the regression equation but I don't really understand the purpose of it. Are those the standard errors of the estimated slope coefficient? And how does the inclusion of this information help with the statistical analyses? Thanks

regression normal-distribution regression-coefficients standard-error

share|cite|improve this question

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

$endgroup$

add a comment | 

$begingroup$

$$
beginalignat14
P =
11&.32
&+ 0&.71 ,textPASN
&+ 1&.54 ,textDIS
&- 1&.02 ,textDIS^2
&+ 3&.44 ,textFUEL
&+ 1&.36 ,textFIRST
&+ 1&.12 ,textBIS \[-25px]
(5&.16)
& (0&.11)
& (1&.91)
& (0&.41)
& (1&.17)
& (0&.91)
& (0&.52)
endalignat \[25px]
R^2 = 0.56;
~~ textRSS = 211.22;
~~ textRRleft(1,textd.f.right) = 9.48;
~~ Wleft(1right) = 17.11
$$

I often see that standard errors are displayed under the regression equation but I don't really understand the purpose of it. Are those the standard errors of the estimated slope coefficient? And how does the inclusion of this information help with the statistical analyses? Thanks

regression normal-distribution regression-coefficients standard-error

share|cite|improve this question

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

$endgroup$

share|cite|improve this question

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

share|cite|improve this question

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

edited May 25 at 12:15

Nat

357138

edited May 25 at 12:15

Nat

357138

asked May 24 at 22:05

girlonline2girlonline2

161

asked May 24 at 22:05

girlonline2girlonline2

161

1 Answer
1

active

oldest

votes

5

$begingroup$

Yes. The estimated standard error gives the analyst (or reader) an idea of how precise the parameter estimate (estimated coefficient/slope) is: the larger the standard error, the less precise the estimate. To help you see this, recall that the standard errors are directly tied to confidence intervals of parameter estimates in simple multiple regression by the following:

begineqnarray*
hatbeta_j & pm & t_alpha/2,n-ptimes (Standard,Error)
endeqnarray*

Where $hatbeta_j$ is the $j$-th parameter estimate, $n$ is the number of observations, $p$ is the number of parameters to be estimated in the regression model, and $t_alpha/2,n-p$ is the $alpha/2$ quantile of a Student's $t$-distribution with $n-p$ degrees of freedom.

share|cite|improve this answer

edited May 25 at 1:01

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

$endgroup$

add a comment | 

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5

$begingroup$

Yes. The estimated standard error gives the analyst (or reader) an idea of how precise the parameter estimate (estimated coefficient/slope) is: the larger the standard error, the less precise the estimate. To help you see this, recall that the standard errors are directly tied to confidence intervals of parameter estimates in simple multiple regression by the following:

begineqnarray*
hatbeta_j & pm & t_alpha/2,n-ptimes (Standard,Error)
endeqnarray*

Where $hatbeta_j$ is the $j$-th parameter estimate, $n$ is the number of observations, $p$ is the number of parameters to be estimated in the regression model, and $t_alpha/2,n-p$ is the $alpha/2$ quantile of a Student's $t$-distribution with $n-p$ degrees of freedom.

share|cite|improve this answer

edited May 25 at 1:01

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

$endgroup$

add a comment | 

5

$begingroup$

Yes. The estimated standard error gives the analyst (or reader) an idea of how precise the parameter estimate (estimated coefficient/slope) is: the larger the standard error, the less precise the estimate. To help you see this, recall that the standard errors are directly tied to confidence intervals of parameter estimates in simple multiple regression by the following:

begineqnarray*
hatbeta_j & pm & t_alpha/2,n-ptimes (Standard,Error)
endeqnarray*

Where $hatbeta_j$ is the $j$-th parameter estimate, $n$ is the number of observations, $p$ is the number of parameters to be estimated in the regression model, and $t_alpha/2,n-p$ is the $alpha/2$ quantile of a Student's $t$-distribution with $n-p$ degrees of freedom.

share|cite|improve this answer

edited May 25 at 1:01

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

$endgroup$

add a comment | 

$begingroup$

Yes. The estimated standard error gives the analyst (or reader) an idea of how precise the parameter estimate (estimated coefficient/slope) is: the larger the standard error, the less precise the estimate. To help you see this, recall that the standard errors are directly tied to confidence intervals of parameter estimates in simple multiple regression by the following:

begineqnarray*
hatbeta_j & pm & t_alpha/2,n-ptimes (Standard,Error)
endeqnarray*

Where $hatbeta_j$ is the $j$-th parameter estimate, $n$ is the number of observations, $p$ is the number of parameters to be estimated in the regression model, and $t_alpha/2,n-p$ is the $alpha/2$ quantile of a Student's $t$-distribution with $n-p$ degrees of freedom.

share|cite|improve this answer

edited May 25 at 1:01

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

$endgroup$

share|cite|improve this answer

edited May 25 at 1:01

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145

answered May 24 at 22:43

StatsStudentStatsStudent

6,40432145