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Inclusion of standard error in regression equation
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Inclusion of standard error in regression equation
Useful heuristic for inferring multicollinearity from high standard errorsStandard error of regression coefficient without raw dataCoefficient Decreases but Standard Errors stay the Same with Inclusion of Control VariablesHow to estimate standard error of prediction error in Table 3.3 of Hastie el al (2017)?In regression, what is the limit for correlation between the dependent variable and those being regressed on it?Interpretation of standard error of ARIMA parametersestimation of standard errors after logistic regressionStandard error of the mean of two estimatesStandard error of coefficient estimates for model II regressionQuestions about standard error
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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
asked 8 hours ago
girlonline2girlonline2
161
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add a comment |
$begingroup$
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
asked 8 hours ago
girlonline2girlonline2
161
$endgroup$
add a comment |
$begingroup$
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
asked 8 hours ago
girlonline2girlonline2
161
$endgroup$
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
regression normal-distribution regression-coefficients standard-error
asked 8 hours ago
girlonline2girlonline2
161
asked 8 hours ago
girlonline2girlonline2
161
asked 8 hours ago
girlonline2girlonline2
161
asked 8 hours ago
girlonline2girlonline2
161
asked 8 hours ago
girlonline2girlonline2
161
161
add a comment |
add a comment |
1 Answer
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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:
begin{eqnarray*}
hat{beta_{j}} & pm & t_{alpha/2,n-p}times (Standard,Error)
end{eqnarray*}
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.
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
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1 Answer
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$begingroup$
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:
begin{eqnarray*}
hat{beta_{j}} & pm & t_{alpha/2,n-p}times (Standard,Error)
end{eqnarray*}
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.
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
$endgroup$
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:
begin{eqnarray*}
hat{beta_{j}} & pm & t_{alpha/2,n-p}times (Standard,Error)
end{eqnarray*}
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.
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
$endgroup$
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:
begin{eqnarray*}
hat{beta_{j}} & pm & t_{alpha/2,n-p}times (Standard,Error)
end{eqnarray*}
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.
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
$endgroup$
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:
begin{eqnarray*}
hat{beta_{j}} & pm & t_{alpha/2,n-p}times (Standard,Error)
end{eqnarray*}
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.
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
edited 5 hours ago
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
answered 8 hours ago
StatsStudentStatsStudent
6,30432145
6,30432145
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