Mfcttrf

What are the real benefits of using Salesforce DX?

Have 1.5% of all nuclear reactors ever built melted down?

Website returning plaintext password

Should one buy new hardware after a system compromise?

Should breaking down something like a door be adjudicated as an attempt to beat its AC and HP, or as an ability check against a set DC?

Python program to find the most frequent letter in a text

Employer demanding to see degree after poor code review

How to patch glass cuts in a bicycle tire?

Why do most published works in medical imaging try to reduce false positives?

What is a really good book for complex variables?

How to invert colors of a picture on Mac?

Why does Mjolnir fall down in Age of Ultron but not in Endgame?

How strong are Wi-Fi signals?

Is the taxi route omitted in low visibility (LVP)?

How long until a random word with letters "A", "B", "C" ends in the pattern "ABC"?

Does Nitrogen inside commercial airliner wheels prevent blowouts on touchdown?

Plot twist where the antagonist wins

Any advice on creating fictional locations in real places when writing historical fiction?

Inconsistent results from Wolfram Could

What is the largest (size) solid object ever dropped from an airplane to impact the ground in freefall?

Would Jetfuel for a modern jet like an F-16 or a F-35 be producable in the WW2 era?

Why is this Simple Puzzle impossible to solve?

What is quasi-aromaticity?

Grammar Question Regarding "Are the" or "Is the" When Referring to Something that May or May not be Plural

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

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

2

$begingroup$

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

share|cite|improve this question

asked 8 hours ago

girlonline2girlonline2

161

$endgroup$

add a comment | 

2

$begingroup$

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

share|cite|improve this question

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

share|cite|improve this question

asked 8 hours ago

girlonline2girlonline2

161

$endgroup$

share|cite|improve this question

asked 8 hours ago

girlonline2girlonline2

161

share|cite|improve this question

asked 8 hours ago

girlonline2girlonline2

161

asked 8 hours ago

girlonline2girlonline2

161

asked 8 hours ago

girlonline2girlonline2

161

1 Answer
1

active

oldest

votes

4

$begingroup$

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 5 hours ago

answered 8 hours ago

StatsStudentStatsStudent

6,30432145

$endgroup$

add a comment | 

Your Answer

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "65"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f409998%2finclusion-of-standard-error-in-regression-equation%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

4

$begingroup$

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 5 hours ago

answered 8 hours ago

StatsStudentStatsStudent

6,30432145

$endgroup$

add a comment | 

4

$begingroup$

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 5 hours ago

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:

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 5 hours ago

answered 8 hours ago

StatsStudentStatsStudent

6,30432145

$endgroup$

share|cite|improve this answer

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