What is J in while calculating SST in multiple regression?
$begingroup$
I am little confused what actually is the J in the formula of the SST and SSR for multiple regression
SST= $Y^Tleft[ 1-frac{1}{n}Jright]Y$
SSR=$Y^Tleft[ H-frac{1}{n}Jright]Y$
matrices statistics regression linear-regression
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
$endgroup$
add a comment |
$begingroup$
I am little confused what actually is the J in the formula of the SST and SSR for multiple regression
SST= $Y^Tleft[ 1-frac{1}{n}Jright]Y$
SSR=$Y^Tleft[ H-frac{1}{n}Jright]Y$
matrices statistics regression linear-regression
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
$endgroup$
add a comment |
$begingroup$
I am little confused what actually is the J in the formula of the SST and SSR for multiple regression
SST= $Y^Tleft[ 1-frac{1}{n}Jright]Y$
SSR=$Y^Tleft[ H-frac{1}{n}Jright]Y$
matrices statistics regression linear-regression
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
$endgroup$
I am little confused what actually is the J in the formula of the SST and SSR for multiple regression
SST= $Y^Tleft[ 1-frac{1}{n}Jright]Y$
SSR=$Y^Tleft[ H-frac{1}{n}Jright]Y$
matrices statistics regression linear-regression
matrices statistics regression linear-regression
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
edited Dec 8 '18 at 16:27
V. Vancak
11.3k3926
11.3k3926
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
asked Dec 8 '18 at 4:26
surbhi groversurbhi grover
61
61
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$J$ is the matrix of all $1$s. i.e., let
$$
mathbf{1}=(1,1,...,1)^Tin mathbb{R}^n,
$$
then
$$
J = mathbf{1}mathbf{1}^T.
$$
While $frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T in mathbb{R}^n$, then
$$
frac{1}{n}Jy= (bar{y}_n, bar{y}_n, ..., bar{y}_n)^T,
$$
which is an essential part of any sum of squares.
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3030696%2fwhat-is-j-in-while-calculating-sst-in-multiple-regression%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$J$ is the matrix of all $1$s. i.e., let
$$
mathbf{1}=(1,1,...,1)^Tin mathbb{R}^n,
$$
then
$$
J = mathbf{1}mathbf{1}^T.
$$
While $frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T in mathbb{R}^n$, then
$$
frac{1}{n}Jy= (bar{y}_n, bar{y}_n, ..., bar{y}_n)^T,
$$
which is an essential part of any sum of squares.
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
$endgroup$
add a comment |
$begingroup$
$J$ is the matrix of all $1$s. i.e., let
$$
mathbf{1}=(1,1,...,1)^Tin mathbb{R}^n,
$$
then
$$
J = mathbf{1}mathbf{1}^T.
$$
While $frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T in mathbb{R}^n$, then
$$
frac{1}{n}Jy= (bar{y}_n, bar{y}_n, ..., bar{y}_n)^T,
$$
which is an essential part of any sum of squares.
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
$endgroup$
add a comment |
$begingroup$
$J$ is the matrix of all $1$s. i.e., let
$$
mathbf{1}=(1,1,...,1)^Tin mathbb{R}^n,
$$
then
$$
J = mathbf{1}mathbf{1}^T.
$$
While $frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T in mathbb{R}^n$, then
$$
frac{1}{n}Jy= (bar{y}_n, bar{y}_n, ..., bar{y}_n)^T,
$$
which is an essential part of any sum of squares.
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
$endgroup$
$J$ is the matrix of all $1$s. i.e., let
$$
mathbf{1}=(1,1,...,1)^Tin mathbb{R}^n,
$$
then
$$
J = mathbf{1}mathbf{1}^T.
$$
While $frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T in mathbb{R}^n$, then
$$
frac{1}{n}Jy= (bar{y}_n, bar{y}_n, ..., bar{y}_n)^T,
$$
which is an essential part of any sum of squares.
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
answered Dec 8 '18 at 16:24
V. VancakV. Vancak
11.3k3926
11.3k3926
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3030696%2fwhat-is-j-in-while-calculating-sst-in-multiple-regression%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
