What is the formula of the linear regression with an error propagation
0
$begingroup$
I am in Physics Licenciature and a day the teacher showed me a formula for the linear regression with error propagation, and time after, I was searching this formula and I didn't find it. Then I am frustrated, so any answer will be well received.
physics linear-regression error-propagation
edited Jan 7 at 0:25
Bernard
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
$endgroup$
add a comment |
0
$begingroup$
I am in Physics Licenciature and a day the teacher showed me a formula for the linear regression with error propagation, and time after, I was searching this formula and I didn't find it. Then I am frustrated, so any answer will be well received.
physics linear-regression error-propagation
edited Jan 7 at 0:25
Bernard
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
$endgroup$
1
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
1
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
1
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26
add a comment |
0
0
0
$begingroup$
I am in Physics Licenciature and a day the teacher showed me a formula for the linear regression with error propagation, and time after, I was searching this formula and I didn't find it. Then I am frustrated, so any answer will be well received.
physics linear-regression error-propagation
edited Jan 7 at 0:25
Bernard
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
$endgroup$
I am in Physics Licenciature and a day the teacher showed me a formula for the linear regression with error propagation, and time after, I was searching this formula and I didn't find it. Then I am frustrated, so any answer will be well received.
physics linear-regression error-propagation
physics linear-regression error-propagation
edited Jan 7 at 0:25
Bernard
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
edited Jan 7 at 0:25
Bernard
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
edited Jan 7 at 0:25
Bernard
124k741117
edited Jan 7 at 0:25
Bernard
124k741117
edited Jan 7 at 0:25
Bernard
124k741117
124k741117
asked Jan 6 at 23:41
El boritoEl borito
664216
asked Jan 6 at 23:41
El boritoEl borito
664216
asked Jan 6 at 23:41
El boritoEl borito
664216
664216
1
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
1
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
1
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26
add a comment |
1
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
1
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
1
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26
1
1
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
1
1
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
1
1
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26
add a comment |
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1
$begingroup$
Does this link help at all en.m.wikipedia.org/wiki/Propagation_of_uncertainty ? It was, by the way, the first hit on a google for “propagation of error”.
$endgroup$
– LoveTooNap29
Jan 6 at 23:50
$begingroup$
I know the propagation of uncertainty and its calculus, but I don't know the uncertaintly of the linear regression of various data
$endgroup$
– El borito
Jan 6 at 23:55
1
$begingroup$
Well, it is not very clear what you are asking for anyway. Are you asking: if $Y_n =alpha +sum_{i=1}^N beta_i X_{n,i}+epsilon_n$, (i.e. a linear regression model with an intercept and $N$ independent variables) and $Var(X_{n,i})=sigma_i^2$ then what is $Var(Y_n)$? If so, then this is indeed answered already in the linked article I provided (up to some assumptions on $epsilon_n$)...
$endgroup$
– LoveTooNap29
Jan 7 at 0:08
$begingroup$
It's not what I was looking for, but in fact an answer like that would be very useful.
$endgroup$
– El borito
Jan 7 at 0:17
1
$begingroup$
Hmm, perhaps you should ask your lecturer then? Anyway, the result I eluded to in my previous comment is just an application of the general formula for variance of a sum of (possibly correlated) RVs: $$Var(X_1+dotsc +X_n)=sum_{i=1}^n Var(X_i)+2sum_{i <j} Cov(X_i X_j).$$
$endgroup$
– LoveTooNap29
Jan 7 at 0:26