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what are $SSE$ and $S_y,x$?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Help with problem: Estimated Standard Deviation of Regression Equation (Simple Linear)The unbiased estimator of the variance of $widehatbeta_1$ in simple linear regressionWhat is the most efficient way to calculate $R^2$?ANOVA - Distribution of $hatbeta_1$ still exists although $beta_1=0$ under $H_0$?Specifying the design matrix to minimize a prediction interval in a multivariate regression settingSimple linear regression and sum of squared errorsLinear regression: minimize both vertical and horizontal distance?Simple linear regression of the true values onto the fitted values?Logistic Regression Adjusting for True Population ProportionBayesian Regression Simplifying the posterior










0












$begingroup$


I'm a BC student who is trying to solve some statistic quizzes.



there is a multiple choice question that is this:




In a simple regression model $y=a+bx+e$ our given data is this:
$$ barx = 2, bary = 3, S_x = 4, S_y = 5, r = 0.6 $$ find
SSE and $S_y,x$.



  1. $16, 4$

  2. $14, 4$

  3. $4, 14$

  4. $4, 16$



I must confess I have no idea what is a $S_y,x$! but for SSE here is my work (I've assumed that $s_y$ is the sum of all $y$):



beginalign
textSSE = (1-r^2) textSST &= (1-r^2)sum(y-bar y)^2 \
&= (1-r^2) left(sum y^2 -frac(sum y)^2n right) \
&= (1-r^2)left(sum y^2 -fracS^2_yn right) \
&= (1-r^2)left( sum y^2 -fracS^2_yleft. S_y middle/ bar y right. right) \
&= (1-r^2)left( sum y^2 -S_y bar y right)
endalign



but in this case, I can't find $sum y^2$. I want some help.



thank in advance.






regression linear-regression







share|cite|improve this question











$endgroup$











  • $begingroup$
    Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
    $endgroup$
    – MachineLearner
    Mar 26 at 8:34










  • $begingroup$
    @MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:25







  • 1




    $begingroup$
    You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
    $endgroup$
    – MachineLearner
    Mar 26 at 9:28










  • $begingroup$
    @MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:30







  • 1




    $begingroup$
    I wanted to say $S^2_y$ is the sample variance. The square is important.
    $endgroup$
    – MachineLearner
    Mar 26 at 11:45















0












$begingroup$


I'm a BC student who is trying to solve some statistic quizzes.



there is a multiple choice question that is this:




In a simple regression model $y=a+bx+e$ our given data is this:
$$ barx = 2, bary = 3, S_x = 4, S_y = 5, r = 0.6 $$ find
SSE and $S_y,x$.



  1. $16, 4$

  2. $14, 4$

  3. $4, 14$

  4. $4, 16$



I must confess I have no idea what is a $S_y,x$! but for SSE here is my work (I've assumed that $s_y$ is the sum of all $y$):



beginalign
textSSE = (1-r^2) textSST &= (1-r^2)sum(y-bar y)^2 \
&= (1-r^2) left(sum y^2 -frac(sum y)^2n right) \
&= (1-r^2)left(sum y^2 -fracS^2_yn right) \
&= (1-r^2)left( sum y^2 -fracS^2_yleft. S_y middle/ bar y right. right) \
&= (1-r^2)left( sum y^2 -S_y bar y right)
endalign



but in this case, I can't find $sum y^2$. I want some help.



thank in advance.






regression linear-regression







share|cite|improve this question











$endgroup$











  • $begingroup$
    Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
    $endgroup$
    – MachineLearner
    Mar 26 at 8:34










  • $begingroup$
    @MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:25







  • 1




    $begingroup$
    You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
    $endgroup$
    – MachineLearner
    Mar 26 at 9:28










  • $begingroup$
    @MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:30







  • 1




    $begingroup$
    I wanted to say $S^2_y$ is the sample variance. The square is important.
    $endgroup$
    – MachineLearner
    Mar 26 at 11:45













0












0








0


1



$begingroup$


I'm a BC student who is trying to solve some statistic quizzes.



there is a multiple choice question that is this:




In a simple regression model $y=a+bx+e$ our given data is this:
$$ barx = 2, bary = 3, S_x = 4, S_y = 5, r = 0.6 $$ find
SSE and $S_y,x$.



  1. $16, 4$

  2. $14, 4$

  3. $4, 14$

  4. $4, 16$



I must confess I have no idea what is a $S_y,x$! but for SSE here is my work (I've assumed that $s_y$ is the sum of all $y$):



beginalign
textSSE = (1-r^2) textSST &= (1-r^2)sum(y-bar y)^2 \
&= (1-r^2) left(sum y^2 -frac(sum y)^2n right) \
&= (1-r^2)left(sum y^2 -fracS^2_yn right) \
&= (1-r^2)left( sum y^2 -fracS^2_yleft. S_y middle/ bar y right. right) \
&= (1-r^2)left( sum y^2 -S_y bar y right)
endalign



but in this case, I can't find $sum y^2$. I want some help.



thank in advance.






regression linear-regression







share|cite|improve this question











$endgroup$




I'm a BC student who is trying to solve some statistic quizzes.



there is a multiple choice question that is this:




In a simple regression model $y=a+bx+e$ our given data is this:
$$ barx = 2, bary = 3, S_x = 4, S_y = 5, r = 0.6 $$ find
SSE and $S_y,x$.



  1. $16, 4$

  2. $14, 4$

  3. $4, 14$

  4. $4, 16$



I must confess I have no idea what is a $S_y,x$! but for SSE here is my work (I've assumed that $s_y$ is the sum of all $y$):



beginalign
textSSE = (1-r^2) textSST &= (1-r^2)sum(y-bar y)^2 \
&= (1-r^2) left(sum y^2 -frac(sum y)^2n right) \
&= (1-r^2)left(sum y^2 -fracS^2_yn right) \
&= (1-r^2)left( sum y^2 -fracS^2_yleft. S_y middle/ bar y right. right) \
&= (1-r^2)left( sum y^2 -S_y bar y right)
endalign



but in this case, I can't find $sum y^2$. I want some help.



thank in advance.






regression linear-regression




regression linear-regression






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 18 hours ago









Lee David Chung Lin

4,50841342




4,50841342










asked Mar 25 at 19:24









Peyman mohseni kiasariPeyman mohseni kiasari

13711




13711











  • $begingroup$
    Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
    $endgroup$
    – MachineLearner
    Mar 26 at 8:34










  • $begingroup$
    @MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:25







  • 1




    $begingroup$
    You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
    $endgroup$
    – MachineLearner
    Mar 26 at 9:28










  • $begingroup$
    @MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:30







  • 1




    $begingroup$
    I wanted to say $S^2_y$ is the sample variance. The square is important.
    $endgroup$
    – MachineLearner
    Mar 26 at 11:45
















  • $begingroup$
    Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
    $endgroup$
    – MachineLearner
    Mar 26 at 8:34










  • $begingroup$
    @MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:25







  • 1




    $begingroup$
    You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
    $endgroup$
    – MachineLearner
    Mar 26 at 9:28










  • $begingroup$
    @MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
    $endgroup$
    – Peyman mohseni kiasari
    Mar 26 at 9:30







  • 1




    $begingroup$
    I wanted to say $S^2_y$ is the sample variance. The square is important.
    $endgroup$
    – MachineLearner
    Mar 26 at 11:45















$begingroup$
Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
$endgroup$
– MachineLearner
Mar 26 at 8:34




$begingroup$
Do you have the sample size $n$? For $S_y,x$ I would have guessed that this is the covariance for the sample but $S_y,x=rS_xS_y=12$ is not a value from the possible answers.
$endgroup$
– MachineLearner
Mar 26 at 8:34












$begingroup$
@MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
$endgroup$
– Peyman mohseni kiasari
Mar 26 at 9:25





$begingroup$
@MachineLearner no, All the information that is given is that. it is not clear for me too. but I know that the answer is number 1. we can find $n$ by $fracS_ybar y$ but it is 5/3 and not an integer! I'm so confused. may $S_y$ is not the sum.
$endgroup$
– Peyman mohseni kiasari
Mar 26 at 9:25





1




1




$begingroup$
You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
$endgroup$
– MachineLearner
Mar 26 at 9:28




$begingroup$
You cannot find $n$ by $S_y/bary$ (if $S_y$ is the sample variance). You could use $bary=nsum_i=1^ny_i$ but you don't have the sum either.
$endgroup$
– MachineLearner
Mar 26 at 9:28












$begingroup$
@MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
$endgroup$
– Peyman mohseni kiasari
Mar 26 at 9:30





$begingroup$
@MachineLearner OMG! I'd thought that $S_y$ is the sum of all $y$. thank you for that information. now I can think about the problem again.
$endgroup$
– Peyman mohseni kiasari
Mar 26 at 9:30





1




1




$begingroup$
I wanted to say $S^2_y$ is the sample variance. The square is important.
$endgroup$
– MachineLearner
Mar 26 at 11:45




$begingroup$
I wanted to say $S^2_y$ is the sample variance. The square is important.
$endgroup$
– MachineLearner
Mar 26 at 11:45










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