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

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

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  

  
  
  
  

 | 
show 1 more comment

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

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

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

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

$endgroup$

share|cite|improve this question

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

share|cite|improve this question

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

edited 17 hours ago

Lee David Chung Lin

4,50841342

edited 17 hours ago

Lee David Chung Lin

4,50841342

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711

asked Mar 25 at 19:24

Peyman mohseni kiasariPeyman mohseni kiasari

13711