We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies.
The way to use simulation is adding information to the problem.
I think the key point to this question is to understand the math behind linear regression and the Peason correlation.
From the problem statement, we know that
y= -3/4*x-2 +e (1);
and
x=-3/4*y -7/4 +e (2).
The linear regression coefficient beta is Sxy/Sxx ( in y=beta*x+e format), where S regresents (summation of the difference.....please check the linear regression lecture notes).
So, applying the regular beta formular to our problem, we get
Sxy/Sxx= -3/4 from (1) ......(3);
and
Syx/Syy=-3/4 from (2) ........(4);
Recall that the Peason corelation is:
r=Sxy/(sqrt(Sxx)*sqrt(Syy))
Here Sxy=Syx.
So, if we multiply (3) and (4) and sqrt the result, we get:
sqrt(Sxy*Syx/(Sxx*Syy))=r=+ or - 3/4.
Since y and x are negtive corellated based on the negative beta, we get the r = -0.75.
Day 6: Correlation and Regression Lines #1
You are viewing a single comment's thread. Return to all comments →
The way to use simulation is adding information to the problem. I think the key point to this question is to understand the math behind linear regression and the Peason correlation. From the problem statement, we know that y= -3/4*x-2 +e (1); and x=-3/4*y -7/4 +e (2). The linear regression coefficient beta is Sxy/Sxx ( in y=beta*x+e format), where S regresents (summation of the difference.....please check the linear regression lecture notes). So, applying the regular beta formular to our problem, we get Sxy/Sxx= -3/4 from (1) ......(3); and Syx/Syy=-3/4 from (2) ........(4); Recall that the Peason corelation is: r=Sxy/(sqrt(Sxx)*sqrt(Syy)) Here Sxy=Syx. So, if we multiply (3) and (4) and sqrt the result, we get: sqrt(Sxy*Syx/(Sxx*Syy))=r=+ or - 3/4. Since y and x are negtive corellated based on the negative beta, we get the r = -0.75.
Please excuse me if there are some types.
thanks, it was helpful
why Sxy = Syx ?