Econometrics Questions Help Please

xcfzm94

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I am having a hard time with proofs in econometrics (as i think alot do) but I would really appreciate some help into these questions

1) y= Bo + Bi log(x) +u

Bo= intercept
Bi= slope
u = error term

If im calculating for OLS estimators does the log change anything really? I mean mathematically speaking would the log not just be added to x on the standard OLS estimate for intercept and slope?


2) I am given an equation

Y = Bo + u where Variance of u (var (u)= 10) ,

and it asks me to derive the OLS estimators and variances of the estimates how do i go about doing this without a slope variable?

3) Given
Y= Bo + Σ(j=1) Bi xij + u

show that (estimated mean of error term) u^= 1/nΣu^ (estimated error term)
show that the covariance between estimated residuals or independent variables is zero
show that y and x bar (mean) go through the regression line
show (estimated ybar)=ybar


You do not (and i do not expect) someone do outright do my homework but an explanation on how i should solve it would be helpful, a link or a short guide.
 
I am having a hard time with proofs in econometrics (as i think alot do) but I would really appreciate some help into these questions

1) y= Bo + Bi log(x) +u

Bo= intercept
Bi= slope
u = error term

If im calculating for OLS estimators does the log change anything really? I mean mathematically speaking would the log not just be added to x on the standard OLS estimate for intercept and slope?


2) I am given an equation

Y = Bo + u where Variance of u (var (u)= 10) ,

and it asks me to derive the OLS estimators and variances of the estimates how do i go about doing this without a slope variable?

3) Given
Y= Bo + Σ(j=1) Bi xij + u

show that (estimated mean of error term) u^= 1/nΣu^ (estimated error term)
show that the covariance between estimated residuals or independent variables is zero
show that y and x bar (mean) go through the regression line
show (estimated ybar)=ybar


You do not (and i do not expect) someone do outright do my homework but an explanation on how i should solve it would be helpful, a link or a short guide.

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

An ordinary least squares (OLS) uses the error estimates to obtain the coefficients. That is
E2 = \(\displaystyle \Sigma\, (f(x_i; a_1, a_2, a_3, ...a_n) - y_i)^2\)
Using you first problem we would have a1=Bo and a2=Bi to get
E2 = \(\displaystyle \Sigma\, (Bo\, +\, Bi*log(x_i)\, -\, y_i)^2\)
so the log doesn't change anything.

For your second question, a1=Bo and there are no more parameters.
 
What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

An ordinary least squares (OLS) uses the error estimates to obtain the coefficients. That is
E2 = \(\displaystyle \Sigma\, (f(x_i; a_1, a_2, a_3, ...a_n) - y_i)^2\)
Using you first problem we would have a1=Bo and a2=Bi to get
E2 = \(\displaystyle \Sigma\, (Bo\, +\, Bi*log(x_i)\, -\, y_i)^2\)
so the log doesn't change anything.

For your second question, a1=Bo and there are no more parameters.

For my first Question i just applied log to the x components of the normal equation for OLS

For my second question Is my estimated Bo =Bo and Var (Bo) = E(Bo^)-Bo (where Bo^ is estimated Bo) ? or how do i calculate variance here?

third question i am stuck finding the OLS estimates first of all
 
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