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    1. If
    crime = Bo + B1 female+ u

    where:
    Crime = 1= if crime is commited by person
    =0= if not

    Female=1= if person is female
    =0= if not

    to calculate OLS estimates of Bo and B1 do i just use regular OLS estimates? or the generic dummy variable estimate is B1= yhat-ybar and Bo= ybar, or original estimates?

    2. If given the estimate of random variable y, what is the expectation of variance of y? How do you determine if it is biased, how would you solve its bias (if there is one)



    For Q1, i would like confirmation or not,
    Q2 a any sort of guide would be helpful
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    For Q1.) Correct you just use ordinary least squares as a method to find the regression coefficients.
    Q2.) google variance, and calculate the variance of Y (substitute in B0+B1x+u). It will be biased depending on your assumptions about the error term. Bias can be found by taking the expectations of Y. If E(Y) = B1 then it is unbiased, if it doesn't then it must be biased.

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    Rhys
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    (Original post by skg94)
    1. If
    crime = Bo + B1 female+ u

    where:
    Crime = 1= if crime is commited by person
    =0= if not

    Female=1= if person is female
    =0= if not

    to calculate OLS estimates of Bo and B1 do i just use regular OLS estimates? or the generic dummy variable estimate is B1= yhat-ybar and Bo= ybar, or original estimates?

    2. If given the estimate of random variable y, what is the expectation of variance of y? How do you determine if it is biased, how would you solve its bias (if there is one)



    For Q1, i would like confirmation or not,
    Q2 a any sort of guide would be helpful
    Because you the dependent variable is binary, the expected value of the dependent variable will be the probability of success. The variance of the dependent variable will be the variance of a binary random variable. The only difference is the probability of success depends on x. This means the variance, since it depends on the probability of success i.e P(crime=1) will also depend on x. Look up linear probability models on youtube.

    An unbiased estimator has a sampling distribution with expectation equal to the parameter being estimated. So if you can calculate the expectation of the estimator you can confirm whether or not it is indeed the parameter being estimated. An estimator is an estimation procedure which can be applied to a sample. An estimate is just one possible realization. The sampling distribution of the estimator is what you would get if you took many samples and applied the procedure to each one to get many estimates. In practice you would only calculate one sample. But with the sampling procedure you may be able to calculate the expected value of the estimator, it's variance, or even see how it will be distributed.

    In OLS, if the x's are not random, since the expected value of the errors is assumed to be zero. The estimators of the population coefficients are unbiased. If there is a misspecification error in your model like the omission of an important variable then there could be bias.
 
 
 
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