please help answer this question Suppose we know that the conditional variance o

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please help answer this question

Suppose we know that the conditional variance of the error terms takes the following form: V[U|X] = ožX. 1. Write down the Weighted Least Squares regression model. 2. Show that the error terms in the Weighted Least Squares regression model under question (1) are homoscedastic. 3. The coefficient of determination in the WLS regression, R = 0.99, is larger than the coefficient Rº in regression model (4). Consider the following statement: • "The Weighted Least Squares regression explains more variation in exam scores than the OLS regression model and, therefore, is better than the OLS regression model.” Is this statement correct? Justify your answer.

Explanation / Answer

As the variance function is given as V[u(x)]=v^2*x, thus the weight factor is sqrt(x). Thus the least square function becomes SUMMATION[y-a-bx)^2/x]. Now differentiating it w.r.t a and b we get summation(y-a-bx)/x =0 and summation(x*(y-a-bx)/x)=0 , thus we finally get y(mean)=a+b*x(mean).

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