4. Show that the vector of observed residuals can be expressed as e = (I – H)e.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.(f) Compute the sum of the squared residuals for the line found in part (b).There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How would I derive LSE for B0 and B1 and their variance?
- Construct an example of a regression model that satisfies the assumptionE(ui | Xi) = 0 but for which E(U | X ) ≠0n.For the regression model Yi = b0 + eI, derive the least squares estimator.An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) test
- Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?If there is a positive correlation between X and Y, then the regression equation Y = bX + a will have _____.
- Find the marginal PDFs of X and Y.Please don't copy Using XTWX for information matrix show the variance of the MLE of beta in logistic regression is 1/a +1/b+1/c+1/d where outcome no outcome exp a b not exp c dX” denote the number of children ever born to a woman, and let “Y” denote years ofeducation for the woman. A simple model relating fertility to years of education is X = β0 + β1Y + u where u is the unobserved error. (i) What kind of factors are contained in u? Are these likely to be correlated with level of education?
