(Requires Appendix material)If the Gauss-Markov conditions hold, then OLS is BLUE. In addition, assume here that X is nonrandom. Your textbook proves the Gauss-Markov theorem by using the simple regression model Yi = β0 + β1Xi + ui and assuming a linear estimator Substitution of the simple regression model into this expression then results in two conditions for the unbiasedness of the estimator: = 0 and = 1.
The variance of the estimator is var(
X1,…, Xn)= Different from your textbook, use the Lagrangian method to minimize the variance subject to the two constraints. Show that the resulting weights correspond to the OLS weights.
A firm’s warranty costs are $225,000 per year.A competitor’s warranty costs are $75,000 per year.What are the non-value-added costs?
A firm’s warranty costs are $225,000 per year.A competitor’s warranty costs are $75,000 per year.What are the non-value-added costs?
A)$50,000
B)$75,000
C)$150,000
D)$225,000
(Requires Appendix material)Your textbook considers various distributions such as the standard normal, t, χ2, and F distribution, and relationships between them. (a)Using statistical tables, give examples that the following relationship holds:
(Requires Appendix material)Your textbook considers various distributions such as the standard normal, t, χ2, and F distribution, and relationships between them.
(a)Using statistical tables, give examples that the following relationship holds: F ,∞ = (b)t∞ is distributed standard normal, and the square of the t-distribution with n2 degrees of freedom equals the value of the F distribution with (1, n2)degrees of freedom. Why does this relationship between the t and F distribution hold?
Consider the simple regression model Yi = β0 + β1Xi + ui where Xi > 0 for all i, and the conditional variance is var(ui Xi)= θX
Consider the simple regression model Yi = β0 + β1Xi + ui where Xi > 0 for all i, and the conditional variance is var(ui
Xi)= θX where θ is a known constant with θ > 0.
(a)Write the weighted regression as i = β0
0i + β1
1i + i. How would you construct i, 0i and 1i?
(b)Prove that the variance of is i homoskedastic.
(c)Which coefficient is the intercept in the modified regression model? Which is the slope?
(d)When interpreting the regression results, which of the two equations should you use, the original or the modified model?
Gwen traveled to New York City on a business trip for her employer.Gwen spent 4 days in business meetings and conferences and then spent 2 days sightseeing in the area.Gwen’s
Gwen traveled to New York City on a business trip for her employer.Gwen spent 4 days in business meetings and conferences and then spent 2 days sightseeing in the area.Gwen’s plane fare for the trip was $250.Meals cost $160 per day.Hotels and other incidental expenses amounted to $250 per day.Gwen was not reimbursed by her employer for any expenses.Her AGI for the year is $50,000 and she itemizes but has no other miscellaneous itemized deductions.Gwen may deduct (after limitations)
A)$570.
B)$890.
C)$1,890.
D)$1,570.