Suppose that you observe a random sample (z., )}N, from the model where e, independent of z. Ee, = 0, Var(e) -o >0, and where h(z.) - . Consider the OLS estimator of 8 given by 3- (E W.)/ (E ?), and the alternative estimator When the data exhibit evidence of strong heteroskedasticity (e.g. we reject the null hypothesis in the Breusch-Pagan test), which estimator would you prefer to use? 3 or r Why?
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- Q.8). In a regression calculation, a researcher finds that the explanatory variable x has mean 100 and SD 10, and the response variable y has mean 250 and SD 40. The regression equation is found to be y^ = 450 and y? 2x. What is the correlation between x (a) cannot tell from the information available (b) -0.8 (c) -0.5 (d) 0.4 (e) 0.1 Q.10) a) What are the differences between the data and information? b) Explain the differences between the types of StatisticsLet wages denote hourly wages, educ years of education, and exper years of experience, and suppose log(wages) = f1 + 62educ + B3exper +e where E[eleduc, exper] = 0. Let b1, b2, and bz be our estimates for B1, B2, and ß3 and r23 denote the sample correlation between {educ,}", and {exper, }". Which of the following statements is true? II O a. The variance of b3 does not depend on r23. O b. The variance of b, is increasing in E" (educ, – educ,)² (all else equal). O c. The variance of b2 is at least as large as o²/ E", (educ, - educ,)2 for o? Var(eleduc, exper). O d. The variance of b2 depends on the sign of r23. O e. The variance of b2 always increases as r23 increases (all else equal).13. The population relationship between household food expenditure, household income and household size is log(FoodExpenditure) = a + B, log(HH _Income)+ B,HH _size +u . Suppose you are interested in estimating this population relationship. In which of the following cases OLS estimator of B and B2 will be biased, assume what's described is the only problem? a) The variance of u is correlated with log(HH_Size). b) The mean of u depends on log(HH_ Size). c) The variance of u is large. d) Both a) and b) will cause biased estimates of the coefficients.
- If independent random variables 'X' and 'Y' have the variances 36 and 16 respectively, find the correlation coefficient between (X + Y) and (X- Y) assuming X and Y are zero mean.Suppose x binom(6, p) and define estimator T=x/6to estimate p. Then, variance of t isSuppose X~ Binom (6,p) and define an estimator T=X/6 to estimate p. Then variance of T is
- Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a = 3 and unknown. Find the Minimum Variance Unbiased Estimator for B. Show your work, and explain how you know your estimator is the MVUE.Example 6-12. Let X be a r.v. with mean µ and variance o2. Show `that X-b3, as a function of b, is minimised when b = µ. | CS Scanned with CamScannerX,X, and X, is a random sample of size 3 from a population 3. with mean value u and variance o2, T, T, T, are the 3. estimators used to estimate mean value u, where T=X,+X,-X,T,= 2X,+3X, - 4X,& T, ax,+x,+x) 1 (ax,+X,+X,) (i) Are T, and T, unbiased estimators ? 1 2 (ii) Find the value of such that T, is unbiased estimator 3 for u. With this value of A is T, a consistent estimator ? (iii) 3 (iv) Which is the best estimator ?
- Suppose that: E) = - 38 (mu) / 35 and E(Y) = 11 (mu) Prove that the following are unbiased estimators of (mu), if not, calculate the bias: (mu.hat) = 6X + YSuppose that the general fertility rate, g f rt , is following an AR(1) process shown in the image below A) if y1<1, what is the expression for the mean and variance of g f t rt showing any assumptions that were made . b) suppose that Var (€|gfrt-1)= as shown in the image below. explain why you may not obtain a best linear unbiased estimator of y0 and y1 by estimating (3) using OLS.On the basis of observations made on 39 cotton plants, the totai correlation of yıeid of cotton (X,), number of bolls, 1.e., seed vessels (.X,) and height (X,) are found to be: ,= 0.8, r,, = 0.65 and r, = 0.7 23