Consider the simple regression y i x i i where E x 0 and E 2 x 2 a What is the minimum mean squared error linear estimator of b For the estimator in part a, show that ratio of the mean squared error of to that of the ordinary least squares estimator b is is the square of the population analog to the t ratio for testing the hypothesis that 0, which is given in (5 11) How do you interpret the behavior of this ratio as MSE B MSE b where t2 (1 7 )' o x'x

Question: Consider the simple regression y i = x i + i where E[ | x] = 0 and E[ 2 | x] =

Consider the simple regression y_i= βx_i+ ε_iwhere E[ε | x] = 0 and E[ε²| x] = σ²

a. What is the minimum mean squared error linear estimator of β?

b. For the estimator in part a, show that ratio of the mean squared error of β to that of the ordinary least squares estimator b is

MSE [B] MSE [b] where t2: (1+7?)' [o?/x'x]

τ is the square of the population analog to the ??t ratio?? for testing the hypothesis that β = 0, which is given in (5-11). How do you interpret the behavior of this ratio as τ ?????

MSE [B] MSE [b] where t2: (1+7?)' [o?/x'x]

Step by Step Solution

★★★★★

3.49 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

First c y c x c So E c x and Var 2 c c Therefore MSE 2 c x 1 2 s 2 c c To minimize this we set MSE c ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Econometric Analysis Questions!

A researcher developed the following multiple regression model to explain the variation in hours worked by married women. H = Î²0 + Î²1X1 + Î²2X2 + Î²3X3 +...

The demand for cable. The following table gives data used by a telephone cable manufacturer to predict sales to a major customer for the period 19681983. The variables in the table are defined as...

Estimating the capital asset pricing model (CAPM). In Section 6.1 we considered briefly the well-known capital asset pricing model of modern portfolio theory. In empirical analysis, the CAPM is...

1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with E(uilz;) = 0 and...

,.kindly solve please 1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with...

University of California, Los Angeles Department of Statistics Statistics 100C Instructor: Nicolas Christou Homework 3 EXERCISE 1 Answer the following questions: a. Suppose y1 , y2 , . . . , yn are...

@ help here please EXERCISE 4.36. In Example 4.20, use Eq. 4.16 to verify that the fake spheres with a = 2 and a = , have no umbilical points. (4.16) T. EXAMPLE 4.20 (Fake Spheres). We wish to...

\fEXERCISE 4.36. In Example 4.20, use Eq. 4.16 to verify that the fake spheres with a = 2 and a = , have no umbilical points. (4.16) T. EXAMPLE 4.20 (Fake Spheres). We wish to construct surfaces of...

EXERCISE 4.36. In Example 4.20, use Eq. 4.16 to verify that the fake spheres with a = 2 and a = , have no umbilical points. (4.16) T. EXAMPLE 4.20 (Fake Spheres). We wish to construct surfaces of...

,.. the following question please (2) Curvature of the utility function and the smoothing desire Consider a household that lives for three periods: 1, 2, and 3. Ignore interest rates, dis- counting,...

Guardsmark, a private security company, hired Kadah as a security guard. His record was fine, until one day he was accused of sexually assaulting Plancarte, a janitor at the office building where...

According to Honda Motor Co., Inc., the exchange rate (yen per U.S. dollar) from 1998 through 2005 was 123, 128, 112, 111, 125, 122, 113, and 108. Determine the mean and median for these data. Is...

Suppose that a CAT scan of a human liver shows cross - sections spaced 1 . 5 cm apart. The liver is 1 5 cm long and the cross - sectional areas, in square centimeters, are 0 , 1 8 , 5 8 , 7 9 , 9 4 ,...

c. Suppose you now added a start-to-start relationship between activities F and G to the new Gantt chart. How does this additional relationship change the expected completion date for the project?

For the classical normal regression model y = X + with no constant term and K regressors, what is plim F[K, n k] = plim R2/K/(1 R2) / (n k), assuming that the true value of is zero?

Let ei be the ith residual in the ordinary least squares regression of y on X in the classical regression model, and let i be the corresponding true disturbance. Prove that plim (ei i) = 0.

the paulson company year end balance sheet is shown below. It's cost of common equity is 18%, it's before tax cost of debt is 12%, and it's marginal tax rate is 40%. Assume that the firms long term...

Question 3 [12 marks]: State with proper reasoning whether the following statements are TRUE or FALSE. 1. Suppose f(n)=n(1sinn) (defined over non-negative reals). Then f(n)/O(n). 2. Suppose...

If you can provide some explanation to the calculation (finance calculator if possible). It would be appreciated. Before Mrs. Smith arrives, you study her account file and notice she has different...