4. Let B be an n-dimensional random vector of zero mean and positive-definite covariance matrix Q. Suppose measurements of the formy = WB are made where the rank of W is m. If ß is the linear minimumvariance estimate of ß based on y, show that the covariance of theerror B - B has rank n - m.

Given that β be an n-dimensional random vector of zero mean and positive definite covariance matrix…

Answered: 4. Let ß be an n-dimensional random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let Y=Z3+ € denote the standard form of the multivariate regression model where Y is a matrix of n observations on m dependent variables, Z is the nx (r + 1) design matrix, 3 is the matrix of regression coefficients and denotes the error matrix. Let Σ denote the m × m covariance matrix of any row of e and assume the rows are independent. The least square estimate for 3 is 3 = (Z'Z)-¹Z'Y. The projection matrix is H = Z(Z'Z)-¹Z'. Let the ith column of 3 be denoted by 3, and the i, jth element of Σ by oij. Define the sample covariance matrix of the residuals by Prove (e) E(Σ) = Σ (f) cov(₁,3)=0 1 n-p-1
a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x², where x = x-5.75. The associated design matrix, X, is 1 - 1.75 2.25 3.25 1 the entries in one column are all 1 and the entries in the other column sum to 0. (Simplify your answer. Use ascending order.) B. Therefore, the columns of X are orthogonal because b. Write the normal equations for the data from part (a). Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answer.) O A. [Bo B₁] = Bo 421-0
Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 9. 8. 8 7 6. 10 4 7 Marks in 2nd Test (Y) 8 7 10 8 10 9. 8 6. (a) Find the least square regression line of Y on X. / (b) Test the hypothesis that marks in the two tests are linearly related.
5
Calculate SSCP (sum of squares and cross products) Calculate the Pearson correlation X Y 2 9 1 10 3 6 0 8 4 2
Can someone please explain to me ASAP??!!
Consider the simple linear regression model Y = a +Bx + E for i = 1,2,...,n. The variances of two estimators i.e. V(@) and V(B) are defined as respectively Nanersite of ARm of Select one: and V(8) +2 (+ %3! V(a) = o? %3D v(a) = o? ; and V(B) = Syx o v(a) = o (:-mnd v(A) - and V(B) = o v(a) = o? (1 + and V(B): Syx = a4 o va) = (; +)md V(f) = and V(ß) Syy %3D Syr fs fo fa 24 & 5 7 V E R Y D T-
Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 8 8. 10 4 7 Marks in 2nd Test (Y) 8 7 7. 10 5 8. 10 6. (a) Find the least square regression line of Y on X. / 7,
Prove that b is an unbiased estimator for ß. What are the essential conditions to prove ordinary least squares (OLS) estimator is unbiased? E(b) = ß

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4. Let ß be an n-dimensional random vector of zero mean and positive- definite covariance matrix Q. Suppose measurements of the form y = WB are made where the rank of W is m. If ß is the linear minimum variance estimate of ß based on y, show that the covariance of the error B- B has rank n - m.