2. Calculate the covariance matrix using thefollowing four samples.5.1(4.95.23.53.03.8X = {x, =X31.41.31.30. 2/0.2/0. 2,'5.44. 61.20.4/

Use the following formulae, to obtain the solution. Mean, x¯=∑i=1nxinVariance,…

Answered: 2. Calculate the covariance matrix…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1.The least squares estimate of β0 is i. 2.3176 ii. 0.7176 iii. 0.8824 iv. 1.8990 2. The least squares estimate of β1 is i. 0.4773 ii. 0.2990 iii. 0.2061 iv. 0.9265 3. The linear correlation coefficient r is i. 0.4122 ii. 0.1700 iii. 0.2990 iv. 0.5683
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1. Suppose a X value is produced by a random process that has a mean of 1 and a variance of 9, while a Y value is produced by a random process that has a mean of 9 and a variance of 1. Let Z = 3X - 2Y. Compute: a. the mean and variance of Z assuming X and X are independent. b. the mean and variance of Z assuming X and X are not independent and their correlation coefficient is 0.50.
2. Two fair dice are thrown. Let U be the minimum score of the two dice and let V be the maximum score of the two dice. a. Display f(u,v) in a table. b. Find the covariance and correlation between U and V.
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An investigator has a data set which contains a response variable(y) and four explanatory variables(xı, x2, X3, X4). A correlation matrix was produced from the data set and is provided below. Correlations Y X1 X2 X3 X1 0.785 X2 0.731 0.690 X3 0.603 0.343 0.771 Х4 0.745 0.742 0.500 0.630 Does the correlation matrix provide evidence that multicollinearity may be an issue? Explain your reasoning.

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2. Calculate the covariance matrix using the following four samples. 5.1 4.9 /5.2 3.5 3.0 3.8 X = {x, = X3 X4 %3D , X2 1.4 1.3 1.3 0.2/ 0.2 0.2/ 5.4 4.6 1.2 0.4