Suppose three tests are administered to a random sample of college students. Let X₁, ... ; ,XN be observationvectors in R³ that list the three scores of each student, and for j = 1,2,3, let xj denote a student's score on the jthexam. Suppose the covariance matrix of the data isS =52265226 5213 2626 65Let y = C₁x1 + €2x2 + c3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁ ≥ 0. Find theconstants C₁, C2, C3 so that the variance of y over the data set is as large as possible.

Answered: Image /qna-images/answer/f5a7586e-6d03-4979-b058-6337e45469ee.jpg

Answered: Suppose three tests are administered to…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

See similar textbooks

Similar questions

Find the second-order contact matrix PQ mentioned in the text.
Suppose you have obtained from SPSS the correlation matrix in Appendix 1. According to the information in this matrix, which two variables exhibit the strongest linear relationship?
1. Generate random 100 MVN data, p=20. The covariance matrix should be positive semi- definite symmetric matrix. (1) Show the generated data matrix. (2) Plot the scatter plot to show the correlation among variables.
An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the %3D second part. The accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column). The class is composed of 100 students. Y 10 15 2 6. 2 10 4 15 20 10 10 1 15 14 Compute the covariance between the scores of students from the two parts of the quiz.
A fair dice with sides numbered with {1, 2, 3, 4, 5, 6} was rolled three times. Let X denote number of times 6 was rolled in the first two rolls and let Y denote the total number of 6 rolled. Find the covariance of X and Y.
Create a correlation matrix Table in APA style to report the correlations among these variables, along with their Ms and SDs.
Which of the following is the correct covariance matrx for the datasets x and y: a x = [58, 40, 65, 20, 97, 20, 27, 65, 83, 60] hy [58, 78, 65, 20, 97, 60, 67, 65, 83, 60] hi [ O [[690.94444444 367.27777778] [367.27777778 204.9 ]] [ El O [[690.94444444 167.27777778] [367.27777778 404.9 ]] O [[90.94444444 367.27777778] [367.27777778 404.9 ]] O [[690.94444444 367.27777778] [367.27777778 404.9 ]]
The index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.
Let B 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 B is the linear minimum variance estimate of B based on y, show that the covariance of the error B - B has rank n - m.
Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i 1,..., n.
Which scatterplot shows a nonlinear association?
5 Calculate XkYk for the n = 5 data points (x₁,Y₁ ) = (2,4), (×2,Y₂) = (3,5), (X3,Y3) = (4,8), (×4,Y4) = (5,10), and k=1 (X5,5) = (6,14). 5 Σ XK Yk² k=1 [ (Simplify your answer.)

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS