Q3. Let x1,..., IN be data in R™ with sample covariance C = XX". Suppose u; is aneigenvector of C corresponding to the eigenvalues A;, with A, 2 2 2 ...Am 2 0. LetP; be the orthogonal projection onto the Span({u;}).(i)Show that the sample variance of P;x1,.., P¿xN is X;.

This question seeks to prove that the sample variance of the projections of a set of data points…

Answered: 00 Q3. Let ₁,...,xN be data in Rm with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
Let Z~Normal(0,1). Define X1 = Z and X2 = Z2. Calculate the Spearman correlation coefficient for the pair (X1, X2).
Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.
5 Calculate XkYk for the n = 5 data points (×₁,Y₁ ) = (2,4), (×2,Y₂) = (3,5), (×3,Y3) = (4,8), (×4,Y4) = (5,10), and k=1 (X5,5) = (6,14). 5 Σ xxYk = [ k=1 (Simplify your answer.)
Let x1, x2, ... , X, be a random sample from N(u, o2), and let 0 = (6x1 - 2x2) -(4x3 -3x4) %3D be an estimator of the parameter µ, calculate the bias of this estimator.
Compute E(310) for the following model, where & wn(0, 0.16), i.e., a white noise process with mean zero and variance 0.16. Please give the exact answer. 1 Me=Mt-2+ Ct, 30 = 1.
There are 3000 stocks in the long-short stock market, which will be traded for 250 days in the next year. Set X and Y to be the daily holding amount of each stock And the return of the next day, and X and Y are respectively sampled from the normal distribution of N (0.100000NO, 2E-2). Use enough data to estimate Calculate the R2 of X and Y linear regression to be 001. Assume that positions among stocks are not correlated, and returns between stocks are not correlated. Define a day’s PNL as the day’s receipt beneficial PNL= 3000∑xy Find the expectation of PN and the sharpe rate of PNL every day
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
Suppose that Y = Bo + BıXite, i - 1,..., n where E(€;) = 0 and Var(e;) = o². Let 3o and 3₁ be the least squares estimates. (a) Find Var(Bo) (treating the X's as fixed). (b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. i=1 (c) Show that ₁ ê¡¿Ÿ¿ = 0. What is the interpretation of this result? (d) Suppose you did a regression of Y's on the observed residuals. (In other words, treat the ê¿ as the X;'s.) What intercept and slope would you get?

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

00 Q3. Let ₁,...,xN be data in Rm with sample covariance C = NXXT. Suppose u; is an eigenvector of C corresponding to the eigenvalues A₁, with A₁ A₂ ≥...Am 20. Let P; be the orthogonal projection onto the Span({u;}). (i) Show that the sample variance of Pix,..., PiN is λ₁.