代做STAT 615、代写R设计、R程序语言调试、代写LogisticsDetails

日期：2019-03-14 10:55

Assignment 04, STAT 615

Available points: 55

55 points = 100%

Instructions

You may work together on the problems but please write them up individually. If your

solutions were obtained through working as a group please state the collaborators at

the beginning of your home work.

You need not type them but please organize your work neatly, write legibly. Number

the pages, write your name on each page, and indicate the number of the problem and

sub-problem. Leave at least 1” margins for grading!

Show the relevant snippets of your R code in your write-up.

Go over the solutions once they are posted and make sure you understand them.

Please submit your write-up as a single pdf file (either typed or scanned), following

the filename convention and other details posted in http://www.ece.rice.edu/

~erzsebet/STAT615/STAT615-LogisticsDetails.pdf.

Problem 1 (10 points total)

When testing whether or not β1 = 0, why is the F test a one-sided test even though Ha

includes both β1 < 0 and β1 > 0?

Problem 2 (10 points total)

Show that the ratio SSR

SST

is the same whether Y is regressed on X or X is regressed on Y .

1

Problem 3 (20 points total)

Consider the following functions of the random variables Y1, Y2, Y3:

W1 = Y1 + Y2 + Y3

W2 = Y1  Y2

W3 = Y1  Y2  Y3

1. (5 points) State the above in matrix notation. I.e., express the vector W = [W1, W2, W3]T

as the product of a matrix and the vector Y = [Y1, Y2, Y3]T

2. (5 points) Express the expectation of the random vector W in terms of the expectations

of the Yi’s.

3. (10 points) Express the variance-covariance matrix of W in terms of the variances and

covariances of the Yi

’s (i.e., compute the elements of the Cov(W) matrix).

Problem 4, (15 points total)

1. (8 points) Prove (in the context of simple linear regression) the following, where β1 and

σ

2 are, respectively, the true (unknown) regression slope and variance of the errors,

xi are the levels of the regressor variable X, and mX is the mean of X. MSR is the

Regression Sum of Squares.

E[MSR] = σ2 + β21Xni=1xi mX)2

2. (7 points) Using the notation in lectures, show (in the context of regression test) that

the ANOVA F0 statistic is the square of the t0 statistic, i.e., F0 , where F0 and t0

denote the F-statistic and t-statistic, respectively: