2. Setup:Suppose we know the following:[1 10]110X = 1 121 15[114]Y = 2= €-0.25Var(8) = 9.0.257.356 -0.587]-0.587 0.048Identify the following (only algebra required, no complicated matrix calculations):(a) What are the x-values in the dataset?1(b) Find the equation of the regression line in the form ŷ = B₁ + B₁x.(c) Find Var(8o), Var (3₁).(d) Find COV (30, 31).

The variable is,The variable is,The coefficient vector is .The variance-covariance matrix of is .

Answered: 2. Setup: Suppose we know the…

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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Question

2. Setup:
Suppose we know the following:
[1 10]
1
10
X = 1 12
1 15
[114]
Y = 2
= €
-0.25
Var(8) = 9.
0.25
7.356 -0.587]
-0.587 0.048
Identify the following (only algebra required, no complicated matrix calculations):
(a) What are the x-values in the dataset?
1
(b) Find the equation of the regression line in the form ŷ = B₁ + B₁x.
(c) Find Var(8o), Var (3₁).
(d) Find COV (30, 31).

Expert Solution

Step 1: Write the given information.

The variable $X$ is,

$X equals open square brackets table row 1 row 1 row 1 row 1 row 1 end table space space space table row 10 row 10 row 12 row 15 row 15 end table close square brackets$

The variable $Y$ is,

$Y equals open square brackets table row 2 row 3 row 2 row 4 row 3 end table close square brackets$

The coefficient vector is $beta with hat on top equals open square brackets table row cell negative 0.25 end cell row cell 0.25 end cell end table close square brackets$ .

The variance-covariance matrix of $beta with hat on top$ is $V a r open parentheses beta with hat on top close parentheses equals 9 times open square brackets table row cell 7.356 end cell cell negative 0.587 end cell row cell negative 0.587 end cell cell 0.048 end cell end table close square brackets$ .