Consider a set of data (x₁, y₁), i = 1, 2,...,n and the simple linear regression model given by: Y₁ = Bo + B₁x₁ + Ei with E (₁) = 0, Var(e) = o² and all &'s are independent and normally distributed. Suppose further that a random sample of size 10 is selected and the fitted regression equation is obtained: with SB1 d) e) f) = 0.071 and SSxx = 1568.625. ŷ₁2.106 0.933x₁ Calculate and interpret the correlation coefficient. (x₁-x)] Derive the variance of w where w = ₁ + SSxx Find the value of the variance of w in e) if Var (&) is known to be 9.
Consider a set of data (x₁, y₁), i = 1, 2,...,n and the simple linear regression model given by: Y₁ = Bo + B₁x₁ + Ei with E (₁) = 0, Var(e) = o² and all &'s are independent and normally distributed. Suppose further that a random sample of size 10 is selected and the fitted regression equation is obtained: with SB1 d) e) f) = 0.071 and SSxx = 1568.625. ŷ₁2.106 0.933x₁ Calculate and interpret the correlation coefficient. (x₁-x)] Derive the variance of w where w = ₁ + SSxx Find the value of the variance of w in e) if Var (&) is known to be 9.
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
![Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:
Yi = Bo + B₁x₁ + εi
with E() = 0, Var(ε;) = o² and all &'s are independent and normally distributed.
Suppose further that a random sample of size 10 is selected and the fitted regression equation is
obtained:
with
SB₁
d)
e)
f)
= 0.071 and SSxx = 1568.625.
ŷi 2.106 0.933x₁
Calculate and interpret the correlation coefficient.
Derive the variance of w where w = ₁
(x₁-x)]
10 SS.xx
+ ₁.
Find the value of the variance of w in e) if Var (₁) is known to be 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c17a710-26d7-4116-b1b9-95b1f447e8a0%2F963222fa-f990-4012-a93f-60aef64e66f2%2Fufgvncn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:
Yi = Bo + B₁x₁ + εi
with E() = 0, Var(ε;) = o² and all &'s are independent and normally distributed.
Suppose further that a random sample of size 10 is selected and the fitted regression equation is
obtained:
with
SB₁
d)
e)
f)
= 0.071 and SSxx = 1568.625.
ŷi 2.106 0.933x₁
Calculate and interpret the correlation coefficient.
Derive the variance of w where w = ₁
(x₁-x)]
10 SS.xx
+ ₁.
Find the value of the variance of w in e) if Var (₁) is known to be 9.
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