Solution Found!
Let X and Y be random variables with respective means ?X
Chapter 4, Problem 5E(choose chapter or problem)
Let \(X\) and \(Y\) be random variables with respective means \(\mu_{X}\) and \(\mu_{Y}\),
respective variances \(\sigma_{X}^{2}\) and \(\sigma_{Y}^{2}\), and correlation coefficient \(\rho\). Fit the line \(y=a+b x\) by the method of least squares to the probability distribution by minimizing the expectation
\(K(a, b)=E\left[(Y-a-b X)^{2}\right]\)
with respect to \(a\) and \(b\). Hint: Consider \(\partial K / \partial a=0\) and \(\partial K / \partial b=0\), and solve simultaneously.
Equation Transcription:
,
Text Transcription:
X
Y
mu_X
mu_Y,
sigma_X^2
sigma_Y^2
y=a+bx
K(a,b)=E[(Y-a-bX)^2]
a
b
Partial K/Partial a=0
Partial K/Partial b=0
Questions & Answers
QUESTION:
Let \(X\) and \(Y\) be random variables with respective means \(\mu_{X}\) and \(\mu_{Y}\),
respective variances \(\sigma_{X}^{2}\) and \(\sigma_{Y}^{2}\), and correlation coefficient \(\rho\). Fit the line \(y=a+b x\) by the method of least squares to the probability distribution by minimizing the expectation
\(K(a, b)=E\left[(Y-a-b X)^{2}\right]\)
with respect to \(a\) and \(b\). Hint: Consider \(\partial K / \partial a=0\) and \(\partial K / \partial b=0\), and solve simultaneously.
Equation Transcription:
,
Text Transcription:
X
Y
mu_X
mu_Y,
sigma_X^2
sigma_Y^2
y=a+bx
K(a,b)=E[(Y-a-bX)^2]
a
b
Partial K/Partial a=0
Partial K/Partial b=0
ANSWER:Answer
Step 1 of 3
Here the given line is
By using the method of least squares fitting the given line
K=E(y - a-bx)2
=0
=0
=0