This post provides practice problems to reinforce the concept of correlation coefficient discussed in this
post in a companion blog. The post in the companion blog shows how to evaluate the covariance and the correlation coefficient of two continuous random variables and . It also discusses the connection between and the regression curve and the least squares regression line.
The structure of the practice problems found here is quite simple. Given a joint density function for a pair of random variables and (with an appropriate region in the xyplane as support), determine the following four pieces of information.
 The covariance
 The correlation coefficient
 The regression curve
 The least squares regression line
The least squares regression line whose slope and yintercept are given by:
where , , and .
.
For some of the problems, the regression curves coincide with the least squares regression lines. When the regression curve is in a linear form, it coincides with the least squares regression line.
As mentioned, the practice problems are to reinforce the concepts discussed in this post.
.
Practice Problem 4A 

Practice Problem 4B 

Practice Problem 4C 

Practice Problem 4D 

Practice Problem 4E 

Practice Problem 4F 

Practice Problem 4G 

Practice Problem 4H 

Practice Problem 4I 

Practice Problem 4J 

Practice Problem 4K 
For this problem, only work on the regression curve . Note that and do not exist. 
Problem  ………..Answer 

4A 

4B 

4C 

4D 

4E 

4F 

4G 

4H 

4I 

4J 

4K 

Daniel Ma mathematics
Dan Ma math
Daniel Ma probability
Dan Ma probability
Daniel Ma statistics
Dan Ma statistics
2018 – Dan Ma
Tagged: Correlation Coefficient, Covariance, Joint Distribution, Least Squares Regression Line, Probability, Probability and Statistics, Regression Curve
[…] Practice Problem Set 4 – Correlation Coefficient  Probability and Statistics Problem Solve (22:00:15) : […]
[…] The concept of covariance and correlation coefficient is given detailed treatment in this post in a companion blog. Practice problems are available here. […]