statistics exam
Measures of Association Between Two Variables Statistics (exercises)
Aleksandra Pawłowska
Jun 2, 2020
Glossary
Covariance A measure of linear association between two variables. Positive values indicate a positive relationship; negative values indi- cate a negative relationship. Correlation coefficient A measure of linear association between two variables that takes on values between -1 and +1. Values near +1 indicate a strong positive linear relationship; values near -1 indicate a strong negative linear relationship; and values near zero indicate the lack of a linear relationship.
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 1
Five observations taken for two variables follow.
1 Develop a scatter diagram with x on the horizontal axis (use excel).
2 What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
3 Compute and interpret the sample covariance. 4 Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 1 – solution
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 1 – solution
1 What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? negative relationship
2 Compute and interpret the sample covariance. -60 3 Compute and interpret the sample correlation coefficient.
-0.97, there is strong negative correlation between x and y
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 2
Five observations taken for two variables follow.
1 Develop a scatter diagram for these data (use excel). 2 What does the scatter diagram indicate about a relationship
between x and y? 3 Compute and interpret the sample covariance. 4 Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 2 – solution
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 2 – solution
1 What does the scatter diagram indicate about a relationship between x and y? positive relationship
2 Compute and interpret the sample covariance. 26.5, it suggests positive relationship between x and y
3 Compute and interpret the sample correlation coefficient. 0.69, there is positive (but not strong) linear relationship between x and y
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 3
Nielsen Media Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage of households watching a program among those with televisions in use. The following data show the Nielsen television ratings and share data for the Major League Baseball World Series over a nine-year period (Associated Press, October 27, 2003).
1 Develop a scatter diagram with rating on the horizontal axis (use excel). 2 What is the relationship between rating and share? Explain. 3 Compute and interpret the sample covariance. 4 Compute the sample correlation coefficient. What does this value tell us
about the relationship between rating and share?
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 3 – solution
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 3 – solution
1 What is the relationship between rating and share? Explain. positive relationship
2 Compute and interpret the sample covariance. 10, it suggests positive relationship
3 Compute the sample correlation coefficient. What does this value tell us about the relationship between rating and share? 0.99, so that means that there is strong linear positive relationship between rating and share
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 4
A department of transportation’s study on driving speed and miles per gallon for midsize automobiles resulted in the following data:
Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 4 – solution
Compute and interpret the sample correlation coefficient. -0.91, so there is strong linear negative relationship between speed and miles per gallon
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 5
The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 Index (S&P 500) are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S&P 500 is based on the price of stocks for 500 companies. If both the DJIA and S&P 500 measure the performance of the stock market, how are they correlated? The following data show the daily percent increase or daily percent decrease in the DJIA and S&P 500 for a sample of nine days over a three-month period (The Wall Street Journal, January 15 to March 10, 2006).
1 Show a scatter diagram (use excel). 2 Compute the sample correlation coefficient for these data. 3 Discuss the association between the DJIA and S&P 500. Do you need to
check both before having a general idea about the daily stock market performance?
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 5 – solution
Aleksandra Pawłowska Measures of Association Between Two Variables
Task 5 – solution
1 Compute the sample correlation coefficient for these data. 0.91
2 Discuss the association between the DJIA and S&P 500. Do you need to check both before having a general idea about the daily stock market performance? there is strong positive linear relationship
Aleksandra Pawłowska Measures of Association Between Two Variables