Statistics

MA3110: Module 6 Correlation and Regression

Exercise 6.1

Linear Correlation

1

In this exercise, you will solve three questions, where you will be asked to calculate a linear correlation

coefficient and determine whether there is a linear correlation between the two given variables.

Solve the following problems:

 Listed below are baseball team statistics, consisting of the proportions of wins and the result of this

difference: Difference (number of runs scored) - (number of runs allowed). The statistics are from a

recent year, and the teams are NY—Yankees, Toronto, Boston, Cleveland, Texas, Houston, San

Francisco, and Kansas City.

Difference 1 6 3 5 5 –5 8 8 5 1 1 6 –2 1 4

Wins 0 .5 9 9 0 .5 3 7 0 .5 3 1 0 .4 8 1 0 .4 9 4 0 .5 0 6 0 .3 8 3

o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the

critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics.

Use α = 0.05.

o Is there sufficient evidence to conclude that there is a linear correlation between the

proportion of wins and the above difference?

 A classic application of correlation involves the association between temperature and the number of

times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 minute and the

corresponding temperatures in °F:

C hi r ps i n 1 Mi n 8 8 2 1 1 8 8 1 1 0 4 8 6 4 1 2 0 0 1 0 3 2 9 6 0 9 0 0

T emper at ur e (°F) 6 9 .7 9 3 .3 8 4 .3 7 6 .3 8 8 .6 8 2 .6 7 1 .6 7 9 .6

o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the

critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics.

Use α = 0.05.

o Is there a linear correlation between the number of chirps in 1 minute and the

temperature?

MA3110: Module 6 Correlation and Regression

Exercise 6.1

Linear Correlation

2

 Given below is a control chart for the temperature of a freezer unit in a restaurant. The owner of

the restaurant is deciding whether or not to buy a new unit. The two charts display the temperature

for the past two weeks. Write a paragraph analyzing the control charts and argue whether the

owner should buy a new unit or not. (5-6 sentences)

Submission Requirements:

 Submit your work in a single Microsoft Word or Excel document.

 The answer to each question should be supported with an appropriate rationale or the correct

steps.

Evaluation Criteria:

 Correctly answered each question

 Included appropriate steps or rationale to determine the answer to each question