MA3110 Exercise 61 Linear Correlation Complete Solution

Question: #7912

MA3110: Module 6 Correlation and Regression
Exercise 6.1
Linear Correlation

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
163
55
–5
88
51
16
–214 Wins
0.599
0.537
0.531
0.481
0.494
0.506
0.383
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: Chirps in 1 Min
882
1188
1104
864
1200
1032
960
900 Temperature(°F)
69.7
93.3
84.3
76.3
88.6
82.6
71.6
79.6
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?

 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