Linear Correlation Assignments

In this assignment, you should solve four 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:
1. 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
a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using ? = 0.05.
b. Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference?

2. One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min 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
a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using ? = 0.05.
b. Is there a linear correlation between the number of chirps