Question

The following data contains coaches' salaries and team revenues (in millions of dollars) for ten college basketball teams. Use this data to complete parts (a) through (c). Salary Revenue 0.7 0.7 3.0 1.1 15.0 0.8 11. 6 1.2 .4 1.6 14.7 1.5 9.9 0.2 2.3 0.5 7.6 1.3 17.4 0.4 5.4 7 a. Compute the covariance. (Round to three decimal places as needed.) b. Compute the coefficient of correlation. (Round to three decimal places as needed.) c. What conclusions can you reach about the relationship between a coach's salary and revenue? O A. There is a moderate positive relationship between a coach's salary and revenue. As a coach's salary increases, revenue tends to increase. OB. There is a slight relationship between a coach's salary and revenue. Increases in a coach's salary cause increases in revenue. OC. There is a strong positive relationship between a coach's salary and revenue. As a coach's salary increases, revenue always increases. OD. There is no relationship between a coach's salary and revenue.

Answer 1

Answer:

We know that the formula of Covariance is

Cov(x,y) =_2[** {(x,-x)(y-7)

And the formula of Correlation is

Σ(x; - X)(y - y) ΧΥ /Σ(x; – Σ)? Σy, - y)2

Thus from the given data the calculation of Covariance and Correlation using the above formula, have been shown in the following table:

obs 0.8 1.6 Salary (X) Revenue (Y) Xbar-X 3.0 0.23 1.11 15.01 -0.17 11.6 0.13 -0.27 -0.67 1.5 -0.57 0.73 0.5 0.43 1.3 17.4 -0.37 0.4 5.4 0.53 0.93 9.43 0.2 Ybar-Y Sq. (Xbar-X) Sq. (Ybar-Y) (Xbar-X)*(Ybar-Y) 6.431 0.0529 41.3449 1.4789 -5.57 0.0289 31.0249 0.9469 -2.17 0.0169 4.7089 -0.2821 2.03 0.0729 4.1209 -0.5481 -5.27 0.4489 27.7729 3.53091 -0.47 0.3249 0.2209 0.2679 7.13 0.5329 50.8369 5.20491 1.83 0.1849 3.3489 0.7869 -7.97 0.1369 63.5209 2.94891 4.03 0.2809 16.2409 2.13591 Total 2.08 243.14 16.47 0.456 4.931 Correlation 0.732 Covariance 1.647 8 9 10 Mean SD

(a) Covariance=1.647

(b) Correlation=0.732

(c) From the covariance and correlation coefficient value we can conclude that there is a moderate positive relationship between a coach's salary and revenue. As a coach's salary increases, revenue tends to increase. The relationship is moderate because coefficient 0.732 lies between 0.5 and 0.8 as usually accepted in statistics.