Answer :
Answer:
(a) The covariance is 179.05.
(b) The coefficient of correlation between the coach's salary and revenue is 0.7947.
(c) The correct option is (A).
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The formula to compute correlation between two variables X and Y is:
[tex]r(X,Y)=\frac{Cov(X, Y)}{\sqrt{V(X).V(Y)}}[/tex]
The formula to compute covariance is:
[tex]Cov(X, Y)=n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}[/tex]
The formula to compute the variances are:
[tex]V(X)=n \sum{X^2}-\left(\sum{X}\right)^2\right\\V(Y)=n \sum{Y^2}-\left(\sum{Y}\right)^2\right[/tex]
Let, X = Salary and Y = Revenue.
(a)
Consider the table attached below.
Compute the covariance as follows:
[tex]Cov(X, Y)=n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}[/tex]
[tex]=(10\times 136.66)-(10.5\times 113.1)\\=1366.6-1187.55\\=179.05[/tex]
Thus, the covariance is 179.05.
(b)
Compute the variance of X and Y as follows:
[tex]V(X)=n \sum{X^2}-\left(\sum{X}\right)^2\right[/tex]
[tex]=(10\times 13.17)-(10.5)^{2}\\=21.45[/tex]
[tex]V(Y)=n \sum{Y^2}-\left(\sum{Y}\right)^2\right[/tex]
[tex]=(10\times 1515.79)-(113.1)^{2}\\=2366.29[/tex]
Compute the correlation coefficient as follows:
[tex]r(X,Y)=\frac{Cov(X, Y)}{\sqrt{V(X).V(Y)}}[/tex]
[tex]=\frac{179.05}{\sqrt{21.45\times 2366.29}}[/tex]
[tex]=0.7947[/tex]
Thus, the coefficient of correlation between the coach's salary and revenue is 0.7947.
(c)
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
A correlation coefficient value between 0.70 to 1.00 is considered as a strong positive relation between the two variables.
The correlation between the coach's salary and revenue is 0.7947. This is implies that there was a strong positive relationship between a coach's salary and revenue, i.e. an increase in the salary would have resulted as an increase in the revenue.
Thus, the correct option is (A).