1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
weqwewe [10]
3 years ago
6

The following data contains​ coaches' salaries and team revenues​ (in millions of​ dollars) for ten college basketball teams. Us

e these data to complete parts​ (a) through​(c).
Salary 0.4 0.8 1.4 1.3 1.2 1.9 0.5 0.9 1.5 0.6

Revenue 4.9 7.5 17.2 18.2 11.5 13.6 8.0 6.0 18.0 8.2

a. Compute the covariance.

b. Compute the coefficient of correlation.

c. What conclusions can you reach about the relationship between a​ coach's salary and​ revenue?

A.There is a strong positive relationship between a​ coach's salary and revenue. As a​ coach's salary​ increases, revenue always increases.

B.There is a moderate positive relationship between a​ coach's salary and revenue. As a​ coach's salary​ increases, revenue tends to increase.

C. There is a slight relationship between a​ coach's salary and revenue. Increases in a​ coach's salary cause increases in revenue.

D.There is no relationship between a​ coach's salary and revenue.
Mathematics
1 answer:
Gwar [14]3 years ago
6 0

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 <em>X</em> and <em>Y</em> is:

r(X,Y)=\frac{Cov(X, Y)}{\sqrt{V(X).V(Y)}}

The formula to compute covariance is:

Cov(X, Y)=n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}

The formula to compute the variances are:

V(X)=n \sum{X^2}-\left(\sum{X}\right)^2\right\\V(Y)=n \sum{Y^2}-\left(\sum{Y}\right)^2\right

Let, <em>X</em> = Salary  and <em>Y</em> = Revenue.

(a)

Consider the table attached below.

Compute the covariance as follows:

Cov(X, Y)=n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}

                 =(10\times 136.66)-(10.5\times 113.1)\\=1366.6-1187.55\\=179.05

Thus, the covariance is 179.05.

(b)

Compute the variance of <em>X</em> and <em>Y</em> as follows:

V(X)=n \sum{X^2}-\left(\sum{X}\right)^2\right

         =(10\times 13.17)-(10.5)^{2}\\=21.45

V(Y)=n \sum{Y^2}-\left(\sum{Y}\right)^2\right

         =(10\times 1515.79)-(113.1)^{2}\\=2366.29

Compute the correlation coefficient as follows:

r(X,Y)=\frac{Cov(X, Y)}{\sqrt{V(X).V(Y)}}

            =\frac{179.05}{\sqrt{21.45\times 2366.29}}

            =0.7947

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).

You might be interested in
In psychology lab, Tetiana is conducting an experiment on depth perception using the Howard-Dolman box. Inside the box are two v
erma4kov [3.2K]

Answer:

within-groups

Step-by-step explanation:

According to my research on the scientific method, I can say that based on the information provided within the question the independent variable is being manipulated within groups, because she is not using a pretest and her design is within-groups. This is because she is using the posttest-only control group design which is a research design where at least two groups, one of which does not receive a treatment or intervention, and data is collected on the outcome measure after the treatment or intervention.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

7 0
3 years ago
PLZ ANSWER QUICK IT WILL HELP A LOT!
Ber [7]

Answer:

A

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
In May Mr. Lee's earings were 60 percent of the Lee family's total income. In June Mr. Lee earned 20 percent more than in May. I
murzikaleks [220]

Answer: 64.29%

Step-by-step explanation:

Let the total earnings of the Lee family in May be x

Amount earned by Mr Lee in May = 60% of x = 0.6x

Amount earned by other family members in May = x - 0.6x (total earnings - Mr Lee's earnings) = 0.4x

Amount earned by Mr Lee in June = 20% more than what Mr Lee earned in May.

That is, amount earned by Mr Lee in June = 1.2 × 0.6x = 0.72x

Amount earned by other members of the family in June remains unchanged, that is = 0.4x

Total amount earned by the Lee family in June = 0.72x + 0.4x = 1.12x

Percentage of total earnings in June earned by Mr. Lee = (0.72x/1.12x) × 100% = 64.29%.

QED!

6 0
3 years ago
The population of the African country Uganda has been growing at a steady rate for
dem82 [27]
Well hey...
2.25 ÷ 2.17 = 1.03 people on square miles
7 0
3 years ago
Read 2 more answers
The number 75 can be written as the sum of the squares of 3 different positive integers. what is the sum of these 3 integers? 17
ioda

75=7^2+5^2+1^1\\\\ 7+5+1=13

6 0
3 years ago
Other questions:
  • 1. Lin deposited $300 in her savings account which has a 2% interest rate per year. How much is in her account after 1 year? Aft
    10·1 answer
  • What is the equation of a line, in slope-intercept form, that passes through (−8, 1) and has a slope of 5/6 ?
    10·1 answer
  • The pitch of a musical note varies inversely as its wavelength. If a tone has a pitch of 440 vibrations per second and a wavelen
    11·2 answers
  • A bicycle wheel has a circumference of 62 inches. Find the diameter of the wheel. If necessary, round to the tenths place. 39.5
    8·2 answers
  • To make violet paint, Iris mixes 0.25
    5·1 answer
  • Which is the graphed of y=|-2x+1|?
    9·1 answer
  • the ratio of blue circles to total circles is 4 to 5. there are more than 10 circles. describe what this group would look like.
    8·1 answer
  • Answer correctly please !!!! Will mark Brianliest !!!!!!!!!!!!!!
    12·2 answers
  • A cone and cylinder have the same radius and the same volume. The cylinder has a height of 10m and a radius of 12m. Find the vol
    14·2 answers
  • The base of an isosceles right triangle is 30 cm. What is its area?<br>No spamming​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!