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
Show that B = {[a, b) ⊂ ℝ | a &lt; b} is a basis for a topology on ℝ
loris [4]

Answer:

Remember that a set \mathcal{B} is a base for some topology on \mathbb{R} if satisfy the following properties:

1. \mathbb{R}=\cup\{B: B\in\mathcal{B}\}

2. For B, B^* \in \mathcal{B}, If p\in B\cap B^* then exist B_p\in\mathcal{B} such that p\in B_p\subset B\cap B^*.

Now, for B=\{[a,b)\subset\mathbb{R}| a < b\} we verify the above properties:

1. It's clear that \mathbb{R}=\cup_{a,b \text{ with }a

2. Let B=[a,b), B^*=[c,d) \in \mathcal{B}, p\in B\cap B^*. Without loss of generality suppose that a. Then c\leq p < b, this implies that p\in[c,b) and B_p=[c,d) \in \mathcal{B} and B_p\subset B\cap B^*.

Then, B satisfy the two properties. This show that B is a basis for a topology in \mathbb{R}

6 0
3 years ago
1 or 2?<br><br> Look at the picture. <br> Thank u!
photoshop1234 [79]

Answer: 2

Step-by-step explanation:

7 0
3 years ago
Kelly makes $10 more per hour than her regular pay when she is working overtime. Yesterday, she worked 8 regular hours and 4 ove
Mademuasel [1]

Kelly's regular pay is $10 per hour and overtime pay is $20 per hour.

<h3>What is equation?</h3>

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. Solving this equation, we get the value of the variable x as x = 7.

Here,

Let her regular pay be x and overtime pay be y.

8x+4y=160

y=x+10

8x+4(x+10)=160

8x+4x+40=160

12x=120

x=10

y=x+10

=10+10

=20

Kelly receives a regular pay rate of $10 and a $20 overtime pay.

To know more about equation,

brainly.com/question/24169758

#SPJ4

7 0
1 year ago
Which relation is a function?
Luden [163]

A relation is <em>not</em> a function if it has repeated "x" values.

A. (3, _) repeats

B. is a function

C. (5, _) repeats

D. (-4, _) repeats

8 0
3 years ago
:(((( i can't get this one! Please help...
ValentinkaMS [17]

Answer:

  4877 fish

Step-by-step explanation:

Each year, the fish population is multiplied by 1-6% = 0.94, so after 8 years it has been multiplied by 0.94^8 ≈ 0.609569.

At that time, the population is ...

  8000×0.609569 ≈ 4877 . . . fish

6 0
3 years ago
Other questions:
  • If a crate contains 25,500 ounces (oz) of rice, about how many pounds (lb) does it contain? [1 pound = 16 ounces] 408,000 lb 425
    10·2 answers
  • PLEASE HELP ASAP FOR 15 POINTS There are white, blue, and red boats in a marina. Two-thirds of the boats in the marina are white
    8·1 answer
  • Find the value of x and the value of y. A.x = 15, y = 10 B.x = 20, y = 50 C.x = 50, y = 10 D.x = 50, y = 20
    14·1 answer
  • Find an equation of the line that satisfies the given conditions. through (6, 9); parallel to the line passing through (7, 7) an
    11·1 answer
  • 170%of 40 is what number
    15·1 answer
  • What is the value of x?
    13·1 answer
  • Someone help me ?? Please
    10·1 answer
  • Can someone please help guide me
    8·1 answer
  • Select the correct answer.
    15·2 answers
  • What is the answer to 10-2•9+(-1)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!