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
Vaselesa [24]
3 years ago
6

Five observations taken for two variables follow.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
3 0

Answer:

a) Figure attached

b) If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

c) Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}

We can find the numerator like this:

\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106

And then:

Cov(X,Y) = \frac{106}{5-1}=26.5

d) r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693  

Step-by-step explanation:

Part a

For this part we use excel in order to create the scatterplot and we got the result on the figure attached.

Part b

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

Part c

The sample covariance is defined as:

Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}

We can find the numerator like this:

\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106

And then:

Cov(X,Y) = \frac{106}{5-1}=26.5

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=5 \sum x = 80, \sum y = 50, \sum xy = 906, \sum x^2 =1552, \sum y^2 =586  

r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693  

So then the correlation coefficient would be r =0.693

You might be interested in
Please I need to know today?
GenaCL600 [577]

Answer:

The three collinear poitns are D, A, and E.

Step-by-step explanation:

Collinear points are points that all reside on the same line. Since we are looking for 3 seperate points we need a line with 3 points. There are only 2 lines on the picture and only one has three lines getting you your answer.

8 0
3 years ago
Oscar needs to purchase soft drinks for a staff party. He is
PilotLPTM [1.2K]

Answer:

sorry getting points

Step-by-step explanation:

4 0
2 years ago
Add 7/10 + 1/6 enter your answer below as a fraction in lowest terms, using the slash(/) as the fraction bar
san4es73 [151]

Answer:

13/15

Step-by-step explanation:

pls mark me brainliest

4 0
3 years ago
17. Which of the following equations would graph a line parallel to 3y = x + 5? (
Naddik [55]

The equation 3y = x + 1 would graph a line parallel to 3y = x + 5 ⇒ 1st

Step-by-step explanation:

Parallel lines have same slopes and different y-intercepts

To find which equation would graph a line parallel to 3y = x + 5

1. Put the equation in the form of y = mx + c

2. m is the slope of the line and c is the y-intercept

3. Look for the equation which has the same values of m and different

   values of c

∵ 3y = x + 5

- Divide each term of the equation by 3 to put the equation in the

 form of y = mx + c

∴ y = \frac{1}{3} x + \frac{5}{3}

∴ m = \frac{1}{3}

∴ c = \frac{5}{3}

The first answer:

∵ 3y = x + 1

- Divide each term of the equation by 3

∴ y = \frac{1}{3} x + \frac{1}{3}

∴ m = \frac{1}{3}

∴ c = \frac{1}{3}

∵ The two equations have same slope m = \frac{1}{3}

∵ The two equations have different y-intercepts c = \frac{5}{3}

   and c = \frac{1}{3}

∴ 3y = x + 5 and 3y = x + 1 represent two parallel lines

The equation 3y = x + 1 would graph a line parallel to 3y = x + 5

Learn more:

You can learn more about slope of a line in brainly.com/question/12954015

#LearnwithBrainly

8 0
3 years ago
Sebastian and Mia want to buy a home valued at $250,000. The property tax for this location is 1%. Based on the current value of
denis-greek [22]
1% of $250,000 is $2,500

Your answer is C
5 0
3 years ago
Read 2 more answers
Other questions:
  • Santos flipped a coin 300 times. The coin landed heads up 175 times. Find the ratio of heads to total number of coin flips. Expr
    9·2 answers
  • If g(x)= x^2-2x-6 and h(x)= 2x^2-5x+2 find (h-g) (-2)
    7·1 answer
  • Identify the variable in the expression 5a-2
    11·2 answers
  • A person must be at least 42 inches tall to ride the Roller Coast at an amusement park. Let h represent the height of any person
    13·1 answer
  • Find m ∠TUL<br> m∠TUV=167<br> m∠TUL=(x+11)<br> m∠LUV=(11x)
    15·2 answers
  • This question is tricky
    11·1 answer
  • The perimeter of a rectangle is 160 feet. If the length of the rectangle is 28 feet more than the width, what are the dimensions
    7·1 answer
  • 8a - 36 for a = 7 and b = 1<br> 8a - 3b =
    13·1 answer
  • The product of two positive numbers is 48. Determine the two numbers if one number is triple the other
    15·2 answers
  • Which is the graph of g(x) = (0.5)* + 3 – 4?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!