Question

The following is a set of data from a sample of n=11 items. Complete parts (a) through (c):

X Y

34 17

16 8

6 3

40 20

14 7

30 15

8 4

38 19

36 18

36 18

8 4

**a.** Compute the sample covariance.

(Round to three decimal places as needed.)

**b.** Compute the coefficient of
correlation.r=

(Round to three decimal places as needed.)

**c.** How strong is the relationship between X
and Y? Explain.

A. The variables X and Y have a strong positive correlation because as X increases, Y tends to increase also.

B.The variables X and Y have a perfect negative correlation because all points fall on a straight line with a negative slope.

C.The variables X and Y have a perfect positive correlation because all points fall on a straight line with a positive slope.

D.The variables X and Y have no correlation.

Answer #1

a) The sample covariance is

b) The coefficient of correlation is

Here

Let

and
,

and so on

Using the bove formula ,

.

Verify using R command below.

*X <- c(34, 16 , 6 , 40 , 14, 30 , 8 ,38 ,36 , 36, 8
)
Y <- c( 17 , 8 , 3 , 20 , 7 , 15 , 4 , 19 , 18, 18 , 4)
cov(X,Y)
cor(X,Y)*

**> cov(X,Y)
[1] 93.78182
> cor(X,Y)
[1] 1**

c) Since , The variables X and Y have a perfect positive correlation because all points fall on a straight line with a positive slope.

Correct choice is (C).

4. Use the given data set to complete parts (a) through (c)
below. (Use a=0.05.)
x
y
10
9.13
8
8.13
13
8.73
9
8.78
11
9.27
14
8.09
6
6.13
4
3.09
12
9.14
7
7.27
5
4.73
a. Construct a scatterplot
Find the linear correlation coefficient, r, then determine
whether there is sufficient evidence to support the claim of a
linear correlation between the two variables.
The linear correlation coefficient is r=_____.
(Round to three decimal places as...

Use the given data set to complete parts (a) through (c)
below. (Use
alphaαequals=0.05.)
x
1010
88
1313
99
1111
1414
66
44
1212
77
55
y
7.467.46
6.766.76
12.7412.74
7.117.11
7.827.82
8.848.84
6.086.08
5.385.38
8.168.16
6.436.43
5.735.73
LOADING...
Click here to view a table of critical values for the
correlation coefficient.
a. Construct a scatterplot. Choose the correct graph below.
A.
04812160481216xy
A scatterplot has a horizontal x-scale from 0 to 16 in
increments of 2 and a vertical...

Use the given data set to complete parts (a) through (c)
below. (Use
alphaαequals=0.05.)
x
1010
88
1313
99
1111
1414
66
44
1212
77
55
y
7.457.45
6.786.78
12.7412.74
7.117.11
7.817.81
8.858.85
6.096.09
5.395.39
8.148.14
6.416.41
5.735.73
LOADING...
Click here to view a table of critical values for the
correlation coefficient.
b. Find the linear correlation coefficient, r, then determine
whether there is sufficient evidence to support the claim of a
linear correlation between the two variables.
The linear...

Consider the following sample data for two variables. x = 16,
6,4,2 and Y= 5,11,6,8 a. Calculate the sample covariance
Sxy= b. Calculate the sample correlation coefficient
rxy= c. Describe the relationship between x and y. Choose the
correct answer below. A. There is a positive linear relationship
between x and y. B. There is no linear relationship between x and
y. C. There is a perfect negative linear relationship between x and
y. D. There is a perfect positive linear...

Each week coaches in a certain football league face a decision
during the game. On fourth-down, should the team punt the ball or
go for a first-down? To aid in the decision-making process,
statisticians at a particular university developed a regression
model for predicting the number of points scored (y) by a team
that has a first-down with a given number of yards (x) from the
opposing goal line. One of the models fit to data collected on five
league...

DATA SET
x
y
2.1
3.9
3.8
1.3
2.9
3.6
4.7
4.9
(a) Draw a scatter diagram of the data.
Compute the linear correlation coefficient. The linear correlation
coefficient for the four pieces of data
is____________
(b) Draw a scatter diagram of the data with the
additional data point(10.4,9.3).
Compute the linear correlation coefficient with the additional
data point. The linear correlation coefficient for the pieces of
data is_________
Comment on the effect the additional data point has on
the...

Each week coaches in a certain football league face a decision
during the game. On fourth-down, should the team punt the ball or
go for a first-down? To aid in the decision-making process,
statisticians at a particular university developed a regression
model for predicting the number of points scored (y) by a team
that has a first-down with a given number of yards (x) from the
opposing goal line. One of the models fit to data collected on five
league...

A) Two variables have a high covariance. This means the two
variables have a strong relationship. T/F
B) For a variable x, the sample mean is 8 and the sample
standard deviation is 2. One of the observations is 15. Is this
observation an outlier?
Group of answer choices
Yes, the z-score is greater than 3
No, the z-score is between -3 and 3
Yes, the z-score is between -3 and 3
No, the z-score is less than -3
C)...

For the accompanying data set, (a) draw a scatter diagram of
the data, (b) by hand, compute the correlation coefficient, and
(c) determine whether there is a linear relation between x and
y.
x y
2 4
4 8
6 12
6 12
7 20
Data set
x
22
44
66
66
77
y
44
88
1212
1212
2020
Critical Values for Correlation Coefficient
n
3
0.997
4
0.950
5
0.878
6
0.811
7
0.754
8
0.707
9
0.666
10...

Match the following
sample correlation coefficients with the explanation of what that
correlation coefficient means. Type the correct letter in each
box.
1. ?= −.15
2. ?= .92
3. ?= −.97
4. r= -1
The regression line is the straight line that bests fits a set
of data points according to what?
A. Most accurate regression criterion
B. Least-squares criterion.
C. Greatest-squares criterion
D. None of the above
4. ?=−1
A. a strong negative relationship between ? and
?
B....

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