Question

For each of the following data sets, choose the most appropriate response from the choices below the table. | ||||||||

Data Set #1 |
Data Set #2 |
|||||||

x | y | x | y | |||||

10 | 18 | -22 | 92 | |||||

13 | 12 | -19 | 85 | |||||

18 | 8 | -16 | 71 | |||||

24 | 2 | -13 | 75 | |||||

27 | 0 | -10 | 68 | |||||

32 | 4 | -7 | 69 | |||||

21 | 7 | -5 | 66 | |||||

41 | 13 | 0 | 62 | |||||

45 | 17 | 2 | 59 | |||||

a. | A strong positive linear relation exists | a. | A strong positive linear relation exists | |||||

b. | A strong negative linear relation exists | b. | A strong negative linear relation exists | |||||

c. | No linear relation exists | c. | No linear relation exists | |||||

Determine
the linear correlation coefficient for each dataset in problem
#10. |
||||||||

Linear Correlation for Data Set #1: | ||||||||

Linear Correlation for Data Set #2: |

Answer #1

Data Set 1

c. No linear relation exists

*X Values*

∑ = 231

Mean = 25.667

∑(X - M_{x})^{2} = SS_{x} = 1140

*Y Values*

∑ = 81

Mean = 9

∑(Y - M_{y})^{2} = SS_{y} = 330

*X and Y Combined*

*N* = 9

∑(X - M_{x})(Y - M_{y}) = 22

*R Calculation*

r = ∑((X - M_{y})(Y - M_{x})) /
√((SS_{x})(SS_{y}))

r = 22 / √((1140)(330)) = 0.0359

Data set 2

b. A strong negative linear relation exists

*X Values*

∑ = -90

Mean = -10

∑(X - M_{x})^{2} = SS_{x} = 548

*Y Values*

∑ = 647

Mean = 71.889

∑(Y - M_{y})^{2} = SS_{y} = 908.889

*X and Y Combined*

*N* = 9

∑(X - M_{x})(Y - M_{y}) = -655

*R Calculation*

r = ∑((X - M_{y})(Y - M_{x})) /
√((SS_{x})(SS_{y}))

r = -655 / √((548)(908.889)) = -0.9281

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...

This does not copy well! Looking for the Correlation
coefficient by hand.
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.
data set.
x - 2 4 6 6 7
y - 4 8 11 12 19
Click here to view the critical values table.
LOADING...
(a) Draw a scatter diagram of the data. Choose the...

For the following data (a) display the data in a scatter plot,
(b) calculate the correlation coefficient r, and (c) make a
conclusion about the type of correlation. The ages (in years) of 6
children and the number of words in their vocabulary. (b) The
correlation coefficient r is nothing. (Round to three decimal
places as needed.) (c) Which of the following best describes the
type of correlation that exists between age and vocabulary size?
A. Weak positive linear correlation...

Compute each of the following probabilities. Label each problem
clearly and show all your work. Use the numbers you computed in
earlier parts of the project based on the class data set.
Problem 1: Suppose all of the Skittles in the class data set
are combined into one large bowl and you are going to randomly
select one Skittle.
(a) What is the probability that you select a green Skittle? (4
points)
(b) What is the probability that you select...

For the following data (a) display the data in a scatter plot,
(b) calculate the correlation coefficient r, and (c) make a
conclusion about the type of correlation.
The ages (in years) of
six
children and the number of words in their vocabulary
Choose the correct scatter plot
(b) The correlation coefficient r is
____
(Round to three decimal places as needed.)
(c) Which of the following best describes the type of
correlation that exists between age and vocabulary size?...

For the following data (a) display the data in a scatter plot,
(b) calculate the correlation coefficient r, and (c) make a
conclusion about the type of correlation.
The ages (in years) of
six
children and the number of words in their vocabulary
Age, x
Vocabulary size, y
1
300
2
700
3
1000
4
1450
5
2100
6
2400
make a scatter plot based on this
(b) The correlation coefficient r is
____?
(Round to three decimal places as...

Use the following information regarding a variable (Y) and a
variable (X) to answer the next 7 questions.
n =
8
∑ x = 56
∑ y = 296
∑ x 2 = 428
∑ y 2 = 11,920
∑ xy = 2,257
The sample covariance equals
26.43
-9.17
9.17
12.12
3 points
QUESTION 23
Refer to above data.
The sample correlation coefficient equals:
a.
-0.94
b.
1.67
c.
.991
d.
.85
3 points
QUESTION 24
Given the...

The four data sets below were created by statistician Francis
Anscomb. They show why it is important to examine the scatter plots
for your data, in addition to finding the correlation coefficient,
in order to evaluate the appropriateness of fitting a linear
model.
Set 1
Set 2
Set 3
Set 4
x
y
x
y
x
y
x
y
10
8.04
10
9.14
10
7.46
8
6.58
8
6.95
8
8.14
8
6.77
8
5.76
13
7.58
13
8.74
13...

Construct a scattergram for each data set. Then calculate r and
r2 for each data set. Interpret their values. Complete parts a
through d.
a.
x
−1
0
1
2
3
y
−3
0
1
4
5
Calculate r.
r=. 9853. (Round to four decimal places as
needed.)Calculate
r2=0.9709(Round to four decimal places as needed.)
Interpret r. Choose the correct answer below.
A.There is not enough information to answer this question.
B.There is a very strong negative linear relationship between...

Calculate the linear correlation coefficient for the data
below.
Calculate
the linear correlation coefficient for the data below.
x : 4, 6, 13, 10, 8, 7, 9, 11, 12, 5
y : 17, 12, 0, 5, 9, 10, 7, 2, 1, 14

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