1.) Five observations taken for two variables follow.
xi
4
6
11
3
16
yi
50
40
40
60
30
(a)
Develop a scatter diagram with x on the horizontal
axis.
A
scatter plot with 5 points is given.
The horizontal axis is labeled: x, and ranges from 0
to 20.
The vertical axis is labeled: y, and ranges from 0 to
80.
The leftmost point on the plot is at about (3 , 30).
Moving right, the second point is above and to the right of the
first point.
The third point is to the right of the second point.
The fourth point is above and to the right of the third
point.
The fifth point is above and to the right of the fourth
point.
A
scatter plot with 5 points is given.
The horizontal axis is labeled: x, and ranges from 0
to 20.
The vertical axis is labeled: y, and ranges from 0 to
80.
The leftmost point on the plot is at about (3 , 60).
Moving right, the second point is below and to the right of the
first point.
The third point is below and to the right of the second
point.
The fourth point is to the right of the third point.
The fifth point is below and to the right of the fourth
point.
A
scatter plot with 5 points is given.
The horizontal axis is labeled: x, and ranges from 0
to 20.
The vertical axis is labeled: y, and ranges from 0 to
80.
The leftmost point on the plot is at about (3 , 50).
Moving right, second point is below and to the right of the
first point.
The third point is below and to the right of the second
point.
The fourth point is to the right of the third point.
The fifth point is below and to the right of the fourth
point.
A
scatter plot with 5 points is given.
The horizontal axis is labeled: x, and ranges from 0
to 20.
The vertical axis is labeled: y, and ranges from 0 to
80.
The leftmost point on the plot is at about (3 , 48).
Moving right, second point is below and to the right of the
first point.
The third point is above and to the right of the second
point.
The fourth point is below and to the right of the third
point.
The fifth point is below and to the right of the fourth
point.
(b)
What does the scatter diagram developed in part (a) indicate
about the relationship between the two variables?
The scatter diagram indicates that there is
relationship between the two variables.
(c)
Compute the sample covariance.
Based on the sample covariance, what can be said about the
relationship between the two variables?
There is a strong positive linear relationship between the two
variables. There is a strong negative linear relationship between
the two variables. There is no relationship
between the two variables. There is a positive linear relationship
between the two variables, but the strength of this relationship
cannot be determined based on the sample covariance. There is a
negative linear relationship between the two variables, but the
strength of this relationship cannot be determined based on the
sample covariance.
(d)
Compute the sample correlation coefficient. (Round your answer
to three decimal places.)
Based on the sample correlation coefficient, what can be said
about the relationship between the two variables?
There is a strong positive linear relationship between the two
variables. There is a strong negative linear relationship between
the two variables. There is no relationship
between the two variables. There is a positive linear relationship
between the two variables, but the strength of this relationship
cannot be determined based on the sample correlation coefficient.
There is a negative linear relationship between the two variables,
but the strength of this relationship cannot be determined based on
the sample correlation coefficient.
2.
Suppose the following data set contains the monthly adjusted
stock prices for technology company A, and a consumer-goods company
B from 2013–2018.
Date
A
B
6/1/2013
43.44
64.71
7/1/2013
49.71
67.54
8/1/2013
53.60
65.98
9/1/2013
54.00
64.00
10/1/2013
60.40
68.44
11/1/2013
64.32
71.99
12/1/2013
67.69
69.55
1/1/2014
60.29
65.40
2/1/2014
63.43
67.68
3/1/2014
67.57
69.38
4/1/2014
74.39
71.08
5/1/2014
79.87
70.11
6/1/2014
85.47
68.17
7/1/2014
87.95
66.05
8/1/2014
94.37
72.73
9/1/2014
93.21
73.29
10/1/2014
99.99
76.42
11/1/2014
110.21
79.84
12/1/2014
102.66
80.43
1/1/2015
109.03
74.35
2/1/2015
119.64
75.64
3/1/2015
116.32
72.77
4/1/2015
117.00
70.58
5/1/2015
121.84
70.14
6/1/2015
117.76
70.01
7/1/2015
113.85
68.61
8/1/2015
105.91
63.66
9/1/2015
103.91
64.82
10/1/2015
112.66
68.89
11/1/2015
111.51
68.09
Date
A
B
12/1/2015
99.54
72.31
1/1/2016
91.98
74.42
2/1/2016
91.35
73.77
3/1/2016
103.67
75.65
4/1/2016
90.02
73.61
5/1/2016
94.90
75.09
6/1/2016
91.37
78.49
7/1/2016
99.69
80.36
8/1/2016
101.51
81.62
9/1/2016
108.82
83.92
10/1/2016
109.30
81.13
11/1/2016
106.36
77.63
12/1/2016
112.09
79.17
1/1/2017
117.49
82.53
2/1/2017
132.76
86.53
3/1/2017
139.88
85.35
4/1/2017
139.87
82.93
5/1/2017
148.80
82.31
6/1/2017
140.82
83.40
7/1/2017
145.45
85.95
8/1/2017
160.49
89.06
9/1/2017
151.36
86.80
10/1/2017
166.11
81.27
11/1/2017
167.88
84.49
12/1/2017
166.90
89.35
1/1/2018
165.11
83.90
2/1/2018
175.72
73.80
3/1/2018
166.14
74.55
4/1/2018
163.63
72.68
5/1/2018
186.86
83.31
(a)
Develop a scatter diagram with company A stock price on the
horizontal axis and company B stock price on the vertical axis.
A scatter diagram has a horizontal axis labeled "B Adjusted
Stock Price" with values from 0 to 100 and a vertical axis labeled
"A Adjusted Stock Price" with values from 0 to 200. The scatter
diagram has 60 points. A pattern goes up and right from (64, 43) to
(89, 187).
A scatter diagram has a horizontal axis labeled "A Adjusted
Stock Price" with values from 0 to 200 and a vertical axis labeled
"B Adjusted Stock Price" with values from 0 to 100. The scatter
diagram has 60 points. A pattern goes up and right from (43, 64) to
(187, 89).
A scatter diagram has a horizontal axis labeled "A Adjusted
Stock Price" with values from 0 to 200 and a vertical axis labeled
"B Adjusted Stock Price" with values from 0 to 100. The scatter
diagram has 60 points. A pattern goes down and right from (43, 89)
to (187, 64).
A scatter diagram has a horizontal axis labeled "B Adjusted
Stock Price" with values from 0 to 100 and a vertical axis labeled
"A Adjusted Stock Price" with values from 0 to 200. The scatter
diagram has 60 points. A pattern goes down and right from (64, 187)
to (89, 43).
(b)
What appears to be the relationship between these two stock
prices?
The scatter diagram shows a
relationship with
company A stock prices associated with higher company B stock
prices.
(c)
Compute the sample covariance. (Round your answer to two decimal
places.)
Interpret the sample covariance.
There is a positive relationship between the two variables.
There is a negative relationship between the two variables.
There is no relationship between the two
variables.
(d)
Compute the sample correlation coefficient. (Round your answer
to two decimal places.)
What does this value indicate about the relationship between the
stock price of company A and the stock price of company B?
There is a moderately strong positive relationship between the
two variables. There is a moderately strong negative relationship
between the two variables. There is no
relationship between the two variables. There is a positive
relationship between the two variables, but the strength of this
relationship cannot be determined based on the sample correlation
coefficient. There is a negative relationship between the two
variables, but the strength of this relationship cannot be
determined based on the sample correlation coefficient.
3.
A random sample of 30 colleges from Kiplinger's list of the best
values in private college provided the data shown in the variable named Admit Rate (%)
shows the percentage of students that applied to the college and
were admitted, and the variable named 4 yr Grad. Rate (%) shows the
percentage of students that were admitted and graduated in four
years.
(a)
Develop a scatter diagram with Admit Rate (%) as the independent
variable.
A
scatter diagram has 30 points.
The horizontal axis is labeled Admit Rate (%) and ranges from 0
to 100.
The vertical axis is labeled 4-yr Grad. Rate (%) and ranges
from 0 to 100.
The points plotted from the horizontal axis values of 6 to 81
are evenly scattered between the vertical axis values of 62 and
88.
A
scatter diagram has 30 points.
The horizontal axis is labeled Admit Rate (%) and ranges from 0
to 100.
The vertical axis is labeled 4-yr Grad. Rate (%) and ranges
from 0 to 100.
Most of the points follow a trend that starts at the point (6 ,
86) and moves downward towards the point (81 , 66). The points
become more scattered as the value on the horizontal axis
increases.
A
scatter diagram has 30 points.
The horizontal axis is labeled Admit Rate (%) and ranges from 0
to 100.
The vertical axis is labeled 4-yr Grad. Rate (%) and ranges
from 0 to 100.
Most of the points follow a trend that starts at the point (6 ,
47) and moves upward towards the point (81 , 89). The points are
plotted close together with very little scatter.
A
scatter diagram has 30 points.
The horizontal axis is labeled Admit Rate (%) and ranges from 0
to 100.
The vertical axis is labeled 4-yr Grad. Rate (%) and ranges
from 0 to 100.
Most of the points follow a trend that starts at the point (6 ,
89) and moves downward towards the point (81 , 47). The points are
plotted close together with very little scatter.
What does the scatter diagram indicate about the relationship
between the two variables?
There appears to be
relationship between the two variables. This implies that
admission rates are associated with
graduation rates.
(b)
Compute the sample correlation coefficient. (Round your answer
to two decimal places.)
What does the value of the sample correlation coefficient
indicate about the relationship between the Admit Rate (%) and the
4 yr Grad. Rate (%)?
The sample correlation coefficient indicates
relationship between the two variables.