Descriptive Statistics – Exercises 8
1. What do you mean by r=0 , r=1, r=-1 ?
(2-5) (a) Draw a scatter diagram of the data
(b) Compute the correlation coefficient
(c) Determine whether there is a linear relation between x and
y?
2.
X
y
3.
2
4
4
8
6
10
6
13
7
20
X
y
4.
2
10
3
9
5
7
6
4
6
2
X
y
5.
2
8
6
7
6
6
7
9
9
5
X
Y
27
30
22
26
15
25
35
42
30
38
52
40
35
32
55
54
40
50
40
43
6. Does studying for an exam pay off? The number of hours studied
x, is compared with the exam grade received y:
X
Y
Find r.
2
80
Descriptive Statistics WS 2010/2011
5
80
1
70
4
90
2
60
1
7. A marketing firm wished to determine whether the no. of
television commercials broadcast were linearly correlated with the
sales of its product. The data, obtained from each of several cities,
are shown in the following table:
Commercials 12
x
Sales, Units
7
y
6
9
15
11
15
8
16
12
6
5
10
14
12
9
6
11
11
8
Draw a scatter diagram and calculate r.
8. The national highway system is made up of interstate highways
and non-interstate highways. Listed are 15 randomly selected US
states and their corresponding no. of miles of interstate and noninterstate highway
State
AL
VT
NH
RI
AZ
IA
WI
NY
NE
UT
TX
OK
WV
AK
GA
Descriptive Statistics WS 2010/2011
Interstate
905
320
235
71
1167
782
745
1674
482
940
3233
930
549
1082
1245
Non-interstate
2715
373
589
197
1565
2433
3404
3476
2496
1253
10157
2431
1195
1030
3384
2
a. Construct a scatter diagram using x= inter-state and y= non
interstate miles.
b. Describe the pattern displayed, including any unusual
characteristics
c. Calculate the correlation coefficient.
d. Remove Texas from the data and repeat parts a through c.
e. Compare the results.
9. An engineer wanted to determine how the weight of a car affects gas
mileage. The following data represent the weights of various domestic
cars and their gas mileages in the city for the 2008 model year.
Car Weight
Miles per Gallon
3765
19
3984
18
3530
21
3175
22
2580
27
3730
18
2605
26
3772
17
3310
20
2991
25
2752
26
a) Determine which variable is the likely explanatory variable and
which is the likely response variable.
b) Draw a scatter diagram of the data
c) Compute r
d) Does a linear relation exits between the weight of a car and its
miles per gallon in the city?
Descriptive Statistics WS 2010/2011
3
10. A doctor wanted to determine whether a relation exists between a
male’s age and his HDL (so called good) cholesterol. He randomly
selected 17 of his patients and determined their HDL cholesterol levels.
He obtained the following data:
Age
HDL Cholesterol
38
57
42
54
46
34
32
56
55
35
52
40
61
42
61
38
26
47
38
44
66
62
30
53
51
36
27
45
52
38
49
55
39
28
a) Draw a scatter diagram of the data treating age as the
explanatory variable. What type of relation, if any, appears to
exist between age and HDL cholesterol?
b) Compute the linear correlation coefficient between age and HDL
cholesterol
c) Does a linear relation exist between age and HDL cholesterol?
Descriptive Statistics WS 2010/2011
4
0
