Deck 3: Descriptive Study of Bivariate Data

Question 1

Observations on two or more variables recorded for the individual sampling units are called ______ or multivariate data.

Answer 1

bivariate

Question 2

Classify the following statement as "single variable", "bivariate", or multivariate".
Age and weight of college students.

Answer 2

bivariate

Question 3

The total frequency for any row is given in the bottom margin.

Answer 3

False

Question 4

In statistical terminology, contingency tables correspond to cross-classified or cross-tabulated data.

Question 5

Final grades of students enrolled in a Introductory Statistics course are summarized below.
Calculate the remaining marginal totals.

A) 58, 78, 102, 55, 87
B) 58, 78, 102, 33, 53
C) 58, 78, 64, 30, 87
D) 40, 78, 102, 55, 57

Question 6

Final grades of students enrolled in an Introductory Statistics course are summarized below.
Complete the following table by calculating the relative frequencies separately for each row. Round your answers to three decimal places.

Question 7

A survey was conducted to study the degree of satisfaction with the service of passengers from New York City to Washington D.C. The following table shows the relative frequencies.
Complete the table of cross-tabulated frequencies.

Question 8

Given the following table of relative frequencies by row, complete the table of cross-tabulated frequencies.

Question 9

In a group of 180 college students, 43 are science majors, 66 are freshmen, and 31 are both. Based on these data, complete the following two-way frequency table.

Question 10

In a group of 280 college students, 55 are science majors, 86 are freshmen, and 50 are both. Based on these data, calculate the relative frequencies.

Question 11

The value of the correlation coefficient r, is always between -1 and ______.

Question 12

The magnitude of the correlation coefficient r, indicates the strength of a linear relation.

Question 13

The sign of the correlation coefficient r, indicates the weakness of a linear relation.

Question 14

If the pattern of (x, y) values is a band that runs from ______ left to ______ right, then
r > 0.

Question 15

If all (x, y) values lie exactly on a straight line with a ______ slope, then r = +1.

Question 16

A value of r really close to -1 means that the linear association ______.

A) is very weak
B) is very strong
C) cannot be determined
D) None of these

Question 17

Match the following values of r with the correct diagrams. Write your answer in the form letter (A, B, or C) followed by the Roman numeral (I, II, or III).
(A) r = -.2, (B) r = .6, (C) r = .5

Question 18

In the following instance, would you expect a positive, negative, or zero correlation?
The size of an apartment and the sex of the tenant.

Question 19

Consider the data set

A) Complete the table.
Use the formula

to calculate the sample correlation. Round your answer to three decimal places.

Question 20

Consider the data set
Find the sample correlation coefficient using the formula

.

Question 21

Is the correlation in the figure about
(a) .2, (b) -.4, (c) .4, (d) .8, or (e) -.9?

Question 22

Estimate the correlation coefficient of the figure below.

A) .5
B) .1
C) -.5
D) -.8

Question 23

Find the scatter diagram that corresponds to the correlation coefficient r = -.8.

A)

B)

C)

D)

Question 24

Calculations from a data set of n = 36 pairs of (x, y) values have provided the following results.

Obtain the correlation coefficient.

Question 25

Calculations from a data set of n = 32 pairs of (x, y) values have provided the following results.

Obtain the correlation coefficient.

Question 26

The false correlation produced by a lurking variable is called ________ correlation.

Question 27

An observed correlation between two variables may be caused by the influence of a third variable.

Question 28

Suppose from a data set of distance measurements in yards and time measurements in hours, the value of r is found to be 0.82. What would the value of r be if the distances were measured in feet and time in minutes.

A) -.82
B) .82
C) .27
D) .01

Question 29

A scientist in a center for disease control observes that the number of bacteria in a culture and air pollution in the city rise with time. Is there exists a lurking variable in this case?

Question 30

Usually, the predictor or ______ variable is denoted by the letter ______.

Question 31

An experimental study of the relation between two variables is often motivated by a need to predict one from the other. The first step in such a study is to plot and examine the scatter diagram.

Question 32

The numerical value of r indicates how effectively y can be predicted from x.

Question 33

A line is determined by two constants. One of these constants is the ______, that is, its height above the origin.

Question 34

A line is determined by two constants. One of these constants is the ______, that is, the amount that y increases whenever x is increased by one unit.

Question 35

Consider the line

A) What is its intercept?
B) What is its slope?

Question 36

What is the graph of the line
.

A)

B)

C)

D)

Question 37

A fabric manufacturer has determined that the resistance y of a fiber is given by
y = 18x - 155
where x (in grams) denotes the amount of a synthetic compound used to make the fiber.

A) If 44 grams of the synthetic compound are used, what is the resistance?
B) At least how many grams of synthetic compound must be used to have a positive resistance?

Question 38

For the data set, compute the least squares estimates.

A)
B)

Question 39

In an experiment to study the relation between the speed of an athlete running 100 meters, y (meters/second) and the environment temperature, x (Celsius degrees), her trainer collected the following statistics:
Find the equation of the least squares fitted line.

Question 40

For one coastal state, there is a high correlation between ice cream sales and number of people swimming in the ocean. Suggest a possible lurking variable and explain what is meant by the term lurking variable.

Question 41

Consider the data set

Calculate the
(a) sample means
(b) S_xx , S_xy , S_yy
(c) sample correlation coefficient.

Question 42

Consider the data set
Calculate the
(a) sample means
(b)S_xx , S_xy , S_yy
(c) sample correlation coefficient.

Question 43

Find the least square fitted line when the values of y and x are

Question 44

Find the least squares fitted line when the values of y and x are