Deck 3: Finding Relationships Among Variables

Question 1

Correlation can be affected by the measurement scales applied to X and Y variables.

Answer 1

False

Question 2

Correlation is a single-number summary of a scatterplot.

Answer 2

True

Question 3

Statisticians often refer to the pivot tables that display counts as contingency tables or crosstabs.

Answer 3

True

Question 4

To form a scatterplot of X versus Y,X and Y must be paired variables.

Question 5

A trend line on a scatterplot is a line or a curve that "fits" the scatter as well as possible.

Question 6

It is possible that the data points are close to a curve and have a correlation close to 0,because correlation is relevant only for measuring linear relationships.

Question 7

We must specify appropriate bins for side-by-side histograms in order to make fair comparisons of distributions by category.

Question 8

Relationships between two variables are less evident when counts are expressed as percentages of row totals or column totals.

Question 9

Problems in data analysis where we want to compare a numerical variable across two or more subpopulations are called comparison problems.

Question 10

We do not even try to interpret correlations numerically except possibly to check whether they are positive or negative.

Question 11

Strongly related variables have a relationship close to zero if the relationship is nonlinear.

Question 12

Side-by-side box plots allow you to quickly see how two or more categories of a numerical variable compare.

Question 13

If the standard deviation of X is 15,the covariance of X and Y is 94.5,the coefficient of correlation r = 0.90,then the variance of Y is 7.0.

Question 14

The cutoff for defining a large correlation is

Question 15

An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers.

Question 16

The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit.

Question 17

The Filters field of a pivot table contains the data you want summarize.

Question 18

If the standard deviations of X and Y are 15.5 and 10.8,respectively,and the covariance of X and Y is 128.8,then the coefficient of correlation r is approximately 0.77.

Question 19

The correlation between two variables is a unitless and is always between -1 and +1.

Question 20

If the coefficient of correlation r = 0 .80,the standard deviations of X and Y are 20 and 25,respectively,then Cov(X,Y)must be 400.

Question 21

Correlation and covariance can be used to examine relationships between numerical variables as well as for categorical variables that have been coded numerically.

Question 22

We are usually on the lookout for large correlations near

A) +1
B) -1
C) Either of these options
D) Neither of these options

Question 23

The tool that provides useful information about a data set by breaking it down into categories is the

A) histogram
B) scatterplot
C) pivot table
D) spreadsheet

Question 24

To examine relationships between two categorical variables,we can use

A) counts and corresponding charts of the counts
B) scatterplots
C) histograms
D) none of these options

Question 25

Displaying all correlations between 0.6 and 0.999 on a scatterplot as green and all correlations between -1.0 and -0.6 as red is known as

A) rank-order formatting
B) categorical formatting
C) coded formatting
D) numerical formatting
E) conditional formatting

Question 26

The limitation of covariance as a descriptive measure of association is that it

A) only captures positive relationships
B) does not capture the units of the variables
C) is very sensitive to the units of the variables
D) is invalid if one of the variables is categorical
E) none of these options

Question 27

The scatterplot is a graphical technique used to make apparent the relationship between two numerical variables.

Question 28

Scatterplots are also referred to as

A) crosstabs
B) contingency charts
C) X-Y charts
D) all of these options
E) none of these options

Question 29

Correlation is useful only for

A) assessing the weakness of a linear relationship
B) conveying the same information in a simpler format than a scatterplot
C) measuring the strength of a linear relationship
D) automatically calculating covariances
E) measuring the strength of a nonlinear relationship

Question 30

A line or curve superimposed on a scatterplot to quantify an apparent relationship is known as a(n)

A) average
B) trend line
C) data point
D) positive variable
E) slope

Question 31

We study relationships among numerical variables using

A) correlation
B) covariance
C) scatterplot charts
D) all of these options
E) none of these options

Question 32

The Excel function that allows you to count using more than one criterion is

A) COUNTIF
B) COUNTIFS
C) SUMPRODUCT
D) VLOOKUP
E) HLOOKUP

Question 33

A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is

A) side-by-side box plot
B) side-by-side pivot table
C) both of these options
D) neither of these options

Question 34

The most common data format is

A) long
B) short
C) stacked
D) unstacked

Question 35

Correlation and covariance measure

A) the strength of a linear relationship between two numerical variables
B) the direction of a linear relationship between two numerical variables
C) the strength and direction of a linear relationship between two numerical variables
D) the strength and direction of a linear relationship between two categorical variables
E) none of these options

Question 36

Tables used to display counts of a categorical variable are called

A) crosstabs
B) contingency tables
C) both of these options
D) neither of these options

Question 37

We can infer that there is a strong relationship between two numerical variables when

A) the points on a scatterplot cluster tightly around an upward sloping straight line
B) the points on a scatterplot cluster tightly around a downward sloping straight line
C) either of these options
D) neither of these options

Question 38

If the correlation of variables is close to 0,then we expect to see

A) an upward sloping cluster of points on the scatterplot
B) a downward sloping cluster of points on the scatterplot
C) a cluster of points around a trendline on the scatterplot
D) a cluster of points with no apparent relationship on the scatterplot
E) no explanation of what the scatterplot should look like based on the correlation

Question 39

Example of comparison problems include

A) salary broken down by male and female subpopulations
B) cost of living broken down by region of a country
C) recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo
D) Starting salary of recent graduates broken down by academic major
E) all of these options

Question 40

Counts for categorical variable are often expressed as percentages of the total.

Question 41

The four areas of a pivot table are

A) Crosstabs,Fields,Rows,Columns
B) Data,Count,Contingency,Percentage
C) Filters,Rows,Columns,Values
D) Sort,Rows,Columns,Count

Question 42

Changing the location of fields in a pivot table is known as

A) slicing
B) dicing
C) sorting
D) pivoting

Question 43

Which of the following are considered numerical summary measures?

A) mean and variance
B) variance and correlation
C) correlation and covariance
D) covariance and variance
E) first quartile and third quartile

Question 44

A scatterplot allows one to see

A) whether there is any relationship between two variables
B) what type of relationship there is between two variables
C) Both options are correct.
D) Neither option is correct.
An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size,approximate location of the household within the neighborhood,and indication of whether those surveyed owned or rented their home,gross annual income of the first household wage earner,gross annual income of the second household wage earner (if applicable),size of the monthly home mortgage or rent payment,and the total indebtedness (excluding the value of a home mortgage)of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations
$\begin{array}{| l| lllll| l}\begin{array}{l|llll}\hline &\text { Family Size }&\text {Location }&\text {Ownership }&\text {First hoome }&\text {Second lnoome }&\text { Monthly Payment }&\text {Utilties }&\text {Debt: }\\\hline \text { Family Size}&1.000 & & & & \\ \text {Location }&-0.010 & 1.000 & & & \\ \text {Dunership }&-0.025 & -0.386 & 1.000 & & \\ \text {First hoome }&-0.063 & -0.537 & 0.445 & 1.000 & \\ \text {Second hoome }&-0.058 & -0.508 & 0.424 & 0.884 & 1.000 \\ \text {Monthly Payment }&-0.076 & -0.511 & 0.552 & 0.514 & 0.478 &1.000\\ \text { Utilities}&0.256 & -0.346 & 0.935 & 0.388 & 0.366&0.489&1.000 \\ \text {Debt }&0.294 & -0.461 & 0.744 & 0.560 & 0.523&0.605&0.778&1.000\\\hline \end{array}\end{array}$

Question 45

The tables of counts that result from pivot tables are often called

A) samples
B) sub-tables
C) specimens
D) crosstabs

Question 46

One characteristic of "paired variables" is

A) one is a negative value and the other is a positive value
B) both are positive values
C) they have the same number of observations
D) they have a variable number of observations