Deck 3: Finding Relationships Among Variables

Question 1

A the correlation 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
C)A cluster of points around a trendline
D)A cluster of points with no apparent relationship
E)We cannot say what the scatterplot should look like based on the correlation

Answer 1

D

Question 2

We study relationships among numerical variables using

A)Correlation
B)Covariance
C)Scatterplots
D)All of these options
E)None of these options

Answer 2

D

Question 3

We are usually on the lookout for large correlations near

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

Answer 3

C

Question 4

Generally speaking,if two variables are unrelated (as one increases,the other shows no pattern),the covariance will be

A)a large positive number
B)a large negative number
C)a positive or negative number close to zero
D)a positive or negative number close to +1 or -1

Question 5

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 6

The most common data format is

A)Long
B)Short
C)Stacked
D)Unstacked

Question 7

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 8

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

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

Question 9

If Cov(X,Y)= - 16.0,variance of X = 25,variance of Y = 16 then the sample coefficient of correlation r is

A)+ 1.60
B)- 1.60
C)- 0.80
D)+ 0.80
E)Cannot be determined from the given information

Question 10

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

A)Side-by-side boxplots
B)Side-by-side histograms
C)Both of these options
D)Neither of these options

Question 11

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 12

The correlation is best interpreted

A)By itself
B)Along with the covariance
C)Along with the corresponding scatterplot
D)Along with the corresponding contingency chart
E)Along with the mean and standard deviation

Question 13

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

Question 14

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 15

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 16

Which of the following are considered measures of association?

A)Mean and variance
B)Variance and correlation
C)Correlation and covariance
D)Covariance and variance
E)First quartile and third quartile

Question 17

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 18

A perfect straight line sloping downward would produce a correlation coefficient equal to

A)+1
B)-1
C)0
D)+2
E)-2

Question 19

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 20

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 21

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

Question 22

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

Question 23

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

Question 24

Correlation has the advantage of being in the same original units as the X and Y variables

Question 25

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

Question 26

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

Question 27

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 28

Correlation is a single-number summary of a scatterplot

Question 29

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

Question 30

Joint categories for categorical variables cannot be used to make inferences about the relationship between the individual categorical variables.

Question 31

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 32

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

Question 33

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

Question 34

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

Question 35

Generally speaking,if two variables are unrelated,the covariance will be a positive or negative number close to zero

Question 36

The tables that result from pivot tables are called:

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

Question 37

The cutoff for defining a large correlation is >0.7 or <-0.7.

Question 38

Which of the following statements are false?

A)Contingency tables are traditional statistical terms for pivot tables that list counts.
B)Time series plot is a chart showing behavior over time of a time series variable.
C)Pivot table is a table in Excel that summarizes data broken down by one or more numerical variables.
D)None of these options

Question 39

Which of the following are true statements of pivot tables?

A)They allow us to "slice and dice" data in a variety of ways.
B)Statisticians often refer to them as contingency tables or crosstabs.
C)Pivot tables can list counts,averages,sums,and other summary measures,whereas contingency tables list only counts.
D)All of these options

Question 40

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

Question 41

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 42

A data set from a sample of 399 Michigan families was collected.The characteristics of the data include family size (large or small),number of cars owned by family (1,2,3,or 4),and whether family owns a foreign car.Excel produced the pivot table shown below. Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car.

Question 43

Which two variables have the strongest linear relationship with annual salary?

Question 44

Which of the variables have a negative linear relationship with the household's average monthly expenditure on utilities?

Question 45

Of those in the sample who went partying the weekend before the final exam,what percentage of them did well in the exam?

Question 46

A sample of 30 schools produced the pivot table shown below for the average percentage of students graduating from high school.Use this table to determine how the type of school (public or Catholic)that students attend affects their chance of graduating from high school.

Question 47

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 48

Which of the variables have essentially no linear relationship with the household's average monthly expenditure on utilities?

Question 49

The students at small community college in Iowa apply to study either English or Business.Some administrators at the college are concerned that women are being discriminated against in being allowed admittance,particularly in the business program.Below,you will find two pivot tables that show the percentage of students admitted by gender to the English program and the Business school.The data has also been presented graphically.What do the data and graphs indicate?

Question 50

Which of the variables have a positive linear relationship with the household's average monthly expenditure on utilities?

Question 51

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

Question 52

For which of the two variables,number of years of prior work experience or number of years of post-secondary education,is the relationship with salary stronger? Justify your answer.

Question 53

What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam?

Question 54

Of those in the sample who did well on the final exam,what percentage of them went partying the weekend before the exam?

Question 55

The percentage of the US population without health insurance coverage for samples from the 50 states and District of Columbia for both 2003 and 2004 produced the following table of correlations.
What does the table for the two given sets of percentages tell you in this case?

Question 56

How would you characterize the relationship between gender and annual salary?

Question 57

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

Question 58

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

Question 59

What percentage of the students in the sample spent the weekend studying and did well in the final exam?

Question 60

If we draw a straight line through the points in a scatterplot and most of the points fall close to the line,there is a strong positive linear relationship between the two variables.

Question 61

What is the average annual salary of the employed Internet users in this sample?

Question 62

Approximate the percentage of these internet users who are women.

Question 63

Approximate the percentage of these Internet users who are in the 58-71 age group.

Question 64

Of those in the sample who went partying the weekend before the final exam,what percentage of them did poorly in the exam?

Question 65

Approximate the percentage of these Internet users who are currently employed.

Question 66

If the sample is a good representation of the population,what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying?

Question 67

What percentage of these Internet users who are married.

Question 68

What percentage of these internet users has formal education beyond high school?

Question 69

There are two scatterplots shown below.The first chart shows the relationship between the size of the home and the selling price.The second chart examines the relationship between the number of bedrooms in the home and its selling price.Which of these two variables (the size of the home or the number of bedrooms)seems to have the stronger relationship with the home's selling price? Justify your answer.

Question 70

A health magazine reported that a man's weight at birth has a significant impact on the chance that the man will suffer a heart attack during his life.A statistician analyzed a data set for a sample of 798 men,and produced the pivot table and histogram shown below.Determine how birth weight influences the chances that a man will have a heart attack.

Question 71

If the sample is a good representation of the population,what percentage of those who spent the weekend studying should we expect to do poorly on the final exam?

Question 72

Approximate the percentage of these Internet users who are single with no formal education beyond high school.

Question 73

Of those in the sample who did well in the final exam,what percentage of them spent the weekend before the exam studying?

Question 74

Approximate the percentage of these Internet users who are married with formal education beyond high school.

Question 75

Approximate the percentage of these Internet users who are men under the age of 30.

Question 76

Approximate the percentage of these internet users who are women in the 30-43 age group.

Question 77

The following scatterplot compares the selling price and the appraised value. Is there a linear relationship between these two variables? If so,how would you characterize the relationship?

Question 78

If the sample is a good representation of the population,what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam?

Question 79

What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam?

Question 80

The table shown below contains information technology (IT)investment as a percentage of total investment for eight countries during the 1990s.It also contains the average annual percentage change in employment during the 1990s.Explain how these data shed light on the question of whether IT investment creates or costs jobs.(Hint: Use the data to construct a scatterplot)