Deck 12: Association Between Variables Measured at the Interval-Ratio Level

Question 1

On a scatterplot, the regression line

A) is drawn parallel to the horizontal axis
B) is always perpendicular to the vertical axis
C) comes as close as possible to touching every score
D) touches at least half of the scores

Answer 1

comes as close as possible to touching every score

Question 2

The symbol Y' ("Y-prime") stands for

A) the 1st Y score
B) the highest score on Y
C) the value of Y when X is zero
D) the predicted score on Y

Answer 2

the predicted score on Y

Question 3

One key assumption of correlation analysis is that the variables have an essentially __________ relationship.

A) linear
B) non-linear
C) curvilinear
D) circular

Answer 3

linear

Question 4

The direction of a relationship between variables can be detected on a scatterplot by considering the angle of the regression line. The relationship is

A) positive when the line slopes upward from left to right
B) positive when the line slopes downward from left to right
C) negative when the line slopes upward from left to right
D) negative when the line slopes downward from right to left

Question 5

By convention, the dependent variable is arrayed along the ______________ in a scatterplot.

A) vertical axis (the ordinate)
B) regression line
C) horizontal axis (the abscissa)
D) calibration line

Question 6

According to the study of gender and housework cited in the text,

A) husbands and wives spend roughly equal hours on housework each week
B) men in relationships where the man is the sole breadwinner spent the most time on housework
C) wives in dual-career families spent almost no time on housework
D) marital satisfaction was highest when both husbands and wives contributed to housework

Question 7

The appropriate measure of association for situations in which both variables are interval-ratio in level of measurement is

A) Pearson's r
B) gamma
C) chi square
D) the slope (b)

Question 8

For summarizing the relationship between X and Y, the points of minimized variation for the conditional distributions of Y provide us with

A) several regression lines to choose from
B) the best fitting regression line
C) a regression line that touches all of the dots
D) regression lines with negative slopes

Question 9

Visual examination of a scatterplot indicates the existence of an association between variables when

A) the distribution of Y changes as X changes
B) the regression line is parallel to the horizontal axis
C) the regression line is perpendicular to the horizontal axis
D) no single regression line can be found

Question 10

By convention, the independent variable is arrayed along the ______________ in a scatterplot.

A) vertical axis (the ordinate)
B) regression line
C) horizontal axis (the abscissa)
D) calibration line

Question 11

The conditional mean of Y for any value of X is found by

A) adding the Y scores for the specific value of X and dividing by N
B) adding all the Y scores and dividing by X
C) subtracting the mean of Y from the overall mean of X
D) any of the above

Question 12

There is no linear relationship between two interval-ratio variables when the regression line on a scatterplot

A) is parallel to the horizontal axis
B) does not touch all of the scores
C) is not an equal distance from all of the scores
D) is bimodal

Question 13

After scores of all cases have been located on a scatterplot, a straight line drawn so that it comes as close as possible to touching every score is called the

A) regression line
B) line of approximation
C) cluster line
D) scatterplot summary

Question 14

For interval-ratio level variables, the scatterplot is analogous to ___________ for nominal and ordinal level variables.

A) chi square
B) percentages
C) row marginals
D) bivariate tables

Question 15

If the regression line on a scatterplot slopes upward from left to right, the relationship is

A) bivariate
B) strong
C) parallel
D) positive

Question 16

In a scatterplot, the point of minimized variation for scores of Y for a given value of X (the independent variable) is

A) the sum of the conditional Y scores
B) the standard deviation of the conditional Y scores
C) the mean of the conditional Y scores
D) the predicted Y score

Question 17

When referring to interval-ratio variables, a commonly used synonym for association is

A) probability
B) predictability
C) correlation
D) causation

Question 18

A perfect association between variables can be seen on a scatterplot when

A) all dots lie an equal distance from the regression line
B) all dots lie on the regression line
C) the regression line forms a right angle at its intersection with the X axis
D) the regression line is parallel to the X axis

Question 19

Scatterplots do NOT give information about the _____________ of a relationship

A) strength
B) direction
C) linearity
D) significance

Question 20

Scatterplots give information about the _____________ of a relationship.

A) strength
B) direction
C) linearity
D) all of the above

Question 21

The Y intercept is the point where

A) the horizontal axis connects to the vertical axis
B) the regression line crosses the horizontal axis of the scatterplot
C) the regression line meets the conditional mean of Y
D) the regression line crosses the vertical axis of the scatterplot

Question 22

A researcher wants to measure the strength of the association between income (measured in dollars per year) and education (measured in number of years of formal schooling). Which of the following would be the most appropriate measure of association?

A) the slope (b)
B) gamma
C) chi square
D) Pearson's r

Question 23

If a = 5 and b = 10, what would the value of Y be when X = 100?

A) unknown, more information is needed
B) 1000
C) 1005
D) 5001

Question 24

The slope (b) is an awkward measure of the strength of a relationship because

A) it varies from 0 to 1.00
B) it decreases in value as the relationship increases in strength
C) it can have a negative sign when the relationship is actually positive
D) its upper limit is greater than 1.00

Question 25

The position of the least-squares regression line is defined by two elements:

A) the X intercept and the slope of the line
B) the X intercept and the Y intercept
C) the Y intercept and the slope of the line
D) the intersection point of the X and Y axes and the slope of the line

Question 26

The coefficient of determination may be interpreted with a logic akin to

A) chi square
B) the standard deviation
C) PRE
D) bivariate tables

Question 27

If the slope (b) is zero, the value of r

A) would also be zero
B) would be 1.00
C) would be - 1.00
D) cannot be determined from the information given

Question 28

In regression analysis, the symbol "a" stands for

A) the scores on the Y variable
B) the slope
C) the Y intercept
D) the X intercept

Question 29

The explained variation represents

A) the conditional distributions of Y
B) the amount that Y varies
C) the improvement in our ability to predict Y when taking X into account
D) the sum of the squares of all scores of Y

Question 30

If a = 2 and b = 4, what would the value of Y be when X = 1?

A) 4
B) 6
C) 2
D) 1

Question 31

When working with interval-ratio data, the optimal strategy for predicting Y while taking X into account would be to

A) use the regression line
B) guess randomly
C) ignore the slope (b)
D) always predict the Y intercept (a)

Question 32

If the slope of a regression line is 1.5, then

A) for every unit of change in X there is a change of 1.5 units in Y
B) for every unit of change in Y there is a change of 1.5 in X
C) the score of each case is 1.5 times higher on Y than on X
D) Y causes X

Question 33

A researcher asked a sample of dual career families about the percentage of the family budget contributed by the wife's job (Y) and the total number of children (X). Pearson's r for this relationship is -0.34. Which of the following is an appropriate interpretation of these results?

A) For every dollar contributed by the wife, the number of children increases by .34
B) For every additional child, the wife must work longer hours
C) Every additional child lowers the economic wellbeing of the family
D) As number of children increase, the percentage of the budget contributed by the wife decreases

Question 34

If a regression line is parallel to the horizontal axis of the scatterplot, the slope (b) will be

A) 1.00
B) -1.00
C) 0.00
D) 0.45

Question 35

If you wanted to measure the association between the age of people (in years) and the number of arrests for driving while intoxicated, the most appropriate measure of association would be

A) gamma
B) lambda
C) phi
D) Pearson's r

Question 36

When working with interval-ratio data, the optimal strategy for predicting Y while ignoring X will be to use the

A) mode of the Y scores for every case
B) median Y score for every case
C) mean Y score for every case
D) lowest Y score for every case

Question 37

If a line is drawn through the conditional means of Y, the line will

A) always be perfectly linear
B) rarely be perfectly straight
C) always be parallel to the horizontal axis
D) always be parallel to the vertical axis

Question 38

One important function of the least-squares regression equation is that

A) we can use it to tell if a relationship is linear
B) it summarizes all possible scores on the two variables
C) it makes the scatterplot symmetrical
D) it allows us to predict Y scores for any value of X

Question 39

If the regression line showing the effect of education on income has a slope of 1000,

A) the variables are not related
B) every year of education increases income by 1000
C) every change in education increases income
D) the Y intercept would be 1.00

Question 40

A study of traffic safety show a correlation of 0.57 between average speed of traffic and number of fatal accidents for a particular stretch of highway. This means that

A) drivers should speed up to get through this areas as quickly as possible
B) as speed increases, fatalities decrease
C) fatalities tend to increase as average speed increases
D) every 1 mile per hour increase in average speed increases the number of traffic fatalities by .57.

Question 41

If we calculate an r of .60, the proportion of the variation of Y that is explained by X is

A) .36
B) .40
C) .60
D) .64

Question 42

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r² is reported as .40. Which of the following would be a correct interpretation?

A) Mobility explains 16% of the variation in number of friends
B) There is a strong positive relationship between number of friends and mobility
C) As mobility increases, number of friends decreases
D) Mobility explains 40% of the variation in number of friends

Question 43

Dummy variables make it possible to include ________ in regression analysis

A) nominal variables
B) variables measuring intelligence
C) interval-ratio variables
D) variables with more than two scores

Question 44

The amount of error in predicting Y that remains after X has been taken into account is

A) the unexplained variation of Y
B) r - 1.00
C) always zero
D) r

Question 45

A researcher reports a Pearson r of .57 between gender (female = 0, males = 1) and involvement in juvenile delinquency. Which of the following is an appropriate interpretation?

A) females are more delinquent
B) there is no relationship between the variables
C) delinquency increases as gender "increases"
D) only males were delinquent