Deck 15: Association Between Variables Measured at the Interval-Ratio Level

Question 1

Scattergrams give information about the ____ of a relationship.

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

Answer 1

all of the above

Question 2

On a scattergram,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 2

comes as close as possible to touching every score.

Question 3

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

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

Answer 3

positive.

Question 4

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 5

By convention,the dependent variable is arrayed along the ____ in a scattergram.

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

Question 6

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

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

Question 7

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 8

In a scattergram,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 9

Visual examination of a scattergram 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

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.

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

Scattergrams do NOT give information about the ____ of a relationship.

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

Question 13

After scores of all cases have been located on a scattergram,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)scattergram summary.

Question 14

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

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

Question 15

By convention,the independent variable is arrayed along the ____ in a scattergram.

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

Question 16

A perfect association between variables can be seen on a scattergram 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 17

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

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 18

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

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

Question 19

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

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

Question 20

The direction of a relationship between variables can be detected on a scattergram 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 21

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 22

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 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

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 25

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 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

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 scattergram symmetrical.
D)it allows us to predict Y scores for any value of X.

Question 28

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 29

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 30

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 31

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

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

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

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 34

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 35

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)speed kills.
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 36

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 37

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 38

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 scattergram.
C)the regression line meets the conditional mean of Y.
D)the regression line crosses the vertical axis of the scattergram.

Question 39

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 40

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 41

For a sample of 15 rural counties in one state,a researcher has collected information about the rate of deaths due to traffic accidents per 1,000,000 population and the percentage of the population which consists of males,age 16 to 25.For these variables,find the least squares regression line and compute r and r squared.Write a sentence or two summarizing and explaining your results.

Question 42

If we fail to reject the null hypothesis in a test of significance for a Pearson's r,we conclude that

A)there is a negative association between the variables.
B)no inference can be made about the relationship of the two variables in the population.
C)the relationship exists but its direction and strength are unknown.
D)the variables are related in the population.

Question 43

In addition to random sampling,interval-ratio level of measurement,and a normal sampling distribution,model assumptions for testing Pearson's r for significance include

A)bivariate normal distributions.
B)a linear relationship.
C)uniformity in the variance of the Y scores around the regression line for all values of X.
D)all of the above

Question 44

One important limitation of the study of poverty and crime reported in the text is

A)the variables were nominal.
B)the sample was non-random.
C)prediction is not the same thing as association.
D)correlation is not the same thing as causation.

Question 45

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 46

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

Question 47

In the study reported in the text,the Pearson's r between the measures of poverty and crime was 0.54.Which of the following is a reasonable interpretation of this result?

A)poverty causes crime
B)crime causes poverty
C)as poverty increases,crime decreases
D)there is a moderate,positive correlation between poverty and crime

Question 48

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 49

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 50

When testing Pearson's r for significance,the null hypothesis is that

A)there is no difference between the variables in the population from which the sample was drawn.
B)there is no linear association between the variables in the population from which the sample was drawn.
C)there is no difference between the sample and the population from which the sample was drawn.
D)r = 1.00.

Question 51

The text reported information about the relationship between crime and poverty.The sample used was

A)1000 randomly selected Americans.
B)a group of inmates from a federal penitentiary.
C)a large group of high school students.
D)the fifty states.