Question 1

What does a correlation coefficient do?
A)It allows us to draw conclusions about whether one variable causes another variable.
B)It creates a correlational design, rather than an experimental design.
C)It simplifies a complex pattern involving many scores into one easily interpreted statistic.
D)It summarizes the X scores and the Y scores separately.

Accepted Answer

The correlation coefficient simplifies the relationship between two variables into a single statistic, making it easier to interpret the strength and direction of the relationship.

Question 2

When the correlation coefficient representing the relationship between X and Y is intermediate, then all of the following are true except
A)there is not a perfectly consistent association.
B)there are different Y scores associated with a single X score.
C)prediction of Y from a known X score has some error.
D)all data points fall on the regression line.

Accepted Answer

When the correlation coefficient is intermediate, not all data points fall on the regression line. This means that there is some degree of variability in the relationship between X and Y, and not all Y scores are perfectly predicted by a given X score.

Question 3

Dr.Johnston has calculated a correlation between the number of cigarettes smoked per week and the age of his patients at the point of their first heart attack as r = -0.92.Dr.Johnston and his associates claim there apparently is no relationship between smoking and heart attacks.What error has Dr.Johnson made?
A)No error has been made; an r = -0.92 is so close to 0 that there is no relationship.
B)A correlation coefficient this close to -1 means there probably is a relationship, but we probably should do a significance test just to be sure.
C)Not everyone who smokes has a heart attack.
D)Dr.Johnston should know there are numerous factors involved when a person has a heart attack.

Accepted Answer

A correlation coefficient of -0.92 indicates a strong negative relationship between the two variables, contradicting the claim of no relationship. However, a significance test is indeed necessary to confirm the statistical significance of this correlation.

Question 4

"The more you save, the less you spend" describes
A)a positive linear correlation.
B)a negative linear correlation.
C)no correlation.
D)a nonlinear correlation.

Accepted Answer

The statement suggests an inverse relationship between saving and spending, which means that as someone saves more, their spending will decrease. This is an example of a negative linear correlation.

Question 5

The best-fitting line through a scatterplot is known as the
A)linear scatterplot line.
B)linear correlation line.
C)linear variance line.
D)linear regression line.

Accepted Answer

The best-fitting line through a scatterplot is known as the linear regression line, which is used in statistics to model the relationship between two variables.

Question 6

In general, a positive correlation means as the values of one variable  ________, there is a tendency for the values of the other variable to  ________.
A)increase; increase
B)increase; decrease
C)decrease; increase
D)decrease; decrease

Accepted Answer

A positive correlation means that as the values of one variable increase, there is a tendency for the values of the other variable to also increase.

Question 7

A linear regression procedure should ultimately yield a value called
A)Y prime.
B)rho.
C)the slope.
D)the proportion of variance accounted for.

Accepted Answer

The answer of A linear regression procedure should ultimately yield...

Question 8

When plotting correlational data, the appropriate graph to use is the
A)line graph.
B)bar graph.
C)histogram.
D)scatterplot.

Accepted Answer

When plotting correlational data, the best choice is a scatterplot. This type of graph shows the relationship between two variables by plotting them on a two-dimensional graph. Each point on the graph represents a pair of scores for the two variables being studied. The scatterplot allows the researcher to visually examine the relationship between the variables, such as whether they have a positive, negative, or zero correlation. A line graph is used to show trends over time, a bar graph is used to show comparisons between groups, and a histogram is used to show the distribution of a single variable.

Question 9

"The bigger they are, the harder they fall" describes
A)a positive linear correlation.
B)a negative linear correlation.
C)no correlation.
D)a nonlinear correlation.

Accepted Answer

The answer of "The bigger they are, the harder they...

Question 10

If you have a Pearson correlation coefficient of .30, what is the proportion of variance accounted for?
A).09
B).90
C).60
D).30

Accepted Answer

The proportion of variance accounted for by a Pearson correlation coefficient (r) is found by squaring the coefficient (r^2). So, .30 squared is .09, which means 9% of the variance is accounted for.

Question 11

The values of rho are
A)between -1 and +1.
B)unrestricted.
C)between 0 and +1.
D)any positive number.

Accepted Answer

Rho values, which measure the strength and direction of a linear relationship between two variables, range between -1 and +1. A value of -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

Question 12

Which of the following r-values indicates the weakest relationship between two variables?
A)+0.45
B)-0.30
C)+0.03
D)-0.45

Accepted Answer

The r-value (correlation coefficient) measures the strength and direction of a linear relationship between two variables. An r-value of +0.03 indicates the weakest relationship among the options given, as it is closest to 0.

Question 13

Which relationship is stronger, r = +0.62 or r = -0.62?
A)An r = +0.62 represents a stronger relationship than r = -0.62.
B)An r = -0.62 represents a stronger relationship than r = +0.62.
C)There is no difference in the strength of the two relationships.
D)Without seeing a scatterplot of the data, there is no way to determine which is stronger.

Accepted Answer

The strength of a relationship in correlation is indicated by the absolute value of the correlation coefficient (r), regardless of the sign. Both +0.62 and -0.62 have the same absolute value, indicating equal strength in their relationships, but in opposite directions.

Question 14

Professor Miller has found the correlation between a person's "need for affiliation" found by taking a test to determine the need to be with others) and the number of hours spent watching television is −0.69.He should conclude
A)as we observe people with higher and higher need for affiliation, we see a tendency for those people to spend less and less time watching television.
B)there is not much of a relationship between the two variables because the r is negative.
C)as we observe people with higher and higher need for affiliation, we see a tendency for those people to spend more and more time watching television.
D)the people who watch more television tend to have more need to be around others.

Accepted Answer

A negative correlation coefficient (−0.69) indicates an inverse relationship between the two variables. This means that as the need for affiliation increases, the number of hours spent watching television tends to decrease.

Question 15

Which of the following r-values indicates the strongest relationship between two variables?
A)+0.65
B)-0.89
C)+0.10
D)-0.10

Accepted Answer

The strength of a relationship between two variables in correlation is indicated by the absolute value of the correlation coefficient (r-value), regardless of the sign. A value of -0.89 has the highest absolute value among the options, indicating the strongest relationship.

Question 16

We should do a scatterplot of the data when we compute a correlation because the scatterplot allows us to
A)see the particular relationship and map out the best way to summarize it.
B)determine the exact value of the correlation coefficient.
C)determine whether a relationship is likely to exist in the population from which the sample is taken.
D)predict accurate Y scores for known X scores.

Accepted Answer

A scatterplot allows us to visually assess the relationship between two variables, helping us understand the nature and strength of the relationship, which aids in summarizing it effectively.

Question 17

A U-shaped pattern is an example of a
A)curvilinear relationship.
B)non-relationship.
C)positive relationship.
D)negative relationship.

Accepted Answer

A U-shaped pattern represents a curvilinear relationship because the direction of the relationship between the two variables changes at least once.

Question 18

In general, a zero correlation means
A)as the values of one variable increase, there is no tendency for the values of the other variable to change in any consistent, predictable fashion.
B)as the values of one variable increase, there is a tendency for the values of the other variable also to increase.
C)as the values of one variable increase, there is a tendency for the values of the other variable to decrease.
D)as the values of one variable decrease, there is a tendency for the values of the other variable also to decrease.

Accepted Answer

A zero correlation indicates that there is no linear relationship between the two variables, meaning as one variable changes, the other does not change in a predictable way.

Question 19

In a linear relationship, as the X scores increase, the Y scores change
A)in only one direction.
B)only in the negative direction.
C)only in the positive direction.
D)in the positive and then in the negative direction.

Accepted Answer

In a linear relationship, the change in Y scores for an increase in X scores is consistent in one direction, either positive or negative, but not both or changing directions. This means as X increases, Y either consistently increases or decreases, but does not switch between increasing and decreasing.

Question 20

What are the consequences of having a restricted range?
A)Obtaining a smaller r than otherwise would be the case.
B)Obtaining a larger r than otherwise would be the case.
C)Having a curvilinear instead of a linear relationship.
D)Having a correlation with a different direction than otherwise would be found.

Accepted Answer

A restricted range in data can lead to an underestimation of the true strength of a relationship between variables, resulting in a smaller correlation coefficient (r) than would be observed with a full range of data. This is because the variability that the correlation coefficient relies on to measure the strength of the relationship is artificially limited.

Quiz 10: Describing Relationships Using Correlation and Regression

What does a correlation coefficient do?

When the correlation coefficient representing the relationship between X and Y is intermediate, then all of the following are true except

"The more you save, the less you spend" describes

The best-fitting line through a scatterplot is known as the

In general, a positive correlation means as the values of one variable , there is a tendency for the values of the other variable to .

A linear regression procedure should ultimately yield a value called

When plotting correlational data, the appropriate graph to use is the

"The bigger they are, the harder they fall" describes

If you have a Pearson correlation coefficient of .30, what is the proportion of variance accounted for?

The values of rho are

Which of the following r-values indicates the weakest relationship between two variables?

Which relationship is stronger, r = +0.62 or r = -0.62?

Professor Miller has found the correlation between a person's "need for affiliation" found by taking a test to determine the need to be with others) and the number of hours spent watching television is −0.69.He should conclude

Which of the following r-values indicates the strongest relationship between two variables?

We should do a scatterplot of the data when we compute a correlation because the scatterplot allows us to

A U-shaped pattern is an example of a

In general, a zero correlation means

In a linear relationship, as the X scores increase, the Y scores change

What are the consequences of having a restricted range?