Question 1

Which of the following correlations represents the strongest relationship between two variables?
A)−.85
B).01
C).50
D).80

Accepted Answer

A correlation of −.85 indicates a strong negative relationship between two variables, stronger than the other options listed.

Question 2

The observation that Y decreases as X increases suggests
A)a positive correlation.
B)no correlation.
C)a negative correlation.
D)a curvilinear correlation.

Accepted Answer

A negative correlation is indicated when one variable decreases as the other increases.

Question 3

If the scores on X give us no information about the scores on Y , the sets of scores likely have
A)a positive correlation.
B)a negative correlation.
C)no correlation.
D)curvilinear correlation.

Accepted Answer

If the scores on X give us no information about the scores on Y, it means there is no relationship between the variables, indicating no correlation.

Question 4

Which of the following is true of correlations?
A)They cannot be used to determine statistical significance.
B)They provide the basis for transforming observations to scales.
C)They are particularly useful with nominal scales.
D)They describe the direction and magnitude of relationships between two variables.

Accepted Answer

Correlations are used to describe the direction (positive or negative) and magnitude (strength) of the relationship between two variables, allowing researchers to understand how variables change together.

Question 5

Given the following ordered pairs, you can infer that the correlation is most likely 8 7
7 6
3 2
1 2
1 2
A)positive.
B)negative.
C)zero.
D)perfect.

Accepted Answer

The pairs show that as the value of the first number increases or decreases, the value of the second number tends to also increase or decrease respectively, indicating a positive correlation.

Question 6

Correlation measures the magnitude and ____ of a relationship.
A)strength
B)consistency
C)direction
D)regression

Accepted Answer

Correlation measures both the magnitude and direction of a relationship between two variables, indicating how one variable may change in relation to another.

Question 7

Each point on a scatter diagram shows
A)the variance of a set of scores.
B)the standard deviation of a set of scores.
C)where an individual scored compared to the mean.
D)where an individual scored on both X and Y .

Accepted Answer

A scatter diagram (or scatter plot) is used to show the relationship between two variables, where each point represents the values of those two variables for a single observation. Thus, each point shows where an individual scored on both the X (horizontal) and Y (vertical) axes.

Question 8

What do scatter diagrams do?
A)Allow visualization of the relationship between two variables
B)Create an objective measure of reliability
C)Relate univariate observations to bivariate distributions
D)Demonstrate the statistical validity of measures

Accepted Answer

Scatter diagrams, also known as scatter plots, are graphical representations used to visualize the relationship between two variables, showing how one variable is affected by another. This helps in identifying patterns, trends, or potential correlations between the variables.

Question 9

People who drink more caffeinated beverages tend to experience more alertness and psychomotor activity. This demonstrates a(n)
A)positive correlation.
B)negative correlation.
C)zero correlation.
D)unknown.

Accepted Answer

A positive correlation is indicated when two variables move in the same direction, meaning as the consumption of caffeinated beverages increases, so does the level of alertness and psychomotor activity.

Question 10

What is the point of least squares for the set of scores [2, 7, 8, 11]?
A)Indeterminate
B)4
C)7
D)10

Accepted Answer

The point of least squares, often referred to in the context of the mean or average, minimizes the sum of the squared deviations from each data point. For the set [2, 7, 8, 11], the mean is (2+7+8+11)/4 = 28/4 = 7. This is the value that minimizes the sum of squared deviations, making it the point of least squares.

Question 11

A scatter diagram is a
A)bivariate plot of individual data points.
B)univariate plot of individual data points.
C)form of the stem and leaf display.
D)method of calculating variance.

Accepted Answer

A scatter diagram is a bivariate plot because it displays two variables for each data point, typically with one variable along the x-axis and the other along the y-axis.

Question 12

What is the point of least squares for the set of scores [4, 6, 8, 10]?
A)Indeterminate
B)4
C)7
D)10

Accepted Answer

The point of least squares, often referred to in the context of the least squares method for linear regression, minimizes the sum of the squares of the differences between the observed and predicted values. For a set of scores without a specified model, it's interpreted as the mean of the values. The mean of [4, 6, 8, 10] is (4+6+8+10)/4 = 28/4 = 7.

Question 13

In correlation analysis, we ask whether two variables
A)can be measured.
B)experience regression.
C)have a causal relationship.
D)covary.

Accepted Answer

The answer of In correlation analysis, we ask whether two...

Question 14

If the line that comes closest to all points in a scatter diagram is perfectly straight, the correlation between the two variables is
A)linear.
B)curvilinear.
C)positive.
D)unknown.

Accepted Answer

A perfectly straight line that comes closest to all points in a scatter diagram indicates a linear relationship between the two variables, meaning as one variable increases or decreases, the other variable does so in a consistent, straight-line manner.

Question 15

Diagrams that use a single point to show a person's scores on two measures are called ____ plots.
A)validity
B)regression
C)scatter
D)normality

Accepted Answer

Scatter plots are diagrams that use points to show the relationship between two variables, including a person's scores on two different measures.

Question 16

Correlation coefficients describe the
A)degree of linearity of relation between X and Y .
B)mean of X and Y .
C)direction and magnitude of relationship between X and Y .
D)causality of relationships between X and Y .

Accepted Answer

Correlation coefficients describe the direction and magnitude of the relationship between two variables.

Question 17

The correlation equals +1 for which of the following four pairs of numbers?
A)(−2, −4), (0, 0), (2, 4), (4, 8)
B)(0, 0), (1, 1), (2, 4), (3, 9)
C)(−2, −9), (0, −5), (2, -1), (4, 3)
D)(−2, −2), (0, −5), (2, −1), (4, −9)

Accepted Answer

A correlation of +1 indicates a perfect positive linear relationship between two variables. In option A, as one variable increases, the other variable increases in a perfectly linear manner, doubling in this case.

Question 18

In a negative correlation,
A)individuals tend to maintain the same or a similar relative performance.
B)scores on one variable tell us nothing about scores on a second.
C)individuals who score low on one variable tend to score low on a second.
D)high scores on the X variable are associated with low scores on the Y variable.

Accepted Answer

In a negative correlation, there is an inverse relationship between two variables, meaning as one variable increases, the other decreases. This is accurately described by option D, where high scores on one variable (X) are associated with low scores on the other variable (Y).

Question 19

Suppose that you have two variables, one with a mean of 15 and another with a mean of 19. If you know only that one person's score on the first variable is 14, the best prediction of that person's score on the other is
A)0.
B)15.
C)19.
D)indeterminate.

Accepted Answer

Given only the means of two variables and a score from one variable, the best prediction for a score on the other variable is its mean, which is 19 in this case.

Question 20

The best-fitting straight line through a set of points in a scatter diagram is known as the
A)regression line.
B)linear line.
C)correlation line.
D)perfect correlation.

Accepted Answer

The best-fitting straight line through a set of points in a scatter diagram is known as the regression line, which is used in linear regression analysis to model the relationship between two variables.

Quiz 3: Correlation and Regression

Which of the following correlations represents the strongest relationship between two variables?

The observation that Y decreases as X increases suggests

If the scores on X give us no information about the scores on Y , the sets of scores likely have

Which of the following is true of correlations?

Given the following ordered pairs, you can infer that the correlation is most likely 8 7 7 6 3 2 1 2 1 2

Correlation measures the magnitude and ____ of a relationship.

Each point on a scatter diagram shows

What do scatter diagrams do?

People who drink more caffeinated beverages tend to experience more alertness and psychomotor activity. This demonstrates a(n)

What is the point of least squares for the set of scores [2, 7, 8, 11]?

A scatter diagram is a

What is the point of least squares for the set of scores [4, 6, 8, 10]?

In correlation analysis, we ask whether two variables

If the line that comes closest to all points in a scatter diagram is perfectly straight, the correlation between the two variables is

Diagrams that use a single point to show a person's scores on two measures are called ____ plots.

Correlation coefficients describe the

The correlation equals +1 for which of the following four pairs of numbers?

In a negative correlation,

Suppose that you have two variables, one with a mean of 15 and another with a mean of 19. If you know only that one person's score on the first variable is 14, the best prediction of that person's score on the other is

The best-fitting straight line through a set of points in a scatter diagram is known as the