Question 1

Covariation refers to the degree of association between two variables.

Accepted Answer

Covariation refers to the extent to which two variables are related to each other, or vary together. Therefore, the statement is true.

Question 2

The strength of association between two variables is determined by the size of the correlation coefficient.

Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables. The value of the correlation coefficient ranges from -1 to +1, where a value of +1 represents a perfect positive correlation, 0 represents no correlation, and -1 represents a perfect negative correlation. Therefore, the size of the correlation coefficient does determine the strength of association between two variables.

Question 3

To measure whether a relationship between two variables exists, we rely on the concept of statistical significance.

Accepted Answer

Statistical significance is a commonly used method for determining whether the relationship between two variables exists or not.

Question 4

Regression analysis assumes a linear relationship is a bad description of the relationship between two variables.

Accepted Answer

Regression analysis does not inherently assume a linear relationship is bad; it can model both linear and non-linear relationships depending on the type of regression used (e.g., linear regression for linear relationships, polynomial regression for non-linear relationships).

Question 5

It is possible for a correlation to be statistically significant and still lack substantive significance.

Accepted Answer

Statistical significance refers to the likelihood that the correlation observed did not occur by chance, while substantive significance refers to whether the correlation is meaningful or important in a practical sense. Therefore, a correlation can be statistically significant but not have any practical relevance or impact.

Question 6

In a regression model, if independent variables exhibit multicollinearity, then:
A) the strength of association of variables changes according to the beta coefficient.
B) determination of the best fitting line requires maximization of the vertical distances of all the points from the line.
C) standardization augments the effects of using different scales of measurement.
D) computing factor scores is the least effective approach to regression analysis.
E) the estimation of separate regression coefficients for the correlated variables becomes difficult.

Accepted Answer

Multicollinearity makes it difficult to estimate separate regression coefficients for correlated variables because there will be ambiguity about the exact relationship between each independent variable and the dependent variable. This can make it challenging to accurately interpret the impact of each variable on the outcome, and could lead to potentially erroneous conclusions.

Question 7

A scatter plot wherein the dots form an ellipse indicates a positive relationship between variables.

Accepted Answer

An ellipse in a scatter plot indicates a correlation between variables and the direction of the correlation depends on the orientation of the ellipse. If the ellipse is vertical and narrow, it indicates a strong positive relationship.

Question 8

Scatter diagrams are a visual way to describe the relationship between two variables and the covariation they share.

Accepted Answer

Scatter diagrams use a visual representation, typically with points on a graph, to show the relationship and covariation between two variables.

Question 9

Large samples result in more confidence that a relationship exists, even if it is weak.

Accepted Answer

Large samples provide a more accurate representation of the population and reduce the likelihood of random variability, increasing the confidence that any observed relationship is not due to chance. Thus, even if the relationship is weak, a larger sample will provide stronger evidence of its existence.

Question 10

Multicollinearity is a(n):
A) statistical procedure that estimates regression equation coefficients which produce the lowest sum of squared differences between the actual and predicted values of the dependent variable.
B) statistical technique which analyzes the linear relationship between a dependent variable and multiple independent variables by estimating coefficients for the equation for a straight line.
C) estimated regression coefficient that has been recalculated to have a mean of zero and a standard deviation of 1.
D) statistic that compares the amount of variation in the dependent measure "explained" or associated with the independent variables to the "unexplained" or error variance.
E) situation in which several independent variables are highly correlated with each other.

Accepted Answer

Multicollinearity is a situation in which several independent variables in a regression analysis are highly correlated with each other, which can cause issues with accurately estimating the relationship between the independent variables and the dependent variable.

Question 11

Regression analysis assumes there is a straight line relationship between the independent and dependent variables.

Accepted Answer

Regression analysis assumes that there is a linear relationship between the independent and dependent variables. This means that the relationship between the two variables can be graphed as a straight line. However, this assumption may not always hold true, and non-linear relationships may require different types of regression analysis.

Question 12

The pattern of covariation around the regression line which is not constant around the regression line and varies in some way when the values change from small to medium and large is known as _____.
A) multiple regression
B) homoskedasticity
C) heteroskedasticity
D) normal distribution
E) constant association

Accepted Answer

Heteroskedasticity refers to the unequal distribution of errors (residuals) for different levels of predictor variables, resulting in a non-constant variance around the regression line. Option A (multiple regression) refers to a statistical technique that involves analyzing the relationship between multiple independent variables and a dependent variable. Option B (homoskedasticity) refers to the equal distribution of errors (residuals) for different levels of predictor variables, resulting in a constant variance around the regression line. Option D (normal distribution) refers to a symmetrical distribution of data points around the mean. Option E (constant association) does not accurately describe the pattern of covariation around the regression line.

Question 13

The smaller the size of the coefficient of determination, the stronger the linear relationship between the two variables being examined.

Accepted Answer

This statement is false. The coefficient of determination, also known as R-squared, measures the proportion of variation in one variable that can be explained by the other variable in a linear regression. Therefore, a larger coefficient of determination indicates a stronger linear relationship between the two variables.

Question 14

In a regression analysis, the horizontal distance between the estimated regression line and the actual data points is the unexplained variance called error.

Accepted Answer

In regression analysis, the vertical distance between the estimated regression line and the actual data points represents the error or unexplained variance, not the horizontal distance.

Question 15

The least squares procedure determines the best-fitting line by maximizing the vertical distances of all the data points from the line.

Accepted Answer

The least squares procedure minimizes the sum of the squared vertical distances (i.e., residuals) of all the data points from the line.

Question 16

The use of the Pearson correlation coefficient assumes the variables have a normally distributed population.

Accepted Answer

The Pearson correlation coefficient assumes that both variables have a normal distribution in their population. If this assumption is not met, then other correlation coefficients (e.g., Spearman's rho) may be more appropriate.

Question 17

_____ refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.
A) Linearity
B) Curvilinearity
C) Multicollinearity
D) Heteroskedasticity
E) Homoskedasticity

Accepted Answer

Homoskedasticity refers to a consistent pattern of covariation around the regression line, regardless of the magnitude of the values. This means that there is constant variance in the residuals across all levels of the predictor variable.

Question 18

When two variables have a curvilinear relationship, the formula that best describes the linkage is very simple.

Accepted Answer

When two variables have a curvilinear relationship, the formula that best describes the linkage is generally more complex than a simple linear equation. A quadratic or higher order equation may be necessary to accurately model the relationship.

Question 19

The use of a simple regression model assumes that the error terms associated with making predictions are dependently distributed.

Accepted Answer

The use of a simple regression model assumes that the error terms associated with making predictions are independently distributed. In other words, the errors are not related to each other and their values don't depend on previous errors. This assumption is important to ensure the validity of the model and the accuracy of its predictions. If the errors are dependently distributed, it may indicate the presence of some hidden variables or trends that are not accounted for in the model, which can lead to biased or inconsistent results.

Question 20

Which of the following is an advantage of the partial least squares method of structural equation modeling?
A) Solutions are possible with the simplest models, which are based on a few questions.
B) The method is parametric, so it can be applied to data that is not normally distributed.
C) The measurement requirements are very rigid and are designed to work exclusively with nominal data.
D) Only one type of analysis is possible.
E) Solutions can be obtained with both small and large samples.

Accepted Answer

The advantage of the partial least squares method of structural equation modeling is that solutions can be obtained with both small and large samples.

Quiz 12: Examining Relationships in Quantitative Research