Question 1

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 to determine if the relationship between two variables is significant or not. We use statistical tests to calculate the probability of observing a relationship as strong or stronger than the one we observed if no relationship exists. If the probability is low enough (usually 5% or lower), we conclude that the relationship is statistically significant.

Question 2

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 _____.

Accepted Answer

Heteroskedasticity is 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. A is incorrect because multiple regression refers to a statistical technique used to analyze the relationship between multiple independent variables and a dependent variable. B is incorrect because homoskedasticity refers to the pattern of covariation around the regression line which is constant around the regression line and does not vary with changes in the values of the independent variable. D is incorrect because normal distribution refers to the distribution of data in a bell curve shape around the mean. E is incorrect because constant association refers to the situation where the covariation between two variables is consistent across all values of the independent variable.

Question 3

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

Accepted Answer

Regression analysis assumes a linear relationship between two variables. However, if a linear relationship is not present, then a different type of analysis may be needed or a transformation of the variables may be necessary to create a linear relationship.

Question 4

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

Accepted Answer

With a larger sample size, the variability in the data is typically reduced, resulting in a stronger signal-to-noise ratio. This increases the likelihood of detecting a relationship, even if it is weak. Additionally, larger sample sizes can provide more statistical power, allowing for more accurate estimation of the strength and significance of the relationship.

Question 5

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

Accepted Answer

Statistical significance only indicates that the correlation observed is unlikely to be due to chance, but it does not necessarily imply that the correlation is meaningful or important in the real world.

Question 6

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 7

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

Accepted Answer

Regression analysis assumes a linear relationship between the independent and dependent variables, which means that the change in one variable directly affects the change in the other variable in a straight line.

Question 8

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

Accepted Answer

The use of the Pearson correlation coefficient assumes that the variables have a normally distributed population. If the data is not normally distributed, non-parametric correlation methods, such as Spearman's rank correlation coefficient, should be used instead.

Question 9

Which of the following is an advantage of the partial least squares method of structural equation modeling?

Accepted Answer

The advantage of partial least squares method of structural equation modeling is that it allows for solutions to be obtained with both small and large samples. This is particularly beneficial when the sample size is limited or when data collection can be expensive or time-consuming.

Question 10

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

Accepted Answer

The coefficient of determination, also known as R-squared, measures the proportion of variability in the dependent variable that is explained by the independent variable(s). Therefore, the larger the coefficient of determination, the stronger the linear relationship between the two variables being examined.

Question 11

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 equation that describes the linkage is typically more complex than a simple linear formula.

Question 12

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 and identically distributed (i.e. the errors are not correlated with each other and have the same variance). A dependent distribution of error terms would violate this assumption and make the model invalid.

Question 13

In a regression model, if independent variables exhibit multicollinearity, then:

Accepted Answer

When independent variables exhibit multicollinearity, the estimation of separate regression coefficients for the correlated variables becomes difficult. This is because in the presence of multicollinearity, it becomes hard to attribute the effect of a single independent variable on the dependent variable while holding other independent variables constant. This can lead to unstable and unreliable estimates of the individual regression coefficients.

Question 14

Multicollinearity is a(n):

Accepted Answer

Multicollinearity refers to a situation where several independent variables in a regression analysis are highly correlated with each other. This correlation can make it difficult to estimate the independent contribution of each variable to the dependent variable and can result in unstable or inconsistent coefficient estimates.

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 determines the best-fitting line by minimizing the sum of the squared vertical distances of all the data points from the line.

Question 16

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

Accepted Answer

Scatter diagrams are used to show the relationship and the pattern of the relationship between two variables. They are a visual representation of the correlation, association or the direction between the variables.

Question 17

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

Accepted Answer

This statement is true. The correlation coefficient measures the strength of the linear relationship between two variables, with values ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation). The larger the absolute value of the correlation coefficient, the stronger the association between the two variables.

Question 18

_____ refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.

Accepted Answer

Homoskedasticity refers to the constant variance of errors or residuals around the regression line, regardless of the magnitude of the predictor variable. This means that the variability of the errors is the same for all levels of the predictor variable.

Question 19

Covariation refers to the degree of association between two variables.

Accepted Answer

Covariation indicates the extent to which two variables vary or change together. It is a measure of the relationship or association between two variables.

Question 20

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

Accepted Answer

An ellipse-shaped scatter plot indicates a positive correlation between two variables, meaning that as one variable increases, the other tends to increase as well.

Quiz 12: Examining Relationships in Quantitative Research