Question 1

If all variables are analyzed together and the goal is to form groups or give meaning to a set of variables or respondents, the statistical technique is referred to as a(n) _____ method.
A) dependence
B) interdependence
C) causal
D) quantitative
E) qualitative

Accepted Answer

Interdependence techniques, such as cluster analysis or factor analysis, are used to form groups or give meaning to a set of variables or respondents by analyzing all variables together without distinguishing between dependent and independent variables.

Question 2

Which of the following can be used to examine the statistical difference between the means of two or more groups if the dependent variable is metric and the independent variable(s) is nonmetric?
A) ANOVA
B) Spearman's Correlation
C) Cluster analysis
D) Correlation
E) Factor analysis

Accepted Answer

ANOVA (Analysis of Variance) can be used to examine statistical differences between the means of two or more groups when the dependent variable is metric and the independent variable(s) is nonmetric. ANOVA compares the variability within groups to the variability between groups to determine if there is a significant difference in means. Spearman's Correlation, Cluster analysis, Correlation, and Factor analysis are not appropriate for this type of analysis.

Question 3

Billy has a dependent variable that is measured with ratio data. All of the following are statistical techniques that would be appropriate for him to use EXCEPT _____.
A) multiple regression
B) ANOVA
C) discriminant analysis
D) correlation analysis
E) all of the above are appropriate

Accepted Answer

Discriminant analysis is not appropriate for ratio data. The other statistical techniques listed are appropriate for ratio data.

Question 4

This type of regression has a single metric dependent variable and a single metric independent variable.
A) ANOVA
B) Multiple regression
C) Bivariate regression
D) Univariate regression
E) MANOVA regression

Accepted Answer

Bivariate regression is specifically designed for analyzing the relationship between a single dependent variable and a single independent variable. ANOVA is used for analyzing the variance between groups, while multiple regression involves multiple independent variables. Univariate regression is a general term for any regression analysis involving a single dependent variable, but it does not specify the use of metric variables. MANOVA involves multiple dependent variables.

Question 5

The _____ method minimizes the distances from the straight line to all the points on a scatter diagram. It measures these distances by looking at the errors in predicting Y from X and minimizes the sum of the squared deviations between the actual values and the straight line predicted by the regression.
A) minimal squares
B) least squares
C) r-squared
D) regression sum of squares
E) residual sum of squares

Accepted Answer

The description matches the definition of least squares regression method.

Question 6

All of the following are assumptions of simple regression EXCEPT _____.
A) linear relationship
B) causality
C) metric measures
D) normally distributed population
E) independent and normally distributed error terms

Accepted Answer

Simple regression does not imply causality, but rather looks at the relationship between two variables. The other assumptions listed (linear relationship, metric measures, normally distributed population, independent and normally distributed error terms) are all requirements for simple regression.

Question 7

Which of the following assesses the statistical significance of the overall regression model? A) t statistic B) Spearman's rho C) correlation coefficient D) R² E) F-ratio

Accepted Answer

The F-ratio is used to assess the statistical significance of the overall regression model. The t-statistic is used to test the significance of individual coefficients, Spearman's rho measures the strength of monotonic association between two variables, and the correlation coefficient measures the strength of linear association between two variables. R² is not a known statistical measure.

Question 8

Which of the following tell us how much of the variance in the dependent variable is explained by the independent variable in regression?
A) regression coefficient
B) F-ratio
C) t statistic
D) Spearman's rho
E) VIF

Accepted Answer

The answer of Which of the following tell us how...

Question 9

_____ is a method of adjusting for different units of measure across variables. A) Multicollinearity B) Standardization C) Correlation D) Coefficient of determination E) Adjusted R²

Accepted Answer

Standardization (also known as normalization) is a method of adjusting for different units of measure across variables by subtracting the mean and dividing by the standard deviation. This results in a standardized score or z-score that represents how many standard deviations an observation is from the mean. It allows for meaningful comparisons between variables with different units of measure.

Question 10

The proportion of the variability in the dependent variable that can be explained by the several independent variables in the regression model is known as the _____.
A) multiple coefficient of determination
B) standardized beta
C) correlation coefficient
D) Pearson's rho
E) VIF

Accepted Answer

The multiple coefficient of determination (also known as R-squared) indicates the proportion of the variance in the dependent variable that can be accounted for by the independent variables in a multiple regression model. It ranges between 0 and 1, with higher values indicating a stronger relationship between the variables.

Question 11

Which of the following is used when you can predict the direction of your hypothesized relationship?
A) unstandardized test
B) standardized test
C) one-tailed test
D) two-tailed test
E) multi-tailed test

Accepted Answer

A one-tailed test is used when you can predict the direction of your hypothesized relationship. This means that you have a specific prediction about whether the relationship will be positive or negative. A one-tailed test allows you to focus exclusively on the direction you predicted, which can increase the power of your test.

Question 12

Frank has hypothesized a relationship between two variables, but he cannot predict the direction of the hypothesized relationship. Which of the following is appropriate in this situation?
A) unstandardized test
B) standardized test
C) one-tailed test
D) two-tailed test
E) multi-tailed test

Accepted Answer

A two-tailed test would be appropriate in this situation as it allows for the possibility of the relationship being in either direction, without making any assumptions about the direction. This is the most conservative approach, as it avoids the risk of falsely rejecting the null hypothesis if the relationship turns out to be in the opposite direction than initially hypothesized.

Question 13

Multicollinearity in multiple regression analysis refers to _____.
A) the correlation among the dependent variables
B) the correlation between the independent and dependent variables
C) level of significance of the model
D) the correlation among the independent variables
E) explained variance

Accepted Answer

Multicollinearity refers to the correlation among the independent variables in multiple regression analysis. It can cause issues with the accuracy and stability of the coefficients and can make it difficult to determine the individual effects of each independent variable on the dependent variable.

Question 14

Which of the following is NOT a problem caused by multicollinearity in multiple regression? A) The F-test of the overall multiple regression model may indicate a statistically significant relationship, but the t-tests for the individual coefficients may not indicate any as significant. B) The regression coefficients can have a sign opposite that of the actual relationship. C) It impacts the size of the R²and the ability to predict values of the dependent variable. D) With a high degree of collinearity we cannot rely on the individual coefficients to interpret the results. E) All of these choices are problems caused by multicollinearity in multiple regression.

Accepted Answer

Multicollinearity impacts the size of the R²and the ability to predict values of the dependent variable. The other options (A, B, D, E) are all problems caused by multicollinearity in multiple regression.

Question 15

How does a researcher know when multicollinearity is too high? A) A sample correlation coefficient between two independent variables is greater than ±0.60. B) The variance inflation factor equals zero. C) The variance inflation factor is equal to 1. D) The tolerance factor is high, such as greater than 1.0 E) The R² is less than 20%.

Accepted Answer

A sample correlation coefficient greater than ±0.60 indicates a high degree of correlation between two independent variables, which can indicate multicollinearity. Other factors such as variance inflation factor and tolerance can also be used to detect multicollinearity, but a high correlation coefficient is a good initial signal.

Question 16

A linear relationship is a straight-line association between two or more variables.

Accepted Answer

A linear relationship is characterized by a constant rate of change between two variables, resulting in a straight-line pattern on a graph.

Question 17

Covariation is when one variable consistently and systematically changes relative to another variable.

Accepted Answer

Covariation refers to the relationship between two variables where they consistently and systematically change in a corresponding way.

Question 18

A scatter diagram or scattergram plots the values of a variable for all observations within the sample.

Accepted Answer

A scatter diagram, or scatter plot, plots the values of two variables for all observations within the sample, showing the relationship between them.

Question 19

A Pearson correlation measures the linear association between two metric variables.

Accepted Answer

This statement is true. A Pearson correlation coefficient quantifies the direction and strength of the linear relationship between two metric (continuous) variables. It can range from -1 to 1, where -1 indicates a perfect negative relationship, 0 indicates no relationship, and 1 indicates a perfect positive relationship.

Question 20

The square of the correlation coefficient is called the coefficient of determination or r².

Accepted Answer

This statement is true. The coefficient of determination is calculated by squaring the correlation coefficient.

Quiz 14: Examining Relationships Using Correlation and Regression

If all variables are analyzed together and the goal is to form groups or give meaning to a set of variables or respondents, the statistical technique is referred to as a(n) _____ method.

Which of the following can be used to examine the statistical difference between the means of two or more groups if the dependent variable is metric and the independent variable(s) is nonmetric?

Billy has a dependent variable that is measured with ratio data. All of the following are statistical techniques that would be appropriate for him to use EXCEPT _____.

This type of regression has a single metric dependent variable and a single metric independent variable.

All of the following are assumptions of simple regression EXCEPT _____.

Which of the following assesses the statistical significance of the overall regression model?

Which of the following tell us how much of the variance in the dependent variable is explained by the independent variable in regression?

_____ is a method of adjusting for different units of measure across variables.

The proportion of the variability in the dependent variable that can be explained by the several independent variables in the regression model is known as the _____.

Which of the following is used when you can predict the direction of your hypothesized relationship?

Frank has hypothesized a relationship between two variables, but he cannot predict the direction of the hypothesized relationship. Which of the following is appropriate in this situation?

Multicollinearity in multiple regression analysis refers to _____.

Which of the following is NOT a problem caused by multicollinearity in multiple regression?

How does a researcher know when multicollinearity is too high?

A linear relationship is a straight-line association between two or more variables.

Covariation is when one variable consistently and systematically changes relative to another variable.

A scatter diagram or scattergram plots the values of a variable for all observations within the sample.

A Pearson correlation measures the linear association between two metric variables.

The square of the correlation coefficient is called the coefficient of determination or r2.

The square of the correlation coefficient is called the coefficient of determination or r².