Question 1

A factor loading indicates how strongly a measured variable is correlated with a factor.

Accepted Answer

A factor loading is a measure that indicates the strength of the relationship between a measured variable and a factor. Therefore, the statement “A factor loading indicates how strongly a measured variable is correlated with a factor” is true. Factors can be used to explain relationships between variables and to reduce the complexity of data analysis.

Question 2

In multiple regression,the dependent variable must be continuous and interval-scaled.

Accepted Answer

Multiple regression is a statistical method used to explore the relationship between a dependent variable and two or more independent variables. The dependent variable in multiple regression must be continuous and interval-scaled, meaning it can take on any value on a continuous scale. Examples of continuous and interval-scaled variables include height, weight, temperature, and income. Variables that are not continuous and interval-scaled, such as categorical variables (e.g., gender, race, education level) or ordinal variables (e.g., Likert scales), cannot be used as dependent variables in multiple regression.

Question 3

Nominal and ordinal scales are referred to as metric scales.

Accepted Answer

These are nonmetric scales.

Question 4

The purpose of factor analysis is to summarize the information contained in a large number of variables into as large a number of factors as possible.

Accepted Answer

Factor analysis is a multivariate interdependence technique that statistically identifies a reduced number of factors from a larger number of measured variables.

Question 5

The type of measurement scales used will determine which multivariate statistical techniques are appropriate for the data.

Accepted Answer

Different multivariate statistical techniques are appropriate for different types of data scales, such as nominal, ordinal, interval, and ratio scales. It is important to choose the appropriate statistical method based on the scale of the data being analyzed.

Question 6

Multiple regression analysis includes a single independent variable but several dependent variables.

Accepted Answer

Multiple regression analysis is an extension of simple regression analysis allowing a metric dependent variable to be predicted by multiple independent variables.

Question 7

The basic types of multivariate techniques are metric methods and nonmetric methods.

Accepted Answer

The two basic types of mulitvariate techniques are dependence methods and interdependence methods.

Question 8

In multiple regression,the coefficient of multiple determination indicates the percentage of the variation in Y that can be explained by all independent variables.

Accepted Answer

The coefficient of multiple determination, also known as R squared, represents the proportion of variability in the dependent variable that can be explained by the independent variables in the model. It is expressed as a percentage ranging from 0% to 100%, with higher values indicating a better fit of the model to the data. Therefore, statement A is true.

Question 9

Multidimensional scaling is a type of interdependence method.

Accepted Answer

Multidimensional scaling is a type of interdependence method used to represent data in a lower-dimensional space while preserving the distances between objects or cases. It is often used in social sciences, marketing research, and psychology to analyze and visualize similarity or dissimilarity data.

Question 10

Partial correlations measure the variance inflation among independent variables.

Accepted Answer

Partial correlation is the correlation between two variables after taking into account the fact that they are correlated with other variables too.

Question 11

Multicollinearity in regression analysis refers to how strongly interrelated the independent variables in a model are.

Accepted Answer

Multicollinearity occurs when two or more independent variables in a regression model are highly correlated with each other, meaning they are interrelated. This can lead to issues with interpreting the significance and accuracy of coefficients, and can also make it difficult to determine the unique contribution of each variable to the dependent variable.

Question 12

Multivariate statistical analysis permit the researcher to consider the effects of three or more variables at the same time.

Accepted Answer

Multivariate statistical analysis involves analyzing the relationships between three or more variables simultaneously, making it possible for the researcher to consider the effects of multiple variables together.

Question 13

Discriminant analysis predicts a categorical dependent variable based on a linear combination of independent variables.

Accepted Answer

Discriminant analysis is a statistical technique used to classify individuals or objects into two or more categories based on a set of independent variables. It predicts a categorical dependent variable based on a linear combination of independent variables.

Question 14

In multiple regression,dummy variables are those that have no effect on the dependent variable.

Accepted Answer

A dummy variable uses 0 and 1 to code the different levels of a dichotomous variable.

Question 15

Mulitvariate dependence techniques are variants of the general linear model (GLM).

Accepted Answer

Multivariate dependence techniques, such as MANOVA and MANCOVA, are indeed variants of the general linear model.

Question 16

MANOVA predicts multiple continuous dependent variables with multiple continuous independent variables.

Accepted Answer

The independent variables are categorical.

Question 17

To determine whether the discriminant analysis can be used as a good predictor,information provided in the "confusion matrix" is used.

Accepted Answer

The confusion matrix provides information about the performance of the model in terms of correctly and incorrectly classified cases. From this information, we can calculate various metrics such as overall accuracy, sensitivity, specificity, and precision. These metrics can be used to evaluate the performance of the discriminant analysis model and determine if it is a good predictor or not.

Question 18

The variate is a mathematical way in which a set of variables can be represented with one equation.

Accepted Answer

The variate is indeed a mathematical representation of a set of variables with one equation.

Question 19

In a regression equation,the beta coefficients indicate the effect on the dependent variable of a 1-unit increase in any of the independent variables.

Accepted Answer

This statement is true. Beta coefficients in a regression equation represent the change in the dependent variable that occurs with a one-unit increase in the corresponding independent variable, while holding all other independent variables constant.

Question 20

Several dummy variables can be included in a regression model.

Accepted Answer

Dummy variables can be used to represent categorical variables in a regression model. They take on the values of 0 or 1 to indicate the absence or presence of a certain category, respectively. Multiple dummy variables can be included in a regression model to represent multiple categories.

Quiz 24: Introducing Multivariate Statistical Analysis