MCQ without choices Flashcards
What is the primary objective of Functional Data Analysis (FDA)?
B. Analysing data collected over a continuous domain
Which statistical technique is commonly used in Functional Data Analysis for smoothing and summarizing data?
A. Functional Principal Component Analysis (FPCA)
In FDA, what does the term ”functional data” refer to?
C. Data with repeated measures over a continuum
Which of the following is a key assumption in Functional Data Analysis?
D. Functional smoothness
What role does the concept of a ”functional basis” play in Functional Data Analysis?
B. It provides a set of functions to represent data
Which of the following is not a characteristic of functional data?
C. Must be equally spaced or perfect measurements
Which of the following factors does not influence the selection of the smoothing parameter in functional data analysis?
D. Computational resources available
What does the smoothing parameter λ in functional data analysis control?
B. The degree of flexibility in the fitted curve
Which of the following statements about the smoothing parameter λ is true?
D. A larger smoothing parameter leads to a smoother curve
How does cross-validation help in selecting the smoothing parameter λ?
A. By minimising the sum of squared errors (SSE)
Which of the following techniques is commonly used to select the smoothing parameter λ in func-tional data analysis?
D. Generalized Cross-Validation (GCV)
What happens if the smoothing parameter λ is too small in functional data analysis?
B. Under-smoothing of the curve occurs
What happens if the smoothing parameter λ is too large in functional data analysis?
A. Over-smoothing of the curve occurs
What does the smoothing parameter λ control in Roughness Penalty Smoothing Method for functional data analysis?
C. The trade-off between smoothness and goodness of fit
What is the purpose of the smoothing parameter λ in functional data analysis?
D. To control the degree of smoothing in the fitted curve
What is the primary objective of Generalized Cross-Validation in determining the optimal smoothing parameter λ?
C. To select the smoothing parameter that generalizes best to unseen data
What is the primary objective of Functional Data Analysis (FDA)?
B. Analysing data collected over a continuous domain
What is the role of basis functions in functional data analysis?
C. To represent the functional data in terms of a finite set of functions
What is the primary purpose of a roughness penalty in functional data analysis?
A. To increase the complexity of the model
B. To penalize the smoothness of the fitted curve
C. To minimize the computational time required for analysis
D. To enforce linearity in the relationship between variables
B. To penalize the smoothness of the fitted curve
What is the main objective of Functional Linear Regression Analysis (FLRA)?
A. To estimate the functional relationship between two or more functional variables
B. To model the relationship between a functional or scalar response variable and one or more functional or scalar predictors
C. To compute the mean value of a functional variable
D. To identify outliers in functional data
B. To model the relationship between a functional or scalar response variable and one or more functional or scalar predictors
Which of the following best describes the difference between Traditional Linear Regression Analysis and Functional Linear Regression Analysis (FLRA)?
A. Traditional linear regression involves scalar variables, while FLRA involves functional variables
B. Traditional linear regression only considers fixed values for regression coefficients, while FLRA allows coefficients to vary as functions of time
C. Traditional linear regression only allows for one predictor variable, while FLRA can handle multiple functional predictors
D. Traditional linear regression assumes linear relationships, while FLRA assumes non-linear relationships
A. Traditional linear regression involves scalar variables, while FLRA involves functional variables
When might the Permutation F -Test methodology be used in Functional Linear Regression Analysis?
A. To estimate the functional relationship between two scalar variables
B. To assess the goodness of fit of the Functional Linear Regression model
C. To evaluate the statistical significance of relationships among functional independent variables and dependent variables
D. To determine the linearity assumption of the Functional Linear Regression mode
C. To evaluate the statistical significance of relationships among functional independent variables and dependent variables
Which of the following scenarios is not included in Functional Linear Regression Analysis?
A. The response variable is scalar or multivariate, and the independent variable is functional
B. The response variable is functional, and the independent variable is scalar
C. Both the response and independent variables are functional
D. Both the response and independent variables are scalars
D. Both the response and independent variables are scalars
What is the main objective of Functional Principal Component Analysis (FPCA)?
A. To identify outliers in functional data
B. To estimate the relationship between functional variables and scalar outcomes
C. To reduce the dimensionality of functional data while preserving the most important variability
D. To assess the goodness of fit of functional regression models
C. To reduce the dimensionality of functional data while preserving the most important variability