In educational research, what could be considered a 'group' when applying a multilevel model to student performance data?
Classrooms or schools
Test scores
Subjects (math, science, etc.)
Individual students
How do you interpret a standardized coefficient (beta) in multiple linear regression?
It determines the goodness of fit of the regression model.
It represents the unstandardized effect of the predictor on the outcome.
It represents the effect of a one-unit change in the predictor on the outcome, in standard deviation units.
It indicates the statistical significance of the predictor.
If we add more independent variables to a linear regression model, what will happen to the R-squared value?
Depend on the significance of the added variables
Remain the same
Always decrease
Always increase
Which robust regression technique is particularly well-suited for handling datasets with a high proportion of outliers?
RANSAC (Random Sample Consensus)
Ordinary Least Squares (OLS) regression
Huber regression
Theil-Sen estimator
What is the primary role of a link function in a Generalized Linear Model?
It transforms the predictor variables to follow a normal distribution.
It calculates the residuals between the observed and predicted values.
It establishes a connection between the linear predictor and the mean of the response variable.
It determines the optimal number of predictor variables to include in the model.
What is the primary purpose of using hierarchical linear models (HLMs)?
To analyze data with nested or grouped structures.
To improve the accuracy of predictions in linear regression.
To handle missing data in a linear regression model.
To analyze data with a single level of variability.
The performance of the Theil-Sen estimator can be sensitive to which characteristic of the data?
The presence of multicollinearity (high correlation between independent variables)
The non-normality of the residuals
The presence of categorical variables
The presence of heteroscedasticity (unequal variances of errors)
The Theil-Sen estimator is known for its robustness and non-parametric nature. What does 'non-parametric' imply in this context?
It does not have any parameters that need to be estimated from the data
It does not require a linear relationship between the variables
It does not require a dependent variable for model fitting
It does not require assumptions about the distribution of the data
A model has a high R-squared but a low Adjusted R-squared. What is a likely explanation?
The model has high bias.
The model is overfitting.
The model is a perfect fit.
The model is too simple.
How does Lasso Regression differ from Ridge Regression in terms of feature selection?
Ridge Regression tends to shrink all coefficients towards zero but rarely sets them exactly to zero.
Lasso Regression can shrink coefficients to exactly zero, effectively performing feature selection.
Neither Lasso nor Ridge Regression performs feature selection; they only shrink coefficients.
Both Lasso and Ridge Regression can shrink coefficients to zero, but Lasso does it more aggressively.