In educational research, what could be considered a 'group' when applying a multilevel model to student performance data?
Subjects (math, science, etc.)
Individual students
Classrooms or schools
Test scores
Which evaluation metric is particularly sensitive to outliers in the dependent variable?
Adjusted R-squared
MAE
R-squared
RMSE
In the context of GLMs, what is the purpose of the inverse link function?
To obtain predictions on the scale of the response variable
To estimate the variance of the response variable
To transform the predictor variables before analysis
To assess the goodness-of-fit of the GLM
What happens to the bias and variance of a linear regression model as the regularization parameter (lambda) increases?
Bias decreases, Variance increases
Bias increases, Variance decreases
Bias increases, Variance increases
Bias decreases, Variance decreases
Which of the following is a common indicator of multicollinearity when examining a correlation matrix?
Negative correlation coefficients between the dependent and independent variables
Low correlation coefficients between all independent variables
High correlation coefficients between some independent variables
High correlation coefficients between the dependent variable and independent variables
How do polynomial features help in capturing non-linear relationships in data?
They make the model less complex and easier to interpret.
They introduce non-linear terms, allowing the model to fit curved relationships.
They convert categorical variables into numerical variables.
They reduce the impact of outliers on the regression line.
What is a common consequence of autocorrelation in linear regression?
Biased coefficient estimates
Inflated standard errors of coefficients
Reduced model fit
Heteroscedasticity
What is the primary purpose of using hierarchical linear models (HLMs)?
To analyze data with nested or grouped structures.
To analyze data with a single level of variability.
To handle missing data in a linear regression model.
To improve the accuracy of predictions in linear regression.
What is the primary reason multicollinearity poses a problem in linear regression?
It reduces the model's predictive accuracy on new data.
It violates the assumption of linearity between the dependent and independent variables.
It inflates the variance of the regression coefficients, making them unreliable.
It makes the model too complex.
What is a key advantage of using Elastic Net Regression over Lasso Regression when dealing with highly correlated features?
Elastic Net tends to outperform Lasso when the number of features is much larger than the number of samples.
Elastic Net can select groups of correlated features together, while Lasso might select only one feature from the group.
Elastic Net is less prone to overfitting than Lasso when dealing with noisy datasets.
Elastic Net is computationally less expensive than Lasso for high-dimensional data.