What is a common consequence of autocorrelation in linear regression?
Reduced model fit
Inflated standard errors of coefficients
Biased coefficient estimates
Heteroscedasticity
The Theil-Sen estimator is known for its robustness and non-parametric nature. What does 'non-parametric' imply in this context?
It does not require a dependent variable for model fitting
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 assumptions about the distribution of the data
What is the primary advantage of using Adjusted R-squared over R-squared when evaluating linear regression models?
Adjusted R-squared penalizes the inclusion of irrelevant variables.
Adjusted R-squared always increases when new predictors are added.
Adjusted R-squared is less sensitive to outliers compared to R-squared.
Adjusted R-squared is easier to interpret than R-squared.
Which technique is particularly useful for feature selection when dealing with high-dimensional datasets where the number of features exceeds the number of samples?
Ordinary Least Squares Regression
Elastic Net Regression
Ridge Regression
Lasso Regression
What is the primary difference between L1 and L2 regularization in the context of feature selection?
L1 regularization can shrink some feature coefficients to exactly zero, performing feature selection, while L2 regularization generally shrinks coefficients towards zero without making them exactly zero.
L1 regularization is less effective when dealing with highly correlated features compared to L2 regularization.
L2 regularization is more computationally expensive than L1 regularization.
L2 regularization forces the model to use all available features, while L1 regularization selects a subset of features.
How do hierarchical linear models help avoid misleading conclusions in nested data analysis?
By treating all observations as independent
By ignoring individual-level variations
By accounting for the correlation between observations within groups
By assuming all groups have the same effect on the outcome
What happens to the bias and variance of a linear regression model as the regularization parameter (lambda) increases?
Bias increases, Variance increases
Bias increases, Variance decreases
Bias decreases, Variance decreases
Bias decreases, Variance increases
When using Principal Component Analysis (PCA) as a remedy for multicollinearity, what is the primary aim?
To remove all independent variables from the model
To introduce non-linearity into the model
To increase the sample size of the dataset
To create new, uncorrelated variables from the original correlated ones
How do GLMs handle heteroscedasticity, a situation where the variance of residuals is not constant across the range of predictor values?
They ignore heteroscedasticity as it doesn't impact GLM estimations.
They use non-parametric techniques to adjust for heteroscedasticity.
They implicitly account for it by allowing the variance to be a function of the mean.
They require data transformations to stabilize variance before analysis.
How does the Variance Inflation Factor (VIF) quantify multicollinearity?
By measuring the correlation between two independent variables
By determining the difference between the predicted and actual values of the dependent variable
By calculating the proportion of variance in one independent variable explained by all other independent variables
By measuring the change in R-squared when an independent variable is added to the model