What type of data is particularly well-suited for analysis using hierarchical linear models?
Time series data
Cross-sectional data
Nested data
Experimental data
Which evaluation metric is particularly sensitive to outliers in the dependent variable?
RMSE
MAE
R-squared
Adjusted R-squared
What is a potential drawback of removing a highly correlated independent variable to deal with multicollinearity?
It may result in a loss of valuable information and reduce the model's accuracy.
It may improve the model's overall fit but reduce its interpretability.
It may lead to an increase in the model's complexity.
It has no drawbacks and is always the best solution.
What is the primary purpose of using hierarchical linear models (HLMs)?
To analyze data with a single level of variability.
To analyze data with nested or grouped structures.
To handle missing data in a linear regression model.
To improve the accuracy of predictions in linear regression.
Which robust regression technique is particularly well-suited for handling datasets with a high proportion of outliers?
Theil-Sen estimator
Huber regression
RANSAC (Random Sample Consensus)
Ordinary Least Squares (OLS) regression
Which metric is in the same units as the dependent variable, making it easier to interpret directly?
If a predictor has a p-value of 0.02 in a multiple linear regression model, what can you conclude?
The predictor explains 2% of the variance in the outcome.
The predictor has a practically significant effect on the outcome.
The predictor is not statistically significant.
The predictor is statistically significant at the 0.05 level.
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.
L2 regularization forces the model to use all available features, while L1 regularization selects a subset of features.
L2 regularization is more computationally expensive than L1 regularization.
L1 regularization is less effective when dealing with highly correlated features compared to L2 regularization.
What does a high Cook's distance value indicate?
The observation has both high leverage and high influence
The observation is not an outlier
The observation has low leverage but high influence
The observation has high leverage but low influence
In multiple linear regression, what does a coefficient of 0 for a predictor variable indicate?
The variable has no impact on the predicted value.
The variable is not statistically significant.
The variable has a non-linear relationship with the outcome.
The variable is perfectly correlated with another predictor.