What is a common consequence of autocorrelation in linear regression?
Reduced model fit
Biased coefficient estimates
Heteroscedasticity
Inflated standard errors of coefficients
How do hierarchical linear models help avoid misleading conclusions in nested data analysis?
By assuming all groups have the same effect on the outcome
By ignoring individual-level variations
By treating all observations as independent
By accounting for the correlation between observations within groups
In the context of GLMs, what is the purpose of the inverse link function?
To transform the predictor variables before analysis
To estimate the variance of the response variable
To obtain predictions on the scale of the response variable
To assess the goodness-of-fit of the GLM
What type of data is particularly well-suited for analysis using hierarchical linear models?
Experimental data
Nested data
Time series data
Cross-sectional data
What happens to the bias and variance of a linear regression model as the regularization parameter (lambda) increases?
Bias increases, Variance increases
Bias decreases, Variance decreases
Bias decreases, Variance increases
Bias increases, Variance decreases
You are working with a dataset that has a skewed distribution of errors. Which metric would be a more appropriate measure of model performance?
RMSE, as it is less sensitive to skewed distributions.
Adjusted R-squared, as it is not affected by the distribution of errors.
MAE, as it is less influenced by extreme values in a skewed distribution.
R-squared, as it provides a standardized measure of fit.
In which scenario might you prefer Huber regression over RANSAC for robust regression?
When the outliers are expected to be clustered together
When dealing with high-dimensional data with a large number of features
When the proportion of outliers is relatively small
When it's important to completely discard the outliers from the analysis
Which technique is particularly useful for feature selection when dealing with high-dimensional datasets where the number of features exceeds the number of samples?
Lasso Regression
Ridge Regression
Elastic Net Regression
Ordinary Least Squares Regression
What distinguishes a random slope model from a random intercept model in HLM?
Random slope models allow slopes to vary, while random intercept models don't.
Random slope models are used for smaller datasets, while random intercept models are used for larger datasets.
Random slope models allow intercepts to vary, while random intercept models don't.
Random slope models handle categorical variables, while random intercept models handle continuous variables.
In which scenario would you prioritize using MAE over RMSE as your primary evaluation metric?
When you need a metric that is easy to compute.
When the dataset contains a large number of outliers.
When you want to give more weight to larger errors.
When you want a metric that is robust to outliers.