What distinguishes a random slope model from a random intercept model in HLM?
Random slope models handle categorical variables, while random intercept models handle continuous variables.
Random slope models are used for smaller datasets, while random intercept models are used for larger datasets.
Random slope models allow slopes to vary, while random intercept models don't.
Random slope models allow intercepts to vary, while random intercept models don't.
What does Adjusted R-squared penalize that R-squared does not?
Non-linearity in the relationship
Inclusion of irrelevant predictor variables
Number of data points
Presence of outliers
How do Generalized Linear Models (GLMs) extend the capabilities of linear regression?
By enabling the response variable to follow different distributions beyond just normal distribution.
By assuming a strictly linear relationship between the response and predictor variables.
By allowing only categorical predictor variables.
By limiting the analysis to datasets with a small number of observations.
What hyperparameter controls the strength of regularization in Ridge, Lasso, and Elastic Net Regression?
Learning Rate
Number of Iterations
Regularization Parameter
Tolerance
Which of the following scenarios would benefit from using a hierarchical linear model?
Analyzing the effect of a new drug on patients in different hospitals
Classifying emails as spam or not spam
Predicting the price of a house based on its size and location
Forecasting stock prices based on historical data
How does the Variance Inflation Factor (VIF) quantify multicollinearity?
By measuring the change in R-squared when an independent variable is added to the model
By calculating the proportion of variance in one independent variable explained by all other independent variables
By measuring the correlation between two independent variables
By determining the difference between the predicted and actual values of the dependent variable
What is a common consequence of autocorrelation in linear regression?
Reduced model fit
Inflated standard errors of coefficients
Heteroscedasticity
Biased coefficient estimates
How does stepwise selection work in feature selection?
It iteratively adds or removes features based on a statistical criterion, aiming to find the best subset.
It ranks features based on their correlation with the target variable and selects the top-k features.
It uses L1 or L2 regularization to shrink irrelevant feature coefficients to zero.
It transforms the original features into a lower-dimensional space while preserving important information.
Why is evaluating the model on a separate test set crucial in Polynomial Regression?
To calculate the model's complexity and determine the optimal degree of the polynomial.
To estimate the model's performance on unseen data and assess its generalization ability.
To visualize the residuals and check for any non-linear patterns.
To fine-tune the model's hyperparameters and improve its fit on the training data.
What is the primary reason multicollinearity poses a problem in linear regression?
It makes the model too complex.
It inflates the variance of the regression coefficients, making them unreliable.
It violates the assumption of linearity between the dependent and independent variables.
It reduces the model's predictive accuracy on new data.