Which of the following is a method for detecting outliers in linear regression?
Leverage values
All of the above
Cook's distance
Residual plots
Which metric penalizes large errors more heavily than smaller errors, making it particularly sensitive to outliers?
R-squared
Root Mean Squared Error (RMSE)
Adjusted R-squared
Mean Absolute Error (MAE)
What distinguishes a random slope model from a random intercept model in HLM?
Random slope models are used for smaller datasets, while random intercept models are used for larger datasets.
Random slope models handle categorical variables, while random intercept models handle continuous variables.
Random slope models allow intercepts to vary, while random intercept models don't.
Random slope models allow slopes to vary, while random intercept models don't.
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
Lasso Regression
Ridge Regression
Elastic Net Regression
What does the adjusted R-squared value tell you in multiple linear regression?
The presence of outliers in the data.
The statistical significance of the overall model.
The accuracy of the model's predictions.
The proportion of variance in the outcome explained by the predictors, adjusted for the number of predictors in the model.
What is the primary goal of regularization techniques in linear regression?
To prevent overfitting by adding a penalty to the complexity of the model.
To speed up the training process of the linear regression model.
To handle missing data points in the dataset more effectively.
To improve model interpretability by selecting only the most relevant features.
Which of the following is a common method for addressing multicollinearity in multiple linear regression?
Increasing the sample size.
Removing one or more of the correlated predictor variables.
Ignoring the issue, as it has no impact on the model.
Transforming the outcome variable.
Which of the following robust regression methods iteratively identifies and removes outliers before fitting a standard linear regression model?
None of the above
RANSAC (Random Sample Consensus)
Theil-Sen estimator
Huber regression
Which of the following scenarios would benefit from using a hierarchical linear model?
Forecasting stock prices based on historical data
Predicting the price of a house based on its size and location
Analyzing the effect of a new drug on patients in different hospitals
Classifying emails as spam or not spam
How do polynomial features help in capturing non-linear relationships in data?
They make the model less complex and easier to interpret.
They convert categorical variables into numerical variables.
They reduce the impact of outliers on the regression line.
They introduce non-linear terms, allowing the model to fit curved relationships.