How do Generalized Linear Models (GLMs) extend the capabilities of linear regression?
By assuming a strictly linear relationship between the response and predictor variables.
By enabling the response variable to follow different distributions beyond just normal distribution.
By limiting the analysis to datasets with a small number of observations.
By allowing only categorical predictor variables.
What does a Variance Inflation Factor (VIF) value greater than 10 generally suggest?
Heteroscedasticity
Perfect multicollinearity
Severe multicollinearity
No multicollinearity
Logistic regression, a specific type of GLM, is best suited for modeling which type of response variable?
Continuous
Time-to-event data
Count data
Binary (two categories)
The performance of the Theil-Sen estimator can be sensitive to which characteristic of the data?
The presence of heteroscedasticity (unequal variances of errors)
The presence of multicollinearity (high correlation between independent variables)
The presence of categorical variables
The non-normality of the residuals
What is the primary goal of regularization techniques in linear regression?
To speed up the training process of the linear regression model.
To prevent overfitting by adding a penalty to the complexity of the model.
To handle missing data points in the dataset more effectively.
To improve model interpretability by selecting only the most relevant features.
What does heteroscedasticity refer to in the context of multiple linear regression?
The presence of outliers in the data.
Non-constant variance of errors across different levels of the predictor variables.
Multicollinearity among the predictor variables.
Non-linearity in the relationship between predictors and outcome.
Which of the following is a potential drawback of using robust regression methods?
They are not applicable to datasets with categorical variables
They always require data normalization before model fitting
They can be computationally more expensive than OLS regression
They always result in models with lower predictive accuracy than OLS regression
What advantage does Polynomial Regression offer over simple Linear Regression when dealing with non-linear relationships between variables?
It simplifies the model, making it easier to interpret.
It always results in a better fit regardless of the data distribution.
It introduces polynomial terms, enabling the model to fit curved relationships in the data.
It reduces the need for feature scaling.
What happens to the bias and variance of a linear regression model as the regularization parameter (lambda) increases?
Bias increases, Variance decreases
Bias increases, Variance increases
Bias decreases, Variance decreases
Bias decreases, Variance increases
What does multicollinearity refer to in the context of multiple linear regression?
A high correlation between the outcome variable and a predictor variable.
A high correlation between two or more predictor variables.