Poisson regression, another type of GLM, is particularly well-suited for analyzing which kind of data?
Count data of rare events
Continuous measurements
Ordinal data with a specific order
Proportions or percentages
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 assess the goodness-of-fit of the GLM
To obtain predictions on the scale of the response variable
Which of the following is NOT a valid approach to address multicollinearity?
Removing one or more of the highly correlated independent variables
Centering or scaling the independent variables
Increasing the sample size of the dataset
Transforming the independent variables (e.g., using principal component analysis)
You are comparing two linear regression models for predicting house prices. Model A has a lower RMSE than Model B. What does this imply about their predictive performance?
Model B is definitely overfitting the data.
Model A has a higher R-squared value than Model B.
Model A, on average, has smaller prediction errors than Model B.
Model A is guaranteed to make better predictions on all new data points.
What type of data is particularly well-suited for analysis using hierarchical linear models?
Cross-sectional data
Experimental data
Nested data
Time series data
What does a high Cook's distance value indicate?
The observation has low leverage but high influence
The observation is not an outlier
The observation has both high leverage and high influence
The observation has high leverage but low influence
Why is evaluating the model on a separate test set crucial in Polynomial Regression?
To estimate the model's performance on unseen data and assess its generalization ability.
To calculate the model's complexity and determine the optimal degree of the polynomial.
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.
Which of the following is a method for detecting outliers in linear regression?
Residual plots
Cook's distance
All of the above
Leverage values
Which metric is in the same units as the dependent variable, making it easier to interpret directly?
R-squared
RMSE
MAE
Adjusted R-squared
What does Adjusted R-squared penalize that R-squared does not?
Presence of outliers
Number of data points
Non-linearity in the relationship
Inclusion of irrelevant predictor variables