Why might centering or scaling independent variables be insufficient to completely resolve multicollinearity?
It doesn't address the fundamental issue of high correlations between the variables.
It can make the model more complex and harder to interpret.
It requires a large sample size to be effective.
It only works for linear relationships between variables.
What does heteroscedasticity in a residual plot typically look like?
A straight line with non-zero slope
A random scattering of points
A funnel shape, widening or narrowing along the x-axis
A U-shape or inverted U-shape
What is the primary advantage of using Adjusted R-squared over R-squared when evaluating linear regression models?
Adjusted R-squared is less sensitive to outliers compared to R-squared.
Adjusted R-squared is easier to interpret than R-squared.
Adjusted R-squared penalizes the inclusion of irrelevant variables.
Adjusted R-squared always increases when new predictors are added.
In multiple linear regression, what does a coefficient of 0 for a predictor variable indicate?
The variable has a non-linear relationship with the outcome.
The variable is not statistically significant.
The variable is perfectly correlated with another predictor.
The variable has no impact on the predicted value.
Poisson regression, another type of GLM, is particularly well-suited for analyzing which kind of data?
Proportions or percentages
Count data of rare events
Ordinal data with a specific order
Continuous measurements
What does Adjusted R-squared penalize that R-squared does not?
Presence of outliers
Non-linearity in the relationship
Number of data points
Inclusion of irrelevant predictor variables
What is a key limitation of relying solely on Adjusted R-squared for model evaluation in linear regression?
It is difficult to interpret.
It can be misleading when comparing models with different numbers of predictors.
It is highly sensitive to outliers.
It doesn't provide information about the magnitude of prediction errors.
What does heteroscedasticity refer to in the context of multiple linear regression?
Multicollinearity among the predictor variables.
The presence of outliers in the data.
Non-constant variance of errors across different levels of the predictor variables.
Non-linearity in the relationship between predictors and outcome.
Logistic regression, a specific type of GLM, is best suited for modeling which type of response variable?
Time-to-event data
Binary (two categories)
Count data
Continuous
What is the primary purpose of using hierarchical linear models (HLMs)?
To analyze data with a single level of variability.
To handle missing data in a linear regression model.
To analyze data with nested or grouped structures.
To improve the accuracy of predictions in linear regression.