What does Adjusted R-squared penalize that R-squared does not?
Non-linearity in the relationship
Number of data points
Presence of outliers
Inclusion of irrelevant predictor variables
The performance of the Theil-Sen estimator can be sensitive to which characteristic of the data?
The non-normality of the residuals
The presence of multicollinearity (high correlation between independent variables)
The presence of heteroscedasticity (unequal variances of errors)
The presence of categorical variables
Which metric penalizes large errors more heavily than smaller errors, making it particularly sensitive to outliers?
Mean Absolute Error (MAE)
Root Mean Squared Error (RMSE)
Adjusted R-squared
R-squared
Which regularization technique adds a penalty term proportional to the sum of the squared absolute values of the coefficients to the cost function?
Ridge Regression
Elastic Net
Lasso Regression
Linear Regression
Which of the following scenarios would benefit from using a hierarchical linear model?
Forecasting stock prices based on historical data
Classifying emails as spam or not spam
Analyzing the effect of a new drug on patients in different hospitals
Predicting the price of a house based on its size and location
In Polynomial Regression, how does model interpretation change compared to simple Linear Regression?
It becomes more complex as the relationship between the target and predictors might not be linear.
Interpretation is not relevant in Polynomial Regression.
Polynomial Regression makes no difference to model interpretation.
It becomes simpler because polynomial terms capture more variance, making the model easier to understand.
What does heteroscedasticity in a residual plot typically look like?
A U-shape or inverted U-shape
A random scattering of points
A straight line with non-zero slope
A funnel shape, widening or narrowing along the x-axis
What happens to the bias and variance of a linear regression model as the regularization parameter (lambda) increases?
Bias decreases, Variance increases
Bias increases, Variance decreases
Bias increases, Variance increases
Bias decreases, Variance decreases
If we add more independent variables to a linear regression model, what will happen to the R-squared value?
Always decrease
Remain the same
Always increase
Depend on the significance of the added variables
What is the primary motivation for using robust regression over ordinary least squares (OLS) regression?
To reduce the computational complexity of the regression analysis
To handle datasets with non-linear relationships between variables more effectively
To mitigate the impact of outliers on the fitted regression line
To improve the interpretability of the regression coefficients