MS-DS Master of Data science Statistical Inference & Regression Models 4

Question 1

LASSO regression differs from ridge regression primarily because LASSO:

Accepted Answer

Can reduce some coefficients exactly to zero, performing variable selection

Answer

LASSO's L1 penalty (λΣ|β|) can set coefficients to exactly zero, effectively performing automatic variable selection unlike ridge.

Question 2

A researcher applies the Box-Cox transformation to the response variable in a linear regression. The primary reason for this transformation is to:

Accepted Answer

Address non-normality and non-constant variance in residuals

Answer

The Box-Cox transformation finds an optimal power transformation of Y to better satisfy normality and homoscedasticity assumptions.

Question 3

In Bayesian inference, the posterior distribution is proportional to:

Accepted Answer

The likelihood times the prior

Answer

Bayes' theorem states posterior ∝ likelihood × prior, combining observed data evidence with prior beliefs.

Question 4

When using stepwise regression for variable selection, a major statistical concern is:

Accepted Answer

Inflated Type I error rates and optimistically biased model fit statistics

Answer

Stepwise selection involves multiple testing, inflating Type I error rates and producing overly optimistic R² and p-values for the selected model.

Question 5

The Gauss-Markov theorem guarantees that OLS estimators are BLUE. What does BLUE stand for?

Accepted Answer

Best Linear Unbiased Estimators

Answer

Gauss-Markov proves OLS produces Best (minimum variance) Linear Unbiased Estimators when its classical assumptions hold.

MS-DS Master of Data science Practice Test