MS-DS Master of Data science FREE Master of Data Science: Statistical Inference & Regression Models Questions and Answers 3

Question 1

In ridge regression, what effect does increasing the regularization parameter lambda have on the coefficient estimates?

Accepted Answer

Coefficients are shrunk toward zero but remain nonzero

Answer

Coefficients are driven exactly to zero

Answer

Coefficients become larger in magnitude

Answer

Coefficients become unconstrained

Question 2

What is the interpretation of a 95% prediction interval for a new observation in linear regression?

Accepted Answer

A new individual observation will fall within this interval with approximately 95% probability

Answer

95% of the sample data falls within this interval

Answer

The true regression line falls within this interval 95% of the time

Answer

The mean response at that predictor value is within this interval 95% of the time

Question 3

Which method is most appropriate for handling non-constant variance (heteroscedasticity) in a regression model?

Accepted Answer

Using weighted least squares estimation

Answer

Adding more predictor variables

Answer

Increasing the sample size

Answer

Removing outliers from the dataset

Question 4

In the context of hypothesis testing for regression coefficients, what does a Type II error represent?

Accepted Answer

Failing to reject the null hypothesis when it is false

Answer

Rejecting the null hypothesis when it is true

Answer

Accepting the alternative hypothesis correctly

Answer

Rejecting the alternative hypothesis when it is true

Question 5

What is the key advantage of using adjusted R-squared over R-squared when comparing regression models?

Accepted Answer

It penalizes the addition of predictors that do not improve the model

Answer

It is always larger than R-squared

Answer

It measures the total variance in the data

Answer

It eliminates the need for residual analysis

Question 6

When bootstrapping is used for inference on a regression coefficient, what is the primary advantage over traditional parametric methods?

Accepted Answer

It does not require assumptions about the distribution of errors

Answer

It always produces narrower confidence intervals

Answer

It eliminates the need for a sufficiently large sample size

Answer

It guarantees unbiased coefficient estimates