Data Science Data Science Statistical Concepts and Analysis Questions and Answers 3

Question 1

What does the coefficient of determination (R-squared) value of 0.85 indicate in a regression model?

Accepted Answer

85% of the variance in the dependent variable is explained by the model

Answer

The model has 85% accuracy

Answer

The correlation between variables is 0.85

Answer

The model will predict correctly 85% of the time

Question 2

A data scientist applies the Bonferroni correction when conducting 20 simultaneous hypothesis tests at alpha = 0.05. What is the adjusted significance level for each individual test?

Accepted Answer

0.0025

Answer

0.05

Answer

0.01

Answer

0.001

Question 3

Which of the following best describes a Type II error in statistical testing?

Accepted Answer

Failing to reject a false null hypothesis

Answer

Rejecting a true null hypothesis

Answer

Rejecting a false null hypothesis

Answer

Accepting a true null hypothesis

Question 4

When applying Principal Component Analysis (PCA), what does the first principal component represent?

Accepted Answer

The direction of maximum variance in the data

Answer

The feature with the highest mean value

Answer

The variable most correlated with the target

Answer

The axis with the least noise

Question 5

A bootstrap sampling procedure draws 1,000 samples of size n with replacement from the original dataset. What is the primary purpose of this technique?

Accepted Answer

To estimate the sampling distribution of a statistic

Answer

To increase the original sample size

Answer

To remove outliers from the dataset

Answer

To perform feature selection

Question 6

In Bayesian statistics, what does the posterior distribution represent?

Accepted Answer

The updated belief about parameters after observing data

Answer

The probability of the data given the model parameters

Answer

The initial belief about parameters before observing data

Answer

The likelihood function multiplied by a constant