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

An R-squared of 0.85 means the independent variables in the model explain 85% of the variance in the dependent variable.

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

The Bonferroni correction divides the overall significance level by the number of tests: 0.05 / 20 = 0.0025.

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

A Type II error occurs when we fail to reject the null hypothesis even though it is actually false, meaning we miss a real effect.

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 first principal component captures the direction (linear combination of features) along which the data exhibits the greatest variance.

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

Bootstrapping repeatedly resamples the data to approximate the sampling distribution of a statistic, enabling confidence interval estimation without parametric assumptions.

Data Science Practice Test

Data Science Practice Test

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