Data Science Data Science Statistical Concepts and Analysis Questions and Answers 3 — Questions and Answers
Question 1: What does the coefficient of determination (R-squared) value of 0.85 indicate in a regression model?
- The model has 85% accuracy
- 85% of the variance in the dependent variable is explained by the model (Correct answer)
- The correlation between variables is 0.85
- The model will predict correctly 85% of the time
Correct answer: 85% of the variance in the dependent variable is explained by the model
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?
- 0.05
- 0.01
- 0.0025 (Correct answer)
- 0.001
Correct answer: 0.0025
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?
- Rejecting a true null hypothesis
- Failing to reject a false null hypothesis (Correct answer)
- Rejecting a false null hypothesis
- Accepting a true null hypothesis
Correct answer: Failing to reject a false null hypothesis
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?
- The feature with the highest mean value
- The direction of maximum variance in the data (Correct answer)
- The variable most correlated with the target
- The axis with the least noise
Correct answer: The direction of maximum variance in the data
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?
- To increase the original sample size
- To estimate the sampling distribution of a statistic (Correct answer)
- To remove outliers from the dataset
- To perform feature selection
Correct answer: To estimate the sampling distribution of a statistic
Bootstrapping repeatedly resamples the data to approximate the sampling distribution of a statistic, enabling confidence interval estimation without parametric assumptions.
Question 6: In Bayesian statistics, what does the posterior distribution represent?
- The probability of the data given the model parameters
- The initial belief about parameters before observing data
- The updated belief about parameters after observing data (Correct answer)
- The likelihood function multiplied by a constant
Correct answer: The updated belief about parameters after observing data
The posterior distribution combines the prior belief with the observed data (via the likelihood) to produce an updated probability distribution over the parameters.
Data Science Data Science Statistical Concepts and Analysis Questions and Answers 3
What does the coefficient of determination (R-squared) value of 0.85 indicate in a regression model?