Data Science Data Science Statistical Concepts and Analysis Questions and Answers 2 — Questions and Answers
Question 1: A data scientist observes that two variables have a Pearson correlation coefficient of -0.92. What does this indicate?
- A strong positive linear relationship
- A strong negative linear relationship (Correct answer)
- No linear relationship
- A weak negative linear relationship
Correct answer: A strong negative linear relationship
A Pearson correlation of -0.92 indicates a strong negative linear relationship, meaning as one variable increases, the other decreases proportionally.
Question 2: Which assumption is NOT required for a valid ordinary least squares (OLS) linear regression?
- Linearity between predictors and response
- Homoscedasticity of residuals
- Normal distribution of independent variables (Correct answer)
- Independence of observations
Correct answer: Normal distribution of independent variables
OLS regression requires normality of residuals, not normality of the independent variables themselves.
Question 3: In a hypothesis test, a p-value of 0.03 with a significance level of 0.05 leads to which conclusion?
- Fail to reject the null hypothesis
- Reject the null hypothesis (Correct answer)
- Accept the alternative hypothesis as proven
- The test is inconclusive
Correct answer: Reject the null hypothesis
Since the p-value (0.03) is less than the significance level (0.05), we reject the null hypothesis.
Question 4: What is the primary purpose of cross-validation in predictive modeling?
- To increase the training dataset size
- To estimate how well a model generalizes to unseen data (Correct answer)
- To eliminate all bias from the model
- To select the features with highest correlation
Correct answer: To estimate how well a model generalizes to unseen data
Cross-validation estimates a model's generalization performance by repeatedly training and testing on different subsets of the data.
Question 5: A dataset has a mean of 50, a median of 42, and a mode of 38. What type of skewness does this distribution exhibit?
- Negative skew
- No skew
- Positive skew (Correct answer)
- Bimodal distribution
Correct answer: Positive skew
When the mean is greater than the median, which is greater than the mode, the distribution is positively (right) skewed.
Question 6: Which metric is most appropriate for evaluating a classification model when the dataset has a 95:5 class imbalance?
- Accuracy
- F1 Score (Correct answer)
- R-squared
- Mean Absolute Error
Correct answer: F1 Score
The F1 Score balances precision and recall, making it far more informative than accuracy when classes are heavily imbalanced.
Data Science Data Science Statistical Concepts and Analysis Questions and Answers 2
A data scientist observes that two variables have a Pearson correlation coefficient of -0.92.
What does this indicate?