MS-DS Master of Data science Exploratory Data Analysis 3 — Questions and Answers
Question 1: When computing Pearson correlation between two variables yields r = 0, what can be definitively concluded?
- The variables are statistically independent
- There is no linear relationship between the variables (Correct answer)
- One variable has no variance
- The variables have equal means
Correct answer: There is no linear relationship between the variables
Pearson r = 0 only rules out a linear association; nonlinear relationships (e.g., quadratic) can still exist with r = 0.
Question 2: Which plot is BEST suited for detecting heteroscedasticity in residuals after fitting a regression model?
- Histogram of residuals
- Residuals vs. fitted values plot (Correct answer)
- Q-Q plot of the response variable
- Pair plot of predictors
Correct answer: Residuals vs. fitted values plot
Plotting residuals against fitted values reveals fan-shaped or patterned spread, which indicates non-constant variance (heteroscedasticity).
Question 3: What is the interquartile range (IQR) used to define in the standard box plot outlier rule?
- The range of the entire dataset
- The spread of the middle 50% of data used to set whisker fences (Correct answer)
- The standard deviation of the distribution
- The distance between mode and median
Correct answer: The spread of the middle 50% of data used to set whisker fences
The standard Tukey rule flags points beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR as outliers, where IQR = Q3 − Q1.
Question 4: A dataset has 10% missing values in a predictor column. To determine whether the missingness is MCAR, MAR, or MNAR, which EDA step is most informative?
- Replacing missing values with the median immediately
- Comparing distributions of other variables between missing and non-missing groups (Correct answer)
- Removing all rows with missing values before analysis
- Computing the column mean ignoring missing values
Correct answer: Comparing distributions of other variables between missing and non-missing groups
If other variables differ systematically between the missing and observed groups, missingness is likely MAR or MNAR rather than completely random.
Question 5: In a time series EDA, a plot of autocorrelation function (ACF) shows significant spikes at lags 12, 24, and 36. What pattern does this indicate?
- A trend component
- Annual seasonality (period = 12) (Correct answer)
- Random white noise
- Structural break
Correct answer: Annual seasonality (period = 12)
Significant ACF spikes at multiples of 12 in monthly data indicate a recurring annual seasonal pattern.
Question 6: Which measure of spread is MOST appropriate when the distribution is heavily skewed?
- Standard deviation
- Variance
- Interquartile range (Correct answer)
- Range
Correct answer: Interquartile range
The IQR captures the spread of the central 50% of data and is resistant to the extreme values that inflate standard deviation and variance under skew.
Question 7: What does a mosaic plot primarily visualize?
- Distribution of a single continuous variable
- Association between two or more categorical variables (Correct answer)
- Correlation between two continuous variables
- Temporal trend in a numeric variable
Correct answer: Association between two or more categorical variables
A mosaic plot uses tile area to represent joint frequencies, making it easy to spot deviations from independence in categorical cross-tabulations.
MS-DS Master of Data science Exploratory Data Analysis 3
When computing Pearson correlation between two variables yields r = 0, what can be definitively concluded?