MRA Statistical Analysis & Interpretation 3 — Questions and Answers
Question 1: A regression model has an adjusted R² of 0.62. What does this indicate?
- 62% of variance in the outcome is explained by predictors, adjusted for model complexity (Correct answer)
- 62% of the data points fall within one standard deviation
- The model has a 62% chance of predicting correctly
- 62% of predictors are statistically significant
Correct answer: 62% of variance in the outcome is explained by predictors, adjusted for model complexity
Adjusted R² measures explained variance while penalizing for unnecessary predictors, making it useful for model comparison.
Question 2: What is multicollinearity in regression analysis?
- When residuals are not normally distributed
- When two or more predictor variables are highly correlated with each other (Correct answer)
- When the outcome variable has multiple modes
- When sample size is too small for regression
Correct answer: When two or more predictor variables are highly correlated with each other
Multicollinearity occurs when predictors are highly intercorrelated, making it difficult to isolate individual effects.
Question 3: A market researcher conducts 20 significance tests simultaneously without correction. What problem does this create?
- Decreased statistical power
- Inflated Type I error rate (false positives) (Correct answer)
- Increased Type II error rate
- Reduced sample representativeness
Correct answer: Inflated Type I error rate (false positives)
Running multiple tests without adjustment inflates the familywise error rate, increasing the chance of at least one false positive.
Question 4: Which measure best describes the 'average distance' of data points from the mean?
- Variance
- Standard deviation (Correct answer)
- Range
- Coefficient of variation
Correct answer: Standard deviation
Standard deviation is expressed in the same units as the data and represents average deviation from the mean.
Question 5: In factor analysis, what does 'communality' measure?
- The total variance of the factor solution
- The proportion of a variable's variance explained by the extracted factors (Correct answer)
- The correlation between two factors
- The number of factors retained
Correct answer: The proportion of a variable's variance explained by the extracted factors
Communality is the proportion of each observed variable's variance accounted for by the common factors.
Question 6: A skewed distribution has a mean of 80, median of 75, and mode of 70. What type of skew does this indicate?
- Negative (left) skew
- Positive (right) skew (Correct answer)
- Symmetric distribution
- Bimodal distribution
Correct answer: Positive (right) skew
When mean > median > mode, the tail extends to the right, indicating positive (right) skew.
Question 7: What is the purpose of bootstrapping in statistical analysis?
- To increase sample size through recruitment
- To estimate sampling distributions by resampling from existing data with replacement (Correct answer)
- To remove outliers from a dataset
- To standardize variables to a common scale
Correct answer: To estimate sampling distributions by resampling from existing data with replacement
Bootstrapping repeatedly resamples the collected data to empirically build sampling distributions and estimate confidence intervals.
MRA Statistical Analysis & Interpretation 3
A regression model has an adjusted R² of 0.62.
What does this indicate?