CBE CBE Business Statistics and Data Analysis 2 — Questions and Answers
Question 1: Heteroskedasticity in a regression model refers to:
- Multicollinearity among independent variables
- Non-constant variance of the error terms across observations (Correct answer)
- A non-linear relationship between variables
- Correlation between the error term and regressors
Correct answer: Non-constant variance of the error terms across observations
Heteroskedasticity occurs when the variance of regression residuals is not constant across all levels of the independent variables, violating a key OLS assumption.
Question 2: The Gini coefficient is used in business economics primarily to measure:
- Price level changes over time
- The degree of income or wealth inequality in a distribution (Correct answer)
- Market concentration in an industry
- Productivity growth across firms
Correct answer: The degree of income or wealth inequality in a distribution
The Gini coefficient ranges from 0 (perfect equality) to 1 (perfect inequality) and is the standard measure of income or wealth distribution inequality.
Question 3: In econometrics, instrumental variable (IV) estimation is used to address:
- Multicollinearity in large datasets
- Endogeneity bias when regressors are correlated with the error term (Correct answer)
- Non-stationarity in time series data
- Small sample bias in linear models
Correct answer: Endogeneity bias when regressors are correlated with the error term
IV estimation uses an instrument—a variable correlated with the endogenous regressor but not with the error term—to obtain consistent coefficient estimates.
Question 4: A business economist uses index numbers primarily to:
- Calculate nominal GDP from real GDP data
- Compare values across time or groups relative to a base period (Correct answer)
- Measure the volatility of financial asset returns
- Estimate the statistical significance of economic trends
Correct answer: Compare values across time or groups relative to a base period
Index numbers express values as a percentage relative to a base period (typically 100), enabling comparisons of prices, outputs, or other variables over time.
Question 5: Which statistical test is most appropriate for comparing whether the means of two independent groups are significantly different?
- Chi-square test
- F-test for overall regression significance
- Two-sample t-test (Correct answer)
- Durbin-Watson test
Correct answer: Two-sample t-test
The two-sample (independent samples) t-test evaluates whether the population means of two separate groups differ, assuming approximate normality.
Question 6: In the context of business forecasting, the mean absolute percentage error (MAPE) is used to:
- Identify structural breaks in a time series
- Measure forecast accuracy as a percentage of actual values (Correct answer)
- Decompose a series into trend, seasonal, and cyclical components
- Test whether residuals follow a normal distribution
Correct answer: Measure forecast accuracy as a percentage of actual values
MAPE expresses forecast errors as a percentage of actual values, providing an intuitive, scale-independent measure of model accuracy.
CBE CBE Business Statistics and Data Analysis 2
Heteroskedasticity in a regression model refers to: