CBE CBE Business Statistics and Data Analysis 1 — Questions and Answers
Question 1: In regression analysis, the R-squared (R²) statistic measures:
- The slope of the regression line
- The proportion of variance in the dependent variable explained by the independent variable(s) (Correct answer)
- The statistical significance of individual coefficients
- The correlation between two independent variables
Correct answer: The proportion of variance in the dependent variable explained by the independent variable(s)
R² ranges from 0 to 1 and indicates how well the regression model fits the data by showing the share of variance in the outcome explained by the predictors.
Question 2: A Type I error in hypothesis testing occurs when:
- A false null hypothesis is not rejected
- A true null hypothesis is incorrectly rejected (Correct answer)
- The sample size is too small to detect an effect
- The test statistic exceeds the critical value
Correct answer: A true null hypothesis is incorrectly rejected
A Type I error (false positive) is the mistake of rejecting the null hypothesis when it is actually true, with its probability equal to the significance level α.
Question 3: Which measure of central tendency is most affected by extreme outliers in a dataset?
- Mode
- Median
- Mean (Correct answer)
- Interquartile range
Correct answer: Mean
The mean is calculated using all values in the dataset, so extreme outliers pull it significantly away from the center of the distribution.
Question 4: In time series analysis, autocorrelation refers to:
- The correlation between two different economic variables
- The correlation of a variable with its own past values (Correct answer)
- The relationship between sample size and variance
- The degree to which a variable follows a normal distribution
Correct answer: The correlation of a variable with its own past values
Autocorrelation (serial correlation) measures the degree to which a time series is correlated with lagged versions of itself, violating OLS regression assumptions.
Question 5: The standard error of the mean (SEM) decreases as:
- Population variance increases
- Sample size increases (Correct answer)
- Confidence level increases
- The number of variables in the model increases
Correct answer: Sample size increases
SEM equals the population standard deviation divided by the square root of sample size, so larger samples produce more precise estimates of the population mean.
Question 6: A 95% confidence interval for a population parameter means:
- There is a 95% probability the parameter falls in this interval
- If repeated samples were taken, 95% of such intervals would contain the true parameter (Correct answer)
- The sample statistic is within 5% of the true value
- The data has a 5% measurement error rate
Correct answer: If repeated samples were taken, 95% of such intervals would contain the true parameter
A 95% CI is a frequentist concept meaning that the construction procedure produces intervals containing the true parameter 95% of the time across repeated sampling.
CBE CBE Business Statistics and Data Analysis 1
In regression analysis, the R-squared (R²) statistic measures: