Answer-first summary for fast verification
Answer: I and IV only
## Explanation Let's analyze each statement: **I. Correct** - In OLS regression, one of the key assumptions is that the error term has zero mean (E(ε) = 0) and constant variance (homoskedasticity). **II. Incorrect** - There is no assumption that the variance of the independent variable is positively correlated with the variance of the error term. In fact, the independent variable is assumed to be fixed (non-stochastic) in classical regression, or if stochastic, it should be uncorrelated with the error term. **III. Incorrect** - While the independent variable is assumed to be uncorrelated with the error term, the dependent variable (Y) is by definition correlated with the error term since Y = β₀ + β₁X + ε. The dependent variable depends directly on the error term. **IV. Correct** - The assumption of constant variance applies to both the error terms and the residuals. Homoskedasticity means the variance of residuals is constant across all levels of the independent variable. Therefore, only statements **I and IV** are correct, making option **C** the correct choice. **Key OLS Assumptions:** - Linearity in parameters - Random sampling - No perfect multicollinearity - Zero conditional mean of errors - Homoskedasticity - No autocorrelation - Normality of errors (for inference)
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Which of the following statements about the ordinary least squares regression model (or simple regression model) with one independent variable are correct?
I. In the ordinary least squares (OLS) model, the random error term is assumed to have zero mean and constant variance. II. In the OLS model, the variance of the independent variable is assumed to be positively correlated with the variance of the error term. III. In the OLS model, it is assumed that the correlation between the dependent variable and the random error term is zero. IV. In the OLS model, the variance of the residuals is assumed to be constant.
A
I, II, III and IV
B
II and IV only
C
I and IV only
D
I, II, and III only
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