Answer: (-5.97%, 9.37%)

**Step 1: Calculate the predicted value of WPO** Using the regression equation: WPO = -3.2% + 0.49(S&P 500) Given S&P 500 excess return = 10%: WPO = -3.2% + 0.49 × 10% = -3.2% + 4.9% = 1.7% **Step 2: Determine the critical t-value** - Sample size n = 32 - Degrees of freedom = n - 2 = 32 - 2 = 30 - For a 95% confidence interval with two-tailed test, α = 0.05, α/2 = 0.025 - t₀.₀₂₅,₃₀ = 2.04 (from t-distribution table) **Step 3: Calculate the margin of error** Margin of error = t-value × standard error of forecast = 2.04 × 3.76% = 7.67% **Step 4: Construct the confidence interval** CI = Predicted value ± Margin of error = 1.7% ± 7.67% = (1.7% - 7.67%, 1.7% + 7.67%) = (-5.97%, 9.37%) **Key concepts:** - Confidence intervals for regression predictions account for both parameter uncertainty and prediction error - The standard error of forecast incorporates both the regression coefficient uncertainty and the residual variance - Degrees of freedom for simple linear regression is n-2 (one for intercept, one for slope)

Author: Nikitesh Somanthe