Explanation

To determine the 95% prediction interval for the stock's monthly return, follow these steps:

1. Calculate the predicted value of the dependent variable (Yf): The predicted value is derived using the estimated intercept (b0) and slope (b1) of the regression model, along with the forecasted value of the independent variable (Xf). $Yf = b0 + b1 \times Xf$ Substituting the given values: $Yf = 1.2\% + 1.0 \times 3.5\% = 4.7\%$

2. Construct the prediction interval: The prediction interval accounts for the uncertainty in the forecast and is calculated as: $Yf \pm (t_{\text{critical}} \times S_f)$ Where:

   • $t_{\text{critical}}$ is the critical t-value (±2.032 for a 5% significance level).
   • $S_f$ is the standard error of the forecast (1.4%).

   Substituting the values: $4.7\% \pm (2.032 \times 1.4\%) = 4.7\% \pm 2.8448\%$ This results in the interval: $(1.8552\%, 7.5448\%)$ Rounded to one decimal place, the interval is approximately 1.9% to 7.5%.

Why Option B is Correct:

• It correctly incorporates the predicted value of the dependent variable and the critical t-values to construct the prediction interval.

Why Option A is Incorrect:

• It mistakenly uses the forecasted value of the independent variable (3.5%) directly, leading to an incorrect interval.

Why Option C is Incorrect:

• It neglects the critical t-values, resulting in an overly narrow interval.