求 95% confidence internval的表述

问题如下：

Using information from Exhibit 2, Vasileva should compute the 95% prediction interval for Amtex share return for month 37 to be:

选项：

–0.0882 to 0.1025.

–0.0835 to 0.1072.

0.0027 to 0.0116.

解释：

A is correct. The 95% prediction iinterval for the dependent variable given a certain value of the independent variable is calculated as:

Prediction interval = $\widehat{Y}\pm{t_{c}s_f}$

and the predicted value $\widehat{Y}=\widehat{b}_0+\widehat{b}_1X_i$

Therefore:

Predicted value = 0.0095 + (0.2354 × (–0.01)) = 0.0071

$s_f={0.0022}^{0.5}=0.0469$

$t_c=2.032$

The lower limit for the prediction interval = 0.0071 – (2.032 × 0.0469) = –0.0882

The upper limit for the prediction interval = 0.0071 + (2.032 × 0.0469) = 0.1025