本题详解

问题如下：

Elena Vasileva recently joined EnergyInvest as a junior portfolio analyst. Vasileva’s supervisor asks her to evaluate a potential investment opportunity in Amtex, a multinational oil and gas corporation based in the United States. Vasileva’s supervisor suggests using regression analysis to examine the relation between Amtex shares and returns on crude oil.

Vasileva notes the following assumptions of regression analysis:

■ Assumption 1. The error term is uncorrelated across observations.

■ Assumption 2. The variance of the error term is the same for all observations.

■ Assumption 3. The dependent variable is normally distributed.

Vasileva runs a regression of Amtex share returns on crude oil returns using the monthly data she collected. Selected data used in the regression are presented in Exhibit 1, and selected regression output is presented in Exhibit 2. She uses a 1 percent level of significance in all her tests.

Critical t-values for a 1 percent level of significance:

One-sided, left side: −2.441

One-sided, right side: +2.441

Two-sided: ±2.728

Vasileva expects the crude oil return next month, Month 37, to be −0.01. She computes the standard error of the forecast to be 0.0469.

Using information from Exhibit 2, the 99 percent prediction interval for Amtex share return for Month 37 is best described as:

选项：

Yˆ f ± 0.0053.

Yˆ f ± 0.0469.

Yˆ f ± 0.1279.

解释：

C is correct. The predicted share return is 0.0095 + [0.2354 × (−0.01)] = 0.0071.

The lower limit for the prediction interval is 0.0071 − (2.728 × 0.0469) = −0.1208, and the upper limit for the prediction interval is 0.0071 + (2.728 × 0.0469) =0.1350.

A is incorrect because the bounds of the interval should be based on the standard error of the forecast and the critical t-value, not on the mean of the dependent variable.

B is incorrect because bounds of the interval are based on the product of the standard error of the forecast and the critical t-value, not simply the standard error of the forecast.