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粗眉毛辣椒油 · 2024年02月07日

题目和答案解析

  1. FRM I
  2. Quantitative

NO.PZ2020010304000054

问题如下：

Suppose that for a linear regression, an estimation of slope is stated as having a one-sided p-value of 0.04. What does this mean?

选项：

解释：

The p-value tells us the “probability of observing a test statistic that is more extreme than the one computed from the observed data when the null hypothesis is true.” In other words, if the estimate of the slope is true, then in a randomized trial the probability of getting a larger new slope estimate is 4%.Assuming a normal distribution, this will correspond to the value of x that solves the following equation:

1 - Φ(x) = 0.04

Using the excel function NORMSINV gives x = 1.75.

不太懂题目的考点，也不明白解析。

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1 个答案

李坏_品职助教 · 2024年02月08日

嗨，从没放弃的小努力你好：


题目的意思是，在线性回归中，斜率（slope）估计值的单尾（one-sided）p值是0.04，问你这是啥意思？


单尾0.04的p值意味着：如果斜率（slope）的估计值是准确的，那么我们随机挑选一个样本，样本的斜率值大于我们估计值的概率是4%.

（这个考点有点超纲，计算过程是不会在FRM里面考的，了解一下即可。）


p值是0.04，说明φ（x）（这个叫正态分布累积概率分布函数）是1-0.04=0.96。我们需要用正态分布的反函数，也就是excel里面的NormsInv函数来反求X的值。

使用excel函数计算过程如下：

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加油吧，让我们一起遇见更好的自己！

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