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csspyj · 2022年09月08日

这道题考的不是X的置信区间吗？怎么变成求X系数b1的置信区间了

  1. CFA II
  2. Quantitative

NO.PZ2018101001000014

问题如下：

Harry is a supermarket’s employer and he is interested in using math model to solve some problems. Recently, he wants to know the relationship among commodity demand volume(V), commodity prices(P) and consumer income level(I). The dependent variable is commodity demand volume and the other two is the independent variables. After doing the multiple regression analysis, he gets the following results:

What is the upper confidence interval of consumer income level’s regression coefficient at 0.1 level?

选项：

A.

3.467

B.

8.919

C.

9.798

解释：

B is correct.

考点: Interpret Regression Coefficient, Assumptions and F-test.

解析: Regression Coefficient Confidence Interval的公式是b1^±tcSb1^，这里的b1^等于6.193，Sb1^ 等于1.652。已知n为150，所以自由度（df）=n-k-1=147。当样本容量足够大(大于120)时，在α =0.1的情况下，tc近似于1.65，所以对于本题来说，置信区间上限等于6.193+1.65*1.652=8.919，选择B选项。

难道不是X+1.65Sx吗，怎么算的b1+1.65Sb1

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1 个答案

星星_品职助教 · 2022年09月09日

同学你好，

本题的问题是：“What is the upper confidence interval of consumer income level’s regression coefficient at 0.1 level?”，即求的是回归模型系数估计的置信区间上端点。

对于X本身求置信区间的考法在二级已经非常少了。

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