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succi_z · 2023年02月26日

为什么tc=1.65？

  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。

alpha=0.1，双尾的话，不是应该是80%的置信区间吗？1.65是如何得出的呢？

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1 个答案

星星_品职助教 · 2023年02月27日

同学你好，

α=0.1说明置信度为1-0.1=0.9.，即双尾总面积为0.1，对应90%置信区间。并不是单尾面积为0.1,。

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