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藤原谢小圆 · 2023年12月04日

为什么此题coefficient=t-stat*SE

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。

coefficient=6.193=t-stat*SE=(3.749)*(1.652)

但是t-stat*SE不应该= X bar-μ0吗?

1 个答案

品职助教_七七 · 2023年12月05日

嗨,爱思考的PZer你好:


“t-stat*SE= X bar-μ0”的这种形式,对应的是与均值相关的t统计量的计算。如果针对均值设定置信区间,或者要检验总体均值是否等于一个特定的数,才需要用到这个公式。这种情况是一级的考点,二级基本上不会再考了。

本题需要设定的置信区间针对的是回归方程中的回归系数b1,不再是均值,所以t统计量和置信区间也是围绕着b1展开的。此时表格中的t统计量的公式为:

t-statistic = b1 cap / Sb1 cap;

置信区间为 b1 cap ± tc × Sb1 cap。 其中b1 cap 和 Sb1 cap为表格中直接给出,不需要自行计算。


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