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沐沐的方盒 · 2023年07月06日

这题整体不会,求老师整体讲解一下。

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。

如题

2 个答案

星星_品职助教 · 2023年07月08日

@沐沐的方盒

tc是t分布对应的关键值,即公式中的“reliability factor”,更常见的说法是“critical value”。这个值需要查表来求,但本题因为样本量比较大,直接用正态分布背过的关键值1.65来近似替代了。

星星_品职助教 · 2023年07月07日

同学你好,

这道题是一个一级知识点的复习和应用。一级时学过Confidence interval的具体公式为:

Confidence Interval = [ Point Estimate +/- (reliability factor) * Standard error] 

具体应用在回归系数估计的场景中,公式可具体化为:

此后可参照答案解析,每个值的取值都有说明。如果答案解析中的某个步骤仍有疑问,可以就具体步骤进一步提问。

本题属于二级内容开始前对一级的复习,了解即可。二级考试中再去考察一级内容的可能性不大。

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