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廖廖酱 · 2021年05月17日

No.PZ2018101001000014

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。

老师请问下题目中at 0.1 level表达的是什么意思?告诉我们at 0.1 level是不是就能知道置信度是90%?然后如果是双尾检验就可以查t表中P=0.05时样本数所对应的关键值?

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星星_品职助教 · 2021年05月17日

@ 廖廖酱 回复追问:

不是的。t表中的p是固定概率值,指的是单尾概率。

p-value不需要查表。会直接在题干中的表格里(一般是最后一列)给出。例如下图:

星星_品职助教 · 2021年05月17日

同学你好,

题干的这种说法不是很规范,正规的说法是at 0.1 significance level或者是10% level of significance。即significance level=10%,confidence level=90%

相当于本题要求的就是90%的confidence interval。

以原版书中给的单尾t表为例,此刻就要找到单侧的尾部面积。90%的confidence interval相当于两侧尾部面积一共为10%,即单侧尾部面积为5%。

此刻就要找“t表中P=0.05时所对应的关键值”,对应上自由度df=n-k-1=147。就可以查到关键值在1.653-1.658之间。这道题直接用的就是1.65.

注意这也不是正规的考法。考试最大的可能是给出一系列的关键值让考生选择。根据p=0.05和df=147选择即可。

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