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廿三里 · 2021年03月01日

表格中的t值

NO.PZ2018101001000015

问题如下:

Donne builds a multiple regression model where the dependent variable is natural population growth rate (GR), and the independent variables are Gross National Income(GNI)、Consumer Price Index(CPI) and GDP. She believes that GNI has a positive effect to the natural population growth rate. The results as following:

Given the significance level is 0.05, which of the following statements is most likely correct?

选项:

A.

The null hypothesis isH0:bGNI0H_0:b_{GNI}\geq0 , and we should not reject H0.

B.

The null hypothesis is H0:bGNI0H_0:b_{GNI}\leq0, and we should not reject H0.

C.

The null hypothesis is H0:bGNI0H_0:b_{GNI}\leq0  , and we should reject H0.

解释:

C is correct.

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

解析: 题目说Donne相信GNI对人口自然增长率有积极的影响,即斜率大于0,我们把想要拒绝的放在原假设,所以原假设应该是H0:bGNI0H_0:b_{GNI}\leq0。通过表格,我们发现GNI的t统计量等于3.0000,已知当样本容量足够大(n=200),α=0.05时,临界值近似于1.65,所以t统计量大于临界值,我们应该拒绝原假设。所以C选项正确。

老师说表格在没有特殊说明的情况下,t和p都是默认检测b1=0的,但是这道题题目问的是单尾检验,b1是否小于等于0,为什么又可以直接用表格中的t值来判断
1 个答案

星星_品职助教 · 2021年03月02日

同学你好,

无论检验的是b1=0,b1≤0,还是b1≥0,对应的t-statistics都是不变的。

从t-statistics的公式可以看出,以上三个检验,对应的b1都是直接代入0(不会代入“小于0”或“大于0”)。

这三个检验的区别在于三个拒绝域是不同的。但拒绝域取决于备择假设,对于t-statistics的计算是没有影响的。

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NO.PZ2018101001000015 问题如下 nne buil a multiple regression mol where the pennt variable is naturpopulation growth rate (GR), anthe inpennt variables are Gross NationIncome(GNI)、Consumer PriInx(CPI) anG. She believes thGNI ha positive effeto the naturpopulation growth rate. The results following:Given the significanlevel is 0.05, whiof the following statements is most likely correct? A.The null hypothesis isH0:bGNI≥0H_0:b_{GNI}\geq0H0​:bGNI​≥0 , anwe shoulnot rejeH0. B.The null hypothesis is H0:bGNI≤0H_0:b_{GNI}\leq0H0​:bGNI​≤0, anwe shoulnot rejeH0. C.The null hypothesis is H0:bGNI≤0H_0:b_{GNI}\leq0H0​:bGNI​≤0 , anwe shoulrejeH0. C is correct.考点: Interpret Regression Coefficient, Assumptions anF-test.解析: 题目说nne相信GNI对人口自然增长率有积极的影响,即斜率大于0,我们把想要拒绝的放在原假设,所以原假设应该是H0:bGNI≤0H_0:b_{GNI}\leq0H0​:bGNI​≤0。通过表格,我们发现GNI的t统计量等于3.0000,已知当样本容量足够大(n=200),α=0.05时,临界值近似于1.65,所以t统计量大于临界值,我们应该拒绝原假设。所以C正确。 为什么这里就直接可以用t,但是前面那题就要自己算t。考试的时候如果检验值不等于0的话,t数值都不能直接用吗?

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2024-02-26 22:39 1 · 回答

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