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Darlene · 2024年03月31日

significance t=0 是代表not significance,所以是not reject H0?

NO.PZ2023040502000037

问题如下:

Dennehy believe that the number of defective assemblies per hour is a function of the outside air temperature and the speed (production rate) of the assembly lines.

The regression model: Dt = b0 + b1Airt + b2Rt + εt

Dennehy would like to confirm that nonstationarity is not a problem. To test for this he conducts Dickey-Fuller tests for a unit root on each of the time series. The results are reported in Exhibit 2.


Assuming a 5% level of significance, the most appropriate conclusion that can be drawn from the Dickey–Fuller results reported in Exhibit is that the:

选项:

A.

test for a unit root is inconclusive for the dependent variable

B.

dependent variable exhibits a unit root but the independent variables do not

C.

independent variables exhibit unit roots but the dependent variable does not

解释:

The Dickey–Fuller test uses a regression of the type:xt-xt-1 =b0+g xt-1t

The null hypothesis is H0: g= 0 versus the alternative hypothesis H1: g< 0 (a one-tail test). If g=0 the time series has a unit root and is nonstationary. Thus, if we fail to reject the null hypothesis, we accept the possibility that the time series has a unit root and is nonstationary. Based on the t ratios and their significance levels in Exhibit 2, we reject the null hypothesis that the coefficient is zero for both outside air temperature and assembly line speed (i.e., the independent variables). We do not reject the null for the dependent variable, defective assemblies per hour.

这张表的解读和答案正好相反:1,所有的value of test stat都是小于t,所以not reject Ho。 2,dependent variable的singinficance of t是大于0,所以是significant,reject H0,所以没有unit root,而两个independent variable 等于0,not significant,not reject Ho,所以有unit root。我的理解怎么正好相反呢?


1 个答案

品职助教_七七 · 2024年04月01日

嗨,努力学习的PZer你好:


significance of t是p-value的别称,只要这个值小于significance level就拒绝原假设。有p-value的题目只看p-value即可,不需要考虑test statistic或critical value。

如果significance of t=0,就是必然拒绝原假设(H0为g=0,有unit root)。说明两个X变量都没有unit root。

而Y变量的p-value=0.1123,大于了significance level=0.05。所以不能拒绝原假设,即Y有unit root,

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