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lcrcp3 · 2023年09月14日

如题

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.

这道题不用算吗?答案说的是个啥啊

1 个答案
已采纳答案

星星_品职助教 · 2023年09月17日

同学你好,

不用算。

表格中给出DF test result,其中“significance of t”就是test的p-value。根据p-value小于significance level的原则,可知两个x(independent variables)的系数都拒绝原假设,即都不为0。

由于本题为DF test,所以independent variables的系数≠0就是g≠0,结论为independent variables是stationary的序列,即no unit root。


本题中关于DF test的具体做法属于超纲内容,由于在一道很老的mock题里出现了,故保留下来,了解即可。

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NO.PZ2023040502000037 问题如下 nnehybelieve ththe number of fective assemblies per hour is a function of theoutsi air temperature anthe spee(proction rate) of the assembly lines.The regression mol: = + b1Airt + b2Rt+ εtnnehy woullike to confirmthnonstationarity is not a problem. To test for this he conctsckey-Fuller tests for a unit root on eaof the time series. The results arereportein Exhibit 2.Assuming a 5% level of significance, the mostappropriate conclusion thcawn from the ckey–Fuller resultsreportein Exhibit is ththe: A.test for a unit root is inconclusive for the penntvariable B.pennt variable exhibits a unit root but theinpennt variables not C.inpennt variables exhibit unit roots but thepennt variable es not The ckey–Fuller test uses a regression of the type:xt-xt-1=b0+g xt-1+εtThe null hypothesis is H0:g= 0 versus the alternative hypothesis H1: g 0 (a one-tailtest). If g=0 the time series ha unit root anis nonstationary. Thus, if wefail to rejethe null hypothesis, we accept the possibility ththe timeseries ha unit root anis nonstationary. Baseon the t ratios antheirsignificanlevels in Exhibit 2, we rejethe null hypothesis ththecoefficient is zero for both outsi air temperature anassembly line speei.e., the inpennt variables). We not rejethe null for the penntvariable, fective 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 rejeHo。 2,pennt variable的singinficanof t是大于0,所以是significant,rejeH0,所以没有unit root,而两个inpennt variable 等于0,not significant,not rejeHo,所以有unit root。我的理解怎么正好相反呢?

2024-03-31 12:06 1 · 回答