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台风来了 · 2023年08月02日

关于standard error的计算?

NO.PZ2023040502000013

问题如下:

The following exhibit is the results of a regression of the monthly return for an electric utility equity index for the previous 203 months (the dependent variable) against the monthly returns for the S&P 500 Index and the difference between the monthly returns on long-term U.S. government bonds and one-month U.S. Treasury bills (SPREAD) (the two independent variables).


Hamilton wants to test the null hypothesis that the coefficient on SPREAD is equal to 1 against the alternative hypothesis that it is not equal to 1. Based on the results in Exhibit 1, the value of the test statistic relating to Hamilton’s null hypothesis about the value of the coefficient on SPREAD is closest to:

选项:

A.

4.28

B.

0.24

C.

0.11

解释:

The null hypothesis is H0: bspread= 1.

The calculated value of the t-statistic is t = (1.0264 – 1.0)/standard error.

The standard error is 1.0264/4.28 = 0.24.

The calculated value for t = (1.0264 – 1.0)/0.24 = 0.11.

老师,您好!


standard error的计算公式是怎样的? 在这题中The standard error is 1.0264/4.28 = 0.24, 这个是怎么得来的呢?谢谢!

2 个答案

星星_品职助教 · 2023年08月28日

@台风来了

这个t-statistic对应的原假设是b1=0。相当于原回复中公式里的B1项代入的是0.

星星_品职助教 · 2023年08月03日

同学你好,

t-statistic的公式如下:

表格中给出的t-statistic=4.280是默认B1=0时的结果。再代入表格中的b1 cap=1.0264,即可反求stand error=1.0264/4.28 = 0.24。

Jimmyz · 2024年07月16日

老师,请问这里为什么默认B1=0?