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Oliva · 2023年11月29日

用另一个公式计算

* 问题详情,请 查看题干

NO.PZ202208220100000205

问题如下:

Calculate the joint F-statistic and determine whether SMB and MOM together contribute to explaining RET in Model 3 at a 1% significance level (use a critical value of 4.849).

选项:

A.2.216, so SMB and MOM together do not contribute to explaining RET B.8.863, so SMB and MOM together do contribute to explaining RET C.9.454, so SMB and MOM together do contribute to explaining RET

解释:

B is correct. To determine whether SMB and MOM together contribute to theexplanation of RET, at least one of the coefficients must be non-zero.

So, H0:bSMB = bMOM = 0 and Ha: bSMB ≠ 0 and/or bMOM ≠ 0.

We use the F-statistic, where

with q = 2 and n – k – 1 = 90 degrees of freedom. The test is one-tailed, right side,with α = 1%, so the critical F-value is 4.849.

Model 1 does not include SMB and MOM, so it is the restricted model. Model3 includes all of the variables of Model 1 as well as SMB and MOM, so it is the unrestricted model.

Using data in Exhibit 1 and Exhibit 3, the joint F-statistic is calculated as


Since 8.863 > 4.849, we reject H0. Thus, SMB and MOM together do contribute to the explanation of RET in Model 3 at a 1% significance level.

[(0.9230-0.9070)/2]÷[(1-0.9230)/90]=9.3506 请问这个计算哪里错了?怎么结果不一样

1 个答案
已采纳答案

品职助教_七七 · 2023年11月29日

嗨,从没放弃的小努力你好:


1)提问的列式[(0.9230-0.9070)/2]÷[(1-0.9230)/90]中,使用的是Multiple R,缺少平方。应该直接使用平方后的R-squared。即Model 1(Restricted model)的R-squared为0.823,Model 3(Unrestricted model)的R-squared为0.852

列式应为(0.852-0.823)/2 ÷ (1-0.852)/90

2)这道题的题干只保留三位小数,所以如果用R-squared来计算,后面省略的小数会对计算造成一定影响。

这道题里Model 1的R-squared应该是0.8230378;Model 3的R-squared应该是0.8521575。

所以,精确计算结果如下:

分子= (0.8521575-0.8230378)/ 2=0.01455985

分母=(1-0.8521575)/90=0.0016426944

计算得到F=8.8634


综上,不要使用R-squared的方法来算F,教材给出首选公式是基于SSE的。用R-squared来算往往都会因四舍五入产生问题;

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努力的时光都是限量版,加油!

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