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lea · 2022年11月16日

为什么df是90？

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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.

95 sample - k - 1 = 95-3-1= 91

为什么是90呢？

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1 个答案

星星_品职助教 · 2022年11月17日

同学你好，

F统计量分母上的自由度（n-k-1）对应的是SSE（unrestricted），也就是unrestricted model的SSE的自由度。

所以，直接从对应的ANOVA表中找到SSEu的自由度90即可；

根据提问，再补充两个小内容：

① 自由度n-k-1中的k是unrestricted model中的自变量数量，即k=5；

② 95是TSS的自由度，即n-1。所以n-k-1=（n-1）-k=95-5=90.

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