这里超纲吗?需要掌握计算吗?具体在哪个章节讲过?
星星_品职助教 · 2022年08月30日
同学你好,
logistic或logit model在多元回归和大数据中都有涉及。针对的是Y变量为二值变量的情况,即题干中的“She employs a logistic regression with the dependent variable of A, which takes on a value of 1 for a company listed on a US exchange and otherwise 0.”
logistic model中解出的Y实际上是一个概率,这个概率计算出来后需要和一个门槛值(threshold)对比,超过门槛值则Y=1,低于门槛值则Y=0.
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Log odds这点没有特殊强调过,但其实就是名字所代表的含义,即对“odds”取Ln。Odds为一级数量学过的知识点,一件事的odds=这件事发生的概率/这件事不发生的概率。设这件事的发生概率为P,则log odds=Ln P/(1-P)。
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case中说明“a company in the fund which does not have gender diversity on its board, the probability, based on the model, of being listed on a US exchange is 0.65”,
再结合上面的“D1 is 1 for firms with two or more female board members, and otherwise 0.” 可知,此时D1=0,在这种情况下,“being listed”的概率为0.65.
代入Log odds的公式,可得Ln 0.65/(1-0.65)=0.6190.
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题目中问的是:“Based on the logistic model and with a diverse board, the probability of Tekdat being listed....”,可知要求的是D1=1时的概率P。
此时还知道D1的系数为0.8(The regression coefficient of D1 in the logistic model is 0.80 and is statistically significant.)
所以,当D1=1时,方程会比D1=0时整体增加0.8×1=0.8。也就是方程此时的Y值为原来的0.6190再加上0.8,0.6190+0.8=1.4190。即Ln P/(1-P)=1.4190.
方程两边同时取“e”,消掉Ln,可得P/(1-P)=e的1.4190次方,解出P=0.8052