8月mock题B卷上半场，中出现logistic model 并且要求计算

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.

------

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)。

-----

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.

------

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