利用python写出代码①读入binary.csv文件，其中gpa为在校成绩，gre为分数，rank为本科生母校的声望，admit为入学批准。把rank改名为prestige。查看数据描述性统计，每一列的标准差，prestige与admin的值相应的数量关系,并生成各参数的直方图。 ②利用statsmodels.formula,将prestige作为分类变量，利用smf进行预测，并将预测评分存入 predict 列中,设定预测值>0.5时表示预测被录取，计算预测录取数量，实际录取数量和预测命中率；分别用logit和ols进行测试，并比较预测效果。 ③利用sklearn，设为虚拟变量。除gre、gpa外，加入了上面常见的虚拟变量（注意，引入的虚拟变量列数应为虚拟变量总列数减1，减去的1列作为基准），利用sklean进行预测，预测值admit为0/1二值，计算计算预测录取数量，实际录取数量和预测命中率。分别用LogisticRegression和LogisticRegressionCv（其中cv=10）进行测试，并比较预测效果。 ④利用train_test_split把数据随机分为训练集和训练集，其中1/3为测试集，重做logit、ols、LogisticRegression和LogisticRegressionCV，比较其效果

以下是代码实现，其中用到了pandas、numpy、matplotlib、statsmodels、sklearn等库：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf
from sklearn.preprocessing import OneHotEncoder
from sklearn.linear_model import LogisticRegression
from sklearn.linear_model import LogisticRegressionCV
from sklearn.model_selection import train_test_split

# 读取数据
data = pd.read_csv('binary.csv')
data = data.rename(columns={'rank': 'prestige'})

# 描述性统计
print(data.describe())

# 标准差
print("Standard deviation of each column:")
print(data.std())

# prestige与admit的值相应的数量关系
print("Prestige vs. admit:")
print(data.groupby('prestige')['admit'].value_counts())

# 直方图
data.hist()
plt.show()

# 利用statsmodels进行预测
model = smf.logit('admit ~ prestige', data=data).fit()
data['predict'] = model.predict(data)
data['predict'] = np.where(data['predict'] > 0.5, 1, 0)
print("Logit results:")
print("Predicted admit count:", data['predict'].sum())
print("Actual admit count:", data['admit'].sum())
print("Hit rate:", sum(data['predict'] == data['admit'])/len(data))

model = smf.ols('admit ~ prestige', data=data).fit()
data['predict'] = model.predict(data)
data['predict'] = np.where(data['predict'] > 0.5, 1, 0)
print("OLS results:")
print("Predicted admit count:", data['predict'].sum())
print("Actual admit count:", data['admit'].sum())
print("Hit rate:", sum(data['predict'] == data['admit'])/len(data))

# 利用sklearn进行预测
enc = OneHotEncoder(drop='first')
prestige_dummy = pd.DataFrame(enc.fit_transform(data[['prestige']]).toarray())
prestige_dummy.columns = ['prestige_2', 'prestige_3', 'prestige_4']

X = pd.concat([data[['gre', 'gpa']], prestige_dummy], axis=1)
y = data['admit']

# LogisticRegression
model = LogisticRegression().fit(X, y)
data['predict'] = model.predict(X)
print("LogisticRegression results:")
print("Predicted admit count:", data['predict'].sum())
print("Actual admit count:", data['admit'].sum())
print("Hit rate:", sum(data['predict'] == data['admit'])/len(data))

# LogisticRegressionCV
model = LogisticRegressionCV(cv=10).fit(X, y)
data['predict'] = model.predict(X)
print("LogisticRegressionCV results:")
print("Predicted admit count:", data['predict'].sum())
print("Actual admit count:", data['admit'].sum())
print("Hit rate:", sum(data['predict'] == data['admit'])/len(data))

# 利用train_test_split进行测试
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)

# LogisticRegression
model = LogisticRegression().fit(X_train, y_train)
y_predict = model.predict(X_test)
print("LogisticRegression test results:")
print("Predicted admit count:", y_predict.sum())
print("Actual admit count:", y_test.sum())
print("Hit rate:", sum(y_predict == y_test)/len(y_test))

# LogisticRegressionCV
model = LogisticRegressionCV(cv=10).fit(X_train, y_train)
y_predict = model.predict(X_test)
print("LogisticRegressionCV test results:")
print("Predicted admit count:", y_predict.sum())
print("Actual admit count:", y_test.sum())
print("Hit rate:", sum(y_predict == y_test)/len(y_test))

# 利用statsmodels进行测试
model = smf.logit('admit ~ prestige', data=pd.concat([X_train, y_train], axis=1)).fit()
y_predict = model.predict(pd.concat([X_test, y_test], axis=1))
y_predict = np.where(y_predict > 0.5, 1, 0)
print("Logit test results:")
print("Predicted admit count:", y_predict.sum())
print("Actual admit count:", y_test.sum())
print("Hit rate:", sum(y_predict == y_test)/len(y_test))

model = smf.ols('admit ~ prestige', data=pd.concat([X_train, y_train], axis=1)).fit()
y_predict = model.predict(pd.concat([X_test, y_test], axis=1))
y_predict = np.where(y_predict > 0.5, 1, 0)
print("OLS test results:")
print("Predicted admit count:", y_predict.sum())
print("Actual admit count:", y_test.sum())
print("Hit rate:", sum(y_predict == y_test)/len(y_test))

注意：本代码仅供参考，具体实现需要根据实际情况进行调整。