R 3.3

data3.3 <- read.csv("/Users/nicolechen/Desktop/R_proj/For postgrad/Dataset2024forpost/ex3.3.csv")
glm.logit <- glm(admit~gre+gpa+rank,family=binomial(link=logit) ,data=data3.3)
# 建立admit关于gpa，gre和rank的1ogistic 回归模型，数据为data3.3
summary(glm.logit) #模型汇总
## 
## Call:
## glm(formula = admit ~ gre + gpa + rank, family = binomial(link = logit), 
##     data = data3.3)
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -3.449548   1.132846  -3.045  0.00233 ** 
## gre          0.002294   0.001092   2.101  0.03564 *  
## gpa          0.777014   0.327484   2.373  0.01766 *  
## rank        -0.560031   0.127137  -4.405 1.06e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 499.98  on 399  degrees of freedom
## Residual deviance: 459.44  on 396  degrees of freedom
## AIC: 467.44
## 
## Number of Fisher Scoring iterations: 4

以上结果可以看出，gre, gpa和rank都显著，所以得到回归模型

\[\ln\frac{\widehat{p}}{1-\widehat{p}} = -3.449548 + 0.002294*gre + 0.777014*gpa - 0.560031*rank \]

R 3.6

data3.6 <- read.csv("/Users/nicolechen/Desktop/R_proj/For postgrad/Dataset2024forpost/ex3.6.csv")
model <- glm(y ~ x1 + x2 + x3, family = poisson(link = "log"), data = data3.6)
summary(model)
## 
## Call:
## glm(formula = y ~ x1 + x2 + x3, family = poisson(link = "log"), 
##     data = data3.6)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  2.92331    0.23440  12.471  < 2e-16 ***
## x1           0.18978    0.06844   2.773  0.00556 ** 
## x2          -0.30919    0.11210  -2.758  0.00581 ** 
## x3           0.08594    0.11087   0.775  0.43825    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 43.907  on 11  degrees of freedom
## Residual deviance: 27.848  on  8  degrees of freedom
## AIC: 96.713
## 
## Number of Fisher Scoring iterations: 4
exp(coef(model))
## (Intercept)          x1          x2          x3 
##  18.6028490   1.2089844   0.7340426   1.0897436

x1 (年龄) = 1.21：这个指数系数表示年龄每增加一个单位（从青年到中年或中年到老年），预期的满意度增加约1.21倍。也就是说，年龄越大，客户满意度略微上升。

x2 (性别) = 0.73：这个指数系数表示性别的影响。男性客户（x2 = 1）与女性客户（x2 = 0）相比，满意度的预期值降低为女性满意度的73%。这表明在相同的其他条件下，男性客户的满意度低于女性客户。

x3 (居住地) = 1.09：这个指数系数表示居住地的影响。居住在城市的客户（x3 = 1）的满意度大约是居住在农村客户（x3 = 2）的1.09倍。城市客户的满意度略高于农村客户。