alr3The package seems to be no longer available for download,But you can use the data inside
链接：https://pan.baidu.com/s/1xg-V5nPulRf6Tvna26dlTQ?pwd=0s1u
提取码：0s1u
Data can be downloaded here,Use after downloading the dataRstudio打开就能使用,No need to load anything else

单变量回归

Predict the amount of water in the Snake River area of ​​Wyoming 数据：snake

一.Data preparation operations,散点图

library(tidyverse)
snake
names(snake) <- c("content","yield") 
a <- ggplot(snake,aes(content,yield))+
  geom_point(colour='blue',shape=19,size=3)+
  labs(x="water content of snow",
       y=" water yield ",
       title = "scatterplot of snow vs.yield")+
  theme(plot.title = element_text(size=12,hjust=0.5))
a

二.进行拟合

#用lmfunction for linear regression
yield.fit <- lm(yield~content,data=snake)
install.packages("flextable")
library(flextable)#Use this package to display the results
as_flextable(yield.fit)
#Add straight lines to the original scatterplot,Look at the fitting effect
intercept <- yield.fit$coefficients[[1]]
slope <-yield.fit$coefficients[[2]] 
a+geom_abline(slope=slope,intercept=intercept,col='red',size=2)

三.residual test

#检验
par(mfrow=c(2,2))
plot(yield.fit)
#Normal with upper cornersQQThe figure shows that it basically obeys a normal distribution
#使用car包中的qqPlot函数检验
library(car)
par(mfrow=c(1,1))
qqPlot(yield.fit)

多变量线性回归

一.数据的预处理

数据集：water,The data is still in the link I shared above

newdata <- water[,-1]#去掉第一列
#相关性的检查
library(corrplot)
correlation <- cor(newdata)
corrplot(correlation,method="ellipse")
#Build a scatterplot matrix
pairs(~.,data=newdata)

二.Model construction and evaluation

fit <- lm(BSAAM~.,data=newdata)
as_flextable(fit)

观察可以发现,有几个变量的t统计量p值明显大于0.05,Therefore, a stepwise regression method is considered to optimize the model

#优化
fit1 <- step(fit)
summary(fit1)
#Generate diagnostic plots
par(mfrow=c(2,2))
plot(fit1)
#方差膨胀因子
vif(fit1)
#BP检验
library(lmtest)
bptest(fit1)#p大于0.05Then accept the absence of heteroscedasticity
#预测：
newdata$forecast <- predict(fit1)
newdata
ggplot(newdata,aes(forecast,BSAAM))+
  geom_point()+geom_smooth(method="lm")+
  labs(title="Forecast versus Actuals")+
  theme(plot.title = element_text(size=20,hjust=0.5))

Stepwise regression results：

诊断图：

Variance inflation factor and BP检验：

Predicted and fitted values

Other problems in linear models

一.定性特征

It is actually a dummy variable,For example, gender equals male1,否则等于0
以ISLR包中的Carseats数据为例：

install.packages("ISLR")
library(ISLR)
data("Carseats")
str(Carseats)

在这个例子中,我们将预测sales变量,对于因子,RMetrics are automatically encoded at analysis time.Model establishment and analysis are shown below：

sale.fit <- lm(Sales~Advertising+ShelveLoc,data=Carseats) 
summary(sale.fit)

二.交互项

数据集为MASS包中的Boston数据

library(MASS)
data("Boston")
Boston

建立medv（房屋价值）关于lstat（Percentage of low socioeconomic status households）和age（房屋年龄）Model with interaction terms

lm(medv~lstat*age,data=Boston) %>% summary()

to get the model：
medv=36-1.19lstat-0.0007age+0.004age*lstat