学习笔记 | 回归模型 | 04 残差波动

观测值与预测值之间的差就是残差，残差符合正态分布

 

计算结果表明：

Total Variation = Residual Variation + Regression Variation

总波动（Y与Y均值的平方和[方差]） = 残差波动（Y与Y观测值的差的平方和） + 回归波动（Y观测值与Y均值的差的平方和）

 

summary(fit) 中看到的R平方 = cor（Y,X）的平方

给模型加入一个完全不相关的（cor=0）的元素，模型不变

 

函数predict

Description

predict is a generic function for predictions from the results of various model fitting functions. The function invokes particular methods which depend on the class of the first argument.

根据线性模型给出三个预测值，基本值，最低值，最高值

课程中使用的例子：predict(fit, data.frame(x=mean(x)), interval='confidence')

 

自定义函数eliminate

 

# Eliminate the specified predictor from the dataframe by

# regressing all other variables on that predictor

# and returning a data frame containing the residuals

# of those regressions.

eliminate <- function(predictor, dataframe){

  # Find the names of all columns except the predictor.

  others <- setdiff(names(dataframe), predictor)

  # Calculate the residuals of each when regressed against the given predictor

  temp <- sapply(others, function(other)regressOneOnOne(predictor, other, dataframe))

  # sapply returns a matrix of residuals; convert to a data frame and return.

  as.data.frame(temp)

}