博客
关于我
用线性回归计算缺失值
阅读量:352 次
发布时间:2019-03-04

本文共 2672 字,大约阅读时间需要 8 分钟。

  • Missing data

    Missing data can grocely be classified into three types:

    1. MCAR(Missing Completely At Random), which means that there is nothing systematic about why some date is missing. That is, there is no relationship between the fact that data is missing and either the observed or unobserved covariates.
    2. MAR(Missing At Random), resembles MCAR because there still is an element of randomness.
    3. MNAR(Missing Not At Random), implies that the fact that fata is missing is directly correlated with the value of the misssing data.
  • How to deal with missing data

    1. Just delete missing entries
    2. Replaceing missing values with the mean or median
    3. Linear Regression

      First, several predictors of the variable with missing values are identified using a correlation matrix. The best predictors are selected and used as independent variables in a regression equation.

      The variable with missing data is used as the dependent variable.

      Second, cases with complete data for the predictor variables are used to generate the regression equation;

      Third, the equation is then used to predict missing values for incomplete cases in an iterative process.

      以上是单变量线性回归

    4. 多元线性回归

      Linear regression has signigicant limits like:

      • It can’t easily match any data set that is non-linear
      • It can only be used to make predictions that fit within the range of the training data set
      • It can only be fit to data sets with a single dependent variables and a single independent variable

      This is where multiple regression comes in. It is specifically designed to create regressions on models with a single dependent variable and multiple independent variables.

      Equation for multiple regpression takes the form:

      y = b 1 ∗ x 1 + b 2 ∗ x 2 + . . . + b n ∗ x n + a y=b_1*x_1+b_2*x_2+...+b_n*x_n+a y=b1x1+b2x2+...+bnxn+a
      b i b_i bi coefficients;

      x i x_i xi independent variables; also called predictor variables

      y i y_i yi dependent vairables; also called criterion variable

      a a a a constant stating the value of the depnedent variable;

      How to fit a multiple regression model ?

      Similarly to minimized the sum of squared errors to find B in the linear regression, we minimize the sum of squared errors to find all the B terms in multiple regression.

      Exactly we use stochastic gradient descent(随机梯度下降).

      How to make sure the model fits the data well ?

      Use the same r 2 r^2 r2 value that was used for linear regression.

      r 2 r^2 r2 which is called the coefficient of determination, states the portion of change in the data set that is predicted by the model. It’s a value ranging from 0 to 1. With 0 stating that the model has no ability to predict the result and 1 stating that the model predicts the result perfectly.

  • References

转载地址:http://pjge.baihongyu.com/

你可能感兴趣的文章
mysql数据库死锁的产生原因及解决办法
查看>>
MySQL数据库的事务管理
查看>>
mysql数据库的备份与恢复
查看>>
Mysql数据库的条件查询语句
查看>>
MySQL数据库的高可用
查看>>
Mysql数据库相关各种类型的文件
查看>>
MYSQL数据库简单的状态检查(show processlist)
查看>>
MYSQL数据库简单的状态检查(show status)
查看>>
MySQL数据库系列
查看>>
MYSQL数据库自动本地/异地双备份/MYSQL增量备份
查看>>
mysql数据库表增添字段,删除字段、修改字段的排列等操作,还不快来
查看>>
MySQL数据库被黑了
查看>>
mysql数据库设计
查看>>
MySQL数据库设计与开发规范
查看>>
MYSQL数据库进阶操作
查看>>
MySQL数据库配置文件调优详解
查看>>
MySQL数据库酒店客房管理系统(含MySQL源码) 结课作业 做的不是很好
查看>>
mysql数据库里的一些坑(读高性能mysql有感)
查看>>
MySQL数据库面试题(2021最新版)
查看>>
MySQL数据库高并发优化配置
查看>>