【Dealing with Missing Data】: Handling Missing Data in Linear Regression

# 1. Introduction

In the process of data processing and analysis, missing data is a common yet troublesome issue. How to effectively handle these missing data points is one of the important factors affecting the accuracy and reliability of the analysis results. This article will start with the basics of linear regression, introduce missing data handling methods, focusing on the practice of missing data handling in linear regression, through data preparation, missing data handling examples, and ultimately demonstrate example analysis and results discussion, to provide readers with practical ideas and methods for dealing with missing data.

# 2. Basics of Linear Regression

### 2.1 What is Linear Regression

Linear regression is a statistical method used to explore the relationship between independent variables and dependent variables. In linear regression, we attempt to describe the linear relationship between independent variables (features) and dependent variables (targets) by fitting a straight line or a hyperplane in a high-dimensional space.

### 2.2 The Principle of Linear Regression

The core idea of linear regression is to determine the best-fitting line (or hyperplane) by minimizing the sum of squared errors between actual observed values and model predictions. This can be achieved through the least squares method, i.e., finding the model parameters that minimize the error.

### 2.3 Applications of Linear Regression

Linear regression is one of the most commonly used regression analysis methods in the field of data analysis, widely used in economics, finance, biostatistics, and other fields. It can be used not only for prediction and modeling but also for interpreting and inferring relationships between variables. Linear regression is also the foundation of many machine learning algorithms.

In practical work, we often encounter situations where data contains missing values. The following will introduce how to handle missing data issues in linear regression. Next, we will discuss in detail the impact of missing data and commonly used methods for filling and deleting missing data.

# 3. Methods for Handling Missing Data

### 3.1 The Impact of Missing Data

Missing data is frequently encountered in real-world data analysis. If not processed, it may lead to inaccurate analysis results, and even affect the final decision-making. Missing data affects the integrity and accuracy of the data, making the data distribution uneven, thereby affecting the training and prediction results of the model. Therefore, handling missing data is an important part of data preprocessing.

### 3.2 Common Methods for Filling Missing Data

In dealing with missing data, filling is a common strategy. The following introduces some commonly used methods for filling missing data:

#### 3.2.1 Filling with Mean, Median, Mode

- **Mean Filling**: Use the mean of the feature to fill in the missing values, suitable for continuous data.
- **Median Filling**: Use the median of the feature to fill in the missing values, which is not sensitive to outliers, suitable for data with outliers.
- **Mode Filling**: Use the mode of the feature to fill in the missing values, suitable for discrete data.

#### 3.2.2 Filling with Constants

Sometimes, a specific value (e.g., 0, -1) can be used to fill in missing data. This method is simple and crude, but it may introduce noise and is not suitable for all scenarios.

#### 3.2.3 Filling with Similar Data

Based on other features of the data, fill in the missing data with the feature values of similar data. This method requires the calculation of data similarity and is suitable for situations where the data have strong correlations.

### 3.3 The Impact and Methods of Deleting Missing Data

#### 3.3.1 The Impact of Deleting Missing Data

Deleting missing data will reduce the sample size, potentially leading to data bias, making the established model less accurate, and losing useful information carried by the data, thereby affecting the comprehe