Examples of Linear Regression: Methods for Predicting Continuous Variables

Linear regression is a commonly used machine learning algorithm used to predict the linear relationship between a continuous variable and one or more independent variables. This article will introduce how linear regression works and demonstrate the prediction process through an example and Python code.

1. Working principle of linear regression

Linear regression is a supervised learning algorithm that uses a set of independent variables (or features) to Predict the value of a continuous variable. In simple linear regression, only one independent variable predicts the value of the dependent variable; in multiple linear regression, there are multiple independent variables predicting the value of the dependent variable. This algorithm can be used to predict the values ​​of continuous variables such as house prices and sales. By finding the line of best fit, linear regression can provide predictions and explanations of the dependent variable.

The basic idea of ​​linear regression is to minimize the error between the predicted value and the actual value by finding a best-fitting straight line. The straight line can be expressed in the form of y=mx b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the intercept.

To find the best-fitting straight line, we use the least squares method. The core idea of ​​this method is to find a straight line that minimizes the sum of the distances of all data points to the straight line.

2. Example of Linear Regression

Now let’s look at an example. Suppose we have a set of data representing the housing area of ​​a certain city. and price. We want to use linear regression to predict the price of an area of ​​​​a house. We can take the area of ​​the house as the independent variable x and the price as the dependent variable y.

First, we need to import the necessary libraries and data:

import numpy as np
import matplotlib.pyplot as plt

# 数据
x = np.array([70, 80, 100, 120, 150, 180, 200])
y = np.array([320, 360, 420, 480, 600, 720, 800])

Next, we can plot the scatter points of the data Figure:

plt.scatter(x, y)
plt.xlabel('房屋面积（平方米）')
plt.ylabel('价格（万元）')
plt.show()

It can be seen from the scatter plot that there is a certain linear relationship between house area and price. Now we can use linear regression to fit the data and predict the price of a new house square footage.

from sklearn.linear_model import LinearRegression

# 创建线性回归模型
model = LinearRegression()

# 训练模型
model.fit(x.reshape(-1, 1), y)

# 预测房屋面积为120平方米的价格
new_x = np.array([120])
predicted_y = model.predict(new_x.reshape(-1, 1))
print(predicted_y) # 输出 [452.85714286]

We use the LinearRegression model in the Scikit-learn library to create a linear regression model and train it using the training data. Then, we used the model to predict the price of a new house with an area of ​​​​120 square meters, and the predicted result was 452,857 yuan.

Finally, we can draw the fitting straight line and the prediction results:

# 绘制拟合直线
line_x = np.linspace(50, 220, 100)
line_y = model.predict(line_x.reshape(-1, 1))
plt.plot(line_x, line_y, color='r')

#绘制预测结果
plt.scatter(new_x, predicted_y, color='g')

# 绘制原始数据
plt.scatter(x, y)

# 添加标签和标题
plt.xlabel('房屋面积（平方米）')
plt.ylabel('价格（万元）')
plt.title('房屋面积与价格的线性关系')

plt.show()

As can be seen from the above figure, the fitting straight line fits the data well, And the prediction results are relatively accurate.

3. Summary

This article introduces the working principle of linear regression and demonstrates how to use Python to perform linear regression through a practical example predict. Linear regression is a simple but effective machine learning algorithm that can be used to solve many practical problems, such as housing price prediction, sales prediction, etc. In practical applications, we need to select appropriate features and models according to specific problems, and perform data preprocessing and model optimization to obtain better prediction results.

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