linear regression (math.)
It is a common machine learning algorithm and a commonly used algorithm in artificial intelligence. It is a method used to predict a linear relationship between a numerical output variable and one or more independent variables. For example, you can use a linear regression model to predict house prices based on the size of the house, its location, its surroundings, and so on.
The main idea is to describe the relationship between the independent and output variables by constructing a linear model. The model can be represented as:
y = a0 + a1*x1 + a2*x2 + … + an*xn
Where y is the output variable (also known as the response variable), x1, x2, ..., xn are the independent variables (also known as the characteristics), and a0, a1, a2, ..., an are the regression coefficients, which are used to indicate the effect of the independent variables on the output variable.
goal
The goal is to find the optimal values of the regression coefficients so that the model fits the data best. A common method is least squares, which minimizes the sum of the squares of the differences between the observed values and the predicted values of the model. Optimization algorithms such as gradient descent can be used to solve for the optimal value of the regression coefficients.
Usage Scenarios
It can be used for many problems, such as predicting sales, stock prices, income, education levels, etc. It can also be used for multivariate problems, such as predicting the price of a house, taking into account a number of factors such as the size, location, age, number of bedrooms, etc. of the house.
Next, a simple example of predicting the price of a house is written for linear regression:
Analysis:
Linear regression algorithms are based on the principles of statistics and the method of least squares to predict the test data by fitting it to the training data. In the case of predicting the price of a house, the input variables to the model usually include the size of the house, the number of bedrooms, the number of bathrooms, the number of garages, and other important characteristics. A linear regression model combines these variables to form a linear equation and then finds the optimal coefficients to maximize the fit to the training data.
When the model is trained, the AI can use the model to predict the price of a new home. The user simply inputs data about the characteristics of the home and then the model produces a prediction. In this way, AI can help buyers and sellers better understand the housing market conditions and evaluate and sell their homes in a more valuable way.
# Import the required libraries
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
# Load data
data = pd.read_csv('house_prices.csv')
# Processing data
X = [:, :-1].values
y = [:, 1].values
# Delineate the dataset by dividing the data into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
# Instantiation of linear regression models
lin_reg = LinearRegression()
# Training models
lin_reg.fit(X_train, y_train)
# Predict the results of the test set
y_pred = lin_reg.predict(X_test)
# Output model evaluation results
print('Coefficients: \n', lin_reg.coef_)
print('Mean squared error: %.2f' % ((y_pred - y_test) ** 2))
> print('Variance score: %.2f' % lin_reg.score(X_test, y_test))
Summary:
Linear regression is a basic machine learning algorithm whose main task is to fit a set of data to produce a prediction or to model a relationship between two or more variables.
In linear regression, it is necessary to first find a specific linear equation for a given data set - often referred to as "least squares", where "least squares" means a straight line that minimizes the sum of the squared errors. This is the line that minimizes the sum of squared errors. Once this line is found, it can be used to make predictions or model relationships between variables.
However, it should be noted that in practice, due to a variety of factors, the data points rarely fall exactly on the straight line of linear regression. Therefore, it is necessary to use an error function to measure the distance between the data points and the fitted straight line and further optimize the fitting effect of linear regression.
Overall, by analyzing and processing the given data, linear regression can help us to predict the trend of future events, and also provide a quantitative and reliable basis for decision-making in business and science.
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