# Regression Analysis
# Simple regression 简单回归
Simple regression analysis, also known as simple linear regression, is a statistical tool used in social science research to understand the relationship between two variables. It involves a dependent variable, which is the variable we're interested in explaining or predicting, and an independent variable, which is the variable we use to predict or explain the dependent variable.
The goal of simple regression analysis is to fit a straight line that best describes the relationship between the dependent and independent variables. The line is described by the equation Y = a + bX + e, where Y is the dependent variable, X is the independent variable, a is the y-intercept, b is the slope of the line (also known as the regression coefficient), and e is the error term.
In the context of social science research, simple regression can be used to answer questions like "What is the relationship between income (independent variable) and spending (dependent variable)?" or "Does educational attainment (independent variable) predict job satisfaction (dependent variable)?".
简单回归分析，也被称为单变量线性回归，是社会科学研究中用于理解两个变量之间关系的统计工具。它包含一个因变量，也就是我们希望解释或预测的变量，以及一个自变量，也就是我们用来预测或解释因变量的变量。
简单回归分析的目标是找到一条最能描述因变量和自变量关系的直线。这条直线可以由等式 Y = a + bX + e 来描述，其中Y是因变量，X是自变量，a是Y轴截距，b是直线的斜率（也被称为回归系数），e是误差项。
在社会科学研究的背景下，简单回归可以用来回答像"收入（自变量）和消费（因变量）之间有什么关系？"或者"教育程度（自变量）是否可以预测工作满意度（因变量）？"这样的问题。
# Multiple regression 多元回归
Multiple regression analysis is a statistical technique used in social science research to understand the relationship between one dependent variable and two or more independent variables. It extends the simple linear regression model to include multiple independent variables, thus allowing for the examination of the effect of each independent variable on the dependent variable while controlling for the effects of other independent variables.
The goal of multiple regression is to model the relationship between the dependent and independent variables and to understand how much of the variance in the dependent variable can be explained by the independent variables. The general form of the multiple regression equation is Y = a + b1X1 + b2X2 + ... + bnXn + e, where Y is the dependent variable, X1 through Xn are the independent variables, a is the y-intercept, b1 through bn are the coefficients of the independent variables, and e is the error term.
In social science research, multiple regression analysis can be used to answer questions like "How do age, income, and education (independent variables) affect life satisfaction (dependent variable)?" or "What is the combined effect of parenting style, peer influence, and school environment (independent variables) on academic performance (dependent variable)?"
多元回归分析是社会科学研究中用于理解一个因变量和两个或更多自变量之间关系的统计技术。它扩展了简单线性回归模型，包括多个自变量，从而允许在控制其他自变量的效应时，检验每个自变量对因变量的影响。
多元回归的目标是模型化因变量和自变量之间的关系，并理解自变量能解释因变量变化的多少。多元回归方程的一般形式是Y = a + b1X1 + b2X2 + ... + bnXn + e，其中Y是因变量，X1到Xn是自变量，a是Y轴截距，b1到bn是自变量的系数，e是误差项。
在社会科学研究中，多元回归分析可以用来回答像"年龄、收入和教育（自变量）如何影响生活满意度（因变量）？"或者"养育方式、同伴影响和学校环境（自变量）对学业成绩（因变量）的综合影响是什么？"这样的问题。