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Understanding Linear Regression

Linear regression is a widely used statistical method for modeling the relationship between a dependent variable and one or more independent variables. It is a fundamental tool in the field of Statistics and data analysis, commonly employed for prediction and inference in various fields including economics, finance, social sciences, engineering, and healthcare.

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Key Concepts:

1. Dependent Variable (Y): Also known as the outcome variable, the dependent variable is the variable being predicted or explained in the regression model. It is denoted as Y and is influenced by one or more independent variables.
2. Independent Variable(s) (X): Also known as predictor variables, independent variables are the variables that are hypothesized to have an effect on the dependent variable. In simple linear regression, there is only one independent variable (X), while in multiple linear regression, there are multiple independent variables.
3. Linear Relationship: Linear regression assumes that there exists a linear relationship between the independent variable(s) and the dependent variable. This means that the relationship can be represented by a straight line when plotted on a graph.
4. Regression Equation: The regression equation represents the mathematical relationship between the independent and dependent variables. In simple linear regression, the equation takes the form Y = β0 + β1X + ε, where β0 and β1 are the intercept and slope coefficients, respectively, and ε represents the error term.
5. Least Squares Method: The least squares method is commonly used to estimate the parameters of the regression equation by minimizing the sum of the squared differences between the observed and predicted values of the dependent variable.

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