It assumes that there's a linear relationship between the input variables (independent variables) and the output variable (dependent variable).

The primary goal of linear regression is to find the best-fitting linear equation that describes the relationship between the variables. In a simple linear regression, there is only one independent variable, while in multiple linear regression, there are multiple independent variables.

The equation for a simple linear regression model with one independent variable is typically represented as:

Y=β0​+β1​X+ϵ

Where:

• $Y$ is the dependent variable.
• $X$ is the independent variable.
• 0β0​ is the y-intercept (constant term).
• 1β1​ is the slope of the line (the coefficient of the independent variable).
• $ϵ$ represents the error term, which accounts for the variability or randomness in the data that the model cannot explain.

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The goal of linear regression is to estimate the coefficients ( 0β0​ and 1β1​ ) that minimize the difference between the predicted values and the actual observed values. This is usually done by the method of least squares, which finds the line that minimizes the sum of the squared differences between the observed and predicted values.

Linear regression is widely used for various purposes, including predicting sales based on advertising spending, analyzing the relationship between variables, making forecasts, and understanding the impact of different factors on an outcome.