what are residuals in linear regression

Residuals in linear regression refer to the difference between an observed value of the response variable and the value of the response variable predicted from the regression line. In other words, it is the vertical distance between a data point and the regression line. Each data point has one residual, which can be positive if it is above the regression line, negative if it is below the regression line, or zero if the regression line passes through the point. Residuals are used to validate the assumptions of a linear regression model, and they should ideally follow a normal distribution. Residual plots are commonly used to visualize and analyze residuals against the line of best fit, helping to ensure that the errors are independent and normally distributed.