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A regression line, often referred to as a trend line or line of best fit, is a straight line that best represents the data on a scatter plot. It is a fundamental concept in statistics used to model the relationship between two variables. One variable is typically considered independent (predictor) and the other is dependent (response). The regression line aims to minimize the vertical distances between the observed data points and the line itself, thus providing a visual summary of the general trend in the data.

The most common method for calculating the regression line is the method of least squares. This method finds the line that minimizes the sum of the squared differences between the observed y-values and the y-values predicted by the line. The equation of a simple linear regression line is typically represented as y = mx + b, where 'y' is the dependent variable, 'x' is the independent variable, 'm' is the slope of the line (representing the average change in y for a one-unit increase in x), and 'b' is the y-intercept (the predicted value of y when x is zero).

Regression lines are used for various purposes, including understanding correlation, making predictions, and identifying patterns. For instance, in economics, a regression line might show the relationship between advertising expenditure and sales. In science, it could illustrate the effect of temperature on a chemical reaction rate. While a regression line provides a simplified representation, it's important to remember that it does not imply causation, and the strength of the relationship is often assessed using correlation coefficients.