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# Equation of the Regression Line **2.6 Equation of the Regression Line and Application to Time Series** The equation of the regression line is used to represent graphically a linear model from a set of points to observe trends. The equation has the form: **y = mx + b** Where: * **y** = Depende...

# Equation of the Regression Line **2.6 Equation of the Regression Line and Application to Time Series** The equation of the regression line is used to represent graphically a linear model from a set of points to observe trends. The equation has the form: **y = mx + b** Where: * **y** = Dependent variable * **x** = Independent variable * **m** = Slope of the line * **b** = y-intercept of the line **Calculating m and b:** The slope (m) is calculated as follows: $m = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2}$ The y-intercept (b) is calculated as follows: $b = \bar{y} - m\bar{x}$ **Interpretation from the graph:** * If the sign of m is positive, the line increases (positive slope). * If the sign of m is negative, the line decreases (negative slope).