How to Calculate the Slope of Regression Line

Calculating the slope of a regression line helps to determine how quickly your data changes. Regression lines pass through linear sets of data points to model their mathematical pattern. The slope of the line represents the change of the data plotted on the y-axis to the change of the data plotted on the x-axis. A higher slope corresponds to a line with greater steepness, while a smaller slope's line is more flat. A positive slope indicates that the regression line rises as the y-axis values increase, while a negative slope implies the line falls as y-axis values increase.

    Pick two points that fall on the regression line. Data points on graph are written as ordered pairs (x,y), where "x" represents a value on the horizontal axis and "y" represents a value on the vertical axis.

    Subtract the "x" value of the first point from the "x" value of the second point to get the change in "x." For example, suppose the two points (3,6) and (9,15) are on the regression line. Using this example, 9 - 3 = 6, which is the calculated change in the "x" value.

    Subtract the "y" value of the first point from the "y" value of the second point to calculate the change in "y." Continuing with the previous example, (3,6) and (9,15) on the regression line, the calculated change in the "y" value is 15 - 6 = 9.

    Divide the change in "y" by the change in "x" to obtain the slope of the regression line. Using the previous example yields 9 / 6 = 1.5. Note that the slope is positive, which means the line rises as the y-axis values increase.

    Tips

    • Slope is frequently denoted by the letter "m" in mathematics.

References

About the Author

William Hirsch started writing during graduate school in 2005. His work has been published in the scientific journal "Physical Review Letters." He specializes in computer-related and physical science articles. Hirsch holds a Ph.D. from Wake Forest University in theoretical physics, where he studied particle physics and black holes.

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