How to Use a Trend Line Equation to Find a Predicted Value

A trend line is a mathematical equation that describes the relationship between two variables. It is produced from raw data obtained by measurement or testing. The simplest and most common trend line equations are linear, or straight, lines. Once you know the trend line equation for the relationship between two variables, you can easily predict what the value of one variable will be for any given value of the other variable.

You should already have a trendline based on a data set you've taken or gathered with the line representing a general trend of that data. Then, you can move onto predictions.

Predicting a Value

    Examine your trend line equation to ensure it is in the proper form. The equation for a linear relationship should look like this: y = mx + b. "x" is the independent variable and is usually the one you have control over. "y" is the dependent variable that changes in response to x.

    The other two letters, m and b, stand for actual numbers that are specific to your data, so your trend line equation will have numerical values in place of m and b. Specifically, "m" refers to the slope of the line and "b" refers to the y-intercept (the value you get when x = 0 and the line crosses/intercepts the y axis).

    Rewrite the equation and replace the generic symbols x and y with the actual names of your variables. For example, if your equation was for the relationship between a person's blood pressure and their salt intake, salt intake would be the independent variable and blood pressure the dependent. Your equation would look like this: Blood Pressure = m * Salt Intake + b.

    Decide which of the two variables you want to predict. You will assign a number value to the other, predictive, variable. So to predict blood pressure, you would choose salt intake as the predictive variable you assign a number to.

    Decide at which value of your predictive variable you want to make your prediction. In the case of the blood pressure example, you would choose at what level of salt intake you want to predict blood pressure.

    Rearrange the equation, if necessary, so the variable you want to predict is alone on one side of the equal sign. To predict blood pressure at a given level of salt intake you would leave the equation as Blood Pressure = m x Salt Intake + b. However, to predict the salt intake of a person with a specific blood pressure, you would rearrange the equation to Salt Intake = (Blood Pressure - b) รท m.

    Substitute the chosen numerical value of the predictive variable into the equation. Using a calculator, solve the equation to find the predicted value of the other variable.

    Tips

    • It is possible for b to be zero, so your equation could just look like y = mx. The procedure above will also work for other more complicated trend line equations such as polynomials.

Uses for a Trendline: Trend Lines and Predictions

A trendline is most often used to display data that increases or decreases at a specific and steady rate (at least within a specific timeline). That means that a trendline is a great tool for predicting what value something will have in the future; trend lines and predictions go hand in hand.

Some examples could be for predicting population size, predicting the amount of a certain molecule in a solution over time, or creating an equation that can then be used in the future to predict similar information with other data sets.

References

About the Author

Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.

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