How to Find an Equation for a Linear Model

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A linear model has a direct relationship between the two variables. For example, the annual earnings of a person working on a base salary plus commission could be represented by a linear model. With a linear equation, you can find other outcomes, such as what the total income would be if the salesman sold 20 more units. To find the equation for the linear model, you need to know at least two points on the line so that you can calculate the slope and the y-intercept.

Things You'll Need

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  • Subtract the first independent variable, or x-coordinate, from the second independent variable. For example, if you want to model unit sales versus earnings, unit sales would be the independent variable and earnings would be the dependent variable. If you knew that the salesman would make $50,000 when he sold 40,000 units or $90,000 when he sold 80,000 units, the first independent variable is 40,000 units and the second independent variable is 80,000 so you subtract 40,000 from 80,000 to get 40,000.

  • Subtract the first dependent variable, or y-coordinate, from the second dependent variable. For this example, earnings would be the dependent variable. If you knew that the salesman would make $50,000 when he sold 40,000 units or $90,000 when he sold 80,000 units, the first dependent variable is $50,000 units and the second independent variable is $90,000 so you subtract $90,000 from $50,000 to get $40,000.

  • Divide the difference in the dependent variables by the difference in the independent variables to find the slope. In this example, $40,000 by 40,000 to get 1 as the slope.

  • Multiply the slope by the first independent variable. In this example, multiply the slope of 1 by 40,000 to get 40,000.

  • Subtract the Step 4 result from the first dependent variable to get the y-intercept. In this example subtract 40,000 from 50,000 to get 10,000 as the y-intercept.

  • Plug in the slope for m and the y-intercept for b in the following equation to find the linear model: y = mx + b. Completing the example, plug in 1 for m and 10,000 for b to find the equation is y = 1x + 10,000.

References

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