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GMAT: Statistical Analysis With Categorical Data
How to Find The Equation of a Trend Line

What is a trend line and how is it useful? That's what you'll learn, as well as the formulas you need to use and the numbers you need to find for the equation of a trend line, in this lesson. You'll also see what steps you need to take to manipulate the formulas to your desired equation.

How to Find The Equation of a Trend Line

The Steps

In this lesson, we'll talk about finding the equation of a trend line. In the real world, your data will usually be scattered like in this graph instead of lining up neatly in a straight line.

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Example10

In some real world cases though, your data will look like it follows a line. If it does, then you'll be able to approximate your data with a line and a linear equation. This line that you approximate your data with is called the trend line. If this line is a straight line, then you'll be able to find an equation for this line.

In this lesson, we'll talk about finding an equation for trend lines that are straight lines. For these types of trend lines, you'll be able to find an equation in the slope-intercept form where m is your slope and b is your y-intercept. Remember, your slope is how steep your line is. A flat horizontal line has a slope of 0. A diagonal line on the graph has a slope of 1. Steeper lines have larger slopes. Your y-intercept is where your line crosses the y-axis.

Y=m+b

To find your equation of a trend line, follow these steps.

Step 1: Draw your trend line.

You begin by drawing your trend line. You want your trend line to follow your data. You want to have roughly half your data above the line and the other half below the line like this.

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Example11

Step 2: Locate two points on the line.

Your next step is to locate two points on the trend line. Look carefully at your trend line and look for two easy to figure out points on the line. Ideally, these are points where the trend line crosses a clearly identifiable location.

For the trend line that we just drew, we can see these two easily identifiable points.

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We can easily identify these two points as (3, 3) and (12, 6).

Step 3: Plug these two points into the formula for slope.

The formula for slope is this one.

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We can label our first point as (x1,y1) and our second point as (x2,y2). So our x1 is 3, our y1 is 3, our x2 is 12, and our y2 is 6. Plugging these values into the equation for slope and evaluating, we get this.

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So our slope is 1 / 3.

Step 4: Choose the smaller point and plug those values along with the slope into the point-slope formula to find the equation of the line.

Your last step uses the point with the smaller numbers to help you find the equation of your trend line. You'll want to use the smaller point as using smaller numbers is easier to work with. You'll be plugging the values of this point into the point-slope formula for the equation of a line to find the equation of your trend line. Your point will be labeled like before: (x1,y1). The point-slope formula is this one.

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