In the last section, you studied the difference between positive linear associations and negative linear associations. Once you know that a data set has a linear association, you can use a trend line to make predictions. In this section, you will practice generating a trend line and using that trend line to make predictions from the data.

The graph below shows the relationship between the length of an alligator (in centimeters) and the belly width of an alligator (in centimeters).

Click and drag the circles below to place a trend line on the graph. Your trend line will not connect every point, but should follow the trend in the data.

Use the trend line you estimated in the graph to answer the questions below.

• What is the y-intercept, or starting point, of your trend line?

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  Approximately where does your trend line cross the y-axis?

   

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  The y-intercept is near (0, −3).
• What is the approximate slope of your trend line?

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  What is the change in y as compared to the change in x for the two points on the trend line?

   

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  The slope is about 30 over 105 30 105 or 2 over 7 2 7 .
• Use your trend line to estimate the belly width of an alligator that has a length of 30 centimeters.

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  What point on the trend line has an x-coordinate of 30?

   

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  About 4 centimeters
• Use your trend line to estimate the length of an alligator that has a belly width of 35 centimeters.

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  What point on the trend line has a y-coordinate of 35?

   

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  About 140 centimeters

Pause and Reflect

How does a trend line help you to make predictions from a scatterplot?

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A trend line gives you a visual anchor to estimate the patterns in the data. Once you have a trend line, you can use the points on the trend line to make predictions about what additional points in the data set might look like.

Practice

1. The graph below shows the relationship between the amount of television watched in one week and a student’s grade point average.
   

   Use a trend line to estimate the grade point average a student would have if they watched 27 hours of television each week.

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   Along which axis do you need to look for a value of 27?
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   Check Your Answer

   About 1.75
2. The scatterplot below shows the relationship between the sales at an ice cream store and the outdoor air temperature.
   

   Use a trend line to estimate the temperature required for $700 in ice cream sales.

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   Along which axis do you need to look for a value of 700?
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   Check Your Answer

   About 28°C