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Determining the Equation of a Line Fit to Data




 

Videos to help Grade 8 students learn how to informally fit a straight line to data displayed in a scatter plot and determine the equation of a line.

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Common Core For Grade 8

New York State Common Core Math Grade 8, Module 6, Lesson 9.

Lesson 9 Student Outcomes

• Students informally fit a straight line to data displayed in a scatter plot.
• Students determine the equation of a line fit to data.
• Students make predictions based on the equation of a line fit to data.

Lesson 9 Summary

• A line can be used to represent the trend in a scatter plot.
• Evaluating the equation of the line for a value of the independent variable will determine a value predicted by the line.
• A good line for prediction is one that goes through the middle of the points in a scatter plot and for which the points tend to fall close to the line.

Lesson 9 Classwork

Example 1: Crocodiles and Alligators

Scientists are interested in finding out how different species adapt to finding food sources. One group studied crocodiles to find out how their bite force was related to body mass and diet. The table below displays the information they collected on body mass (in pounds) and bite force (in pounds).
As you learned in the previous lesson, it is a good idea to begin by looking at what a scatter plot tells you about the data. The scatter plot below displays the data on body mass and bite force for the crocodiles in the study.

Exercises 1–5

1. Describe the relationship between body mass and bite force for the crocodiles shown in the scatter plot.

2. Draw a line to represent the trend in the data. Comment on what you considered in drawing your line.

3. Based on your line, predict the bite force for a crocodile that weighs 220 pounds. How does this prediction compare to the actual bite force of the crocodile in the data set that weighed 220 pounds?

4. Several students decided to draw lines to represent the trend in the data. Consider the lines drawn by Sol, Patti, Marrisa, and Taylor, which are shown below.
For each student, indicate whether or not you think the line would be a good line to use to make predictions. Explain your thinking.
a. Sol’s line
b. Patti’s line
c. Marrisa’s line
d. Taylor’s line

5. What is the equation of your line? Show the steps you used to determine your line. Based on your equation, what is your prediction for the bite force of a crocodile with a bite force of 200 pounds?




Exercise 6

6. Patti drew vertical line segments from two points to the line in her scatter plot. The first point she selected was for a Dwarf Croc. The second point she selected was for an Indian Gharial Crocodile.
a. Would Patti’s line have resulted in a predicted bite force that was closer to the actual bite force for the Dwarf Crocodile or for the Indian Gharial Crocodile? What aspect of the scatter plot supports your answer?
b. Would it be preferable to describe the trend in a scatter plot using a line that makes the differences in the actual and predicted values large or small? Explain your answer.

Exercise 7: Used Cars
7. The plot below shows the age (in years) and price (in dollars) of used Honda Civic cars that were advertised in a local newspaper.
a. Based on the scatter plot above, describe the relationship between the age and price of the used cars.
b. Nora drew a line she thought was close to many of the points and found the equation of the line. She used the points (13, 6000) and (7, 12000) on her line to find the equation. Explain why those points made finding the equation easy.
c. Find the equation of Nora’s line for predicting the price of a used car given its age. Summarize the trend described by this equation.
d. For which car in the data set would the predicted value based on the line be farthest from the actual value? How can you tell?
e. What does the equation predict for the cost of a 10-year-old car? How close was the prediction using the line to the actual cost of the 10-year-old car in the data set? Given the context of the data set, do you think the difference between the predicted price and the actual price is large or small?
f. Is typical of the differences between predicted prices and actual prices for the cars in this data set? Justify your answer.


 

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