Houston Independent School District



Name: _________________________________________________________ Per: ________ Grade: _____________

HW 2.10 Fitting a Line to Data*

DIRECTIONS: Show all work and answer questions #1- #10 on a separate sheet of paper. Use graph paper for #3. Staple all work behind this sheet.

Car dealers across North America use the “Blue Book” to help them determine the value of used cars that customers trade in when purchasing new vehicles. The book lists on a monthly basis the amount paid at recent used-car auctions and indicates the trade-in values according to condition and optional features. A study was completed to determine whether the odometer reading would serve as a useful predictor of trade-in value. Five-year-old cars of the same make, model, condition, and options have been randomly selected. The trade-in value and mileage are shown below.

|Odometer Reading |Trade-in Value ($) |

|58,000 |3800 |

|93, 100 |2400 |

|72,200 |3100 |

|52,000 |4000 |

|67,700 |3200 |

|88,100 |2700 |

|62,500 |3900 |

|95,100 |2500 |

|83,100 |2600 |

|43,400 |4300 |

|39,000 |5500 |

1) What kind of relationships would you expect between trade-in value and odometer reading for the randomly selected cars? Explain your answer.

2) Code the data to make it easier to use and record the adjustments (for example, record trade-in value in hundred thousands of dollars and code $3,500,000 as $35).

3) Construct a scatterplot of the coded data on graph paper. Which variable should be the independent variable and which is the dependent variable? Do you think that odometer reading depends on trade-in value or trade-in value depends on the odometer reading? Remember to include scales and labels for your axes.

4) Does the scatterplot confirm your description in #1? Explain your answer.

5) On your scatterplot for #3, draw a line that you think summarizes or fits the data. Pick two ordered pairs on the line you drew on the scatterplot of trade-in value and odometer reading. Use your ordered pairs to write an equation of the line in slope-intercept form.

6) What does the variable y represent in your equation? What does the variable x represent in your equation?

7) What is the slope of the line? Interpret the slope in the context of this problem.

8) Use your equation from #5 to predict the trade-in value of a vehicle with 52,000 miles.

9) According to the data, the actual trade-in value of a car with 52,000 miles was $4,000. How close was your prediction? Calculate the residual (actual value – predicted value). Did you over-predict or under-predict your estimate? Justify your answer.

10) Follow the instructions on the NCTM Illuminations website “Line of Best Fit” () to determine the equation for a line of best fit for the given data set. Record the computer-generated equation and compare it to equation from #5.

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