Student Worksheet, Algebra I Activity

Based on AP* Statistics Problem 6, 1997

Often one looks at data to formulate a picture or make a decision about a past, present, or future event.

It is important to remember that when answering questions about real data that your answers are written in complete sentences and in the context of the problem.

You are planning to sell a used 1988 automobile and want to establish an asking price that is competitive with that of other cars of the same make and model that are on the market. A review of newspaper advertisements for used cars yields the following data for 12 different cars of this make and model.

Production Year	1990	1991	1992	1987	1993	1991	1993	1985	1984	1982	1986	1979
Asking Price in $	6000	7700	8800	3400	9800	8400	8900	1500	1600	1400	2000	1000

1. Often it is difficult to work with large or small data, for example numbers as large as $2,300,000,000. It is easier to work with coded data, that is, data that has been recalculated by a rule or transformation. In the above case, we would rewrite the number as $2.3 billion.

a. Use this idea to code the data in the table above. For the data, Production Year, calculate the number of years since 1979. Using this rule, 1979 will be coded as 0 and 1980 will be coded as 1, and so forth.

b. Code the asking price of the automobile in thousands of dollars. For example, $7700 will be written as $7.7 (thousands of dollars).

2. Complete the table of values below using your coded data.

Production Year	Asking Price (in thousands of $)
(1990) 11	6
(1991) 12	7.7
...	...

3. Draw a scatter plot of the coded data. Be sure to label your axes with the appropriate variables and scales.

4. Write an equation for a linear model for this data.

a. What is the slope of the line? In terms of the problem, explain the meaning of the slope.

b. What is the Asking Price intercept (y-intercept)? In terms of the problem, explain the meaning of the Asking Price intercept (y-intercept).

5. Use your model to predict a selling price for your 1988 automobile.

a. Do you think that this price is a reasonable answer for this automobile? Use the data in the problem to support your answer. (Remember to use complete sentences.)

b. What is the Asking Price intercept (y-intercept)? In terms of the problem, explain the meaning of the Asking Price intercept (y-intercept).

6. A friend bought a new car last year, and he decides to sell it now. Use your model to predict the price of this car. Do you think that this is a reasonable price for this automobile? Support your answer. (Remember to use complete sentences.)

7. In questions 5 and 6, you used your mathematical model to predict the asking price of two automobiles. Explain which of the two prices you would expect to be the most accurate and why.

8. Using the coded data and the linear model you wrote in problem 4, complete the table of values below.

Year	Actual Asking Price (in thousands of $)	Predicted Asking Price (in thousands of $)	Difference (Actual - Predicted)
...	...	...	...

9. Draw a scatter plot for (year, difference).

10. If all of the Predicted Asking Price values were equal to the Actual Asking Price values, where would the points (year, difference) be located on the graph in problem 9? What would this tell you about your model?