Question 2: Analyzing data and interpreting results
Used car age and price
- Unit 5
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multi-part question built on a data set or summary statistics: you calculate things like outlier fences, compare distributions, pick the right measure of center or spread, and justify a claim in context. It focuses on Practices 3 and 4. On the exam: Question 2 of 4 (official name: Multi-Focus on Practices 3 and 4). Section II has 4 free-response questions in 90 minutes (50% of the score); each question is worth 10 points and 12.5% of the score. The exam is fully digital in Bluebook, a graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.
The question and its sources
Show the work that leads to each answer, and explain your reasoning in the context of the situation. A graphing calculator with statistical capabilities, the formula sheet and the statistical tables are available. Use the information given to answer parts A through F, and label any subparts (for example, i and ii).
The car listings
A student collected the age, in years, and the listed price, in thousands of dollars, of 10 used cars of the same make and model for sale in her area. The data are in the table.
Source: Hypothetical scenario
Age and price of 10 used cars
| Car | Age (years) | Price (thousands of dollars) |
|---|---|---|
| 1 | 1 | 24.9 |
| 2 | 2 | 21.6 |
| 3 | 2 | 23.8 |
| 4 | 3 | 19.7 |
| 5 | 4 | 20.3 |
| 6 | 5 | 15.2 |
| 7 | 6 | 16.4 |
| 8 | 7 | 12.0 |
| 9 | 8 | 12.9 |
| 10 | 9 | 8.6 |
Source: Hypothetical data
Suggested time: 22 minutes
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Part (A)
2 points(i) Describe the scatterplot you would construct to display these data. Include which variable goes on each axis, the axis labels and scales, and what is plotted. (ii) Describe the relationship between age and price.
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Part (B)
2 pointsUse technology to answer each part. (i) Calculate the equation of the least-squares regression line for predicting price from age. Define any variables you use. (ii) Calculate the correlation coefficient, r.
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Part (C)
1 pointInterpret the slope of the least-squares regression line in context.
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Part (D)
3 pointsCar 6 is 5 years old and is listed at $15,200. (i) Use the regression line to predict the price of a 5-year-old car. (ii) Calculate the residual for Car 6. (iii) Determine whether the regression line overestimates or underestimates the price of Car 6.
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Part (E)
1 pointInterpret the coefficient of determination, r², in context.
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Part (F)
1 pointUse the regression line to predict the price of a 20-year-old car of this model. Explain why this prediction is not reasonable.
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