Question 6.42
7. How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort. Fuel consumption is measured in miles per gallon of gasoline used and speed is measured in miles per hour.
| Speed | 6.2 | 12.4 | 18.6 | 24.9 | 31.1 |
| Fuel | 11.2 | 18.1 | 23.5 | 29.4 | 33.6 |
| Speed | 37.3 | 43.5 | 49.7 | 55.9 | 62.1 |
| Fuel | 39.9 | 37.3 | 33.8 | 31.1 | 28.4 |
| Speed | 68.4 | 74.6 | 80.8 | 87.0 | 93.2 |
| Fuel | 26.0 | 23.8 | 21.8 | 20.0 | 18.3 |
Table 6.15: Data from T. N. Lam, Estimating fuel consumption from engine size, Journal of Transportation Engineering, 11 1 (1985): 339–357.
- Which is the explanatory variable?
- Make a scatterplot. Describe the form of the relationship. Explain why the form of the relationship makes sense.
- How would you describe the direction of this relationship?
- Is the relationship reasonably strong or quite weak? Explain your answer.
7.
(a) Speed
(b)
Sample response: Initially, the form is linear, but then it switches direction and bends upward.
(c) Relationship is positive for speeds under 40 mph; relationship is negative for speeds above 40 mph.
(d) Quite strong; little scatter about the piecewise linear then curved pattern