Speed and density The following data relate traffic Density (measured as number of cars per mile) and the average Speed of traffic (in mph) on city highways. The data were collected at the same location at 10 different times randomly selected within a span of 3 months.

1. Describe the relationship between Speed and Density.

2. Fit a model to predict Speed from Density. Comment on the appropriateness of the model.

3. If the traffic density is 56 cars/mile and you observe a speed of 32.5 mph, what is the residual? What is the residual for an observed speed of 36.1 mph with a traffic density of 20 cars/mile?

4. Which of the two residuals in part c is more unusual? Explain.

5. A new data point has come in. For this observation, Density = 125 cars/mile and Speed = 55 mph. What would happen to the slope and the correlation if this point were included?

6. Predict the speed of traffic for a density of 200 cars/mile. Is your prediction reasonable? Explain briefly.

7. If you standardize both variables, what equation predicts the standardized speed from the standardized density?

8. If you standardize both variables, what equation predicts the standardized density from the standardized speed?

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Density Speed 69 25.4 32.5 28.6 11.5 21.3 22.1 22.3 18.5 37.2 44.6 26.4 27.07 9.64 56 62 119 84 74 73 90 38 22 Mean 68.7 SD