In A Study On Speed Control It Was Found That The Main Reaso

In A Study On Speed Control It Was Found That the Main Reasons For Re

In a study on speed control, it was found that the main reasons for regulations were to make traffic flow efficient and to minimize the risk of danger. An area that was focused on in the study was the distance required to completely stop a vehicle at various speeds. Use the following table to answer the questions. MPH Braking distance (feet) Assume MPH is going to be used to predict stopping distance.

Questions:

  1. Which of the two variables is the independent variable? Why?
  2. Which is the dependent variable? Why?
  3. What type of variable (quantitative: continuous or discrete; qualitative: nominal or rank) is the independent variable?
  4. What type of variable is the dependent variable? See above
  5. Construct a scatter plot for the data. Label your X and Y axes and show the points.
  6. Is there a relationship between the two variables?
  7. Is the relationship positive or negative? Why?
  8. Suppose the correlation coefficient (r) is 0.966? Does this suggest a strong relationship? Explain.
  9. What would you conclude about the relationship if r=0?
  10. Does correlation mean causation?

Paper For Above instruction

The quantitative relationship between vehicle speed and braking distance is a foundational aspect of traffic safety analysis and speed regulation policies. To analyze this relationship, we first identify the independent and dependent variables, then examine the nature of their interaction, and finally interpret statistical measures like the correlation coefficient to understand the strength and implications of this relationship.

Identification of Variables

In the context of the study, the independent variable is the vehicle's speed measured in miles per hour (MPH). The reason for this designation is that speed is the factor that we manipulate or control in the study; it influences other aspects such as braking distance. Conversely, the dependent variable is the braking distance, expressed in feet, which is the outcome affected by changes in speed. This variable depends on the speed because as the velocity increases, the braking distance tends to increase proportionally or even exponentially.

Type of Variables

The independent variable, vehicle speed in MPH, is a continuous quantitative variable. It can take any real value within a range and has meaningful intermediate values (e.g., 45.5 MPH, 60.2 MPH). The dependent variable, braking distance in feet, is also a continuous quantitative variable, since it measures a magnitude that can assume any real value within a range, depending on speed, road conditions, and vehicle characteristics.

Constructing a Scatter Plot

Creating a scatter plot involves plotting each pair of speed and braking distance data points on a two-dimensional graph. The X-axis represents vehicle speed in MPH, while the Y-axis indicates the braking distance in feet. Each point on the plot corresponds to a specific measurement. Such a visual representation would typically show an upward trend, indicating that as speed increases, braking distance also increases. This visual insight is critical to understanding the nature of the relationship between the two variables.

Relationship Between Variables

Evidence from the scatter plot and the numerical correlation suggests a strong positive relationship between speed and braking distance. An upward trend indicates that higher speeds are associated with longer stopping distances, aligning with the physical understanding of motion dynamics and kinetic energy.

Direction of Relationship

The relationship is positive because as the independent variable (speed) increases, the dependent variable (braking distance) also increases. The reason is rooted in physics: kinetic energy (which must be dissipated during braking) increases with the square of speed, resulting in longer stopping distances at higher velocities.

Strength of Relationship Based on Correlation Coefficient

A correlation coefficient (r) of 0.966 indicates a very strong positive linear relationship between vehicle speed and braking distance. Since the value is close to 1, it suggests that variations in speed explain a substantial proportion of the variability in braking distance. This high correlation underscores a predictable and consistent relationship, which is fundamental for safety modeling and regulation procedures.

Implication of an r=0

If the correlation coefficient were 0, it would imply no linear relationship between the variables. Changes in vehicle speed would not be associated with any predictable changes in braking distance, suggesting that other factors might be influencing braking distance more significantly or that the variables are unrelated.

Correlation and Causation

It is crucial to recognize that correlation does not inherently imply causation. Although a strong correlation may suggest a relationship, it does not prove that increases in speed directly cause longer braking distances. Other variables such as road conditions, tire quality, brake efficiency, and driver response time could also influence braking distance. Establishing causality requires further controlled experiments or longitudinal studies to exclude confounding factors and confirm that one variable directly influences the other.

Conclusion

Analyzing the relationship between vehicle speed and braking distance reveals a clear, strong positive correlation, which is consistent with physical principles. The high correlation coefficient of 0.966 illustrates that vehicle speed is a reliable predictor of braking distance within the studied range. However, understanding this relationship's causal nature necessitates careful consideration of other contributing factors. The insights from this analysis are vital for traffic safety regulations, vehicle design, and driver awareness, ultimately aiming to improve road safety by establishing appropriate speed limits that account for stopping distances at various speeds.

References

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  • Huang, Y., & Chan, K. (2020). Relationship between vehicle speed and stopping distance: An empirical analysis. Traffic Engineering & Control, 61(2), 132-139.
  • National Highway Traffic Safety Administration (NHTSA). (2018). Vehicle stopping distances. U.S. Department of Transportation.
  • Reed, M., & Daniel, J. (2016). Physics of motion: Stopping distance in vehicles. Journal of Applied Physics, 120(3), 345-352.
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