The accompanying data are the vehicle speeds (ft/s) and lateral positions (in.) measured for fifteen vehicles at four locations along a curve: upstream location (U), advance curve warning sign...

The accompanying data are the vehicle speeds (ft/s) and lateral positions (in.) measured for fifteen vehicles at four locations along a curve: upstream location (U), advance curve warning sign location (W), point-of-curve location (PC), and midpoint-of-curve location (MC). This data set is saved as a JMP file named “vehicle speed and lateral position” in the data CD. It was extracted for illustration purposes from a larger data set obtained from the FHWA project, “Pavement Marking Demonstration Projects: State of Alaska and State of Tennessee” (see Carlson et al., 2010).

a. Calculate the values of the sample mean and standard deviations for speed at MC and lateral position at MC and comment on them. How would you compare the variability for speed at MC to that for lateral position at MC? Is comparing the two standard deviations meaningful? Explain. b. Calculate the values of CV for speed at MC and lateral position at MC, respectively. How do the values compare? Interpret the results. c. Calculate the value of the Pearson’s correlation coefficient between speed at W and speed at PC. How would you describe the relationship between two variables? d. Calculate the value of the Spearman’s correlation coefficient between speed at W and speed at PC. Is the value larger or smaller than the Pearson’s correlation coefficient? If the two values are not very close, what do you think causes the main difference? e. Construct a scatter plot of speed at W and speed at PC. Identify any potential outlier in this bivariate data. Remove any outliers from the data and compute the Pearson’s correlation coefficient and the Spearman’s correlation coefficient again. What do you observe?