A Pennsylvania research firm conducted a study in which 30 drivers (of ages 18 to 82 years old) were sampled, and for each one, the maximum distance (in feet) at which he/she could read a newly designed sign was determined. The goal of this study was to explore the relationship between a driver's age and the maximum distance at which newly designed signs were legible (clear enough to read), and then use the study's findings to improve safety for older drivers. (Data collected by Last Resource, Inc, Bellfonte, PA.) The raw data has been summarized using StatCrunch below. Correlation between Driver Age (years) and Sign Legibility Distance (feet) is: -0.76012657 (P-value < 0.0001) Simple linear regression results: Sign Legibility Distance (feet) = 562.76259 - 2.6537201 Driver Age (years) Independent Variable: Driver Age (years) Dependent Variable: Sign Legibility Distance (feet)

a. State the direction of the relationship between the two variables and interpret its meaning in the context of this problem.

b. Explain whether or not the use of regression analysis to produce the equation of the "line of best fit" was appropriate in this situation. Be specific.

c. Predict the maximum distance at which the sign would be legible for 60-year-old drivers. Show how you arrived at your answer and interpret its meaning in the context of this problem.

d. Upon viewing the fitted line plot, a Pennsylvania government agency representative exclaims the newly designed sign can be seen up to 375 feet by a 75-year-old driver. Thoroughly explain whether or not the representative's guess is reasonable.

e. Suppose a Pennsylvania government agency wanted to design a sign appropriate for an even wider range of drivers than were present in the original study. Can you predict the maximum distance at which the sign would be legible for a 90-year-old? Is this prediction reliable? Explain.