Question 3 For this problem, use R to answer all of the questions (you do not need to perform the regression by hand). A research firm collected data on a sample of n = 30 drivers to Investigate the relationship between the age of a driver and the distance the driver can see. The data is given below: Age Distance Age Distance 18 510 55 420 20 590 63 350 22 560 65 420 23 510 66 300 23 460 67 410 25 490 68 300 27 560 70 390 28 510 71 320 29 460 72 370 32 410 73 280 37 420 74 420 41 460 75 460 46 450 77 360 49 380 79 310 53 460 82 360 a) Find the least squares estimate for the regression line Y = P, + BX; + 6. b) Estimate the standard deviation of the error term e; () Test the null hypothesis that , = 0, using a = 0.05. Is the model useful? d) Calculate RE. Explain what this means, and comment on whether or not it suggests the model is good. e) Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good. () What would you predict the distance that a 50-year-old driver can see to be? g) Give a 95% prediction interval for the distance that an individual 50-year-old can see. h) Give a 95% confidence interval for the mean distance that 50-year-olds can see